ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Iu addition. we make svuthesized beam sizes the same as possible at both wavelengths. using weighting aud tapering schemes. in order to münunuize the beam size effect on the flux comparison.," In addition, we make synthesized beam sizes the same as possible at both wavelengths, using weighting and tapering schemes, in order to minimize the beam size effect on the flux comparison."3 After proper weighting and taperie schemes. we could match the beam sizes to within," After proper weighting and tapering schemes, we could match the beam sizes to within."4 The details of applied weighting aud tapering schemes are listed in Table 2. with final svuthesized bemus., The details of applied weighting and tapering schemes are listed in Table \ref{tab_beam} with final synthesized beams.5 Driees robust paraiueter is used (?7).. which is a knob to provide intermediate weighting between natural aud uniform weighting.," Briggs' robust parameter is used \citep{briggs1995}, which is a knob to provide intermediate weighting between natural and uniform weighting."6 The parameter of 2 gives a weieliting close to natural weieliting aud 2 close to nuiform weighting., The parameter of $2$ gives a weighting close to natural weighting and $-2$ close to uniform weighting.7" Total iux CF.) of the thermal dust coutiuumau emission represents the total mass (Mr) of the source. if the source is optically thin at the observational frequeucies. where wy. DQ(DI4) Mp. aud D are opacity (nass absorption cocficient) of the dust serais. blackbody radiation intensity of a dust temperature Dy. total mass. and distance to the source. respectively,"," Total flux $F_\nu$ ) of the thermal dust continuum emission represents the total mass $M_T$ ) of the source, if the source is optically thin at the observational frequencies, where $\kappa_\nu$, $B_\nu(T_{d})$, $M_T$ , and $D$ are opacity (mass absorption coefficient) of the dust grains, blackbody radiation intensity of a dust temperature $T_{d}$, total mass, and distance to the source, respectively."8" The opacity of dust erains (&,) depeuds on dust properties such as sizes. colmpoucuts. aud shapes."," The opacity of dust grains $\kappa_{\nu}$ ) depends on dust properties such as sizes, components, and shapes."9" Hf the dependence is simple. for example a power law (E,cr7). the dust eran propertics can be studied by observations at two frequencies."," If the dependence is simple, for example a power law $\kappa_\nu \varpropto \nu^\beta$ ), the dust grain properties can be studied by observations at two frequencies."10 In addition. in the case that the Ravleigh-Jeans approxination of blackbody radiation is applicable (ivmKT). the relationship between spectral indexes of the observed flux deusities (0) aud spectral indexes of the dust exin opacity (2) is simply. Note that this relation is valid only iu the optically thin asstuuption aud the Ravleigh-Jeaus approximation.," In addition, in the case that the Rayleigh-Jeans approximation of blackbody radiation is applicable $h\nu \ll kT$ ), the relationship between spectral indexes of the observed flux densities $\alpha$ ) and spectral indexes of the dust grain opacity $\beta$ ) is simply, Note that this relation is valid only in the optically thin assumption and the Rayleigh-Jeans approximation."11 ? showed that ./ mainly depends on the size distribution of dust erains rather than their coupoucuts and shapes: sunall (j| (~ 1) is likely indicating dust erain size distribution up to 3A., \citet{draine2006} showed that $\beta$ mainly depends on the size distribution of dust grains rather than their components and shapes; small $\beta$ $\sim 1$ ) is likely indicating dust grain size distribution up to $3 \lambda$.12 Since our observations are up to 3 numi 9~l would sugeest a grain size distribution up to about 1 cm.," Since our observations are up to 3 mm, $\beta \sim 1$ would suggest a grain size distribution up to about 1 cm."13 Figure d preseuts maps of Lilis IRS 2. Litls IRS 3. and L1157.," Figure \ref{fig_betamap} presents maps of L1448 IRS 2, L1448 IRS 3, and L1157."14" Dust coutimaiun maps at and hhave been separately constructed using different weiehtiues and taperimes as described in refsoc,bsand Table2inordertohaveassimilarsuyithesitedbeamsaspos v"," Dust continuum maps at and have been separately constructed using different weightings and taperings as described in \\ref{sec_obs} and Table \ref{tab_beam}15 in order to have as similar synthesized beams as possible at the two wavelengths."16alues of cach source have been calculated using the two contimmun images., Afterwards $\beta$ values of each source have been calculated using the two continuum images.17 Only regions above three signal-to-noise ratio (SNR) levels on the both maps have Όσοι used to derive ) assunmniue where g4 and my are frequencies correspouding to and ddata. as listed in Table 2..," Only regions above three signal-to-noise ratio (SNR) levels on the both maps have been used to derive $\beta$ assuming where $\nu_1$ and $\nu_0$ are frequencies corresponding to and data, as listed in Table \ref{tab_beam}."18 Note that the Ravleigh-Jeans approximation aud the optically thin assuuption are used., Note that the Rayleigh-Jeans approximation and the optically thin assumption are used.19 In the case of an average dust temperature of about 30 I&. the upper lait of frequencies to which the Ravleigh-Jeans approximation cau be applied is about 625 GIIz.," In the case of an average dust temperature of about 30 K, the upper limit of frequencies to which the Rayleigh-Jeans approximation can be applied is about 625 GHz."20 Since the higher frequencyof our data is about 230 GIIz. the assumption is valid for this study.," Since the higher frequencyof our data is about 230 GHz, the assumption is valid for this study."21 However. caution should be taken in comparison at sibmullimeter wavelengths for cold objects such as the Class 0 YSO envelopes.," However, caution should be taken in $\beta$ comparison at submillimeter wavelengths for cold objects such as the Class 0 YSO envelopes."22The rate of supernova explosions is astrophysically important because it determines the rate at which heavy elements are dispersed into the interstellar medium. thereby constraming galactic chemical evolution.,"The rate of supernova explosions is astrophysically important because it determines the rate at which heavy elements are dispersed into the interstellar medium, thereby constraining galactic chemical evolution."23 Since the progenitors of core-collapse supernovae (SNec) are believed to be short-lived massive stars. the SNee rate is expected to reflect the star-formation rate. increasing with redshift like ~(1+2°° for zo«0.5 (Hopkins&Beacom2006).," Since the progenitors of core-collapse supernovae (SNcc) are believed to be short-lived massive stars, the SNcc rate is expected to reflect the star-formation rate, increasing with redshift like $\sim(1+z)^{3.6}$ for $z<0.5$ \citep{hopkins}."24. Thermonuclear type Ia supernovae (SNIa) have both long- and short-lived progenitors so the SNIa rate has a delayed component making the SNla rate rise more slowly with redshift. ~(1+2) (Pritchetetal.2008)..," Thermonuclear type Ia supernovae (SNIa) have both long- and short-lived progenitors so the SNIa rate has a delayed component making the SNIa rate rise more slowly with redshift, $\sim(1+z)^{2}$ \citep{pritchet}."25 The SNla rate is now known to a precision of about 20%., The SNIa rate is now known to a precision of about $20\%$.26 Measurements have profited from the high luminosity of SNIa which make them relatively easy to detect and identify., Measurements have profited from the high luminosity of SNIa which make them relatively easy to detect and identify.27 Furthermore. their utility as cosmological distance indicators has motivated intense searches.," Furthermore, their utility as cosmological distance indicators has motivated intense searches."28 An example is the Supernova Legacy Survey (SNLS) at the Canada-France- Telescope (CFHT) performed between 2003 and 2008., An example is the Supernova Legacy Survey (SNLS) at the Canada-France-Hawaii Telescope (CFHT) performed between 2003 and 2008.29" Using early SNLS data. Neilletal.(2006) derived a SNIa rate at a redshift z~0.5 of where /is=Ho/70kmsec""!Mpc'."," Using early SNLS data, \citet{neill2006}30 derived a SNIa rate at a redshift $z\sim 0.5$ of where $h_{70}=H_0/70\km\,\second^{-1}\Mpc^{-1}$."31 The rate for SNee is more difficult to measure because observed SNec have a magnitude distribution that peaks roughly 1.5mag fainter than SNIa and covers a range of more than Smag (Richardsonetal.," The rate for SNcc is more difficult to measure because observed SNcc have a magnitude distribution that peaks roughly $1.5\,{\rm mag}$ fainter than SNIa and covers a range of more than $5\,{\rm mag}$ \citep{richardson}."322002)... The local rate was measured by Cappellaroetal.(1999) using. 137 supernovae discovered by eye and photographically.," The local rate was measured by \citet{Capp1999}33 using 137 supernovae discovered by eye and photographically."34 Most had spectroscopic identification. about half being SNIa and half SNee (SNIb/e and SNID.," Most had spectroscopic identification, about half being SNIa and half SNcc (SNIb/c and SNII)."35 After etficiency corrections. the SNec rate was found to be a factor 2.441.3 greater than the SNIa rate.," After efficiency corrections, the SNcc rate was found to be a factor $2.4\pm1.3$ greater than the SNIa rate."36 The SNee rate at z~0.3 was measured by Cappellaroal.(2005) and more recently by Botticellaetal.(2005)., The SNcc rate at $z\sim0.3$ was measured by \citet{Capp2005} and more recently by \citet{Bott2008}.37 The latter used images taken over a six year period with typically four months between images., The latter used images taken over a six year period with typically four months between images.38 They found 18 SNee candidates and 13 SNla candidates (of which a total of 25 are spectroscopically confirmed) to find a SNee rate at z~0.26 a factor 4+2 greater than the SNla rate., They found 18 SNcc candidates and 13 SNIa candidates (of which a total of 25 are spectroscopically confirmed) to find a SNcc rate at $z\sim0.26$ a factor $4\pm2$ greater than the SNIa rate.39 Finally. Dahleretal.(2004) used the Advanced Camera for Surveys οἱ the Hubble Space Telescope to obtain images for five epochs separated by ~45days.," Finally, \citet{dahlen} used the Advanced Camera for Surveys on the Hubble Space Telescope to obtain images for five epochs separated by $\sim45\,{\rm days}$."40" For redshifts <1. they found 17 SNla candidates (with some spectroscopic identification) anc 16 SNee candidates (no spectroscopic identification) which allowed them to derive R,./R;,=3.6x2.0 at z-0. and RR,22.5E1.0 at z~0.8."," For redshifts $<1$, they found 17 SNIa candidates (with some spectroscopic identification) and 16 SNcc candidates (no spectroscopic identification) which allowed them to derive $R_{cc}/R_{Ia}=3.6\pm2.0$ at $z\sim0.4$ and $R_{cc}/R_{Ia}=2.5\pm1.0$ at $z\sim0.8$."41 All existing measurements of the SNee rate suffer from the fact that the discovery procedure involved the comparison of images separated in time by intervals comparable to or greater than the characteristic ~|month time scales of supernovae.," All existing measurements of the SNcc rate suffer from the fact that the discovery procedure involved the comparison of images separated in time by intervals comparable to or greater than the characteristic $\sim 1\,{\rm month}$ time scales of supernovae."42 Consequently. well-sampled light curves for most candidates are not available. complicatir£& the type identification and efficiency caleulations.," Consequently, well-sampled light curves for most candidates are not available, complicating the type identification and efficiency calculations."43" The SLS ""rolling search"" avoids this problem because of its high cadence monitoring of four |deg- fields in the e. 7. /' and z' bands over a total of5 years."," The SNLS “rolling search” avoids this problem because of its high cadence monitoring of four $1\,deg^2$ fields in the $g^\prime$, $r^\prime$, $i^\prime$ and $z^\prime$ bands over a total of 5 years."44 During each 6 month observing seaso1 for each field. typically four observations perlunation were obtained in the 7’ and /' bands. three in the z' band and two inthe ¢’ band.," During each 6 month observing season for each field, typically four observations perlunation were obtained in the $r^\prime$ and $i^\prime$ bands, three in the $z^\prime$ band and two in the $g^\prime$ band."45 This strategy yields well-sampled light curves (e.g. Figs. 1.. 5," This strategy yields well-sampled light curves (e.g. Figs. \ref{lcIa}, ,"46 and 3)) with high efficiency for all events occurring during the observing season, \ref{lcplateau} and \ref{lcCC}) ) with high efficiency for all events occurring during the observing season47The source count models can be accessed through the world wicle web at Alip:££www.irdsas.ac.jpicppícounts CPP is supported. by a Japan Society [or the Promotion of Science (JSPS) fellowship.,The source count models can be accessed through the world wide web at $http://www.ir.isas.ac.jp/\sim cpp/counts/$ CPP is supported by a Japan Society for the Promotion of Science (JSPS) fellowship.48 CPP thanks the referee Steve Eales and Lideo Alatsuhara lor significant. comments and suggestions., CPP thanks the referee Steve Eales and Hideo Matsuhara for significant comments and suggestions.49 CPP would like to thank Professor Haruyuki Okuda for providing him with the chance to spend a very fruitful ancl eventful time at the Institute of Space and Astronautical Science. Japan.," CPP would like to thank Professor Haruyuki Okuda for providing him with the chance to spend a very fruitful and eventful time at the Institute of Space and Astronautical Science, Japan."50metallicity to 47 Tuc with [M/H]=—0.6.,metallicity to 47 Tuc with $\mh=-0.6$.51" Given the errors, the isochrone fit for the Aquarius stream is consistent with the Sgr dwarf."," Given the errors, the isochrone fit for the Aquarius stream is consistent with the Sgr dwarf."52 We thus investigated a possible link between the Aquarius stream and the Sagittarius dwarf debris., We thus investigated a possible link between the Aquarius stream and the Sagittarius dwarf debris.53" The details of this investigation are given in Appendix A. The overall result is that the Aquarius stream's kinematics match those of the Sagittarius dwarf debris, calculated using a variety of potential models (oblate, spheroid, prolate, triaxial) from Law (2005, 2009)."," The details of this investigation are given in Appendix A. The overall result is that the Aquarius stream's kinematics match those of the Sagittarius dwarf debris, calculated using a variety of potential models (oblate, spheroid, prolate, triaxial) from Law (2005, 2009)."54" The oblate model shows a potential match for a small section of nearby debris when considering the line-of-sight velocity in the Galactic rest-frame, V, alone."," The oblate model shows a potential match for a small section of nearby debris when considering the line-of-sight velocity in the Galactic rest-frame, $\vgal$, alone."55" However, the full kinematics of Vy,Vr,Vz displays that the kinematics of the Aquarius stream and this nearby section are actually quitedifferent?°."," However, the full kinematics of $\VPHI,\ \VR,\ \VZ$ displays that the kinematics of the Aquarius stream and this nearby section are actually quite."56. The possible connection is further ruled out by the fact that the oblate halo potential model does not compare well with other observational data for Sgr dwarf debris., The possible connection is further ruled out by the fact that the oblate halo potential model does not compare well with other observational data for Sgr dwarf debris.57" Since the Aquarius stream lies in the southern part of the RAVE data, it could not be discovered in the main, northern SDSS survey."," Since the Aquarius stream lies in the southern part of the RAVE data, it could not be discovered in the main, northern SDSS survey."58" Thus the stream is far removed from the SDSS-discovered substructures, including the Canis Major overdensity at (1,b)=(240°,—8?) (Martinezetal.2005) and the Virgo overdensity at (1,b)=(300°,+60°) (Juriéetal.2008)."," Thus the stream is far removed from the SDSS-discovered substructures, including the Canis Major overdensity at $(l,\ b)=(240^\circ,\ -8^\circ)$ \citep{Martinez2005} and the Virgo overdensity at $(l,\ b)=(300^\circ,\ +60^\circ)$ \citep{Juric2008}."59". Further, the stream is located between the southern SEGUE SDSS stripes so it unsurprising that this has not been detected in this survey."," Further, the stream is located between the southern SEGUE SDSS stripes so it unsurprising that this has not been detected in this survey."60 The stream’s Galactic latitude of b=—60° rules out a relation to the more planar Monoceros stream (b< 40°) (Penarrubiaetal.2005)., The stream's Galactic latitude of $b=-60^\circ$ rules out a relation to the more planar Monoceros stream $b<40^\circ$ ) \citep{Penarrubia2005}.61". Its velocities and latitude are also inconsistent with the thick disk asymmetries detected by Parkeretal.(2003, 2004).."," Its velocities and latitude are also inconsistent with the thick disk asymmetries detected by \citet{Parker2003, Parker2004}. ."62" The Hercules-Aquila cloud, again detected using SDSS photometry, is located at |=40° and extends above and below the plane by 50° Belokurovetal. (2007).."," The Hercules-Aquila cloud, again detected using SDSS photometry, is located at $l=40^\circ$ and extends above and below the plane by $50^\circ$ \citet{Belokurov2007}. ."63 The velocities of the b>0° segment are =+180kmst and the structure ranges over heliocentricVga) distances of d=10—20kpc.," The velocities of the $b>0^\circ$ segment are $\vgal = +180\,\kms$ and the structure ranges over heliocentric distances of $d=10 - 20\,\kpc$."64 The Hercules-Aquila cloud is near the Aquarius stream on the sky., The Hercules-Aquila cloud is near the Aquarius stream on the sky.65" However, despite the lack of velocity data below the plane, it can be clearly seen that the two entities are separate: the centering in (1, b) for the two are shifted from each other and their distance ranges are clearly incompatible."," However, despite the lack of velocity data below the plane, it can be clearly seen that the two entities are separate: the centering in (l, b) for the two are shifted from each other and their distance ranges are clearly incompatible."66" Additionally, in Section 6.1 we trace the orbit of a simple model for the Aquarius stream and the resulting region of phase-space that the debris inhabits does not overlap with the Hercules-Aquila cloud in (1,b, και)."," Additionally, in Section \ref{subsec:sat} we trace the orbit of a simple model for the Aquarius stream and the resulting region of phase-space that the debris inhabits does not overlap with the Hercules-Aquila cloud in $l,\ b,\ \vgal$ )."67" We have calculated orbits for candidate stars in the potential of Helmi et al (2006), which has contributions from a disk, bulge, and dark halo."," We have calculated orbits for candidate stars in the potential of Helmi et al (2006), which has contributions from a disk, bulge, and dark halo."68" Table 4 gives averages for various quantities derived from these orbits as well as the median quantities for the overall kinematics, using both sets of distances."," Table \ref{tab4} gives averages for various quantities derived from these orbits as well as the median quantities for the overall kinematics, using both sets of distances."69" Note that we chose the median as it gives more consistent results, and for this reason we also excluded the two most distant stars with d>9 kpc as their kinematics differed greatly from the others."," Note that we chose the median as it gives more consistent results, and for this reason we also excluded the two most distant stars with $d> 9$ kpc as their kinematics differed greatly from the others."70" Also, the values for the pericentre and apocentre only include non-radial orbits."," Also, the values for the pericentre and apocentre only include non-radial orbits."71" Figure 6 shows the L,-Lyerp and L,-Energy (Lindblad) planes for orbits based on both distance estimates, where to aid comparison to other studies we use here energies as calculated in Dinescuetal. (1999)."," Figure \ref{f6} shows the $L_z$ $L_\mathrm{perp}$ and $L_z$ -Energy (Lindblad) planes for orbits based on both distance estimates, where to aid comparison to other studies we use here energies as calculated in \citet{Dinescu1999}."72". Note that the scatter of the isochrone distance results is large so the majority of these points lie off the plot, as do some of the RPM distance results."," Note that the scatter of the isochrone distance results is large so the majority of these points lie off the plot, as do some of the RPM distance results."73" We plot for reference stars in the Geneva Copenhagen survey (Nordstrometal.2004), which is comprised mainly of thin and some thick disk stars."," We plot for reference stars in the Geneva Copenhagen survey \citep{Nordstrom2004}, which is comprised mainly of thin and some thick disk stars."74 The circular orbit loci for this potential are also shown in the Lindblad diagram., The circular orbit loci for this potential are also shown in the Lindblad diagram.75 To show the typical error covariance we also ran a Monte Carlo (MC) simulation for each star (with the RPM , To show the typical error covariance we also ran a Monte Carlo (MC) simulation for each star (with the RPM distances).76"Fromthe errors in distances,proper motion and radial distances).velocity we generated a sample of 1000 points representative of each distribution, which"," Fromthe errors in distances,proper motion and radial velocity we generated a sample of 1000 points representative of each distribution, which"77So far we have ignored the effects of extinction iu our conrparisou of observations and models,So far we have ignored the effects of extinction in our comparison of observations and models.78 Frou detailed studies of obscured Calactic giant regions there is evidence that the extinction to the stars is highly variable with values between Ay=0 and Ay=L5inasg (Bhuin. Danuneli. Conti 1999: Bhun. Couti. Diuauineli 2000) for the very voung regions.," From detailed studies of obscured Galactic giant regions there is evidence that the extinction to the stars is highly variable with values between $A_K=0$ and $A_K=4.5\,$ mag (Blum, Damineli, Conti 1999; Blum, Conti, Damineli 2000) for the very young regions."79 If high extinction is prescut in the regious of LIRGs. then the predicted fractious of regions. coiucidences aud older star clusters will be affected.," If high extinction is present in the regions of LIRGs, then the predicted fractions of regions, coincidences and older star clusters will be affected."80 Althouehl we have no way derive the extinctions from the current Pan observations. we cau obtain some estimates from optical spectroscopy.," Although we have no way derive the extinctions from the current $\alpha$ observations, we can obtain some estimates from optical spectroscopy."81 AATIOO and Lippari et al. (, AAH00 and pari et al. (822000) have measured extinctions of up to Ay& L2amag using the Bahuer decrement for a few regions in Arp 299 and NCC 3256 respectively.,"2000) have measured extinctions of up to $A_V \simeq 4.2\,$ mag using the Balmer decrement for a few regions in Arp 299 and NGC 3256 respectively."83" This is equivalent to extinctions at the observed wavelength of Pad of up to Apa,zm OSimae."," This is equivalent to extinctions at the observed wavelength of $\alpha$ of up to $A_{{\rm Pa}\alpha} \simeq 0.5\,$ mag."84 The ages of these regions from the observed equivalent widtls of Πα are of between 3 and GNINDIVY using Leitherer et al. (, The ages of these regions from the observed equivalent widths of $\alpha$ are of between 3 and Myr using Leitherer et al. (851999) models.,1999) models.86 Although the measured extinctions are not high enough to compromise the detection of regions at nearinfrared wavelengths. we cannot rule out the possibility that verv voung regious («23 Myr) suffer from elevated extinctions. even at nem-iufrared waveleneths.," Although the measured extinctions are not high enough to compromise the detection of regions at near-infrared wavelengths, we cannot rule out the possibility that very young regions $<3\,$ Myr) suffer from elevated extinctions, even at near-infrared wavelengths."87 1f this were the cases we would be missing the vounecst regions. and hence the observed fraction of regions and coimcidences will be lower lits.," If this were the case, we would be missing the youngest regions, and hence the observed fraction of regions and coincidences will be lower limits."88 This would iu turi translate in even vounger age distribution of the detected population of star clusters., This would in turn translate in even younger age distribution of the detected population of star clusters.89 The observed luminosity and mass functious of old elobular clusters around galaxies and voung star clusters observed in interacting galaxies appear to be distinctivelv different. with the former having a log-normal shape. aud the latter a power law form with no evidence for a turnover (sce for instance Ehueercen Efremov 1997: Whitinore et al.," The observed luminosity and mass functions of old globular clusters around galaxies and young star clusters observed in interacting galaxies appear to be distinctively different, with the former having a log-normal shape, and the latter a power law form with no evidence for a turnover (see for instance Elmegreen Efremov 1997; Whitmore et al."90 1999: Zepf et al., 1999; Zepf et al.91 1999)., 1999).92 This poses an interesting problem if the clusters observed iu salaxies are vounger versious of todav's globular clusters., This poses an interesting problem if the clusters observed in galaxies are younger versions of today's globular clusters.93 Oue of the proposed solutions is that the mass distribution of old elobular clusters was initially a power law that was later modified by selective destruction of low mass star clusters to become a log-norimat like wass fiction (see Fall Zhang 2001 for a detailed discussion. and also Whitmore 2000).," One of the proposed solutions is that the mass distribution of old globular clusters was initially a power law that was later modified by selective destruction of low mass star clusters to become a log-normal like mass function (see Fall Zhang 2001 for a detailed discussion, and also Whitmore 2000)."94 Although including a detailed treatineut of the problem of cluster destruction is bevoud the scope of this paper. we can attempt to see its effects on our calculations.," Although including a detailed treatment of the problem of cluster destruction is beyond the scope of this paper, we can attempt to see its effects on our calculations."95 If clusters in Arp 299 and NGC 3256 have been forming at a coustaut rate for approximately LOO Nr. then ~50% of all clusters with masses above 5«104M. should be destroyed during that period to account for the observed fraction of star clusters.," If clusters in Arp 299 and NGC 3256 have been forming at a constant rate for approximately $100\,$ Myr, then $\simeq 50\%$ of all clusters with masses above $5\times 10^4\,{\rm M}_\odot$ should be destroyed during that period to account for the observed fraction of star clusters."96 Note that Zepf et al. (, Note that Zepf et al. (971999) proposed selective destruction of low mass clusters as oue possibility to account for the observed optical colors and Iuinosities of clusters in NGC 3256 (the other possibility was a very voung aee for the clusters).,1999) proposed selective destruction of low mass clusters as one possibility to account for the observed optical colors and luminosities of clusters in NGC 3256 (the other possibility was a very young age for the clusters).98 Finally we cousider the effects of the formation of Pan shells ou the measured uuuber of coincidences., Finally we consider the effects of the formation of $\alpha$ shells on the measured number of coincidences.99 Iu the Auteunae galaxy there is evidence that many of the slightly older. nore massive clusters (1.0. 5-LOADNIwr) have blown large Te shells around themselves. hence there is no lounger a good correspondence between the distribution of Ila and the f-hand ceuter of the cluster (Whitinore ct al.," In the Antennae galaxy there is evidence that many of the slightly older, more massive clusters (i.e., Myr) have blown large $\alpha$ shells around themselves, hence there is no longer a good correspondence between the distribution of $\alpha$ and the $I$ -band center of the cluster (Whitmore et al."100 1999)., 1999).101 Such Pana shells ave diffuse and will not be identifies as reeious. causing the προς of coincidences to be underestimated iu the 57 Myv age range.," Such $\alpha$ shells are diffuse and will not be identified as regions, causing the number of coincidences to be underestimated in the $5-7\,$ Myr age range."102 For ages 2TMyr the region endussion will not be detecte as its ΕΕ will be below our detection threshok (Section 5.2).," For ages $>7\,$ Myr the region emission will not be detected as its luminosity will be below our detection threshold (Section 5.2)."103 The result of missing some coiucideuces because of the presence of Pan shells would be an age distribution of the clusters shelthy vouuger than iuferre in Section 5.3., The result of missing some coincidences because of the presence of $\alpha$ shells would be an age distribution of the clusters slightly younger than inferred in Section 5.3.104 Note that this effect is ouly relevant to the most imassive clusters in Arp 299 iud NGC 3256 where we expect to see coincidences with the preseut detection threshold., Note that this effect is only relevant to the most massive clusters in Arp 299 and NGC 3256 where we expect to see coincidences with the present detection threshold.105 Iu this paper we have presented Z$T/NICMOS broad-baud and uarrow-baud Pao tuagine of a sample of 5 LIRGs., In this paper we have presented /NICMOS broad-band and narrow-band $\alpha$ imaging of a sample of 8 LIRGs.106" The sample galaxies exhibit a range of infrared huninosities (logLy,=10.91.I1L82L.). as well as a varicty of dynamical stages: isolated galaxies interacting ealaxies aud mergers."," The sample galaxies exhibit a range of infrared luminosities $\log L_{\rm IR} = 10.94-11.82\,{\rm L}_\odot$ ), as well as a variety of dynamical stages: isolated galaxies interacting galaxies and mergers."107 The Pan images have allowed us to identify the location of regions. whereas the Z7-baud contimmiun nuages have revealed the star clusters.," The $\alpha$ images have allowed us to identify the location of regions, whereas the $H$ -band continuum images have revealed the star clusters."108 In all ealaxies iu our sample except NGC 6210 aud Zw 019.057 we have detected a large number of star clusters and regions., In all galaxies in our sample except NGC 6240 and Zw 049.057 we have detected a large number of star clusters and regions.109 The absolute Z£-baud magnitudes of the identified SSCs range up to MyL7.2inag.," The absolute $H$ -band magnitudes of the identified SSCs range up to $M_H=-17.2\,$ mag."110 A huge fraction of the region population (exchiding the nuclear emission) shows huuimosities iu excess of that of 30 Doradus. the prototypical giant region.," A large fraction of the region population (excluding the nuclear emission) shows luminosities in excess of that of 30 Doradus, the prototypical giant region."111 The main characteristic of the Pao emissiou. iu the isolated LIRGs iu our sample is the lack of stroug uuclear cluission., The main characteristic of the $\alpha$ emission in the isolated LIRGs in our sample is the lack of strong nuclear emission.112 Most of the regions are distributed along the spiral rius of the galaxies., Most of the regions are distributed along the spiral arms of the galaxies.113 The interacting/imereine LIRGs ou the other hand. show bright unclear Pan enission together with widely spread star formation along the the spiral iris and at the interface of interacting ealaxies.," The interacting/merging LIRGs on the other hand, show bright nuclear $\alpha$ emission together with widely spread star formation along the the spiral arms and at the interface of interacting galaxies."114 The fraction of nuclear Pan eiissiou to the total cnussion varies from system to system. as it depends ou factors sch as the age of the interaction process. the initial eas content of the ealaxics and the relative masses of the ealaxies.," The fraction of nuclear $\alpha$ emission to the total emission varies from system to system, as it depends on factors such as the age of the interaction process, the initial gas content of the galaxies and the relative masses of the galaxies."115 We have analyzed the properties — bIuninosities. sizes aud huuimositv functions — of regions in LIRGs at au uuprecedeuted spatial resolution (between 15 and 78 pe).," We have analyzed the properties – luminosities, sizes and luminosity functions – of regions in LIRGs at an unprecedented spatial resolution (between 15 and 78 pc)."116 Cdant reeious are ubiquitous in LIRGs aud are located not only near the nuclei of interacting galaxies. but also at the interface of iuteracting ealaxies and along the spiral arms.," Giant regions are ubiquitous in LIRGs and are located not only near the nuclei of interacting galaxies, but also at the interface of interacting galaxies and along the spiral arms."117 This population of lughiy luminous regions is uot observed iu uormal galaxies., This population of highly luminous regions is not observed in normal galaxies.118 We lave fitted power laws to the region LFs of Arp 299 and NGC 3256 and found that the iudices are within the values previously measured iu the disks of normal galaxies., We have fitted power laws to the region LFs of Arp 299 and NGC 3256 and found that the indices are within the values previously measured in the disks of normal galaxies.119 We lave compared the properties of the regions in LIRCGs with a small sample of normal galaxies observed with the same spatial resolution and found that eiaut veeious are more common in LIRGs than in normal ealaxies., We have compared the properties of the regions in LIRGs with a small sample of normal galaxies observed with the same spatial resolution and found that giant regions are more common in LIRGs than in normal galaxies.120 The iueasured sizes of eiut regious in, The measured sizes of giant regions in121assumptions. ie. the self-similarity of the solutions).,"assumptions, i.e. the self-similarity of the solutions)."122 PelleGer&ον(1992) further developed the general theory. of non-sell-similar solutions of hyvdromagnetie disk winds., \citet{Pelletier92} further developed the general theory of non-self-similar solutions of hydromagnetic disk winds.123 In these models the transler of excess energy (o (he escaping particles is made at the expense ol the rotational energv of the matter in the disk and it is mediated by the magnetic field., In these models the transfer of excess energy to the escaping particles is made at the expense of the rotational energy of the matter in the disk and it is mediated by the magnetic field.124 While this (vpe of model gained popularity. the issue of jet/outlfow formation took a different turn. with the introduction of acdvection-dominated accretion flow (ADAF) (ο...Naravan&Yi1994:Mlanmotoetal. 1997).," While this type of model gained popularity, the issue of jet/outlfow formation took a different turn with the introduction of advection-dominated accretion flow (ADAF) \citep[e.g.,][]{Narayan94,Manmoto97}."125. These radiativelv inefficient. accretion [lows (RIAF) were found to have positive Bernoulli integral of the flow and could therefore fulfill the condition necessary for the launching of jet/wind outflows: as such they present potentially interesting sites for the oriein of such oulllows., These radiatively inefficient accretion flows (RIAF) were found to have positive Bernoulli integral of the flow and could therefore fulfill the condition necessary for the launching of jet/wind outflows; as such they present potentially interesting sites for the origin of such outflows.126 The positivity of the Bernoulli integral has been discussed and analysed by Blanclord&Begelman(1999) who pointed out Chat 1 is due to the combination of energy. transfer by (he viscous torques [rom the inner to the outer sections of the flow (the gas of the flow becomes bounded al its inner edge) and the local dissipation of the flows azimuthal kinetic energy which is not radiated away but stored in Che fluid to increase its internal energv., The positivity of the Bernoulli integral has been discussed and analysed by \citet{BB99} who pointed out that it is due to the combination of energy transfer by the viscous torques from the inner to the outer sections of the flow (the gas of the flow becomes bounded at its inner edge) and the local dissipation of the flow's azimuthal kinetic energy which is not radiated away but stored in the fluid to increase its internal energy.127 The latter authors then argued Chat ἰ excess energv can be carried away (o infinity (along with some fraction of the accreti mass and angular moment) to produce continuous outflows from all radii to infinitv. whi leaving (he remaining flow with negative Bernoulli constant to naturally acerete onto the compact object: advection-dominated. inflow-outllow solution (ADIOS)., The latter authors then argued that the excess energy can be carried away to infinity (along with some fraction of the accreting mass and angular momentum) to produce continuous outflows from all radii to infinity while leaving the remaining flow with negative Bernoulli constant to naturally accrete onto the compact object: advection-dominated inflow-outflow solution (ADIOS).128 In (his case. while (he necessary excess energy is (transferred by (the viscous torques from the flows more highly bound inner section. (he necessary separation of mass to components with positive and negalive total energv is still left unspecified.," In this case, while the necessary excess energy is transferred by the viscous torques from the flow's more highly bound inner section, the necessary separation of mass to components with positive and negative total energy is still left unspecified."129 An altogether different model (hat offers a simplified picture of such a separation was presented by Subramanianetal.(1999) who proposed that in the tenuous. collisionless plasma of an ADAF particles (protons) could be accelerated. via a second-orcler Fermi acceleration bv (he shear motions of the underlying quasi-Ixeplerian azimuthial flow.," An altogether different model that offers a simplified picture of such a separation was presented by \citet{Subramanian99} who proposed that in the tenuous, collisionless plasma of an ADAF particles (protons) could be accelerated via a second-order Fermi acceleration by the shear motions of the underlying quasi-Keplerian azimuthal flow."130 Thev ren argued that if sulliciently laree pressure is built in (he accelerated. particle proton population (the electrons generally lose energy on time scales short compared to their transit me through the svstem and cannot build an energy densitv that could be dynamically nuportant) aud for favorable geometries of the disk magnetic field (large scale poloidal loops wal open up above the disk) (he relativistic particle population could naturally (through je action of the gravitational field) segregate itself [rom the non-relativistic one. carrving ME to infinity only the accelerated (Ezi imc) portion of the disk plasma.," They then argued that if sufficiently large pressure is built in the accelerated particle proton population (the electrons generally lose energy on time scales short compared to their transit time through the system and cannot build an energy density that could be dynamically important) and for favorable geometries of the disk magnetic field (large scale poloidal loops that open up above the disk) the relativistic particle population could naturally (through the action of the gravitational field) segregate itself from the non-relativistic one, carrying off to infinity only the accelerated $E \gsim m_pc^2$ ) portion of the disk plasma."131 In this case the eneine is a combination of the particle acceleration and the action of the gravitational fiel., In this case the engine is a combination of the particle acceleration and the action of the gravitational field.132 Finally. a model along the same lines was proposed by Contopoulos&Ixazanas(1995) who suggested that even in the case of a completev turbulent magnetic field. a separation of (he relativistic and non-relativistic particle populaAions is possible through the production οἱ relativistic neutrons in the collisions of the relativistic protons with the ambient plasma ancl the ensuing production of relativistic neutrons.," Finally, a model along the same lines was proposed by \citet{Contopoulos95} who suggested that even in the case of a completely turbulent magnetic field, a separation of the relativistic and non-relativistic particle populations is possible through the production of relativistic neutrons in the collisions of the relativistic protons with the ambient plasma and the ensuing production of relativistic neutrons."133" T1ο subsequent decay of neutrons back into protons produces then a proton fluid in regions o[ space devoid of inertia whose ratio (and hence its asvanptotie Lorentz Fact) depends only on the ratio ήστι. where Ris the size of the svstem and 7, the neutron lie time and can lead to highly relativistic flows for black hole masses Af210A.."," The subsequent decay of neutrons back into protons produces then a proton fluid in regions of space devoid of inertia whose energy-to-mass ratio (and hence its asymptotic Lorentz factor) depends only on the ratio $R/c \tau_{\rm134n}$, where $R$ is the size of the system and $\tau_{\rm n}$ the neutron life time and can lead to highly relativistic flows for black hole masses $M \gsim 10^8 \Msun$."135 In the present note we lollow a similar simplifiel view to study outflows in objects powered bv accretion: We consider the presence of (2-dimensional) shocks as a means of dissipation of (he accretion kinetic energy in a [ashion similar to that considered by, In the present note we follow a similar simplified view to study outflows in objects powered by accretion: We consider the presence of (2-dimensional) shocks as a means of dissipation of the accretion kinetic energy in a fashion similar to that considered by136the group regime. where fossils fall on the Lj;—c relation of non-fossil galaxy groups.,"the group regime, where fossils fall on the $L_R-\sigma$ relation of non-fossil galaxy groups."137 We will discuss these features in Section 6 in the light of other scaling relations., We will discuss these features in Section 6 in the light of other scaling relations.138 Group velocity dispersions are based on our spectroscopic observations of the sample in Table | and NED for the rest of the systems., Group velocity dispersions are based on our spectroscopic observations of the sample in Table 1 and NED for the rest of the systems.139 They are calculated using the following relation. also used in the comparison sample of Osmond&Ponman(20043:3/2). +.," They are calculated using the following relation, also used in the comparison sample of \citet{osmond04}:, ."140 This estimator corrects for a statistical bias. which results if one uses the normal unbiased estimator for o7 and then takes the square root to obtain e (which is then not unbiased).," This estimator corrects for a statistical bias, which results if one uses the normal unbiased estimator for $\sigma^2$ and then takes the square root to obtain $\sigma$ (which is then not unbiased)."141 This correction is the origin of the term 3/2 (rather than |) in the denominator of the above equation., This correction is the origin of the term 3/2 (rather than 1) in the denominator of the above equation.142 If excess X-ray luminosity in fossils were the only difference between the X-ray properties of fossils and non-fossil groups. then hey wouldbe expected to deviate from the Ly7 relation known or non-fossil groups and clusters.," If excess X-ray luminosity in fossils were the only difference between the X-ray properties of fossils and non-fossil groups, then they wouldbe expected to deviate from the $L_X-T$ relation known for non-fossil groups and clusters."143 This appeared to be the case rom an earlier ROSAT study (Jonesetal.2003). based on very imited statistics., This appeared to be the case from an earlier ROSAT study \citep{jones03} based on very limited statistics.144 Two fossil groups. for which Jonesetal.(2003) could measure the temperature. were found to have high. X-ray uminosity for their gas temperature.," Two fossil groups, for which \citet{jones03} could measure the temperature, were found to have high X-ray luminosity for their gas temperature."145 Based on this finding. it was argued that fossils are low-entropy systems due to their higher gas density. in comparison to non-fossils.," Based on this finding, it was argued that fossils are low-entropy systems due to their higher gas density, in comparison to non-fossils."146 However we have shown in Khosroshahietal.(2006). that the X-ray temperature of the RX 11416.442315 was underestimated in the analysis., However we have shown in \citet{kmpj06} that the X-ray temperature of the RX J1416.4+2315 was underestimated in the analysis.147 The present wider study shows that the above system is not an exception and. as it is seen in Fig 4.. fossils fall on the conventional byT. relation of non-fossil groups and clusters.," The present wider study shows that the above system is not an exception and, as it is seen in Fig \ref{LT}, fossils fall on the conventional $L_X-T$ relation of non-fossil groups and clusters."148 Hence. if from our earlier arguments we assert that is enhanced in fossils. then it follows that they must also have £Lelevatedx. mean temperature values. such that they remain on the standard group Ly7 relation.," Hence, if from our earlier arguments we assert that $L_X$ is enhanced in fossils, then it follows that they must also have elevated mean temperature values, such that they remain on the standard group $L_X-T$ relation."149 Mahdavi&Geller(2001):XueWu(9000). have presented Lx70 relations for clusters and groups.," \citet{mahdavi01,xue00} have presented $L_X-\sigma$ relations for clusters and groups."150 Osmond(2004) found a slope of 2.31 + 0.61 in Lxσ for heir sample of galaxy groups with intergalactic X-ray emission. flatter than the value of 4.5+1.1 found by Helsdon&Ponman (2000)..," \citet{osmond04} found a slope of 2.31 $\pm$ 0.61 in $L_X-\sigma$ for their sample of galaxy groups with intergalactic X-ray emission, flatter than the value of $4.5 \pm 1.1$ found by \citet{helsdon00}. ."151 There is a good deal of scatter in the relation. which may in »art account for the disagreement between various studies.," There is a good deal of scatter in the relation, which may in part account for the disagreement between various studies."152 While Ponmanetal. (1996). Mulchaey&Zabludoff 1908): Helsdon&Pon-man(2000). and Mahdavi&Geller(2001). find that groups are consistent with the cluster-relation slope of z+ . Mahdavi (1997.2000) and Xue&Wu(2000). find significantly flatter relations in groups with a slope similar to the finding of Osmond (2004). ," While \citet{ponman96}, \citet{mz98}; \citet{helsdon00} and \citet{mahdavi01} find that groups are consistent with the cluster-relation slope of $\approx 4$ , Mahdavi (1997,2000) and \citet{xue00} find significantly flatter relations in groups with a slope similar to the finding of \citet{osmond04}. ."153Figure 5. shows the distribution of fossil groups inthe plane of Lx.—0 along with the non-fossil groups and clusters., Figure \ref{lxsigma} shows the distribution of fossil groups inthe plane of $L_X-\sigma$ along with the non-fossil groups and clusters.154 Fossils appear more X-ray luminous thannon-fossil groups for a given, Fossils appear more X-ray luminous thannon-fossil groups for a given155reliability.,reliability.156" In refobserved,, the direct observations are compared with the images and in refresults,, values measured on the sharpened images are reported."," In \\ref{observed}, the direct observations are compared with the de-convolved images and in \\ref{results}, values measured on the sharpened images are reported."157" In refring,, one-dimensional cuts along the major axis of the observed and de-convolved iimage are displayed."," In \\ref{ring}, one-dimensional cuts along the major axis of the observed and de-convolved image are displayed."158" It would have been more natural to select the observation atum,, having the highest spatial resolution, but the sscan map data are of considerably higher S/N, outweighing the apparent resolution advantage of the shorter wavelength data."," It would have been more natural to select the observation at, having the highest spatial resolution, but the scan map data are of considerably higher S/N, outweighing the apparent resolution advantage of the shorter wavelength data."159" In the analysed sub-frame, the flux was conserved within by the MEM routine."," In the analysed sub-frame, the flux was conserved within by the MEM routine."160" Prior to the de-convolution, a stellar point source with photospheric flux of mmJy at refresults)) was subtracted from the PACS image."," Prior to the de-convolution, a stellar point source with photospheric flux of mJy at \\ref{results}) ) was subtracted from the PACS image."161" The resulting sharpened image reveals a central and a central depression with a depth of about2%,, which is consistent with the debris residing in a ring or belt around the star."," The resulting sharpened image reveals a central and a central depression with a depth of about, which is consistent with the debris residing in a ring or belt around the star."162" With standard assumptionsregarding the emitting grains (astronomical silicates, a blow-out size limit ag,=0.6 ffor the VV star and a —3.5 power law index for the size distribution) we find that the ssurface brightness profiles along the major and minor axes are well reproduced assuming a disk inclination of about aand a two-parameter model for the surface density, X(r)."," With standard assumptionsregarding the emitting grains (astronomical silicates, a blow-out size limit $a_{\rm min}= 0.6$ for the V star and a $-3.5$ power law index for the size distribution) we find that the surface brightness profiles along the major and minor axes are well reproduced assuming a disk inclination of about and a two-parameter model for the surface density, $\Sigma(r)$."163" These parameters are the peak density position, rmax, and the power law index of the surface density profile for r>rmax."," These parameters are the peak density position, $r_{\rm max}$, and the power law index of the surface density profile for $r > r_{\rm max}$."164" The best fit to the surface brightness profiles is consistent with a ring-like disc, having values of rmax~85 AAU and X(r>rg)οςr3, respectively."," The best fit to the surface brightness profiles is consistent with a ring-like disc, having values of $r_{\rm max} \sim 85$ AU and $\Sigma(r > r_{\rm max}) \propto r^{-3}$, respectively."165" A more elaborate model, with the size distribution computed self-consistently and taking into account the profiles also at other wavelengths, will be presented by Augereau et al. ("," A more elaborate model, with the size distribution computed self-consistently and taking into account the profiles also at other wavelengths, will be presented by Augereau et al. ("166in prep.).,in prep.).167 This roughly AAU wide ring or belt at about AAU from the star appears similar to the EKB of the Solar System., This roughly AU wide ring or belt at about AU from the star appears similar to the EKB of the Solar System.168" Based on an analogy with the debris disc around Fomalhaut and on theoretical expectations, it is quite possible that another gas giant planet, ,cc, could be orbiting the star inside the inner belt edge."," Based on an analogy with the debris disc around Fomalhaut and on theoretical expectations, it is quite possible that another gas giant planet, c, could be orbiting the star inside the inner belt edge."169" Given the age of the system, GGyr, the direct detection of ,cc, for instance by means of coronography, can be expected to be hard (see,e.g.,Beichmanetal. 2006).."," Given the age of the system, Gyr, the direct detection of c, for instance by means of coronography, can be expected to be hard \citep[see, e.g.,][]{beichman2006}. ."170" Based on imaging observations with PACS in the three photometric bands at um,, aand wwe find that"," Based on imaging observations with PACS in the three photometric bands at , and we find that"171"more possibly ambipolar diffusion. cau become dominant in the high density cold gas. the turbulent diffusion in the carly stages of accretion is able to form a light aud large rotationally supported disk very quickly. iun only a few LO! yy,","more possibly ambipolar diffusion, can become dominant in the high density cold gas, the turbulent diffusion in the early stages of accretion is able to form a light and large rotationally supported disk very quickly, in only a few $10^4$ yr."172 Finally. we should remark that other mechanisms to remove or reduce the effects of the magnetic braking in the inner regions of protostellar cores have been also investigated in the literature receutly.," Finally, we should remark that other mechanisms to remove or reduce the effects of the magnetic braking in the inner regions of protostellar cores have been also investigated in the literature recently."173 Heunebelle&Cia-rdi(2009). verified that the maeuetic brakiug efficiency may decrease significantly when the rotation axis of the core is unisaligued with the direction of the regular magnetic field., \citet{hennebelle_ciardi_2009} verified that the magnetic braking efficiency may decrease significantly when the rotation axis of the core is misaligned with the direction of the regular magnetic field.174" They claim that even for small angeles of the order of 10.20"" there are significant differences with respect to the aligned case;", They claim that even for small angles of the order of $10-20^o$ there are significant differences with respect to the aligned case.175 Also. in a concoiitaut work to the present one. Wrasnopolskyetal.(2011) have exanuned the Wall effect on disk formation.," Also, in a concomitant work to the present one, \citet{krasnopolsky_etal_2011} have examined the Hall effect on disk formation."176 They found that a ITall-àuduced magnetic torque can diffuse magnetic flux outward aud generate a rotationally supported disk in the collapsing flow. even when the core is initially however the spun-up material remains too sub-Keplerian (Lictal.2011).," They found that a Hall-induced magnetic torque can diffuse magnetic flux outward and generate a rotationally supported disk in the collapsing flow, even when the core is initially non-rotating, however the spun-up material remains too sub-Keplerian \citep{li_etal_2011}."177. Of course. in the uear future. these imechamisus must be tested along with the just proposed turbulent magnetic reconnection aud even with ambipolar diffusou. iu order to assess the relative müportance of cach effect ou disk formation aud evolution.," Of course, in the near future, these mechanisms must be tested along with the just proposed turbulent magnetic reconnection and even with ambipolar diffusion, in order to assess the relative importance of each effect on disk formation and evolution."178 Nonetheless. «λος ATID turbuleuce is expected to be present iu these magnetic cores (e... Dallesteros-Paredes&:MacLimactal 2010.. ind references therein). turbulent reconnection arises as a natural wuechauisia for removing magnetic flux excess and allowing the formation of these disks.," Nonetheless, since MHD turbulence is expected to be present in these magnetic cores (e.g., \citealt{ballesteros-paredes_maclow_2002, melioli_etal_2006, leao_etal_2009, santos-lima_etal_2010}, and references therein), turbulent reconnection arises as a natural mechanism for removing magnetic flux excess and allowing the formation of these disks."179 lu recent nunierical study in SNLO. we showed that magnetic reconnection iu a turbulent cloud cau efficicutly transport magnetic flux from the iuner denser regions to the periphery of the cloud thus enabling the cloud. to collapse to form a star.," In recent numerical study in SX10, we showed that magnetic reconnection in a turbulent cloud can efficiently transport magnetic flux from the inner denser regions to the periphery of the cloud thus enabling the cloud to collapse to form a star."180 Tere. also by iuneaus of fully 3D ATID sinmlatious. we have investigated the same mechanisni acting in a votating collapsing cloud core and shown that the magnetic flux excess of the inner regions of the system can be effectively removed allowing the formation of a rotationally sustained protostellar disk.," Here, also by means of fully 3D MHD simulations, we have investigated the same mechanism acting in a rotating collapsing cloud core and shown that the magnetic flux excess of the inner regions of the system can be effectively removed allowing the formation of a rotationally sustained protostellar disk."181 Another cupirical finding in SNIO is that the eficiency ofthe magnetic field expulsion via recounectiou diffisivity increases with the source gravitational field., Another empirical finding in SX10 is that the efficiency of the magnetic field expulsion via reconnection diffusivity increases with the source gravitational field.182 This is a natural cousequeuce ofdiffusion iu the presence of the gravitational field which pulls oue component (gas and does not act on the other weightless courponeut anaenetie feld)., This is a natural consequence of diffusion in the presence of the gravitational field which pulls one component (gas) and does not act on the other weightless component (magnetic field).183 Di terms of the problem im haud. this implies that more massive protostars can induce magnetic field segregation even for weaker level of turbulence.," In terms of the problem in hand, this implies that more massive protostars can induce magnetic field segregation even for weaker level of turbulence."184 We plan to explore nuucerically this issue iu a forthcoming work., We plan to explore numerically this issue in a forthcoming work.185 Tn this paper we showed that the concept of reconnection diffusion (L05) successfully works iu the formation of protostellar disks., In this paper we showed that the concept of reconnection diffusion (L05) successfully works in the formation of protostellar disks.186 Together with our earlier testing of magnetic field removal through recounection diffusion from collapsing clouds this paper supports a considerable change of the paradieui of star formation., Together with our earlier testing of magnetic field removal through reconnection diffusion from collapsing clouds this paper supports a considerable change of the paradigm of star formation.187 Tudeed. in the presence of reconnection diffusion. there is no necessity to appeal to ambipolar diffusion.," Indeed, in the presence of reconnection diffusion, there is no necessity to appeal to ambipolar diffusion."188 The latter wav still be nuportaut iu low ionization. low turbulence cuvirouments. but. iu anv case. the domain of its applicability is seriously challeuged.," The latter may still be important in low ionization, low turbulence environments, but, in any case, the domain of its applicability is seriously challenged."189 The application of the reconnection diffusion concept to protostellar disk formation aud. i a more eencral framework. to accretion disks in seueral is natural as the disks are expected to be turbulent. chabling our appeal to LV99 model of fast recounection.," The application of the reconnection diffusion concept to protostellar disk formation and, in a more general framework, to accretion disks in general, is natural as the disks are expected to be turbulent, enabling our appeal to LV99 model of fast reconnection."190" An Huportant accepted source of turbulence iu accretion disks is the well known magueto-rotational instability (MRI) (Chandrasekhar 1960. Balbus ITawleyv 1991)""s but at carlicy stages turbulence can be induced by the ντοςπασα motions associated with the disk. formation."," An important accepted source of turbulence in accretion disks is the well known magneto-rotational instability (MRI) (Chandrasekhar 1960, Balbus Hawley 1991), but at earlier stages turbulence can be induced by the hydrodynamical motions associated with the disk formation."191 Turbulence is ubiquitous in astrophysical environments as it follows from theoretical considerations based on the high Revuolds uuubers of astrophysical flows and is stronely supported bv studies of spectra of the interstellar electron ceusitv fluctuations (sec Arvinstrongetal.1995:Chepurnov&Lazarian 2010)) as well as of WT (Lazarian2009. for a review aud references therein: Chepurnovctal. 2010)) and CO lines (see Padoanetal. 200901).," Turbulence is ubiquitous in astrophysical environments as it follows from theoretical considerations based on the high Reynolds numbers of astrophysical flows and is strongly supported by studies of spectra of the interstellar electron density fluctuations (see \citealt{armstrong_etal_1995, chepurnov_lazarian_2010}) ) as well as of HI \citealt{lazarian_2009} for a review and references therein; \citealt{chepurnov_etal_2010}) ) and CO lines (see \citealt{padoan_etal_2009}) )."192 The application of the recomnection diffusion mechanisia to already formed accretion disks will be investigated im detail elsewhere., The application of the reconnection diffusion mechanism to already formed accretion disks will be investigated in detail elsewhere.193 It should be noted however that former studies of the injection of turbulence in accretion disks have shown that at this stage turbulence may be ineffective to maenetic fiux diffusion outward (Rothstein&Lovelace2008)., It should be noted however that former studies of the injection of turbulence in accretion disks have shown that at this stage turbulence may be ineffective to magnetic flux diffusion outward \citep{rothstein_lovelace_2008}.194. Appealing to the LV99 inodel of fast maguetic reconnection and inspired by the successful demonstration of removal of magnetic feld through reconnection diffusion from nunerical models of nolecular clouds in SX10 we have performed uuucerical simulations and demonstrated that: l., Appealing to the LV99 model of fast magnetic reconnection and inspired by the successful demonstration of removal of magnetic field through reconnection diffusion from numerical models of molecular clounds in SX10 we have performed numerical simulations and demonstrated that: 1.195 The concept of reconnection diffusion is applicable o the formation of protostellar disks with radius ~100 AU., The concept of reconnection diffusion is applicable to the formation of protostellar disks with radius $\sim 100$ AU.196 The extension of this concept to accretion disks is OYeseen., The extension of this concept to accretion disks is foreseen.197 2., 2.198 In the eravitational field. reconnection diffusion uitigates magnetic breaking allowing the formation of xotostellar disks.," In the gravitational field, reconnection diffusion mitigates magnetic breaking allowing the formation of protostellar disks."199 3., 3.200 The removal of magnetic field through recounectiou diffusion is fast cuough to explain observatious without he necessity of appealing to cuhanced fluid resistivity., The removal of magnetic field through reconnection diffusion is fast enough to explain observations without the necessity of appealing to enhanced fluid resistivity.201stellar masses inferred from the CBO7 library are on average 0.12 dex lower than the BCO3-based ones. with a large (0.17 dex) scatter.,"stellar masses inferred from the CB07 library are on average 0.12 dex lower than the BC03-based ones, with a large (0.17 dex) scatter."202 The lack of a clear trend with stellar mass or redshift of the ratio of the two estimates translates into a lack of systematic difference between the best-fit Schechter parameters in the two cases., The lack of a clear trend with stellar mass or redshift of the ratio of the two estimates translates into a lack of systematic difference between the best-fit Schechter parameters in the two cases.203 The largest disagreement was found at 2— 3. where the effect of the TP-AGB phase is expected to be the most important.," The largest disagreement was found at $z \sim 2 - 3$ , where the effect of the TP-AGB phase is expected to be the most important."204 The main result of this study is the steepening of the faint- slope: the value of« increases from —1.4420.03 at z~0.8 to —1.56£0.16 at z~3. and then flattens up to z~4.," The main result of this study is the steepening of the faint-end slope: the value of $\alpha$ increases from $-1.44 \pm 0.03$ at $z\sim 0.8$ to $-1.86 \pm 0.16$ at $z\sim 3$, and then flattens up to $z\sim 4$."205 We have confirmed the steepening of the low-mass end. which had been pointed out by previous authors. with deeper and higher quality photometry.," We have confirmed the steepening of the low-mass end, which had been pointed out by previous authors, with deeper and higher quality photometry."206 Our results are unaffected by degeneracies in the M parameter. and they are insensitive to the choice of either the stellar templates or the functional shape fitted to the GSMF. as well as to the limitations of the small area covered by ERS observations.," Our results are unaffected by degeneracies in the $M^*$ parameter, and they are insensitive to the choice of either the stellar templates or the functional shape fitted to the GSMF, as well as to the limitations of the small area covered by ERS observations."207 We computed the SMD as a function of redshift and compared it with the integrated star formation histories derived by Hopkins&Beacom(2006) and Reddy&Steidel(2009)., We computed the SMD as a function of redshift and compared it with the integrated star formation histories derived by \cite{hopkins06} and \cite{reddy09}.208 The finer sampling of the GSMF at low masses and the steep inferred faint-end slopes determine the higher SMD estimates at >2 than most previous works. solving the disagreement observed by previous authors between the SMD and the integrated SFRD at these redshifts.," The finer sampling of the GSMF at low masses and the steep inferred faint-end slopes determine the higher SMD estimates at $z>2$ than most previous works, solving the disagreement observed by previous authors between the SMD and the integrated SFRD at these redshifts."209 However. despite the steep GSMF that we find. the integrated star formation history still exceeds the direct measure of the SMD at z~2 by a factor of ~2—3. even when our data are analysed together with the results of previous large surveys to ensure a good sampling of also the bright-end tail of the GSMF.," However, despite the steep GSMF that we find, the integrated star formation history still exceeds the direct measure of the SMD at $z\sim 2$ by a factor of $\sim 2-3$, even when our data are analysed together with the results of previous large surveys to ensure a good sampling of also the bright-end tail of the GSMF."210 Finally. we compared our GSMF and SMD estimates with the predictions of four models of galaxy formation and evolution.," Finally, we compared our GSMF and SMD estimates with the predictions of four models of galaxy formation and evolution."211 All models predict a larger abundance of low mass galaxies than observations. at least up to z~3.," All models predict a larger abundance of low mass galaxies than observations, at least up to $z\sim3$."212 They also underestimate the stellar mass of high mass galaxies in. the highest redshift bin. although cosmic variance effects prevent us from drawing firm conclusions. at these redshifts.," They also underestimate the stellar mass of high mass galaxies in the highest redshift bin, although cosmic variance effects prevent us from drawing firm conclusions at these redshifts."213 The overabundance of low mass galaxies translates into a general overestimation of the total SMD with respect to the data up to zo2. while this density is underestimated at z>3 owing to the dearth of massive galaxies at these redshifts.," The overabundance of low mass galaxies translates into a general overestimation of the total SMD with respect to the data up to $z\sim 2$, while this density is underestimated at $z\gtrsim 3$ owing to the dearth of massive galaxies at these redshifts."214 The exact degree of disagreement depends on the particular model., The exact degree of disagreement depends on the particular model.215 Future CANDELS data will cover a larger sky area and allow a finer sampling of both the bright-end of the GSMF and its normalization. and at the same time they will be deep enough to accurately probe the GSMF faint-end.," Future CANDELS data will cover a larger sky area and allow a finer sampling of both the bright-end of the GSMF and its normalization, and at the same time they will be deep enough to accurately probe the GSMF faint-end."216 These. together with spectroscopic follow-up campaigns. will reduce the uncertainties in the stellar masses. and they will significantly improve our results and our understanding of the stellar mass assembly process.," These, together with spectroscopic follow-up campaigns, will reduce the uncertainties in the stellar masses, and they will significantly improve our results and our understanding of the stellar mass assembly process."217in the immediate vicinity of the black hole.,in the immediate vicinity of the black hole.218 Furthermore. at millimeter wavelengths the blurring due to interstellar electron scattering ts subdominant.," Furthermore, at millimeter wavelengths the blurring due to interstellar electron scattering is subdominant."219 Thus. at wavelengths of 1.3mm and below it is possible to image the emitting region surrounding Ser A*.," Thus, at wavelengths of $1.3\,\mm$ and below it is possible to image the emitting region surrounding Sgr A*."220 Even with the strong gravitational lensing in the vicinity of the horizon. imaging the immediate vicinity of the black hole requires extraordinary resolutions.," Even with the strong gravitational lensing in the vicinity of the horizon, imaging the immediate vicinity of the black hole requires extraordinary resolutions."221 The silhouette cas= by the horizon on the surrounding emission is roughly 53+2 ," The silhouette cast by the horizon on the surrounding emission is roughly $53\pm2\,\muas$ ."222At the present time. this resolution is accessible only via asl...millimeter-wavelength very-long baseline interferometry (mm-VLBI).," At the present time, this resolution is accessible only via millimeter-wavelength very-long baseline interferometry (mm-VLBI)."223 VLBI observations of Ser A* at 1.4mm using the Institut de Radioastronomie Milliméttrique (IRAM) 30m telescope at Pico Veleta and one of the 15m dishes at Plateau de Bure. produced the size estimate of 110—60j/as. with the large uncertainties due to limited calibration accuracy (?)..," VLBI observations of Sgr A* at $1.4\,\mm$ using the Institut de Radioastronomie Milliméttrique (IRAM) $30\,\m$ telescope at Pico Veleta and one of the $15\,\m$ dishes at Plateau de Bure, produced the size estimate of $110\pm60\,\muas$, with the large uncertainties due to limited calibration accuracy \citep{Kric_etal:98}."224 The first successful mm-VLBI observation of Ser A* with Earth-scale baselines was performed in April. 2007. during which visibilities were measured on the 4.6«10°km baseline between Mauna Kea. Hawaii to Mount Graham. Arizona (?)..," The first successful mm-VLBI observation of Sgr A* with Earth-scale baselines was performed in April, 2007, during which visibilities were measured on the $4.6\times10^3\,\km$ baseline between Mauna Kea, Hawaii to Mount Graham, Arizona \citep{Doel_etal:08}."225 By fitting these with a gaussian model. ?— found a typical intrinsic source size of 3773jas (after correcting for the sub-dominant broadening due to interstellar electron scattering). smaller than the black hole silhouette.," By fitting these with a gaussian model, \citet{Doel_etal:08} found a typical intrinsic source size of $37^{+5}_{-3}\,\muas$ (after correcting for the sub-dominant broadening due to interstellar electron scattering), smaller than the black hole silhouette."226 Since that time a number of groups have analyzed the 2007 mm-VLBI data using various physically motivated accretion models for the emission region (????).. inferring from these efforts the black hole spin vector.," Since that time a number of groups have analyzed the 2007 mm-VLBI data using various physically motivated accretion models for the emission region \citep{Brod_etal:09,Huan-Taka-Shen:09,Mosc_etal:09,Dext-Agol-Frag-McKi:10}, inferring from these efforts the black hole spin vector."227 Despite finding generally similar results. these have been limited by the lack of multiple long baseline observations and the limited north-south coverage obtained.," Despite finding generally similar results, these have been limited by the lack of multiple long baseline observations and the limited north-south coverage obtained."228 Recently. a second. and considerably set of mm-VLBI observations have been (?).. largerproviding the opportunity to revisit. and substantially reportedimprove. constraints the black hole spin and accretion physics.," Recently, a second, and considerably larger set of mm-VLBI observations have been reported \citep{Fish_etal:10}, providing the opportunity to revisit, and substantially improve, constraints upon the black hole spin and accretion physics."229 Here we uponreport upon the first effort to do this using a physically motivated accretion model. similar to that described in ?.. that fits the known spectral and polarization properties of Ser A*.," Here we report upon the first effort to do this using a physically motivated accretion model, similar to that described in \citet{Brod_etal:09}, that fits the known spectral and polarization properties of Sgr A*."230 In addition to improving the resulting parameter estimation. it is now possible to identify statistical signatures of both the asymmetry of the image and the importance of the underlying physics that governs the image morphology.," In addition to improving the resulting parameter estimation, it is now possible to identify statistical signatures of both the asymmetry of the image and the importance of the underlying physics that governs the image morphology."231 Section 2. summarizes the full set of mm-VLBI observations we consider.," Section \ref{sec:SoO}232 summarizes the full set of mm-VLBI observations we consider."233 Section 3. describes the models we consider and how the resulting visibility data is produced., Section \ref{sec:VM} describes the models we consider and how the resulting visibility data is produced.234 How models are compared and the parameter estimates are produced ts discussed in Section 4.., How models are compared and the parameter estimates are produced is discussed in Section \ref{sec:BDA}.235 The fitting process and results are presented in Section 5.. and our best estimates for the black hole spin vector can be found in Section 6..," The fitting process and results are presented in Section \ref{sec:MF}, and our best estimates for the black hole spin vector can be found in Section \ref{sec:EBHS}."236 Section 7. describes the implications for different potential future observations.," Section \ref{sec:OFO}237 describes the implications for different potential future observations."238 Finally concluding remarks are collected in Section 8.., Finally concluding remarks are collected in Section \ref{sec:C}.239 In the analysis presented. here we make full use of the recent observations described in?) and ?.., In the analysis presented here we make full use of the recent observations described in \citet{Fish_etal:10} and \citet{Doel_etal:08}.240 In both cases. observations targeting Ser A¥ were made at 1.3mm using the Submillimeter Telescope (SMT)) on Mt. Graham in Arizona. 10m dishes in the Combined Array for Research in Millimeter-wave Astronomy (CARMA)) at Cedar Flat. California. and the James Clerk Maxwell Telescope (JCMT)) located on Mauna Kea. Hawaii.," In both cases, observations targeting Sgr A* were made at $1.3\,\mm$ using the Submillimeter Telescope ) on Mt. Graham in Arizona, $10\,\m$ dishes in the Combined Array for Research in Millimeter-wave Astronomy ) at Cedar Flat, California, and the James Clerk Maxwell Telescope ) located on Mauna Kea, Hawaii."241 9? report upon measurements obtained on the nights of the April. 11 12. 2007. using theJCMT.. and a single dish.," \citet{Doel_etal:08} report upon measurements obtained on the nights of the April, 11 12, 2007, using the, and a single dish."242 19 visibility amplitudes were obtained on the and baselines. with an upper limit on April 11th. 2007 along the baseline.," 19 visibility amplitudes were obtained on the and baselines, with an upper limit on April 11th, 2007 along the baseline."243 The locations of these observations on the u—v plane are indicated in the lower-left panel of Figure 1.. labeled 2007.," The locations of these observations on the $u$ $v$ plane are indicated in the lower-left panel of Figure \ref{fig:Vobs}, labeled 2007."244 Signal-to-noise ratios typical of the short and long baselines are 8 and 4. respectively.," Signal-to-noise ratios typical of the short and long baselines are 8 and 4, respectively."245 During this time. observations the single-dish flux was estimated via the full array. operating as a stand-alone instrument. to be 2.4—+0.25Jy.," During this time, observations the single-dish flux was estimated via the full array, operating as a stand-alone instrument, to be $2.4\pm0.25\,\Jy$."246 This is similar to the visibility obtained on the baselines andamplitudes consistent with a single. compact gaussian component (?)..," This is similar to the visibility amplitudes obtained on the baselines and consistent with a single, compact gaussian component \citep{Doel_etal:08}."247 This flux is anomalously low in comparison to the typical I.3mm flux of ~3Jy. and was taken as evidence for Ser A* appearing in a quiescent state.," This flux is anomalously low in comparison to the typical $1.3\,\mm$ flux of $\sim3\,\Jy$, and was taken as evidence for Sgr A* appearing in a quiescent state."248 This interpretation is supported by the lack of a significant difference between analyses of each day separately (?).., This interpretation is supported by the lack of a significant difference between analyses of each day separately \citep{Brod_etal:09}.249 Full details of the observations. calibration and. data processing can be found in ?..," Full details of the observations, calibration and data processing can be found in \citet{Doel_etal:08}."250 9? report upon more recent observations performed on the nights of April. 5-7. 2009. to the 95. 96. and 97 days of 2009.," \citet{Fish_etal:10} report upon more recent observations performed on the nights of April, 5–7, 2009, corresponding to the 95, 96, and 97 days of 2009."251 These made correspondinguse of theJCMT..SMT.. and two dishes. operated as independent VLBI stations.," These made use of the, and two dishes, operated as independent VLBI stations."252 54 visibility amplitudes were obtained on and baselines on all days. and to both of the baselines on days 96 and 97.," 54 visibility amplitudes were obtained on and baselines on all days, and to both of the baselines on days 96 and 97."253 Positions of the observations on each day are indicated in the upper panels of Figure 1.. labeled 2009.95. 2009.96. and 2009.97.," Positions of the observations on each day are indicated in the upper panels of Figure \ref{fig:Vobs}, labeled 2009.95, 2009.96, and 2009.97."254 Signal-to-noise ratios typical of the short and long baselines are 17 and 5. respectively.," Signal-to-noise ratios typical of the short and long baselines are 17 and 5, respectively."255 Thus. this second data set represents a significant improvement in both the number and precision of the data obtained.," Thus, this second data set represents a significant improvement in both the number and precision of the data obtained."256" In addition to the VLBI baselines. the presence of two independent dishes in the array allowed the measurement of very-short baseline visibilities. probing angular scales ~10""."," In addition to the VLBI baselines, the presence of two independent dishes in the array allowed the measurement of very-short baseline visibilities, probing angular scales $\sim10''$."257 These found substantially more correlated flux density than the baselines did. inconsistent with a single compact gaussian component.," These found substantially more correlated flux density than the baselines did, inconsistent with a single compact gaussian component."258— The interpretation of the difference in correlated flux density between the baselines and the baselines is presently —unclear. and it may be possible for geometric models annular rings. extended double multiplesource) to fit the data.," The interpretation of the difference in correlated flux density between the baselines and the baselines is presently unclear, and it may be possible for multiple geometric models (e.g., annular rings, extended double source) to fit the data."259 (e.g..Within the context of our analysis. we will assume that this difference is due to a separate large-scale component not present during the 2007 observations.," Within the context of our analysis, we will assume that this difference is due to a separate large-scale component not present during the 2007 observations."260 This is indirectly supported by the fact that the source sizes inferred from the mid and long baseline data are unchanged despite the variations in the visibility magnitudes, This is indirectly supported by the fact that the source sizes inferred from the mid and long baseline data are unchanged despite the variations in the visibility magnitudes261for Si).,for Si).262 As noted. those temperatures agree well with the (ranges of) temperatures ΟΕΕ Ες of these IT- and We-like ious (this is also true for O. see below).," As noted, those temperatures agree well with the (ranges of) temperatures of maximum emissivities of these H- and He-like ions (this is also true for O, see below)."263" The G value that we derive for indicates simular log(77) for the different elements: 6.95+0.25, 6,82-EO.2. and G.87250.5 for S. Si ancl Me. respectively."," The $\cal G$ value that we derive for indicates similar $\log(T)$ for the different elements: $\pm$ 0.25, $\pm$ 0.2 and $\pm$ 0.5 for S, Si and Mg, respectively."264 While the G ratios for Me and Si are sinular to those of OD stars (@vhatever heir nature} reported bv2008).. the G ratio derived. for S can only ο Compared to those of the magnetic objects 7 SSco aud 01 CC. as well as to those of giant and main-sequence stars (only supereiants having ueher ratios).," While the $\cal G$ ratios for Mg and Si are similar to those of OB stars (whatever their nature) reported by, the $\cal G$ ratio derived for S can only be compared to those of the magnetic objects $\tau$ Sco and $\theta^1$ C, as well as to those of giant and main-sequence stars (only supergiants having higher ratios)."265" If may be noted that the above eniperatfures corresponds to ~0.7keV. which agrees well with the ""cool temperature of the ""hot"" elobal model (see next section)."," It may be noted that the above temperatures corresponds to $\sim$ 0.7keV, which agrees well with the “cool” temperature of the “hot” global model (see next section)."266 At temperatures los(D) of 6.8.7.0. Ry (calculated using ATOMDD as above) is about 2 for S. 2.65 or Si aud 2.12 for Meg.," At temperatures $\log(T)$ of 6.8–7.0, ${\cal R}_0$ (calculated using ATOMDB as above) is about 2 for S, 2.65 for Si, and 2.42 for Mg."267" It is well known that R-i-mR,ΕΣ”:ο where we can neglect he density depeudence for massive stars."," It is well known that ${\cal R} = \frac{f}{i}= {\cal R}_0\, \frac{1}{1 + \phi / \phi_c + n_e / n_c}$, where we can neglect the density dependence for massive stars."268 The UV flux o depends on the stellar output but also he dilution factor., The UV flux $\phi$ depends on the stellar output but also the dilution factor.269" We derive the UW flix for uusing the model (C£;, 2IOkIS aud log(g)2L0) iu he grid of O-star atmosphere models calculated with CMEGEN which is closest to the parameters derived from a dedicated atinosphere fitting of 6||uazüs.", We derive the UV flux for using the model $T_{eff}$ =40kK and $\log(g)$ =4.0) in the grid of O-star atmosphere models calculated with CMFGEN which is closest to the parameters derived from a dedicated atmosphere fitting of .270 After averaging the flix iu⋅ the velocity interval ποσαthe rest waveleneths of the > transitions⋅⋅ (following. a simular⋅⋅ path as (2006).. see also Tables)). we thenà derivedWyre a adoati radiusm1: ©tq LOO.02 LR.2 frouy. the R ratios of Si. and formation«3.2 R« for Me (the ratio itself corresponding to R.):," After averaging the flux in the velocity interval nearthe rest wavelengths of the $\rightarrow$ transitions (following a similar path as , see also \ref{wav}) ), we then derived a formation radius of $\pm$ $R_*$ from the $\cal R$ ratios of Si, and $<$ $R_*$ for Mg (the ratio itself corresponding to $R_*$."271 The lines are too noisy to provide a meamnefil sulphurcoustraiut on the formation radius., The sulphur lines are too noisy to provide a meaningful constraint on the formation radius.272 Such rather close radii are similar to those ecuerally found for O-stars2009). inchiding 05 CC2005): therefore. it cannot be used to discriminate between various N-ray enudssion models.," Such rather close radii are similar to those generally found for O-stars, including $\theta^1$ C: therefore, it cannot be used to discriminate between various X-ray emission models."273" It may be worth ποιο, though. that our values fit well the temperature vs formation radius relation found by2008)."," It may be worth noting, though, that our values fit well the temperature vs formation radius relation found by."274. Following(2009).. we derive an abundance ratio Mle/Si. relative to the solar abundance of(1989).. of IZEO.11 using the U-like aud IHe-like resonance lines.," Following, we derive an abundance ratio Mg/Si, relative to the solar abundance of, of $\pm$ 0.11 using the H-like and He-like resonance lines."275 Χοποια abundances in CNO elements ave uot cutirely surprising since ddisplavs both a nitrogen overabundance aud an enriched surrouudiug uebulathereim)., Non-solar abundances in CNO elements are not entirely surprising since displays both a nitrogen overabundance and an enriched surrounding nebula.276. However. changes iu he Mg/Si ratio are not expected (see also nex section).," However, changes in the Mg/Si ratio are not expected (see also next section)."277 Finally. we may try to use the ratio of IT-to-IIe ines for oxvecu to check whether our Lypotlesis of a cooler plasiia dis seusible.," Finally, we may try to use the ratio of H-to-He lines for oxygen to check whether our hypothesis of a cooler plasma is sensible."278 The triplet is very roisv in the RCS data. but the flux in the r liue cau 6 coustrained to 2.L40.6\10 *ppleem 7 (observed) or 69⋅+E19«105 Ds (corrected. for absorption).," The triplet is very noisy in the RGS data, but the flux in the r line can be constrained to $\pm$ $\times10^{-5}$ $^{-2}$ $^{-1}$ (observed) or $69\pm19\times10^{-5}$ $^{-2}$ $^{-1}$ (corrected for absorption)."279 This corresponds to a IL-to-ITe ratio of 0.672:0.20. viclding a temperature of Ιου).~6.35.," This corresponds to a H-to-He ratio of $\pm$ 0.20, yielding a temperature of $\log(T)\sim6.35$."280 This is much lower than the eniperatures fouul above: it would be difficult /CN kFGepxoktugeo this measurement iu the contextof an isothermal asma. thereby confinnünug our wpothesis of a multicteniperature plasma.," This is much lower than the temperatures found above: it would be difficult to reproduce this measurement in the contextof an isothermal plasma, thereby confirming our hypothesis of a multi-temperature plasma."281 This result is certainly far from perfect because of its high uncertainty. but it constitutes a lint owards the non-uuiforuni teniperature of the X- cluitting regions.," This result is certainly far from perfect because of its high uncertainty, but it constitutes a hint towards the non-uniform temperature of the X-ray emitting regions."282 Clobal fits were simultaneously made onu the IIEC MEG and 0th order spectra. using. a binning. ensuring at least 20 counts per bin (see Sect.," Global fits were simultaneously made on the HEG, MEG and 0th order spectra, using a binning ensuring at least 20 counts per bin (see Sect."283 2)., 2).284 Results of the fits are preseuted iu. Table 9.., Results of the fits are presented in Table \ref{tabglobal}.285 Note again that the quoted leo errors are sometimes axvinetricali the value shown here always is the larecst value., Note again that the quoted $\sigma$ errors are sometimes asymetrical: the value shown here always is the largest value.286 We. used two sets of modelsthat both assume thermal plasimaiu collisional ionization equilibria (CTE)., We used two sets of modelsthat both assume thermal plasmain collisional ionization equlibrium (CIE).287 First. we used models with discrete temperature cononents or ap," First, we used models with discrete temperature components or in"288 First. we used models with discrete temperature cononents or ape," First, we used models with discrete temperature components or in"289 First. we used models with discrete temperature cononents or apec," First, we used models with discrete temperature components or in"290 First. we used models with discrete temperature cononents or apec ," First, we used models with discrete temperature components or in"291 First. we used models with discrete temperature cononents or apec M," First, we used models with discrete temperature components or in"292"We have investigated the variability. of Sevtert 1 and 2 galaxies on short aud long timescales and ‘ound iudicatious for variability in three Sevtert 2.0 ealaxies on short timescales (NCC 1068. IRAS 0117-0710. NGC ὠδδ),","We have investigated the variability of Seyfert 1 and 2 galaxies on short and long timescales and found indications for variability in three Seyfert 2.0 galaxies on short timescales (NGC 1068, IRAS 0147-0740, NGC 4388)."293 À possible explanation for this variability uieht be the presence of boreholes iu the absorbing nolecular torus around the central black hole region., A possible explanation for this variability might be the presence of boreholes in the absorbing molecular torus around the central black hole region.294 Significant N-rav variability during the pointed and survey observations were detected for 58 percent of he Sevfert 1 ealaxics., Significant X-ray variability during the pointed and survey observations were detected for 58 percent of the Seyfert 1 galaxies.295lower than the true ones.,lower than the true ones.296 This accounts for the than-expected normalisation of the WL-derived mass-concentration relation evident in Fig. 2.., This accounts for the lower-than-expected normalisation of the WL-derived mass-concentration relation evident in Fig. \ref{mcplot}.297 We aim to provide an explanation for these biases in Section 5 below., We aim to provide an explanation for these biases in Section \ref{sec:errorsources} below.298" Note that we have chosen to use medians, rather than means to quantify bias."," Note that we have chosen to use medians, rather than means to quantify bias."299" The rationale behind this is that, in a non-Gaussian distribution as is the case here (log-normal), the mean, unlike the median, depends on the scatter as overpredictions can be arbitrarily high, whereas values can clearly not be underpredicted by more than100%."," The rationale behind this is that, in a non-Gaussian distribution as is the case here (log-normal), the mean, unlike the median, depends on the scatter as overpredictions can be arbitrarily high, whereas values can clearly not be underpredicted by more than."300. From the amount of scatter evident in our results (see Figs., From the amount of scatter evident in our results (see Figs.301" 3 and 5)) one should not be surprised to find that the mean mass and concentration show, in general, a positive bias with respect to their median counterparts."," \ref{histogram} and \ref{fig:scatter}) ) one should not be surprised to find that the mean mass and concentration show, in general, a positive bias with respect to their median counterparts."302" For completeness, we show the difference between mean and median bias in Fig."," For completeness, we show the difference between mean and median bias in Fig."303 C1 in appendix C.., \ref{fig:mean} in appendix \ref{sec:mean}.304 The bias and scatter in cluster masses derived from weak, The bias and scatter in cluster masses derived from weak305(0.2-0.5 )) in the ONC and evolve these stars forward using theoretical stellar evolution models auc different angular mormentuui loss rates.,(0.2–0.5 ) in the ONC and evolve these stars forward using theoretical stellar evolution models and different angular momentum loss rates.306 In. 822 we present the theoretical framework of these uodels aud how they were applied to to the observatioual data., In 2 we present the theoretical framework of these models and how they were applied to to the observational data.307 Iu 833 we will apply these moclels o data from both the Pleiades and the ONC., In 3 we will apply these models to data from both the Pleiades and the ONC.308 These calculations will coustrain the two parameters of the angular momentum loss mechanisms. the saturation threshold and the disk-lockiug lifetime. eadiug to a single preferred. model.," These calculations will constrain the two parameters of the angular momentum loss mechanisms, the saturation threshold and the disk-locking lifetime, leading to a single preferred model."309 Iufrared excess data for stars in the ONC is also used as au additional initial condition to test this model., Infrared excess data for stars in the ONC is also used as an additional initial condition to test this model.310 In 811 we discuss the implications of these results. inclucling the uniqueness of our model aud how it cau be applied to further observational data iu he pre-MS.," In 4 we discuss the implications of these results, including the uniqueness of our model and how it can be applied to further observational data in the pre-MS."311 To construct inodels of low-mass stars. we used the Yale Rotating Evolution Code (YREC. Guenther et al.," To construct models of low-mass stars, we used the Yale Rotating Evolution Code (YREC, Guenther et al."312 1992)., 1992).313 YREC is a Heuyey code which solves tle equations of stellar structure in one dimeusioun., YREC is a Henyey code which solves the equations of stellar structure in one dimension.314 YREC uses the nuclear reaction rates of Gruzinov Balicall (1998) aud the equation ol state from Saumon. Chabrier van Horn (1995).," YREC uses the nuclear reaction rates of Gruzinov Bahcall (1998) and the equation of state from Saumon, Chabrier van Horn (1995)."315 Our models have a metallicity of Z = 0.0176 aud a mixing length of a = L.815. calibrated such that a 1.0 inodel will reproduce the solar radius aud luminosity at the solar age.," Our models have a metallicity of $Z$ = 0.0176 and a mixing length of $\alpha$ = 1.845, calibrated such that a 1.0 model will reproduce the solar radius and luminosity at the solar age."316 The input physics for these models is discussed iu Sills. Pinsonueault. 'Terudrup (2000).," The input physics for these models is discussed in Sills, Pinsonneault, Terndrup (2000)."317 Although the theoreticalmodels for magnetic star-disk interaction discussed in 31 are sophisticated aud complex in their formulation. the treatment of disk-lockiug for our angular momentum moclels is quite simple. since the disk aud star corotate at a fixed angular velocity.," Although the theoretical models for magnetic star-disk interaction discussed in 1 are sophisticated and complex in their formulation, the treatment of disk-locking for our angular momentum models is quite simple, since the disk and star corotate at a fixed angular velocity."318 When the star is its period is held coustant over the lifetime of the clisk. 77:4. aud the angular momentuui Change is then a function of stars moment of inertia.," When the star is disk-locked, its period is held constant over the lifetime of the disk, $\tau_{disk}$, and the angular momentum change is then a function of star's moment of inertia."319 When the age of the stellar model reaches τικ. (he star ds released. [rou disk-Iockiug aud evolves uuder equatious (1) aud (2) below.," When the age of the stellar model reaches $\tau_{disk}$, the star is released from disk-locking and evolves under equations (1) and (2) below."320 The disk lifetime. 75:44. is relative to the birthliue (0 Myr) aid not to the observed age of the star. τε.," The disk lifetime, $\tau_{disk}$, is relative to the birthline (0 Myr) and not to the observed age of the star, $\tau_\star$."321 We use the birthline of Palla Staller (1991). which is the cdeuterium-burniug main sequence and corresponds to the upper envelope of T Tauri stars in the H-R diagram.," We use the birthline of Palla Staller (1991), which is the deuterium-burning main sequence and corresponds to the upper envelope of T Tauri stars in the H-R diagram."322 The time evolution of the stellar mome of inertia was takeu from the YREC stellar inodels. in which solic-bocdy rotation was enforced.," The time evolution of the stellar moment of inertia was taken from the YREC stellar models, in which solid-body rotation was enforced."323 Stellar mocels of this mass rauge that included iuterual angular momentuu trausport were nearly kleutical to solid body models (Sills. Pinsouneault. Terndrup 2000).," Stellar models of this mass range that included internal angular momentum transport were nearly identical to solid body models (Sills, Pinsonneault, Terndrup 2000)."324 Rotating stars that lose mass through maguetized stellar winds will also lose angular mouentum., Rotating stars that lose mass through magnetized stellar winds will also lose angular momentum.325 To quantify this loss rate. we used a prescription for angular momentui loss adopted from Ixawaler (1988) and MacGregor Brennan (1991). aud described in Wrishuamurthi et al. (," To quantify this loss rate, we used a prescription for angular momentum loss adopted from Kawaler (1988) and MacGregor Brennan (1991), and described in Krishnamurthi et al. ("3261997).,1997).327 We write, We write328"from equation (A4)) and taking only terms linear in à, and (2.",from equation \ref{eqn:quad}) ) and taking only terms linear in $\delta z_c$ and $\hat Q$.329 Here. we note that OQ~©(d2) so that the second term in the bracket is lower order than (27.," Here, we note that $\hat Q\sim\mathcal{O}(d_c^2)$ so that the second term in the bracket is lower order than $\hat Q^2$."330" In order to find the magnification for this image. we differentiate equation (A4)). and find. substituting : =:y|ὅτε, for which 8: is given by equation (A5)). into equation (A6)). we obtain. alt Note that the total magnification for the given source position is usually dominated by one or two images found close to the critical curve."," In order to find the magnification for this image, we differentiate equation \ref{eqn:quad}) ), and find, Then substituting $z=z_0+\delta z_c$ , for which $\delta z_c$ is given by equation \ref{eqn:delc}) ), into equation \ref{eqn:part}) ), we obtain, Note that the total magnification for the given source position is usually dominated by one or two images found close to the critical curve."331 Thus. we consider only the case for which the non-perturbed PSPL images lie close to the unit circle. so we have leu]=1|A and A<1.," Thus, we consider only the case for which the non-perturbed PSPL images lie close to the unit circle, so we have $|z_0|=1+\Delta$ and $\Delta\ll 1$."332" Then. we find the expression for the inverse magnification for the QL approximation (up to the order of d? ). extreme wide-binary case. one can rewrite the lens equation (À 1)) as1 ""m position and the mass of the first lens component are the origin and the unit mass so that £4 =O. +2= dy.ey= 1. €)=qu. and dq=(L|qu):/74,.."," Then, we find the expression for the inverse magnification for the QL approximation (up to the order of $d_c^3$ ), For the extreme wide-binary case, one can rewrite the lens equation \ref{eqn:lenseq}) ) as Here the position and the mass of the first lens component are the origin and the unit mass so that $z_1=0$, $z_2=-d_1$, $\epsilon_1=1$, $\epsilon_2=q_w$, and $d_1=(1+q_w)^{1/2}d_w$."333 We note that. apart from the constant translation. the first non-PSPL term here is essentially the shear. >=qud472quedA⋅↽|du)! for the CRL4 approximation.," We note that, apart from the constant translation, the first non-PSPL term here is essentially the shear, $\gamma=q_w d_1^{-2}=q_w d_w^{-2}(1+q_w)^{-1}$ for the CRL approximation."334". Analogous to the extreme close binary.. ifp ~<J1. the image position for the CRL approximation can be found by the perturbative approach. but here the corresponding PSPL source position would be&|qud,=τυly! "," Analogous to the extreme close binary, if $\gamma\ll 1$, the image position for the CRL approximation can be found by the perturbative approach, but here the corresponding PSPL source position would be $\zeta+q_w d_w^{-1}=z_0-\bar z_0^{-1}$."335"Then. the image deviation ὅτι—2.:9 of CRL from PSPL is Using this result and the derivative of equation (A 10)). we find From the same argument used for the QL approximation of the extreme close binary. wecan set |:y|=1|A. and then the inverse magnification for the CRL approximation (up to the order of d.) is By comparing equations (A8)) and (A14)). we therefore establish the magnification correspondence (up to the order of d dz) between the close binary with Q=d24,(1|q.)? and the wide binarywith >=πμle)| when Q~-& 1."," Then, the image deviation $\delta z_w=z-z_0$ of CRL from PSPL is Using this result and the derivative of equation \ref{eqn:crl}) ), we find From the same argument used for the QL approximation of the extreme close binary, wecan set $|z_0|=1+\Delta$, and then the inverse magnification for the CRL approximation (up to the order of $d_w^{-3}$ ) is By comparing equations \ref{eqn:magc}) ) and \ref{eqn:magw}) ), we therefore establish the magnification correspondence (up to the order of $d_c^2\sim d_w^{-2}$ ) between the close binary with $\hat Q=d_c^2 q_c (1+q_c)^{-2}$ and the wide binarywith $\gamma=d_w^{-2} q_w (1+q_w)^{-1}$ when $\hat Q\simeq\gamma\ll 1$ ."336and absence of € IIT absorption therefore sugeecsts a ~BO51I classification with au uncertainty of roughly half a spectral subtype aud lack of strong constraints ou the luminosity class.,and absence of C III absorption therefore suggests a $\sim$ B0.5–1I classification with an uncertainty of roughly half a spectral subtype and lack of strong constraints on the luminosity class.337 However. we caution that if C TIT is weak due to abundance anomalies or uear-critical rotation then this limit may not apply. and the weakness of the Ue I lines permit a classification of O9.5DOI that is broadly consistent with the Pascheu-series line streustlis.," However, we caution that if C III is weak due to abundance anomalies or near-critical rotation then this limit may not apply, and the weakness of the He I lines permit a classification of O9.5–B0I that is broadly consistent with the Paschen-series line strengths."338 Figue 3 shows RV curves for the two conmpoucuts of the system., Figure \ref{fig:rv} shows RV curves for the two components of the system.339 Taking the 9.20-dav period reported by Donanos(2007)— as a starting point. an crror-weighted. 472 fitgp to the radia. velocitics of the absorptiou-lne componcut vieldecd bes-fit values for the orbital period of days. cousistent wih an iude)ondenut deteriuuation using a Lomb-Scarele periodogran (Press&Reybicki1989).. a xvstende velocity of and πο]auplitude |.," Taking the 9.20-day period reported by \cite{bonanos} as a starting point, an error-weighted $\chi^2$ fit to the radial velocities of the absorption-line component yielded best-fit values for the orbital period of days, consistent with an independent determination using a Lomb-Scargle periodogram \citep{press}, a systemic velocity of and semi-amplitude ."340 The corresponding fit to the cussion line RV has a systemic velocity ando semuieuuplitude, The corresponding fit to the emission line RV has a systemic velocity of and semi-amplitude.341 Exrors are derived οι he fitting residuals using the bootstrap method (Efron&Tibshirawi1991)., Errors are derived from the fitting residuals using the bootstrap method \citep{efron}.342. We note tlat systemic velocity ¢erved from the emission line fit js somewhat ower than that derived from the companion. and is in closer aerecment with the mean radial velocities of other W«] supereiautsOo (see Paper D.," We note that systemic velocity derived from the emission line fit is somewhat lower than that derived from the companion, and is in closer agreement with the mean radial velocities of other Wd1 supergiants (see Paper I)."343 Discrepaucies iu lis parameter are commonly observed in early-typespectroscopic binaries (e.g. the 98-day ΟΠ(Ώ|Os.51 iuarv1191014: Ramctal. 2001)) although the effect is simall iun comparison with some οher evolved Svstenas (cec.228766: Massey&€'onti1977:Dauwetal. 20023) in which wind contaminaion stronely affects derived systemic velocities.," Discrepancies in this parameter are commonly observed in early-typespectroscopic binaries (e.g. the 9.8-day O7III(f)+O8.5I binary; \citealt{rauw01}) ) although the effect is small in comparison with some other evolved systems (e.g.; \citealt{massey,rauw02}) ) in which wind contamination strongly affects derived systemic velocities."344 Taking these values vields a nass ratio aud masses or the two colmponents of: and Finally. micasuremeuts of blended lvdrogen lires with Gaussian fits tend to vield svstematically lower values of A4 and A» than methods such as spectral «liseutauelimg (Sinon&Sturm1991) that are less affected by lending (Andersen1975:ποιον&Clausen2007).," Taking these values yields a mass ratio and masses for the two components of: and Finally, measurements of blended hydrogen lines with Gaussian fits tend to yield systematically lower values of $K_1$ and $K_2$ than methods such as spectral disentangling \citep{simon} that are less affected by blending \citep{andersen,southworth}."345. The paucity of stroug lines free from siguificaut interstellar. tellure and wind contamination iu fjo ᾖ- alc I-baud spectra of ~BO supergiauts makes the extent oftjs effect on our determination of A4 aud Wap. hard to quautity. and we therefore note that our method nav uncderestinate the masses of the two components ofW13.," The paucity of strong lines free from significant interstellar, telluric and wind contamination in the $R$ - and $I$ -band spectra of $\sim$ B0 supergiants makes the extent of this effect on our determination of $K_\text{em}$ and $K_\text{abs}$ hard to quantify, and we therefore note that our method may underestimate the masses of the two components of."346". To coustrai Εκ, we folded the R-baud photonetric data reported by Boanos(2007) on to the 9.27l dav period determined frou the RV data."," To constrain $\text{sin}^3i$, we folded the $R$ -band photometric data reported by \cite{bonanos} on to the 9.271 day period determined from the RV data."347 The data were binned ο reduce he considerable scatter prescut in the light curve. which is most probably a consequence of iutriusic aperiodic variaΗΠΑ iu one or both compoιομι low-evel photometric aud spectroscopic variabilit vis a feature of all tranusitiojii supereiauts in Well. witi the blue ivpergiants disλανι rapid phnotoimetrie variability. at he ~0.1 maguitude level and the earhk-B supereiauts also variable (Bonanos2007:Clarkctal. 2010a).," The data were binned to reduce the considerable scatter present in the light curve, which is most probably a consequence of intrinsic aperiodic variability in one or both components: low-level photometric and spectroscopic variability is a feature of all transitional supergiants in Wd1, with the blue hypergiants displaying rapid photometric variability at the $\sim$ 0.1 magnitude level and the early-B supergiants also variable \citep{bonanos, clark10}. ."348. Therefore. eivoen the linited dataset and shallow ~0.15r machiΡοude," Therefore, given the limited dataset and shallow $\sim$ 0.15 magnitude"349For marginalisation we instead use a method that is based on subtracting the magnitude of an arbitrarily chosen low-redshift (so its magnitude depends only on the IIubble constant) andanchor SN from the magnitudes of SNe in a data set then mareinalisine over magnitude of anchor SN.,For marginalisation we instead use a method that is based on subtracting the magnitude of an arbitrarily chosen low-redshift (so its magnitude depends only on the Hubble constant) anchor SN from the magnitudes of SNe in a data set and then marginalising over magnitude of anchor SN.350 The resulting likelihood. function is derived in the Appendix., The resulting likelihood function is derived in the Appendix.351 Εις is equivalent to marginalising over the nuisance parameter {fy with a Gaussian prior centered around its value derived from the anchor SN. alongwith the corresponding standard deviation.," This is equivalent to marginalising over the nuisance parameter $H_0$ with a Gaussian prior centered around its value derived from the anchor SN, alongwith the corresponding standard deviation."352 The method can be easily eeneralized. to à case where the priors on Lfy are specified separately as described in the Appenclix., The method can be easily generalized to a case where the priors on $H_0$ are specified separately as described in the Appendix.353 We now compare the analytically marginalised. likelihood function in Eq X5 to the results of Bavesian marginalisation over fy., We now compare the analytically marginalised likelihood function in Eq \ref{eq:marglik} to the results of Bayesian marginalisation over $H_0$.354 For this purpose we consider parameter estimation for GDOA., For this purpose we consider parameter estimation for GD04.355 We assume a Hat ACDAL universe for this exercise., We assume a flat $\Lambda$ CDM universe for this exercise.356 The dimensionless Hubble parameter is given by and [latness implies O4=1Qi., The dimensionless Hubble parameter is given by and flatness implies $\Ol = 1 - \Om$.357 Thus. the only free parameters are Z/ü and Oxy.," Thus, the only free parameters are $H_0$ and $\Om$."358 The normalized likelihood function is given by llere à;=quofhbeeav(oziHo.O31). where the subscript Pompe.V and “ij=jc? is the covariance matrix.," The normalized likelihood function is given by Here $x_i = \mu_i - \mu_{\rm theory} (z_i; H_0,\Om)$, where the subscript $i=1,\ldots,N$ and $\Sigma_{ij} = \delta_{ij}\,\sigma_i^2$ is the covariance matrix."359 The superscript T denotes the matrix operation of taking the transpose of a matrix., The superscript 'T' denotes the matrix operation of taking the transpose of a matrix.360" The posterior probability for parameters Ox; ancl Lfy is given by We choose a uniform prior for Oy; in the range 0x Llane for ff,=1005kms!Mpe in the range 04x:1."," The posterior probability for parameters $\Om$ and $H_0$ is given by We choose a uniform prior for $\Om$ in the range $0 \le \Om \le 1$ and for $H_0 = 100h\,\rm km \,s^{-1}\,Mpc^{-1}$ in the range $0.4 \le h \le 1$."361 The mareinalised probability clistribution for the matter density is given by The probability density is normalized after carrving out the integration., The marginalised probability distribution for the matter density is given by The probability density is normalized after carrying out the integration.362 A similar probability density function for the matter density can be obtained by the Bayesian inversion of the marginalised likelihood. function. given in I., A similar probability density function for the matter density can be obtained by the Bayesian inversion of the marginalised likelihood function given in Eq.363 AD., A5.364 ligure 1. plots a comparison between the two probability densities ancl shows that the two clistributions are nearly identical., Figure \ref{fig:comparison} plots a comparison between the two probability densities and shows that the two distributions are nearly identical.365 For completeness some details are repeated. here. from GSLOS., For completeness some details are repeated here from GSL08.366 For our analysis we have considered a [at .ACDM universe. which can be easily generalized to à more general model of dark energy.," For our analysis we have considered a flat $\Lambda$ CDM universe, which can be easily generalized to a more general model of dark energy."367redwards and to higher luminosities away [rom the zero-age main sequence (ZAAIS). due to the increasing helium content of their cores.,"redwards and to higher luminosities away from the zero-age main sequence (ZAMS), due to the increasing helium content of their cores."368 This movement continues until the point of core hydrogen exhaustion. when the star has reached the reached the terminal age MS CEXMS or MIS turn-oll).," This movement continues until the point of core hydrogen exhaustion, when the star has reached the reached the terminal age MS (TAMS or MS turn-off)."369 Finally. after the turn-olf. the post-main-sequence evolution is driven by the burning of heavier elements which leads to much more rapid movement in the CMD.," Finally, after the turn-off, the post-main-sequence evolution is driven by the burning of heavier elements which leads to much more rapid movement in the CMD."370 Vhis relatively high velocity in the CMD means that post-main-sequence evolution has the potential to give. precise ages., This relatively high velocity in the CMD means that post-main-sequence evolution has the potential to give precise ages.371 Llowever. for voung galactic clusters the paucity of stars in this region of the CAID means such an age can depend on just one star. and such ages are rightly treated with some scepticism.," However, for young galactic clusters the paucity of stars in this region of the CMD means such an age can depend on just one star, and such ages are rightly treated with some scepticism."372 Conversely. the main-sequence evolution (from the ZAMS to the turn-oll) has a larger number of stars. but the movement is often subtle. ancl using the normal technique of simv plotting isochrones over the data leads to large uncertainties in age. and to questions over objectivity.," Conversely, the main-sequence evolution (from the ZAMS to the turn-off) has a larger number of stars, but the movement is often subtle, and using the normal technique of simply plotting isochrones over the data leads to large uncertainties in age, and to questions over objectivity."373 However. we have been developing a method of making objective fits to colour-magnituce data. which should allow us to unlock the information in this stage ofa star's evolution.," However, we have been developing a method of making objective fits to colour-magnitude data, which should allow us to unlock the information in this stage of a star's evolution."374 The technique. called 77 fitting. can be viewed as an extension of X7 to data points with uncertainties in two or more observables. and to models which are distributions (not just lines) in the data space.," The technique, called $\tau^2$ fitting, can be viewed as an extension of $\chi^2$ to data points with uncertainties in two or more observables, and to models which are distributions (not just lines) in the data space."375 The ain of this paper is to apply the 7? fitting technique o the main-sequence evolution of voung stars. and use he resulting ages to create à revised age scale for. PAIS stars.," The aim of this paper is to apply the $\tau^2$ fitting technique to the main-sequence evolution of young stars, and use the resulting ages to create a revised age scale for PMS stars."376 Surprisingly. this leads to a significantly older ages han the commonly. used. contraction ages. a result. which we will discuss in Section 11..," Surprisingly, this leads to a significantly older ages than the commonly used contraction ages, a result which we will discuss in Section \ref{discuss}."377 To derive this result. we irst have to update our statistical techniques. originally. described. in ?.. since. as we discuss in Section 4. the echnique will not. work for the isochrones we wish to it.," To derive this result we first have to update our statistical techniques originally described in \cite{2006MNRAS.373.1251N}, , since, as we discuss in Section \ref{stats}, the technique will not work for the isochrones we wish to fit."378 We therefore lav out the changes which need to be made by following an example through fitting (Section 5)). esting the goodness of fit (Section 6)) and determining the uncertainties in the derived. parameters (Section 7)).," We therefore lay out the changes which need to be made by following an example through fitting (Section \ref{fit}) ), testing the goodness of fit (Section \ref{goodness}) ) and determining the uncertainties in the derived parameters (Section \ref{uncer}) )."379 Before doing so. however. we discuss the data ane models we use (Sections 2. ancl Sections 3)).," Before doing so, however, we discuss the data and models we use (Sections \ref{data} and Sections \ref{models}) )."380 We deal with the ellects of interstellar extinction in Section S.. and the details of each cluster in Section 9..," We deal with the effects of interstellar extinction in Section \ref{extin}, and the details of each cluster in Section \ref{individual}."381 We draw all the results together in our discussion in Section 11.., We draw all the results together in our discussion in Section \ref{discuss}.382 To compare a set of ages derived. from MS. evolution with contraction ages we need a sample of clusters aud associations which have contraction ages. ancl for cach of which data are available for AIS fitting.," To compare a set of ages derived from MS evolution with contraction ages we need a sample of clusters and associations which have contraction ages, and for each of which data are available for MS fitting."383 Our sample. is. therefore. based on the groups we placed. in age order using the PATS in ?..," Our sample is, therefore, based on the groups we placed in age order using the PMS in \cite{2008MNRAS.386..261M}."384 Clearly. for cach of these groups we require stars in the appropriate mass range to show significant ALS evolution. but we also require. extinetions and reliable distance measurements.," Clearly, for each of these groups we require stars in the appropriate mass range to show significant MS evolution, but we also require extinctions and reliable distance measurements."385 CY. photometry can provide all three of these., $UBV$ photometry can provide all three of these.386 First the €D/ D.V. diagram provides extinctions., First the $U-B$ $B-V$ diagram provides extinctions.387 Second. the upper part of VsV. diagram is age sensitive. tracing the evolution of stars from the ZAMS to the turn-oll.," Second, the upper part of $V$ $B-V$ diagram is age sensitive, tracing the evolution of stars from the ZAMS to the turn-off."388. Finally. in the age range of interest the lower mass stars are still close to the ZAAIS. and the sequence turns redwards. making it ideal as a distance measure.," Finally, in the age range of interest the lower mass stars are still close to the ZAMS, and the sequence turns redwards, making it ideal as a distance measure."389 Furthermore. the CBV. photo-electric system is very consistent and. well characterised.," Furthermore, the $UBV$ photo-electric system is very consistent and well characterised."390 However. to ensure we maintain the highest level of consistency we have restricted. ourselves as far as possible to the data of Johnson and collaborators. primarily taken in the 1950s and 1960s.," However, to ensure we maintain the highest level of consistency we have restricted ourselves as far as possible to the data of Johnson and collaborators, primarily taken in the 1950s and 1960s."391 As we shall show later. the quality of these data when combined with the transformations of 7. is impressive. eiving 77 values which mean the model is a good fit to the data.," As we shall show later, the quality of these data when combined with the transformations of \cite{1998A&A...333..231B} is impressive, giving $\tau^2$ values which mean the model is a good fit to the data."392 Clearly we wish to avoid PAIS stars contaminating our sample at faint maenituces and red colours. and so for most objects we apply a cut in observed 2BV which roughly corresponds to (23τους0.0.," Clearly we wish to avoid PMS stars contaminating our sample at faint magnitudes and red colours, and so for most objects we apply a cut in observed $B-V$ which roughly corresponds to $(B-V)_0 < 0.0$."393 Alost of the datasets we use have robust. uncertainties derived from. comparisons of many measurements of stars., Most of the datasets we use have robust uncertainties derived from comparisons of many measurements of stars.394 ‘This presents us with a problem. as the quoted uncertainties in colour are always smaller than those in maenitucle.," This presents us with a problem, as the quoted uncertainties in colour are always smaller than those in magnitude."395 Conventional error analysis vieles a correlation between. sav. V and £2V. and in previous work we have always xen careful to include that correlation when modeling the uncertainties.," Conventional error analysis yields a correlation between, say, $V$ and $B-V$, and in previous work we have always been careful to include that correlation when modeling the uncertainties."396 The starting point for such an analvsis is hat V and. D are measured. independently. ancl so. the uncertainties in | and D.V are 81 and dl?|8/7 respectively.," The starting point for such an analysis is that $V$ and $B$ are measured independently, and so the uncertainties in $V$ and $B-V$ are $\delta V$ and $\sqrt{\delta V^2+\delta B^2}$ respectively."397 Such an analysis also leads to the conclusion hat the uncertainty in D.V must be larger than that in V. in direct. contradiction to the quoted uncertainties for most of the data presented here.," Such an analysis also leads to the conclusion that the uncertainty in $B-V$ must be larger than that in $V$, in direct contradiction to the quoted uncertainties for most of the data presented here."398 “Phis is because it is not shoton statistics which are the driver of the uncertainties. rut changes in the transpareney.," This is because it is not photon statistics which are the driver of the uncertainties, but changes in the transparency."399 In this work. we therefore model the uncertainties as uncorrelatect.," In this work, we therefore model the uncertainties as uncorrelated."400 Although we will tery other models later. we begin by using “CGeneva-Bessell” isochrones.," Although we will try other models later, we begin by using “Geneva-Bessell” isochrones."401" For the stellar interior we follow the suggestion of 2.. and use the ""basic mocel set” (Le. set πο} of the Geneva. isochrones (?).."," For the stellar interior we follow the suggestion of \cite{2001A&A...366..538L}, and use the “basic model set” (i.e. set “c”) of the Geneva isochrones \citep{1992A&AS...96..269S}."402 Temporal interpolation is a much more significant issue for post-MS isochrones than the PALS isochrones we have fitted in the past. as there are sharp cliscontinuities in the rate of change of magnitude and colour with time. as exemplified by the MS turn-olf.," Temporal interpolation is a much more significant issue for post-MS isochrones than the PMS isochrones we have fitted in the past, as there are sharp discontinuities in the rate of change of magnitude and colour with time, as exemplified by the MS turn-off."403. We therefore use the code provided on the website to interpolate the isochrones to the appropriate age., We therefore use the code provided on the website to interpolate the isochrones to the appropriate age.404 We then convert from Iuminosity and cllective temperature to colours and magnitudes using the tables of ?.. assuming the colours of Vega are zero (though V= 0.03).," We then convert from luminosity and effective temperature to colours and magnitudes using the tables of \cite{1998A&A...333..231B}, assuming the colours of Vega are zero (though $V=0.03$ )."405 We also use Bessell et al's colour dependent extinction vectors., We also use Bessell et al's colour dependent extinction vectors.406 For some of the most luminous stars the gravities are rather low. and fall just outside the range of gravities given by 7..," For some of the most luminous stars the gravities are rather low, and fall just outside the range of gravities given by \cite{1998A&A...333..231B}."407 In these cases we extrapolate the models by. simply setting the colour to that for the lowest available gravity., In these cases we extrapolate the models by simply setting the colour to that for the lowest available gravity.408 In these cases a linear extrapolation would be cilferent by less than 0.001 mags. implving that the overall error due to the extrapolation is much smaller than the uncertainties in colour.," In these cases a linear extrapolation would be different by less than 0.001 mags, implying that the overall error due to the extrapolation is much smaller than the uncertainties in colour."409 For reasons explained in Section 9.2 we used the Tveho-2 photometry for σ Ori., For reasons explained in Section \ref{sori} we used the Tycho-2 photometry for $\sigma$ Ori.410 In this case we have used the conversion givenin 7. to convert the Geneva-Dessell isochrones into the Tvcho svstem.," In this case we have used the conversion givenin \cite{2000PASP..112..961B}411 to convert the Geneva-Bessell isochrones into the Tycho system."412 (2.statethattheTvcho- We used the reddening vector derived in ?..," \citep[][state that the Tycho-1 and Tycho-2 systems should be identical.]413{2000A&A...357..367H}414 We used the reddening vector derived in \cite{2008MNRAS.386..261M}. ."4152,.416006).. has a relatively low abundance in (Glasseold1996).. and is presumably below the current detection limit even if it might be present in6.," $^+$ has a relatively low abundance in \citep{glassgold96}, and is presumably below the current detection limit even if it might be present in."417. We observed abundant carbon chains and radicals in6.. including CO. SiCs. CN. HON. CS. Coll. Can. Cyl. HICSN. and CII4CN. all of which are linear.," We observed abundant carbon chains and radicals in, including CO, $_2$, CN, HCN, CS, $_2$ H, $_3$ N, $_4$ H, $_3$ N, and $_3$ CN, all of which are linear."418 This characteristic feature is similar to those of ancl (seeCernicharoetal.2000). although (hese lines are much fainter in6.," This characteristic feature is similar to those of and \citep[see][]{cernicharo00}419 although these lines are much fainter in."420. The most intriguing characteristic of is (he strong CN emission., The most intriguing characteristic of is the strong CN emission.421 The integrated intensity ratio of the CN (2.1) eroup aud the CO (21) transition is 4.6. a factor of 2.2 larger than the value in 2008)..," The integrated intensity ratio of the CN (2–1) group and the $^{13}$ CO (2–1) transition is 4.6, a factor of 2.2 larger than the value in \citep{he08}. ."422 CN is mainly formed (τος the photocissociation of IICN. According to Heetal.(2008).. the IIPCN 2)/PCO ὢ1) integrated intensity ratio in is 4.5. a [actor of 3.2 larger than that in6.," CN is mainly formed through the photodissociation of HCN, According to \citet{he08}, the $^{13}$ CN $^{13}$ CO (2–1) integrated intensity ratio in is 4.5, a factor of 3.2 larger than that in."423.. Therefore. our observations provide strong evidence (hat reaction (3)) dominates the chemistry of CN and ICN in AGB stars and the photodissociation is more efficient in the more evolved C-rich envelopeG.," Therefore, our observations provide strong evidence that reaction \ref{hcn}) ) dominates the chemistry of CN and HCN in AGB stars and the photodissociation is more efficient in the more evolved C-rich envelope."424. The above discussion also suggests that about 30% CN formed from IICN has been destroved., The above discussion also suggests that about $\%$ CN formed from HCN has been destroyed.425 On the other hand. CN can be reprocessed into ΕΠ through the reaction We do find that the ILC4N line intensities relative to the @CO (21) transition in ave a factor of ~3 larger than those inIRC+10216.. indicating efficient formation of 1IC4N in6.," On the other hand, CN can be reprocessed into $_3$ N through the reaction We do find that the $_3$ N line intensities relative to the $^{13}$ CO (2–1) transition in are a factor of $\sim3$ larger than those in, indicating efficient formation of $_3$ N in."426. We did not find evidence for the enhancement of (he C4N radical. suggesting that photoclissociation of 11CN into C4N is insignificant in this object.," We did not find evidence for the enhancement of the $_3$ N radical, suggesting that photodissociation of $_3$ N into $_3$ N is insignificant in this object."427 shows strong Cll emission., shows strong $_2$ H emission.428 The CSI radical is dominantly produced through the photodissociation reaction Our observations show that the Coll line intensities relative to the CO (1)transition in, The $_2$ H radical is dominantly produced through the photodissociation reaction Our observations show that the $_2$ H line intensities relative to the $^{13}$ CO (2–1)transition in429that in the B band light curve the Dux varies from under 9 mJy to over 24 mJy. so the majority of the tux measured must be nuclear (assuming that the star light is constant).,"that in the B band light curve the flux varies from under 9 mJy to over 24 mJy, so the majority of the flux measured must be nuclear (assuming that the star light is constant)."430 In the V band the maximum to minimum variation is slightlv smaller but still more than a factor of 2., In the V band the maximum to minimum variation is slightly smaller but still more than a factor of 2.431 This dillerence in variability amplitude can be caused by stronger star light contamination in the V band but it is also possible that the AGN V emission is intrinsically less variable., This difference in variability amplitude can be caused by stronger star light contamination in the V band but it is also possible that the AGN V emission is intrinsically less variable.432 The power density spectrum (PDS) can be used. to quantify the variability amplitude as a function of the time-scale of the variations. or correspondingly. of their Fourier requency.," The power density spectrum (PDS) can be used to quantify the variability amplitude as a function of the time-scale of the variations, or correspondingly, of their Fourier frequency."433 The PDS is constructed. through the modulus squared. of the discrete. Fourier. Transform. (DET). (Pressetal. 1992)., The PDS is constructed through the modulus squared of the discrete Fourier Transform (DFT) \citep{Press}.434. For the normalisation used in our calculations. he integral of the PDS over frequency equals the normalised variance of the light curve.," For the normalisation used in our calculations, the integral of the PDS over frequency equals the normalised variance of the light curve."435 For most AGN X-ray light curves. the PDS has a power aw shape of slope 1 bending to a steeper slope at. high requencies (c.g. Summons— et iin prep... Mellardyctal.2004. 2005)).," For most AGN X-ray light curves, the PDS has a power law shape of slope $\sim -1$ bending to a steeper slope at high frequencies (e.g. Summons et in prep., \citealt{McHardy4051,McHardyMCG}) ),"436 which is similar to the PDS found in stellar mass black hole binaries in the soft sta| (seo[ον2007.ora review)., which is similar to the PDS found in stellar mass black hole binaries in the soft state \citep[see][for a review]{uttleyreview}.437 Lt is customary to multiply the variability »ower by frequency when plotting the PDS. to highlight deviations of the power law slope from 1 as. in this case. he low frequency. part of the PDS appears approximately lat and the breaks are more noticeable.," It is customary to multiply the variability power by frequency when plotting the PDS, to highlight deviations of the power law slope from –1 as, in this case, the low frequency part of the PDS appears approximately flat and the breaks are more noticeable."438 We use this παπατα of presentation in Fig. 4.., We use this standard of presentation in Fig. \ref{pds}.439" ln Summonsetal.(2007) we show the X-ray PDS of aancl explore the significance of an apparent cuasi-periodic oscillation (QPO) at a frequency of ~510""Lz.", In \citet{summons} we show the X-ray PDS of and explore the significance of an apparent quasi-periodic oscillation (QPO) at a frequency of $\sim5 \times 10 ^{-6}$ Hz.440 The new. intensively sampled light curve obtained for this object. shown in Fig. 3..," The new, intensively sampled light curve obtained for this object, shown in Fig. \ref{intensive},"441 with a sampling rate of three times claily and a length. of four months. covers the frequency. range 1034. llz.," with a sampling rate of three times daily and a length of four months, covers the frequency range $10^{-7}-3.4\times 10^{-5}$ Hz."442 This range covers the time-scales corresponding to the peak frequency. of the possible OPO very well and allows us to test its significance conclusively., This range covers the time-scales corresponding to the peak frequency of the possible QPO very well and allows us to test its significance conclusively.443 We caleulated the PDS using the long term Hlight curves and short term Iligght. curves discussed in Summonsetal.(2007) and added the new intensive cata., We calculated the PDS using the long term light curves and short term light curves discussed in \citet{summons} and added the new intensive data.444 Phe resulting PDS is shown in solid lines in bie. 4..," The resulting PDS is shown in solid lines in Fig. \ref{pds},"445 where the segments correspond to the cillerent X-ray light curves used., where the segments correspond to the different X-ray light curves used.446 We fitted a bending power law model defined as to the PDS using the Monte. Carlo fitting technique of Uttleyetal.(2002)., We fitted a bending power law model defined as to the PDS using the Monte Carlo fitting technique of \citet{psresp}.447". Phe low-frequency slope op. the high frequency slope ag. the bend. frequeney fi, and the normalisation ;À were allowed to vary."," The low-frequency slope $ \alpha_L$, the high frequency slope $\alpha_H$, the bend frequency $f_b$ and the normalisation $A$ were allowed to vary."448" The fitting parameters are ap=OS. ag=2.2. fy10"" IIz. consistent with the values obtained by Summonsetal.(2007). for the same bending power law model."," The best-fitting parameters are $\alpha_L=0.8$, $\alpha_H=2.2$, $f_b=5.8\times 10^{-6}$ Hz, consistent with the values obtained by \citet{summons} for the same bending power law model."449 The corresponding model is shown by the dashed line in Fig. 4.., The corresponding model is shown by the dashed line in Fig. \ref{pds}.450 The simple bending power law provided an excellent.fit to the new data acceptance probability). making the possible QPO feature unnecessary.," The simple bending power law provided an excellentfit to the new data acceptance probability), making the possible QPO feature unnecessary."451 We also computed the PDS of the B band data. shown by the dotted line in Fig. 4..," We also computed the PDS of the B band data, shown by the dotted line in Fig. \ref{pds}."452" Phe long term light curve was used to constrain the PDS at frequencies 35107.2 Uz and the intensive light curve. covered the range 2.]0'7.10"" Lz.", The long term light curve was used to constrain the PDS at frequencies $3\times10^{-8}-2\times 10^{-7}$ Hz and the intensive light curve covered the range $2\times10^{-7}-7\times 10^{-6}$ Hz.453 We fixed az= 0.8. tthe best- value found for the X-ray PDS. for direct comparison with those data.," We fixed $\alpha_L=0.8$ , the best-fitting value found for the X-ray PDS, for direct comparison with those data."454 Fie., Fig.455 5. shows the (solid lines) anc, \ref{contours} shows the (solid lines) and456 5. shows the (solid lines) ancl, \ref{contours} shows the (solid lines) and457The history of star formation and chemical enrichment of galaxies is encoded in the ages and chemical compositions of their stellar populations.,The history of star formation and chemical enrichment of galaxies is encoded in the ages and chemical compositions of their stellar populations.458 In particular. powerful insights on the processes leading to the assembly of the Galactic halo are gained by studies of the chemical abundances of their constituent. populations of field stars and elobular clusters (GC's).," In particular, powerful insights on the processes leading to the assembly of the Galactic halo are gained by studies of the chemical abundances of their constituent populations of field stars and globular clusters (GCs)."459 It is only natural to extend such studies to the nearest giant spiral galaxy. M 31.," It is only natural to extend such studies to the nearest giant spiral galaxy, M 31."460even cooler blackbodies (see DeLucaetal.2001).,even cooler blackbodies (see \citealt{del04}) ).461 Thus. there is no single category of rotatiou-powered pulsar iuto which ffits neatly.," Thus, there is no single category of rotation-powered pulsar into which fits neatly."462 The cussion of many intermecdiate-aged pulsars is dominated bv high-cucerey 5-ravs. probably even those not vet detected because of the lanited sensitivity of EGRET.," The emission of many intermediate-aged pulsars is dominated by high-energy $\gamma$ -rays, probably even those not yet detected because of the limited sensitivity of EGRET."463 The spin parameters of aare not inconsistent with those of known y-ray pulsars., The spin parameters of are not inconsistent with those of known $\gamma$ -ray pulsars.464" However. its location is confused with the EGRET source 3EC J1856|0111 that is about 1° fromτὸ, and is coincident with the supernova remnant Wl."," However, its location is confused with the EGRET source 3EG J1856+0114 that is about $1^{\circ}$ from, and is coincident with the supernova remnant W44."465 This EGRET source is hard but variable (Nolanetal.2003)., This EGRET source is hard but variable \citep{nol03}.466 We can assume that the fux of ο] J185610111. zm3.6.1019 Cres οσα? lo Gs a conservative upper lit on the eamuna-rav flux of PSR J1852|0010.," We can assume that the flux of 3EG J1856+0114, $\approx 3.6\times 10^{-10}$ ergs $^{-2}$ $^{-1}$, is a conservative upper limit on the gamma-ray flux of PSR J1852+0040."467 Since the upper limit on the spin-down flux {πι of PSR J1852|OOI0 is ες1019 eres cin? sb. it could be an as-vot undetected 5-ray pulsar with au cficieucy of a few percent. typical of vouug or middle-aged pulsars.," Since the upper limit on the spin-down flux $\dot E/4\pi d^2$ of PSR J1852+0040 is $4\times 10^{-10}$ ergs $^{-2}$ $^{-1}$, it could be an as-yet undetected $\gamma$ -ray pulsar with an efficiency of a few percent, typical of young or middle-aged pulsars."468 Even though the X-ray huninosity of lis consistent with miuinual NS cooling curves for au age of 10? tyr (Pageetal.2001). its blackbody temperature inplies an cmitting area that is just z0.5% of the NS surface.," Even though the X-ray luminosity of is consistent with minimal NS cooling curves for an age of $10^{3-4}$ yr \citep{pag04}, its blackbody temperature implies an emitting area that is just $\approx4690.5\%$ of the NS surface."470 This is cousisteut with the hiehlv modulated pulse profile comiug from a πα] rotating hot spot whose measured temperature falls well above any reasonable NS cooling curve., This is consistent with the highly modulated pulse profile coming from a small rotating hot spot whose measured temperature falls well above any reasonable NS cooling curve.471 The most likelv region for localized heating of the NS surface is at the magnetic poles., The most likely region for localized heating of the NS surface is at the magnetic poles.472" The canonical area for tle polar cap is A,=2287RO/Pe=~1410)? αμ”."," The canonical area for the polar cap is $A_{pc} =473{2\pi^2 R^3 / {P c}} \approx 1 \times 10^{10}$ $^2$."474 This is only 1054 of the area implied bv the fit to 1ο X-ray προςτι using the blackbody model., This is only $10\%$ of the area implied by the fit to the X-ray spectrum using the blackbody model.475 In the outer-eap model for στα pulsars (Wangetal.19098).. 1ο N-rav luminosity of the hot polar cap is Dnuited n ⋝⋅↖↽↑∐↸∖≼∶≺≻↕≼⊔⋅↸∖↕↸⊳∐≓⋅↧∏∐⋜⋯↙↸⊳∏∐⋅↸∖∐↑∢∪↖↖⇁∪↕≯⊀∖⊽⋃≈⊇∖ ↕∣⋮⋝⇉⋖∫≽∣⋅∐∣⋅↱≻↴∖↴⋝⇉∐⋚↕∩⊔≼∶⋟↴∖↴↓≼∐↰⋯↴∖↴↕↑↕∐∶↴⋁⋜⋯⋜↧↖⇁↸∖↥⋅⋜↧∶↴∙⊾↸∖ ↸∖∐∖↥⋅∶↴∙⊾⋅↖↽↻↸∖↥⋅↻⋜∐⋅↑↕↸⊳↕↸∖∪↕⋟⊏⊺≈↓∙∶≩↸∖↥⋅∶↴∙∷∖↴∙↽∕∏∐∖⋯⋜⋯↕∐∐∐⊔ ∐∐∐∪↴∖↴↕⋅↖↽↕↴∖↴⊓↴⋝∪↻≈∙↗⊔∑⊢∖⊽⋃↓∖ ↽∩⋮⋝⇉↸∖↥⋅∶↴∙⋱∖↴↴∖↴↓∙∐↸∖↥⋅," In the outer-gap model for $\gamma$ -ray pulsars \citep{wan98}, the X-ray luminosity of the hot polar cap is limited by the Goldreich-Julian $e^{\pm}$ current flow of $\dot N_0 \approx 2476\times 10^{32}\,(P/0.105\,{\rm s})^{-2}\,(B/10^{12}\,{\rm477G})$ $^{-1}$ depositing an average energy per particle of$E_f478\approx 4.3$ ergs."479↸∖ ∐∖↕≯↥⋅⋜↧↸⊳↑↕∪∐⋅↗↳⊽∪↕≯↑∐↸∖↸⊳↿∐⋅↥⋅↸∖∐↑↥⋅↸∖⋜↧↸⊳∐↕∐∶↴∙⊾∐↸∖↴∖↴↿∐⋅↕⋟⋜↧↸⊳↸∖↕↴∖∷∖↴↸∖↑↑∪ ∣⊇∙↑∐∖⋯⋜⋯↕⋯⋯⊔↻∪↴∖↴↴∖↴∏," The maximum luminosity is $L({\rm bol}) \approx f480E_f \dot N_0 < 4 \times 10^{32}$ ergs $^{-1}$."481⋝↕↸∖↸∖↴∖↴↑↕↕⊔⋜↧↑↸∖≼↕≯∪↥⋅⋜↧↷↴≓↥⋅⋜↧⋅↖⇁↻∏↕↴∖↴⋜∐⋅ ∐∖⋜∐⋅↕↴∖↴≼∐∖⋜↧↑∐∐∐↸∖∙∖↖⊽∐∐↸∖↕≯⋜↧∐↕∐∶↴⋁↴∖↴∐∪↥⋅↑∪↕⋟↑∐↸∖≺⋔↴∖↴↸∖↥⋅↖↽↸∖≼⇂ ⊸∖⊽≓↥⋅⋜↧⋅↖↽↕⋯⊔↕∐∪↴∖↴↕↑⋅↖↽∪↕⋟↕⋟≋↕⊰⋅∐≺∖∖⋅↱↗⊇⊔∣∩∐∣," Here the fraction $f$ of the current reaching the surface is set to 1/2, the maximum possible estimated for a $\gamma$ -ray pulsar near its death line."482 ⋝↴⋝∙↖↽⋜⋃∪↥⋅≺∐∖↥⋅⊣≻↕∟⋯⋜↧∶↴∙⊾∐↕↑⋯∐∖∙↑↕∐↴∖↴↻↥⋅↸∖≼↕↸⊳↑↕∪∐⋜∏∏≻∐↸∖↴∖↴∪∐↕⋅↖⇁ ∪⋜↧⊔⋜⋯↕⋯⋜↧∐⋅↖⇁↸∖↕−⊔↸⊳↕↸∖∐↑↷↴≓↥⋅⋜↧⋅↖↽↻∏↕↴∖↴⋜∐⋅∙⊏↕↑↕∐∖↥⋅∏∐∖↷≓ ↥⋅⋜↧⋅↖⇁↸∖↨∟↴∎↸⊳↕↸∖∐↸⊳⋅↖⇁∪↥⋅↑∐↸∖⊈⋚↕⋝∐↸∖↕≼⊔," While falling short of the observed X-ray luminosity of by an order-of-magnitude, this prediction applies only to a maximally efficient $\gamma$ -ray pulsar."483↴∖↴↕∐↘↽↸∖↕∙↖⇁↑∪↴⋝↸∖↕∪↖↖⇁↸∖↥⋅∙↴∖↴∪↕∏↴∖↴⋯↸∖↸⊳∐⋜⋯↕↴∖↴⋯↕↴∖↴∐⋜∐⋅≼↧↻↥⋅↸∖↴∖∷∖↴↸∖≺↧↑∪⋜⋯⊳∪∏∐↑↕≯∪↥⋅↑∐↸∖⊸∖↕ ↥⋅⋜↕⋅↖↽↕∏↕∐∐∪↴∖↴↕↑⋅↖↽∪↕≯↕⋟≋↕⊰⋅∐≺∖∖⋅↱⊐⊇⊔∣∩∐∣⋈↕⋟∪↕⋜∐⋅⊣⊳⋜⋯∐↸∖⋜↧↑↕∐∶↴," Either the $\gamma$ -ray efficiency or the $B_{\rm p}$ field is likely to be lower, so this mechanism is hard pressed to account for the X-ray luminosity of."484⋁ ⊔∪≼∐∖↕↴∖↴∪↕≯∐⋜∐⋅≺∐∐∶↴∙⊾∙∖↽⋀∖↕∏↴∖↴∐⋯∪↖↽⊔∩∩↕∙⊇∩∩⊇⋝↻↥⋅↸∖≼∐↸⊳↑↸∖↖↽↸∖∐ ↸∖↴∖↴↴∖↴⊸∖⊽≓↥⋅⋜↧⋅↖⇁↕∏∐∐∐∪↴∖↴↕↑⋅↖⇁↑∐⋜," Polar-cap heating models of \citet{har01,har02} predict even less X-ray luminosity than \citet{wan98}."485⋯↖↖⊽⋜⋯∶↴∙⊾↸∖↑⋜↧↕∙∐∩∩≺∖∖⋝∙∙⊺⋜∐↘↽↸∖∐⋜↧↑ ace value. all such 1nodols fall short of predictiug the apparent area. feniperature. aud ποπ]τν of the N-arax enission from," Taken at face value, all such models fall short of predicting the apparent area, temperature, and luminosity of the X-ray emission from."486" While the temperature and huuinositv of aaro ereater than those of middle-aged pulsars. its Ποπεν is less than those of ANPs. which have £L,—1079 eyes «T and thermal spectral components of kTupm0.1 keV (Mereghetti2002)."," While the temperature and luminosity of are greater than those of middle-aged pulsars, its luminosity is less than those of AXPs, which have $L_x \sim 10^{34-35.5}$ ergs $^{-1}$ and thermal spectral components of $kT_{\rm BB} \simgt 0.4$ keV \citep{mer02}."487. The spectrum of lis sugecstive of a maguctar of low X-ray luuinosity. perhaps like the quiescent state of the transient. ANP NTE Jlslo197 (Ilalperu&Cotthelf2005).," The spectrum of is suggestive of a magnetar of low X-ray luminosity, perhaps like the quiescent state of the transient AXP XTE J1810–197 \citep{hal05}."488". According to the magnetar theory. the X-ray ciission ultimately derives from the decay of an enormous magnetic feld (Bo>Lis10175 G: Dunean&""Thompson1996))."," According to the magnetar theory, the X-ray emission ultimately derives from the decay of an enormous magnetic field $B \simgt 4.4 \times 10^{13}$ G; \citealt{dun96}) )."489 Although ccould be an “anomalous.” fast ANP. the implied magnetic field strength is insufficient to power the observed XN-rav Iuuinositv over the lifetime of the pulsar. estimated as Lytangc8s10H eres. since the available lmaguctic euerev is onlv ~BPR?/6=3«107(B/105)? eres.," Although could be an “anomalous,” fast AXP, the implied magnetic field strength is insufficient to power the observed X-ray luminosity over the lifetime of the pulsar, estimated as $L_x \tau_{\rm SNR} \sim4908 \times 10^{44}$ ergs, since the available magnetic energy is only $\approx B^2 R^3/6 = 3 \times 10^{43} (B/10^{13})^2$ ergs."491 More detailed predictions invoking the magnetar theory (e.g.. currents on twisted magnetic field lines external to the star: Thompson.Lvutikov.&νακατά20023) are μιαν] insufficient to sustain the observed N-rav enassion.," More detailed predictions invoking the magnetar theory (e.g., currents on twisted magnetic field lines external to the star; \citealt*{tho02}) ) are similarly insufficient to sustain the observed X-ray emission."492" Although binary NS N-vay transicuts in quiescence often have huuinositics similar to that ofJ1852]0010.. their spectra. as sununnuuidzed. eg. bv ""Toiisickal.(2001). are characterized as softer blackbodies covering the full NS surface. rather thau a sanall hot spot."," Although binary NS X-ray transients in quiescence often have luminosities similar to that of, their spectra, as summarized, e.g., by \citet{tom04}, are characterized as softer blackbodies covering the full NS surface, rather than a small hot spot."493 Even if the hotter enuüssiou frou: is hypothesized to come from residual accroetion. the current observations distavor a binary scenario based ou its steady. long-teri flix. lack of orbital Doppler delay. and absence of characteristic red noise in its timing spectrum.," Even if the hotter emission from is hypothesized to come from residual accretion, the current observations disfavor a binary scenario based on its steady long-term flux, lack of orbital Doppler delay, and absence of characteristic red noise in its timing spectrum."494" The unclassified star «1"" from the ppositiou. while unlikely to be a binary companion of J1852]0010.. prevents us frou deriving a constrainius upper limit on optical emission from either the pulsar itself or a fall-back accretiou disk."," The unclassified star $<1^{\prime\prime}$ from the position, while unlikely to be a binary companion of , prevents us from deriving a constraining upper limit on optical emission from either the pulsar itself or a fall-back accretion disk."495" Even if ppossesses a fossil accretion disk. it may be unable to accrete because the maeuetospheric radius is 5,—23«1oply(QUIM.CLB77 ca which is 3«10? cm for an assinued inaguetic moment y=B,,S/2zm100 C au? aud an observed L=GADQB/R3.7<010? eres s+."," Even if possesses a fossil accretion disk, it may be unable to accrete because the magnetospheric radius is $r_{\rm m} = 3 \times49610^8\,\mu_{30}^{4/7}\,(M/M_{\odot})^{1/7}\,497L_{37}^{-2/7}\,R_6^{-2/7}$ cm, which is $3 \times 10^9$ cm for an assumed magnetic moment $\mu = B_{\rm p}\,R^3/2 \approx 10^{30}$ G $^3$ and an observed $L = GM\dot m/R = 3.7 \times 10^{33}$ ergs $^{-1}$."498" Therefore. the iaguetie dipole pressure ejects any potential accreting matter well outside the leht evlinder radius. rj,=eP/2x5«105 em."," Therefore, the magnetic dipole pressure ejects any potential accreting matter well outside the light cylinder radius, $r_{\ell} = cP/2\pi = 5499\times 10^8$ cm."500" Only in the case of By as small as τον105 G could bbea ""slow rotator.” with Pz since the equilibriun (or απ). period for disk P4.accretion is Pog=3.6pho)(AL/AL.)PTBoPΠρο κ, While such a value of By is common among low-niass X-ray binaries. it would be surprising for such a voung NS."," Only in the case of $B_{\rm p}$ as small as $7501\times 10^8$ G could be a “slow rotator,” with $P \approx502P_{\rm eq}$, since the equilibrium (or minimum) period for disk accretion is $P_{\rm eq} = 3.6\,\mu_{30}^{6/7}\,(M/M_{\odot})^{-2/7}\,503L_{37}^{-3/7}\,R_6^{-3/7}$ s. While such a value of $B_{\rm p}$ is common among low-mass X-ray binaries, it would be surprising for such a young NS."504 For an intermediate value of the maguetic feld streneth. ccould be iu the propeller regime. P—Lg. ta which matter is flune out from the maenuetospheric radius :t a rate ip. which causes it to spin down at a rate P (ogMenonetal.1999:Zavli- 2001). where Zz107 ο em? is the NS momeut of inertia.," For an intermediate value of the magnetic field strength, could be in the propeller regime, $P < P_{\rm eq}$, in which matter is flung out from the magnetospheric radius at a rate $\dot m$, which causes it to spin down at a rate $\dot P \approx 2\,\dot m\,r_{\rm505m}^2\,I^{-1}\,P\,(1-P/P_{\rm eq})$ \citep[e.g.,][]{men99,zav04}, , where $I506\approx 10^{45}$ g $^2$ is the NS moment of inertia."507" The observed upper IitP«7«10 ll sol sets an upper mit of ii<3.7«101(4,/105011)2 gs lin the propeller scenario."," The observed upper limit$\dot P < 7 \times 10^{-14}$ s $^{-1}$ sets an upper limit of $\dot m < 3.7 \times 10^{16}\,(r_{\rm m}/10^8\,{\rm508cm})^{-2}$ g $^{-1}$ in the propeller scenario."509 But in that case. it is not clear how the hiehlv pulsed. thermal ταν enission is produced.," But in that case, it is not clear how the highly pulsed, thermal X-ray emission is produced."510 Even if the bulk of the fall-back material is ejected. as," Even if the bulk of the fall-back material is ejected, as"511Cataclysmic variable stars (CVs) are short-perioc binary systems which typically consist of a cool main-sequence star transferring mass via a gas stream ancl accretion disc to a white dwarf primary.,Cataclysmic variable stars (CVs) are short-period binary systems which typically consist of a cool main-sequence star transferring mass via a gas stream and accretion disc to a white dwarf primary.512" Phe impact of the stream. with the accretion disce forms a so-called ""bright spot’. which in systems that are significantly. inclined to our line of sight can cause a rise in the observed Hux as this region rotates into view. resulting in an ""orbital hump' in the lightcurve."," The impact of the stream with the accretion disc forms a so-called `bright spot', which in systems that are significantly inclined to our line of sight can cause a rise in the observed flux as this region rotates into view, resulting in an `orbital hump' in the lightcurve."513 In high-inclination svstems eclipses of the white ewarf. bright spot ancl dise by the red. cwarl secondary can also occur.," In high-inclination systems eclipses of the white dwarf, bright spot and disc by the red dwarf secondary can also occur."514 Analysis of these eclipses can vield determinations of system parameters such as the mass ratioq. the orbital inclination and the radius of the accretion disc Ly citealtwoodsOa)).," Analysis of these eclipses can yield determinations of system parameters such as the mass ratio, the orbital inclination and the radius of the accretion disc $R_{d}$ \\citealt{wood89a}) )."515 Eclipsing systems are therefore. valuable sources of data on CVs., Eclipsing systems are therefore valuable sources of data on CVs.516 Dwarf novae are a sub-tvpe of CVs which show intermittent luminosity increases of 25 magnitudes. known as outbursts.," Dwarf novae are a sub-type of CVs which show intermittent luminosity increases of 2–5 magnitudes, known as outbursts."517 X. Further. sub-tvpe. of dwarf. novae. are the SU. UAla stars. which exhibit) superoutbursts. at regular intervals. during which the luminosity increases bv 0.7 magnitudes over the normal outburst maximum.," A further sub-type of dwarf novae are the SU UMa stars, which exhibit superoutbursts at regular intervals, during which the luminosity increases by $\sim0.7$ magnitudes over the normal outburst maximum."518 These superoutbursts are characterised by the presence of superhumps increases in brightness that usually recur at a slightly longer period than the orbital evcle., These superoutbursts are characterised by the presence of superhumps – increases in brightness that usually recur at a slightly longer period than the orbital cycle.519 Phere is found to be a relationship between this superhump period excess ¢ and the mass ratio C2).., There is found to be a relationship between this superhump period excess $\epsilon$ and the mass ratio \citep{patterson98}.520 Determinations of the mass ratios of SU UAla stars are therefore useful to calibrate this relation. which can then be used to determine the mass ratios ofother SU UMa stars.," Determinations of the mass ratios of SU UMa stars are therefore useful to calibrate this relation, which can then be used to determine the mass ratios of other SU UMa stars."521 OU Vir is a faint (V —Ls: 7)) eclipsing CV with a period. of 1.75 hr which has been seen in outburst and probably superoutburst (2).. marking it as à SU UMa dwarf nova.," OU Vir is a faint (V $\sim18$; \citealt{mason02}) ) eclipsing CV with a period of 1.75 hr which has been seen in outburst and probably superoutburst \citep{vanmunster00}, , marking it as a SU UMa dwarf nova."522 ?. presented. time-resolved. multi-colour. photometry ancl spectroscopy of OU Vir. concluding that the eclipse is of the bright spot and disc. but not the white dwarf.," \citet{mason02} presented time-resolved, multi-colour photometry and spectroscopy of OU Vir, concluding that the eclipse is of the bright spot and disc, but not the white dwarf."523 In this paper we present lighteurves of OU Vir. obtained with ULTILACAM. an ultra-fast. triple-beam CCD camera: for more details see ?:: Dhillon et al..," In this paper we present lightcurves of OU Vir, obtained with ULTRACAM, an ultra-fast, triple-beam CCD camera; for more details see \citet{dhillon01b}; Dhillon et al.,"524 in preparation., in preparation.525 OU. Vir was observed on the nights of 16 May. 2002 and 19. 20. 22 and 25 May 2003 usingULTILACAM on the," OU Vir was observed on the nights of 16 May 2002 and 19, 20, 22 and 25 May 2003 usingULTRACAM on the"526but to reconstruct the visibilities on each bolometer separately and combine the visibilities afterwards.,but to reconstruct the visibilities on each bolometer separately and combine the visibilities afterwards.527 Such a strategy would increase the length of the phase-shifting sequences. but in a reasonable (and tractable) way thanks to the intrinsic shortness of our proposed phase-shifting scheme.," Such a strategy would increase the length of the phase-shifting sequences, but in a reasonable (and tractable) way thanks to the intrinsic shortness of our proposed phase-shifting scheme."528~1210Hs 4.,$\sim 1 \times 10^{-14}$ $^{-1}$.529 Phe model results appear to be consistent with the observational data., The model results appear to be consistent with the observational data.530 We consider then in particular for the cxtragalactic comparison. galaxies where AGN - and/or starburst - activities may have enhanced the cosmic ray ionization rates as well as. in some cases. created ULIICGs.," We consider then in particular for the extragalactic comparison, galaxies where AGN - and/or starburst - activities may have enhanced the cosmic ray ionization rates as well as, in some cases, created ULIRGs."531 In ? we selected: well-known galaxies. such as Arp 220 or M S2 as examples of sources with active nuclei. and where therefore the cosmic ray ionization rate may be enbanced.," In \citet{Baye09a} we selected well-known galaxies, such as Arp 220 or M 82 as examples of sources with active nuclei, and where therefore the cosmic ray ionization rate may be enhanced."532 Arp 220 is the prototypical ultraluminous galaxy while M82 is the prototypical starburst., Arp 220 is the prototypical ultraluminous galaxy while M82 is the prototypical starburst.533 Recently (2). ο has been discovered in these two regions and its fractional abundance has been estimated to be ~ 10 7., Recently \citep{VanderTak08} $_{3}$ $^+$ has been discovered in these two regions and its fractional abundance has been estimated to be $\sim$ $\times$ $^{-9}$.534" ""These authors fou that observations of M. 82 are matched by a hieh-¢ PDR. Le. an evolved starburst while N-ray models are best a reproducing the observations of Arp 220."," These authors found that observations of M 82 are matched by a $\zeta$ PDR, i.e., an evolved starburst while X-ray models are best at reproducing the observations of Arp 220."535 In fact. our models indicate that one can obtain high abundance of this ion à low (i.e in à PDR) as well as high (ie dense star forming eas) extinction as long as the ¢ is ~ 13 l and the metallicity is solar.," In fact, our models indicate that one can obtain high abundance of this ion at low (i.e in a PDR) as well as high (i.e dense star forming gas) extinction as long as the $\zeta$ is $\sim$ $^{-13}$ $^{-1}$ and the metallicity is solar."536 At high extinction. which could represen the nuclear part of the galaxy. the abundance is higher. providing possibly a better match for the observations.," At high extinction, which could represent the nuclear part of the galaxy, the abundance is higher, providing possibly a better match for the observations."537 We note here that we are not attempting to model Arp 220 that. since as 2? pointed out. it has a quite unusual geometry.," We note here that we are not attempting to model Arp 220 that, since as \citet{VanderTak08}538 pointed out, it has a quite unusual geometry."539 Another interesting object which has been recently studied in molecular emission is Mrk 231. a ULIBCG.," Another interesting object which has been recently studied in molecular emission is Mrk 231, a ULIRG."540 A hieh resolution SPIRE FILS spectrum reveals the presence of ions such as and H120 (?)..," A high resolution SPIRE FTS spectrum reveals the presence of ions such as $^+$, $^+$ and $_2$ $^+$ \citep{VanderWerf10}."541 While abuncances are not derived. we can use our Table 2. to determine what tvpe of model is able to produce high fractional abundances 10.| 27) of these three ions.," While abundances are not derived, we can use our Table \ref{tab:3} to determine what type of model is able to produce high fractional abundances $\ge$ $^{-10}$ ) of these three ions."542. We ⇁⋅find that the only. regime. is. an environment with low metallicity (0.1. solar). very hieh cosmic. rav ionisation.- rates (2 1017? 1 *) and low visual extinction.," We find that the only regime is an environment with low metallicity (0.1 solar), very high cosmic ray ionisation rates $\ge$ $^{-16}$ $^{-1}$ ) and low visual extinction."543 ? explained the high abundances of these ions bv involving XDIt-chemistry., \citet{VanderWerf10} explained the high abundances of these ions by involving XDR-chemistry.544 We find that. in agreement with 7.. determining the origin of molecular emission from λος such as Mrk 231 is not trivial when both sources of energy (CLR ane N-ravs) are present.," We find that, in agreement with \citet{Papa10a}, determining the origin of molecular emission from ULIRGs such as Mrk 231 is not trivial when both sources of energy (CR and X-rays) are present."545 Finally. our results are necessarily indicative rather than specific in that we do not estimate molecular line intensities.," Finally, our results are necessarily indicative rather than specific in that we do not estimate molecular line intensities."546 Our study was motivated. by the recent. investigation of filaments around the central galaxies of clusters of galaxies bv ? and by the considerations of the ellects of high cosmic rav ionization rates in ULIRGs by ? as well as recent Lerschel results., Our study was motivated by the recent investigation of filaments around the central galaxies of clusters of galaxies by \citet{Baye10a} and by the considerations of the effects of high cosmic ray ionization rates in ULIRGs by \citet{Papa10a} as well as recent Herschel results.547 We find that several species. many detected in extragalactic environments. are in fact tracers of very high ionization fractions.," We find that several species, many detected in extragalactic environments, are in fact tracers of very high ionization fractions."548 The general conclusions that we can draw from this study are as follows:, The general conclusions that we can draw from this study are as follows:549come back to considering how these characteristics should be interpreted below.,come back to considering how these characteristics should be interpreted below.550" In our observations, B19444-17 nulls about 2/3 of the time, somewhat higher than the value given by DCHR, but closer to null percentage reported by Rankin, (1986)."," In our observations, B1944+17 nulls about 2/3 of the time, somewhat higher than the value given by DCHR, but closer to null percentage reported by Rankin, (1986)."551" The majority of these null pulses can readily be distinguished from the bursts; however, there is a small portion of weak pulses that are difficult to identify as either nulls or pulses."," The majority of these null pulses can readily be distinguished from the bursts; however, there is a small portion of weak pulses that are difficult to identify as either nulls or pulses."552" Interestingly, the distinction between nulls and pulses is easier to define at L band, as can be seen in the respective null histograms of Fig. 2.."," Interestingly, the distinction between nulls and pulses is easier to define at L band, as can be seen in the respective null histograms of Fig. \ref{nullhistograms}."553" Given that the nulls and pulses cannot be fully distinguished, we can choose an intensity threshold that will be conservative and reliable either in selecting pulses or nulls, but not both."," Given that the nulls and pulses cannot be fully distinguished, we can choose an intensity threshold that will be conservative and reliable either in selecting pulses or nulls, but not both."554" In Fig. 2,,"," In Fig. \ref{nullhistograms},"555" we have taken the latter option—that is, using low thresholds that will tend to slightly underestimate the null population."," we have taken the latter option—that is, using low thresholds that will tend to slightly underestimate the null population."556" Then, using this conservative discriminator of nulls, we have computed the burst- and null-length histrograms in Figure 3.."," Then, using this conservative discriminator of nulls, we have computed the burst- and null-length histrograms in Figure \ref{burstnullfreq}."557" These show that 1-pulse bursts and nulls have the highest frequency, but we see that very long bursts and nulls also occur."," These show that 1-pulse bursts and nulls have the highest frequency, but we see that very long bursts and nulls also occur."558" In the 7000- 327-MHz observation, for instance, a small number of bursts of 40-50 P, and two of 80-90 P, were encountered alongside the more frequent long nulls ranging up to 300 Pi."," In the 7000-pulse 327-MHz observation, for instance, a small number of bursts of 40-50 $P_1$ and two of 80-90 $P_1$ were encountered alongside the more frequent long nulls ranging up to 300 $P_1$."559 Even qualitatively we immediately see that the nulls in B1944+17 are distributed within the PS in a very non-random manner., Even qualitatively we immediately see that the nulls in B1944+17 are distributed within the PS in a very non-random manner.560" Recent investigations into pulsar nulling have raised two important new questions about their distributions: a) whether they are randomly distributed(e.g.,, Redman Rankin 2009; Rankin Wright 2007); and b) whether they are periodic (HR07/09)."," Recent investigations into pulsar nulling have raised two important new questions about their distributions: a) whether they are randomly distributed, Redman Rankin 2009; Rankin Wright 2007); and b) whether they are periodic (HR07/09)."561" With such a large null fraction, one would expect to see few long sequences in any given observation."," With such a large null fraction, one would expect to see few long sequences in any given observation."562 The tendency of B1944+17’s bursts and nulls to clump into sequences of roughly 20-100 pulses immediately indicates a non-random distribution., The tendency of B1944+17's bursts and nulls to clump into sequences of roughly 20-100 pulses immediately indicates a non-random distribution.563 Application of the, Application of the564"The average amplitude of quasar variability has been seen to depend on several factors: time lag between measurements, Iuninositv of the quasar (2.. 2.. 2.. 2 εν 7)). wavoleugth of observation (?2.. 7.. 24). aud black hole mass (7... 23).","The average amplitude of quasar variability has been seen to depend on several factors: time lag between measurements, luminosity of the quasar \citealt{vandenberk04}, , \citealt{devries05}, , \citealt{wilhite08}, , \citealt{bauer09a}, \citealt{macleod10}, , \citealt{meusinger11}) ), wavelength of observation \citealt{vandenberk04}, \citealt{devries05}, \citealt{meusinger11}) ), and black hole mass \citealt{wilhite08}, \citealt{bauer09a}) )."565 The dependence of variability amplitude on redshift is less obvious: ? measured a slight increase in the variability with redshift. while ?— measured a slight decrease.," The dependence of variability amplitude on redshift is less obvious; \cite{vandenberk04} measured a slight increase in the variability with redshift, while \cite{devries05} measured a slight decrease."566 More receuthl ? and? have measured no significant dependeuce of variability amplitude ou redshift.," More recently, \cite{macleod10} and \cite{meusinger11} have measured no significant dependence of variability amplitude on redshift."567 Iu practice. the vauiabilitv-Iuninositv trend measured is of the form: A linear relation has indeed been observed (?.. ?)). although there are conflicting results for the value of he power-law slope o. perhaps due to selection effects.," In practice, the variability-luminosity trend measured is of the form: A linear relation has indeed been observed \citealt{vandenberk04}, \citealt{bauer09a}) ), although there are conflicting results for the value of the power-law slope $\alpha$, perhaps due to selection effects."568 If faint quasars are included in the analysis for which one cannot observe the full exteut of the variability. the ucasured slope will become artificially shallow: this effect nost clearly manifests itself as a flattening in the relation at the lowest observable Iuminosities. as is illustrated iu feure 5b of ?..," If faint quasars are included in the analysis for which one cannot observe the full extent of the variability, the measured slope will become artificially shallow; this effect most clearly manifests itself as a flattening in the relation at the lowest observable luminosities, as is illustrated in figure 5 of \cite{bauer09a}."569 The low-huninosity luit of the binning scheme in this work is chosen to exclude this regime frou he data set., The low-luminosity limit of the binning scheme in this work is chosen to exclude this regime from the data set.570 The value of the coustaut C depeuds ou he details of the normalization of the data. as described yolow.," The value of the constant $C$ depends on the details of the normalization of the data, as described below."571 When studyiug how the variability of a large quasar sample depends ou one of the quasars’ properties. we uust treat the parameters as iudependcutly as possible.," When studying how the variability of a large quasar sample depends on one of the quasars' properties, we must treat the parameters as independently as possible."572 To this end. we use a mnethod introduced bv 7 and adopted in ὧν," To this end, we use a method introduced by \cite{vandenberk04} and adopted in \cite{bauer09a}."573 Four basic quantities are kuown or all of the quasars iu our sample: tine lag between neasnreimients 7. Iniinositv L. estimated black hole mass M. aud redshift :.," Four basic quantities are known for all of the quasars in our sample: time lag between measurements $\tau$, luminosity $L$, estimated black hole mass $M$, and redshift $z$."574 There are kuown correlations between all of these parameters. due to plivsical relationships or artificial effects such as detection biases in fux-lTiuüted survers.," There are known correlations between all of these parameters, due to physical relationships or artificial effects such as detection biases in flux-limited surveys."575 To avoid these complications aud study only the dependence of variability on hiinosity. we would like to identify a set of quasars with identical properties except for their luminosity. aud then examine how the variability differs between them.," To avoid these complications and study only the dependence of variability on luminosity, we would like to identify a set of quasars with identical properties except for their luminosity, and then examine how the variability differs between them."576 To approximate this procedure. we have split cach parameters range uto bius: 8 bins in r. G bius in AM. 6 bins in z. and 1 bins iu £.," To approximate this procedure, we have split each parameter's range into bins: 8 bins in $\tau$, 6 bins in $M$, 6 bins in $z$, and 4 bins in $L$."577 The biu limits are given in table 1: quasars with properties outside the eiven ranges are not used in the analysis., The bin limits are given in table \ref{bin_limits}; quasars with properties outside the given ranges are not used in the analysis.578 To iieasure quasar variability we use a quantity simular to that of the structure function., To measure quasar variability we use a quantity similar to that of the structure function.579 We define: where Am is the magnitude difference between two incdependecut observations of au object. aud c6 ids the error on those imeasurements.," We define: where $\Delta m$ is the magnitude difference between two independent observations of an object, and $\sigma$ is the error on those measurements."580 This is similar to the structure function as used in 7? ancl ?: however. here instead of beiug an ensemble measurement. oue V ids measured for cach pair of magnitude measurements of a quasar.," This is similar to the structure function as used in \cite{vandenberk04} and \cite{bauer09a}; however, here instead of being an ensemble measurement, one $V$ is measured for each pair of magnitude measurements of a quasar."581 Four measurements of a quasar will vield six Arm ineasurcmecnts. and therefore six different V nieasureients for the single quasar.," Four measurements of a quasar will yield six $\Delta m$ measurements, and therefore six different $V$ measurements for the single quasar."582 As V is imaginary when Ar is less than the measurement error σ. we ouly use data which show significant (7 lo) variability.," As $V$ is imaginary when $\Delta m$ is less than the measurement error $\sigma$, we only use data which show significant $>1 \sigma$ ) variability."583 This cut on the data is described further im section 5.1.., This cut on the data is described further in section \ref{datacuts_section}.584 For each multidimensional biu. a mean variability anplitude V is determined bv taking the mean of all V. values measured for that biu.," For each multi-dimensional bin, a mean variability amplitude $\overline{V}$ is determined by taking the mean of all $V$ values measured for that bin."585 Then. holding coustaut the iudices for time lag. mass. redshift. aud waveleneth. one can compare the V. values across the £L bins.," Then, holding constant the indices for time lag, mass, redshift, and wavelength, one can compare the $\overline{V}$ values across the 4 $L$ bins."586 This procedure vields 8&ος6=288 possible Lpoint plots of mean variability amplitude Wo versus hDmunuinositv. or 1152 possible V. values.," This procedure yields $8 \times 6 \times 6 = 288$ possible 4-point plots of mean variability amplitude $\overline{V}$ versus luminosity, or 1152 possible $\overline{V}$ values."587 Most of the imulti-diieusional bins are not well populated by the quasar sample (for example. ligh-redshift low-luninosity bins).," Most of the multi-dimensional bins are not well populated by the quasar sample (for example, high-redshift low-luminosity bins)."588 Iu fact. we obtain 103 bins with at least 50 measurement pairs. which is the mini. we require in order to aclequatcly determine V.," In fact, we obtain 403 bins with at least 50 measurement pairs, which is the minimum we require in order to adequately determine $\overline{V}$."589 To examine the overall behavior of V with respect to L one can normalize the [-poiut measured trends together and average the resulting uoriualized data in each £ bin to fud a simple. mecamineful result of how the variability scales with the quasar Iuninosity.," To examine the overall behavior of $\overline{V}$ with respect to $L$ one can normalize the 4-point measured trends together and average the resulting normalized data in each $L$ bin to find a simple, meaningful result of how the variability scales with the quasar luminosity."590 The normalization consists of an additive constant in log(V}. ic. each L-poiut measured trend has its own constant C as defined in equation 2..," The normalization consists of an additive constant in $\overline{V}$ ), i.e. each 4-point measured trend has its own constant $C$ as defined in equation \ref{v_vs_l_equation}."591 The 7. M. aud :onudtidunensonal bin that has the best statistics is chosen to be the standard. aud the log(V) versus log(L) treuds from all other 7. M. aud : bins are normalized to that standard using one constant offset per r. M. 2 combination.," The $\tau$, $M$, and $z$ multi-dimensional bin that has the best statistics is chosen to be the standard, and the $\overline{V}$ ) versus $L$ ) trends from all other $\tau$, $M$, and $z$ bins are normalized to that standard using one constant offset per $\tau$, $M$, $z$ combination."592 The constant is determined by ininimizine the chi square difference. between the V values frou the two datasets in the same £ bin. for the L bius where there exist data from both sets;," The constant is determined by minimizing the chi square difference between the $\overline{V}$ values from the two datasets in the same $L$ bin, for the $L$ bins where there exist data from both sets."593 For a visual representation of the normalization procedure. see fieure [d in ?..," For a visual representation of the normalization procedure, see figure 4 in \cite{bauer09a}."594" After averaging the normalized data. we are left with one Vom, versus £ troud with arbitrary y axis normalization but meauinetul slope."," After averaging the normalized data, we are left with one $V_{\mathrm{norm}}$ versus $L$ trend with arbitrary $y$ axis normalization but meaningful slope."595 This nonualization technique has been shown to give results for variability amplitude versus timelag 7 that are consistent with indepeudent measurements (see table liu ?.., This normalization technique has been shown to give results for variability amplitude versus timelag $\tau$ that are consistent with independent measurements (see table 4 in \cite{bauer09a}.596 In this wav. we study how the variability scales with bhuunmositv. comparing only objects with simular values of the other parameters.," In this way, we study how the variability scales with luminosity, comparing only objects with similar values of the other parameters."597" After the normalization. deviations from the mean Vu,£ relation will not be caused by known. but lensine-indepencdent. correlations such as that between variability aud time lag."," After the normalization, deviations from the mean $V_{\mathrm{norm}}-L$ relation will not be caused by known, but lensing-independent, correlations such as that between variability and time lag."598 Using the normalization constants calculated in this wav. cach measured variability amplitude V. is normalized according to its r. AZ. and : bin: the resulting Vac then canbe usedto estimatethequasars lensing magnification.as detailed below.," Using the normalization constants calculated in this way, each measured variability amplitude $V$ is normalized according to its $\tau$ , $M$ , and $z$ bin; the resulting $V_{\mathrm{norm}}$ then canbe usedto estimatethequasar's lensing magnification,as detailed below."599 We note that. for data taken in a single pass-band. the," We note that, for data taken in a single pass-band, the"600calculated small-scale density spectra in turbulent interstellar plasmas.,calculated small-scale density spectra in turbulent interstellar plasmas.601 They also considered compressible turbulence in plasmas with ;2 less than unity that mateh those found in the magnetic tubes of T Tauri stars., They also considered compressible turbulence in plasmas with $\beta$ less than unity that match those found in the magnetic tubes of T Tauri stars.602 Thev argued that the dvnamies of the eascade is roughly independent of 3., They argued that the dynamics of the cascade is roughly independent of $\beta$.603 In the above mentioned papers. il was assumed (hat ATID wave-packets propagate al the Alfvénn speed. in a direction either parallel or antiparallel with respect to the local mean magnetic field and that the nonlinear interactions are restricted to collisions between oppositelv. directed wave-packets.," In the above mentioned papers, it was assumed that MHD wave-packets propagate at the Alfvénn speed, in a direction either parallel or antiparallel with respect to the local mean magnetic field and that the nonlinear interactions are restricted to collisions between oppositely directed wave-packets."604 Maron&Goldreich(2001) made simulations of ihe interaction between oppositely directed. Alfvénn waves., \citet{maron..01} made simulations of the interaction between oppositely directed Alfvénn waves.605" In our previous paper (Paper D)). instead. of a wave spectrum. we assumed a mean frequency, 2=Fue; while in this paper. we (reat different. [requency values."," In our previous paper \citeauthor{vasc..00}) ), instead of a wave spectrum, we assumed a mean frequency, $\varpi = F w_i$, while in this paper, we treat different frequency values."606 The wave frequency obtained. from laboratory experiments (e.g..Burkeetal.1998)... ον0.101. could be taken as the upper limit for the wave spectrum.," The wave frequency obtained from laboratory experiments \citep[e.g.,][]{moralez..98}, $\Omega_{sup} \sim 0.1 \Omega_i$ , could be taken as the upper limit for the wave spectrum."607 On the other hand. Scheurwater showed that Allvénn wave [requencies can be greater than 107j.," On the other hand, \citet{scheur..88} showed that Alfvénn wave frequencies can be greater than $10^{-5} \Omega_i$."608 We. therefore. study the frequency interval 10.20;<Q<0.10;," We, therefore, study the frequency interval $10^{-5} \Omega_i \leq \Omega609\leq 0.1 \Omega_i$."610 Assuming this frequency spectrum. we caleulate the damping lengths and corresponding f.—(002)2/e4 parameter for all the damping mechanisms treated in section 3..," Assuming this frequency spectrum, we calculate the damping lengths and corresponding $f = \langle \delta v^2 \rangle^{1/2}611/ v_A$ parameter for all the damping mechanisms treated in section \ref{dampmech}."612 Thus. hereafter. f is not a [ree parameter anvmore.," Thus, hereafter, $f$ is not a free parameter anymore."613 We assume that the energy released by the damping of the Alfvénn waves in a given volume is radiated away., We assume that the energy released by the damping of the Alfvénn waves in a given volume is radiated away.614 Thus. we have πι = T1032) where I is given by Figure 2.. 7 is the optical clepth. σ is the Stefan-Doltzmann constant. and 2d. (he area.," Thus, we have dV = T^4 A, where $T$ is given by Figure \ref{fig2}, , $\tau$ is the optical depth, $\sigma$ is the Stefan-Boltzmann constant, and $A$, the area."615 For a given 7 and temperature profile. we know the amount of energy that is radiated away.," For a given $\tau$ and temperature profile, we know the amount of energy that is radiated away."616 This must be equal to the energy dissipated by the Alfvénn waves. which is determined by / and the damping mechanism usec.," This must be equal to the energy dissipated by the Alfvénn waves, which is determined by $f$ and the damping mechanism used."617 Figure 7 shows the results of our caleulations. which were made for three different values of the optical depth 7 and for 10?<F0.1.," Figure \ref{fig7} shows the results of our calculations, which were made for three different values of the optical depth $\tau$ and for $10^{-5}618\leq F \leq 0.1$."619 Since the star is nol strongly obscured bv the tube. it is Likely that the mean optical depth is less than 1.," Since the star is not strongly obscured by the tube, it is likely that the mean optical depth is less than 1."620 Taking into account the values of the adiabatic heating (Martin1996) and calculating the associated optical depth. we obtain 7~107.," Taking into account the values of the adiabatic heating \citep*{martin} and calculating the associated optical depth, we obtain $\tau \sim 10^{-3}$."621 However. lor the sakeof completeness. we made the calculations [or 7T=[0? and 7= Las well.," However, for the sakeof completeness, we made the calculations for $\tau = 10^{-2}$ and $\tau = 1$ as well."622 Figure 7 shows the damping lengths divided by the length of the tube. caleulated according to equation (32)). for the nonlinear and turbulent. damping mechanisms mentioned above.," Figure \ref{fig7} shows the damping lengths divided by the length of the tube, calculated according to equation \ref{consist}) ), for the nonlinear and turbulent damping mechanisms mentioned above."623 The left column of Figure 7. shows the nonlinear dampinglengths., The left column of Figure \ref{fig7} shows the nonlinear dampinglengths.624 We note that even [or 7=10? with the lowest frequeney (F=10 7). the damping length is less than the," We note that even for $\tau = 10^{-3}$ with the lowest frequency $(F = 10^{-5})$ , the damping length is less than the"625We have calculated the linear torque exerted by a planet on a circular orbit on a disc containing à toroidal magnetic field.,We have calculated the linear torque exerted by a planet on a circular orbit on a disc containing a toroidal magnetic field.626 In contrast to the nonmagnetic case. there is no singularity at the corotation radius. where the frequency of the perturbation matches the orbital frequency.," In contrast to the nonmagnetic case, there is no singularity at the corotation radius, where the frequency of the perturbation matches the orbital frequency."627 However. there are two new singularities on both sides of corotation. where the frequency of the perturbation in a frame rotating with the uid matches that of à slow MIID wave propagating along the field line.," However, there are two new singularities on both sides of corotation, where the frequency of the perturbation in a frame rotating with the fluid matches that of a slow MHD wave propagating along the field line."628 These socalledresonances are Closer to the planet than the Lindblad resonances., These so–called are closer to the planet than the Lindblad resonances.629 In addition. on each side of the planet. there are two turning points located bevond the magnetic resonance.," In addition, on each side of the planet, there are two turning points located beyond the magnetic resonance."630 One of them coinncides with the Lindblad resonance., One of them ncides with the Lindblad resonance.631 For values of m larger than some critical value moa. there is a third turning point between the magnetic resonance and corotation. on each side of the planet.," For values of $m$ larger than some critical value $m_{\rm632crit}$, there is a third turning point between the magnetic resonance and corotation, on each side of the planet."633 Like in the nonmagnetic case. waves propagate outside the outermost turning points.," Like in the nonmagnetic case, waves propagate outside the outermost turning points."634 But here they also propagate inside the intermediate turning points when mbmg. or between the intermediate and innermost turning points when mmo (see figure 1)).," But here they also propagate inside the intermediate turning points when $m<m_{\rm crit}$, or between the intermediate and innermost turning points when $m>m_{\rm crit}$ (see figure \ref{fig1}) )."635 The singular modes excited at the magnetic resonances can therefore propagate., The singular modes excited at the magnetic resonances can therefore propagate.636 There is a significant torque exerted on the region of the disc inside the outermost turning points (which comnnceide with the Lindblad resonances for the values of m of interest)., There is a significant torque exerted on the region of the disc inside the outermost turning points (which ncide with the Lindblad resonances for the values of $m$ of interest).637 Like the Lindblad torque. this torque is negative inside the planet's orbit and. positive outside its orbit.," Like the Lindblad torque, this torque is negative inside the planet's orbit and positive outside its orbit."638 Phe whole region around corotation. not just à narrow zone around the magnetic resonances. contribute to this torque.," The whole region around corotation, not just a narrow zone around the magnetic resonances, contribute to this torque."639 In other words. the magnetic resonances contribute to a global. not a point-like. torque.," In other words, the magnetic resonances contribute to a global, not a point-like, torque."640 Since these resonances are closer to the planet than the Lindblad resonances. they couple more strongly to the tidal potential.," Since these resonances are closer to the planet than the Lindblad resonances, they couple more strongly to the tidal potential."641 Pherefore. the torque exerted around the magnetic resonances dominate over the Lindblad torque if the magnetic field is large enough.," Therefore, the torque exerted around the magnetic resonances dominate over the Lindblad torque if the magnetic field is large enough."642 Lf in addition 3—c/e3 increases fast enough with radius. the outer magnetic resonance becomes less important (it disappears altogether when there is no magnetic field outside the planets orbit) and the total torque is then negative. dominated by the inner magnetic resonance.," If in addition $\beta \equiv c^2/v_A^2$ increases fast enough with radius, the outer magnetic resonance becomes less important (it disappears altogether when there is no magnetic field outside the planet's orbit) and the total torque is then negative, dominated by the inner magnetic resonance."643 This corresponds to à positive torque on the planet. which leads to outward migration.," This corresponds to a positive torque on the planet, which leads to outward migration."644 The amount by which 3 has to increase outward for the total torque exerted on the cise to be negative depends mainly on the magnitude of 3., The amount by which $\beta$ has to increase outward for the total torque exerted on the disc to be negative depends mainly on the magnitude of $\beta$.645 We have found that for 51 at corotation. the cumulative torque (obtained by summing up the contributions from all the values of m) exerted on the dise is negative when 2 increases at least as fast as r7.," We have found that for $\beta =1$ at corotation, the cumulative torque (obtained by summing up the contributions from all the values of $m$ ) exerted on the disc is negative when $\beta$ increases at least as fast as $r^2$."646 Wo x£c. the cumulative. torque becomes negative. for⋅ values of⋅ ή) between 107⊐ and 10. whereas it⋠⋠ is negative. for⋅ ην)=107Dp if 47Xa.1 ," If $\beta647\propto r^3$, the cumulative torque becomes negative for values of $\beta(r_p)$ between $10^2$ and 10, whereas it is negative for $\beta(r_p)=10^2$ if $\beta \propto r^4$."648The migration timescales that correspond to the torques calculated above are rather short., The migration timescales that correspond to the torques calculated above are rather short.649" The orbital decay timescale of a planet of mass AM, at radius ry, is 7=M,FO,EAL). where 1) is the cumulative torque exerted by the planet on the disc."," The orbital decay timescale of a planet of mass $M_p$ at radius $r_p$ is $\tau = M_p r_p^2 \Omega_p / |T|$, where $T$ is the cumulative torque exerted by the planet on the disc."650" Remembering that Pox(AL,/AL Νο get: In a standard dise model. X~100. 10 & em2 at Lau (see. for instance. Papaloizou Terquem. 1999)."," Remembering that $T \propto (M_p/M_\ast)^2$, we get: In a standard disc model, $\Sigma \sim651100$ $10^3$ g $^{-2}$ at 1 au (see, for instance, Papaloizou Terquem 1999)."652" Pherefore. 7~10 10"" vr for a one earth mass planet at 1 au in à nonmagnetic disc. as 7~10? in that case (sce fig. 113)."," Therefore, $\tau \sim 10^5$ $10^6$ yr for a one earth mass planet at 1 au in a nonmagnetic disc, as $\tilde{T} \sim 10^3$ in that case (see fig. \ref{fig6}) )."653 This is in agreement with Ward (1986. 1997).," This is in agreement with Ward (1986, 1997)."654 In a magnetic disc. |Z] may become larger. leading to an even shorter migration timescale (note that given the limited accuracy of the numerical scheme used. as indicated in section 7.2.2.. only orders of magnitude for the migration timescale are obtained here).," In a magnetic disc, $|\tilde{T}|$ may become larger, leading to an even shorter migration timescale (note that given the limited accuracy of the numerical scheme used, as indicated in section \ref{sec:caseBne0}, only orders of magnitude for the migration timescale are obtained here)."655 However. it: is important to keep in mind that these timescales arefecal.," However, it is important to keep in mind that these timescales are."656 Once the planet. migrates outward out of the region where 2 increases with radius. it may enter a region where 3 behaves dillerently and then resume inward migration for instance.," Once the planet migrates outward out of the region where $\beta$ increases with radius, it may enter a region where $\beta$ behaves differently and then resume inward migration for instance."657 Such a situation would be expected to occur in a turbulent magnetized cise in which the large scale field structure changes sullicicntly slowly., Such a situation would be expected to occur in a turbulent magnetized disc in which the large scale field structure changes sufficiently slowly.658 Unless the magnetic field is above equipartition. it is unstable by the magnetorotational instability (Balbus Haley 1991. 1998 and references therein). the saturated nonlinear outcome of which is MIID turbulence.," Unless the magnetic field is above equipartition, it is unstable by the magnetorotational instability (Balbus Hawley 1991, 1998 and references therein), the saturated nonlinear outcome of which is MHD turbulence."659 In a turbulent magnetized cisc. the main component of the field is toroidal. as shown by numerical simulations (Llawley. Ganmmic Balbus 1995: Brandenburg et al.," In a turbulent magnetized disc, the main component of the field is toroidal, as shown by numerical simulations (Hawley, Gammie Balbus 1995; Brandenburg et al."660 1995)., 1995).661 Global simulations have also shown that the turbulence saturates at a level corresponding to 3LOO if there is no mean flux or to lower values of 3 if there is a mean flux (Llawley 2001: Steinacker Papaloizou 2002)., Global simulations have also shown that the turbulence saturates at a level corresponding to $\beta \sim 100$ if there is no mean flux or to lower values of $\beta$ if there is a mean flux (Hawley 2001; Steinacker Papaloizou 2002).662 Also. substantial spatial inhomogeneities are created by racial variations of the Maxwell stress (Lawlev 2001: Steinacker Papaloizou 2002). so that the field may display significant eradients.," Also, substantial spatial inhomogeneities are created by radial variations of the Maxwell stress (Hawley 2001; Steinacker Papaloizou 2002), so that the field may display significant gradients."663 On the basis of the work presented here. we are Led to speculate that in such a disc the planet would sulfer alternately inward and outward migration. or even no migration at all.," On the basis of the work presented here, we are led to speculate that in such a disc the planet would suffer alternately inward and outward migration, or even no migration at all."664 lt would then oscillates back and forth in some region of the disc. or undergo some kind of dilfusive migration. either outward or inward depending on the field gradients encountered.," It would then oscillates back and forth in some region of the disc, or undergo some kind of diffusive migration, either outward or inward depending on the field gradients encountered."665 Note however that in a turbulent cise the magnetic field may. vary locally on timescales shorter than the timescales needed to establish the tvpe of tidal response assumed in this paper., Note however that in a turbulent disc the magnetic field may vary locally on timescales shorter than the timescales needed to establish the type of tidal response assumed in this paper.666 lt has been pointed out that protoplanctary dises may be ionized enough for the magnetic field to couple to the matter only in their innermost and outermost parts (Cammie 1996: Eromang. TFerquem Balbus 2002).," It has been pointed out that protoplanetary discs may be ionized enough for the magnetic field to couple to the matter only in their innermost and outermost parts (Gammie 1996; Fromang, Terquem Balbus 2002)."667 A planet forming at around one astronomical unit. where the ionization fraction is very low. would then migrate inward on the timescale calculated by Ware (10560. L997) until it reaches smaller radii where the field is coupled to the matter.," A planet forming at around one astronomical unit, where the ionization fraction is very low, would then migrate inward on the timescale calculated by Ward (1986, 1997) until it reaches smaller radii where the field is coupled to the matter."668 At this point. there would be a magnetic field inside the planet's orbit but not outside its orbit.," At this point, there would be a magnetic field inside the planet's orbit but not outside its orbit."669 Ehe torque on the planet would then reverse. and. outward migration would occur.," The torque on the planet would then reverse, and outward migration would occur."670 However. as soon as the planet would. reenter the nonmagnetic region. inward. migration would resume.," However, as soon as the planet would re–enter the nonmagnetic region, inward migration would resume."671 Hence. the planet would stall at the border between the magnetic and nonmagnetic regions.," Hence, the planet would stall at the border between the magnetic and nonmagnetic regions."672 lnwarcl migration in a magnetized disc may then either be very significantly slowed down. occur only on limited. scales. or not occur at all.," Inward migration in a magnetized disc may then either be very significantly slowed down, occur only on limited scales, or not occur at all."673 Phe planet would then be able to grow to become a terrestrial planet or the core of a giant planet., The planet would then be able to grow to become a terrestrial planet or the core of a giant planet.674 When the planet becomes massive enough (about 10 earth masses). the interaction with the dise becomes nonlinear. with a eap being opened. up around the planets orbit.," When the planet becomes massive enough (about 10 earth masses), the interaction with the disc becomes nonlinear, with a gap being opened up around the planet's orbit."675" Because a rather strong torque is exerted in the vicinity of the planet in the presence of a magnetic field. a gap should open up more easily and be ""cleaner in a turbulent magnetic disc than in a"," Because a rather strong torque is exerted in the vicinity of the planet in the presence of a magnetic field, a gap should open up more easily and be 'cleaner' in a turbulent magnetic disc than in a"676instability is shown to exist in the linear regime.,instability is shown to exist in the linear regime.677 To test the magnetic field amplification model against observations one needs to determine the saturated magnetic field accurately., To test the magnetic field amplification model against observations one needs to determine the saturated magnetic field accurately.678 The saturation of the instability cannot be determined in linear theory as the reaction of the instability on the Ch momentun distribution is not automatically included in the linear calculation., The saturation of the instability cannot be determined in linear theory as the reaction of the instability on the CR momemtum distribution is not automatically included in the linear calculation.679 Although there are numerical simulations of the instability that extend to the nonlinear regime. different: saturation levels have been predicted: (Niemiec. 2008).," Although there are numerical simulations of the instability that extend to the nonlinear regime, different saturation levels have been predicted \citep{netal08,rs08}."680. In this paper. the instability is discussed in the quasilinear formalism in which the reaction of the instability on the CR. distribution can be included. self-consistentlv.," In this paper, the instability is discussed in the quasilinear formalism in which the reaction of the instability on the CR distribution can be included self-consistently."681 So. in this formalism one can estimate the saturation analvticallv. with both nonresonant and resonant clüffusion orocesses considered.," So, in this formalism one can estimate the saturation analytically, with both nonresonant and resonant diffusion processes considered."682 The. treatment of the nonresonant diffusion presented. here is similar to that used. for the irehose instability. (Davidson1972)., The treatment of the nonresonant diffusion presented here is similar to that used for the firehose instability \citep{d72}.683. We emphasize the major difference between the Cl streaming instability and he firehose instability., We emphasize the major difference between the CR streaming instability and the firehose instability.684 Phe former is caused by streaming motion and the latter is due to a pressure anisotropy with excess of parallel pressure over. the perpendicular oessure (with respect to the mean magnetic field)., The former is caused by streaming motion and the latter is due to a pressure anisotropy with excess of parallel pressure over the perpendicular pressure (with respect to the mean magnetic field).685 To some extent. the streaming instability also resembles the Weibel instabilitya nonresonant. purely growing mocdoe driven by anisotropy in the particle distribution (Weibel1959).," To some extent, the streaming instability also resembles the Weibel instability—a nonresonant, purely growing mode driven by anisotropy in the particle distribution \citep{w59}."686. In Sec 2 the kinetic theory of CR streaming instabilities is discussed with emphasis on the nonresonant instability., In Sec 2 the kinetic theory of CR streaming instabilities is discussed with emphasis on the nonresonant instability.687 Quasilinear cilfusion driven by the nonresonant instability is discussed. in both the short anc lone wavelength approximations in the nonresonant regime in Sec 3 and in the resonant regime in Sec 4., Quasilinear diffusion driven by the nonresonant instability is discussed in both the short and long wavelength approximations in the nonresonant regime in Sec 3 and in the resonant regime in Sec 4.688 Application to SN shocks is discussed in Sec 5., Application to SN shocks is discussed in Sec 5.689 We outline the kinetic theory of CR streaming instabilities including both the usual resonant instability ancl the nonresonant instability and focus particularly on the latter., We outline the kinetic theory of CR streaming instabilities including both the usual resonant instability and the nonresonant instability and focus particularly on the latter.690 Our treatment builds on other recent. discussions of linear kinetic theory of the CR-induced nonresonant instability (Reville.Wirk&Dully2006:AmatoBlasi2008).," Our treatment builds on other recent discussions of linear kinetic theory of the CR-induced nonresonant instability \citep{retal06,ab08}."691.. For convenience we assume a single species of CRs with charge q and mass m., For convenience we assume a single species of CRs with charge $q$ and mass $m$ .692 To model CR streaming at velocity cj; along the mean magnetic field we consider a class of streamingdistributions in momentum space eiven by where and vy are the nondimensional momenta (normalized wy)by me) parallel andperpendicular to the mean magnetic field. respectively. σ is an integer =Lo meu: is the CR number density. e is the ClUs velocity written as a function⋅. of ej and ny. w=(32|2AL/2uc. and For the standard. DSA one has p=2 (Bell1978:Drury1983) and when the nonlinear ellect on DSA is included. p deviates from this canonical value (Kichler1984).," To model CR streaming at velocity $v_{CR}$ along the mean magnetic field we consider a class of streamingdistributions in momentum space given by where $u_\parallel$ and $u_\perp$ are the nondimensional momenta (normalized by $mc$ ) parallel andperpendicular to the mean magnetic field, respectively, $\sigma$ is an integer $\geq1$, $n_{CR}$ is the CR number density, $v$ is the CR's velocity written as a function of $u_\parallel$ and $u_\perp$, $u=(u^2_\perp+u^2_\parallel)^{1/2}$, and For the standard DSA one has $p=2$ \citep{b78,d83} and when the nonlinear effect on DSA is included, $p$ deviates from this canonical value \citep{e84}."693.. Ehe distribution with σ=1 corresponds to that used in (1986)., The distribution with $\sigma=1$ corresponds to that used in \citet{m86}.694. The distribution (1)) implies where cosaoyfi , The distribution \ref{eq:fcr}) ) implies where $\cos\alpha\equiv u_\parallel/u$.695In the second expression in (3)). one chooses (8.0) in place of (yori) as independent variables.," In the second expression in \ref{eq:ncr}) ), one chooses $(u,\alpha)$ in place of $(u_\parallel,u_\perp)$ as independent variables."696 Ho can be verified. that averaging the parallel velocity ey; over the distribution (1)) gives the streaming velocity. neg. which is independent. of the choice of the xvwameter o.," It can be verified that averaging the parallel velocity $v_\parallel$ over the distribution \ref{eq:fcr}) ) gives the streaming velocity $v_{CR}$, which is independent of the choice of the parameter $\sigma$."697" The Cl current is then given by dey,=quent.", The CR current is then given by $J_{CR}=qn_{CR}v_{_{\rm CR}}$ .698 Phe presence of streaming. CRs allects the rvackeround plasma in two wavs. due to their charge density and their. current. density. respectively.," The presence of streaming CRs affects the background plasma in two ways, due to their charge density and their current density, respectively."699 The background Xdasma must have a charge density and a current. density hat are equal and opposite to those of the ος., The background plasma must have a charge density and a current density that are equal and opposite to those of the CRs.700 This requires that the electrons and ions (assumed to be protons) rave dilferent charge densities. n.zny. and that they move relative to cach other with streaming velocities οxzey). which are assumed to be along the guiding magnetic field.," This requires that the electrons and ions (assumed to be protons) have different charge densities, $n_e\ne n_p$, and that they move relative to each other with streaming velocities $v_e\ne v_p$, which are assumed to be along the guiding magnetic field."701 The neutralization conditions require (Achterberg1983) These properties of the background. plasma drive the nonresonant instability attributed to the Clts., The neutralization conditions require \citep{a83} These properties of the background plasma drive the nonresonant instability attributed to the CRs.702 A formal procedure to derive the dispersion relation involves separating the plasma response tensor into that for a background. plasma. denoted by νεο plus that for the CR component. denoted by νε.," A formal procedure to derive the dispersion relation involves separating the plasma response tensor into that for a background plasma, denoted by $K_{ij}$, plus that for the CR component, denoted by $\Delta K_{ij}$."703 The background plasma can be regarded as a cold. magnetizecl plasma. while the CR component is described by the distribution. (1)).," The background plasma can be regarded as a cold, magnetized plasma, while the CR component is described by the distribution \ref{eq:fcr}) )."704 Assume that the gvrofrequeney ofCRs is 2=[q|D/m. where B is the mean background magnetic field.," Assume that the gyrofrequency of CRs is $\Omega=|q|B/m$, where $B$ is the mean background magnetic field."705 A useful approximation is Ακ1. where Ay is the perpendicular wave number. OQ=Ofs and ~=(1|u7)-7 is the Lorentz factor. of CRs.," A useful approximation is $k_\perp v_\perp/\tilde{\Omega}\ll1$, where $k_\perp$ is the perpendicular wave number, $\tilde{\Omega}=\Omega/\gamma$ and $\gamma=(1+u^2)^{1/2}$ is the Lorentz factor of CRs."706 The approximation implies thatin the response tensor. only the first evroharmonies terms are important.," The approximation implies thatin the response tensor, only the first gyroharmonics terms are important."707" For the background. plasma. one assumes (4A«C and the low- approximations.c« Όλα)JApey| and o«x ο, where ©; is the evrolrequeney of ions in the background plasma."," For the background plasma, one assumes $v^2_A\ll c^2$ and the low-frequency approximations,$\omega\ll\Omega_i$ , $\omega\ll |k_\parallel v_\parallel|$ and $\omega\ll708\tilde{\Omega}$ , where $\Omega_i$ is the gyrofrequency of ions in the background plasma."709 The background: magnetic field. is assumed. to be along the 3-axis., The background magnetic field is assumed to be along the 3-axis.710 Since AsusxOFfw2 can be set to ox. only the 2;2 components of the response tensor are relevant.," Since $K_{33}\propto \Omega^2_i/\omega^2$ can be set to $\infty$ , only the $2\times2$ components of the response tensor are relevant."711 For the background plasma. these components can be written as," For the background plasma, these components can be written as"712"Ἐνοςvif? spectrum derived for the range around GGHz: The spectral index d£,/dv between GGHz and the K band amounts to <0.39.",$F_\nu \propto \nu^{1/3}$ spectrum derived for the range around GHz: The spectral index ${\rm d}F_\nu / {\rm d}\nu$ between GHz and the K band amounts to $\le 0.39$.713" We note that this value is very similar to that of other galactic nuclei, like Sgr A* (BDM96), 881 (Reuter and Lesch 1996); 1104 (Jauch and Duschl, in prep.),"," We note that this value is very similar to that of other galactic nuclei, like Sgr A* (BDM96), 81 (Reuter and Lesch 1996); 104 (Jauch and Duschl, in prep.),"714 where a=1/3., where $\alpha = 1/3$.715" If NGC 1068 has the same spectral shape as these other galactic nuclei, then a fraction of F7?""** could indeed be contributed from the nucleus of NGC 1068."," If NGC 1068 has the same spectral shape as these other galactic nuclei, then a fraction of $F_{\rm K}^{\rm 30\,mas}$ could indeed be contributed from the nucleus of NGC 1068."716" However, one has to admit that very little is known about the true nuclear spectrum of 11068 in the intermediate frequency range."," However, one has to admit that very little is known about the true nuclear spectrum of 1068 in the intermediate frequency range."717" To persue our speculation, we assume — as a working hypothesis — that also between GGHz and the IR range, the spectrum goes like v!/?."," To persue our speculation, we assume – as a working hypothesis – that also between GHz and the IR range, the spectrum goes like $\nu^{1/3}$."718 We then follow BDM96 and interpret this as optically thin synchrotron radiation of quasi-monoenergetic electrons., We then follow BDM96 and interpret this as optically thin synchrotron radiation of quasi-monoenergetic electrons.719" The mean electron energy then is fairly well constrained since the maximum of ΓΡ has to be at frequencies above the K band, but not much higher as otherwise the total nuclear flux from the center of 11068 would be too large."," The mean electron energy then is fairly well constrained since the maximum of $F_\nu^{\rm nuc}$ has to be at frequencies above the K band, but not much higher as otherwise the total nuclear flux from the center of 1068 would be too large."720 The situation is less clear with the SSA frequency., The situation is less clear with the SSA frequency.721 We cannot rule out that SSA in fact occurs at frequencies even smaller than GGHz., We cannot rule out that SSA in fact occurs at frequencies even smaller than GHz.722" As a consequence of this, the source radius discussed below is only a lower limit."," As a consequence of this, the source radius discussed below is only a lower limit."723 For details we refer the reader toBDM96!.., For details we refer the reader to.724" If we assume that the maximum of P7""* is indeed achieved around um, and that SSA of the source becomes important for frequencies below GGHz, we find as emitting region a homogeneous sphere of radius R~ 2105?cm (~0.7mpc~130AU0.01 mas) with a magnetic field B~ 11G (assumed to be the same everywhere in this region)."," If we assume that the maximum of $F_\nu^{\rm nuc}$ is indeed achieved around $\mu$ m, and that SSA of the source becomes important for frequencies below GHz, we find as emitting region a homogeneous sphere of radius $R \sim 7252\,10^{15}\,$ cm $\sim 0.7\,{\rm 726mpc}\sim 130\,{\rm AU\sim 0.01\,mas}$ ) with a magnetic field $B \sim 11\,$ G (assumed to be the same everywhere in this region)."727" The relativistic electrons have a number density ne1.110? cm-?, a mean energy E~2.7 GeV and a width of the energy distribution AE/E~1."," The relativistic electrons have a number density $n_{\rm e} \sim 1.1\,10^3\,{\rm cm}^{-3}$ , a mean energy $E \sim 2.7\,$ GeV and a width of the energy distribution $\Delta E / 728E \sim 1$."729 In reffigspect wwe show a comparison of the observed fluxes of 11068 core and our model spectrum using the above parameters., In \\ref{figspect} we show a comparison of the observed fluxes of 1068 core and our model spectrum using the above parameters.730" If our speculation applies, it turns out that the main difference between 11068 and other galactic centers analysed on the basis of the same interpretation (Sgr A*: BDM96; 881: Reuter and Lesch 1996; 1104: Jauch and Duschl, in prep.)"," If our speculation applies, it turns out that the main difference between 1068 and other galactic centers analysed on the basis of the same interpretation (Sgr A*: BDM96; 81: Reuter and Lesch 1996; 104: Jauch and Duschl, in prep.)"731 are the source radius and - especially - the energy of the relativistic electrons., are the source radius and - especially - the energy of the relativistic electrons.732" The above size of mmas means that our resolved mmas object is not the synchrotron source itself but rather a larger object, most likely the nuclear torus and/or a circumnuclear scattering halo."," The above size of mas means that our resolved mas object is not the synchrotron source itself but rather a larger object, most likely the nuclear torus and/or a circumnuclear scattering halo."733 We have resolved a compact source with a diameter of dGaussv30 mas in the core of 11068.," We have resolved a compact source with a diameter of $d_{\rm Gauss}\sim 73430\,$ mas in the core of 1068."735 This object is most likely a nuclear torus and/or a circumnuclear scattering halo., This object is most likely a nuclear torus and/or a circumnuclear scattering halo.736 Part of the radiation from the central mmas may be light from the nucleus scattered in the halo., Part of the radiation from the central mas may be light from the nucleus scattered in the halo.737" Under this assumption, we were able to determine physical parameters of the nucleus and compare them to other galactic centers, active and non-active ones."," Under this assumption, we were able to determine physical parameters of the nucleus and compare them to other galactic centers, active and non-active ones."738 One then is tempted to speculate that the higher efficiency of the acceleration mechanism for the electrons may be the true difference between an active galactic center and a normalone., One then is tempted to speculate that the higher efficiency of the acceleration mechanism for the electrons may be the true difference between an active galactic center and a normalone.739emission was found in the radio survey of Filipovic et al. (,emission was found in the radio survey of Filipović et al. (7401998) and they are candidates for AGNs.,1998) and they are candidates for AGNs.741 The source No., The source No.742 103 (RX J0054.9-7226) is identified with the XTE J0055-724 = 1SAX J0054.9-7226 source (Marshall et al., 103 (RX J0054.9-7226) is identified with the XTE J0055-724 = 1SAX J0054.9-7226 source (Marshall et al.743" 1998, Israel 1998)."," 1998, Israel 1998)."744 The detection of pulsations with a period of 59 s withBeppoSAX confirm the X-ray binary nature of this source., The detection of pulsations with a period of 59 s with confirm the X-ray binary nature of this source.745 Stevens et al. (, Stevens et al. (746"1998) identified early type emission-line stars through colour indices and Ha emission for the sources with catalogue indices 3, 69, 103, and 158.","1998) identified early type emission-line stars through colour indices and $\alpha$ emission for the sources with catalogue indices 3, 69, 103, and 158."747 The source No., The source No.748 153 (RX J0100.7-7211) was considered to be consistent with a background AGN shining through the SMC bulge (Paper I)., 153 (RX J0100.7-7211) was considered to be consistent with a background AGN shining through the SMC bulge (Paper I).749 Sources No., Sources No.750 157 and 160 were found to coincide with detector struts and were rejected accordingly (Paper I)., 157 and 160 were found to coincide with detector struts and were rejected accordingly (Paper I).751 Weak hard X-ray binaries are an interesting class of objects as they have been predicted to exist and their number is expected to be large especially in galaxies of low metallicity like the SMC., Weak hard X-ray binaries are an interesting class of objects as they have been predicted to exist and their number is expected to be large especially in galaxies of low metallicity like the SMC.752 In previous work (Bruhweiler et al., In previous work (Bruhweiler et al.753 1987; Wang Wu 1992) candidates for such sources have been found and either classified as low luminosity Be systems or as background objects., 1987; Wang Wu 1992) candidates for such sources have been found and either classified as low luminosity Be systems or as background objects.754" Here, we are searching for candidates of this class by applying the same selection criteria as for the strong (or higher luminosity) hard X-ray binaries as outlined in Paper I:0.5,, and extent likelihood<50."," Here, we are searching for candidates of this class by applying the same selection criteria as for the strong (or higher luminosity) hard X-ray binaries as outlined in Paper I:, and extent likelihood."755". The only difference is to select objects with count rates ofs-!,, i.e. with luminosities below assuming a standard spectral model for the source flux (Paper I)."," The only difference is to select objects with count rates of, i.e. with luminosities below assuming a standard spectral model for the source flux (Paper I)."756 There are 60 such objects and we tentatively classify these sources as class=Bw., There are 60 such objects and we tentatively classify these sources as class=Bw.757 This class is a substantial fraction (25%)) of the total catalogue entries and turns out to be the class with most members., This class is a substantial fraction ) of the total catalogue entries and turns out to be the class with most members.758 We find 15 of these objects which coincide with ddetections., We find 15 of these objects which coincide with detections.759 This may reflect that we are considerably, This may reflect that we are considerably760for LIIS 147 and LIIS 542 are taken from BLR. and for LIIS 4033 from Dahnοἱal.(2004).,"for LHS 147 and LHS 542 are taken from BLR, and for LHS 4033 from \citet{dahn04}."761. Out of the 32 objects listed in Table 1. 22 have J///¥ measurements. 5 only have J and IH. while 2 have no infrared data.," Out of the 32 objects listed in Table 1, 22 have $JHK$ measurements, 8 only have $J$ and $H$, while 2 have no infrared data."762 Also reported in Table 1 ave the infrared. photometric uncertainties (in parentheses) aud (he number of independent observations., Also reported in Table 1 are the infrared photometric uncertainties (in parentheses) and the number of independent observations.763 The model atmospheres used in (his analysis are described al length in Bergeronetal.BRLandBL) with the collision-induced opacities Hom molecular hydrogen updated [rom the work of Jorgensenetal.(2000) and Borvsowetal.(2001)., The model atmospheres used in this analysis are described at length in \citet[][see also BRL and BLR]{bsw95} with the collision-induced opacities from molecular hydrogen updated from the work of \citet{jorgensen} and \citet{borysow01}.764. These models are in local thermodynamic equilibrium. they allow energv transport by convection. aud they can be caleulated with arbitrary mixed hydrogen ancl helium compositions.," These models are in local thermodynamic equilibrium, they allow energy transport by convection, and they can be calculated with arbitrary mixed hydrogen and helium compositions."765 Synthetic are obtained using the procedure outlined in Bergeronοἱal.(1995b) but with the new Vega [Iuxes taken from Bohlin&Gilliland(2004) and the Vega magnitudes from Table Al of Besselletal.(1998)., Synthetic are obtained using the procedure outlined in \citet{bwb95} but with the new Vega fluxes taken from \citet{bohlin04} and the Vega magnitudes from Table A1 of \citet{bessell98}.766". Similarly. in order to compare the photometric observations with the model atmosphere predictions. we convert (see also BRL) the optical and infrared magnitudes mz into observed [fluxes averaged over (he transmission function S4,CLÀX)HEN usinge the followinge equation where is the averaged observed fIux received at Earth."," Similarly, in order to compare the photometric observations with the model atmosphere predictions, we convert (see also BRL) the optical and infrared magnitudes $m$ into observed fluxes averaged over the transmission function $S_m(\lambda)$ using the following equation where is the averaged observed flux received at Earth."767" The transmission functions $,(À) are taken from Bessell(1990). flor the DVRJ fillers on the Johnson-Cousins photometric system. ancl from Bessell&Brett(1988) [or the 7L fillers on the Johnson-Glass svstem."," The transmission functions $S_m(\lambda)$ are taken from \citet{bessell90} for the $BVRI$ filters on the Johnson-Cousins photometric system, and from \citet{bessell88} for the $JHK$ filters on the Johnson-Glass system."768" The constants €,, loreach passband using the new fluxes and zero points [or Vega are ej=—20.4761. cy=—21.00708. eg,=—21.6300. e;=—22.3480. e,=--ο411. ej;=—24.8281. and Cxdy=—25.9877."," The constants $c_m$ foreach passband using the new fluxes and zero points for Vega are $c_B=-20.4761$, $c_V=-21.0798$, $c_R=-21.6300$, $c_I=-22.3480$, $c_J=-23.7417$, $c_H=-24.8387$, and $c_K=-25.9877$."769 These constants differ slightlvo [rom those used by BRL and BLR. whichwere based on older Vega fluxes.," These constants differ slightly from those used by BRL and BLR, whichwere based on older Vega fluxes."770" Note also that with this new calibration. the +0.05 mag correction determined empirically ancl applied by BRL to the J. 1, and A constants is nol required here (see 5.2.1 of BRL)."," Note also that with this new calibration, the +0.05 mag correction determined empirically and applied by BRL to the $J$ , $H$ , and $K$ constants is not required here (see 5.2.1 of BRL)."771"same model outlined in section 4.1 applied to Ser A. it would predict an outer radius of the outflow of about may22.510? Schwarzschild radii (~ 0.0257 at the distance of the galactic center) and an inner accretion rate ALAa)Alas""4.10"" AL.f yr. also consistent with the gas density in the inner accretion flow implied by linear polarization measurements (Aitkenetal.2000:Boweretal.2003: 2005).","same model outlined in section \ref{sec:model} applied to Sgr $^{*}$, it would predict an outer radius of the outflow of about $r_{\rm out}\approx 2.5 \times77210^{3}$ Schwarzschild radii $\sim 0.025$ ” at the distance of the galactic center) and an inner accretion rate $\dot M_{\rm a}(r_{\rm773in})=\dot M_{\rm out} \xi^{p} \simeq 4 \times 10^{-9}$ $M_{\odot}/$ yr, also consistent with the gas density in the inner accretion flow implied by linear polarization measurements \cite{aitken:00,bower:03,bower:05}."774". Altogether. this would indicate that the SMBH at the galactic center is the source of about ο1077 ergs ! of mechanical power (similar to what estimated within jet model fits to Ser A* SED. see e.g. Falcke Biermann 1999, Falcke Markoff 2000). or about 1.5 supernovae every 10 years."," Altogether, this would indicate that the SMBH at the galactic center is the source of about $5\times77510^{38}$ ergs $^{-1}$ of mechanical power (similar to what estimated within jet model fits to Sgr $^{*}$ SED, see e.g. Falcke Biermann 1999, Falcke Markoff 2000), or about 1.5 supernovae every $^5$ years."776 Such a mechanical power input into the galactic center could play a significant role in the production of the TeV ~-rays recently observed by the HESS (High Energy Stereoscopic System) collaboration (Aharonianetal.2004: 2004)... as well as in the heating of the hot (>S keV) diffused plasma detected by (Munoetal.2004).," Such a mechanical power input into the galactic center could play a significant role in the production of the TeV $\gamma$ -rays recently observed by the HESS (High Energy Stereoscopic System) collaboration \cite{aharonian:04,atoyan:04}, as well as in the heating of the hot $> 8$ keV) diffused plasma detected by \cite{muno:04}."777. In section 3.. we have concentrated our attention on the assessment of the effects of relativistic beaming on the measured slope of the Lyin-Lp correlation.," In section \ref{sec:rad}, we have concentrated our attention on the assessment of the effects of relativistic beaming on the measured slope of the $L_{\rm kin}$ $L_{\rm R}$ correlation."778 However. one should expect a second source of scatter in any correlation between kinetic power and nuclear luminosity tin any waveband).," However, one should expect a second source of scatter in any correlation between kinetic power and nuclear luminosity (in any waveband)."779 The large scale power is an average over the typical age of the cavities and bubbles observed in the atmosphere of the galaxies in our sample., The large scale power is an average over the typical age of the cavities and bubbles observed in the X-ray atmosphere of the galaxies in our sample.780 Such an age may be assumed to be of the order of either the buoyant rise time. or the sound crossing time. or the refill time of the radio lobes (Birzan 2004).," Such an age may be assumed to be of the order of either the buoyant rise time, or the sound crossing time, or the refill time of the radio lobes \cite{birzan:04}."781. These estimates typically differ by about a factor of 2. and. for the sample in question. lie in the range {μον10τοῦ yeurs.," These estimates typically differ by about a factor of 2, and, for the sample in question, lie in the range $t_{\rm782age} \sim 10^7 - 10^8$ years."783 On the other hand. the core power is variable on time scale much shorter than that.," On the other hand, the core power is variable on time scale much shorter than that."784 The bias introduced by this fact can be quantitied as follows., The bias introduced by this fact can be quantified as follows.785 First of all. we notice that AGN X-ray lighteurves. where most of the accretion poweremerges. show a characteristic rms-flux relation which implies they have a formally non-linear. exponential form (Uttley.McHardy&Vaughan2005).. and the luminosity follows a log-normal distribution (Nipoti&Binney2005).," First of all, we notice that AGN X-ray lightcurves, where most of the accretion power emerges, show a characteristic rms-flux relation which implies they have a formally non-linear, exponential form \cite{uttley:05}, and the luminosity follows a log-normal distribution \cite{nipoti:05}."786.. Let us. for the sake of simplicity. define as L(/) the luminosity of the AGN. be it bolometric. Kinetic or radio. under the implicit assumption that very close to the central engine jet and accretion are strongly coupled. so that all of them follow a log- distribution.," Let us, for the sake of simplicity, define as $L(t)$ the luminosity of the AGN, be it bolometric, kinetic or radio, under the implicit assumption that very close to the central engine jet and accretion are strongly coupled, so that all of them follow a log-normal distribution."787 Thus. logL is normally distributed with mean jii and variance στ.," Thus, $\log L$ is normally distributed with mean $\mu_l$ and variance $\sigma_l^2$."788" The measured kinetic power Z1, discussed in this work being a long-term time average. it should be determined by the mean of the log-normally distributed £L. ie. (£)=ppexptr|07/2)."," The measured kinetic power $L_{\rm kin}$ discussed in this work being a long-term time average, it should be determined by the mean of the log-normally distributed $L$, i.e. $\langle L \rangle=\mu=\exp{(\mu_l^2+\sigma_l^2/2)}$ ."789 Because the log-normal distribution is positively skewed. the mode nz of the distribution of £L. i.e. the most likely value of a measurement of it. Lou. 18 than the mean: Lasom=expí(qu07).," Because the log-normal distribution is positively skewed, the mode $m$ of the distribution of $L$, i.e. the most likely value of a measurement of it, $L_{\rm obs}$, is than the mean: $L_{\rm790obs}=m=\exp{(\mu_l-\sigma_l^2)}$."791 Therefore the most likely value of the ratio of the mean to the observed luminosity is given by (Nipoti Binney 2005: Uttley et al., Therefore the most likely value of the ratio of the mean to the observed luminosity is given by (Nipoti Binney 2005; Uttley et al.792 2005): where we have introduced the rms (fractional) variability of the observed lightcurve σue=oxpayl.an easily measurable quantity.," 2005): where we have introduced the rms (fractional) variability of the observed lightcurve $\sigma_{\rm rms}^2=\exp{\sigma_l^2}-1$, an easily measurable quantity."793 The higher the rms variability of a lighteurve. the higher is the probability that an instantaneous measurement of the luminosity yields a value smaller than (£5 (Nipoti& 2005). and also the higher the most likely ratio between the two values.," The higher the rms variability of a lightcurve, the higher is the probability that an instantaneous measurement of the luminosity yields a value smaller than $\langle L \rangle$ \cite{nipoti:05}, and also the higher the most likely ratio between the two values."794 Before discussing what are the appropriate values of σημ.2 to be used in Eq. (14)).," Before discussing what are the appropriate values of $\sigma_{\rm795rms}^2$ to be used in Eq. \ref{eq:rms}) ),"796 we also note that the observed slope of the £L5- Lai; correlation may deviate from unity for a log-normal distribution. thus skewing any observed correlation between mean and instantaneous power. like those we have discussed so far.," we also note that the observed slope of the $\langle L \rangle$ $L_{\rm obs}$ correlation may deviate from unity for a log-normal distribution, thus skewing any observed correlation between mean and instantaneous power, like those we have discussed so far."797 It is easy to show that from Eq. (1+)), It is easy to show that from Eq. \ref{eq:rms}) )798 we obtain: Log-normal AGN variability may thus skew the observed relation between jet average kinetic power and instantaneous core luminosity much in the same way relativistic beaming does., we obtain: Log-normal AGN variability may thus skew the observed relation between jet average kinetic power and instantaneous core luminosity much in the same way relativistic beaming does.799 Inspection of Eqs. (14)), Inspection of Eqs. \ref{eq:rms}) )800" and (15)) suggests that the measured slopes of any correlation of the (average) kinetic vs. core power will be substantially affected by variability if. and only if. both στmas, and logevus/0logLa are at least of the order of unity."," and \ref{eq:rms-slope}) ) suggests that the measured slopes of any correlation of the (average) kinetic vs, core power will be substantially affected by variability if, and only if, both $\sigma_{\rm rms}^2$ and $\partial \log \sigma_{\rm rms}^2 /\partial801\log L_{\rm obs}$ are at least of the order of unity."802 Unfortunately. very little is known observationally about the variability amplitude of AGN on very long timescales. especially or AGN of low luminosity as those considered here.," Unfortunately, very little is known observationally about the variability amplitude of AGN on very long timescales, especially for AGN of low luminosity as those considered here."803 Brighter AGN (Seyferts}). on shorter timescales (1-10 years). have indeed rms variability amplitudes that rise steeply with decreasing luminosity. rom about a5.c107 for LxeLol up to ayy.3«LO1 or Lsez1077 (Nandraetal.1997:Markowitz&Edelson2001).," Brighter AGN (Seyferts), on shorter timescales (1-10 years), have indeed rms variability amplitudes that rise steeply with decreasing luminosity, from about $\sigma_{\rm rms}^2 \approx 10^{-2}$ for $L_{\rm X} \approx80410^{44}$ up to $\sigma_{\rm rms}^2 \approx 10^{-1}$ for $L_{\rm X} \approx80510^{42}$ \cite{nandra:97,markowitz:01}."806 However. no evidence is vet found of such a trend continuing down o lower luminosities.," However, no evidence is yet found of such a trend continuing down to lower luminosities."807" On the contrary. suggestions have been made hat 22, may flattens out at lower Lx (Papadakis2004:Paolillo at values of a few times + for the typical X-ray uminosity of the objects in our sample."," On the contrary, suggestions have been made that $\sigma_{\rm rms}^2$ may flattens out at lower $L_{\rm X}$ \cite{papadakis:04,paolillo:04} at values of a few times $^{-1}$ for the typical X-ray luminosity of the objects in our sample."808 This would imply that the observed correlations between large scale and core powers are not skewed by variability bias., This would imply that the observed correlations between large scale and core powers are not skewed by variability bias.809 However. we should also consider the possibility that. if," However, we should also consider the possibility that, if"810causality. however. and the link can be indirect.,"causality, however, and the link can be indirect."811 For instance. 7 recently pointed out the strong correlation between excess racidus ancl the incident stellar Hux. supporting the scenario of ?..," For instance, \citet{fre07} recently pointed out the strong correlation between excess radius and the incident stellar flux, supporting the scenario of \citet{gui06}."812 Incident (ux. like tidal effects also scales with eAt.," Incident flux, like tidal effects also scales with $a/R$."813 Fig., Fig.814 2 shows that. in the present sample. the correlation of excess radius is stronger with aff than with the strength of tidal effects.," \ref{tides} shows that, in the present sample, the correlation of excess radius is stronger with $a/R$ than with the strength of tidal effects."815 The present sample of transiting planet is not sullicient. to distinguish. between the two types of explanations without further modelling. but it does suggest wt tidal effects are not the main factor in determining the size of close-in gas giant planets and that the intensity of vw incident [ux is a better candidate.," The present sample of transiting planet is not sufficient to distinguish between the two types of explanations without further modelling, but it does suggest that tidal effects are not the main factor in determining the size of close-in gas giant planets and that the intensity of the incident flux is a better candidate."816 Ifthe tentative indications provided by the present sample of transiting planets are confirmed. the following overall picture - close-in planets end up the formation phase on orbits with a wide distribution of - tidal interaction with the star circularise the planetary orbit. beginning around {οσαfA)=1.5 for 2-Aly planets. then circularizes it.," If the tentative indications provided by the present sample of transiting planets are confirmed, the following overall picture - close-in planets end up the formation phase on orbits with a wide distribution of - tidal interaction with the star circularise the planetary orbit, beginning around $log(a/R)=1.5$ for $_{\rm J}$ planets, then circularizes it."817 Early signs of circularisation are visible alreacly at larger - for planets lighter than Jupiter. the circularisation is not accompanied. hy significant orbital decay. ancl effect. on the - for planets with mass comparable to Jupiter or slightly heavier. circularisation is accompanied by significant orbital decay. leading to a mass-periocd relation. ancl possible destruction for Al~1.2A. - still heavier planet produce a marked. stellar excess rotation. and corresponding orbital decay. during. the process of tidal evolution and cireularisation.," Early signs of circularisation are visible already at larger - for planets lighter than Jupiter, the circularisation is not accompanied by significant orbital decay and effect on the - for planets with mass comparable to Jupiter or slightly heavier, circularisation is accompanied by significant orbital decay, leading to a mass-period relation, and possible destruction for $M\sim 1-2 M_{\rm J}$ - still heavier planet produce a marked stellar excess rotation, and corresponding orbital decay, during the process of tidal evolution and circularisation."818 LW their initial position exceeds a critical value. they may reach a spin-orbit svnchronous state with the star. - às à result of this evolution. the orbital characteristics of very close-in planets. (Ποι planets) are. profounclly modified by tidal interactions. including the orbital distance ancl period.," If their initial position exceeds a critical value, they may reach a spin-orbit synchronous state with the star, - as a result of this evolution, the orbital characteristics of very close-in planets (“hot” planets) are profoundly modified by tidal interactions, including the orbital distance and period."819" Planets lighter than 2 AZ, ancl closer than a few ανν are ""sheperded along a mass-period trend. controlled. by tidal angular momentum exchange ancl possibly tidal inflation of the planet."," Planets lighter than 2 $M_J$ and closer than a few days are ""sheperded"" along a mass-period trend controlled by tidal angular momentum exchange and possibly tidal inflation of the planet."820 The period-mass relation of close-in planets cannot be used at face value to constrain formation and migration If this interpretation of the data ds. correct. we can roughly divide the mass-period. plane for. exoplanet according to their sensitivity to tidal evolution.," The period-mass relation of close-in planets cannot be used at face value to constrain formation and migration If this interpretation of the data is correct, we can roughly divide the mass-period plane for exoplanet according to their sensitivity to tidal evolution."821 Figure 6 sums up the observable elfects of tidal evolution as inferred here from transiting planets., Figure \ref{fig5} sums up the observable effects of tidal evolution as inferred here from transiting planets.822 Phe possible transition zone where orbital circularisation ancl orbital decay occur is indicated. as well as the Roche limit (with. reasonable assumptions on the mass-radius relation of planets).," The possible transition zone where orbital circularisation and orbital decay occur is indicated, as well as the Roche limit (with reasonable assumptions on the mass-radius relation of planets)."823 Planets at the weak end. of the scale. of tidal effects can conserve eccentric and. misaligned orbits., Planets at the weak end of the scale of tidal effects can conserve eccentric and misaligned orbits.824 Jupiter-mass planets placed near the 3-davs limit will substantially alfect the rotation of their parent star. moving closer in the process by orbital decay. down to 1-2 αν periods.," Jupiter-mass planets placed near the 3-days limit will substantially affect the rotation of their parent star, moving closer in the process by orbital decay, down to 1-2 day periods."825 Planets near the 2-3 Jupiter mass range will undergo strong orbital decay. [acing potential destruction if they start on a close orbit.," Planets near the 2-3 Jupiter mass range will undergo strong orbital decay, facing potential destruction if they start on a close orbit."826 Large planets or brown cdwarfs in the 5-15.r Jupiter-mass range will spin up their host star substantially if they orbi close enough. all the way to synchronous rotation.," Large planets or brown dwarfs in the 5-15 Jupiter-mass range will spin up their host star substantially if they orbit close enough, all the way to synchronous rotation."827 Lighter planets will not allect their star detectably., Lighter planets will not affect their star detectably.828 Lf they are close enough. they will spiral inwards to the Roche limit in a shor time.," If they are close enough, they will spiral inwards to the Roche limit in a short time."829 As more objects. Dill. the diagram. this eloba interpretation can be tested and refined.," As more objects fill the diagram, this global interpretation can be tested and refined."830 In Figure 6.. the two known transiting stars with the lowest masses are also plotted. OGLE-PR-122 (7) anc OGLE-TPR-123 (2)...," In Figure \ref{fig5}, the two known transiting stars with the lowest masses are also plotted, OGLE-TR-122 \citep{pon05} and OGLE-TR-123 \citep{pon06}."831 Phese objects show that the connection with stellar binaries is coherent. with the first object having an orbit still eccentric but clear evidence of excess rotation of the primary. and the second a circular and svachronous orbit.," These objects show that the connection with stellar binaries is coherent, with the first object having an orbit still eccentric but clear evidence of excess rotation of the primary, and the second a circular and synchronous orbit."832 Figure 6. shows. for HD 189733. 7 Boo and OCLE-TR-123. the initial orbital distance assuming that all the angular momentum of the star is put back in the orbit.," Figure \ref{fig5} shows, for HD 189733, $\tau$ Boo and OGLE-TR-123, the initial orbital distance assuming that all the angular momentum of the star is put back in the orbit."833 The initial positions will be placed near the limit of tidal spin-up. which provides accitional support to this interpretation.," The initial positions will be placed near the limit of tidal spin-up, which provides additional support to this interpretation."834 It also suggests one of the reasons for the inaceuraey. of tidal timescales calculated from present. orbital parameters: the initial orbit could have been very dillerent., It also suggests one of the reasons for the inaccuracy of tidal timescales calculated from present orbital parameters: the initial orbit could have been very different.835 For OGLE-PR- for instance. the initial position is above the frame of the plot.," For OGLE-TR-122 for instance, the initial position is above the frame of the plot."836(in particular massive halos) competes with the increase in the comoving size of the error boxes.,(in particular massive halos) competes with the increase in the comoving size of the error boxes.837 Our simple calculations show that in the scenario of CC10.. resolved PLA sources with AL=10AZ. and zx0.5 are likely to have at worst dozens of interlopers in the error box.," Our simple calculations show that in the scenario of \citetalias{CorCor10}, resolved PTA sources with $M\ga 10^{9}\Msol$ and $z\ltsim 0.5$ are likely to have at worst dozens of interlopers in the error box."838 With this low number. one could conceivably perform follow-up observations of cach individual candidate.," With this low number, one could conceivably perform follow-up observations of each individual candidate."839 1f. on the other hand. luminosity distances to the source cannot be determined. this number increases to 107. suggesting that it will become extremely cillicult to clectromagnetically identify the source in the absence of an obvious. tell-tale EAL signature.," If, on the other hand, luminosity distances to the source cannot be determined, this number increases to $\sim 10^{3}$, suggesting that it will become extremely difficult to electromagnetically identify the source in the absence of an obvious, tell-tale EM signature."840 In practice. the number of interloping galaxies may be somewhat larger than the value computed by equations 11- 16.," In practice, the number of interloping galaxies may be somewhat larger than the value computed by equations \ref{eq:NhSV}$ $-$ \ref{eq:NACC}."841 hehalomeassofanggivencandidatehostsystemmwillnoll lnowpbu)gd dod edtlicadilhy appeb CMauinau Cheat) relation will lower the minimum halo mass threshold. for candidacy.," The halo mass of any given candidate host system will not be known a priori, and the intrinsic scatter in the $M_{\rm SMBH}-M_{\rm halo}$ $M_{\rm SMBH}-\sigma_{\rm842 host}$ ) relation will lower the minimum halo mass threshold for candidacy."843 On the other hand. the simple calculations presented. here. co not. consider detailed: demographic properties of resolved. PLA) sources and. plausible hosts. such as the presence of a nuclear stellar core (Makino1997:Hawvindranath.Ho&Filippenko2002:Milosavljeviéetal.2002:Volonteri.Macau&Llaardt2003) or galaxy morphology.," On the other hand, the simple calculations presented here do not consider detailed demographic properties of resolved PTA sources and plausible hosts, such as the presence of a nuclear stellar core \citep[]{Makino97, Ravind+02, Milos+02, VMH03} or galaxy morphology."844 Including such factors in the analysis will narrow the field of candidate hosts, Including such factors in the analysis will narrow the field of candidate hosts.845" As we argue in 3.3. candidate ACN counterparts may be further vetted by examining their UV. and. X-ray emission for features indicative of a central SAIBLI binary (see also Sesanaetal.2011. for an in-depth: discussion of possible high-energy signatures for. pre-decoupling Le, low>by PPA sources)."," As we argue in \ref{subsec:emission}, candidate AGN counterparts may be further vetted by examining their UV and X-ray emission for features indicative of a central SMBH binary (see also \citealt{Sesana+11} for an in-depth discussion of possible high-energy signatures for pre-decoupling — i.e., $t_{\rm GW}>t_{\nu}$ — PTA sources)."846 Lo addition. PLA sources are sullicienthy nearby that it should be possible to observe an interloping AGN together with its host. galaxy.," In addition, PTA sources are sufficiently nearby that it should be possible to observe an interloping AGN together with its host galaxy."847 Lt should therefore be possible to combine the ACN emission. the ealaxy luminosity and the inferred. SMDII mass to. check candidate counterparts.," It should therefore be possible to combine the AGN emission, the galaxy luminosity and the inferred SMBH mass to cross-check candidate counterparts."848 Alotivated by the results of the previous section that the number of plausible host. galaxies in the PTA error box may be tractable for follow-up LEAT searches. we next mocel he EAL emission. properties of SAIBLL binaries detectable ον P'PAXs.," Motivated by the results of the previous section that the number of plausible host galaxies in the PTA error box may be tractable for follow-up EM searches, we next model the EM emission properties of SMBH binaries detectable by PTAs."849 We focus our attention on SMDLIILD binaries that are undergoing luminous accretion. as these are the most omising Class of objects for LEAL identification.," We focus our attention on SMBH binaries that are undergoing luminous accretion, as these are the most promising class of objects for EM identification."850" Normalizing the binary mass AZ and rest-frame period P to the typical orders of magnitude expected. of resolved ""PA sources. AL=10""AZ.Mo and P=loveF4. we write he semi-major axis for the source binary as Binaries detectable by P""PAs have long overcome the so- “final parsec problem."," Normalizing the binary mass $M$ and rest-frame period $P$ to the typical orders of magnitude expected of resolved PTA sources, $M=10^{9}\Msol M_{9}$ and $P=1\yr~P_{1}$, we write the semi-major axis for the source binary as Binaries detectable by PTAs have long overcome the so-called “final parsec” problem."851 The rest-frame time to merger for a binary with mass AZ and semi-major axis e. driven by CN emission alone. is (Peters.1964).," The rest-frame time to merger for a binary with mass $M$ and semi-major axis $a$, driven by GW emission alone, is \citep{Peters64}."852".. Beeause tvpical resolved: sources have AMD=0g773. we normalize the svnimetric mass ralio g—(MaS/MQ|AdsALJ to the value ae—WAL/M,=0.25)0.16."," Because typical resolved sources have $M/\Mch=\eta^{-3/5}\sim 3$, we normalize the symmetric mass ratio $\eta\equiv (M_{2}/M_{1})/[1+M_{2}/M_{1}]^{2}$ to the value $\eta_{1:4}\equiv\eta(M_{2}/M_{1}=0.25)=0.16$ ."853" Note that our ad hoc translation between AL and LM is not very sensitive to the value of q: the ratio AZ/,ME varies by less than a [actor of two in the Aste ", Note that our ad hoc translation between $M$ and $\Mch$ is not very sensitive to the value of $q$; the ratio $M/\Mch$ varies by less than a factor of two in the range $0.1\le M_{2}/M_{1} \le 1$.854shad dunn equation. LS corresponds to binaries in circular orbits. with eccentric orbits merging Faster.," The upper bound in equation \ref{eq:tmerge} corresponds to binaries in circular orbits, with eccentric orbits merging faster."855 Recent work has shown that binarics nw have eccentricities as high as 0.6 at decoupling (Iltoedigetal.2011: see also Armitage&Natarajan2005:Cuadraetal.2009).," Recent work has shown that binaries may have eccentricities as high as $\sim 0.6$ at decoupling \citealt{Roedig+11}; see also \citealt{AN05, Cuadra+09}) )."856 Thus. typical P'EAX-resolved: sources will coalesce on scales of 10° vears.," Thus, typical PTA-resolved sources will coalesce on scales of $\sim 10^{3}$ years."857 However. exceptionally compact sources will coalesce on scales of several vears: for example. a binary with P?=0.1vr approximately the lowest binary period that is expected to be observable with IAAS will merge in Fuere~4vr.," However, exceptionally compact sources will coalesce on scales of several years; for example, a binary with $P=0.1\yr$ — approximately the lowest binary period that is expected to be observable with PTAs — will merge in $t_{\rm merge}\sim 4\yr$."858 The tidal torques of the compact SML binary provide a particularly promising mechanism for producing a tell-tale observable feature., The tidal torques of the compact SMBH binary provide a particularly promising mechanism for producing a tell-tale observable feature.859 Theoretical caleulations (Goldreichjevié2008:6πανταetal.2009:Chang2010). robustly predict that in. geometrically thin circumbinary accretion discs. binary torques can open an annular. low-clensity gap around the orbit of the secondary.," Theoretical calculations \citep{GT80, Artymo+91, ArtLub94, AN02,860 Bate+03, Hayasaki+07,MM08, Cuadra+09, Chang+10} robustly predict that in geometrically thin circumbinary accretion discs, binary torques can open an annular, low-density gap around the orbit of the secondary."861 Ehe σας inside the gap accretes onto the individual SALBIIs while the gas outside is pushed. outward by the tidal torques., The gas inside the gap accretes onto the individual SMBHs while the gas outside is pushed outward by the tidal torques.862 “Phe binary's tidal torques transfer orbital angular momentum into the outer disc. causing the binarv orbit to shrink &radually while maintaining a roughly axisvnunetrics cireumbinary. gap.," The binary's tidal torques transfer orbital angular momentum into the outer disc, causing the binary's orbit to shrink gradually while maintaining a roughly axisymmetric circumbinary gap."863 The gap opens near the resonance radius /?237/702.08. CXrtvimowiczetal.1991)., The gap opens near the resonance radius $R\approx 3^{2/3}a \approx 2.08 a$ \citep{Artymo+91}.864. Numerical. simulations of thin circumbinary disces (see refs., Numerical simulations of thin circumbinary discs (see refs.865 in above paragraph) produce gaps with an azimuthally averaged radius of 1.5.3 times the binary semimajor axis., in above paragraph) produce gaps with an azimuthally averaged radius of $1.5-3$ times the binary semimajor axis.866 Phe exact size ancl shape of the gap is not easily characterized: the geometry depends on the binary masses and orbital cecentricity. as well as the ellicieney of angular momentum transport within the disc.," The exact size and shape of the gap is not easily characterized; the geometry depends on the binary masses and orbital eccentricity, as well as the efficiency of angular momentum transport within the disc."867 Following Milosavljevió&Phinney(2005)... we parametrize the size of the gap as Ry=2Àe. where A~| is a dimensionless parameter.," Following \cite{MP05}, we parametrize the size of the gap as $R_{\lambda}\equiv 2\lambda a$, where $\lambda\sim 1$ is a dimensionless parameter."868" We are interested in cireumbinary discs that are truncated inside Ay~20034,2Hp""GMAO (equation 17))."," We are interested in circumbinary discs that are truncated inside $R_{\lambda}\sim 200 M_{9}^{-2/3}P_{1}^{2/3}869GM/c^{2}$ (equation\ref{eq:aPTA}) )."870 Below. we model surface density profiles and thermal emission spectra of such disces. as well as the thermal emission due to leakage of gas into the cavity and onto incliviclual SAIBLIs.," Below, we model surface density profiles and thermal emission spectra of such discs, as well as the thermal emission due to leakage of gas into the cavity and onto individual SMBHs."871 Adopting a geometrically thin. thermal grav-body.— disc," Adopting a geometrically thin, thermal gray-body disc"87210 previous two decades a wealth of observational elfort has oen invested in studying the redshift réseime 0«21. --nvestigating whether the dominant. factors are linked. to 1¢ Alpe-seale cluster environments (eg.,"the previous two decades a wealth of observational effort has been invested in studying the redshift réggime $0<z<1$, investigating whether the dominant factors are linked to the Mpc-scale cluster environments (eg."873 Prestage Peacock 1988: Lll Lilly 1991: Ellingson. Yee του 1991: Wold 6 al.," Prestage Peacock 1988; Hill Lilly 1991; Ellingson, Yee Green 1991; Wold et al."874 2000: Best 2000) or the kpe-scale properties of the iost galaxies (e.g. Smith Ileckman 1989: Best. Longair Rotttgering 1998: MeLure Dunlop 2000: Dunlop ct al.," 2000; Best 2000) or the kpc-scale properties of the host galaxies (e.g. Smith Heckman 1989; Best, Longair Rötttgering 1998; McLure Dunlop 2000; Dunlop et al."875 003: Zirm. Dickinson Dev 2003)," 2003; Zirm, Dickinson Dey 2003)."876 One of the incontrovertible observational facts which las emerged from these studies. at least at 2<1L. is that 1¢ host galaxies of all powerful racio-Ioud XN are massive L L' ellipticals (eg.," One of the incontrovertible observational facts which has emerged from these studies, at least at $z<1$, is that the host galaxies of all powerful radio-loud AGN are massive $L>L^{\star}$ ellipticals (eg."877 Taylor ct al., Taylor et al.878 1996: MeLure ct al., 1996; McLure et al.879 1999: Dunlop et al., 1999; Dunlop et al.880 2003)., 2003).881" The apparent uniformity of racio-oud AGN host. galaxies has taken on added: importance over the last few vears. following the discovery in nearby (distance z; 150 Alpe) inactive galaxies that a reasonably accurate estimate (AAS,20.3 dex) of the central black-vole mass can be obtained via its correlation with the mass ofthe host spheroidal component (Ixormendsy Lichstone 1995: Magorrian et al."," The apparent uniformity of radio-loud AGN host galaxies has taken on added importance over the last few years, following the discovery in nearby (distance $\ltsim$ 150 Mpc) inactive galaxies that a reasonably accurate estimate $\Delta M_{bh}\simeq 0.3$ dex) of the central black-hole mass can be obtained via its correlation with the mass of the host spheroidal component (Kormendy Richstone 1995; Magorrian et al."882 1998: Gebhardt et al., 1998; Gebhardt et al.883 2000: Ferrarese Merritt 2000: MeLure Dunlop 2002: Marconi Llunt 2003: Tremaine et al., 2000; Ferrarese Merritt 2000; McLure Dunlop 2002; Marconi Hunt 2003; Tremaine et al.884 2002)., 2002).885" Moreover. recent. progress has also indicated: that a similarly accurate black-hole mass estimate (NAM,c0.4 dex) can be obtained for broad-line AGN using emission-lino. widths to derive the virial mass estimate (eg."," Moreover, recent progress has also indicated that a similarly accurate black-hole mass estimate $\Delta M_{bh}\simeq 0.4$ dex) can be obtained for broad-line AGN using emission-line widths to derive the virial mass estimate (eg."886 Ixaspi et al., Kaspi et al.887 2000: AleLure Dunlop 2002: AleLure Jarvis 2002: Vestergaard 2002)., 2000; McLure Dunlop 2002; McLure Jarvis 2002; Vestergaard 2002).888 Consequently. à arge body of work has appeared in the recent literature investigating the possible link between racio luminosity and Xack-hole mass in raclio-loucl AGN (eg.," Consequently, a large body of work has appeared in the recent literature investigating the possible link between radio luminosity and black-hole mass in radio-loud AGN (eg."889 Laor 2000: Lacy οἱ al., Laor 2000; Lacy et al.890 2001: AleLure Dunlop 2001a: MeLure Dunlop 2002: Dettoni et al., 2001; McLure Dunlop 2001a; McLure Dunlop 2002; Bettoni et al.891 2003: Dunlop ct al., 2003; Dunlop et al.892 2003)., 2003).893 Unfortunately. observational studies have traclitionally oen subject to a degeneracy between radio. luminosity and redshift produced as a by-produet of Hux-limited racio samples.," Unfortunately, observational studies have traditionally been subject to a degeneracy between radio luminosity and redshift produced as a by-product of flux-limited radio samples."894 In order to study the properties of radio-Ioud GN separated by a large dynamic range in radio luminosity. it has previously been necessary to select. samples. consisting of objects covering a wide range of redshifts.," In order to study the properties of radio-loud AGN separated by a large dynamic range in radio luminosity, it has previously been necessary to select samples consisting of objects covering a wide range of redshifts."895 This has led to dillicullics in interpreting the data due to the complication of potentially significant evolutionary cllects., This has led to difficulties in interpreting the data due to the complication of potentially significant evolutionary effects.896 However. by selecting our sample of objects from four complete. Iow-frequeney selected: radio samples with successively fainter Uux-clensity limits. it has been possible to construct a sample of radio galaxies which spans three decades in radio Luminosity at a virtually constant cosmic epoch (0.4>< 0.6).," However, by selecting our sample of objects from four complete, low-frequency selected radio samples with successively fainter flux-density limits, it has been possible to construct a sample of radio galaxies which spans three decades in radio luminosity at a virtually constant cosmic epoch $0.4<z<0.6$ )."897 In this respect the motivation for this study is identical to that pursued by Hill Lilly (1991). who investigated the cluster. environments of a sample of 45 racio galaxies spanning a similar range in racio bIuminosities ab 200.5.," In this respect the motivation for this study is identical to that pursued by Hill Lilly (1991), who investigated the cluster environments of a sample of 45 radio galaxies spanning a similar range in radio luminosities at $z\simeq 0.5$."898 ὃν successfully disentanegling the ellects of luminosity and redshift [or the first time. Lill Lilly (1991) were able to demonstrate that z20.5 marks an apparent epoch-dependent. change in cluster environment. with radio galaxies tending to inhabit significantly richer cluster environments than their low-redshift. counterparts.," By successfully disentangling the effects of luminosity and redshift for the first time, Hill Lilly (1991) were able to demonstrate that $z\simeq 0.5$ marks an apparent epoch-dependent change in cluster environment, with radio galaxies tending to inhabit significantly richer cluster environments than their low-redshift counterparts."899 Furthermore. the wide range of radio luminosities in the Lill Lilly sample enabled. them to determine that extended radio Luminosity did not appear to be a strong function of cluster richness.," Furthermore, the wide range of radio luminosities in the Hill Lilly sample enabled them to determine that extended radio luminosity did not appear to be a strong function of cluster richness."900 Developments over. the intervening decade have provided our new studs with two crucial advantages over the previous work of Hill Lilly (1991)., Developments over the intervening decade have provided our new study with two crucial advantages over the previous work of Hill Lilly (1991).901 Firstly. the availability of the TORS (Willott et al.," Firstly, the availability of the 7CRS (Willott et al."902 2003: Lacy. ct al., 2003; Lacy et al.903 1999). and 'TexOx-1000 (Lil Rawlings 2003) racio samples has now allowed. us to compile a sample of 41 radio galaxies at 2oc0.5. which is complete over the full iee-decadoes range in radio power.," 1999) and TexOx-1000 (Hill Rawlings 2003) radio samples has now allowed us to compile a sample of 41 radio galaxies at $z\simeq 0.5$, which is complete over the full three-decades range in radio power."904 Secondly. with the high-resolution imaging provided by the Hubble Space Telescope (HIST). and the improvement in follow-up. observations available with ground-based telescopes. we are now in a position o obtain a wide range of high quality data-sets for our new sample which were not obtainable only ten vears ago.," Secondly, with the high-resolution imaging provided by the Hubble Space Telescope (HST), and the improvement in follow-up observations available with ground-based telescopes, we are now in a position to obtain a wide range of high quality data-sets for our new sample which were not obtainable only ten years ago."905 Consequently. our new sample of z20.5 radio galaxies is he basis for an ambitious project. which will for the first ime svstematically investigate the connection between the radio luminosity of radio galaxies. the properties of their rost galaxies. their location on the fundamental plane. the richness and mass of their cluster environments. and the masses of their central black holes.," Consequently, our new sample of $z\simeq 0.5$ radio galaxies is the basis for an ambitious project, which will for the first time systematically investigate the connection between the radio luminosity of radio galaxies, the properties of their host galaxies, their location on the fundamental plane, the richness and mass of their cluster environments and the masses of their central black holes."906 The results presented. in this paper represent the first μαage of this wide-ranging project. ancl concentrate solely on the analysis of our deep £ band LIS ΛΕΡΟΣ imaging ata.," The results presented in this paper represent the first stage of this wide-ranging project, and concentrate solely on the analysis of our deep $I-$ band HST WFPC2 imaging data."907 The results of our extensive follow-up observations of 1e sample are deferred to a series of future papers., The results of our extensive follow-up observations of the sample are deferred to a series of future papers.908 The structure of the paper is as follows. in Section 2 10 details of the radio-galaxy sample are described. while in Section 3 the LIST observations and data reduction are iscussed.," The structure of the paper is as follows, in Section 2 the details of the radio-galaxy sample are described, while in Section 3 the HST observations and data reduction are discussed."909 In Section 4 the modelling of the LIST imaging is escribed. with the main results presented and compared to literature results on low-recshilt radio galaxies in Section 5.," In Section 4 the modelling of the HST imaging is described, with the main results presented and compared to literature results on low-redshift radio galaxies in Section 5."910 In Section 6 the host-ealaxy properties of our οςΙΙ sub-sample are compared to literature. results to explore. the evidence for dynamical evolution of the most powerful radio ealaxies within the redshift range 0.0<z«OLS., In Section 6 the host-galaxy properties of our 3CRR sub-sample are compared to literature results to explore the evidence for dynamical evolution of the most powerful radio galaxies within the redshift range $0.0<z<0.8$.911 In Section 7 the properties of the radio-galaxy hosts are compared to those of local brightest. cluster galaxies., In Section 7 the properties of the radio-galaxy hosts are compared to those of local brightest cluster galaxies.912 In. Section S the masses of the radio galaxies central black holes. are estimated. and in Section 9 the relationship between black-hole mass and radio luminosity is investigated.," In Section 8 the masses of the radio galaxies' central black holes are estimated, and in Section 9 the relationship between black-hole mass and radio luminosity is investigated."913 The main conclusions are summarized in Section LO., The main conclusions are summarized in Section 10.914" Unless otherwise stated. throughout this paper the following cosmology is assumed: //,=TO tMpe 1.0,203, 04=07."," Unless otherwise stated, throughout this paper the following cosmology is assumed: $H_{0}=70$ $^{-1}$ $^{-1}$, $\Omega_{m}=0.3$, $\Omega_{\Lambda}=0.7$."915 The full 4l-object z=0.5 radio-galaxy sample (hereafter the ZP5 sample) consists of all the narrow-line radio galaxies in the redshift interval 0.4<z0.6 from four. completo. low-[requeney selected radio survevs: θα (Laing. Riley Longair 1983). GCE (Eales et al.," The full 41-object $z\simeq 0.5$ radio-galaxy sample (hereafter the ZP5 sample) consists of all the narrow-line radio galaxies in the redshift interval $0.4<z<0.6$ from four, complete, low-frequency selected radio surveys; 3CRR (Laing, Riley Longair 1983), 6CE (Eales et al."916 1997: Rawlings. Eales," 1997; Rawlings, Eales"917reached only within the innermost disk. well inside 1 AU.,"reached only within the innermost disk, well inside 1 AU."918 Crystalline and amorphous silicate erains inmost protoplanetary disks may Caius have experienced the same large-scale transport phases as the refractory particles [ος in Wild 2., Crystalline and amorphous silicate grains in most protoplanetary disks may thus have experienced the same large-scale transport phases as the refractory particles found in Wild 2.919 While accretion disk models driven by a generic turbulent viscosity have long been invoked as a means to explain large-scale transport (Gail 2001. 2002. 2004: Tschirnuter Gail 2007; Ciesla 2007. 2003. 2009. 2010a.b: Birnstiel et al.," While accretion disk models driven by a generic turbulent viscosity have long been invoked as a means to explain large-scale transport (Gail 2001, 2002, 2004; Tscharnuter Gail 2007; Ciesla 2007, 2008, 2009, 2010a,b; Birnstiel et al."920 2009; IIughes Armitage 2010: ]leinzeller οἱ al., 2009; Hughes Armitage 2010; Heinzeller et al.921 2011: Jacquet et al., 2011; Jacquet et al.922 2011). the detailed physics behind a-viscosity remains unclear. especially considering that the magneto-rotational instability (MBRI) often assumed to be the source of the a-viseosity is unable to drive disk evolution in the magnetically dead midplane regions (e.g.. Matsumura Pudritz 2006) of most interest for planetary formation.," 2011), the detailed physics behind $\alpha$ -viscosity remains unclear, especially considering that the magneto-rotational instability (MRI) often assumed to be the source of the $\alpha$ -viscosity is unable to drive disk evolution in the magnetically dead midplane regions (e.g., Matsumura Pudritz 2006) of most interest for planetary formation."923 Objections have also been raised to the assumption that angular momentum transport in a MBI-driven disk can be described by the standard model for a-viscosity (Pessah. Chan. Psalüs 2008).," Objections have also been raised to the assumption that angular momentum transport in a MRI-driven disk can be described by the standard model for $\alpha$ -viscosity (Pessah, Chan, Psaltis 2008)."924 In contrast. a MGQU disk presents a sell-consistent mechanism for studyiug mixing and (rausport in protoplanetary disks. with no ου parameters bevond the initial choice of a disk massive enough. and cold enough. to be MGU.," In contrast, a MGU disk presents a self-consistent mechanism for studying mixing and transport in protoplanetary disks, with no free parameters beyond the initial choice of a disk massive enough, and cold enough, to be MGU."925 We present here a new set of three-dimensional MGU «disk models similar to those studied previously (e.g.. Boss 2004a. 2006. 2007. 2008). bul with several variations intended to test the robustness of the conclusions about mixing5 and (transport of the previous models.," We present here a new set of three-dimensional MGU disk models similar to those studied previously (e.g., Boss 2004a, 2006, 2007, 2008), but with several variations intended to test the robustness of the conclusions about mixing and transport of the previous models."926 Given that a MGU disk appears to be a likely requirement for the formation of eas eiant planets. by either core accretion (e.g.. Inaba οἱ al.," Given that a MGU disk appears to be a likely requirement for the formation of gas giant planets, by either core accretion (e.g., Inaba et al."927 2003: Chambers 2008) or by clisk instability (e.g.. Boss 2010). these MGU models are intended to learn what cosmochenmical consequences might also derive [rom such phases of rapid disk evolution.," 2003; Chambers 2008) or by disk instability (e.g., Boss 2010), these MGU models are intended to learn what cosmochemical consequences might also derive from such phases of rapid disk evolution."928 The disk evolution calculations were perlormed with a munerical code (hat uses finite differences to solve the three-dimensional equations of hydrodsnamies. radiative (ransler. ancl the Poisson equation for (he gravitational potential.," The disk evolution calculations were performed with a numerical code that uses finite differences to solve the three-dimensional equations of hydrodynamics, radiative transfer, and the Poisson equation for the gravitational potential."929 The code is (he same as (hat used in the previous studies of mixing and transport in disks (Boss 2004a. 2006. 2007. 2003).," The code is the same as that used in the previous studies of mixing and transport in disks (Boss 2004a, 2006, 2007, 2008)."930 The code has been shown to be second-order-accurate in both space and time through convergence testing (Boss Alvhill 1992)., The code has been shown to be second-order-accurate in both space and time through convergence testing (Boss Myhill 1992).931 The equations are solved on a spherical coordinate grid., The equations are solved on a spherical coordinate grid.932" The number of grid points in each spatial direction is: NV,= 51. .Nj=23 in $/2>00. and N,,=256."," The number of grid points in each spatial direction is: $N_r = 51$ , $N_\theta = 23$ in $\pi/2 \ge \theta \ge 0$, and $N_\phi = 256$."933 This relatively low degree of numerical spatial resolution (compared to hieh resolution disk instabilitv models. e.g.. Boss 2010) was chosen in order to evolve the disks as lar Forward in (nme as possible in several vears of computing on a dedicated workstation.," This relatively low degree of numerical spatial resolution (compared to high resolution disk instability models, e.g., Boss 2010) was chosen in order to evolve the disks as far forward in time as possible in several years of computing on a dedicated workstation."934 The radial grid is uniformly spaced between 1l and 10 AU. with boundary conditions at," The radial grid is uniformly spaced between 1 and 10 AU, with boundary conditions at"935"of m, and therefore variations with larger amplitudes than 5530 (see Fig. 3)).","of m, and therefore variations with larger amplitudes than 530 (see Fig. \ref{fig:lc}) )."936" We performed Chi-Square-tests to characterize the significance of the variability, following e.g., ?.."," We performed Chi-Square-tests to characterize the significance of the variability, following e.g., \citet{2003A&A...401..161K}."937" For the reduced X2 we obtain values of 32.2 at 22GGHz, 7.5 at 43GGHz, and 0.9 at 86GGHz."," For the reduced $\chi_\nu^2$ we obtain values of 32.2 at GHz, 7.5 at GHz, and 0.9 at GHz."938" The corresponding probabilities for the source not being variable are far less than Although being formally insignificant, the variations at GGHz appear to correlate with the variations seen at the two lower frequencies."," The corresponding probabilities for the source not being variable are far less than Although being formally insignificant, the variations at GHz appear to correlate with the variations seen at the two lower frequencies."939" To describe the strength of the variability, the modulation index m and the variability amplitude Y (defined as 3 x nm?—m, where mo is the modulation index of the calibrator NRAO5530) are summarized in Table 4,, where Y corresponds to a 3 c variability amplitude, from which systematic variations mg, which are still seen in the calibrator, are subtracted (?).."," To describe the strength of the variability, the modulation index m and the variability amplitude Y (defined as 3 $\times$ $\sqrt{m^2-m_{0}^2}$, where $_{0}$ is the modulation index of the calibrator 530) are summarized in Table \ref{tab:flux}, , where Y corresponds to a 3 $\sigma$ variability amplitude, from which systematic variations $m_0$, which are still seen in the calibrator, are subtracted \citep{1987AJ.....94.1493H}."940 For AA* those from systematic bias corrected Y-amplitudes range between The observed day-to-day variations compare well with similar variations seen by other authors at other times., For A* those from systematic bias corrected Y-amplitudes range between The observed day-to-day variations compare well with similar variations seen by other authors at other times.941" Using the VLA, ? found an increase in the flux density at a level of Since for AA* each VLBI track lasted about 6-7 hours, we are Sgrnot able to detect flux density variations on shorter timescales than this."," Using the VLA, \citet{2006ApJ...650..189Y} found an increase in the flux density at a level of Since for A* each VLBI track lasted about 6-7 hours, we are not able to detect flux density variations on shorter timescales than this."942" A splitting of the VLBI coverage at shorter intervals, e.g. in two or three coverages of equal duration, does not allow measuring the total source flux with sufficient accuracy (main limitation: uv-coverage and lack of secondary calibrator scans) and therefore prevents the significant detection of variability on timescales shorter than 6hhrs."," A splitting of the VLBI coverage at shorter intervals, e.g. in two or three coverages of equal duration, does not allow measuring the total source flux with sufficient accuracy (main limitation: uv-coverage and lack of secondary calibrator scans) and therefore prevents the significant detection of variability on timescales shorter than hrs."943" A nonstationary source, which would vary with a large amplitude during the time of the VLBI experiment, however, would cause significant image degradation, leading to a reduced dynamical range in the CLEAN maps and the appearance of side lobes."," A nonstationary source, which would vary with a large amplitude during the time of the VLBI experiment, however, would cause significant image degradation, leading to a reduced dynamical range in the CLEAN maps and the appearance of side lobes."944" Since this is not observed, we can exclude variations that are much larger than our typical amplitude calibration errors of 10—20 From the measured total flux densities, we calculated a 3-frequency spectral index between 22 and 86GGHz (defined as S,« vy”)."," Since this is not observed, we can exclude variations that are much larger than our typical amplitude calibration errors of $10-20$ From the measured total flux densities, we calculated a 3-frequency spectral index between 22 and GHz (defined as $_{\nu} \propto \nu^{\alpha}$ )."945" We obtained an inverted spectrum, with spectral indices ranging between (0.44 + 0.04) and (0.64 + 0.05)."," We obtained an inverted spectrum, with spectral indices ranging between (0.44 $\pm$ 0.04) and (0.64 $\pm$ 0.05)."946" For AA*, a frequency break in the spectrum was suggested between ~20—100 GGHz (???).. "," For A*, a frequency break in the spectrum was suggested between $\sim 20 - 100$ GHz \citep{1998ApJ...499..731F, 2003ApJ...586L..29Z,9472005ApJ...634L..49A}."948"Below this break frequency, the spectral slope is much shallower (lower) than at higher frequencies, where the so-called sub-mm excess causes an increase in the inverted spectral index (??).. "," Below this break frequency, the spectral slope is much shallower (lower) than at higher frequencies, where the so-called sub-mm excess causes an increase in the inverted spectral index \citep{1997ApJ...490L..77S, 2006JPhCS..54..328K}."949Our observing frequencies are just in the transition region between cm- and sub-mm range., Our observing frequencies are just in the transition region between cm- and sub-mm range.950" Therefore the measured spectral indices are slightly higher than previously reported spectra, resulting from VLBI at cm-wavelengths."," Therefore the measured spectral indices are slightly higher than previously reported spectra, resulting from VLBI at cm-wavelengths."951 ? made simultaneous multi-wavelength observations of AA* in 2003., \citet{2005ApJ...634L..49A} made simultaneous multi-wavelength observations of A* in 2003.952 They describe the spectrum from short centimeter (3.6ccm) to millimeter mmm) wavelengths by a power law of the form S , They describe the spectrum from short centimeter cm) to millimeter mm) wavelengths by a power law of the form S $\propto \nu^{0.43}$.953ος99. ? measured a spectral index of 0.52 between mmm and 2mmm wavelength., \citet{1998ApJ...499..731F} measured a spectral index of 0.52 between mm and mm wavelength.954" The observed spectral indices reported here are fullyconsistent with these previous studies, and confirm the onset of a sub-mm excess over the more shallow power-law shape seen at cm-wavelength."," The observed spectral indices reported here are fullyconsistent with these previous studies, and confirm the onset of a sub-mm excess over the more shallow power-law shape seen at cm-wavelength."955its maxinmn briehtness.,its maximum brightness.956 The average post-imipact maximum-light spectral distribution is shifted to match the average flix [rom 625 nm to 3875 nm at other times., The average post-impact maximum-light spectral distribution is shifted to match the average flux from 625 nm to 875 nm at other times.957 The deviations from this fits al times prior to the impact. and in the days after the impact when the inner coma of comet Tempel 1. had essentially returned to its normal condition. show that the Εκ at short wavelenths was lower al those times.," The deviations from this fits at times prior to the impact, and in the days after the impact when the inner coma of comet Tempel 1 had essentially returned to its normal condition, show that the flux at short wavelenths was lower at those times."958 The 375 mm data point is about 0.2 mag lower (han during the peak post-impact brightness., The 375 nm data point is about 0.2 mag lower than during the peak post-impact brightness.959 This is particularly well seen in the 7/5.∕ 7/7. and 7/8 data points in Fig.," This is particularly well seen in the 7/5, 7/7, and 7/8 data points in Fig."960 Th., 7b.961 For Che quiescent state of the comet. the long ∖∖⊽≀↧↴∖↽≼↲↥≼↲∐≸≟⊔↥↕↽≻∪↕∐↥⋝∖⊽∐≼↲⊳∖⇁∡∖⇁⊳∖⊽∩↲↕∐≀↧↴∐≺∢≀↧↴∐⋡∖↽≀↧↴∣↽≻∪∖⇁≼↲⊔∐↲↓∎↓⊔≼↲≼⊔↕∐↕↽≻≀↧↴≺∢↥≼↲∙↿≼↲≺∢↥≀↧↴⊳∖⇁↕↽≻≼↲≺∢∏⋅∏∐↓⋅⊔∐↲≼↲∐≱≼↲≺∢↥↕⊳∖⇁ small (220.05 mag).," For the quiescent state of the comet, the long wavelength points lie systematically above the fitted impact ejecta spectrum, the effect is small $\approx$ 0.05 mag)."962 Over the full range [rom 375 nm to 925 nm. we observe that the impact eeneraled ejecta were 220.25 mag bluer (han the quiescent comet coma.," Over the full range from 375 nm to 925 nm, we observe that the impact generated ejecta were $\approx$ 0.25 mag bluer than the quiescent comet coma."963 This corresponds to awd per 100 nm change in the slope of the spectrum averaged over (he wavelength range from 375 nm to 925 nm., This corresponds to a $\approx$ per 100 nm change in the slope of the spectrum averaged over the wavelength range from 375 nm to 925 nm.964 This change in color can be explained by an unspecifie combination of two effects., This change in color can be explained by an unspecific combination of two effects.965 First. the particle size distribution of the material ejected after (he impact may contain a lareer fraction of very small particles. much smaller (han (he wavelengths of visible light that leads to a bluer color of the Raleigh scattered light.," First, the particle size distribution of the material ejected after the impact may contain a larger fraction of very small particles, much smaller than the wavelengths of visible light that leads to a bluer color of the Raleigh scattered light."966 Second. it may point to large quantities of pure water ice crvstals that are known to have blue optical rellection spectra (Liev Clark 1985).," Second, it may point to large quantities of pure water ice crystals that are known to have blue optical reflection spectra (Lucey Clark 1985)."967 Infrared observations of the post-impact material have also found indications that the size distribution of impact-ejected material contained more small particles than were released bv (he comet outside of the impact event (IIarker Woodward and Wooden 2005) and (Sugita et al., Infrared observations of the post-impact material have also found indications that the size distribution of impact-ejected material contained more small particles than were released by the comet outside of the impact event (Harker Woodward and Wooden 2005) and (Sugita et al.968 2005)., 2005).969 In combination. the changes in (he comet's color in the hours after impact indicate that the material ejected by (the impact contains smaller particles aud more ice. and is therefore probably more pristine than the material released from the surface of the comet under normal conditions.," In combination, the changes in the comet's color in the hours after impact indicate that the material ejected by the impact contains smaller particles and more ice, and is therefore probably more pristine than the material released from the surface of the comet under normal conditions."970potential in a rotating reference [rame centered. on the cluster centre-of-mass. with the .r-axis directed. away from. the galactie centre and the y-axis in the direction of motion (see Ciersz Llegeic 1997: Vesperini Legeie 1997).,potential in a rotating reference frame centered on the cluster centre-of-mass with the $x$ -axis directed away from the galactic centre and the $y$ -axis in the direction of motion (see Giersz Heggie 1997; Vesperini Heggie 1997).971 A tidal radius (also called the Jacobi radius: Gieles Baumearelt 2008). can then be defined corresponding to the saddle point on the aeaxis of the ellective cluster potential.," A tidal radius (also called the Jacobi radius: Gieles Baumgardt 2008), can then be defined corresponding to the saddle point on the $x$ -axis of the effective cluster potential."972 Within an /-bodvy simulation the user has the freedom to set a length-scale Ro. with one possible choice being that the outermost stars of the initial density. profile are scaled to sit at à. in which case the cluster is said to be Itoche-Iobe filling (e.g. Fanikawa Fukushige 2005).," Within an $N$ -body simulation the user has the freedom to set a length-scale $R_{\rm sc}$ with one possible choice being that the outermost stars of the initial density profile are scaled to sit at $r_{\rm t}$, in which case the cluster is said to be Roche-lobe filling (e.g. Tanikawa Fukushige 2005)."973 Phe Plummoer profile formally. extends to infinite radius so in practice a cut-olf at à radius of is applied to avoid rare cases of large distance.," The Plummer profile formally extends to infinite radius so in practice a cut-off at a radius of $\sim 10 \, r_{\rm h}$ is applied to avoid rare cases of large distance."974 For our Plunimer models described below this leads to Fia2Srn. where rugas ds the position of the outermost star. and. we define κε as the tidal-radius filling factor.," For our Plummer models described below this leads to $r_{\rm max} \simeq 8 \, r_{\rm h}$, where $r_{\rm max}$ is the position of the outermost star, and we define $r_{\rm max} / r_{\rm t}$ as the tidal-radius filling factor."975 The related ratio rj/ri is an important quantity to describe the structure ol star cluster models., The related ratio $r_{\rm h} / r_{\rm t}$ is an important quantity to describe the structure of star cluster models.976" In this work we model parent galaxies with two distinct masses: Ma=9010""M. to represent a dwarl galaxy such as NOGCG6822 and Ak=9.103134. to model a more substantial galaxy such as M31."," In this work we model parent galaxies with two distinct masses: $M_{\rm g} = 9 \times 10^{9} \, M_\odot$ to represent a dwarf galaxy such as $\,6822$ and $M_{\rm g} = 9 \times 10^{10} \, M_\odot$ to model a more substantial galaxy such as M31."977" As discussed. above all clusters are set to orbit at 76,= LOkpe in these model galaxies."," As discussed above all clusters are set to orbit at $R_{\rm gc} = 10\,$ kpc in these model galaxies."978 Six distinct. models are. performed., Six distinct models are performed.979 These are listed in ‘Table 1.., These are listed in Table \ref{t:table1}.980. Models NI. N2 and N3 are all evolved. in. the 6822-like tidal field.," Models N1, N2 and N3 are all evolved in the $\,6822$ -like tidal field."981 They are identical in all respects except for using ιο=7. 14 and 21 so that they have initial ticlal-raclii filling factors of 0.33. 0.66 ancl 1.00. respectively (the corresponding rm/r; ratios are given in Table 1)).," They are identical in all respects except for using $R_{\rm sc} = 7$, 14 and 21 so that they have initial tidal-radii filling factors of 0.33, 0.66 and 1.00, respectively (the corresponding $r_{\rm h} / r_{\rm t}$ ratios are given in Table \ref{t:table1}) )."982 \loclel ΝΟΕ is the same as N2 except that it starts with 95000 single stars and 5000 binaries rather than 100000. single. stars.," Model N2b is the same as N2 except that it starts with $95\,000$ single stars and $5\,000$ binaries rather than $100\,000$ single stars."983 We then have Model MI whieh is evolved in the stronger AIS1-like tical field for comparison., We then have Model M1 which is evolved in the stronger M31-like tidal field for comparison.984 All of these models start with a Plummer density. profile whereas Model Al2 starts with a Wine profile and is also evolved in the M31-like tidal field., All of these models start with a Plummer density profile whereas Model M2 starts with a King profile and is also evolved in the M31-like tidal field.985 Both MI and M2 start with tidal-racii filling factors of 1.00 (rs matches the tidal radius)., Both M1 and M2 start with tidal-radii filling factors of 1.00 $r_{\rm max}$ matches the tidal radius).986 The initial mass of each model is AM258000A. which gives an initial ri of 129 pe for models NI. N2. N2b and N3 compared to 60 pc for models ALL ancl M2.," The initial mass of each model is $M \simeq 58\,000 \, M_\odot$ which gives an initial $r_{\rm t}$ of $129\,$ pc for models N1, N2, N2b and N3 compared to $60\,$ pc for models M1 and M2."987 Each model is evolved. to an age of 20 vr or until of the stars remain. whichever occurs first 1e latter only happens for M2 at an age of 17.4Gvr.," Each model is evolved to an age of $20\,$ Gyr or until of the stars remain, whichever occurs first – the latter only happens for M2 at an age of $17.4\,$ Gyr."988 The simulations are performed using Tesla SLOTO GPUs at Swinburne University., The simulations are performed using Tesla S1070 GPUs at Swinburne University.989 We will also lean on the results of some previous iN- simulations when evaluating our results., We will also lean on the results of some previous $N$ -body simulations when evaluating our results.990 These include models. IX100-00a. and Ix100-00b. of LIurley. (2007) which both featurecl 100000 single stars evolved within a standard Galactic tidal field (Ciersz Llegeic 1997): an orbital speed of 220kms tat Reo=S 5kpe (with corresponding AL.=9.LOM ALY.," These include models K100-00a and K100-00b of Hurley (2007) which both featured $100\,000$ single stars evolved within a standard Galactic tidal field (Giersz Heggie 1997): an orbital speed of $220 \, {\rm km} \, {\rm s}^{-1}$ at $R_{\rm gc} = 8.5\,$ kpc (with corresponding $M_{\rm g} = 9 \times 10^{10} \, M_\odot$ )."991 Phe two models were setup in the same wav and the difference of note was the formation of a long-lived binary composed. of two stellar-mass black holes (12115) in Ix100-00b which altered the central structure of the cluster compared to W100-00a., The two models were setup in the same way and the difference of note was the formation of a long-lived binary composed of two stellar-mass black holes (BHs) in K100-00b which altered the central structure of the cluster compared to K100-00a.992 Along the same lines we will use the results of Alackey ct al. (, Along the same lines we will use the results of Mackey et al. (9932008) who looked at the clfect ofa population of DII-BII binaries on cluster evolution. as well as models including intermeciate-mass black-holes (e.g. Cull et al.,"2008) who looked at the effect of a population of BH-BH binaries on cluster evolution, as well as models including intermediate-mass black-holes (e.g. Gill et al."994 2008)., 2008).995 Also mentioned will be models of 30000 single stars from Liurley et al. (," Also mentioned will be models of $30\,000$ single stars from Hurley et al. ("9962004). mainly [or illustrative purposes.,"2004), mainly for illustrative purposes."997 lt is important to emphasize that unless. otherwise μα»ecified the radii quoted will be based on three-dimoensional ata., It is important to emphasize that unless otherwise specified the radii quoted will be based on three-dimensional data.998 The core radius. r«. comes from a cdensitv-weighted aleulation (C'asertano μι 1985) that is. traditionally used in. N-body models. and. is not. comparable to. the uantitv derived. by observational methods.," The core radius, $r_{\rm c}$, comes from a density-weighted calculation (Casertano Hut 1985) that is traditionally used in $N$ -body models and is not comparable to the quantity derived by observational methods."999 This has been iscussecl in the past (e.g. Wilkinson et al., This has been discussed in the past (e.g. Wilkinson et al.1000 2003: Llurley 2007)., 2003; Hurley 2007).1001 For our purposes this is fine as we use re as an indicator of the cluster cdvnamical state. in. particular to etermine if core-collapse has been reached. rather than to compare to observed results for actual clusters.," For our purposes this is fine as we use $r_{\rm c}$ as an indicator of the cluster dynamical state, in particular to determine if core-collapse has been reached, rather than to compare to observed results for actual clusters."1002 We also use ry as the three-cimensional half-miass racius., We also use $r_{\rm h}$ as the three-dimensional half-mass radius.1003 Here we are mainly interested in the relative values between mocels., Here we are mainly interested in the relative values between models.1004 Llowever. we will also provide the hall-leht radius. yo. calculated. from a two-dimensional projection of the data. to give a reference point for comparing the size of the mocel clusters to real clusters.," However, we will also provide the half-light radius, $r_{\rm h,l}$, calculated from a two-dimensional projection of the data, to give a reference point for comparing the size of the model clusters to real clusters."1005 The cilferent initial filling factors of models NI. N2 and N3 leac to cülferent. initial half-mass radii (see Table 1)) and allow us to investigate the elfect this has on the long-term evolution of star clusters residing within a weak tidal field.," The different initial filling factors of models N1, N2 and N3 lead to different initial half-mass radii (see Table \ref{t:table1}) ) and allow us to investigate the effect this has on the long-term evolution of star clusters residing within a weak tidal field."1006 lt is well established. that the evolution of a star cluster is intricately Linked to the two-body relaxation timescale which is typically characterized by the value at the racius.," It is well established that the evolution of a star cluster is intricately linked to the two-body relaxation timescale which is typically characterized by the value at the half-mass radius,"1007Blandford 2010; Wang et al.,Blandford 2010; Wang et al.1008 2010; Shcherbakov Huang 2011)., 2010; Shcherbakov Huang 2011).1009" Budden eqution, i.e., the second-order equation to the complex function actually corresponds to the same approach (Budden 1972; Zheleznyakov 1977)."," Budden eqution, i.e., the second-order equation to the complex function actually corresponds to the same approach (Budden 1972; Zheleznyakov 1977)."1010" On the other hand, both the standard and the Zheleznyakov-Budden approaches are not quite for quantitative estimates of the polarization of the escaping emission in general case."," On the other hand, both the standard and the Zheleznyakov-Budden approaches are not quite for quantitative estimates of the polarization of the escaping emission in general case."1011" But since we are going to describe the propagation of originally fully polarized waves, not theensemble of waves, we actually need only two equations for observable parameters, i.e., the position angle and the Stokes parameter V."," But since we are going to describe the propagation of originally fully polarized waves, not the of waves, we actually need only two equations for observable parameters, i.e., the position angle and the Stokes parameter $V$."1012" There exists a different approach that allows us immediately write down the equations for these observable quantities, namely, the Stokes parameter V, defining the circular polarization and the position angle p.a., characterizing the orientation of polarization ellipse (Kravtsov Orlov 1990)."," There exists a different approach that allows us immediately write down the equations for these observable quantities, namely, the Stokes parameter $V$, defining the circular polarization and the position angle $p.a.$, characterizing the orientation of polarization ellipse (Kravtsov Orlov 1990)."1013" This approach is valid in the quasi-isotropic case, i.e., in the case when the dielectric tensor can be presented as where the anisotropic part χι is small as compared to isotropic one."," This approach is valid in the quasi-isotropic case, i.e., in the case when the dielectric tensor can be presented as where the anisotropic part $\chi_{ij}$ is small as compared to isotropic one."1014" In this case we have two small parameters — general WKB parameter 1/kL and As a result, the solution can be found by expansion over this two small parameters."," In this case we have two small parameters — general WKB parameter $1/kL$ and As a result, the solution can be found by expansion over this two small parameters."1015" As one can check, these conditions are just realized in the pulsar magnetosphere (Andrianov Beskin 2010)."," As one can check, these conditions are just realized in the pulsar magnetosphere (Andrianov Beskin 2010)."1016" Indeed, in the region r~res;10”R the value of v=wp/w* is much smaller than unity."," Indeed, in the region $r \sim r_{\rm esc} \sim 10^{3}R$ the value of $v = \omega_{\rm p}^2/\omega^2$ is much smaller than unity."1017" Accordingly, the deviation of the refractive indices from unity, |n1,2—1|ev, is also very small here, so we can neglect the wave refraction in the polarization formation region."," Accordingly, the deviation of the refractive indices from unity, $|n_{1,2}-1| \sim v$, is also very small here, so we can neglect the wave refraction in the polarization formation region."1018" 'The Kravtsov-Orlov equation is the equation for the complex angle O=0)+i0», where O is a position angle and O5 determines the circular polarization by the relation Here I is the intensity of the wave."," The Kravtsov-Orlov equation is the equation for the complex angle $\Theta = \Theta_1 + i \Theta_2$, where $\Theta_1$ is a position angle and $\Theta_2$ determines the circular polarization by the relation Here $I$ is the intensity of the wave."1019 The components of the dielectric tensor xi; are to be written in a frame of unitary vectors a and b in the picture plane where a is determined by the projection of the vector Ve., The components of the dielectric tensor $\chi_{ij}$ are to be written in a frame of unitary vectors ${\bf a}$ and ${\bf b}$ in the picture plane where ${\bf a}$ is determined by the projection of the vector $\nabla \varepsilon$.1020" Finally, is the ray torsion (see Kravtsov Orlov 1990 for more detail)"," Finally, is the ray torsion (see Kravtsov Orlov 1990 for more detail)."1021 It can be easily understood that the rotation of position angle described by the ray torsion is fictious and describes only the rotation of coordinate system., It can be easily understood that the rotation of position angle described by the ray torsion is fictious and describes only the rotation of coordinate system.1022" As a result, we can write down Here is a coordinate along the ray propagation, and the angle Bg(1) defines the orientation of the external magnetic field in the picture plane 3)."," As a result, we can write down Here $l$ is a coordinate along the ray propagation, and the angle $\beta_{B}(l)$ defines the orientation of the external magnetic field in the picture plane )."1023" Further, where the signs correspond to the regions before/after the cyclotron resonance and Finally, εν} are the components of plasma dielectric tensor in the frame where the z-axis directs along the wave propagation and the external magnetic field lies in the xz- plane (see Appendix C)."," Further, where the signs correspond to the regions before/after the cyclotron resonance and Finally, $\varepsilon_{i'j'}$ are the components of plasma dielectric tensor in the frame where the $z$ -axis directs along the wave propagation and the external magnetic field lies in the $xz$ -plane (see Appendix C)."1024 We would like to note that in these equations the circular polarization is defined as it is common in radio astronomy (positive V corresponds to LHC polarization)., We would like to note that in these equations the circular polarization is defined as it is common in radio astronomy (positive $V$ corresponds to LHC polarization).1025 Nonrelativistic version of the above equations is given in Czyz et al. (, Nonrelativistic version of the above equations is given in Czyz et al. (10262007).,2007).1027"2008). As one can see on Fig. 10,,"," As one can see on Fig. \ref{angles},"1028 in the geometrical optics region Eqns. (70))-(71)), in the geometrical optics region Eqns. \ref{t1}) \ref{t2}) )1029 describe of the angle Θι near the value 0;=fg-Γδ., describe of the angle $\Theta_{1}$ near the value $\Theta_{1} = \beta_{B} + \delta$.1030" As the ray moves into the region of rarefied plasma, the length of the spatialoscillations L~c/(wAn) increases and in the region becomes larger than the characteristic length r."," As the ray moves into the region of rarefied plasma, the length of the spatial $L \sim c/(\omega \Delta \, n)$ increases and in the region becomes larger than the characteristic length $r$."1031" As a result, the angles Θι and O» become constant for r>>resc."," As a result, the angles $\Theta_{1}$ and $\Theta_{2}$ become constant for $r \gg r_{\rm esc}$."1032 They are the values that characterize the outgoing radiation., They are the values that characterize the outgoing radiation.1033" Thus, the basic equations (70))-(71)) generalize ones obtained by Andrianov Beskin (2010) for zero drift velocity U=0 when Re[e,,]=0 and, hence, 6= 0."," Thus, the basic equations \ref{t1}) \ref{t2}) ) generalize ones obtained by Andrianov Beskin (2010) for zero drift velocity ${\bf U}=0$ when ${\rm Re}\,[\varepsilon_{x'y'}] = 0$ and, hence, $\delta = 0$ ."1034" In particular, they now include into consideration the aberration effect considered by Blaskiewicz et al. ("," In particular, they now include into consideration the aberration effect considered by Blaskiewicz et al. ("10351991).,1991).1036" This effect was also considered by Petrova Lyubarskii (2000), but for the infinite magnetic field only."," This effect was also considered by Petrova Lyubarskii (2000), but for the infinite magnetic field only."1037 It is important that in Eqns. (70))-(71)), It is important that in Eqns. \ref{t1}) \ref{t2}) )1038 the angle ©; is measured relative to the laboratory frame because these equations contain the difference between ©; and fp only., the angle $\Theta_1$ is measured relative to the laboratory frame because these equations contain the difference between $\Theta_1$ and $\beta_{B}$ only.1039 Equations above have the following important property., Equations above have the following important property.1040" For homogeneous media (fg= const, ei;= const) the parameters of polarization ellipse O1 and Θο remain constant if the following conditions are valid: Here (see the definition of e»;; in Appendix D)"," For homogeneous media $\beta_{B} = $ const, $\varepsilon_{ij} =$ const) the parameters of polarization ellipse $\Theta_1$ and $\Theta_2$ remain constant if the following conditions are valid: Here (see the definition of $\epsilon_{i'j'}$ in Appendix D)"1041Our * value of 2.1+0.2 is consistent with that of the CMF in the OMC-1 region (Ikeda&Kitamura2009)..,Our $\gamma$ value of $\pm$ 0.2 is consistent with that of the CMF in the OMC-1 region \citep{ike09b}.1042 This agreement confirms that our observations could resolve star-forming cores even at the large distance of ~ 1 kpc., This agreement confirms that our observations could resolve star-forming cores even at the large distance of $\sim $ 1 kpc.1043 A poor spatial resolution is one of the major causes of the underestimation of y., A poor spatial resolution is one of the major causes of the underestimation of $\gamma$.1044" To examine the dependence of y on the spatial resolution, we created the smoothed OMC-1 data cubes by changing the effective resolutions, as described in 84.2,, and derived the y values for the smoothed cubes, as shown in Figure 16.."," To examine the dependence of $\gamma$ on the spatial resolution, we created the smoothed OMC-1 data cubes by changing the effective resolutions, as described in \ref{coreProperties}, and derived the $\gamma$ values for the smoothed cubes, as shown in Figure \ref{gamma-res}. ."1045" It is clearly shown that our resolution of 22"", corresponding to 0.097 pc for $140, can correctly estimate the y value within the uncertainties."," It is clearly shown that our resolution of $''$, corresponding to 0.097 pc for S140, can correctly estimate the $\gamma $ value within the uncertainties."1046" Actually, our ¥ value is consistent with that in the study by Tachiharaetal.(2002),, having a spatial resolution enough to resolve 0.1 pc-scale cores."," Actually, our $\gamma$ value is consistent with that in the study by \citet{tac02}, having a spatial resolution enough to resolve 0.1 pc-scale cores."1047" In addition, Figure 16 predicts that γ is considerably underestimated for the case that becomes larger than 0.1 pc, which is the minimum radius of the cores in the OMC-1 region at the highest resolution of 0.061 pc."," In addition, Figure \ref{gamma-res} predicts that $\gamma$ is considerably underestimated for the case that becomes larger than 0.1 pc, which is the minimum radius of the cores in the OMC-1 region at the highest resolution of 0.061 pc."1048" Therefore, the small 7 value of ~ 1.7 in RCW 106 (Wongetal.2008) is likely due to the coarse spatial resolution of 0.78 pc at the distance of 3.6 kpc (Lockman1979)."," Therefore, the small $\gamma$ value of $\sim$ 1.7 in RCW 106 \citep{won08}1049 is likely due to the coarse spatial resolution of 0.78 pc at the distance of 3.6 kpc \citep{loc79}."1050". This study concludes that the power-law shape with y > 2 in CMF holds even in tenuous structures with the densities of 1054 of the S140 region, in addition to our recent work by Ikeda&Kitamura(2009) in OMC-1."," This study concludes that the power-law shape with $\gamma$ $>$ 2 in CMF holds even in tenuous structures with the densities of $^{3\mbox{\scriptsize --}4}$ of the S140 region, in addition to our recent work by \citet{ike09b} in OMC-1."1051" Furthermore, the y values of the CMFs in $140 and OMC-1 are quite consistent with that of the Galactic field-averaged IMF of 2.340.7 (Kroupa2001).."," Furthermore, the $\gamma$ values of the CMFs in S140 and OMC-1 are quite consistent with that of the Galactic field-averaged IMF of $\pm$ 0.7 \citep{kro01a}."1052 These observational facts lead us to the hypothesis that the power-law nature in the IMF originates in molecular cloud structures with densities of less thancm?., These observational facts lead us to the hypothesis that the power-law nature in the IMF originates in molecular cloud structures with densities of less than.1053" Our conclusion of the resemblance between the CMF and the IMF is consistent with the recent theoretical works showing that such a resemblance should be understood as a statistical relation, rather than aone-to-one correspondence between a core and a star to be formed within it."," Our conclusion of the resemblance between the CMF and the IMF is consistent with the recent theoretical works showing that such a resemblance should be understood as a statistical relation, rather than aone-to-one correspondence between a core and a star to be formed within it."1054 Smithetal.(2009) examined the formation and evolution of, \citet{smi09} examined the formation and evolution of1055é] frequencies.,all frequencies.1056 The latter point is mostly based ou nousimitancous observations by studving the energy clistribution at different frequencies (e. Lundgreu ct i, The latter point is mostly based on non-simultaneous observations by studying the energy distribution at different frequencies (e.g. Lundgren et al.1057 1995). but simultaneous dual-frequeucy observations have been mace for the Crab pulsar (see Salluen et al.," 1995), but simultaneous dual-frequency observations have been made for the Crab pulsar (see Sallmen et al."1058 1999 aud references therein) where oulv of all eiat pulses are secu both at GOO and 1100 MITz., 1999 and references therein) where only of all giant pulses are seen both at 600 and 1400 MHz.1059 The results of these studies for the spectral index of giant pulses are somewhat iucouclusive., The results of these studies for the spectral index of giant pulses are somewhat inconclusive.1060 While carler observations conclude that. on average. he spectra index of giant pulses is flatter than he average main pulse spectral index. this fiudiug is not supported by the most recent study where the average spectral index of the giant pulscs is comparable to that of the average main pulse (see discussion by Sallmen et al.," While earlier observations conclude that, on average, the spectral index of giant pulses is flatter than the average main pulse spectral index, this finding is not supported by the most recent study where the average spectral index of the giant pulses is comparable to that of the average main pulse (see discussion by Sallmen et al."1061 1999)., 1999).1062 Tlowever. the Crab pulsar has a very steep radio spectruni. so little may be learut from the relative streneth of its normal aud eiut pulses at either extreme eud of the radio spectrin.," However, the Crab pulsar has a very steep radio spectrum, so little may be learnt from the relative strength of its normal and giant pulses at either extreme end of the radio spectrum."1063 However. we can compare other aspects of the strong pulses frou PSR B1133|16 pulses to the known propertics of giant pulses or those of so-called “elaut nicropulses.," However, we can compare other aspects of the strong pulses from PSR B1133+16 pulses to the known properties of giant pulses or those of so-called “giant micropulses”."1064 The latter have been discovered for the Vela pulsar as very strong narrow pulses of very stall width occurring at fixed. narrow phases (Jolustou et al.," The latter have been discovered for the Vela pulsar as very strong narrow pulses of very small width occurring at fixed, narrow phases (Johnston et al."1065 2001). also showing a power-law cherey distribution.," 2001), also showing a power-law energy distribution."1066 While a power-law visible τι the cuuimlative xobabilitv function of elaut pulse flux deusities clearly separates them from normal pulses. this appears not to o the case for PSR B1133116 in Fie. 16..," While a power-law visible in the cumulative probability function of giant pulse flux densities clearly separates them from normal pulses, this appears not to be the case for PSR B1133+16 in Fig. \ref{fluxdist1133}."1067" It is possible hat a amber of LO ""eiant pulses is too small to produce a recognisable feature. but a rate of one strong pulse in every 100 (at [850 MITZ) is a ιο. ligher rate than or PSRs 21 aud D19372] and is comparable to hat of the Crab pulsar."," It is possible that a number of 40 “giant” pulses is too small to produce a recognisable feature, but a rate of one strong pulse in every 100 (at 4850 MHz) is a much higher rate than for PSRs $-$ 24 and B1937+21 and is comparable to that of the Crab pulsar."1068 The noticeable chauge in slope of the hieh cucrey cud of PSR D1133|16's cumulative xobabilitv functions. when come from low to high radio requencies. nay be au indication of an cierging powcr-aw compoucut.," The noticeable change in slope of the high energy end of PSR B1133+16's cumulative probability functions, when going from low to high radio frequencies, may be an indication of an emerging power-law component."1069 It appears that the stroug pulses in PSR D11533|16 xeferablv occur at the pulse phase of the leading component., It appears that the strong pulses in PSR B1133+16 preferably occur at the pulse phase of the leading component.1070 This is verified by computing the average xofile from the 10 strong pulses at 1850 ΛΠΣ., This is verified by computing the average profile from the 40 strong pulses at 4850 MHz.1071 This profile is shown as the inset to Fig., This profile is shown as the inset to Fig.1072 17. where we compare 1 to the average pulse profile., \ref{giants} where we compare it to the average pulse profile.1073 It becomes obvious that the strong oilses appear to be narrower aud indeed appear mostly at he trailing edee of the leading component. being shelthy offset from its centre.," It becomes obvious that the strong pulses appear to be narrower and indeed appear mostly at the trailing edge of the leading component, being slightly offset from its centre."1074 This implies that anv correlation iu he flux densities of the two normal profile compoucuts, This implies that any correlation in the flux densities of the two normal profile components1075Equation 28).,Equation 28).1076" As noted emlier. since this scenario is nearly face-on. fopr Is a factor ~3.1 higher than the detection fraction =Locos20;520, for isotropic eniission."," As noted earlier, since this scenario is nearly face-on, $f_{\rm opt}$ is a factor $\sim 3.4$ higher than the detection fraction $\approx10771-\cos 2\theta_j\approx 2\bar{\theta_j}^{2}$ for isotropic emission."1078 Equation 3 shows that ifthe average opening anele is ~0.12. which is the value inferred for 00512214 0j(Dirvowsetal.2006:Soderberg2006).. as well as the typical opening angle required to recoucile the observed SCRB rate with the best-bet NS-NS ierecr rate refsecGRB)}. then up to fopr~OL of CW: eveuts will be accompanied by potentially detectable optical afterelows.," Equation \ref{eq:fopt} shows that if the average opening angle is $\bar{\theta}_j\simeq 0.12$, which is the value inferred for 051221A \citep{Burrows+06,Soderberg+06}, as well as the typical opening angle required to reconcile the observed SGRB rate with the best-bet NS-NS merger rate \\ref{sec:GRB}) ), then up to $f_{\rm opt}1079\sim 0.1$ of GW events will be accompanied by potentially detectable optical afterglows."1080" This result is consistent with the rate of a few afterglows per vear mferred by Cowardetal.(2011) for their assmued total ALIGO/Virgo merecr rate of ~135 vrἩ,", This result is consistent with the rate of a few afterglows per year inferred by \citet{Coward+11} for their assumed total ALIGO/Virgo merger rate of $\sim 135$ $^{-1}$.1081 On the other laud. if O; is much larger. 2Ub fee. as found for 0050721 by Grupeet 2006)). then fopr is of order uuity. but the overall CW event rate may be lower than the best-bet ALIGO/Vireo rate.," On the other hand, if $\bar{\theta_j}$ is much larger, $\gtrsim 0.4$ (e.g., as found for 050724 by \citealt{Grupe+06}) ), then $f_{\rm opt}$ is of order unity, but the overall GW event rate may be lower than the best-bet ALIGO/Virgo rate."1082" Bevond cousiderations of depth and cadeuce. a ""uique optical identification of CW events also requires discrimination between off-axis afterelows aud potential contanunauts."," Beyond considerations of depth and cadence, a unique optical identification of GW events also requires discrimination between off-axis afterglows and potential contaminants."1083 We discuss this issue in refsec:compare.., We discuss this issue in \\ref{sec:compare}.1084 NS-NS/NS-BIT imiersers inav also be accompaied by non-thermal radio afterglow cuussion. which cau originate either from the ultravelativistic jet (as in the case of the optical afterglow). or from more spherical. sub-relativistic ejecta (Nakar&Piran901111 hereafter NPIL).," NS-NS/NS-BH mergers may also be accompanied by non-thermal radio afterglow emission, which can originate either from the ultra-relativistic jet (as in the case of the optical afterglow), or from more spherical, sub-relativistic ejecta \citealt{Nakar&Piran11}; hereafter NP11)."1085 The latter includes matter ejected dynamically during the merger process (“tidal tails). or in outflows from the accretion disk (see Figure 1)).," The latter includes matter ejected dynamically during the merger process (“tidal tails”), or in outflows from the accretion disk (see Figure \ref{fig:cartoon}) )."1086 Adopting standard models for svuchrotron emission frou. a relativistic shock. NP11 estimate that the peals racio brightuess for these cases is: where Jog= 04/026. 14 is the observing frequency in Guz: aud dj=200d599 Alpe is the luminosity cistance. again normalized to the ALIGO/Virgo rauge for NS-NS morecrs.," Adopting standard models for synchrotron emission from a relativistic shock, NP11 estimate that the peak radio brightness for these cases is: where $\beta_{0.2}=v_{\rm ej}/0.2c$ , $\nu_1$ is the observing frequency in GHz; and $d_{L} = 200 d_{L,200}$ Mpc is the luminosity distance, again normalized to the ALIGO/Virgo range for NS-NS mergers."1087 Equation 5 also assumes characteristic values of p=2.5 for the electron distribution power law index. aud €.=€p0.1 for the fractions of enerev density impartec to relativistic clectrous aud maenetic fields. respectively.," Equation \ref{eqn:Fp} also assumes characteristic values of $p=2.5$ for the electron distribution power law index, and $\epsilon_{e}=1088\epsilon_{B}=0.1$ for the fractions of energy density imparted to relativistic electrons and magnetic fields, respectively."1089 The radio emission peaks at the deceleration time: The peak brightness depends scusitively on both the properties of the ejecta CE and 0) and on the cireumburst density., The radio emission peaks at the deceleration time: The peak brightness depends sensitively on both the properties of the ejecta $E$ and $\beta$ ) and on the circumburst density.1090 As we diseuss du detail below. the realistic detection threshold for à couvineing detection with the EVLA (even with ~30 hr per epoch) is about 0.5 iis.," As we discuss in detail below, the realistic detection threshold for a convincing detection with the EVLA (even with $\sim 30$ hr per epoch) is about 0.5 mJy."1091 This requirement therefore defines a figure of merit for a radio detection of: With the exception of the velocity paramcter. this figure of merit is identical to the case of off-axis optical afterglows in teris of the dependence ou Ej aud à.," This requirement therefore defines a figure of merit for a radio detection of: With the exception of the velocity parameter, this figure of merit is identical to the case of off-axis optical afterglows in terms of the dependence on $E_j$ and $n$."1092" For quasi-spherical ejecta. a characteristic mass of Ma~LO? AL. in tidal tails or disk winds has an EzmoMaenj2~10""10. ere for the expected range of velocities?)~ο0."," For quasi-spherical ejecta, a characteristic mass of $M_{\rm ej}\sim109310^{-2}$ $_\odot$ in tidal tails or disk winds has an $E\approx M_{\rm ej}v_{\rm ej}^{2}/2\sim 10^{50}-10^{51}$ erg for the expected range of $\beta\sim10940.1-0.3$."1095" This results in at most FOAM,G2Ola,ÜN requiring ay21 ? for a detection."," This results in at most $FOM_{\rm rad}\approx 0.4\,1096n_0^{7/8}$, requiring $n_0\gtrsim 1$ $^{-3}$ for a detection."1097 For more typical densities of =0.1 cem5m associated. with SCRBs (Bergeretal.2005:Soderbergetal. 2006).. the radio enuüssion frou quasi-spherical ejecta will be essentially undetectable uuless the energy seale is uch laveer than ~1073 ere (Figure 6)).," For more typical densities of $\lesssim 0.1$ $^{-3}$ associated with SGRBs \citep{Berger+05,Soderberg+06}, the radio emission from quasi-spherical ejecta will be essentially undetectable unless the energy scale is much larger than $\sim 10^{51}$ erg (Figure \ref{fig:fom}) )."1098 Equations 5- 7. can also be applied to the case of off-axis afterglow cuuission using c1d (Nakar&Pivan2011) along with values for the jet energv aud cireuniburst density inferred from the optical afterglow data (POALpronZ0.1: Equation 1)).," Equations \ref{eqn:Fp}- \ref{eqn:fomr} can also be applied to the case of off-axis afterglow emission using $\beta\approx 1$ \citep{Nakar&Piran11} along with values for the jet energy and circumburst density inferred from the optical afterglow data $FOM_{\rm opt,on}\lesssim 0.1$; Equation \ref{eqn:fomo}) )."1099 In Figure 6 we plot the region of Lo phase-space that is accessible to radio detections (FOAM2 0.2)., In Figure \ref{fig:fom} we plot the region of $E-n$ phase-space that is accessible to radio detections $FOM_{\rm rad}\gtrsim 0.2$ ).1100 As cau be seen from the Figure. none of the existingad SCRB optical afterglow intersect this region. indicating that radio detections of off-axis afterelows are likely to be rare despite the overall isotropy of the signal.," As can be seen from the Figure, none of the existing SGRB optical afterglow intersect this region, indicating that radio detections of off-axis afterglows are likely to be rare despite the overall isotropy of the signal."1101 We now address in detail the estimated mininuuu radio brightuess necessary for a successful detection., We now address in detail the estimated minimum radio brightness necessary for a successful detection.1102 Although faint radio enussion is in principle detectable with a deep integration. a significant challenge is the sinall feld of view of sensitive instruments such as the EVLA (z0.1 deg? at 1 GIIz) requiring ~100200 poiutings to cover a typical CAV error region of teus of square deerees.," Although faint radio emission is in principle detectable with a deep integration, a significant challenge is the small field of view of sensitive instruments such as the EVLA $\approx 0.4$ $^2$ at 1 GHz), requiring $\sim 100-200$ pointings to cover a typical GW error region of tens of square degrees."1103 Tarecting individual galaxies within the error region does not decrease the number of required pointings since there are 100 ealaxies with LoOL within a typical error region (to 200 Mpc).," Targeting individual galaxies within the error region does not decrease the number of required pointings since there are $\sim1104400$ galaxies with $L\gtrsim 0.1\,L^*$ within a typical error region (to 200 Mpc)."1105 Even with oulv 10 miu per pointing. 30 hrper epoch will be required to cover the full error already a substantial allocation of EVLA time.," Even with only 10 min per pointing, $\sim 30$ hrper epoch will be required to cover the full error , already a substantial allocation of EVLA time."1106 Multiple, Multiple1107Unusual spectral. polarization. and Uuctuation properties of the precursors make them puzzling.,"Unusual spectral, polarization, and fluctuation properties of the precursors make them puzzling."1108— To the best of our. knowledge. no attempts have previously. been aimed at explaining the physies of this phenomenon.," To the best of our knowledge, no attempts have previously been aimed at explaining the physics of this phenomenon."1109 Recently Dyvks.Zhang&Cil(2005) have suggested. a geometrical model for the profile of PSI. 1822-09., Recently \citet*{d05} have suggested a geometrical model for the profile of PSR B1822-09.1110 These authors assume that the main pulse and the precursor originate. independently at dillerent locations in. the magnetosphere ancl the precursor. emission. intermittently reverses its direction to form the interpulse., These authors assume that the main pulse and the precursor originate independently at different locations in the magnetosphere and the precursor emission intermittently reverses its direction to form the interpulse.1111 In that model. the mechanism of reversal of the emission direction remains obscure. but for any conceivable switching mechanism it is principally clillieult to explain its dependence on the main pulse intensity.," In that model, the mechanism of reversal of the emission direction remains obscure, but for any conceivable switching mechanism it is principally difficult to explain its dependence on the main pulse intensity."1112 In the present paper. we for the first time propose a physical mechanism of the precursor. formation.," In the present paper, we for the first time propose a physical mechanism of the precursor formation."1113 La our model. the precursor arises as a result of induced scattering of the main pulse emission. into the background by the particles of the ultrarelativistic highhy maenetizecl plasma ofa pulsar.," In our model, the precursor arises as a result of induced scattering of the main pulse emission into the background by the particles of the ultrarelativistic highly magnetized plasma of a pulsar."1114 Our mechanism naturally explains the observed polarization. spectral. and [uctuation properties of the precursor emission as well as suggests its connection to the main pulse.," Our mechanism naturally explains the observed polarization, spectral, and fluctuation properties of the precursor emission as well as suggests its connection to the main pulse."1115 Pulsar radio emission is generated deep in the magnetosphere inside of the open field line tube., Pulsar radio emission is generated deep in the magnetosphere inside of the open field line tube.1116 Lence. it originates ancl propagates in the Dow of the ultrarelativistic clectron-positron plasma. which streams alone the open magnetic lines.," Hence, it originates and propagates in the flow of the ultrarelativistic electron-positron plasma, which streams along the open magnetic lines."1117" As the brightness temperatures of the radio emission are extremely high. Tg~107%10°"" IK. the waves may be subject to elflicient induced scattering oll the plasma particles."," As the brightness temperatures of the radio emission are extremely high, $T_B\sim 10^{25}-10^{30}$ K, the waves may be subject to efficient induced scattering off the plasma particles."1118" According to the radio emission theories. based on the plasma instabilities. the frequeney of the generated waves is close to the local Lorentz-shifted: proper plasma frequency. Ww wp where wy=vn,c?£m. n, is the plasma number density.. ο and n are the electron. charge and mass. and 5 is the plasma Lorentz-Factor. (but.seeMelrose&Geclalin1999.forthecriticismofthis point).."," According to the radio emission theories based on the plasma instabilities, the frequency of the generated waves is close to the local Lorentz-shifted proper plasma frequency, $\omega\sim\omega_p\sqrt{\gamma}$ , where $\omega_p\equiv\sqrt{4\pi1119n_ee^2/m}$, $n_e$ is the plasma number density, $e$ and $m$ are the electron charge and mass, and $\gamma$ is the plasma Lorentz-factor \citep[but see][for the criticism of this1120point]{gm99}."1121 In the vicinity of the emission. region. where the above condition is still valid. induced scattering olf the plasma particles is a collective process.," In the vicinity of the emission region, where the above condition is still valid, induced scattering off the plasma particles is a collective process."1122 The transverse waves are involved. in the induced. three-wave interactions (Luo&Melrose 2006)., The transverse waves are involved in the induced three-wave interactions \citep{lm06}.1123. X particular case of inducecl Ramanscattering in application to the pulsar magnetosphere has been considered by Gangadhara&Ixrishan(1993) and Lyutikoy(1998)., A particular case of induced Ramanscattering in application to the pulsar magnetosphere has been considered by \citet{gk93} and \citet{l98}.1124. As the plasma number density decreases with distance from the neutron star along with the magnetic field strength. προBoxer well above the emission. region w and the collective cllects become negligible.," As the plasma number density decreases with distance from the neutron star along with the magnetic field strength, $n_e\propto1125B\propto r^{-3}$, well above the emission region $\omega\gg\omega_p\sqrt{\gamma}$ and the collective effects become negligible."1126 The cuexternal magnetic field. significantly allects the scattering process on condition that the radio wave frequency in the particle rest. frame is much. less than the electron gvrolrequeney. a!xwe;=eB/me.," The external magnetic field significantly affects the scattering process on condition that the radio wave frequency in the particle rest frame is much less than the electron gyrofrequency, $\omega^\prime\ll\omega_G\equiv eB/mc$."1127 This condition is valid up to the radius of evelotron resonance. which lies in the outer magnetosphere.," This condition is valid up to the radius of cyclotron resonance, which lies in the outer magnetosphere."1128 In the present paper. we examine the induced. scattering. which takes place well above the emission region and well below the evelotron resonance radius.," In the present paper, we examine the induced scattering, which takes place well above the emission region and well below the cyclotron resonance radius."1129 Then the magnetized induced Compton scattering is à single-particle process ancl the incident waves are approximately transverse. clectromagnetic waves polarized either in the plane of the wavevector. and. the ambient magnetic field or perpendicularly to this plane., Then the magnetized induced Compton scattering is a single-particle process and the incident waves are approximately transverse electromagnetic waves polarized either in the plane of the wavevector and the ambient magnetic field or perpendicularly to this plane.1130 In application to. pulsar magnetosphere. induced scattering in a superstrong magnetic field has first. been considered by Blandford&Sceharlemann(1976). anel found to be ellicient.," In application to pulsar magnetosphere, induced scattering in a superstrong magnetic field has first been considered by \citet{bs76} and found to be efficient."1131 Later on the process has been suggested. to explain a number of phenomena in pulsar radio emission (Lyubarskit&Petrova1996:2004a.b).," Later on the process has been suggested to explain a number of phenomena in pulsar radio emission \citep{lp96,p04a,p04b}."1132. In. the present paper. we consider the pulsar radio beam scattering into the background. and particularly concentrate on the erowth of the scattered. component. which is identified with the precursor component of the pulse profile.," In the present paper, we consider the pulsar radio beam scattering into the background and particularly concentrate on the growth of the scattered component, which is identified with the precursor component of the pulse profile."1133 In the preceding literature on the induced scattering in a superstrong magnetic field. the kinetic equation for photon occupation numbers is derived from. an analysis of the scattering by a single relativistic electron and does. not include the particle cüstribution function explicitly. so that it directly. corresponds to the cold plasma case.," In the preceding literature on the induced scattering in a superstrong magnetic field, the kinetic equation for photon occupation numbers is derived from an analysis of the scattering by a single relativistic electron and does not include the particle distribution function explicitly, so that it directly corresponds to the cold plasma case."1134 In the present oer. we generalize the kinetic equation for the more realistic case of a hot plasma.," In the present paper, we generalize the kinetic equation for the more realistic case of a hot plasma."1135 The corresponding formalism js also been outlined in Blandford&Scharlemann(1976).. out. we shall go through the derivation once more in order ο Correct a slight error in that. paper.," The corresponding formalism has also been outlined in \citet{bs76}, but we shall go through the derivation once more in order to correct a slight error in that paper."1136 In the approximation of an infinitely strong magnetic ield. the scattering cross-section in the electron frametakes he form where ris the classical cleetron radius. 6 and 6j are the propagation angles of the incident ancl scattered photons. respectively. OY is the elementary. solid. angle [or the scattered. photons. and the primes denote. the quantities of the electron rest frame.," In the approximation of an infinitely strong magnetic field, the scattering cross-section in the electron frametakes the form where $r_e$ is the classical electron radius, $\theta^\prime$ and $\theta_1^\prime$ are the propagation angles of the incident and scattered photons, respectively, $\rm d\Omega_1^\prime$ is the elementary solid angle for the scattered photons, and the primes denote the quantities of the electron rest frame."1137 The cross-section (1) corresponds to the scattering between the photons with the ordinary polarization. i.c with the electric vectors lving in he plane of the ambient magnetic field.," The cross-section (1) corresponds to the scattering between the photons with the ordinary polarization, i.e with the electric vectors lying in the plane of the ambient magnetic field."1138 The scattering involving the extraordinary polarization states is negligible. since any perturbecl motion of a particle (in the field. of he incident wave) perpendicular to the ambient. magnetic 101 is suppressed.," The scattering involving the extraordinary polarization states is negligible, since any perturbed motion of a particle (in the field of the incident wave) perpendicular to the ambient magnetic field is suppressed."1139 Let us consider the scattering in. the aboratory [rame between the two photon states. & and ky. involving the electrons with the momenta p and p|dp along he magnetic field.," Let us consider the scattering in the laboratory frame between the two photon states, $\bmath{k}$ and $\bmath1140{k_1}$, involving the electrons with the momenta $p$ and $p+\delta1141p$ along the magnetic field."1142 In the scattering act. the momentun xwallel to the magnetic field is conserved: The probability of generating spontaneously. scattered photons per electron per unit time is given by whereafk) is the photon occupation. number. Jcos8. 3 ds the particle velocity in units of e. and the argument of the delta-function signifies the equality of the," In the scattering act, the momentum parallel to the magnetic field is conserved: The probability of generating spontaneously scattered photons per electron per unit time is given by where$n(\bmath k)$ is the photon occupation number, $\eta\equiv11431-\beta\cos\theta$ , $\beta$ is the particle velocity in units of $c$ , and the argument of the delta-function signifies the equality of the"1144power law is ruled out from the fits. unless the gas-to-dust ratio is very low.,"power law is ruled out from the fits, unless the gas-to-dust ratio is very low."1145 The broken power law high energy slope was fixed at à spectral index of 3=1.0 as found in its to the X-ray spectrum alone., The broken power law high energy slope was fixed at a spectral index of $\beta=1.0$ as found in fits to the X-ray spectrum alone.1146 The lower energy. slope was fixed at;=0.5 as expected. for a cooling break in he standard fireball model (Sari.Piran.&Naravan1998)., The lower energy slope was fixed at $\beta=0.5$ as expected for a cooling break in the standard fireball model \citep{Sari}.1147. Below z&LS the fit becomes unacceptably poor (P<2% Yom a X7 test)., Below $z\approx1.8$ the fit becomes unacceptably poor $P<2$ from a $\chi^2$ test).1148 The region shown is curtailed at the upper end at 2=4 based on the limits from the optical spectrum. discussed below., The region shown is curtailed at the upper end at $z=4$ based on the limits from the optical spectrum discussed below.1149 The vertical extent of the region represents he error range on chy., The vertical extent of the region represents the error range on $A_V$.1150 We note that the hatched area is essentially consistent with the requirement of a reddened afterglow (above the solid curve)., We note that the hatched area is essentially consistent with the requirement of a reddened afterglow (above the solid curve).1151 Phe part of the hatched region which does not coincide with the grey shaded. band corresponds to best fitting models where the curvature of the N-ray spectrum is partly due to a cooling break. hence reducing the required absorption.," The part of the hatched region which does not coincide with the grey shaded band corresponds to best fitting models where the curvature of the X-ray spectrum is partly due to a cooling break, hence reducing the required absorption."1152 In fact. the hardness ratio for the orbit 2 spectrum is consistent with that for orbit 3 and also for the combined spectrum: beyond. orbit. 3. providing no evidence for a moving spectral break. but the statistics are too poor to make a firm statement.," In fact, the hardness ratio for the orbit 2 spectrum is consistent with that for orbit 3 and also for the combined spectrum beyond orbit 3, providing no evidence for a moving spectral break, but the statistics are too poor to make a firm statement."1153 We could. of course. have allowed more freedom in the moclel fitting. for example by not fixing the gas-to-dust ratio.," We could, of course, have allowed more freedom in the model fitting, for example by not fixing the gas-to-dust ratio."1154 However. allowing this to be a free parameter finds models with lower ccolumn at a given extinction. whereas. for long CRB afterelows. the columns determined fron N-ravs are more often in excess of those determined. from the reddening (e.g.Starlingetal.," However, allowing this to be a free parameter finds models with lower column at a given extinction, whereas, for long GRB afterglows, the columns determined from X-rays are more often in excess of those determined from the reddening \citep[e.g.][]{Starling}."11552007)... A Larger than expected. cooling break (ASον 0.5) could. in principle reduce the required extinction. but then we would not explain the reddening of the afterglow.," A larger than expected cooling break $\Delta\beta>0.5$ ) could in principle reduce the required extinction, but then we would not explain the reddening of the afterglow."1156 In any case. even with greater [freedom dt is hard to find any reasonable solution at ο«1.5.," In any case, even with greater freedom it is hard to find any reasonable solution at $z<1.5$."1157 We conclude that the burst likely occurred at 2L8. which. combined with the constraint +<2.8. requires 2x:Ae <5.," We conclude that the burst likely occurred at $z\gsim1.8$, which, combined with the constraint $z\lsim2.8$, requires $2\lsim A_V\lsim5$ ."1158 This extinction would be high by typical CRB standards. but quite moderate compared to sight lines close the plane of a disk galaxy or through large clust-enshrouclec star-forming regions.," This extinction would be high by typical GRB standards, but quite moderate compared to sight lines close the plane of a disk galaxy or through large dust-enshrouded star-forming regions."1159 We note that. whilst not common. optically dark bursts in blue galaxies at moderate redshifts. have been identifie before. for example. GRB 970828 (Djorgovskictal.2001).. CRB 000210. (CGorosabeletal.2003).. GRB 051022. (Ro and GRB 070306 (Claunsenetal.2005).," We note that, whilst not common, optically dark bursts in blue galaxies at moderate redshifts, have been identified before, for example, GRB 970828 \citep{Djorgovski01}, GRB 000210 \citep{Gorosabel03}, GRB 051022 \citep{Rol07} and GRB 070306 \citep{Jaunsen08}."1160. Nevertheless. it remains odd that the location of the burs in this case places it within 0.2 aresec. corresponding to at most a kiloparsec or two (at. any. plausible redshif of the optically brightest. part of the host.," Nevertheless, it remains odd that the location of the burst in this case places it within $0.2$ arcsec, corresponding to at most a kiloparsec or two (at any plausible redshift), of the optically brightest part of the host."1161 This strong spatial coincidence between burst position and the optically brightest regions of their hosts is seen in many other low- long GRBs (Fruchteretal. 200G6).. and may be a consequence of the very short. life-times of massive-star GRB progenitors. which do not move far [from the star-forming region of their birth (Larssonetal.," This strong spatial coincidence between burst position and the optically brightest regions of their hosts is seen in many other low-reddening long GRBs \citep{Fruchter06}, , and may be a consequence of the very short life-times of massive-star GRB progenitors, which do not move far from the star-forming region of their birth \citep{Larsson}."11622007).. In the case of GRB 060923. unless there is some separation along the line-of-sight. we require the dust-attenuated GIU to be close to a relatively unreddened region that dominates the optical light of the galaxy.," In the case of GRB 060923A, unless there is some separation along the line-of-sight, we require the dust-attenuated GRB to be close to a relatively unreddened region that dominates the optical light of the galaxy."1163 A plausible &eometry. is one in which high optical-cdepth molecular clouds provide patchy obscuration of a Iarge star-forming complex2004).. and the sight-line to the GiB happens to intersect one of these.," A plausible geometry is one in which high optical-depth molecular clouds provide patchy obscuration of a large star-forming complex, and the sight-line to the GRB happens to intersect one of these."1164 There is great interest in GRBs with very. red. optical-nlhR colours since they could be at. very high. redshift., There is great interest in GRBs with very red optical-nIR colours since they could be at very high redshift.1165". GI 060923,X is arguably the most extreme example found. to-date. being detected in the Ix-band. but with only. deep limits in carly observations in all bluer filters."," GRB 060923A is arguably the most extreme example found to-date, being detected in the K-band, but with only deep limits in early observations in all bluer filters."1166 LE purely due to à Lya break in the near-LR. this would indicate a redshift’ beyond. 2~Ll.," If purely due to a $\alpha$ break in the near-IR, this would indicate a redshift beyond $z\sim11$."1167 However. our later-time optical observations revealed a faint galaxy. presumably. the host. at the same position. which must be at a more moderate redshift. probably 2<2.8 but certainly not above zzd.," However, our later-time optical observations revealed a faint galaxy, presumably the host, at the same position, which must be at a more moderate redshift, probably $z\lsim2.8$ but certainly not above $z\approx4$."1168 The morphology of the host: a bright knot coincident with the GRB itself and extended low surface brightness features may indicate a merger/interaction has produced this burst of star formation.," The morphology of the host: a bright knot coincident with the GRB itself, and extended low surface brightness features may indicate a merger/interaction has produced this burst of star formation."1169 A combined. analysis of the X-ray and optical/nllk data suggest that the burst is also likely to have 2LS in order to reconcile the absorption required in both bands., A combined analysis of the X-ray and optical/nIR data suggest that the burst is also likely to have $z\gsim1.8$ in order to reconcile the absorption required in both bands.1170 There is. of course. a slim chance that the GRB is coincident with an unrelated foreground. galaxy.," There is, of course, a slim chance that the GRB is coincident with an unrelated foreground galaxy."1171 Following the analysis of Piroetal.(2002) we calculate a probability that the afterglow would be found. coincident with an unrelated ealaxy as bright as 2=25.6 to be about a small but non-negligible figure., Following the analysis of \citet{Piro} we calculate a probability that the afterglow would be found coincident with an unrelated galaxy as bright as $R=25.6$ to be about – a small but non-negligible figure.1172 However given the close alignment of the afterglow with the brightest knot of the galaxy. and that the colour and magnitude of the putative host are otherwise very. plausible for a typical long-duration GRB. the conservative explanation remains that this is a case of dust rather than distance.," However given the close alignment of the afterglow with the brightest knot of the galaxy, and that the colour and magnitude of the putative host are otherwise very plausible for a typical long-duration GRB, the conservative explanation remains that this is a case of dust rather than distance."1173 (πο 060923 nonetheless is likely to be representative of some proportion of the dark GRB population. which optical surveys are biased against finding., GRB 060923A nonetheless is likely to be representative of some proportion of the dark GRB population which optical surveys are biased against finding.1174 It is therefore also a good example of the kind of interlopers which we must be able to reject in order to identifv very high redshift GRBs., It is therefore also a good example of the kind of interlopers which we must be able to reject in order to identify very high redshift GRBs.1175 This studs emphasises that carly. deep. photometry in a range of optical ancl nl filters is essential to reliably identify candidates. ancl followup spectroscopy is highly desirable where possible.," This study emphasises that early, deep photometry in a range of optical and nIR filters is essential to reliably identify candidates, and followup spectroscopy is highly desirable where possible."1176 We thank the Ulx Science ancl Technology Facilities Council or financial support. in particular NICE lor a Senior tescarch Fellowship and AJL for a Postdoctoral Fellowship.," We thank the UK Science and Technology Facilities Council for financial support, in particular NRT for a Senior Research Fellowship and AJL for a Postdoctoral Fellowship."1177 The research activities of JG are supported by the Spanish Ministry. of Science. through the progranunes ESP2005-τς00-09 anc AYAPO04-01515., The research activities of JG are supported by the Spanish Ministry of Science through the programmes ESP2005-07714-C03-03 and AYA2004-01515.1178 DAL acknowledges he Instrument Centre lor Danish Astrophysics., DM acknowledges the Instrument Centre for Danish Astrophysics.1179 9) acknowledges support by ai Marie. Curie. Latra-European Fellowship within the 6th European Community Framework 'rosram. under contract number MISLHE-CE-2006-042001. and a Grant of Excellence from the Icelancdie Research Eund.," PJ acknowledges support by a Marie Curie Intra-European Fellowship within the 6th European Community Framework Program under contract number MEIF-CT-2006-042001, and a Grant of Excellence from the Icelandic Research Fund."1180 AO. acknowledges support from the Norwegian Research Council. grant. nr.," AOJ acknowledges support from the Norwegian Research Council, grant nr."1181 166072.We also eratefully acknowledge the work of the wider tteam that makes this research possible., 166072.We also gratefully acknowledge the work of the wider team that makes this research possible.1182Let us imagine that the infall of dwarf galaxies and gas was really the dominating process for the buildiug-up of the ¢D halo aud the GCS.,Let us imagine that the infall of dwarf galaxies and gas was really the dominating process for the building-up of the cD halo and the GCS.1183 Tow many dyvarfs aud their transformed. gas would then have contributed to the ¢D halo elt aud how many GCs nueght belong to the ¢D halo?, How many dwarfs and their transformed gas would then have contributed to the cD halo light and how many GCs might belong to the cD halo?1184 NGC 1399 possesses about 5800 elobular clusters (sec Sect., NGC 1399 possesses about 5800 globular clusters (see Sect.1185 3.2)., 3.2).1186 About 1300 of them would belong to the bulee. Mya21.5 nag (see Sect.," About 1300 of them would belong to the bulge, $M_{\rm V,gal} = -21.5$ mag (see Sect."1187 3.3.1). if one asses an initial specific yequency of Sy=3.2. which is the mean value for the other ellipticals in the Fornax cluster. except NGC L10L aud NGC 1280.," 3.3.1), if one assumes an initial specific frequency of $S_N = 3.2$, which is the mean value for the other ellipticals in the Fornax cluster, except NGC 1404 and NGC 1380."1188 That means that 1500. OCs would belong o the ¢D halo aud its specific frequency would be about Sy=10+41., That means that 4500 GCs would belong to the cD halo and its specific frequency would be about $S_N = 10\pm1$.1189 Note that half of the total GCS (=2900 GCs) are assigned to the metal-poor peak around |Fo/HI| = —— 1.3 dex. aud therefore a least 1600 inetaliich GCs ([Fo/TI] = 0.6 dex) have to be explained by the infall scenario. if oue assunes that all 1300 remaining bulee GCs belong to the ποσαΊο sub-," Note that half of the total GCS $= 2900$ GCs) are assigned to the metal-poor peak around [Fe/H] $\simeq$ $-$ 1.3 dex, and therefore at least 1600 metal-rich GCs ([Fe/H] $\simeq$ $-$ 0.6 dex) have to be explained by the infall scenario, if one assumes that all 1300 remaining bulge GCs belong to the metal-rich sub-population."1190 Tow can dwarf galaxies account for such a high Sy:D, How can dwarf galaxies account for such a high $S_N$?1191 As presented in Sect., As presented in Sect.1192 5. there are iaiuly three scenarios possible.," 5, there are mainly three scenarios possible."1193 Firstly. accreted gas-poor dwarfs possessed high GC frequencies themselves.," Firstly, accreted gas-poor dwarfs possessed high GC frequencies themselves."1194 In this case. the average Sy of all accreted dwarts aud GCs can have values between baud 22 depending on the iuitial couditious (see Table 5).," In this case, the average $S_N$ of all accreted dwarfs and GCs can have values between 4 and 22 depending on the initial conditions (see Table 5)."1195 Secondly. the infalhug ooeas of previously eas-rich cawarfs was effectively couverted iuto elobular clusters.," Secondly, the infalling gas of previously gas-rich dwarfs was effectively converted into globular clusters."1196 Regarding the starburst as au isolated eutitv its resulting systems of stars aud clusters eau have ον values between 10 and 90 (sec Table 6)., Regarding the starburst as an isolated entity its resulting systems of stars and clusters can have $S_N$ values between 40 and 90 (see Table 6).1197 Finally. the stripping of GCs from dwarf galaxies was more effective than the stripping of their field population.," Finally, the stripping of GCs from dwarf galaxies was more effective than the stripping of their field population."1198 That this is in xuucipal possible is indicated by the fact that the Sy value of the outer parts of galaxies that are primarily affected by stripping can be in the order of 30 (see Sect., That this is in principal possible is indicated by the fact that the $S_N$ value of the outer parts of galaxies that are primarily affected by stripping can be in the order of 30 (see Sect.1199 5.1. case 1b).," 5.1, case 1b)."1200 Among these 3 possibilities the stripping of GCs from nAwart salaxies most probably plavs a minor role., Among these 3 possibilities the stripping of GCs from dwarf galaxies most probably plays a minor role.

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