ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Thus we sample the background at twice the radius of the galaxy., Thus we sample the background at twice the radius of the galaxy.3 This is actually the background estimation technique reconimended for LRAC images of extendedsources., This is actually the background estimation technique recommended for IRAC images of extended.4 Confusing sources. normallv in the background. can be oblematic. especially at 16fam.," Confusing sources, normally in the background, can be problematic, especially at $16\;\rm \mu m$."5 For meaningful aperture aperture photometry they. need. to be removed., For meaningful aperture aperture photometry they need to be removed.6 In. some cases the contaminating sources were too close or brigh o attempt. removal (e.g. vee 0951)., In some cases the contaminating sources were too close or bright to attempt removal (e.g. vcc 0951).7 In. some cases the 16pm detections themselves were not at the catalogue »osition and so were taken as “suspect” background sources ancl discarded. (c.g. NGC 4366)., In some cases the $16\;\rm \mu m$ detections themselves were not at the catalogued position and so were taken as “suspect” background sources and discarded (e.g. NGC 4366).8 For the remaining objects iuo showed. nearby contaminating sources we applicc an algorithm to remove them which analyzed the pixe distribution in a series of annuli with axis ratio and position angle equal to that of the galaxies., For the remaining objects that showed nearby contaminating sources we applied an algorithm to remove them which analyzed the pixel distribution in a series of annuli with axis ratio and position angle equal to that of the galaxies.9 Pixels that deviatec bv more than a fixed number of standard. deviations [rom the median value were replaced by the mecian value., Pixels that deviated by more than a fixed number of standard deviations from the median value were replaced by the median value.10 The threshold. for source removal was varied. between two uxl four standard: deviations ancl was sometimes applied --erativelv to achieve the best results., The threshold for source removal was varied between two and four standard deviations and was sometimes applied iteratively to achieve the best results.11 In all cases the results were carefully checked by eve., In all cases the results were carefully checked by eye.12 Integrated fluxes were taken as the total Lux within 10 background annulus., Integrated fluxes were taken as the total flux within the background annulus.13 We stress that these fluxes are measurecl only for the purposes of determining the mean colour of the galaxies., We stress that these fluxes are measured only for the purposes of determining the mean colour of the galaxies.14 Given the way in which the xvkeround. is determined. they are not a eood measure of the true integrated Duxes of the objects.," Given the way in which the background is determined, they are not a good measure of the true integrated fluxes of the objects."15 Lhe colours of he objects. however. should be robustly determined.," The colours of the objects, however, should be robustly determined."16 When we come to plot the colour-magnitude diagram we will use he total Ix-band. magnitude of the galaxies as given in the 2MLASS catalogue. rather inn our measurement from the PALASS Ix-band. image.," When we come to plot the colour-magnitude diagram we will use the total K-band magnitude of the galaxies as given in the 2MASS catalogue, rather than our measurement from the 2MASS K-band image."17" Radial colour profiles were determined using a series of elliptical annuli. with axis ratios and. position angles as given in. ""HIlvperleda.", Radial colour profiles were determined using a series of elliptical annuli with axis ratios and position angles as given in “Hyperleda”.18 Before Huüxes were measured the two images were first. convolved to identical resolutions., Before fluxes were measured the two images were first convolved to identical resolutions.19 This was achieved by convolving cach image with the measured PSE of the other., This was achieved by convolving each image with the measured PSF of the other.20 For example. when considering the Ix-46] colour the 2ALASS K-band image was convolved with the Spitzer blue. peakup PSE and the 16jm image was convolved with the 2ZALASS Wkebaned PSE.," For example, when considering the K-[16] colour the 2MASS K-band image was convolved with the Spitzer blue peakup PSF and the $16\;\rm \mu m$ image was convolved with the 2MASS K-band PSF."21 Instrumental resolutions (EWILIMD ave 2766. 1777. 1799 and 3766 for 2MASS. HUAC 4.5 and Sp/m and 16jm respectively.," Instrumental resolutions (FWHM) are 6, 7, 9 and 6 for 2MASS, IRAC 4.5 and $8\;\rm \mu m$ and $16\;\rm \mu m$ respectively."22Most of the nass in our Universe is believed to be an unknown. collisiouless formi of matter that can oulv interact gravitationally with barvouic matter aud ↕↑↴∖↴↸∖∐,"Most of the mass in our Universe is believed to be an unknown, collisionless form of matter that can only interact gravitationally with baryonic matter and itself ."23⋟⋖⊏↕↸∖↴↑⋜↕∏∐∪∏↸∖↑⋜↧↕⋅↕∩∩↭∙∙↽∕∏∐∖↕⋟∪∐⊔⋜↧↑↕∪∐∪↕≯↕⋜∐⋅∶↴∙⊾↸∖≓ scale structures in our Universe. in particular galaxy clusteriug. is driven by gravitational forces exerted by this dark matter.," The formation of large-scale structures in our Universe, in particular galaxy clustering, is driven by gravitational forces exerted by this dark matter."24" Cold Dark Matter (CDAD) cosinoloey holds that structures erow lierarclically, with simall Ojects collapsing first and then mereine to form, more niassive galaxies aud clusters."," Cold Dark Matter (CDM) cosmology holds that structures grow hierarchically, with small objects collapsing first and then merging to form more massive galaxies and clusters."25 The theory predicts that only dark matter halos with mass siunaller than approximately 105 MIL. can form from 30 fluctuations iu primordial density perturbations., The theory predicts that only dark matter halos with mass smaller than approximately $10^8$ $_\odot$ can form from $\sigma$ fluctuations in primordial density perturbations.26 Consequently more massive svstenis can onlv form by subsequent accretion of these protogalactic fragments.," Consequently, more massive systems can only form by subsequent accretion of these protogalactic fragments."27 For this reason. dwarf galaxies (dark matter subhlalos in CDM cosmology) that contain Iuuinous barvous aud have not vet merged with a host galaxy. cau. to some extent. be considered some of the most primitive building blocks of our universe.," For this reason, dwarf galaxies (dark matter subhalos in CDM cosmology) that contain luminous baryons and have not yet merged with a host galaxy, can, to some extent, be considered some of the most primitive building blocks of our universe."28 However. it is now thought that the inconsistencies between the observed properties of large galaxies aud dwarfs are too many to believe that the former are built up only by means of successive acerctions of the latter.," However, it is now thought that the inconsistencies between the observed properties of large galaxies and dwarfs are too many to believe that the former are built up only by means of successive accretions of the latter."29 We investigate two kev issues identified with this model., We investigate two key issues identified with this model.30 The ⋅ issue⋅ has loug heen known. naauicly that the spatial firstdistribution of the Milkv Wavy satellites shows asviunctric patterns and probably streams2000).. particularly when ouly the innermost satellites are taken into account (Fieure 13).," The first issue has long been known, namely that the spatial distribution of the Milky Way satellites shows asymmetric patterns and probably streams, particularly when only the innermost satellites are taken into account (Figure \ref{fig:HAproj}) )."31 The orbits of these satellites have been found to be prefercutially polar based on wealth of evidence iucbludiug the aliguinent of satellites on the sky1982).. the orientation of the Magellanic StreamL).. the threc- distribution of satellites and their actual velocities1.," The orbits of these satellites have been found to be preferentially polar based on wealth of evidence including the alignment of satellites on the sky, the orientation of the Magellanic Stream, the three-dimensional distribution of satellites and their actual velocities."32. similarly find that nearby clusters such as Virgo and Coma possess calaxy distributions that tend to be aligned with the principal axis of the cluster itself., similarly find that nearby clusters such as Virgo and Coma possess galaxy distributions that tend to be aligned with the principal axis of the cluster itself.33 They conclude that either some dynamical process is responsible or that the orbital parameters of the dwarf galaxies are imprinted on them at the time they enter the host halo., They conclude that either some dynamical process is responsible or that the orbital parameters of the dwarf galaxies are imprinted on them at the time they enter the host halo.34 They concluded that this, They concluded that this35pressure and Pc for the non-thermal pressure and assuming the latter to be dominated by relativistic particles we have It is very remarkable that even at this crude macroscopic level we can see a connection between extreme acceleration efficiency with the shock compression tending to infinity and a spectral hardening towards an exponent of 3.5 corresponding tot=2 as required by Malkov’s asymptotic solution.,pressure and $P_C$ for the non-thermal pressure and assuming the latter to be dominated by relativistic particles we have It is very remarkable that even at this crude macroscopic level we can see a connection between extreme acceleration efficiency with the shock compression tending to infinity and a spectral hardening towards an exponent of $3.5$ corresponding to $\lambda = 2$ as required by Malkov's asymptotic solution.36 This large compression ratio allows us to retrospectively justify the simplified relations we started with using an approximation originally due to Chernyt(1957) (see also Zel'dovichandRaiser 1966))., This large compression ratio allows us to retrospectively justify the simplified relations we started with using an approximation originally due to \citet{Chernyi} (see also \citealp{Zeld}) ).37" The key is to assume that all the swept-up matter is concentrated in a thin shell immediately behind the shock with radial velocity Uy—U, and total mass If the pressure in the interior of the remnant is Pj. then Newton's law of motion applied to an element of the shell gives For a self-similar solution the interior pressure P; will be some fixed fraction a of the post-shock pressure Αρ—U,)."," The key is to assume that all the swept-up matter is concentrated in a thin shell immediately behind the shock with radial velocity $U_0-U_1$ and total mass If the pressure in the interior of the remnant is $P_{\rm int}$, then Newton's law of motion applied to an element of the shell gives For a self-similar solution the interior pressure $P_{\rm int}$ will be some fixed fraction $\alpha$ of the post-shock pressure $A(U_0 - U_1)$."38 Thus or. noting that Uo= dR/dr. fromUi which it is easy to see that the self-similar Sedov- solution with Rο.7° and U«R77 requires Ξ-1/2.," Thus or, noting that $U_0 = dR/dt$ , from which it is easy to see that the self-similar Sedov-like solution with $R\propto t^{2/5}$ and $U\propto R^{-3/2}$ requires $\alpha = 1/2$."39 Thus the interior. pressure is half the immediate post-shock pressure., Thus the interior pressure is half the immediate post-shock pressure.40 That there has to be such a pressure gradient in the shell is obvious because the material that was shocked at early times is moving too fast and would overtake the shell were it not decelerated by an adverse pressure gradient directed towards the interior of the remnant., That there has to be such a pressure gradient in the shell is obvious because the material that was shocked at early times is moving too fast and would overtake the shell were it not decelerated by an adverse pressure gradient directed towards the interior of the remnant.41 It is however remarkable that the Sedov scaling requires the total interior pressure to be half the ram pressure of the shock. again with only a very weak dependence on details of equation of state or particle acceleration.," It is however remarkable that the Sedov scaling requires the total interior pressure to be half the ram pressure of the shock, again with only a very weak dependence on details of equation of state or particle acceleration."42 It follows trivially that the total interior energy of the remnant (hot gas and cosmic rays) is between 3/2 (gas dominated) and 3 (cosmic ray dominated) times the kinetic energy of the remnant and thus in the two extreme cases we have. if gas dominated. and if cosmic ray dominated. Strictly speaking. in the gas dominated case we should not neglect the thickness of the shell. and we should also allow for the fact that the post-shock gas velocity is only 3/4 of the shock velocity.," It follows trivially that the total interior energy of the remnant (hot gas and cosmic rays) is between $3/2$ (gas dominated) and $3$ (cosmic ray dominated) times the kinetic energy of the remnant and thus in the two extreme cases we have, if gas dominated, and if cosmic ray dominated, Strictly speaking, in the gas dominated case we should not neglect the thickness of the shell, and we should also allow for the fact that the post-shock gas velocity is only $3/4$ of the shock velocity."43 Also in the cosmic-ray dominated case. if «b has a significant component from genuine escape as distinct from geometrical dilution. this will slightly affect the Sedov exponent.," Also in the cosmic-ray dominated case, if $\Phi$ has a significant component from genuine escape as distinct from geometrical dilution, this will slightly affect the Sedov exponent."44 However the main point of this section is to demonstrate that the interior pressure is rather tightly constrained and is of order 0.4 to 0.25 times the explosion energy divided by the remnant volume. and that the shock expansion is Well approximated by the standard Sedov formula.," However the main point of this section is to demonstrate that the interior pressure is rather tightly constrained and is of order $0.4$ to $ 0.25$ times the explosion energy divided by the remnant volume, and that the shock expansion is well approximated by the standard Sedov formula."45 Because the total pressure is essentially fixed. if we imagine more and more efficient particle acceleration putting more pressure into Pc. the thermal gas pressure Pc; has to decrease.," Because the total pressure is essentially fixed, if we imagine more and more efficient particle acceleration putting more pressure into $P_C$, the thermal gas pressure $P_G$ has to decrease."46 At the same time the nonlinear reaction terms are making the shock more compressive and increasing the downstream density., At the same time the nonlinear reaction terms are making the shock more compressive and increasing the downstream density.47" Both effect cause the post-shock temperature 7;οPa/p to decrease so that we expect substantially lower post- gas temperatures than in pure gas models of SNRs,", Both effect cause the post-shock temperature $T_{\rm i}\propto P_G/\rho$ to decrease so that we expect substantially lower post-shock gas temperatures than in pure gas models of SNRs.48 Once a fluid element (in this case a spherical annulus) has been shocked it gradually moves back through the dense shell expanding and dropping m pressure until it merges into the tenuous interior region., Once a fluid element (in this case a spherical annulus) has been shocked it gradually moves back through the dense shell expanding and dropping in pressure until it merges into the tenuous interior region.49 The shell thickness is determined by or AR=R/3s«R/12., The shell thickness is determined by or $\Delta R \approx R/ 3 s < R/12$.50 The time taken to transit through the shell is thus for a Sedov scaling. close enough to r.," The time taken to transit through the shell is thus for a Sedov scaling, close enough to $t$."51 Thus if we consider a fluid element that is shocked at time fy. It exits the shell at approximately (1+5/6)fo with a pressure half the post-shock pressure at that time. which in turn is a factor (12-5/6)79?=1/2 what it was at the initial time fo.," Thus if we consider a fluid element that is shocked at time $t_0$, it exits the shell at approximately $(1+5/6) t_0$ with a pressure half the post-shock pressure at that time, which in turn is a factor $(1+5/6)^{-6/5}\approx 1/2$ what it was at the initial time $t_0$."52 Thus between f; and about 215 the pressure has to drop by a factor of about 4., Thus between $t_0$ and about $2t_0$ the pressure has to drop by a factor of about 4.53 After the fluid element has entered the interior region itis a reasonably good approximation to say that it then simply expands in pressure equilibrium with the interior of the remnant where the total pressure is dropping as Physically this is because the interior flow is subsonic and any pressure variations get equilibrated on the sound-crossing time which is short compared to the dynamical time of the remnant., After the fluid element has entered the interior region it is a reasonably good approximation to say that it then simply expands in pressure equilibrium with the interior of the remnant where the total pressure is dropping as Physically this is because the interior flow is subsonic and any pressure variations get equilibrated on the sound-crossing time which is short compared to the dynamical time of the remnant.54" So the history of the parcel of shocked gas is of an initial. rather rapid. drop in pressure by a factor of roughly four between {ο and 2%, followed by a slower power-law 779? decline as the remnant expands."," So the history of the parcel of shocked gas is of an initial, rather rapid, drop in pressure by a factor of roughly four between $t_0$ and $2t_0$ followed by a slower power-law $t^{-6/5}$ decline as the remnant expands."55" Neglecting for the moment any diffusion of the accelerated particles out of the shell and splitting the total pressure into à ""gas"" component 7; from thermal tons and à “cosmic ray"" component P from the relativistic accelerated particles. we have and thus the gas pressure drops faster than the cosmic ray pressure in the expansion."," Neglecting for the moment any diffusion of the accelerated particles out of the shell and splitting the total pressure into a “gas” component $P_G$ from thermal ions and a “cosmic ray” component $P_C$ from the relativistic accelerated particles, we have and thus the gas pressure drops faster than the cosmic ray pressure in the expansion."56 It follows that if the two were initially comparable. the cosmic ray pressure will dominate at later stages of the expansion and the density willhave to drop according to," It follows that if the two were initially comparable, the cosmic ray pressure will dominate at later stages of the expansion and the density willhave to drop according to"57al. (,al. (58"subphotospheric layers), the one retrieved from the inversions (photospheric layers) and Avrett’s model (upper layers).","subphotospheric layers), the one retrieved from the inversions (photospheric layers) and Avrett's model (upper layers)."59" Also, the photospheric model is formed by the model of Christensen-Dalsgaard (subphotospheric layers), the one from the inversions (photosphere) and VAL-C (upper layers)."," Also, the photospheric model is formed by the model of Christensen-Dalsgaard (subphotospheric layers), the one from the inversions (photosphere) and VAL-C (upper layers)."60" The different models did not coincide at the same height for all parameters, or even, some times, discontinuities appeared in the stratification of a given parameter, which made necessary an interpolation at some layers to merge them smoothly."," The different models did not coincide at the same height for all parameters, or even, some times, discontinuities appeared in the stratification of a given parameter, which made necessary an interpolation at some layers to merge them smoothly."61" At the end, the resulting stratifications at the sunspot axis and field-free atmospheres did not satisfy hydrostatic equilibrium and pressures were re-calculated to impose it."," At the end, the resulting stratifications at the sunspot axis and field-free atmospheres did not satisfy hydrostatic equilibrium and pressures were re-calculated to impose it."62" This re-calculation gave rise to a variation of the pressure stratification at both the sunspot axis and quiet sun atmospheres, with a reduced pressure deficit turned at the end into a lower sunspot magnetic field (which"," This re-calculation gave rise to a variation of the pressure stratification at both the sunspot axis and quiet sun atmospheres, with a reduced pressure deficit (which turned at the end into a lower sunspot magnetic field strength)."63" The later merging with Low’s model to generate a strength).deep sunspot also suffers from the same problem, but this represented a minor correction."," The later merging with Low's model to generate a deep sunspot also suffers from the same problem, but this represented a minor correction."64" At this point, we could have opted to improve the sunspot model to match the observed magnetic field strength."," At this point, we could have opted to improve the sunspot model to match the observed magnetic field strength."65" But, given that the retrieved stratifications of the parameters which mainly determine the properties of wave propagation (Alfvénn and sound velocities and pressure scale height after the iterative process) are very similar to those obtained from the inversions (see Figure 3)), we were confident that the model was adequate to study the propagation of waves in the atmosphere of the observed sunspot."," But, given that the retrieved stratifications of the parameters which mainly determine the properties of wave propagation (Alfvénn and sound velocities and pressure scale height after the iterative process) are very similar to those obtained from the inversions (see Figure \ref{fig:comp_mhs_inv}) ), we were confident that the model was adequate to study the propagation of waves in the atmosphere of the observed sunspot."66 In this work our aim is the reproduction of the observed wave pattern by means of numerical calculations., In this work our aim is the reproduction of the observed wave pattern by means of numerical calculations.67 In this respect it is crucial to choose the most appropriate way to introduce the observed velocity as a driver., In this respect it is crucial to choose the most appropriate way to introduce the observed velocity as a driver.68" We have chosen the velocity measured with the lline as the driver of the simulation, since it is the line which is formed the deepest over the set of lines that we have observed."," We have chosen the velocity measured with the line as the driver of the simulation, since it is the line which is formed the deepest over the set of lines that we have observed."69" At the formation height of the line, the numerical simulation should have a vertical velocity as close as possible to the measured LOS velocity."," At the formation height of the line, the numerical simulation should have a vertical velocity as close as possible to the measured LOS velocity."70" The photospheric oscillations are dominated by waves in the 5 minute band and, thus, the power excited in the simulation in this band must resemble the observed one."," The photospheric oscillations are dominated by waves in the 5 minute band and, thus, the power excited in the simulation in this band must resemble the observed one."71" However, it is even more critical to introduce correctly the power at higher frequencies."," However, it is even more critical to introduce correctly the power at higher frequencies."72 Waves with frequencies above the cutoff propagate upward and dominate the higher layers., Waves with frequencies above the cutoff propagate upward and dominate the higher layers.73 The wave pattern at the chromosphere will depend on the power introduced by the driver at those high frequencies as well as on the initial phase of these high frequency waves., The wave pattern at the chromosphere will depend on the power introduced by the driver at those high frequencies as well as on the initial phase of these high frequency waves.74" It is interesting to note that the simulations by Carlsson&Stein(1997) showed that it is possible to derive a transfer function for accurately relating the observed velocity with a piston velocity at the bottom boundary, where the latter may be located at a deeper position."," It is interesting to note that the simulations by \citet{Carlsson+Stein1997} showed that it is possible to derive a transfer function for accurately relating the observed velocity with a piston velocity at the bottom boundary, where the latter may be located at a deeper position."75 This approach is not valid in our case., This approach is not valid in our case.76" Carlsson&Stein(1997) performed one dimensional hydrodynamic simulations, where they only can propagate acoustic longitudinal waves in the vertical direction, and there is a unique transfer function for this wave, without ambiguity."," \citet{ Carlsson+Stein1997} performed one dimensional hydrodynamic simulations, where they only can propagate acoustic longitudinal waves in the vertical direction, and there is a unique transfer function for this wave, without ambiguity."77" However, in the three dimensional case, there are three distinct MHD waves (fast, slow and Alfvénn), and the transfer function cannot be defined in an univocal way."," However, in the three dimensional case, there are three distinct MHD waves (fast, slow and Alfvénn), and the transfer function cannot be defined in an univocal way."78" Moreover, in our simulations, unlike those of Carlsson&Stein(1997),, between the bottom boundary and the formation height of the lline there is the layer where sound and Alfvénn velocities are equal."," Moreover, in our simulations, unlike those of \citet{Carlsson+Stein1997}, between the bottom boundary and the formation height of the line there is the layer where sound and Alfvénn velocities are equal."79" There, the different modes mix up, which makes it impossible to find a unique transfer function."," There, the different modes mix up, which makes it impossible to find a unique transfer function."80" For all these reasons, we have decided to impose the driver at the formation height of the lline, avoiding any hypothesis about the propagation at deeper layers."," For all these reasons, we have decided to impose the driver at the formation height of the line, avoiding any hypothesis about the propagation at deeper layers."81 Several strategies may be developed to that aim., Several strategies may be developed to that aim.82" On the one hand, one can set the observed oscillations as a boundary condition in a computational domain where the bottom boundary coincides with the formation height of theSir."," On the one hand, one can set the observed oscillations as a boundary condition in a computational domain where the bottom boundary coincides with the formation height of the."83" On the other hand, one can calculate the force which corresponds to the measured velocity and introduce it directly into the equation of motion Felipeetal. 2010a)."," On the other hand, one can calculate the force which corresponds to the measured velocity and introduce it directly into the equation of motion \citep[\eg,][]{Felipe+etal2010a}."84". In the case of the first approach, several problems arise."," In the case of the first approach, several problems arise."85" It is not valid just to set the vertical velocity, since it is necessary to impose at the bottom boundary the fluctuations of all the variables self-consistently."," It is not valid just to set the vertical velocity, since it is necessary to impose at the bottom boundary the fluctuations of all the variables self-consistently."86" From the inversion of the Stokes profiles we can retrieve the variations of all these magnitudes, but it is difficult to obtain reliable values with a good spatial and time resolution related to a single layer in geometrical height, not optical depth (seeRodríguezHidalgoetal.2001)."," From the inversion of the Stokes profiles we can retrieve the variations of all these magnitudes, but it is difficult to obtain reliable values with a good spatial and time resolution related to a single layer in geometrical height, not optical depth \citep[see][]{RodriguezHidalgo+etal2001}."87". Another option is to calculate the polarization relations of all the variables which agree with the vertical velocity measured from the Doppler shift, but it is a tough work in such realistic case."," Another option is to calculate the polarization relations of all the variables which agree with the vertical velocity measured from the Doppler shift, but it is a tough work in such a realistic case."88 We founda thus more convenient to introduce the retrieved force as a source function in the momentum equation.," We found thus more convenient to introduce the retrieved force as a source function $S_z(x,z_{Si},t)$ in the momentum equation."89" This driver introduces S;(x,zs;,t)mechanical energy in the system, and consequently, the energy"," This driver introduces mechanical energy in the system, and consequently, the energy"90We present in Fie 1-5 results for the temperature and chemistry at the three representative depths into the dimensional slab: Ay=3.8 and 20 mae.,"We present in Fig \ref{fig:1}- \ref{fig:4} results for the temperature and chemistry at the three representative depths into the one-dimensional slab: $_{\rm v}=3$, 8 and 20 mag."91 The case Ay=3 is intended: to represent. translucent material. Ay=ὃ to represent the extended PDIU gas (as detected in the nuclei of M82. NGC 253. 1C 342 and NGC 4038 by 2)). while Ay=20 represents dense PDI components detected in galaxies (?7)..," The case $_{\rm v}=3$ is intended to represent translucent material, $_{\rm v}=8$ to represent the extended PDR gas (as detected in the nuclei of M82, NGC 253, IC 342 and NGC 4038 by \citealt{Baye09a}) ), while $_{\rm v}=20$ represents dense PDR components detected in galaxies \citep{Baye08a}."92 Fig., Fig.93 1 shows the results for temperature obtained [rom the self-consistent thermal balance. as a function of cosmic rav ionisation rate. at these three values of Ay.," \ref{fig:1} shows the results for temperature obtained from the self-consistent thermal balance, as a function of cosmic ray ionisation rate, at these three values of $_{\rm v}$."94 ME three curves show the same general behaviour. rising from low values at low ionisation rates to temperatures approaching 1.107 Kk for the highest ionisation rates.," All three curves show the same general behaviour, rising from low values at low ionisation rates to temperatures approaching $1\times 10^{4}$ K for the highest ionisation rates."95 As will be evident in the plots of the chemical abundances. reactions at these very high. temperatures clestroy much. of the chemistry.," As will be evident in the plots of the chemical abundances, reactions at these very high temperatures destroy much of the chemistry."96 There is some cdilference in temperature between the three curves shown for low values of the ionisation rate., There is some difference in temperature between the three curves shown for low values of the ionisation rate.97 At Ay=3 mag. the temperature lies between 50 and LOO Ix. [or ionisation rates less than about 1.10.tts 4+.," At $_{\rm v}=3$ mag, the temperature lies between 50 and 100 K for ionisation rates less than about $1\times 10^{-14}$ $^{-1}$."98" ""his relatively high temperature is maintained bv the intense external radiation field.", This relatively high temperature is maintained by the intense external radiation field.99 However at Ay=8 mag. the temperature falls to 710 Ix at the lowest ionisation rates. as expected. since the external radiation field no longer plays a role.," However at $_{\rm v}=8$ mag, the temperature falls to $\sim$ 10 K at the lowest ionisation rates, as expected, since the external radiation field no longer plays a role."100 We note that the models. give. slightly higher temperatures at Ay=20 mag than at Ay=S mag., We note that the models give slightly higher temperatures at $_{\rm v}=20$ mag than at $_{\rm v}=8$ mag.101 This is due to the fact that at high. visual extinctions the € and CO lines become optically thick and hence are less able to cool the gas whilst the cosmic ray heating remains high and constant., This is due to the fact that at high visual extinctions the C and CO lines become optically thick and hence are less able to cool the gas whilst the cosmic ray heating remains high and constant.102 For some mocdels. there were some small cilliculties associated with the convergence of the thermal. balance.," For some models, there were some small difficulties associated with the convergence of the thermal balance."103 For example one sees small spikes in the thermal structure curve for Ay = 3 ancl corresponding features in the plots of the fractional abunclances., For example one sees small spikes in the thermal structure curve for $_{\rm v}$ = 3 and corresponding features in the plots of the fractional abundances.104 These dillieulties are not due to bistability (οι., These difficulties are not due to bistability \citep{Boge06}.105 Rather they arise due to the stilfness of the coupled chemical and thermal balance equations., Rather they arise due to the stiffness of the coupled chemical and thermal balance equations.106 Their influence on the caleulated abundances of observable species is not significant., Their influence on the calculated abundances of observable species is not significant.107 The cllects of high heating rates on the chemistry is further investigated in Bayet et al. (, The effects of high heating rates on the chemistry is further investigated in Bayet et al. (1082010).,2010).109 lig. 2..," Fig. \ref{fig:2},"110 3. and 5in present the results giving the abuncdances of various relevant species at the three specified values of Ay., \ref{fig:3} and \ref{fig:4} present the results giving the abundances of various relevant species at the three specified values of $_{\rm v}$.111 These species were selected. from the 131 available partly. because many of them have already been detected in external galaxies. and partly to illustrate the sensitivity of species to the ionisation rate for a wide chemical variety.," These species were selected from the 131 available partly because many of them have already been detected in external galaxies, and partly to illustrate the sensitivity of species to the ionisation rate for a wide chemical variety."112 The range of abundances shown extends somewhat beyond the values that may be detectable., The range of abundances shown extends somewhat beyond the values that may be detectable.113 Although there are significant dillerences. the three cases are broadly similar in their behaviour with respect to the enhancement of the ionisation rate.," Although there are significant differences, the three cases are broadly similar in their behaviour with respect to the enhancement of the ionisation rate."114 As the ionisation rate is increased. from a value appropriate for the Milky Was. a rich chemistry is maintained up to a critical value of the ionisation rate. bevond which the molecular abuncances fall rapidly as the ionisation rate is further increased.," As the ionisation rate is increased from a value appropriate for the Milky Way, a rich chemistry is maintained up to a critical value of the ionisation rate, beyond which the molecular abundances fall rapidly as the ionisation rate is further increased."115 Lf the ionisation rate is increased to 12 Ll. almost all the chemistry. is ellectively suppressed.," If the ionisation rate is increased to $\times$ $^{-12}$ $^{-1}$, almost all the chemistry is effectively suppressed."116 “Phe driver of this decline in molecular abuncanees is linked to the decline in molecular hydrogen: this occurs when the ionisation rate is about 10.HF sto and Ls becomes a minor species when the ionisation rate is as large as Dosà Ἐν," The driver of this decline in molecular abundances is linked to the decline in molecular hydrogen; this occurs when the ionisation rate is about $\times$ $^{-14}$ $^{-1}$, and $_2$ becomes a minor species when the ionisation rate is as large as $^{-12}$ $^{-1}$."117 [n these conditions. conventional astrochemistrey - based on reactions with Hl» molecules - ceases.," In these conditions, conventional astrochemistry - based on reactions with $_2$ molecules - ceases."118 In this range of ionisation rate. the temperature rises abruptly to some thousands of Kelvin (sce Fig.," In this range of ionisation rate, the temperature rises abruptly to some thousands of Kelvin (see Fig."119 1). and hot atomic hydrogen is very destructive of molecules.," 1), and hot atomic hydrogen is very destructive of molecules."120 However. we can see from the figures that potential molecular tracers can be identified. for tonisation rates of about 1.10. P? + but the molecular abundances drop substantially as & increases much more.," However, we can see from the figures that potential molecular tracers can be identified for ionisation rates of about $\times$ $^{-13}$ $^{-1}$ but the molecular abundances drop substantially as $\zeta$ increases much more."121 We now confine our remarks to the chemically richer regions of parameter space., We now confine our remarks to the chemically richer regions of parameter space.122 There are some cillerences between the panels in Fig., There are some differences between the panels in Fig.123 3. (or 5))., \ref{fig:3} (or \ref{fig:4}) ).124 Some species decline with increasing ionisation rate more rapidlv than others., Some species decline with increasing ionisation rate more rapidly than others.125 For example. sulphur-bearing species may be useful tracers of gas in which &=101° ! but not when ¢=10H s+.," For example, sulphur-bearing species may be useful tracers of gas in which $\zeta = 10^{-16}$ $^{-1}$ but not when $\zeta= 10^{-14}$ $^{-1}$."126 Ammonia has a large fractional abundance for lower lonisation rates. but the abundance declines. rapidly as the ionisation rate increases.," Ammonia has a large fractional abundance for lower ionisation rates, but the abundance declines rapidly as the ionisation rate increases."127 Nitrogen appears in CN-bearing species at levels that are probably significant as the ionisation rate increases. even up to 10ths !.," Nitrogen appears in CN-bearing species at levels that are probably significant as the ionisation rate increases, even up to $\sim 10^{-14}$ $^{-1}$."128 There are some cdillerences between the figures shown., There are some differences between the figures shown.129 At Ay = 3. molecular abundances are significantly lower than those for higher visual cxtinetions.," At $_{\rm130v}$ = 3, molecular abundances are significantly lower than those for higher visual extinctions."131" For example. C'S is. 10 loa.times more abundant at A, = 8 than at A, —= 3."," For example, CS is $\sim 10^4$ times more abundant at $_{\rm v}$ = 8 than at $_{\rm v}$ = 3."132c The intense radiation field assumed. in these moclels to impinge on the slab is responsible for inhibiting the chemistry at Ay = 3.," The intense radiation field assumed in these models to impinge on the slab is responsible for inhibiting the chemistry at $_{\rm133v}$ = 3."134 However. the model results for Ay — 8 and 20 magnitudes are essentially identical. as the external racliation field does not penetrate elfectively to these depths.," However, the model results for $_{\rm v}$ = 8 and 20 magnitudes are essentially identical, as the external radiation field does not penetrate effectively to these depths."135 The behaviour of oxvgen and carbon hydrides and their ions is somewhat cdillerent to the above behaviours., The behaviour of oxygen and carbon hydrides and their ions is somewhat different to the above behaviours.136 Some of these species show fractional abundances of rather high levels for ionisation rates of 1yH s1. while others even sustain these high values for ionisation rates approaching ~10Ps t," Some of these species show fractional abundances of rather high levels for ionisation rates of $10^{-14}$ $^{-1}$, while others even sustain these high values for ionisation rates approaching $\sim 10^{-12}$ $^{-1}$."137" For example. ΟΙ] and LH2O fractional abundances are 10  for an ionisation rate of ~ I +. while OLL and ΟΙ may be as laree as 10. 7 even for an ionisation rate of ~ 012 1,"," For example, OH and $_2$ O fractional abundances are $\sim$ $^{-7}$ for an ionisation rate of $\sim$ $^{-14}$ $^{-1}$, while OH and $^+$ may be as large as $\sim$ $^{-8}$ even for an ionisation rate of $\sim$ $^{-12}$ $^{-1}$."138" ""Phe ions I]; and H150 — are Likely to x abundant for ¢=la7 i: however. the commonly used tracer is probably useless for values of ¢ larger han Ms 5."," The ions $_3^+$ and $_3$ $^+$ are likely to be abundant for $\zeta =13910^{-13}$ $^{-1}$; however, the commonly used tracer $^+$ is probably useless for values of $\zeta$ larger than $^{-13}$ $^{-1}$."140 Phe behaviour of these oxygen and carbon species is a consequence of the thermal stimulation of he endothermuc reactions that mav initiate oxveen and carbon chemistrv by the increase in kinetic temperature arising [rom the higher ionisation rates., The behaviour of these oxygen and carbon species is a consequence of the thermal stimulation of the endothermic reactions that may initiate oxygen and carbon chemistry by the increase in kinetic temperature arising from the higher ionisation rates.141 However. ultimately. he reduction in the Ll» fraction suppresses these reaction networks.," However, ultimately, the reduction in the $_2$ fraction suppresses these reaction networks."142 Given that the metallicity in some galaxies has been measured (see Section ??7)) and the values found to lie in a range often below but sometimes exceeding the solar value. it is worthwhile to explore the predictions of molecular abundances in our model lor varving metallicity.," Given that the metallicity in some galaxies has been measured (see Section \ref{sec:obs}) ) and the values found to lie in a range often below but sometimes exceeding the solar value, it is worthwhile to explore the predictions of molecular abundances in our model for varying metallicity."143" Table 2 shows the computed fractional abundances for some atonis and. molecules of observational interest for three values of the metallicity (0.1. 1.0 and 4.0 times the solar value). for both ""high"" (104% s 4) and slow? (10.1 1) cosmic rav ionisation rates. and for two values of the visual extinction (Αν= 3 and 20 magnitudes)."," Table \ref{tab:3} shows the computed fractional abundances for some atoms and molecules of observational interest for three values of the metallicity (0.1, 1.0 and 4.0 times the solar value), for both “high” $10^{-13}$ $^{-1}$ ) and “low” $10^{-16}$ $^{-1}$ ) cosmic ray ionisation rates, and for two values of the visual extinction $_{\rm v}=$ 3 and 20 magnitudes)."144 Phe results for the case when Ay δ mag are closely similar to those for Ay= 20 mag. and are not shown.," The results for the case when $_{\rm v}=$ 8 mag are closely similar to those for $_{\rm v}=$ 20 mag, and are not shown."145 The “high” ionisation rate is intended to represent the case predicted by 2. for CItDIs. while the," The “high” ionisation rate is intended to represent the case predicted by \citet{Papa10a} for CRDRs, while the"146"The final catalog prepared bv (his approach. which we refer to as our ""Sextractor catalog. contains a total of 1198 cluster candidates brighter than m:zz23.2.","The final catalog prepared by this approach, which we refer to as our “Sextractor” catalog, contains a total of 1198 cluster candidates brighter than $m_V\approx23.2$."147 Approximately 200 of these cluster. candidates. mostly brighter than ry222 but extending to fainter magnitudes than in the Daophot catalog. are in the crowded nuclear region.," Approximately 200 of these cluster candidates, mostly brighter than $m_V\approx22$ but extending to fainter magnitudes than in the Daophot catalog, are in the crowded nuclear region."148 In addition to the various automatically selected catalogs. we also construct a catalog of clusters manually. by carefully examining the WFCS3 images.," In addition to the various automatically selected catalogs, we also construct a catalog of clusters manually, by carefully examining the WFC3 images."149 This allows more difficult cases. such as a compact cluster near a bright star. to be assessed individually. which is not possible with automatically selected samples.," This allows more difficult cases, such as a compact cluster near a bright star, to be assessed individually, which is not possible with automatically selected samples."150 We also found that this approach has the advantage of minimizing contamination bv individual stus in crowded regions. al (lie expense of missing actual clusters in these regions.," We also found that this approach has the advantage of minimizing contamination by individual stars in crowded regions, at the expense of missing actual clusters in these regions."151 The primary shortcoming to (his approach is (hat it is nol possible to automatically reproduce the cluster selection or to quantitatively determine the completeness of the sample., The primary shortcoming to this approach is that it is not possible to automatically reproduce the cluster selection or to quantitatively determine the completeness of the sample.152 Three of us (RC. HIN. CIN) selected clusters independently across (he entire image. using slightly different approachs. but not pushing as deep as (hie automatic catalogs.," Three of us (RC, HK, CK) selected clusters independently across the entire image, using slightly different approachs, but not pushing as deep as the automatic catalogs."153 Our final. manually selected catalog contains 489 star clusters. mostly brighter than nn&22.5.," Our final, manually selected catalog contains 489 star clusters, mostly brighter than $m_V \approx 22.5$."154 Figure 8 shows relatively good agreement between (he manual and both the Daophot (21/27) and Sextractor (22/27) catalogs (i.e. &8054)) for clusters brighter than. (My< —6) as mentioned in the previous section. similar to the =τς agreement Iound between the full catalogs outside of the nuclear region.," Figure \ref{fig:man_auto} shows relatively good agreement between the manual and both the Daophot (21/27) and Sextractor (22/27) catalogs (i.e., $\approx$ ) for clusters brighter than $m_V \lea 22.25$ $M_V \lea -6$ ) as mentioned in the previous section, similar to the $\approx75$ agreement found between the full catalogs outside of the nuclear region."155 The automatic catalogs are deeper. however. aud contain more than double the number of cluster candidates (han ihe manual catalog.," The automatic catalogs are deeper, however, and contain more than double the number of cluster candidates than the manual catalog."156 A careful inspection of the sources that are cliserepant between the Daophot and manual catalogs (220% of the total) indicates that approximately half of these appear to be &ood clusters in crowded regions. while (he other half are mainly remaining blends or superpositions of two close stars.," A careful inspection of the sources that are discrepant between the Daophot and manual catalogs $\approx20$ of the total) indicates that approximately half of these appear to be good clusters in crowded regions, while the other half are mainly remaining blends or superpositions of two close stars."157 This suggests that our automatic catalogs have contanminalion at the =1054. level., This suggests that our automatic catalogs have contamination at the $\approx10$ level.158 In Section 3 we used four distinct approaches to select compact star clusters in M32., In Section 3 we used four distinct approaches to select compact star clusters in M83.159 llere. we study the luminosity [unetion of the clusters. and use the different. catalogs to quantilv the impact that different selection methods have on the results.," Here, we study the luminosity function of the clusters, and use the different catalogs to quantify the impact that different selection methods have on the results."160"where T.—ausudb:Tayo» ds à combination of the system temperature of scans that make up the baseline template:templ OFFS"")? =7a-OFFi;--5-0FFi;ο.The","where $T'_{sys}=a\cdot T_{sys,i,j} + b \cdot T_{sys,i,j+2}$ is a combination of the system temperature of the scans that make up the baseline template: ${\tt OFF^{templ}_{i,j+1}} = a \cdot {\tt OFF_{i,j}}+b\cdot {\tt OFF_{i,j+2}}$."161 the parameters a and b are the best-fit parameters which minimises the quantity /OFFSS Y.," The parameters $a$ and $b$ are the best-fit parameters which minimises the quantity $(({\tt ON_{i,j+1}} - {\tt OFF^{templ}_{i,j+1}})/{\tt OFF^{templ}_{i,j+1}})^2$ ."162 Again. a final spectrum for each polarisation is constructed as a weighted average ol all difference spectra produced in this manner.," Again, a final spectrum for each polarisation is constructed as a weighted average of all difference spectra produced in this manner."163 Vanden Boul et ((2004) proposed another wav of removing problematic baselines. which involves fitting a baseline template to the time-averaged spectrum containing (he line.," Vanden Bout et (2004) proposed another way of removing problematic baselines, which involves fitting a baseline template to the time-averaged spectrum containing the line."164 However. from a detailed comparison between the (wo methods. Hainline et ((2006) demonstrated that their scheme is just as eood at removing baseline-ripples al the scales one would expect (o see a galaxy. emission line.," However, from a detailed comparison between the two methods, Hainline et (2006) demonstrated that their scheme is just as good at removing baseline-ripples at the scales one would expect to see a galaxy emission line."165 As a result. we did not attempt to apply the method bv Vanden Bout et ((2004)., As a result we did not attempt to apply the method by Vanden Bout et (2004).166" The final spectra were corrected [ον atiosphlerie attenuation using the opacity values αἱ GGlIIz for the observing dates MMacddalena. private communication). and converted from antenna temperature to Janskvs by applying an appropriately scaled version of the GBT eain-elevation curve al (αν,"," The final spectra were corrected for atmospheric attenuation using the opacity values at GHz for the observing dates Maddalena, private communication), and converted from antenna temperature to Janskys by applying an appropriately scaled version of the GBT gain-elevation curve at GHz."167 The final IICN(1—0) spectra of J02399 and J16359. reduced using the two independent methods described in the previous section. are shown in Figure 1..," The final $(1-0)$ spectra of J02399 and J16359, reduced using the two independent methods described in the previous section, are shown in Figure \ref{figure:hcn-spectra}."168 The spectra have been smoothed to 50 + bins., The spectra have been smoothed to $50$ $^{-1}$ bins.169 Both methods [ail to get completely rid of residual baseline wigeles in (he final spectra., Both methods fail to get completely rid of residual baseline wiggles in the final spectra.170 However. the spectra reduced wilh GETNOD appear to be slightly less noisy than the spectra reduced with the second reduction method.," However, the spectra reduced with GETNOD appear to be slightly less noisy than the spectra reduced with the second reduction method."171 The riis noise of the spectra reduced using (he GETNOD routine are 0.1 and mmJx. respectively.," The channel-to-channel rms noise of the spectra reduced using the GETNOD routine are 0.1 and mJy, respectively."172" This is somewhat higher (han (he theoretical noise estimates of 0.07 and η], calculated Lor a (vpical svstem temperature 7;,,=38 IN and integration times corresponding to the ones of J02399 and J16359. respectively."," This is somewhat higher than the theoretical noise estimates of 0.07 and mJy, calculated for a typical system temperature $T_{sys}=38\,$ K and integration times corresponding to the ones of J02399 and J16359, respectively."173" Thus. it would seem that although the noise does integrate. down as /1L7""7. the resilual. baseline. wigeles. prevents us fromB reaching. the iheoretical noise limit."," Thus, it would seem that although the noise does integrate down as $t^{-1/2}$, the residual baseline wiggles prevents us from reaching the theoretical noise limit."174 No emission is detected. significantly above the noise al Vege=Okkmss 1 (or any other Vega). which corresponds to the CO redshift and (hus the expected position of the IICN(I—0) line.," No emission is detected significantly above the noise at $V_{LSR}=0$ $^{-1}$ (or any other $V_{LSR}$ ), which corresponds to the CO redshift and thus the expected position of the $(1-0)$ line."175 However. the sensitivity of the observations allow us to put upper limits on the HCN(1—0) line Iuminositv. of these two SMGs.," However, the sensitivity of the observations allow us to put upper limits on the $(1-0)$ line luminosity of these two SMGs."176 In doing so we use (he upper line [αν limits derived from the spectra produced by GETNOD. as it results in the lowest noise," In doing so we use the upper line flux limits derived from the spectra produced by GETNOD, as it results in the lowest noise"177distance with most of the ealactic gas; in that direction. in front of it.,"distance with most of the galactic gas, in that direction, in front of it."178 Second. Schlegel et al. (," Second, Schlegel et al. ("1791998). extinction naps are based on the amount of intrarecl cussion by the dust iutegrated along the whole line of sight through the Galaxy.,1998) extinction maps are based on the amount of infrared emission by the dust integrated along the whole line of sight through the Galaxy.180 The amount of extinction affecting V838 Mou (Ep 9-057 corresponding to ;1—2.7 mag) match the value of Schegel et al., The amount of extinction affecting V838 Mon $E_{B-V}$ =0.87 corresponding to $A_V$ =2.7 mag) match the value of Schegel et al.181 maps in that direction. supporting again the notion that V838 Mon lies at large ealactocentric distances.," maps in that direction, supporting again the notion that V838 Mon lies at large galactocentric distances."182 All hese independent deteriunations support the conclusion that V838 Mon lies in the outer part of the disk ofthe Galaxy. at a distance of 10 kpe from the Sun. corresponding to a galacto-ceutric distance of ~17.5 kpe aud a height above the galactic plaue of ~650 pe.," All these independent determinations support the conclusion that V838 Mon lies in the outer part of the disk of the Galaxy, at a distance of $\sim$ 10 kpc from the Sun, corresponding to a galacto-centric distance of $\sim$ 17.5 kpc and a height above the galactic plane of $\sim$ 650 pc."183 Tyleuda (2001) labeled as “naive interpretation” the early distance estimates of Amari et al. (, Tylenda (2004) labeled as “naive interpretation” the early distance estimates of Munari et al. (1842002a) and Wimesweneger et al. (,2002a) and Kimeswenger et al. (1852002) based ou the first deteriminations of the angular expansion rate of the lieht-echo on carly erouud-based discovery images.,2002) based on the first determinations of the angular expansion rate of the light-echo on early ground-based discovery images.186 The Munuani et al. (, The Munari et al. (18720023) implicit (but quite obvious) assunption was that the light-eclio was originating in a circumstellar disk seen pole-ou.,2002a) implicit (but quite obvious) assumption was that the light-echo was originating in a circumstellar disk seen pole-on.188 Such an assuniptiou was based on the fact that the Nal and KI lines were rot tracing a eireunustellar coniponeut. something to be expected in the case of a homogeneousoO spherical distribution of material centered ou the object itself.," Such an assumption was based on the fact that the NaI and KI lines were not tracing a circumstellar component, something to be expected in the case of a homogeneous spherical distribution of material centered on the object itself."189 It was only much later that high resolution UST imaging revealed tha there is a clear void of circumstellar material precisely. along the Lue of sight to Va3s Mon. regardless of the true 3D shape of the circtunstellar dust giving rise o the lisht-echo.," It was only much later that high resolution HST imaging revealed that there is a clear void of circumstellar material precisely along the line of sight to V838 Mon, regardless of the true 3D shape of the circumstellar dust giving rise to the light-echo."190 So. the now “naive” approach was reasonable at the time.," So, the now “naive” approach was reasonable at the time."191 Fiewe 10 shows the cnerey distribution of the VV. companion in theBW hands (<V>=16.0h2. <Be=l6.736. <U>=16.676 average values from USNO 1.1 photometry described iu sect.l) compared with a Iuruezssvuthetie spectrmu (from the library. of Munari et al.," Figure 10 shows the energy distribution of the V companion in the bands $<$$V$$>$ =16.052, $<$$B$$>$ =16.736, $<$$U$$>$ =16.676 average values from USNO 1.0m photometry described in sect.1) compared with a Kurucz's synthetic spectrum (from the library of Munari et al."192 2001) with parameters appropriate for the VV colmpanion (1100 VI. logg=LO. 0.7).," 2004) with parameters appropriate for the V companion $T_{\rm eff}$ 000 K, $\log g$ =4.0, $-$ 0.7)."193 The match ds excellent., The match is excellent.194 Iu the same figure. the pre-outburst brightuess of Wass Mon frou various sources are plotted.," In the same figure, the pre-outburst brightness of V838 Mon from various sources are plotted."195 In the infrared they come from the 2\LASS aud DENIS surveys. while the D and Πο values are estimates of the same POSS-I and SERC plates according to different authors that used differeut calibrations.," In the infrared they come from the 2MASS and DENIS surveys, while the $B$ and $R_{\rm C}$ values are estimates of the same POSS-I and SERC plates according to different authors that used different calibrations."196 The, The197of state.,of state.198" For the polytropic equation of state p=Kp! the specific enthalpy is f2(AT/(P—1p!. and we obtain In. summary. we need following elements for the description of the hydrostationary equilibrium of a Newtonian radiating disk: (i) the accretion mass function M(z). the rotation curve cr). the central gravitational potential GM,/R and the equation of state p=p(p): Gi) the radiation potential Y. that can be determined from the linear Eq. (13))."," For the polytropic equation of state $p = K \rho^\Gamma$ the specific enthalpy is $h = (K \Gamma / (\Gamma - 1)) \rho^{\Gamma - 1}$, and we obtain In summary, we need following elements for the description of the hydrostationary equilibrium of a Newtonian radiating disk: (i) the accretion mass function $\dot M(z)$, the rotation curve $\omega(r)$, the central gravitational potential $-G M_\mathrm{c} / R$ and the equation of state $p = p(\rho)$; (ii) the radiation potential $\hat \Psi$, that can be determined from the linear Eq. \ref{al}) )."199 It i5 convenient to write 1t down using the integral equation (iit) The distribution of the density or the specific enthalpy., It is convenient to write it down using the integral equation (iii) The distribution of the density or the specific enthalpy.200 This can be obtained from Eqs. (6)), This can be obtained from Eqs. \ref{ac}) )201 and (11)). or from an equation similar to Eq. (15)).," and \ref{aj}) ), or from an equation similar to Eq. \ref{ao}) )."202 In all above formulae the rotation law w=cr) is treated as known apriort., In all above formulae the rotation law $\omega = \omega(r)$ is treated as known apriori.203 A popular choice for test fluid solutions is to assume a (modified) Keplerian rotation is, A popular choice for test fluid solutions is to assume a (modified) Keplerian rotation where $z_0$ is a constant.204",=GM./fi-- .", In this case the centrifugal potential is $\Phi_\mathrm{c} = G M_\mathrm{c} / \sqrt{r^2 + z_0^2}$ .205 Other simple possibilities are: the rigid rotation ω=const. the rotation law «»=vo/r. where const is the linear angular velocity. and w=jo/77. where jo=const is the specific angular momentum.," Other simple possibilities are: the rigid rotation $\omega = \mathrm{const}$, the rotation law $\omega = v_0/r$, where $v_0 = \mathrm{const}$ is the linear angular velocity, and $\omega = j_0/r^2$, where $j_0 = \mathrm{const}$ is the specific angular momentum."206 We will refer to the last two relations as to the v-const and the j-const rotation laws respectively., We will refer to the last two relations as to the $v$ -const and the $j$ -const rotation laws respectively.207 The j-const rotation is exceptional., The $j$ -const rotation is exceptional.208" In this case we have and the radiation equation takes the form Assuming that V. is constant at the spatial infinity. we can conclude that V,=const everywhere."," In this case we have and the radiation equation takes the form Assuming that $\hat \Psi$ is constant at the spatial infinity, we can conclude that $\hat \Psi \equiv \mathrm{const}$ everywhere."209 For the proof. notice that it suffices to deal with the homogeneous case where V-0 as R>co.," For the proof, notice that it suffices to deal with the homogeneous case where $\hat \Psi \to 0$ as $R \to \infty$."210 Multiply the last equation by VY and integrate over FE”., Multiply the last equation by $\hat \Psi$ and integrate over $\mathbb R^3$.211" Integrating by parts and employing the fact that 9,M=0 one arrives at The left hand side ts nonpositive. while the right hand side is nonnegative."," Integrating by parts and employing the fact that $\partial_r \dot M = 0$ one arrives at The left hand side is nonpositive, while the right hand side is nonnegative."212 Therefore =const., Therefore $\hat \Psi = \mathrm{const}$.213 That is a torus with a j-const rotation law is not emitting any radiation in y- and ς-, That is a torus with a $j$ -const rotation law is not emitting any radiation in $r$ - and $z$ -directions.214 Since the j component of the radiation flux vector vanishes identically for the j-const rotation. we conclude that this rotation law is not compatible with the radiation.," Since the $j^\phi$ component of the radiation flux vector vanishes identically for the $j$ -const rotation, we conclude that this rotation law is not compatible with the radiation."215 This is consistent with the picture emerging from the analysis of Lynden-Bell&Pringle(1974):: the radiated luminosity balances the energy budget of the accreting matter and it is accompanied by the shedding of the angular momentum., This is consistent with the picture emerging from the analysis of \citet{LBP}; the radiated luminosity balances the energy budget of the accreting matter and it is accompanied by the shedding of the angular momentum.216 The quantity C m Eq. (11)), The quantity $C$ in Eq. \ref{aj}) )217 is a free parameter., is a free parameter.218 The boundary of the disk is defined as a closed two-surface on which the specific enthalpy vanishes: thus it can not be defined apriort: it is free., The boundary of the disk is defined as a closed two-surface on which the specific enthalpy vanishes; thus it can not be defined apriori; it is free.219 The exception is the test gas approximation without radiation. where the shape of a boundary is completely dictated by the central potential and the rotation curve cx).," The exception is the test gas approximation without radiation, where the shape of a boundary is completely dictated by the central potential and the rotation curve $\omega(r)$."220 Por radiating disks. the shape of a boundary depends also on the luminosity. which in turn is related to the mass accretion rate.," For radiating disks, the shape of a boundary depends also on the luminosity, which in turn is related to the mass accretion rate."221 In order to define uniquely a disk one needs additional information., In order to define uniquely a disk one needs additional information.222 These issues will be discussed in forthcoming sections., These issues will be discussed in forthcoming sections.223 Two of the flux densities are given by //=ὃν. 7=OM.," Two of the flux densities are given by $j^r = \partial_r \Psi$, $j^z = \partial_z \Psi$."224 The third component j can be obtained from the @-th Euler equation., The third component $j^\phi $ can be obtained from the $\phi$ -th Euler equation.225 The formula (7)) yields for a disk with the minimal and maximal radial extensions 75; and rou. respectively. where we employed the condition [U|<wr.," The formula \ref{af}) ) yields for a disk with the minimal and maximal radial extensions $r_\mathrm{in} $ and $r_\mathrm{out}$, respectively, where we employed the condition $|U| \ll \omega r$ ."226 This agrees with the formula derived by Lynden-Bell&Pringle(1974) for the central star that is co-rotating with the disk. if rin< Fac The local formulae for the flux densities are different.," This agrees with the formula derived by \citet{LBP} for the central star that is co-rotating with the disk, if $r_\mathrm{in} \ll r_\mathrm{out}$ The local formulae for the flux densities are different."227 In our case the flux density j is defined uniquely. whereas in the standard approach it is given up to the total divergence (Lynden-Bell&Pringle.," In our case the flux density $\mathbf j$ is defined uniquely, whereas in the standard approach it is given up to the total divergence \citep{LBP}."2281974).. The accretion flow originates outside of the disk and falls onto the central body., The accretion flow originates outside of the disk and falls onto the central body.229 It is concentrated close to the plane z=0., It is concentrated close to the plane $z=0$.230 The quantity M does not depend on r and thus the mass density cannot vanish at the boundary: that means that the actual shape of the disk is not well defined near =0., The quantity $\dot M$ does not depend on $r$ and thus the mass density cannot vanish at the boundary; that means that the actual shape of the disk is not well defined near $z=0$.231 Nevertheless in the formula (17)) we assume that the disk extends from a definite exterior cylinder (ow)to a definite inner cylinder (jy)., Nevertheless in the formula \ref{ap}) ) we assume that the disk extends from a definite exterior cylinder $r_\mathrm{out}$ )to a definite inner cylinder $r_\mathrm{in}$ ).232" Assume that the gas density is low and the gravitational potential is dominated by the central term -GM,/R..", Assume that the gas density is low and the gravitational potential is dominated by the central term $- G M_\mathrm{c} / R^3$.233 It is reasonable to expect (and in fact this expectation can be proved) that there exist solutions of Eq. (10)), It is reasonable to expect (and in fact this expectation can be proved) that there exist solutions of Eq. \ref{ah}) )234 that are well approximated by solutions of the linear inhomogeneous equation Consider the rotation law given by Eq. (16)), that are well approximated by solutions of the linear inhomogeneous equation Consider the rotation law given by Eq. \ref{ar}) )235.One can check that solves Eq. (18)).,".One can check that solves Eq. \ref{aq}) ),"236 with the boundary given by two planes |.= zo., with the boundary given by two planes $|z| = z_0$ .237 In the case ofsmall zo one recoversthe solution of Paezynski (1978):, In the case ofsmall $z_0$ one recoversthe solution of \citet{Paczynski78}: :238"distribution z,5,:)—0.6). though at 45>25 uost sources have a high redshift.","distribution $z_{phot}$ )=0.6), though at $_{AB}>25$ most sources have a high redshift."239" Similarly. at ESL1IWyp «25. late type galaxies have a higher medion redshift (1ied(z,5,:)—1.1) than carly ype oues (nedí(z,5,;:)—0.6) and the vedshitt distribution (Figure 16)) is simular to Driver et al. ("," Similarly, at $_{AB}<$ 25, late type galaxies have a higher median redshift $z_{phot}$ )=1.1) than early type ones $z_{phot}$ )=0.6) and the redshift distribution (Figure \ref{z_histo}) ) is similar to Driver et al. ("2401998) one. though he nuniber of sources at -phot>15 is lower.,"1998) one, though the number of sources at $z_{phot}>1.5$ is lower."241 There is a point to be emphasized about redshift distributions and immorphological tvpes: the detection of galaxies at vel redshift is seriously biased against elliptical galaxies )ecause of Acorrections inthe Pst(W-band., There is a point to be emphasized about redshift distributions and morphological types: the detection of galaxies at high redshift is seriously biased against elliptical galaxies because of $K-corrections$ in the F814W-band.242 At +1. carly type galaxies have Jvcorrections (zxl mag) ereater than late type A/—corrections. maius them zduter.," At $z\approx1$, early type galaxies have $K-corrections$ $\approx 1$ mag) greater than late type $K-corrections$, making them fainter."243 It 1neaus that a cut in apparent maguitude. such as 45 x25. biases the sample toward galaxies with ower A—eorrcctions.," It means that a cut in apparent magnitude, such as $_{AB}<$ 25, biases the sample toward galaxies with lower $K-corrections$."244 To skip this problem. we tried to select a volume-linited sample. based ou our photometric redshifts.," To skip this problem, we tried to select a volume-limited sample, based on our photometric redshifts."245 When selecting all galaxies with i554l. we ounud only 15/4 to be with ip. «25. that is with a reliable morphological classification according to our uecthod.," When selecting all galaxies with $z_{phot}\leq1$, we found only $\%$ to be with $_{AB}<$ 25, that is with a reliable morphological classification according to our method."246 Vice versa it means that a cut off in apparent uaenitude docs uot offer a fair sample for a redshift distribution of the differcut morphological types., Vice versa it means that a cut off in apparent magnitude does not offer a fair sample for a redshift distribution of the different morphological types.247 Probably also the apparent decrease d early-type ealaxies nuniber counts; as shown in Figure 12.. is due to this bias.," Probably also the apparent decrease in early-type galaxies number counts, as shown in Figure \ref{morph_c}, is due to this bias."248 We compared our umunber counts with cdiffereut models. by using galaxy counts 1iodols by Carcdnuer (1998).," We compared our number counts with different models, by using galaxy counts models by Gardner (1998)."249" We adopted a flat cosmological model (yy=0.5. I7,=50 km t 4) in all models."," We adopted a flat cosmological model $q_0=0.5$, $H_0=50$ km $^{-1}$ $^{-1}$ ) in all models."250 We used the Iuninositv function of Marzke et al. (, We used the luminosity function of Marzke et al. (2511998) both considering a sinele Schechter function for all morphological tvpes aud threc different Schechter fits for elliptical. spiral aud irregular ealaxies.,"1998) both considering a single Schechter function for all morphological types and three different Schechter fits for elliptical, spiral and irregular galaxies."252 Our counts are best fitted by considering three LFs. lunuinositv evolution aud a moderate mergiue (Figure 17)) consistent with our interpretations.," Our counts are best fitted by considering three LFs, luminosity evolution and a moderate merging (Figure \ref{ncmod}) ) consistent with our interpretations."253 The imereiue rate in Carducr (1998) μυ» Rocea-Volucrauge Caiderdomi (1990) with umber evolution parameterized as oOx(112)” in the Schechter fit to the LE. aud in order to couscrve the Iunünositv deusitv. Lx(1|:)* isa free parameter.," The merging rate in Gardner (1998) follows Rocca-Volmerange Guiderdoni (1990) with number evolution parameterized as $\phi^* \propto (1+z)^{\eta}$ in the Schechter fit to the LF, and in order to conserve the luminosity density, $L^* \propto (1+z)^{-{\eta}}$; $\eta$ is a free parameter."254 (τους fits to our data are obtained with 5gx:0.5 iu the case of του LFs for the cosinological parameters considered., Good fits to our data are obtained with $\eta\leq0.5$ in the case of three LFs for the cosmological parameters considered.255" The IIDE-S represents a unique opportunity for the study of funt ealaxies up to now. both for its depth (pan,m29 for detection and apaon,s3 for completeness) aud spatial resolution O2 arcsec),"," The HDF-S represents a unique opportunity for the study of faint galaxies up to now, both for its depth $_{AB,lim}\approx29$ for detection and $_{AB,lim}\approx27$ for completeness) and spatial resolution $\approx$ 0.2 arcsec)."256 We presented here colors aud. number counts of IIDE-S ealaxies. along with nuuber comnts determined bv splitting the sample considering the morphology and the colors of the galaxies.," We presented here colors and number counts of HDF-S galaxies, along with number counts determined by splitting the sample considering the morphology and the colors of the galaxies."257 We also analyzed the photometric data to constrain the redshift of ΠΟΓ- ealaxies. and determine the contribution of different redslift populations to the counts.," We also analyzed the photometric data to constrain the redshift of HDF-S galaxies, and determine the contribution of different redshift populations to the counts."258 The main results are the following:, The main results are the following:259with a single Loreutz oscillaor af m-—195 |.,with a single Lorentz oscillator at $\nu_{t}$ =795 $^{-1}$.260 This suele oscillator is responsible for a great varicty of measured spectra. depending on particle specifies (see Bolren aud Iutffinan (1983)... Chap.," This single oscillator is responsible for a great variety of measured spectra, depending on particle specifics (see Bohren and Huffman \cite{boh}, Chap."261 12)., 12).262 Therefore. if thiourea is fo be considered. it could uxXt be in the solid state," Therefore, if thiourea is to be considered, it could not be in the solid state."263 Now. he single. uubroadened ine of the gaseous 110ecule near 20 pam cannot Πας the 21-501 baud. whose width is 2.1 sau. However. broadenius of the line lay aso occur due to the staightforward formation o: [I-bonds aud complexes with iupuritv ious (coordination) or to the presence of thiourea derivatives (see Sewart (1957).. Masunov aud Daurenbere (200) Brvautsev aud Παν (2006).. Brennan (2006))).," Now, the single, unbroadened line of the gaseous molecule near 20 $\mu$ m cannot mimic the $\mu$ m band, whose width is 2.4 $\mu$ m. However, broadening of the line may also occur due to the staightforward formation of H-bonds and complexes with impurity ions (coordination) or to the presence of thiourea derivatives (see Stewart \cite{ste}, , Masunov and Dannenberg \cite{mas} Bryantsev and Hay \cite{bry}, Brennan \cite{bre}) )."264 These are oftve form SC(NRIR2(NR3BED. where the Rs represeut radicals attached to the SCN» root.," These are of the form SC(NR1R2)(NR3R4), where the R's represent radicals attached to the $_{2}$ root."265 The present work. precisely. explores the rossibility o tesing advantage of this propensity o thiourea 1 order to contro the positio- and shape of its 21-4 feature so as to better fi the observatious.," The present work, precisely, explores the possibility of taking advantage of this propensity of thiourea in order to control the position and shape of its $\mu$ m feature so as to better fit the observations."266 DIudeed. atacluneut to a chemically different sticture sliel:Iv shifts the thiourea lines axd nav also eulauce the IR activity o some Lines nearby.," Indeed, attachment to a chemically different structure slightly shifts the thiourea lines and may also enhance the IR activity of some lines nearby."267 Combining the spectra of many associatious of this type wil hopefully All the window occupied by t1ο astronomical baud., Combining the spectra of many associations of this type will hopefully fill the window occupied by the astronomical band.268Iu,In269"eV, while the residual width is σ~50eV’;; which confirms that the broadening of the line is intrinsic to the source and notinstrumental?.","eV, while the residual width is $\sigma \sim 50 $; which confirms that the broadening of the line is intrinsic to the source and not."270. After the subtraction in quadrature of this residual width we get 02.=110+60 eV)., After the subtraction in quadrature of this residual width we get $ \sigma_{\mathrm{int}}^{2} =110\pm60 $ eV).271" However, taking into account the present count statistics of the data, this broadening could be due to the presence of other line components, which are not resolved."," However, taking into account the present count statistics of the data, this broadening could be due to the presence of other line components, which are not resolved."272" In particular, the line profile can be explained with three unresolved Gaussian lines (at 6.4 keV, 6.7 keV and 6.96 keV; see Fig."," In particular, the line profile can be explained with three unresolved Gaussian lines (at 6.4 keV, 6.7 keV and 6.96 keV; see Fig."273 3)., 3).274 Statistically this model gives a similar good fit than models with a single broad line (y7/dof= 161/145) with the strongest line being the 6.7 keV line (EW~400 eV)., Statistically this model gives a similar good fit than models with a single broad line $\chi^2/\rm{dof}=161/145$ ) with the strongest line being the 6.7 keV line $EW\sim 400$ eV).275" Though the other two lines are not statistically required a weak (EW<200 eV) emission line could be present at the energy of the neutral Fe Ka, while the upper limit on the 6.96 keV line is 150 eV. Since the energy centroid of the line detected with Suzaku appears to be in disagreement with the rresults and the EW appears to be lower we went back to the ddata and compared them with the Suzaku results."," Though the other two lines are not statistically required a weak $EW< 200$ eV) emission line could be present at the energy of the neutral Fe $\alpha$, while the upper limit on the 6.96 keV line is $150$ eV. Since the energy centroid of the line detected with Suzaku appears to be in disagreement with the results and the EW appears to be lower we went back to the data and compared them with the Suzaku results."276 The exposure time of the oobservation was only 20 ksec and when we take into account the errors on the flux and line continuum we found that the two lines are consistent within each others., The exposure time of the observation was only 20 ksec and when we take into account the errors on the flux and line continuum we found that the two lines are consistent within each others.277" Furthermore, the energy centroids are consistent within the errors (Eyyy=6.5€0.1 keV; Esuzku=6.66+0.05 keV)."," Furthermore, the energy centroids are consistent within the errors $E_{XMM}=6.5\pm0.1$ keV; $E_{\mathrm {Suzaku}}=6.66\pm 0.05$ keV)."278" Finally, a possible blending of 3 lines was also present in the ddata, but again the low exposure time of this observation does not allow a more detailed analysis of the Fe line profile."," Finally, a possible blending of 3 lines was also present in the data, but again the low exposure time of this observation does not allow a more detailed analysis of the Fe line profile."279" Froma statistical point of view all these models are a good representation of the 0.5—30 keV emission, but they are unable to account for the hardness of the continuum."," From a statistical point of view all these models are a good representation of the 0.5–30 keV emission, but they are unable to account for the hardness of the continuum."280 Furthermore the line energy of the strongest emission line is at odds with a scenario where the 2-10 keV emission is dominated by reflection/scattering off cold material as assumed with the continuum model tested above., Furthermore the line energy of the strongest emission line is at odds with a scenario where the 2–10 keV emission is dominated by reflection/scattering off cold material as assumed with the continuum model tested above.281" One possibility is that the 6.7 keV line is due to reflection from highly ionized matter; we thus replaced the cold reflected (PExRAv) power law component with an ionized reflected component, as is described by the the Ross&Fabian(2005) table (otherwise known as theREFLION model)."," One possibility is that the 6.7 keV line is due to reflection from highly ionized matter; we thus replaced the cold reflected ) power law component with an ionized reflected component, as is described by the the \citet{Ross} table (otherwise known as the model)."282" This model allows different values for the ionization parameter of the reflecting material and it also includes the Fe K emission line, as well as emission lines from other elements in addition to the reflected continuum."," This model allows different values for the ionization parameter of the reflecting material and it also includes the Fe K emission line, as well as emission lines from other elements in addition to the reflected continuum."283 We fixed the Fe abundance to solar and we included a lower column density in front of the reflected component., We fixed the Fe abundance to solar and we included a lower column density in front of the reflected component.284 The photon index of the illuminating X-ray source is left as a free parameter., The photon index of the illuminating X-ray source is left as a free parameter.285 A good fit (see Fig., A good fit (see Fig.286" 2 lower panel and Table 1 model D) of the 0.5-30 keV emission is obtained with a ionization parameter of é-1000*120 erg cm s!, where the value of the ionization is determined mainly by the strength and energy of the Fe line; at this ionization level, Fe K emission is almost entirely due to Fe xxv."," 2 lower panel and Table 1 model D) of the 0.5-30 keV emission is obtained with a ionization parameter of $\xi=2871000^{+170}_{-430}$ erg cm $^{-1}$, where the value of the ionization is determined mainly by the strength and energy of the Fe line; at this ionization level, Fe K emission is almost entirely due to Fe xxv."288" The reflected component is modified by a lower column density absorber with Ny~10? cm, which is probably on a larger scale than the inner high column density absorber."," The reflected component is modified by a lower column density absorber with $289N_{\mathrm{H}}\sim 10^{22}$ $^{-2}$, which is probably on a larger scale than the inner high column density absorber."290 We stress that a second highly absorbed (Ny~3x10cm?) power-law component is still required to account for the HXD-PIN emission and the intrinsic 2-10 keV luminosity is 3x10“ergs7!..," We stress that a second highly absorbed $N_{\rm{H}}\sim2913\times10^{24}$ $^{-2}$ ) power-law component is still required to account for the HXD-PIN emission and the intrinsic 2–10 keV luminosity is $\sim 3\times29210^{44}$."293" The photon index of the illuminating source is now Γ=1.877031, consistent with the mean value measured in unobscured radio quiet AGN (l'a,=1.9; Reeves&Turner 2000))."," The photon index of the illuminating source is now $\Gamma=1.87^{+0.11}_{-0.28}$, consistent with the mean value measured in unobscured radio quiet AGN $\Gamma_\mathrm{mean}=1.9$; \citealt{Reeves00}) )."294" In summary, this model is now able to reproduce in a consistent way all the main characteristic of the the broad band X-ray emission of aand in particular the Fe emission line detected at ~6.7 keV and the flatness of the observed continuum."," In summary, this model is now able to reproduce in a consistent way all the main characteristic of the the broad band X-ray emission of and in particular the Fe emission line detected at $\sim 6.7$ keV and the flatness of the observed continuum."295" Finally, it is worth noting that, independently of the assumed model for the 0.5-10 keV emission, we always need to include an absorbed power law component to account for the HXD-PIN data with a Ny~3-4x 1024οπι-2, and the derived 2-10 keV intrinsic luminosity is always above L(2-10 keV) ~10“ergs!,, ranging from 2x10“erg s!to 4x10“ (see Table 1)."," Finally, it is worth noting that, independently of the assumed model for the 0.5-10 keV emission, we always need to include an absorbed power law component to account for the HXD-PIN data with a $N_{\rm H}\sim 3-4\times 10^{24}$ $^{-2}$, and the derived 2-10 keV intrinsic luminosity is always above L(2–10 keV) $\sim 10^{44}$, ranging from $2\times 10^{44}$ to $4\times 10^{44}$ (see Table 1)."296 The detection of the Fe K emission line at 6.7 keV instead of the 6.4 keV emission line expected from neutral iron may, The detection of the Fe K emission line at 6.7 keV instead of the 6.4 keV emission line expected from neutral iron may297on the bulk velocity. we plot the fraction. of the volume of the universe (at. lowest. velocity. Le. at. highest. stellar density) that contains 684 or 95% of the star-forming halos (Figure 5)).,"on the bulk velocity, we plot the fraction of the volume of the universe (at lowest velocity, i.e., at highest stellar density) that contains $68\%$ or $95\%$ of the star-forming halos (Figure \ref{Fig:VcPdf2}) )."298 The elfect of volume concentration is mild. at =20 (68% of the stars are in 54% of the volume. and 95% in SOM of the volume). while it becomes very strong at 2=60 (68% of stars in 4.6% of the volume. ancl 95% in 16% of the volume).," The effect of volume concentration is mild at $z=20$ $68\%$ of the stars are in $54\%$ of the volume, and $95\%$ in $89\%$ of the volume), while it becomes very strong at $z=60$ $68\%$ of stars in $4.6\%$ of the volume, and $95\%$ in $16\%$ of the volume)."299 In order to quantify the full degree of inhomogeneity and concentration of star formation. we must include the elfect of density Ποιαος as well.," In order to quantify the full degree of inhomogeneity and concentration of star formation, we must include the effect of density fluctuations as well."300 In this section. we thus consider the full PDE of the halo gas fraction within 3 Mpe patches. where the Huctuations result (rom a combination of the relative velocity. distribution considered in the previous section ancl density. fluctuations.," In this section we thus consider the full PDF of the halo gas fraction within 3 Mpc patches, where the fluctuations result from a combination of the relative velocity distribution considered in the previous section and density fluctuations."301 Specifically. the average density in a patch varies due to fluctuations on scales larger than its size.," Specifically, the average density in a patch varies due to fluctuations on scales larger than its size."302 This average density follows a Gaussian distribution and is independent of the relative velocity within the same patch., This average density follows a Gaussian distribution and is independent of the relative velocity within the same patch.303 To lind the moclificd halo mass function within a patch of a given overdensity 05 and bulk velocity (i. we use the hybrid. prescription (which combines the Sheth&'lormen(1999) mass function with the extended: Press- model) introduced. by Barkana&Loch(2004) and generalized by Fseliakhovich.Barkana&Llirata to include ei.," To find the modified halo mass function within a patch of a given overdensity $\delta_R$ and bulk velocity $v\bc$, we use the hybrid prescription (which combines the \citet{Shetht:1999} mass function with the extended Press-Schechter model) introduced by \citet{Barkana:2004} and generalized by \citet{Tseliakhovich:2010b} to include $v\bc$."304 The dependence of the gas fraction in halos above the cooling mass on he two independent: variables is illustratecl in. Figure. 6.., The dependence of the gas fraction in halos above the cooling mass on the two independent variables is illustrated in Figure \ref{Fig:VcDelta}.305 The dependence on both oy and ene (each measured. in terms of its root-mean-square value) is stronger at higher redshifts., The dependence on both $\delta_R$ and $v\bc$ (each measured in terms of its root-mean-square value) is stronger at higher redshifts.306 At a given. recdshift. the dependence on 95 is stronger (i.e. the slope is higher) when ei is higher. since in this case the large halos (above the high cooling mass) are rarer and their abundance is more sensitive to the overdensity of the patch.," At a given redshift, the dependence on $\delta_R$ is stronger (i.e., the slope is higher) when $v\bc$ is higher, since in this case the large halos (above the high cooling mass) are rarer and their abundance is more sensitive to the overdensity of the patch."307 H£ ve consider the total range between O ancl 2 σ. we find that density and velocity Huctuations make comparable contributions to the star-formation Iluctuations on the 3 Alpe scale.," If we consider the total range between 0 and 2 $\sigma$, we find that density and velocity fluctuations make comparable contributions to the star-formation fluctuations on the 3 Mpc scale."308 “Phe relative importance of velocity increases wi1 redshift and it will also increase if we consider larger scales., The relative importance of velocity increases with redshift and it will also increase if we consider larger scales.309 Even at z=20 the velocity causes order unity fluctuations in the stellar density. and these fluctuations shoulc o present at the [aree (100 Alpe) sc:des spanned by the velοσον correlations.," Even at $z=20$ the velocity causes order unity fluctuations in the stellar density, and these fluctuations should be present at the large (100 Mpc) scales spanned by the velocity correlations."310 ‘Phe resuting full PDE of he halo gas fraction is shown in Figure 7 (top panel). bot1 for he star-forming halos. and the star-ess gas minihalos.," The resulting full PDF of the halo gas fraction is shown in Figure \ref{Fig:FPdf} (top panel), both for the star-forming halos, and the star-less gas minihalos."311 The main ellect of the bulk velocities is o shift the. distributicons towards lower gas fractions., The main effect of the bulk velocities is to shift the distributions towards lower gas fractions.312 At redshift 20. the efect is arger on the minihalos.," At redshift 20, the effect is larger on the minihalos."313 In Figure 7 (bottom panel) we show the fraction of the volume of the universe (at the high eas fraction end of the, In Figure \ref{Fig:FPdf} (bottom panel) we show the fraction of the volume of the universe (at the high gas fraction end of the314would allow for a perfect reconstruction of the projected mass surface clensity (modulo the mass-sheet degeneracy. which should be unimportant for large enough fields).,"would allow for a perfect reconstruction of the projected mass surface density (modulo the mass-sheet degeneracy, which should be unimportant for large enough fields)."315 From this mass surface densitv il is possible to caleulate the lensing magnification. and therefore perfectly account for (and correct) the lensine effects on the observed brightness.," From this mass surface density it is possible to calculate the lensing magnification, and therefore perfectly account for (and correct) the lensing effects on the observed brightness."316 Perfect shear maps are unavailable. however. and therelore our ability to infer the magnilication is compromised.," Perfect shear maps are unavailable, however, and therefore our ability to infer the magnification is compromised."317 In (his paper. we investigate how well weak lensing reconstruction can correct the brightnesses of distant supernovae.," In this paper, we investigate how well weak lensing reconstruction can correct the brightnesses of distant supernovae."318 The basie scheme is as follows., The basic scheme is as follows.319 A supernova occurs in a given field. and its peak apparent magnitude is observed ancl calibrated. using some variant of the Phillips(1993) relation.," A supernova occurs in a given field, and its peak apparent magnitude is observed and calibrated, using some variant of the \citet{phillips}320 relation."321 Then the (co-addecd) field containing the supernova is used to estimate (he local shear at the supernova's location by averaging over a smoothing augle 9., Then the (co-added) field containing the supernova is used to estimate the local shear at the supernova's location by averaging over a smoothing angle $\theta$.322 The shear map is then converted to an effective convergence map using some reconstruction algorithm such as that. of (1993).. and the derived convergence is used to correct (he supernova’s standard candle brightness.," The shear map is then converted to an effective convergence map using some reconstruction algorithm such as that of \citet{ks}, and the derived convergence is used to correct the supernova's standard candle brightness."323" In the following section we estimate the variance in convergence lor point sources given knowledge of the smoothed shear map. (57),. which is a direct measure of ihe improvement such an approach can offer."," In the following section we estimate the variance in convergence for point sources given knowledge of the smoothed shear map, $\langle\kappa^2\rangle_\gamma$, which is a direct measure of the improvement such an approach can offer."324 We find that useful corrections require very large background source galaxy densities. and that this method is therefore of only marginal utility.," We find that useful corrections require very large background source galaxy densities, and that this method is therefore of only marginal utility."325 Let us denote bv & the effective convergence. relative to the homogeneous filled-beam value. for a point source.," Let us denote by $\kappa$ the effective convergence, relative to the homogeneous filled-beam value, for a point source."326 Ii Figure 1 we plot the angular power spectrum of the convergence. AZ)=CD(Q)/2x White&Hu2000).. for sources at z;= 2.," In Figure \ref{angpow} we plot the angular power spectrum of the convergence, $\Delta_\kappa^2(\ell)=\ell^2P_\kappa(\ell)/2\pi$ \citep{whitehu}, for sources at $z_s=2$ ."327 To caleulate this. we employ the fitting functions of Eisenstein&IIu(1999). for the linear matter power spectrum. and follow the prescription of Peacock&Dodds(1996). for the non-linear correction.," To calculate this, we employ the fitting functions of \citet{eh99} for the linear matter power spectrum, and follow the prescription of \cite{pd} for the non-linear correction."328" We use a CODE normalized. scale invariant (η= 1) linear power spectrum in a flat ACDM cosmology with total matter density. O,,=0.35. Hubble constant =0.65 (JI=100km/s/ Mpe). and barvon density Q,/7=0.02."," We use a COBE normalized, scale invariant $n=1$ ) linear power spectrum in a flat $\Lambda$ CDM cosmology with total matter density $\Omega_m=0.35$, Hubble constant $h=0.65$ $H_0=100\,h\,\mbox{km}/\mbox{s/Mpc}$ ), and baryon density $\Omega_b h^2=0.02$."329 We also assume that the dark matter is microscopic (e.g.. elementary particles). rather than macroscopic (e.g.. black holes or MACIIOs).," We also assume that the dark matter is microscopic (e.g., elementary particles), rather than macroscopic (e.g., black holes or MACHOs)."330 The latter case leads to enhanced power on microaresecond scales. which decorrelates point source magnification [rom galaxy shear.," The latter case leads to enhanced power on microarcsecond scales, which decorrelates point source magnification from galaxy shear."331 The convergence angular power specirum peaks on arcminute scales (6~ 105). with significant power extending for multiple decades in (.," The convergence angular power spectrum peaks on arcminute scales $\ell\sim10^4$ ), with significant power extending for multiple decades in $\ell$."332 All of this power contributes to the magnification of (almost) point sources like supernovae., All of this power contributes to the magnification of (almost) point sources like supernovae.333 When measuring shear. however. ealaxy correlations must be averaged over large angular patches tosuppress Poisson noise.," When measuring shear, however, galaxy correlations must be averaged over large angular patches tosuppress Poisson noise,"334"curves, which span periods as long as five years, for many AGN.","curves, which span periods as long as five years, for many AGN."335 Beckmann et al. (, Beckmann et al. (3362007) have presented the results from a study of the first 9 month Swift/BAT light curves of 44 AGN.,2007) have presented the results from a study of the first 9 month /BAT light curves of 44 AGN.337" They found that ~30% of Seyferts exhibit significant hard X-ray variability on time scales of ddays, type 1 Seyferts are less variable than Seyferts 2, and a significant anti-correlation between luminosity and variability amplitude."," They found that $\sim 30\%$ of Seyferts exhibit significant hard X–ray variability on time scales of days, type 1 Seyferts are less variable than Seyferts 2, and a significant anti-correlation between luminosity and variability amplitude."338" More recently, Soldi et al. ("," More recently, Soldi et al. ("3392010) reported the results from a preliminary study of the flux variability of 36 AGN using data from the first 5 years of Swift/BAT observations.,2010) reported the results from a preliminary study of the flux variability of 36 AGN using data from the first 5 years of /BAT observations.340 Their results confirmed the hard X-ray variability — luminosity anti-correlation detected by Beckmann et al. (, Their results confirmed the hard X–ray variability – luminosity anti-correlation detected by Beckmann et al. (3412007) at high energies.,2007) at high energies.342 They also showed that an anti-correlation between variability amplitude and BH mass may also exist for Seyfert galaxies., They also showed that an anti-correlation between variability amplitude and BH mass may also exist for Seyfert galaxies.343" In this work, we present the results from a variability study of the five brightest radio-quiet AGN in the recently published catalogue of Baumgartner et al. ("," In this work, we present the results from a variability study of the five brightest radio-quiet AGN in the recently published catalogue of Baumgartner et al. ("344"2011), using the 5 years long BAT light curves that the same authors provide in the 20-50 and 50-100 keV bands (the “soft” and “hard” bands, hereafter).","2011), using the 5 years long BAT light curves that the same authors provide in the 20–50 and 50–100 keV bands (the “soft"" and “hard"" bands, hereafter)."345" Our main aim is to study thespectral variability of the sources with the use of “hardness ratios”, i.e. by simply dividing the hard over the soft band light curves."," Our main aim is to study the variability of the sources with the use of “hardness ratios"", i.e. by simply dividing the hard over the soft band light curves."346 Such ratios have been extensively used in the past for the study of the AGN spectral variability in the 2--10/20 keV band., Such ratios have been extensively used in the past for the study of the AGN spectral variability in the 2–10/20 keV band.347" Their biggest advantage is that they are entirely model-independent; if the hardness ratios are variable, then the spectral shape of the source to be variable, irrespective of the underlying continuum spectrum, and of which spectral component is responsible of the observed variations."," Their biggest advantage is that they are entirely model–independent; if the hardness ratios are variable, then the spectral shape of the source to be variable, irrespective of the underlying continuum spectrum, and of which spectral component is responsible of the observed variations."348" In addition, the presence (or absence) of a correlation between the hardness ratios and the source flux can indicate which model components vary (or not) in AGN."," In addition, the presence (or absence) of a correlation between the hardness ratios and the source flux can indicate which model components vary (or not) in AGN."349 We restricted our study to the 5 brightest Seyferts in the current Swift/BAT catalogue because they are bright enough for an accurate estimation of their soft and hard band fluxes on time scales as short as 20 days., We restricted our study to the 5 brightest Seyferts in the current /BAT catalogue because they are bright enough for an accurate estimation of their soft and hard band fluxes on time scales as short as 20 days.350" As a result, we are able to use the hardness ratios to search for low-amplitude spectral variations on these time scales, almost continuously, over a period of 5 years."," As a result, we are able to use the hardness ratios to search for low-amplitude spectral variations on these time scales, almost continuously, over a period of 5 years."351" This would not be possible to achieve with the study of energy spectra extracted over periods as short as ~ one month, due to low signal-to-noise ratio."," This would not be possible to achieve with the study of energy spectra extracted over periods as short as $\sim$ one month, due to low signal-to-noise ratio."352" In addition, the signal-to-noise ratio of even the 1—2 day binned soft band light curves of these objects is high enough to study their flux variations over a broad range of time scales, i.e. from years down to almost a day."," In addition, the signal-to-noise ratio of even the 1–2 day binned soft band light curves of these objects is high enough to study their flux variations over a broad range of time scales, i.e. from years down to almost a day."353 The sample and the light curves we used are described in Section 2.., The sample and the light curves we used are described in Section \ref{sample}.354 Our results from the flux and spectral variability analysis are reported in Sections 3 and 4.., Our results from the flux and spectral variability analysis are reported in Sections \ref{fluxvar} and \ref{specvar}.355" We discuss possible implications of our results in Section 5,, and we present our conclusions in Section 5.."," We discuss possible implications of our results in Section \ref{discuss}, and we present our conclusions in Section \ref{discuss}."356" The Burst Alert Telescope (BAT; Barthelmy et al.2005) on-board the (Gehrelsetal.,2004) is sensitive to X-ray photons in the kkeV energy range.", The Burst Alert Telescope (BAT; Barthelmy et al.2005) on-board the \citep{gehrels04} is sensitive to X–ray photons in the keV energy range.357 Baumgartner et al. (, Baumgartner et al. (3582011) released a catalog of sources detected in the first 58 months of BAT observations.,2011) released a catalog of sources detected in the first 58 months of BAT observations.359" It consists of 1092 sources, detected at a significance level of at least 4.80."," It consists of 1092 sources, detected at a significance level of at least $4.8{\sigma}$."360 The majority of the sources in this catalogue are AGN (with 519 objects classified as Seyferts)., The majority of the sources in this catalogue are AGN (with 519 objects classified as Seyferts).361" We chose to study the 5 Seyferts which have the highest flux in this catalogue, among all radio-quiet AGN."," We chose to study the 5 Seyferts which have the highest flux in this catalogue, among all radio-quiet AGN."362 Source names and their hard X-ray fluxes are listed in Table 1.., Source names and their hard X-ray fluxes are listed in Table \ref{tsample}.363" A summary of previous findings, regarding the hard X-ray emission of these objects, is presented in the Appendix."," A summary of previous findings, regarding the hard X–ray emission of these objects, is presented in the Appendix."364 Baumgartner et al. (, Baumgartner et al. (365"2011) also provide light curves in eight energy bands: 14—20, 20-24, 24—35, 35-50, 50-75, 75-100, 100—150, and kkeV. These light curves are available fromHEASARC!.","2011) also provide light curves in eight energy bands: 14–20, 20–24, 24–35, 35–50, 50–75, 75–100, 100–150, and keV. These light curves are available from."366". They were extracted from the individual snapshot images from each ~5mmin observation, and the reported count rates are corrected for off-axis effects."," They were extracted from the individual snapshot images from each ${\sim}5$ min observation, and the reported count rates are corrected for off-axis effects."367" We added the count rate of the second, third and fourth band light curves to produce a combined light curve in the 20-50 keV energy band (the “soft” band light curve hereafter; the error on the final count rate was calculated using the usual error propagation rules, i.e. Bevington 1969)."," We added the count rate of the second, third and fourth band light curves to produce a combined light curve in the 20–50 keV energy band (the “soft"" band light curve hereafter; the error on the final count rate was calculated using the usual error propagation rules, i.e. Bevington 1969)."368" In a similar way, we produced 100 keV (*hard"" band, hereafter), and the “full” band (i.e. 20—100 keV) light curves, by adding all the individual light curves in the respective energy ranges."," In a similar way, we produced 50--100 keV (“hard"" band, hereafter), and the “full"" band (i.e. 20--100 keV) light curves, by adding all the individual light curves in the respective energy ranges."369" The resulting light curves were then re-binned to 2 days and 20 days (in the case of NGC 4151, we used a bin size of 1 day,"," The resulting light curves were then re-binned to 2 days and 20 days (in the case of NGC 4151, we used a bin size of 1 day,"370in Table 1.,in Table 1.371 Using Eqs. (4)), Using Eqs. \ref{N}) )372 and (5)) we calculate the inclusive probabilities for various cluster topologies as a function of the angular resolution and the accumulated nunber of events n., and \ref{exact}) ) we calculate the inclusive probabilities for various cluster topologies as a function of the angular resolution and the accumulated number of events $n$.373 By inclusive probabilities we mean that the specified number of j-plets plus any other cluster. counts as all the j-plets + extva-clusters.," By inclusive probabilities we mean that the specified number of $j$ -plets plus any other cluster, counts as all the $j$ -plets + extra-clusters."374 The main experimental properties for the four experiments are summarized in Table 2., The main experimental properties for the four experiments are summarized in Table 2.375 In Fig., In Fig.376 1 we show the inclusive probabilities [or one and more doublets ancl (wo and more doublets for the sample of ILaverah. Park., 1 we show the inclusive probabilities for one and more doublets and two and more doublets for the sample of Haverah Park.377 The chance probability. for clustering within 3° is larger than and hence not statistically significant., The chance probability for clustering within $3^\circ$ is larger than and hence not statistically significant.378 In Fig., In Fig.379 2 we show (he inclusive probabilities for 8 doublets and 2 triplets at dilferent CR-skyv coverages., 2 we show the inclusive probabilities for 8 doublets and 2 triplets at different CR-sky coverages.380" The probability of chance association is only ""small for angular binnine lighter than 37. and O> 4."," The probability of chance association is only “small” for angular binning tighter than $3^\circ$, and $\Omega > 4$ ."381 The chance probability for clustering within 4° and 5° remains always larger thanLOY., The chance probability for clustering within $4^\circ$ and $5^\circ$ remains always larger than.382.. Therefore. the observation of this topology within the approximate angular resolution of the combined data set. is not statistically significant.," Therefore, the observation of this topology within the approximate angular resolution of the combined data set, is not statistically significant."383 This result agrees with previous numerical simulations [17]., This result agrees with previous numerical simulations \cite{uchihori}.384 We now examine whether there is anv evidence for clustering above the statistical expectation when considering the AG.ASA subsample., We now examine whether there is any evidence for clustering above the statistical expectation when considering the AGASA subsample.385 The latter has much better angular resolution., The latter has much better angular resolution.386 In Fig., In Fig.387 3 we show the chance probabilities of observing 5 doublets and one triplet given 58 events al AGASA., 3 we show the chance probabilities of observing 5 doublets and one triplet given 58 events at AGASA.388 The probability is extremely sensitive to (he angular binning., The probability is extremely sensitive to the angular binning.389 In this case. the chance probability. within the experimental angular resolution is less than 10.7.," In this case, the chance probability within the experimental angular resolution is less than $10^{-3}$."390 This result is in verv good agreement with the one recently obtained using numerical simulations of the angular (wo point correlation function of ultrahieh enerev CRs: A 3xLO? probability of chance clustering with a bin size of 2.5 and an energy eut-off αἱ 4.8x1013 eV [19].., This result is in very good agreement with the one recently obtained using numerical simulations of the angular two point correlation function of ultrahigh energy CRs: A $3 \times 10^{-4}$ probability of chance clustering with a bin size of $2.5^\circ$ and an energy cut-off at $4.8 \times 10^{19}$ eV \cite{TT1}.391 Furthermore. when including data from Yakuisk’s experiment above 2.4xLO! eV. the combined probability of chance clustering is reported to be as small as 4xLO°. strongly suggesting that CR sources are point-like on cosmological scales [19]..," Furthermore, when including data from Yakutsk's experiment above $2.4 \times 10^{19}$ eV, the combined probability of chance clustering is reported to be as small as $4 \times 10^{-6}$, strongly suggesting that CR sources are point-like on cosmological scales \cite{TT1}."392 Compact radio quasars (CROSOs) are strong radio emitters. a fact that along with their variability. is indicative of strong beaming.," Compact radio quasars (CRQSOs) are strong radio emitters, a fact that along with their variability, is indicative of strong beaming."393 The bulk of the observed non-thermal enussion of these objects is thought (to be produced in strong. relativistic jets of charged particles emitted by the active nucleus. which is likely formed by an accreting supermassive black hole.," The bulk of the observed non-thermal emission of these objects is thought to be produced in strong, relativistic jets of charged particles emitted by the active nucleus, which is likely formed by an accreting supermassive black hole."394 These powerlul objects have been under suspicion as the primary source of ultrahigh energy CRs for some time now [20.21.22]..," These powerful objects have been under suspicion as the primary source of ultrahigh energy CRs for some time now \cite{bf,sigletal,vir}."395 Therefore. we lind it particularly attractive to examine whether (here exists a correlation between CR-clusters and CROSOs.," Therefore, we find it particularly attractive to examine whether there exists a correlation between CR-clusters and CRQSOs."396 We shall use the 451 CROSOs with flat spectrum ancl declination above —10* degrees taken from the surveys of Ref. [23].., We shall use the 451 CRQSOs with flat spectrum and declination above $-10^\circ$ degrees taken from the surveys of Ref. \cite{kuhr}.397 With the aim of finding the positional coincidences and evaluating (heir significance. we adopt the procedure of Ref. [21]..," With the aim of finding the positional coincidences and evaluating their significance, we adopt the procedure of Ref. \cite{sigletal}."398 First. we look for real correlations between the (wo sets.," First, we look for real correlations between the two sets."399 In order to do so. we consider a circle around (he centroid of each CR event. (his circle has a radius equal to the reported 1 sigma positional error (see Table 2).," In order to do so, we consider a circle around the centroid of each CR event, this circle has a radius equal to the reported 1 sigma positional error (see Table 2)."400 Ifa CRQSO is within (he circle of all members of the cluster. we sav (hat there is a positional coincidence.," If a CRQSO is within the circle of all members of the cluster, we say that there is a positional coincidence."401 We are not giving a higher significance to directional coincidences with small offsets than to coincidences that are not so close. just because the original errors of the CRs are of the order of degrees.," We are not giving a higher significance to directional coincidences with small offsets than to coincidences that are not so close, just because the original errors of the CRs are of the order of degrees."402 As a first (rial. we look for positional coincidences between the CROSO sample auc all the events listed in Table 1.," As a first trial, we look for positional coincidences between the CRQSO sample and all the events listed in Table 1."403 Wehave found that there are no objects which correlate with the direction of triplets. so," Wehave found that there are no objects which correlate with the direction of triplets, so"404High-mass X-ray binaries (HMXBs) are X-ray sources for which high-energy emission stems from accretion onto a compact object (black hole or neutron star) of material coming from a massive companion star.,High-mass X-ray binaries (HMXBs) are X-ray sources for which high-energy emission stems from accretion onto a compact object (black hole or neutron star) of material coming from a massive companion star.405 Until recently. the huge majority of known HMXBs were Be/X-ray binaries. Le a neutron star acereting from a dise around a Be star.," Until recently, the huge majority of known HMXBs were Be/X-ray binaries, i.e a neutron star accreting from a disc around a Be star."406 Most of these sources are transient. even if a few are persistent weak X-ray emitters (Lx~107 erg s! ).," Most of these sources are transient, even if a few are persistent weak X-ray emitters $\textrm{L}_\textrm{x}\,\sim\,10^{34}$ erg $^{-{1}}$ )."407 The other known HMXBs were supergiant X-ray binaries (SGXBs). composed of a compact object orbiting around an early-type supergiant and fed by accretion from the strong radiative wind of the companion.," The other known HMXBs were supergiant X-ray binaries (SGXBs), composed of a compact object orbiting around an early-type supergiant and fed by accretion from the strong radiative wind of the companion."408 These objects are persistent sources (Lx-1076 erg sv! ) and their relative low number compared. to the population of Be/X-ray binaries was explained as the consequence of the short lifetime of supergiant stars.," These objects are persistent sources $\textrm{L}_\textrm{x}\,\sim\,10^{36}$ erg $^{-{1}}$ ), and their relative low number compared to the population of Be/X-ray binaries was explained as the consequence of the short lifetime of supergiant stars."409 The launch of the UNTEGRAL.. in October 2002 completely changed the situation. as many more HMXBs whose companion stars are supergiants were discovered during the monitoring of the Galactic centre and the Galactic plane using the onboard IBIS/ISGRI instruments (??)..," The launch of the \citep[\textit{INTEGRAL}, in October 2002 completely changed the situation, as many more HMXBs whose companion stars are supergiants were discovered during the monitoring of the Galactic centre and the Galactic plane using the onboard IBIS/ISGRI instruments \citep{2003Ubertini, 2003Lebrun}."410 Most of these sources are reported in ?. and ?.. and their studies have revealed two main features that were not present on previously known SGXBs: It then appears that the supergiant HMXBs discovered by can be classified in two classes: one class of considerably obscured persistent sources that we will simply call obscured SGXBs in this paper and another of supergiant fast X-ray transients (SFXTs.?)..," Most of these sources are reported in \citet{2007Bird} and \citet{2007Bodaghee}, and their studies have revealed two main features that were not present on previously known SGXBs: It then appears that the supergiant HMXBs discovered by can be classified in two classes: one class of considerably obscured persistent sources that we will simply call obscured SGXBs in this paper and another of supergiant fast X-ray transients \citep[SFXTs,][]{2006Negueruelaa}."411 High-energy observations can give some information about the compact object or about the processes that lead to the emission but do not allow study of the companion star., High-energy observations can give some information about the compact object or about the processes that lead to the emission but do not allow study of the companion star.412 It is therefore very important to perform wavelength observations of these sources - from optical-to-MIR wavelength - às this represents the only way to characterise the companion or to detect dust around these highly obscured systems., It is therefore very important to perform multi-wavelength observations of these sources - from optical-to-MIR wavelength - as this represents the only way to characterise the companion or to detect dust around these highly obscured systems.413 However. positions given by are not accurate enough ( 2’)) to identify their optical counterparts. because of the large number of objects in the error circle.," However, positions given by are not accurate enough $\sim$ ) to identify their optical counterparts, because of the large number of objects in the error circle."414 Observations with X-ray telescopes like or are therefore crucial because they allow a localisation with a position accuracy of 4” or better. which lowers the number of possible optical counterparts.," Observations with X-ray telescopes like or are therefore crucial because they allow a localisation with a position accuracy of $\arcsec$ or better, which lowers the number of possible optical counterparts."415 We performed optical-to-MIR wavelength observations of several candidate SGXBs recently discovered withINTEGRAL., We performed optical-to-MIR wavelength observations of several candidate SGXBs recently discovered with.416. Optical and ΝΗ observations were carried out at ESO/NTT using EMMI and Sofl instruments and aimed at constraining the spectral type of the companions through accurate astrometry. as well as the spectroscopy and photometry of the candidate counterparts.," Optical and NIR observations were carried out at ESO/NTT using EMMI and SofI instruments and aimed at constraining the spectral type of the companions through accurate astrometry, as well as the spectroscopy and photometry of the candidate counterparts."417 They are reported in the companion paper (?.CHAOShereafter)... and it is shown that most of these sources are actually supergiant stars.," They are reported in the companion paper \citep[][ CHA08 hereafter]{2008Chaty}, and it is shown that most of these sources are actually supergiant stars."418 In this paper. we report MIR photometric observations of the companions of twelve candidate SFXTs and obscured SGXBs that aimed at studying the circumstellar environment of these highly absorbed sources and. more particularly. at detecting any MIR excess in their emission that," In this paper, we report MIR photometric observations of the companions of twelve candidate SFXTs and obscured SGXBs that aimed at studying the circumstellar environment of these highly absorbed sources and, more particularly, at detecting any MIR excess in their emission that"419"090429B. 090812. 090926B) that would be considered ""dark"".","090429B, 090812, 090926B) that would be considered ""dark""."420 Another five bursts (070802. 080129. 080413B. 080605. 090814) have. within errors. all Box=0.5.," Another five bursts (070802, 080129, 080413B, 080605, 090814) have, within errors, all $\beta_{OX} = 0.5$."421" According to the classification of vanderHorstetal.(2009).. the following nine bursts are ""dark"": 070802. 080210. 080218B. 080516. 080805. 080913. 080915. 090429B and 090904B. These fractions of are fully consistent with the hitherto known fraction of darkbursts of (e.g.Fynboetal.. 2009b).."," According to the classification of \cite{hkg09}, the following nine bursts are ”dark”: 070802, 080210, 080218B, 080516, 080805, 080913, 080915, 090429B and 090904B. These fractions of are fully consistent with the hitherto known fraction of darkbursts of \cite[e.g.][]{fjp09}. ."422nmass-loss [rom these objects il is reasonable to adjust (his value upward by a [factor of two. to36-T6.,"mass-loss from these objects it is reasonable to adjust this value upward by a factor of two, to."423. These values are probably overestimated. given that they are higher than the Kennicuttetal.(1994). prediction and we are not measuring the contribution of material ron supernovae and massive AGBs that have already died.," These values are probably overestimated, given that they are higher than the \citet{ken94} prediction and we are not measuring the contribution of material from supernovae and massive AGBs that have already died."424 Some possible explanations or (his overestimation are (he lower limit for our assumed cdust-to-gas ratio may be too ow. Which would increase the derived. MLB for a given. wind optical depth. and also any ‘bursGness’ in (he true star Formation rate. which could either raise or lower the calculated yaclion being returned to the ISM compared to the average value over the past Gyr.," Some possible explanations for this overestimation are the lower limit for our assumed dust-to-gas ratio may be too low, which would increase the derived MLR for a given wind optical depth, and also any `burstiness' in the true star formation rate, which could either raise or lower the calculated fraction being returned to the ISM compared to the average value over the past Gyr."425 Given the fIuctuations observed in the star formation histories of dIs. the [actor of (wo agreement is probably equite reasonable.," Given the fluctuations observed in the star formation histories of dIs, the factor of two agreement is probably quite reasonable."426 In Figure 12 we show a histogram of the fraction of objects brighter than the TRGB that were detected in the optical as a function of — [4.5] color (left panel) and optical depth for carbon-rich AGBs with AMC and SiC wind and two different effective temperatures Gight panel), In Figure \ref{comp_frac} we show a histogram of the fraction of objects brighter than the TRGB that were detected in the optical as a function of $-$ [4.5] color (left panel) and optical depth for carbon-rich AGBs with AMC and SiC wind and two different effective temperatures (right panel).427 This figure clearly shows the trend of decreasing optical completeness with increasing MLB. which supports our conclusion that the AGB stars misidentilied or not detected in the optical have been reddened by cireumstellar material.," This figure clearly shows the trend of decreasing optical completeness with increasing MLR, which supports our conclusion that the AGB stars misidentified or not detected in the optical have been reddened by circumstellar material."428" Frostetal.(L998) report that there are very [ew optically detected carbon stars in the Large Magellanic Cloud (LMC) with MLRs above 9τν, and none above ?HL."," \citet{fro98} report that there are very few optically detected carbon stars in the Large Magellanic Cloud (LMC) with MLRs above $^{-6}$, and none above $^{-5}$."429" Thev adopt a value of — 5x10 5 aas the critical value above which no carbon star will be detected optically,", They adopt a value of = $\times$ $^{-6}$ as the critical value above which no carbon star will be detected optically.430 We detect no AGBs optically with [3.6] [4.5] > L0 (7 = L3. c 5x10  aassuming L = 3000 L. ) and only one with [3.6] —[4.5] > 0.85 (7 — 0.7. — 2x10 ? +) out of the 14 AGDs detected in the IR.," We detect no AGBs optically with $-$ [4.5] $>$ 1.0 $\tau$ = 1.3, $\sim$ $\times$ $^{-5}$ assuming L = 3000 $_{\sun}$ ) and only one with $-$ [4.5] $>$ 0.85 $\tau$ = 0.7, $\sim$ $\times$ $^{-5}$ ) out of the 14 AGBs detected in the IR."431 Given the difference in metallicity of the LMC and WLAI (ου 0.7 dex) aud its effect on the derived MLB. these values are in agreement with ihe Frostetal.(1998). result.," Given the difference in metallicity of the LMC and WLM $\sim$ 0.7 dex) and its effect on the derived MLR, these values are in agreement with the \citet{fro98} result."432 Figure 14 shows the MLR versus bolometric Iuminositv for all of the objects brighter than (he TRGB in our I. CMD., Figure \ref{Mbol} shows the MLR versus bolometric luminosity for all of the objects brighter than the TRGB in our IR CMD.433 Filled circles represent the MLIBs aud Iuminosites assuming all of the AGDs are carbon-rich with cust-to-gas ratios of 7.9x |. winds composed of AMC and. SiC. and Tepy = 2650 IX. Open circles are for the same composition with Typ = 3600 Ix. We also show the classical single-scattering niass-loss limit (bottom dashed line) and (he empirical maximum mass-loss limit found for the LAIC (top solid line) as plotted in vanLoonetal. (1999)..," Filled circles represent the MLRs and luminosities assuming all of the AGBs are carbon-rich with dust-to-gas ratios of $\times$ $^{-4}$, winds composed of AMC and SiC, and $_{eff}$ = 2650 K. Open circles are for the same composition with $_{eff}$ = 3600 K. We also show the classical single-scattering mass-loss limit (bottom dashed line) and the empirical maximum mass-loss limit found for the LMC (top solid line) as plotted in \citet{van99}. ."434 Because we do not know the effective stellar temperature a priori. some \ILRs can be overestimated in the case of the T.pp = 3600 IX template or underestimated for LT.pp = 2650 Ix. since there is a degeneracy in our CMDs between stars wilh cool effective temperatures and stars wilh warmer effective temperatures but significant AILBRs.," Because we do not know the effective stellar temperature a priori, some MLRs can be overestimated in the case of the $_{eff}$ = 3600 K template or underestimated for $_{eff}$ = 2650 K, since there is a degeneracy in our CMDs between stars with cool effective temperatures and stars with warmer effective temperatures but significant MLRs."435 Consequently. some caution should be takenin strictly interpreting this plot.," Consequently, some caution should be takenin strictly interpreting this plot."436 The, The437for the SDSS sample.,for the SDSS sample.438 These results have shown that the bias at each redshift is compatible assuming linear fluctuations and Gaussian density distributions with the QSOs occupying a single halo mass of c3x10?Mc at all redshifts., These results have shown that the bias at each redshift is compatible assuming linear fluctuations and Gaussian density distributions with the QSOs occupying a single halo mass of $\approx3\times10^{12}M_\odot$ at all redshifts.439" If we also assume that there is a host halo mass - BH mass relation (e.g Ferrarese 2002)), this means that QSOs may contain the same BH-mass at all redshifts."," If we also assume that there is a host halo mass - BH mass relation (e.g \citealt{ferrarese02}) ), this means that QSOs may contain the same BH-mass at all redshifts."440 A model with fixed halo mass of Mnato=3.02:0.38x10?Mc; as found by Croometal.(2005) for 2QZ is compared to the evolution of £oo in Fig.," A model with fixed halo mass of $M_{halo}=3.0\pm0.38\times10^{12}M_{\odot}$ as found by \citet{croom05}441 for 2QZ is compared to the evolution of $\xi_{20}$ in Fig."442 2aa and to the overall QSO bias-redshift relation in 2bb. The normalisation for the mass model is also chosen to be the same as that of Croometal.(2005)., \ref{fig:xi20_lam}a a and to the overall QSO bias-redshift relation in \ref{fig:xi20_lam}b b. The normalisation for the mass model is also chosen to be the same as that of \citet{croom05}.443". A fit based on the SDSS, 2QZ and 2SLAQ QSO datasets gives a fitted halo mass of Mnato=3.27£0.41x10?Mc rms=2.0x10?Mo, consistent with the result for 2QZ."," A fit based on the SDSS, 2QZ and 2SLAQ QSO datasets gives a fitted halo mass of $M_{halo}=3.27\pm0.41\times10^{12}M_{\odot}$ with $rms=2.0\times10^{12}M_{\odot}$, consistent with the result for 2QZ."444" withIt can be seen that the single halo mass model is a very good fit to these data, although we note that this model does not represent the evolution of an individual QSO."," It can be seen that the single halo mass model is a very good fit to these data, although we note that this model does not represent the evolution of an individual QSO."445" Following Croometal. (2005),, their equation (24) which assumes the unevolving relation, Mey MjZ? from Ferrarese(2002) then gives Mag75x109Mo, again approximately independent of redshift."," Following \citet{croom05}, , their equation (24) which assumes the unevolving relation, $M_{BH}\approx M_{halo}^{1.82}$ from \citet{ferrarese02} then gives $M_{BH}\approx5\times10^8M_\odot$, again approximately independent of redshift."446 We note that the model dependence of this mass is large with the different Mgr—Mpmu models of and the evolving model of Wyithe&Loeb(2005) predicting masses between 10?M; and 10!?M at fixed z (Croometal.2005).," We note that the model dependence of this mass is large with the different $M_{BH}-M_{DMH}$ models of \citet{ferrarese02} and the evolving model of \citet{wyithe}447 predicting masses between $10^8M_\odot$ and $10^{10}M_\odot$ at fixed $z$ \citep{croom05}."448. Nevertheless the relative Mgr change with z is much less model dependent and this is more important for our purposes here., Nevertheless the relative $M_{BH}$ change with $z$ is much less model dependent and this is more important for our purposes here.449" 'These conclusions only apply if we base our results on the SDSS, 2QZ and 2SLAQ samples."," These conclusions only apply if we base our results on the SDSS, 2QZ and 2SLAQ samples."450" Including the IRAS AGN, SDSS AGN and Keck points only increases the result to Mnato=3.74+0.57x1013 but the single halo mass model is now marginally rejectedMc by the data at the 3clevel (x?=42.8 on 26 dof, P<0.025), with the highest residuals coming from the SDSS AGN and Keck points (see Figs. 2))"," Including the IRAS AGN, SDSS AGN and Keck points only increases the result to $M_{halo}=3.74\pm0.57\times10^{12}M_{\odot}$ but the single halo mass model is now marginally rejected by the data at the $\sigma$ level $\chi^2=42.8$ on 26 dof, $P<0.025$ ), with the highest residuals coming from the SDSS AGN and Keck points (see Figs. \ref{fig:xi20_lam}) )"451 and there is evidence for an increase in halo and hence black-hole masses as we move to lower redshift., and there is evidence for an increase in halo and hence black-hole masses as we move to lower redshift.452" For example, the halo mass corresponding to the SDSS AGN sample at z©0.13 is Mnato=9.2£1.7x10?Me."," For example, the halo mass corresponding to the SDSS AGN sample at $z\approx0.13$ is $M_{halo}=9.2\pm1.7\times10^{12}M_\odot$."453" It might be argued that low redshift Seyfert 2 galaxies may be a different class from the Type I QSOs that dominate at higher redshift but given their lower luminosities, it might be expected that their clustering amplitude represents a lower limit to that of Seyfert I’s at low redshift."," It might be argued that low redshift Seyfert 2 galaxies may be a different class from the Type I QSOs that dominate at higher redshift but given their lower luminosities, it might be expected that their clustering amplitude represents a lower limit to that of Seyfert I's at low redshift."454 In a unified picture these AGN might be expected also to be representative of Seyfert I’s., In a unified picture these AGN might be expected also to be representative of Seyfert I's.455 One caveat is that the SDSS AGN sample may also contain a population of LINERS which may not be comparable to Seyfert I in their clustering properties., One caveat is that the SDSS AGN sample may also contain a population of LINERS which may not be comparable to Seyfert I in their clustering properties.456 Later we shall also argue that their ~20x higher space density means that only a fraction are expected to be obscured Seyfert I’s., Later we shall also argue that their $\approx20\times$ higher space density means that only a fraction are expected to be obscured Seyfert I's.457" We also note that Hickoxetal.(2011) has suggested that obscured QSOs, with το=6.04:0.6h ! Mpc, may show a higher clustering amplitude than unobscured QSOs, with το=5.3-Ε0.6h! Mpc, in their QSO samples."," We also note that \cite{hickox} has suggested that obscured QSOs, with $r_0=6.0\pm0.6$ $^{-1}$ Mpc, may show a higher clustering amplitude than unobscured QSOs, with $r_0=5.3\pm0.6$ $^{-1}$ Mpc, in their QSO samples."458 We postpone further discussion of these two lower redshift clustering points until Sections 7 and 8., We postpone further discussion of these two lower redshift clustering points until Sections 7 and 8.459 We now look at the empirical evidence for the mass and luminosity of QSO hosts from high resolution direct imaging., We now look at the empirical evidence for the mass and luminosity of QSO hosts from high resolution direct imaging.460" Schade,Boyle,&Letawsky(2000) used HST to image X-ray QSOs out to z=0.5, where imaging decomposition is most reliable."," \citet{schade} used HST to image X-ray QSOs out to $z\approx0.5$, where imaging decomposition is most reliable."461 They combined these data with those from similar observations of higher luminosity QSOs from Bahcalletal.(1997) and Boyceetal.(1998)., They combined these data with those from similar observations of higher luminosity QSOs from \citet{bahcall97} and \citet{boyce98}.462. Fig., Fig.463 13c from these authors shows flat distribution of host galaxy luminosity with QSO luminosity., 13c from these authors shows a flat distribution of host galaxy luminosity with QSO luminosity.464a This is particularly the case considering that low luminosity hosts of high luminosity QSOs are particularly difficult to detect., This is particularly the case considering that low luminosity hosts of high luminosity QSOs are particularly difficult to detect.465" These authors also note that when a further decomposition into a bulge and disk is performed, there may then be more dependence of host bulge luminosity on QSO luminosity."," These authors also note that when a further decomposition into a bulge and disk is performed, there may then be more dependence of host bulge luminosity on QSO luminosity."466 The errors on the bulge luminosity become increasingly large and may provide an explanation for the wider scatter that is seen in this relation., The errors on the bulge luminosity become increasingly large and may provide an explanation for the wider scatter that is seen in this relation.467 There are also observations (e.g. Merlonietal. 2010)) and model predictions (e.g. Lamastraetal. 2010)) suggesting that the bulge-BH mass relation may not apply at high redshift (see also McLureetal. 2006))., There are also observations (e.g. \citealt{merloni}) ) and model predictions (e.g. \citealt{lamastra}) ) suggesting that the bulge-BH mass relation may not apply at high redshift (see also \citealt{mclure06}) ).468" The potentially different results for bulge and galaxy luminosities must also be borne in mind because luminosity or more accurately disc stellar mass may better correlated with DM halo mass than bulge mass (e.g Kormendy,Bender,&Cornell2011;Kormendy 2011))."," The potentially different results for bulge and galaxy luminosities must also be borne in mind because luminosity or more accurately disc stellar mass may better correlated with DM halo mass than bulge mass (e.g \citealt{korm11a,korm11b}) )."469 This work was extended to higher redshift by Croometal.(2004) using Gemini ALTAIR+NIRI observations of 10 luminous QSOs out to z=2., This work was extended to higher redshift by \citet{croom04mn} using Gemini $+$ NIRI observations of 10 luminous QSOs out to $z\approx2$.470 Only one host galaxy was detected and the upper limits on the others were compatible with simple passive evolutionmodels of the host from the present day., Only one host galaxy was detected and the upper limits on the others were compatible with simple passive evolutionmodels of the host from the present day.471 Models where the hosts evolved at the same rate as the QSO luminosities were rejected at high significance., Models where the hosts evolved at the same rate as the QSO luminosities were rejected at high significance.472 Again if we assume that the bulge-BH mass relation applies at high redshift then these results continue to imply a, Again if we assume that the bulge-BH mass relation applies at high redshift then these results continue to imply a473The magnification distributions of the total flux of the BLR models. determined by convolving the velocity integrated surface brightness profile with the magnification maps. are presented in Figure 3..,"The magnification distributions of the total flux of the BLR models, determined by convolving the velocity integrated surface brightness profile with the magnification maps, are presented in Figure \ref{fig2}."474 Note that each panel presents a pair of models. denoted at the top of each column: this is because in each pair of models he radial emission properties of the clouds are the same so that the velocity integrated surface brightness profiles are the same.," Note that each panel presents a pair of models, denoted at the top of each column; this is because in each pair of models the radial emission properties of the clouds are the same so that the velocity integrated surface brightness profiles are the same."475 This can be seen in the lowest series of panels in Figure 2.., This can be seen in the lowest series of panels in Figure \ref{fig1}.476 In each panel. hree curves are given: the lightest is the magnification distribution of a single pixel. whereas the thicker. grey line is the distribution or the smaller BLR models.," In each panel, three curves are given; the lightest is the magnification distribution of a single pixel, whereas the thicker, grey line is the distribution for the smaller BLR models."477 The thick black line corresponds to he magnification distribution for the larger BLR models., The thick black line corresponds to the magnification distribution for the larger BLR models.478 As the source size increases. the width of the magnification orobability distribution decreases: in comparing the single pixel source with the smaller BLR model. it is clear that the high magnification tail has been curtailed7.," As the source size increases, the width of the magnification probability distribution decreases; in comparing the single pixel source with the smaller BLR model, it is clear that the high magnification tail has been curtailed."479. The smaller BER. model can. however. suffer significant magnification. with the total flux in the line being boosted by a factor of 1.5-2 in most of the cases.," The smaller BLR model can, however, suffer significant magnification, with the total flux in the line being boosted by a factor of 1.5-2 in most of the cases."480 On the face of it. this is rather surprising as the source radius of | ER is relatively large.," On the face of it, this is rather surprising as the source radius of 1 ER is relatively large."481 It is important to remember. however. that unlike numerous previous microlensing studies. the source here is not uniform. but possesses structure on scales substantially smaller than an ER and this can be more significantly magnified.," It is important to remember, however, that unlike numerous previous microlensing studies, the source here is not uniform, but possesses structure on scales substantially smaller than an ER and this can be more significantly magnified."482 Examining the magnification probability distributions for the larger BLR models reveals that they too can be substantially magnified. although the magnification distribution is narrower than the case of the smaller BLR sources.," Examining the magnification probability distributions for the larger BLR models reveals that they too can be substantially magnified, although the magnification distribution is narrower than the case of the smaller BLR sources."483 In most cases. the BLR can be enhanced by ~ 50%.," In most cases, the BLR can be enhanced by $\sim50\%$ ."484 Interestingly. the BS1-2S82 pair of models are particularly broad compared to the other cases: examining Figure 2. reveals that the surface brightness distributions for these models are quite centrally concentrated compared to the other models. and this small scale structure ean be substantially magnified.," Interestingly, the $BS1$ $BS2$ pair of models are particularly broad compared to the other cases; examining Figure \ref{fig1} reveals that the surface brightness distributions for these models are quite centrally concentrated compared to the other models, and this small scale structure can be substantially magnified."485 Again. this smaller scale structure of the BLR surface brightness distribution results in stronger magnification than a uniform source of the same radius.," Again, this smaller scale structure of the BLR surface brightness distribution results in stronger magnification than a uniform source of the same radius."486 This is further illustrated in Figure + which presents the form of the BLR emission line profile for the smaller BS? model as microlensed by Image C in 2237., This is further illustrated in Figure \ref{fig3} which presents the form of the BLR emission line profile for the smaller BS2 model as microlensed by Image C in 2237.487 The left hand panel presents the magnification map convolved with the BS? surface brightness distribution., The left hand panel presents the magnification map convolved with the BS2 surface brightness distribution.488 The series of coloured circles over the map indicated 16 fiducial locations over the map where the form of the emission line profile were calculated., The series of coloured circles over the map indicated 16 fiducial locations over the map where the form of the emission line profile were calculated.489 These are presented in the right hand panel. with the solid black line being the unlensed emission line profile: note that the flux in the microlensedline profiles has been," These are presented in the right hand panel, with the solid black line being the unlensed emission line profile; note that the flux in the microlensedline profiles has been"490"redshifts, but as well to search for objects in which both the ring and the galaxy are “conveniently” oriented to the line of sight, allowing to simultaneously study their kinematics and structural details.","redshifts, but as well to search for objects in which both the ring and the galaxy are “conveniently” oriented to the line of sight, allowing to simultaneously study their kinematics and structural details."491 The PRC was based on the study of photographs of individual galaxies., The PRC was based on the study of photographs of individual galaxies.492" In the modern era, it is reasonable to use digital sky surveys, such as the SDSS for these purposes."," In the modern era, it is reasonable to use digital sky surveys, such as the SDSS for these purposes."493" Note that we do not discuss in this paper the so-called inner polar rings and discs, observed in the circumnuclear regions of nearby, typically early-type galaxies (seerefer-Afanasiev 2004)."," Note that we do not discuss in this paper the so-called inner polar rings and discs, observed in the circumnuclear regions of nearby, typically early-type galaxies \citep[see references and discussion in] []494{Corsini2003, SilAfan2004}."495". Such structures (~30ofwhichareal-readyknown,seeMoiseevetal.2010) are lost in the bright background of the bulge, and are discovered mainly due to their kinematics, decoupled from the galaxy disc."," Such structures \citep[$\sim30$ of which are496already known, see][]{Moiseev2010} are lost in the bright background of the bulge, and are discovered mainly due to their kinematics, decoupled from the galaxy disc."497" In this paper, we present a new list of PRG candidates, a few of which have already been confirmed."," In this paper, we present a new list of PRG candidates, a few of which have already been confirmed."498 Section 2 describes the technique of catalogue compilation using the data from the Galaxy Zoo project., Section \ref{sec_catalog} describes the technique of catalogue compilation using the data from the Galaxy Zoo project.499 Section 3 describes the division of catalogue objects into several types., Section \ref{sec_ABCD} describes the division of catalogue objects into several types.500 In Section 4 we present the information about five galaxies for which there already exist detailed studies of the internal kinematics., In Section \ref{sect_obs} we present the information about five galaxies for which there already exist detailed studies of the internal kinematics.501 We managed as well to perform spectral observations of six galaxies with the 6-m BTA telescope of the SAO RAS., We managed as well to perform spectral observations of six galaxies with the 6-m BTA telescope of the SAO RAS.502" Five of the observed objects were confirmed to be classical PRGs, and one turned out to be a projection of an interacting pair of galaxies."," Five of the observed objects were confirmed to be classical PRGs, and one turned out to be a projection of an interacting pair of galaxies."503 Section 5 briefly discusses the results of this paper., Section \ref{sec_conclusion} briefly discusses the results of this paper.504 The SDSS covers a significant part of the celestial hemisphere (~1/4 for Data Release 7) and contains optical images of millions of galaxies (Abazajianetal. 2009)., The SDSS covers a significant part of the celestial hemisphere $\sim1/4$ for Data Release 7) and contains optical images of millions of galaxies \citep{sdss7}.505". Unfortunately, there are no sufficiently reliable methods for accurate automatic classification of galaxy images by morphological type."," Unfortunately, there are no sufficiently reliable methods for accurate automatic classification of galaxy images by morphological type."506" Although such algorithms are developed, their reliability is not yet sufficient for mass use (seediscussionandreferencesinLintottetal.2011)."," Although such algorithms are developed, their reliability is not yet sufficient for mass use \citep[see507discussion and references in][]{GalZoo2011}."508". Moreover, the images of such peculiar objects as PRGs are very complex, in many cases an analysis of features of low surface brightness is required to attribute a given galaxy to the PRG candidates."," Moreover, the images of such peculiar objects as PRGs are very complex, in many cases an analysis of features of low surface brightness is required to attribute a given galaxy to the PRG candidates."509" Fortunately, we now have an opportunity to use the results of the unprecedented Galaxy Zooproject!,, in which hundreds of thousands of volunteers around the world are visually classifying the SDSS galaxies."," Fortunately, we now have an opportunity to use the results of the unprecedented Galaxy Zoo, in which hundreds of thousands of volunteers around the world are visually classifying the SDSS galaxies."510" Of course, they are not engaged in a separate search for galaxies with polar rings, but they do submit many expressive examples to the Internet-forum dedicated to the ring galaxies."," Of course, they are not engaged in a separate search for galaxies with polar rings, but they do submit many expressive examples to the Internet-forum dedicated to the ring galaxies."511" Most of the galaxies listed are collisional rings, or rings on the bar resonances."," Most of the galaxies listed are collisional rings, or rings on the bar resonances."512" Note that some galaxies were already mentioned by the forum as the possible PRG candidates, including Hoag-type galaxies."," Note that some galaxies were already mentioned by the forum as the possible PRG candidates, including Hoag-type galaxies."513" But looking at hundreds of these images, we were able to select 92 candidate PRGs that were not included in the PRC catalogue."," But looking at hundreds of these images, we were able to select 92 candidate PRGs that were not included in the PRC catalogue."514 We were guided by the following selection criteria:, We were guided by the following selection criteria:515large loop of Ha emission to the southwest. directly across from which (to the northeast) is a large area of very low surface brightuess [la emission.,"large loop of $\alpha$ emission to the southwest, directly across from which (to the northeast) is a large area of very low surface brightness $\alpha$ emission."516 This low surface brightness feature is coincident with the central region of WLM that is ccleficient (northeast of the two ppeaks in Jacksonetal. 2004))., This low surface brightness feature is coincident with the central region of WLM that is deficient (northeast of the two peaks in \citealt{jac04}) ).517 We take this as further evidence of a partial blowout of the ISAL bv the massive voung stellar population., We take this as further evidence of a partial blowout of the ISM by the massive young stellar population.518 The IRAC images of WLM are shown in Figure 3.., The IRAC images of WLM are shown in Figure \ref{ch12}.519 The appearance of the galaxy retains (he smooth stellar distribution observed in the I image with (he addition of a large population of very luminous objects throughout the galaxy. (AGBs or red supergiants [RSGs]})., The appearance of the galaxy retains the smooth stellar distribution observed in the I image with the addition of a large population of very luminous objects throughout the galaxy (AGBs or red supergiants [RSGs]).520 (2006) detected extremely faint diffuse 8.0 eemission in WLM. coincident with the high surface brightness rreeions IM. and 11M9 (lodge&," \citet{jac06} detected extremely faint diffuse 8.0 emission in WLM, coincident with the high surface brightness regions HM7 and HM9 \citep{hod95}."521Miller1995).. In. §?? we discuss how the distribution of AGD stars compares with that of the other stellar populations.," In \ref{photometry}522 we discuss how the distribution of AGB stars compares with that of the other stellar populations."523 As described in 82 we created a master photometry list. which includes detections in V. L and all four IRAC bands.," As described in 2 we created a master photometry list, which includes detections in V, I, and all four IRAC bands."524 The optical properties of the stellar populations have been discussed by other authors (ILodgeοἱal.1999:Rejkubaet2000; and we will not address (hem here.," The optical properties of the stellar populations have been discussed by other authors \citep{hod99,rej00,min97} and we will not address them here."525 The optical color-magnitude diagram (CMD). shown in Figure 4 is segregated into sections consisting of blue objects (a). AGB stars (b). RSCs (c). and red giants (d). enabling us to ascertain where these stellar tvpes lie in the LR CMD (described below). as the infrared colors of the objects detected with IRAC are much less sensitive to effective temperature (han those in the optical.," The optical color-magnitude diagram (CMD), shown in Figure \ref{Optical_cmd} is segregated into sections consisting of blue objects (a), AGB stars (b), RSGs (c), and red giants (d), enabling us to ascertain where these stellar types lie in the IR CMD (described below), as the infrared colors of the objects detected with IRAC are much less sensitive to effective temperature than those in the optical."526 The loci of stellar types were conservalivelv chosen. with gaps between (hem. so that stars will not be misidentified solely due to photometric errors (though as we discuss below. reddening from dust absorption can certainly lead to such misidentilication).," The loci of stellar types were conservatively chosen, with gaps between them, so that stars will not be misidentified solely due to photometric errors (though as we discuss below, reddening from dust absorption can certainly lead to such misidentification)."527 The 3.6 aabsolute magnitude versus 4.5] IR CMD is shown in Figure 5.., The 3.6 absolute magnitude versus $-$ [4.5] IR CMD is shown in Figure \ref{IR_cmd}.528 The basic structure of the IR CMD is a vertical distribution of stars with — [3.6]4.5] very near zero., The basic structure of the IR CMD is a vertical distribution of stars with $-$ [4.5] very near zero.529 This vertical feature contains all objects where both the 3.6 and 4.5 bbands sample the Ravleigh-Jeans tail ofthe Planck function., This vertical feature contains all objects where both the 3.6 and 4.5 bands sample the Rayleigh-Jeans tail ofthe Planck function.530 Any unrecddened object with spectral type earlier than GO will have [4.5] very. close to zero. while N0—M5 stars become progressively bfuer to a color of —0.25 due to CO absorption at 4.6," Any unreddened object with spectral type earlier than G0 will have $-$ [4.5] very close to zero, while $-$ M5 stars become progressively to a color of $-$ 0.25 due to CO absorption at 4.6"531The presence of a powerful radio source is known to have profound. implications for the properties of both the host ealaxy and the surrounding intergalactic medium. (GM).,The presence of a powerful radio source is known to have profound implications for the properties of both the host galaxy and the surrounding intergalactic medium (IGM).532 While the host galaxies are usually massive. ellipticals with predominantly. old. stellar populations formed at 2~520 (e.g. Inskip et al 2002a). increasing evidence is accumulating nmore recent star formation in many sources (e.g. Wills et al27. ClineHolt et al 2007 and references therein).," While the host galaxies are usually massive ellipticals with predominantly old stellar populations formed at $z \sim 5-20$ (e.g. Inskip et al 2002a), increasing evidence is accumulating for more recent star formation in many sources (e.g. Wills et al 2007, Holt et al 2007 and references therein)."533 Extended: emission regions (ILI) are [frequentIvy observed around radio galaxies (AleCarthy ct al LOST). and their observed: properties (size. luminosity. kinematies and ionisation state) are known to el strongly on those of the radio source (c.g. Best et al2000. Inskip ct al 2002b.c.," Extended emission line regions (EELRs) are frequently observed around radio galaxies (McCarthy et al 1987), and their observed properties (size, luminosity, kinematics and ionisation state) are known to depend strongly on those of the radio source (e.g. Best et al 2000, Inskip et al 2002b,c,"534A number of galaxies in the 2dFGRS have already had their morphologies determined manually by direct examination of the APM Galaxy Survey images (Maddox 11990a.b see Fig. 1)),"A number of galaxies in the 2dFGRS have already had their morphologies determined manually by direct examination of the APM Galaxy Survey images (Maddox 1990a,b see Fig. \ref{fig:exspec}) )."535 The accuracy and completeness of this sample varies a great deal depending on the source of the classification and the range of galaxy magnitudes considered., The accuracy and completeness of this sample varies a great deal depending on the source of the classification and the range of galaxy magnitudes considered.536 In what follows I primarily make use of those galaxies which were ascribed morphologies in the APM Bright Galaxy Catalogue (Loveday 1996)., In what follows I primarily make use of those galaxies which were ascribed morphologies in the APM Bright Galaxy Catalogue (Loveday 1996).537 This catalogue provides a complete sample of classified galaxies down to a magnitude limit of bj=16.44., This catalogue provides a complete sample of classified galaxies down to a magnitude limit of $\bj=16.44$.538 The exact value of this magnitude limit now varies across the sky due to recent re-calibrations of the APM magnitudes (see e.g. Colless 22001 for details of the most recent calibrations of those galaxies included in the 2dFGRS). however this will not have any substantial impact upon the representativeness of our classified sample.," The exact value of this magnitude limit now varies across the sky due to recent re-calibrations of the APM magnitudes (see e.g. Colless 2001 for details of the most recent calibrations of those galaxies included in the 2dFGRS), however this will not have any substantial impact upon the representativeness of our classified sample."539 A significant number of galaxies at fainter magnitudes also have morphologies determined from other sources. but these will be substantiallv less reliable and so are not used in this analvsis.," A significant number of galaxies at fainter magnitudes also have morphologies determined from other sources, but these will be substantially less reliable and so are not used in this analysis."540" Of those b,«16.5 galaxies which have been successfully observed so far in the 2dFGRS. 3899 have a morphological classification (Fig. 2)."," Of those $\bj<16.5$ galaxies which have been successfully observed so far in the 2dFGRS, 3899 have a morphological classification (Fig. \ref{fig:nofz}) )."541 The galaxy morphologies are given in four broad bins: Elliptical. SO. Spiral and Irregular.," The galaxy morphologies are given in four broad bins: Elliptical, S0, Spiral and Irregular."542 However. in the analysis presented here they are rebinned into only two classes: Early (Elliptical.SO) and Late (SpiralIrregular) types.," However, in the analysis presented here they are rebinned into only two classes; Early (Elliptical,S0) and Late (Spiral,Irregular) types."543 The reasons for doing so are two-fold: Firstly. the number of classified galaxies which have been identified as SO or Irregular are. significantly smaller than the number of Spirals.," The reasons for doing so are two-fold: Firstly, the number of classified galaxies which have been identified as S0 or Irregular are significantly smaller than the number of Spirals."544 Therefore the identification of these types will be greatly hindered by the presence of Spiral outliers - which effectively swamp out any identifying signal which may arise from these types., Therefore the identification of these types will be greatly hindered by the presence of Spiral outliers - which effectively swamp out any identifying signal which may arise from these types.545" Secondly. the distinction between Early and Late type galaxies is of fundamental importance to observational cosmology since each can be used in its own redshift-independent distance estimator. ie. 1,0 for Early types (Dressler 11987) and the Tully-Fisher relation for Late types (Tully Fisher 1977)."," Secondly, the distinction between Early and Late type galaxies is of fundamental importance to observational cosmology since each can be used in its own redshift-independent distance estimator, i.e. $D_n-\sigma$ for Early types (Dressler 1987) and the Tully-Fisher relation for Late types (Tully Fisher 1977)."546 Note that this sample of galaxies consists entirely of relatively bright. nearby galaxies and so may not be representative of the entire 2UFGRS galaxy population.," Note that this sample of galaxies consists entirely of relatively bright, nearby galaxies and so may not be representative of the entire 2dFGRS galaxy population."547 Another important point to bear in mind is that as these galaxies are relatively extended on the sky. the spectra observed of them (through the fixed fibre aperture of the 2dF instrument) may not be representative of the entire galaxy.," Another important point to bear in mind is that as these galaxies are relatively extended on the sky, the spectra observed of them (through the fixed fibre aperture of the 2dF instrument) may not be representative of the entire galaxy."548" This so called ""aperture effect” is a difficult issue to address and has led to much discussion in the literature (see e.g. Kochanek. Pahre Falco. 2000: Madgwick 22002)."," This so called `aperture effect' is a difficult issue to address and has led to much discussion in the literature (see e.g. Kochanek, Pahre Falco, 2000; Madgwick 2002)."549 The possible impact of aperture effects on our results is discussed further in Section 6.., The possible impact of aperture effects on our results is discussed further in Section \ref{section:aper}.550 The purpose of this analysis is to relate the spectrum of a galaxy to its morphology., The purpose of this analysis is to relate the spectrum of a galaxy to its morphology.551" In the case of the 2HFGRS each spectrum consists of 1024 channels spanning the wavelength range of approximately3700-8000A.. thereby including all the major optical diagnostics between and Ha (see Folkes 11999, for further details)."," In the case of the 2dFGRS each spectrum consists of 1024 channels spanning the wavelength range of approximately, thereby including all the major optical diagnostics between and $\alpha$ (see Folkes 1999, for further details)."552 As an illustration. the average 2dFGRS spectrum for a representative volume-limited sample is shown in Fig. 3..," As an illustration, the average 2dFGRS spectrum for a representative volume-limited sample is shown in Fig. \ref{fig:aver}."553 Rather than dealing with all 1024. spectral. channels in the subsequent analysis (to represent a given spectrum). it is possible to take advantage of the fact that the vast majority of these channels are redundant by means of some form of data compression.," Rather than dealing with all 1024 spectral channels in the subsequent analysis (to represent a given spectrum), it is possible to take advantage of the fact that the vast majority of these channels are redundant by means of some form of data compression."554 In the analysis presented here use is made of a Principal Component Analysis (PCA. see e.g. Murtagh Heck 987) since this compression algorithm has met with considerable success in dealing with galaxy spectra (e.g. Connolly 1995: Galaz de Lapparent 1998: Folkes 1999: Madgwick 22002).," In the analysis presented here use is made of a Principal Component Analysis (PCA, see e.g. Murtagh Heck 1987) since this compression algorithm has met with considerable success in dealing with galaxy spectra (e.g. Connolly 1995; Galaz de Lapparent 1998; Folkes 1999; Madgwick 2002)."555 PCA is a well established statistical technique which has proved very useful in dealing with high dimensional data sets., PCA is a well established statistical technique which has proved very useful in dealing with high dimensional data sets.556 In the particular case of galaxy spectra we are typically presented with approximately 1000 spectral channels per galaxy. however when used in applications this is usually compressed down to just a few numbers. either by integrating over small line features - yielding equivalent widths - or over wide colour filters.," In the particular case of galaxy spectra we are typically presented with approximately 1000 spectral channels per galaxy, however when used in applications this is usually compressed down to just a few numbers, either by integrating over small line features - yielding equivalent widths - or over wide colour filters."557 The key advantage of using PCA in our data compression is that it allows us to make use of all the information contained in the spectrum of a galaxy ina statistically unbiased way. i.e. without the use ofsuch ad hoc filters.," The key advantage of using PCA in our data compression is that it allows us to make use of all the information contained in the spectrum of a galaxy in a statistically unbiased way, i.e. without the use of such ad hoc filters."558 In order to perform the PCÀ on our galaxy spectra we first construct a representative volume limited sample of the galaxies., In order to perform the PCA on our galaxy spectra we first construct a representative volume limited sample of the galaxies.559" When we apply the PCA to this sample it constructs an orthogonal set of components (eigenspectra, herein denoted PC,.PC..ete) which span the wavelength space occupied by the galaxy spectra."," When we apply the PCA to this sample it constructs an orthogonal set of components (eigenspectra, herein denoted ${\mathbf{PC}}_1$ ${\mathbf{PC}}_2$ ,etc) which span the wavelength space occupied by the galaxy spectra."560 These components have been specifically chosen by the PCA in such a way that as much information (variance) is contained in the first eigenspectrum as possible. and that the amount of the remaining information in all the subsequent eigenspectra is likewise maximised.," These components have been specifically chosen by the PCA in such a way that as much information (variance) is contained in the first eigenspectrum as possible, and that the amount of the remaining information in all the subsequent eigenspectra is likewise maximised."561 Therefore. if the information contained in the first η) elgenspectra is found to be significantly greater than that in the remaining eigenspectra we can significantly compress the data set by swapping each galaxy spectrum (described by 1000 channels) with just those first projections (denoted pei .pes ete).," Therefore, if the information contained in the first $n$ eigenspectra is found to be significantly greater than that in the remaining eigenspectra we can significantly compress the data set by swapping each galaxy spectrum (described by 1000 channels) with just those first $n$ projections (denoted $pc_1$ $pc_2$ etc)."562 The variances corresponding to the first 10 principal components derived in this manner are shown in Table I., The variances corresponding to the first 10 principal components derived in this manner are shown in Table \ref{vari}.563 Note that the PCA is merely a statistical tool. we do not imply (yet) that any of these components are physically significant. but rather we are merely using them as a method of data compression.," Note that the PCA is merely a statistical tool, we do not imply (yet) that any of these components are physically significant, but rather we are merely using them as a method of data compression."564 During the PCA analysis it was found that the eigenspectra became dominated by unphysical broad features from the fifth eigenspectrum (P C) onwards., During the PCA analysis it was found that the eigenspectra became dominated by unphysical broad features from the fifth eigenspectrum ${\mathbf{PC}}_5$ ) onwards.565 This was due to artifacts from sky emission features which we were unable to completely remove during the spectral reduction., This was due to artifacts from sky emission features which we were unable to completely remove during the spectral reduction.566 Rather than restrict. our future analysis to only the tirst four principal components. we have instead repeated the analysis with the wavelength range mmasked out.," Rather than restrict our future analysis to only the first four principal components, we have instead repeated the analysis with the wavelength range masked out."567 This has no noticeable effect on the original first four, This has no noticeable effect on the original first four568axis ratios). but the particular examples shown here are uot directly applicable to close-in plancts (although the extension of the framework to account for additional precession is very simple - see (Batvein2011) aud the references therein).,"axis ratios), but the particular examples shown here are not directly applicable to close-in planets (although the extension of the framework to account for additional precession is very simple - see \citep{2011ApJ...730...95B} and the references therein)."569 Iu the parameter regine described. the general solution to the equation of motion is where eds an integration constant that depends on the initial conditious.," In the parameter regime described, the general solution to the equation of motion is where $c$ is an integration constant that depends on the initial conditions."570 Iu absence of dissipation. the phase space portrait is a familiar set of concentric curves that close onto themselves.," In absence of dissipation, the phase space portrait is a familiar set of concentric curves that close onto themselves."571 However. if dissipation is introduced iu the svstem. the phase space area occupied bv the orbit beeius to contract.," However, if dissipation is introduced in the system, the phase space area occupied by the orbit begins to contract."572 Caven ao sufiicicut amount of time. the particle settles onto the co-precessine fixed point.," Given a sufficient amount of time, the particle settles onto the co-precessing fixed point."573 This is an important distinction between ILuniltonian aud dissipative systeus: Tamiltouian flows cannot have attractors CMorbidelli2002).., This is an important distinction between Hamiltonian and dissipative systems: Hamiltonian flows cannot have attractors \citep{2002mcma.book.....M}.574 The existence of attractors requires the presence ofdissipation., The existence of attractors requires the presence of dissipation.575" Figure 1 illustrates a phase space portrait of un-dissipated. as well as damped motion of a test-particle. perturbed bv au exterior. à=Ui), planet. orbiting a Surlike (M,= LA.) star."," Figure 1 illustrates a phase space portrait of un-dissipated, as well as damped motion of a test-particle, perturbed by an exterior, $m = 15 m_{\oplus}$ planet, orbiting a Sun-like $M_{\star} = 1 M_{\odot}$ ) star."576 Variables are plotted such that the radial distance depicts the ecceutricitv of the test-particle. while the polar angle represeuts the anele between the apsidal lines of the particle aud the planet.," Variables are plotted such that the radial distance depicts the eccentricity of the test-particle, while the polar angle represents the angle between the apsidal lines of the particle and the planet."577 The blue curves depict uu-dissipated orbits. while the opaque grav line shows a cissipated orbit. with 6=0.024.," The blue curves depict un-dissipated orbits, while the opaque gray line shows a dissipated orbit, with $\delta = 0.02 \eta$."578 The red dot outo which the dissipated orbit converges represents the fixed point. which acts as a global attractor for the dissipated system.," The red dot onto which the dissipated orbit converges represents the fixed point, which acts as a global attractor for the dissipated system."579" The sclui-lnajor axes ratio between the test-particle and the alanet is chosen to he a=afa,P1/2. e,P=0.1 an g=23 fvear."," The semi-major axes ratio between the test-particle and the planet is chosen to be $\alpha \equiv a/a_p=1/2$, $e_p = 0.1$ and $g = 23""$ /year."580 Recall that the position of the fixed point is a unction of the perturbing plauct’s eccentricity., Recall that the position of the fixed point is a function of the perturbing planet's eccentricity.581 As wil © apparent below. this is central to our argunent.," As will be apparent below, this is central to our argument."582 If he perturbing planet resided on a circular orbit. the fixed pot would be at the origin.," If the perturbing planet resided on a circular orbit, the fixed point would be at the origin."583 Furthermore. iu our ormulation. whether the fixed point is apsidally alieue (to the right of the origin) or auti-alieued (to the lett of he origin) depends ou the precession rate assigued to he perturbing plauct.," Furthermore, in our formulation, whether the fixed point is apsidally aligned (to the right of the origin) or anti-aligned (to the left of the origin) depends on the precession rate assigned to the perturbing planet."584 Now cousider the evolution of the test-particle without olutting the fourth-order terms iu equation (1)., Now consider the evolution of the test-particle without omitting the fourth-order terms in equation (1).585 The equation of motion now reads Note that with ο=0. aud the square root expauded o first order in c. we recover equation (3).," The equation of motion now reads Note that with $\beta = 0$, and the square root expanded to first order in $e$, we recover equation (3)."586 Here. the square root appears because we uo longer limit ourselves o the linear form of Lagrauge's planetary equations.," Here, the square root appears because we no longer limit ourselves to the linear form of Lagrange's planetary equations."587 The o»rpose of the square root is to correct for the fact that (hb.E) variables are ouly a low-ecceutricity approximation o the true canonical variables. although its iuclusion is iof dustimmental to our results.," The purpose of the square root is to correct for the fact that $(h,k)$ variables are only a low-eccentricity approximation to the true canonical variables, although its inclusion is not instrumental to our results."588 No general analvtical solution for this equation exists. and one must resort to iuuerical integration to explore the clvuamics.," No general analytical solution for this equation exists, and one must resort to numerical integration to explore the dynamics."589 As before. it is uscful to beein the analysis in absence of dissipative effects.," As before, it is useful to begin the analysis in absence of dissipative effects."590 The addition of the non-linear term introduces iuportant qualitative differences iuto the solution., The addition of the non-linear term introduces important qualitative differences into the solution.591 First and foremost. if the perturbing planet is eccentric. there are now up to three uou-trivial fixed poiuts present. instead of one (e.g. (ιδ of MurrayaudDeriott(1999))).," First and foremost, if the perturbing planet is eccentric, there are now up to three non-trivial fixed points present, instead of one (e.g. Ch.8 of \cite{1999ssd..book.....M}) )."592 One of these fixed points can be unstable (saddle poimt) and resides on a critical curve (de. separatiix) that surrounds. both a lbrating as well as circulating orbits.," One of these fixed points can be unstable (saddle point) and resides on a critical curve (i.e. separatrix) that surrounds, both a librating as well as circulating orbits."593 Figure 2 shows the phase space portraits of the particle motion. perturbed by a planet of the same parameters as before. but with differcut ecceutricities.," Figure 2 shows the phase space portraits of the particle motion, perturbed by a planet of the same parameters as before, but with different eccentricities."594 If the perturber’s orbit is circular (Figure. 2A). the situation is quite simular to the lear case.," If the perturber's orbit is circular (Figure 2A), the situation is quite similar to the linear case."595 In fact. if we omit the square root im equation (5). then a simple analytical solution exists.," In fact, if we omit the square root in equation (5), then a simple analytical solution exists."596 Iu this case. the fixed point is at the origin.," In this case, the fixed point is at the origin."597 Iu direct analogy with the results of the previous section. iu presence of dissipation. the fixed point would attract all orbits.," In direct analogy with the results of the previous section, in presence of dissipation, the fixed point would attract all orbits."598 There also exists an eccentricity value for the test particle which scts its precession equal to that of the perturber., There also exists an eccentricity value for the test particle which sets its precession equal to that of the perturber.599 This sot of stationary points is illustrated in Figure 2A as a red circle., This set of stationary points is illustrated in Figure 2A as a red circle.600 However. as long as the perturbers orbit is circular. these stationary configurations are qualitatively no different than amy other ecceutrie orbit.," However, as long as the perturber's orbit is circular, these stationary configurations are qualitatively no different than any other eccentric orbit."601" If we now make the perturber slightly ecceutiie (e,=0.005). the dyvaanuces changes dramatically (Figure 2D)."," If we now make the perturber slightly eccentric $e_p = 0.005$ ), the dynamics changes dramatically (Figure 2B)."602 The first new feature is that the circle of stationary points breaks in two individual fixed points: oue unstable at Aw=x and one stable at Aw=0., The first new feature is that the circle of stationary points breaks in two individual fixed points: one unstable at $\Delta \varpi = \pi$ and one stable at $\Delta \varpi = 0$.603 A critical curve (ie. the separatiis. ereen bold curve iu paucls D-E) is generated at the unstable equilibrimm point aud eucircles the stable one.," A critical curve (i.e. the separatrix, green bold curve in panels B-E) is generated at the unstable equilibrium point and encircles the stable one."604 Secouc the stable fixed point that was at tle center of the figure moves sliehtlv to the loft.," Second, the stable fixed point that was at the center of the figure moves slightly to the left."605 The appearance of new fixed points has ramificatious for dissipative dvuamics., The appearance of new fixed points has ramifications for dissipative dynamics.606 As in the linear example. if dissipation (assumed to be finite but iuch too small to noticeably modify the ανασα. portrait. ic. lid>0) were to be introduced. both of the stable fixed poiuts would act as attractors. with their respective basins of attraction (slow as grav arrows in Figure 2) separated by the critical curve.," As in the linear example, if dissipation (assumed to be finite but much too small to noticeably modify the dynamical portrait, i.e. $\lim \delta \rightarrow 0$ ) were to be introduced, both of the stable fixed points would act as attractors, with their respective basins of attraction (shown as gray arrows in Figure 2) separated by the critical curve."607 The stability of fixed poiuts that do not lie on the critical curve. can be understood in the following qualitative manner.," The stability of fixed points that do not lie on the critical curve, can be understood in the following qualitative manner."608 Consider a s1131l libration evele. centered. on oue of the fixed points.," Consider a small libration cycle, centered on one of the fixed points."609 The excle's lutersections with the x-axis are placed svuuuetrically. relative to the fixed poiut.," The cycle's intersections with the x-axis are placed symmetrically, relative to the fixed point."610 The role of dissipation at the higher eccentricity intersection is to decrease the radius of hibratiou. while that at the lower ecceutiücitv intersection is to increase the radius of libration.," The role of dissipation at the higher eccentricity intersection is to decrease the radius of libration, while that at the lower eccentricity intersection is to increase the radius of libration."611" Of the two antagonist effects; the first wins. because éX ο, "," Of the two antagonist effects, the first wins, because $\dot e \propto e$ ."612Thus. the fixed pointscentered ou libration cycles are stable foci.," Thus, the fixed pointscentered on libration cycles are stable foci."613" As the eccentricity of the perturber is increased further ο €,—0.05 (Figure 2€) aud then to e,—0.1 (Figure woD) the phase-space area cneulted by the immer brauch of 16 separatrix (1.0. orbits centered around the stable hened fixed point) shrinks.", As the eccentricity of the perturber is increased further to $e_p = 0.05$ (Figure 2C) and then to $e_p = 0.1$ (Figure 2D) the phase-space area engulfed by the inner branch of the separatrix (i.e. orbits centered around the stable anti-aligned fixed point) shrinks.614 Suunultaucously. the plase-PAmace area occupied by orbits that are libratiug around ie aligned fixed point erows.," Simultaneously, the phase-space area occupied by orbits that are librating around the aligned fixed point grows."615" When the perturber eccentricity reaches e,=0.12. the apsidally auti-aligued fixeck points collapse outo a single. unstable fixed. point"," When the perturber eccentricity reaches $e_p = 0.12$, the apsidally anti-aligned fixed points collapse onto a single, unstable fixed point"616In order to test the hypothesis that the observed. plateaus indeed reflect the distribution of LGRBs. which are Collapsars. we use the fact that SGRBs are harder. 1993).,"In order to test the hypothesis that the observed plateaus indeed reflect the distribution of LGRBs, which are Collapsars, we use the fact that SGRBs are harder \citep{Kouveliotou93}."617. Restricting (he analvsis only to soft bursts should preferentially remove SGRBs from the sample., Restricting the analysis only to soft bursts should preferentially remove SGRBs from the sample.618 Thereby. LGRBs should dominate the duration distribution of a sample of soft. bursts down to durations that are shorter (han in the case of the entire sample.," Thereby, LGRBs should dominate the duration distribution of a sample of soft bursts down to durations that are shorter than in the case of the entire sample."619 Now. if LGRBs are collapsars and there duration distribution is flat at short times. then Toy distribution of a sample of soft bursts should exhibit a plateau that extends to shorter cdurations (han (he Foo distribution of the whole sample.," Now, if LGRBs are collapsars and there duration distribution is flat at short times, then $T_{90}$ distribution of a sample of soft bursts should exhibit a plateau that extends to shorter durations than the $T_{90}$ distribution of the whole sample."620 We present in fie., We present in fig.621 1 also a distribution of BATSE soft bursts (magenta). which are defined as bursts with hardnessratio!.. IR.<2.6. (he median value of bursts with Zoo>5 sec.," 1 also a distribution of BATSE soft bursts (magenta), which are defined as bursts with hardness, $HR<2.6$, the median value of bursts with $T_{90}>5$ sec."622 Remarkably. (he plateau in (is sample extends from 25 sec down to 0.4 see (15.2/12 X? /dof). over almost (wo orders of magnitude in duration. compared to the original 5 sec in the complete DATSE sample.," Remarkably, the plateau in this sample extends from 25 sec down to $0.4$ sec (15.2/12 $\chi^2$ /dof), over almost two orders of magnitude in duration, compared to the original 5 sec in the complete BATSE sample."623 This lands a strong support to the conclusion that the observed flat. distribution is indeed indicating on the Collapsar origin of the population., This lands a strong support to the conclusion that the observed flat distribution is indeed indicating on the Collapsar origin of the population.624 It also implies that 7242 is a good indicator (hat effectively fillers out a large number of non-Collapsars from the GRD sample., It also implies that $HR$ is a good indicator that effectively filters out a large number of non-Collapsars from the GRB sample.625 The observed plateaus in all three durtion distributions. and most notably in the distribution of the soft Batse bursts. provide a direct. support lor the Collapsars model for LGRBs.," The observed plateaus in all three durtion distributions, and most notably in the distribution of the soft Batse bursts, provide a direct support for the Collapsars model for LGRBs."626 An inspection of different regions of the observed temporal distribution (Fig., An inspection of different regions of the observed temporal distribution (Fig.627 1). under (he interpretation of the plateau as an imprint of the time it takes the jet to break out of the envelope. provides further important information.," 1), under the interpretation of the plateau as an imprint of the time it takes the jet to break out of the envelope, provides further important information."628wwhere Then we substitute p and a from Eqs. (034)),where Then we substitute $p$ and $w$ from Eqs. \ref{eq3b}) )629 and (B6)) to obtain where Thus. we have the system of equations (D4)). (B9)). (B10)). CD6)) for pores. and «e that can be represented in the form where System (DII)) is ready for iterations For a sulliciently small /. the iteration. process converges due to the contraction mapping theorem.," and \ref{eq5b}) ) to obtain where Thus, we have the system of equations \ref{eq3b}) ), \ref{eq7b}) ), \ref{eq8b}) ), \ref{eq5b}) ) for $p,r,s$, and $w$ that can be represented in the form where System \ref{eq9b}) ) is ready for iterations For a sufficiently small $t$, the iteration process converges due to the contraction mapping theorem."630 Le is worth to note that. at every iteration step. we obtain an approximate solution in the form of finite-order polynomials in Y.," It is worth to note that, at every iteration step, we obtain an approximate solution in the form of finite-order polynomials in ${\rm {\bmath Y}}$ ."631 Fhis is obvious from the explicit form of the functions f(.gi.go).gly).Pporscu)IGsiw).S sw). and M(pir.s.ww).," This is obvious from the explicit form of the functions $ f(t,y_1 ,y_2632), g(t,y_1 ,y_2 ), P(t,p,r,s,w), R(t,p,r,s,w), S(t,p,r,s,w)$ , and $W(t,p,r,s,w)$."633 The application of the above procedure to system (01) vields solution (11--14))., The application of the above procedure to system \ref{eq25}) ) yields solution \ref{new1}- \ref{new1Z}) ).634 Llere. we use Eq. (18))," Here, we use Eq. \ref{flux_extended}) )"635 to derive the magnification of an extended. centrally symmetric source with a power-law brightness distribution., to derive the magnification of an extended centrally symmetric source with a power-law brightness distribution.636 Two dillerent types of “power-law” distributions can be found in the literature on the gravitational lensing.," Two different types of “power-law"" distributions can be found in the literature on the gravitational lensing."637 In particular. there are the distributions (Shalvapin2001:Shalvapinctal.2002) wwhere p2 lis the power index. the source centre is at the coordinate origin. the distribution (C 1)) is normalized to unity. and L is related to the rms.," In particular, there are the distributions \citep{shalyapin_01,shalyapin_02}638 where $p > 1$ is the power index, the source centre is at the coordinate origin, the distribution \ref{C1}) ) is normalized to unity, and $L$ is related to the r.m.s."639" radius A,,,, as L=(pο... For fixed /2,4,,; and p.7 ox« the brightness distribution (C1)) tends to the Gaussian one."," radius $R_{rms}$ as $L^2 = \left( {p - 2} \right)R_{rms}^2 $, For fixed $R_{rms} $ and $p \to \infty $ , the brightness distribution \ref{C1}) ) tends to the Gaussian one."640 Along with (C1)). the mocels for limb darkening are also often used in microlensing studies (see. e.g. Dominik 2004)) where £ stands for the source radius. and L=(q|2)Iu.," Along with \ref{C1}) ), the models for limb darkening are also often used in microlensing studies (see, e.g., \citealt{dominik}) ) where $L$ stands for the source radius, and $L^2 = \left( {q + 2}641\right)R_{rms}^2 $."642 Llere. we assume q70.," Here, we assume $q > 0$."643 Linear combinations of distributions (200). (C1). and (C2)) with dillerent parameters vield rather a wide class of symmetric source mocels.," Linear combinations of distributions \ref{gaussian distribution}) ), \ref{C1}) ), and \ref{C2}) ) with different parameters yield rather a wide class of symmetric source models."644 For brightness profile (C1)). the total microlensed Hux (18)) that describes a variable contribution of the critical images. asthe source crosses a fold caustic. is the convolution of (C1)) with (19).," For brightness profile \ref{C1}) ), the total microlensed flux \ref{flux_extended}) ) that describes a variable contribution of the critical images, asthe source crosses a fold caustic, is the convolution of\ref{C1}) ) with \ref{generalized Kcr}) )."645 Ehe result for the amplificationfactor involves integrals that can be expressed. via the hypergeometric function of) (Bateman&Iedélyi1953):, The result for the amplificationfactor involves integrals that can be expressed via the hypergeometric function $_2F_1 $ \citep{bateman}::646"where D is a distance from the observer and chirp mass Menirp=(MiM2)99(Mj+Ma) ??, where Mi and M» are masses of first and second star in the system respectively.","where $D$ is a distance from the observer and chirp mass $M_{chirp}=\left(M_1 M_2\right)^{0.6}\left(M_1+M_2\right)^{-0.2}$ , where $M_1$ and $M_2$ are masses of first and second star in the system respectively."647" We define the DNS population observable in gravitational waves as these with the merger time below the Hubble time and weight all their observable quantities with the volume in which they are observable, i.e. Thus the gravitational wave population is the population residing in multiple galaxies and we assume that the populations in these galaxies resembles the one in the Galaxy."," We define the DNS population observable in gravitational waves as these with the merger time below the Hubble time and weight all their observable quantities with the volume in which they are observable, i.e. Thus the gravitational wave population is the population residing in multiple galaxies and we assume that the populations in these galaxies resembles the one in the Galaxy."648 We neglect the possible detection of the gravitational waves in the merger and ringdown phases of the coalescence., We neglect the possible detection of the gravitational waves in the merger and ringdown phases of the coalescence.649 In subsection 2.3 we described our phenomenological model of pulsar evolution., In subsection \ref{ewolucja} we described our phenomenological model of pulsar evolution.650 In Fig., In Fig.651 2 we present an example of an evolutionary path leading to the formation of a double neutron star., \ref{pdpex} we present an example of an evolutionary path leading to the formation of a double neutron star.652 The example is based on the model AF., The example is based on the model AF.653 The pulsars are born with the rotational period Pinims at the line of birth (the dotted line on Fig. 2))., The pulsars are born with the rotational period $P_{ini}=10\;{\rm ms}$ at the line of birth (the dotted line on Fig. \ref{pdpex}) ).654" The initial value of the magnetic field ,which determines the spin period derivative, is drawn from a flat distribution as described in section 2.3.."," The initial value of the magnetic field ,which determines the spin period derivative, is drawn from a flat distribution as described in section \ref{ewolucja}. ."655 The binary starts on zero age main sequence at t=0., The binary starts on zero age main sequence at $t=0$.656 The first pulsar is born after 28.08 Myrs., The first pulsar is born after 28.08 Myrs.657 The system consists of a pulsar and a massive rejuvenated companion., The system consists of a pulsar and a massive rejuvenated companion.658 The neutron star evolves in the P— plane along the line of constant magnetic field., The neutron star evolves in the $P-\dot P$ plane along the line of constant magnetic field.659 At t=31.26 Myrs the nuclear evolution of the companion plunges the system into the common envelope phase., At t=31.26 Myrs the nuclear evolution of the companion plunges the system into the common envelope phase.660 The magnetic field of the pulsar is quenched and it falls close to the death line., The magnetic field of the pulsar is quenched and it falls close to the death line.661 The companion loses the envelope and becomes a helium star while the neutron star reappears in radio., The companion loses the envelope and becomes a helium star while the neutron star reappears in radio.662" It barely evolves until ¢=37.11 Myrs when the second mass transfer occurs, this time it is a stable Roche lobe overflow."," It barely evolves until $t=37.11$ Myrs when the second mass transfer occurs, this time it is a stable Roche lobe overflow."663 The system becomes an X-ray binary and the neutron star is recycled to a period z0.015., The system becomes an X-ray binary and the neutron star is recycled to a period $\approx 0.01s$.664 The amount of accreted matter is very small ( 10~°Mo) but in this model weallow forfull recycling anyway., The amount of accreted matter is very small $\sim10^{-5}M_\odot$ ) but in this model weallow forfull recycling anyway.665 In other models we limit the accretion, In other models we limit the accretion666Introduction is to decrease a.,Introduction is to decrease $a$.667 Thus one might imagine that the end result is a valueof e oscillating around zero. and both Wine Pringle (2006) and Volonteri ct al (2007) assume this.," Thus one might imagine that the end result is a valueof $a$ oscillating around zero, and both King Pringle (2006) and Volonteri et al (2007) assume this."668 However as Jj decreasesfor a given Jj. the probability p(spindown) of accreting in a stably retrograde fashion (given by f in (2))) approaches zero.," However as $J_h$ decreasesfor a given $J_d$, the probability $p({\rm spindown})$ of accreting in a stably retrograde fashion (given by $f$ in \ref{hemi}) )) approaches zero."669" Evidently Jy, must on average decrease only to the point where the expected spinup in prograde accretion is equal to the expected spindown in retrograde accretion. i.c. or equivalently One has to use the equations of Bardeen (1970). to evaluate the derivatives in this equation. which then defines the mean value e."," Evidently $J_h$ must on average decrease only to the point where the expected spinup in prograde accretion is equal to the expected spindown in retrograde accretion, i.e. or equivalently One has to use the equations of Bardeen (1970) to evaluate the derivatives in this equation, which then defines the mean value $\bar a$."670 We simulate the effect of repeated accretion episodes of the type dicussed. here as follows., We simulate the effect of repeated accretion episodes of the type dicussed here as follows.671" We assume that each episode has mass M, and accretes at the Exddington rate appropriate to the current black hole mass M.", We assume that each episode has mass $\msg$ and accretes at the Eddington rate appropriate to the current black hole mass $M$.672 Phe total angular momentum.) of each episode is given by the recipe (12)). replacing fes by Is M IuHu.," The total angular momentum $J_d$ of each episode is given by the recipe \ref{jd}) ), replacing $\rw$ by $\rsg$ if $\rw >673\rsg$."674" The direction ofJ, is chosen at random from an isotropic distribution.", The direction of ${\bf J}_d$ is chosen at random from an isotropic distribution.675 The disc and hole are assumed to co. or counter.align according to the criterion (1))., The disc and hole are assumed to co– or counter–align according to the criterion \ref{align}) ).676" In contrast to Volonteri et al (2007) we do not assume that all the mass accreting in a major merger has the same orientation of angular momentum. but only the mass A, contained. within cach selfgravitating disc episode. allowing each episode to be randomly oriented."," In contrast to Volonteri et al (2007) we do not assume that all the mass accreting in a major merger has the same orientation of angular momentum, but only the mass $\msg$ contained within each self–gravitating disc episode, allowing each episode to be randomly oriented."677 Figures 1.. 2. show the results of (wo such simulations.," Figures \ref{afig}, \ref{a3fig} show the results of two such simulations."678 The figures omit the epochs when the hole is not accreting. so the horizontal axes measure the accretion time rather than the total elapsed. time.," The figures omit the epochs when the hole is not accreting, so the horizontal axes measure the accretion time rather than the total elapsed time."679 Since the aceretion is always at the current Edclington rate. the accretion time is the shortest. possible time for the hole to acquire. its mass through accretion.," Since the accretion is always at the current Eddington rate, the accretion time is the shortest possible time for the hole to acquire its mass through accretion."680 The two simulations cilfer only in the value of. the ‘vertical’ viscosity coefficient os. which is 0.03 in Lig.," The two simulations differ only in the value of the `vertical' viscosity coefficient $\alpha_2$, which is 0.03 in Fig."681 1] and l1 in Fig 2., \ref{afig} and 1 in Fig \ref{a3fig}.682 The two simulations use the same random. sequence of accretion episode orientations in order to highlight the ellect of changing o»., The two simulations use the same random sequence of accretion episode orientations in order to highlight the effect of changing $\alpha_2$.683 The main dillerence is that the mean value e is somewhat lower in the second case (see below).," The main difference is that the mean value $\bar684a$ is somewhat lower in the second case (see below)."685 As one can sec. the main features inferred. above do appear.," As one can see, the main features inferred above do appear."686 Although the value of e Luetuates widely. its mean α does indeed quickly settle to the value predicted by (18)) in each case.," Although the value of $a$ fluctuates widely, its mean $\bar a$ does indeed quickly settle to the value predicted by \ref{equil}) ) in each case."687 We can fit this as where 2b=0.246 (for as= 0.03). 0.13 (for a»= 1) is fixed by continuity at the changeover between the two powerlaw regimes in each case.," We can fit this as where $A = 0.246$ (for $\alpha_2 = 0.03$ ), $0.13$ (for $\alpha_2 = 1$ ) is fixed by continuity at the changeover between the two power–law regimes in each case."688 In. Fig. 1..," In Fig. \ref{afig},"689 this occurs at Als=2. which in the case with higher vertical viscosity the . ⊏ ⇁ ≼∼↓↕⋜⋯⋏∙≟⋖⋅∪∖⇁⋖⊾↓⋅↓⊳∖∪⊔↓∙∖⇁⋜⊔⋜↧⊔↓⋜↧⊳∖⊳∖∪⇂⋜↧↓⊔↓∪⊳," this occurs at $M_8 \simeq6902$, which in the case with higher vertical viscosity the changeover is only at a mass of almost $10^{10}\msun$."691∖⇂↓∪⊔↳∖↓⋅⋡∖∖⋖⋅≱∖⋖⋅⋖⋅↥⇂⋯↥ for holes of masses 10°10M. we expecta~0:3.0.2 in the first case and e~0.2.0.1 in the second. with excursions ελαον£0.2 about these means.," Wesee that for holes of masses $\sim 10^6 - 10^9\msun$ we expect $\bar a \sim 0.3 - 0.2$ in the first case and $\bar a \sim 0.2 - 0.1$ in the second, with excursions $\Delta a \sim \pm 0.2$ about these means."692 Figures 4.1... 4.1 show the normalized distributions of @ as a function of mass in the case a2=1.," Figures \ref{hist_03}, \ref{hist_1} show the normalized distributions of $a$ as a function of mass in the case $\alpha_2 = 1$."693 We have so [far discussed the evolution of SALBIL mass and spin via accretion., We have so far discussed the evolution of SMBH mass and spin via accretion.694 Figures 1.. 2 show that the herr parameter e always has a strong tendency to move towards the mean value e from any initial value as the hole mass doubles through accretion.," Figures \ref{afig}, \ref{a3fig} show that the Kerr parameter $a$ always has a strong tendency to move towards the mean value $\bar a$ from any initial value as the hole mass doubles through accretion."695 Thus although a coalescence of two SML with comparable masses would presumably cause a discontinuous departure from the mean acerctiondriven trend of Figs. 1.. 2.. ," Thus although a coalescence of two SMBH with comparable masses would presumably cause a discontinuous departure from the mean accretion–driven trend of Figs. \ref{afig}, , \ref{a3fig}, ,"696accretion would drive it back towards the mean trend as it cloubles the mass of the coalesced hole., accretion would drive it back towards the mean trend as it doubles the mass of the coalesced hole.697 In other words coalescences have little longterm ellect on e. although they can strongly alfect the spin for à relatively short time (see the end of the Discussion)," In other words coalescences have little long–term effect on $\bar a$ , although they can strongly affect the spin for a relatively short time (see the end of the Discussion)."698Interstellar dust and star formation activity are strongly linked in galaxies.,Interstellar dust and star formation activity are strongly linked in galaxies.699 Dust grains condense in the cold envelopes of evolved stars and in supernova ejecta., Dust grains condense in the cold envelopes of evolved stars and in supernova ejecta.700 In return. they favour the formation of molecular hydrogen. shield the newly-formed molecules from ultraviolet radiation and participate in the formation and cooling of molecular clouds. which collapse to form new stars.," In return, they favour the formation of molecular hydrogen, shield the newly-formed molecules from ultraviolet radiation and participate in the formation and cooling of molecular clouds, which collapse to form new stars."701 Studies of the ultraviolet. optical and near-infrared emission from large samples of local galaxies have shed some light on the relation between star formation activity and dust content.," Studies of the ultraviolet, optical and near-infrared emission from large samples of local galaxies have shed some light on the relation between star formation activity and dust content."702 Such studies show that. in general. galaxies with the highest star formation rates also suffer the highest ultraviolet and optical attenuation (e.g. 223).," Such studies show that, in general, galaxies with the highest star formation rates also suffer the highest ultraviolet and optical attenuation (e.g., \citealt{Kauffmann2003b,703Brinchmann2004}) )."704 However. observations at ultraviolet. optical and near-infrared wavelengths set only limited constraints on the," However, observations at ultraviolet, optical and near-infrared wavelengths set only limited constraints on the"705of out-of-eclipse points and biuned in το intervals contaiiug approximately 30 individual measurements cach (see Fig. 2)).,of out-of-eclipse points and binned in 6-minute intervals containing approximately 30 individual measurements each (see Fig. \ref{fig:fit}) ).706 The L5-;n time series also exhibited an initial relanation-induced brightuess increase and consequently 139 poiuts corresponding to the fist ~30 iuinutes of observations were rejected. which is more poiuts than iu the 3.6-yan time series.," The $\mu$ m time series also exhibited an initial relaxation-induced brightness increase and consequently 139 points corresponding to the first $\sim$ 30 minutes of observations were rejected, which is more points than in the $\mu$ m time series."707 The analysis of the time series was identical to that of the 3.6-;au time series., The analysis of the time series was identical to that of the $\mu$ m time series.708 The ruis of out-ofeclipse points was 0.002[. which is higher than the theoretical estimate and is similar to that of (1us20.0027 Charbonneauetal.(2005))).," The rms of out-of-eclipse points was 0.0024, which is higher than the theoretical estimate and is similar to that of (rms=0.0027 \citet{charb05}) )."709 We have tested for the linearity of the detector response in the 3.6 and 1.5 micron chaunels im which NO-L is close to the onset of detector non-linear response., We have tested for the linearity of the detector response in the 3.6 and 4.5 micron channels in which XO-1 is close to the onset of detector non-linear response.710 Using a subset of data from the SAGE survey (Meixueretal.2006) obtained in the high dynamic ranec (IDR) mode of IRAC camera with both 0.68 aud 12.0s inteeration tines we are able to determine that both the 3.6 micron and 1.5 micron XO-1 fluxes are unsaturated and in the detector linear reguue response., Using a subset of data from the SAGE survey \citep{meix06} obtained in the high dynamic range (HDR) mode of IRAC camera with both 0.6s and 12.0s integration times we are able to determine that both the 3.6 micron and 4.5 micron XO-1 fluxes are unsaturated and in the detector linear regime response.711 Table shows the absolute NO-1 fluxes and the instrmucutal magnitudes in the four IRAC channels., Table \ref{flux} shows the absolute XO-1 fluxes and the instrumental magnitudes in the four IRAC channels.712 The 5.8 aud 8.0 σον time series were recorded with Si:As detectors and do not thus exhibit the sub-pixel intensity variations evident in the uiuntes3.6prominent mücron and 5 anicron channels., The 5.8 and 8.0 micron time series were recorded with Si:As detectors and do not thus exhibit the prominent sub-pixel intensity variations evident in the 3.6 micron and 4.5 micron channels.713 The first ~30 of observations (139 data points) were rejected as the iustruinent settled iuto à new equilibrium state., The first $\sim$ 30 minutes of observations (139 data points) were rejected as the instrument settled into a new equilibrium state.714 Fig., Fig.715 1 shows intensity variation with time. which is caused bv chauges in the effective gain of individual pixcls over time.," \ref{fig:instru} shows intensity variation with time, which is caused by changes in the effective gain of individual pixels over time."716 This effect has also been been observed by ILuringtonetal.(2007) at nicron with TRAC aud by Demingetal.(2006) at 16 micron with IRS., This effect has also been been observed by \citet{har07} at 8 micron with IRAC and by \citet{dem06} at 16 micron with IRS.717 The intensity variafions are dependent onu the illumination level ofthe individual pixel (I&uutsonetal.2007.2005). pixels with high illuuinatiou will reach their equilibrium within 1 hour. but lower illumination pixels increase in intensity over tine. approximately proportional to the inverse of the logarithin of illumination.," The intensity variations are dependent on the illumination level of the individual pixel \citep{knutson07,knutson07b}, pixels with high illumination will reach their equilibrium within $\sim$ 1 hour, but lower illumination pixels increase in intensity over time, approximately proportional to the inverse of the logarithm of illumination."718 We have decided uot to correct cach pixel iu the mage as I&uutsonetal.(2007) lave done in their 33-hour observation of ITD 189733 in the 8 amicron channel of TRAC aud instead fit a coubined linear and quadratic logarithm fuuctiou of time from the begiuniug ofobservations to the time series of the bright calibrator2809268., We have decided not to correct each pixel in the image as \citet{knutson07} have done in their 33-hour observation of HD 189733 in the 8 micron channel of IRAC and instead fit a combined linear and quadratic logarithm function of time from the beginning of observations to the time series of the bright calibrator.719. The fit to the time series of the calibrator was then used to remove the detector rap from the tine series of Las depicted in Fig. 1, The fit to the time series of the calibrator was then used to remove the detector ramp from the time series of as depicted in Fig. \ref{fig:instru}:720" where Z,,,454 1s the model fis. At is the time since the beeiuuius of observations aud e; are the free parameters."," where $I_{model}$ is the model flux, $\Delta t$ is the time since the beginning of observations and $a_{i}$ are the free parameters."721 The detector ramp intensity decreased in fux durug the 5 hours of observation by ~ 0.2 following a simular trend seen by I&uutsonuetal.(2008) in their 5.8 micron time series of brighter," The detector ramp intensity decreased in flux during the 5 hours of observation by $\sim$ 0.2, following a similar trend seen by \citet{knutson07b} in their 5.8 micron time series of brighter."722 After removal of the detector ramp and normalization. the rus of uubiuned 5.5 1uicron out-ofeclipse points for was 0.0081. whichis hieher than theoretical Poisson noise. based," After removal of the detector ramp and normalization, the rms of unbinned 5.8 micron out-of-eclipse points for was 0.0081, which is higher than theoretical Poisson noise, based"723"show that when considering this effect, a substantially larger proportion (~28% for a ratio of the neutron star radius to the Schwarzschild radius R/r, of 3) of radiation falls on the accretion disk, further enhancing beaming along the disk axis.","show that when considering this effect, a substantially larger proportion $\sim28\%$ for a ratio of the neutron star radius to the Schwarzschild radius $R/r_{s}$ of 3) of radiation falls on the accretion disk, further enhancing beaming along the disk axis."724 The definition of € is such that it always appears with distance d in the combination e?d., The definition of $\xi$ is such that it always appears with distance $d$ in the combination $\xi^{1/2}d$.725" Therefore, the uncertainty in anisotropy factor acts in the same way as an additional uncertainty in the distance to the source."," Therefore, the uncertainty in anisotropy factor acts in the same way as an additional uncertainty in the distance to the source."726" For1826—24,, Homer et al. ("," For, Homer et al. ("727"1998) suggest a limit i<70? based on the low amplitude of the optical modulation at the orbital frequency, in which case equation (1)) gives 0.84X&!€1.5, or 0.85<ei?1.1.","1998) suggest a limit $i<70^\circ$ based on the low amplitude of the optical modulation at the orbital frequency, in which case equation \ref{eq:xib}) ) gives $0.84\lesssim \xi_b^{-1}\lesssim 1.5$, or $0.85<\xi_b^{1/2}<1.1$."728" Therefore even if the distance to wwas perfectly known, anisotropy of the burst emission would represent an uncertainty of about +15% in any quantity that depends on distance."," Therefore even if the distance to was perfectly known, anisotropy of the burst emission would represent an uncertainty of about $\pm 15$ in any quantity that depends on distance."729" For example, using spectral fits to determine Ro, is subject to this uncertaintysince the normalization of the spectrum depends on the solid angle R2. /d?£."," For example, using spectral fits to determine $R_\infty$ is subject to this uncertaintysince the normalization of the spectrum depends on the solid angle $R^2_\infty/d^2\xi$ ."730" Given these uncertainties, in this paper we look for constraints on M and R that are independent of distance and anisotropy."," Given these uncertainties, in this paper we look for constraints on $M$ and $R$ that are independent of distance and anisotropy."731 We first ask what constraints on M and R arise from the comparison between the observed lightcurve and theoretical models of Heger et al. (, We first ask what constraints on $M$ and $R$ arise from the comparison between the observed lightcurve and theoretical models of Heger et al. (7322007).,2007).733" Photospheric radius expansion (PRE) bursts are often used in work to constrain neutron star properties from X-ray bursts, because the peak luminosity of the burst can then be taken to be the Eddington luminosity."," Photospheric radius expansion (PRE) bursts are often used in work to constrain neutron star properties from X-ray bursts, because the peak luminosity of the burst can then be taken to be the Eddington luminosity."734" This cannot be done for bbecause the bursts do not show PRE, implying that they have a peak luminosity below Eddington."," This cannot be done for because the bursts do not show PRE, implying that they have a peak luminosity below Eddington."735" Instead, here we pursue the idea that the model lightcurves which fit the observed lightcurves so well tell us the peak luminosity of the bursts."," Instead, here we pursue the idea that the model lightcurves which fit the observed lightcurves so well tell us the peak luminosity of the bursts."736 Heger et al. (, Heger et al. (7372007) selected from their models one that had a similar recurrence time to the observed bursts in 2000 (the model had f=3.9 hr as opposed to the observed trecur=4.07 hr).,2007) selected from their models one that had a similar recurrence time to the observed bursts in 2000 (the model had $t_{\rm recur}=3.9$ hr as opposed to the observed $t_{\rm recur}=4.07$ hr).738" They showed that, when the distance to ((actually gy! ?d) is chosen to make the predicted peak flux match the observed lightcurve, the theoretical and Observed burst lightcurves show remarkable agreement."," They showed that, when the distance to (actually $\xi_b^{1/2}d$ ) is chosen to make the predicted peak flux match the observed lightcurve, the theoretical and observed burst lightcurves show remarkable agreement."739" They considered fixed values of M and R, but the choice of those two parameters also changes the mapping between observed and model burst fluxes."," They considered fixed values of $M$ and $R$, but the choice of those two parameters also changes the mapping between observed and model burst fluxes."740" Therefore, rather than vary distance alone, we find the value of the ratio of the observed flux to the model flux that gives the best fit between the model and the data."," Therefore, rather than vary distance alone, we find the value of the ratio of the observed flux to the model flux that gives the best fit between the model and the data."741" Taking the peak values, Finodelpk=1.29x1025 (computed f romtheredshifted peakluminosityquotedinH 8R."," Taking the peak values, $F_{\rm model, pk}=1.29\times 10^{25}$ $\,$ (computed from the redshifted peak luminosity quoted in Heger et al."742" wen yeas,that-thgavalug-Sofs1,, we find Fops/Finodet=2.20x10:35."," 2007, with $R=11.2\,$ km and $z=0.26$ ) and $F_{\rm obs,pk}=2.84\times 10^{-8}$, we find $F_{\rm obs}/F_{\rm model}=2.20\times 10^{-33}$."743" Substituting this value into equation (2)), we find where we use the redshift assumed by et al. ("," Substituting this value into equation \ref{eq:Fratio}) ), we find where we use the redshift assumed by Heger et al. ("7442007).,2007).745" Note that the model lightcurve is likely to be Hegerinsensitive to the model gravity, so that the ratio Fons/Fimode1 does not depend sensitively on the M and R used in the model."," Note that the model lightcurve is likely to be insensitive to the model gravity, so that the ratio $F_{\rm obs}/F_{\rm model}$ does not depend sensitively on the $M$ and $R$ used in the model."746" For example, the ignition column depth is weakly dependent on gravity in this burning regime (Bildsten 1998 derives οςg?/?),"," For example, the ignition column depth is weakly dependent on gravity in this burning regime (Bildsten 1998 derives $y_{\rm ign}\propto g^{-2/9}$ )."747" However, this is something that should be exploredγιοι in further simulations."," However, this is something that should be explored in further simulations."748" For now, we assume Fops/Finoael i$ a constant, and take equation (3)) as a joint constraint on R and 1+z."," For now, we assume $F_{\rm obs}/F_{\rm model}$ is a constant, and take equation \ref{eq:Fratio2}) ) as a joint constraint on $R$ and $1+z$."749 The theoretical uncertainty in Fynodei is at present unknown., The theoretical uncertainty in $F_{\rm model}$ is at present unknown.750" The predicted lightcurves depend on the input nuclear physics, and prescription for convection and other mixing processes for example."," The predicted lightcurves depend on the input nuclear physics, and prescription for convection and other mixing processes for example."751" These prescriptions vary from code to code, and currently only simulations from the Kepler code (Woosley et al."," These prescriptions vary from code to code, and currently only simulations from the Kepler code (Woosley et al."752 2004) have been compared to the observations of1826—24., 2004) have been compared to the observations of.753. Further simulations and comparisons are required to determine what range of predicted peak fluxes still produce lightcurves with the correct shape to fit the data., Further simulations and comparisons are required to determine what range of predicted peak fluxes still produce lightcurves with the correct shape to fit the data.754" For now, in order to put an error bar on the prefactor in equation (3)), we assume that the theoretical uncertainty in Τους/Finodel is +10%,, and keep in mind the fact that this number is uncertain."," For now, in order to put an error bar on the prefactor in equation \ref{eq:Fratio2}) ), we assume that the theoretical uncertainty in $F_{\rm obs}/F_{\rm model}$ is $\pm 10$, and keep in mind the fact that this number is uncertain."755" This raises the point that rather than use the peak flux only, we could also fit the entire lightcurve."," This raises the point that rather than use the peak flux only, we could also fit the entire lightcurve."756" In that case there is an extra parameter, the redshift 1--z which stretches the lightcurve in time."," In that case there is an extra parameter, the redshift $1+z$ which stretches the lightcurve in time."757" In principle, this provides a constraint REF"," In principle, this provides a constraint on $1+z$."758 28 kA: egeret1+z 200r.obtained in the fit is sensitive to how much of the lightcurve is included in the fit.," In practice, however, we find that the value of $1+z$ obtained in the fit is sensitive to how much of the lightcurve is included in the fit."759" For example, fitting the entire lightcurve (until about 130s after the peak) we find best-fit values 1+z=1.44, Εους/Fioaat=2.10x10:33,"," For example, fitting the entire lightcurve (until about 130s after the peak) we find best-fit values $1+z=1.44$, $F_{\rm obs}/F_{\rm model}=2.10\times 10^{-33}$."760" If we fit the first 30 seconds only, which includes only the initial decline after the peak rather than the whole tail, we get a best fit of 1+z=1.32 and Fos/Fnodel=2.17x 10:33."," If we fit the first 30 seconds only, which includes only the initial decline after the peak rather than the whole tail, we get a best fit of $1+z=1.32$ and $F_{\rm obs}/F_{\rm model}=2.17\times 10^{-33}$ ."761" Weshow in Figure 1 the separate fits to the entire lightcurve and the first 30 seconds, and we also include the model lightcurve fitted only by matching the peak fluxes, with the value for the redshift"," Weshow in Figure \ref{fig:lc} the separate fits to the entire lightcurve and the first 30 seconds, and we also include the model lightcurve fitted only by matching the peak fluxes, with the value for the redshift"762"ey, ancl radius 4, is given by (e.g..Fransson&Djórusson1998).","$v_{\rm763sh}$ and radius $R_{\rm sh}$ is given by \citep[e.g.,][]{FB98}."764". The number density of relativistic electrons is denoted by ny and 5, is the Lorentz factor of electrons radiating at a tvpical frequency vox52D. where B is the strength. of the magnetic field."," The number density of relativistic electrons is denoted by $n_{\rm rel}$ and $\gamma_{\nu}$ is the Lorentz factor of electrons radiating at a typical frequency $\nu \propto\gamma_{\nu}^2 B$, where $B$ is the strength of the magnetic field."765 The energy distribution of the relativistic electrons injected behind the shock is parameterized as απο)ανo4? [or min€Xμας ancl zero otherwise., The energy distribution of the relativistic electrons injected behind the shock is parameterized as $dn_{\rm rel}(\gamma)/d\gamma \propto\gamma^{-p}$ for $\gamma_{\rm min}\leq\gamma\leq\gamma_{\rm max}$ and zero otherwise.766 The second bracket on the RIIS of equation (1)) is the fraction of the injected energy. which is raciated away as svnchrotron radiation., The second bracket on the RHS of equation \ref{eq:1.1}) ) is the fraction of the injected energy which is radiated away as synchrotron radiation.767 This is determined by three different time scales: / is the dvnamical time (1.e.. theadiabatie cooling lime: roughly. the time since the onset of expansion). Fa07) is the synchrotron cooling time [or electrons radiating al a Irequency ν. and μον} is the cooling time corresponding lo processes other than svnchrotron radiation.," This is determined by three different time scales: $t$ is the dynamical time (i.e., theadiabatic cooling time; roughly, the time since the onset of expansion), $t_{\rm synch}(\nu)$ is the synchrotron cooling time for electrons radiating at a frequency $\nu$, and $t_{\rm other}(\nu)$ is the cooling time corresponding to processes other than synchrotron radiation."768 The extensive observations of SN 1993J allowed a detailed modeling of the svnchrotron radiation produced by the shock., The extensive observations of SN 1993J allowed a detailed modeling of the synchrotron radiation produced by the shock.769 It was shown in Fransson&Djórnsson(1998) (that behind the shock. the energy. densities of relativistic electrons and magnetic field both scaled with the thermal energv density.," It was shown in \citet{FB98} that behind the shock, the energy densities of relativistic electrons and magnetic field both scaled with the thermal energy density."770 Furthermore. the shock expanded into a circumstellar medium in which densitv (egy) varied with radius as 27.," Furthermore, the shock expanded into a circumstellar medium in which density $n_{\rm csm}$ ) varied with radius as $R^{-2}$."771" As a result. nqxB?HanUA,x17."," As a result, $n_{\rm rel}\propto B^2\propto n_{\rm csm}v_{\rm sh}^2\propto t^{-2}$."772 nuplicit in these scaling relations is (he assumption of no time variation in +., Implicit in these scaling relations is the assumption of no time variation in $\gamma_{\rm min}$.773" However. since the deduced value of p was close to (wo. any. variation dn 44, (and/or sya.) would only introduce a logarithmic correction."," However, since the deduced value of $p$ was close to two, any variation in $\gamma_{\rm min}$ (and/or $\gamma_{\rm max}$ ) would only introduce a logarithmic correction."774 The radio observations of SN 2002ap are such that a detailed mocleling is not possible., The radio observations of SN 2002ap are such that a detailed modeling is not possible.775 Hence. in order to limit the scope of our discussion. it will be assumed that the scaling relations obtained for SN 1905. are applicable also for ον 2002ap.," Hence, in order to limit the scope of our discussion, it will be assumed that the scaling relations obtained for SN 1993J are applicable also for SN 2002ap."776 This is not a critical assumption: for exaniple. as is shown below. the cifferent scaling relations used by BIXC give much the same results.," This is not a critical assumption; for example, as is shown below, the different scaling relations used by BKC give much the same results."777 With this background we will now discuss (wo alternative scenarios. where svuchrotvon respectively inverse Compton cooling are responsible for the steep radio spectrum.," With this background we will now discuss two alternative scenarios, where synchrotron respectively inverse Compton cooling are responsible for the steep radio spectrum."778 Consider first the case when svuchrotron radiation dominates other cooling processes (Len. lanea< luper).," Consider first the case when synchrotron radiation dominates other cooling processes (i.e., $t_{\rm synch}<t_{\rm other}$ )."779 With the use of Ray2 e4/. one obtains from equation (1)) the time variation of the optically thin svnchrotron luminosity," With the use of $R_{\rm sh}\approx v_{\rm sh}t$ , one obtains from equation \ref{eq:1.1}) ) the time variation of the optically thin synchrotron luminosity"780M/(Azplt/3)n is the surface number density of the ΙΟΣ.,$\Sigma/(4\pi \rho R^3/3)$ is the surface number density of the KBOs.781 6; and by are the relative initial separations in (he -r-cdirection between bodies 1 and 2 aud bodies 1 ancl 3 respectively., $b_1$ and $b_2$ are the relative initial separations in the $x$ -direction between bodies 1 and 2 and bodies 1 and 3 respectively.782 5 is the offset in the g-direction body 3 would have when bodies 1 and 2 would encounter each other had (heir relative velocity been solely due to the Keplershear of the disk: 3540/2., $\gamma$ is the offset in the $y$ -direction body 3 would have when bodies 1 and 2 would encounter each other had their relative velocity been solely due to the Keplershear of the disk: $3 b_1 \Omega /2$.783 Finally. F53(54.55.5) is à [uncetion that takes on the value 1 if the encounter resulted in the formation of a binary between anv two of the three INBOs involved. and 0 otherwise.," Finally, $F_{L^3}(b_1,b_2,\gamma)$ is a function that takes on the value 1 if the encounter resulted in the formation of a binary between any two of the three KBOs involved and 0 otherwise."784 The choice of limits on the integrals in equation 5 ensures no double counting of the binaries., The choice of limits on the integrals in equation \ref{e19} ensures no double counting of the binaries.785 Expression (5)) can be written as where Expression (6)) agrees with the order of magnitude estimate of Goldreichetal.(2002) if we sel lps=1., Expression \ref{e19}) ) can be written as where Expression \ref{e20}) ) agrees with the order of magnitude estimate of \citet{GLS02} if we set $A_{L^3}=1$.786 I is the value of the constant. djs we determine here., It is the value of the constant $A_{L^3}$ we determine here.787 Since we are interested in close encounters among (he IXDOs. their interaction is well described by Hill's equations (Ill18783:Goldreich&Tremaine1980;PetitIIenon19356) that we modify to include three equal mass bodies besides the Sun.," Since we are interested in close encounters among the KBOs, their interaction is well described by Hill's equations \citep{H78,GT80,PH86} that we modify to include three equal mass bodies besides the Sun."788 The equations of motion. with length scaled by fj and time by Q +. [or body 1: are given by The subscripts 1. 2 aud 3 label the w- and y-coordinates of ABO 1. 2. and 3 respectively.," The equations of motion, with length scaled by $R_{H}$ and time by $\Omega^{-1}$ , for body 1 are given by The subscripts 1, 2 and 3 label the $x$ - and $y$ -coordinates of KBO 1, 2, and 3 respectively."789 sinilar equations of motion can be obtained [or bodies 2 and 3., Similar equations of motion can be obtained for bodies 2 and 3.790 F45(54.55.5) is calculated bv numerically integrating the equations of motion.," $F_{L^3}(b_1,b_2,\gamma)$ is calculated by numerically integrating the equations of motion."791" A binary formation event is detected in the following wav: The equations of motion of the (hiree bodies are integrated until a lime (hat corresponds (o a separation of at least 30435, between all three bodies (after (heir conjunction). assuming that (heir relative. velocity is solely due (o their Keplerian sheer (ie. ignoring (he actual gravitational interaction between the bodies). plus an additional lime of 1200.!."," A binary formation event is detected in the following way: The equations of motion of the three bodies are integrated until a time that corresponds to a separation of at least $30 R_H$ between all three bodies (after their conjunction), assuming that their relative velocity is solely due to their Keplerian sheer (i.e. ignoring the actual gravitational interaction between the bodies), plus an additional time of $120 \Omega^{-1}$."792" I after this time the separation between two bodies is still less than 32), a binary is considered to have formed.", If after this time the separation between two bodies is still less than $3R_H$ a binary is considered to have formed.793" We chose a separation of 34%), instead of Ay to allow for binary orbits that reach slightly outside £25.", We chose a separation of $3 R_H$ instead of $R_H$ to allow for binary orbits that reach slightly outside $R_H$ .794" Numerical integrations are terminated early ifthe separation between IKDOs becomes less than 10.12, and these events are nol", Numerical integrations are terminated early ifthe separation between KBOs becomes less than $10^{-4} R_H$ and these events are not795the brighter component as an M5-£0.5 and the fainter as an M6+0.5 by comparing to active M dwarf templates Figure 2)) in ?..,the brighter component as an $\pm$ 0.5 and the fainter as an $\pm$ 0.5 by comparing to active M dwarf templates (see Figure \ref{fig:NLTT20346_spectra}) ) in \citet{2007AJ....133..531B}.796 SpeX imaging of NLTT 20346 allowed(see us to measure the relative magnitude difference between components (AJ=1.13+0.02) and subsequent J band magnitudes of 11.61+ 0.04 and 12.74+ 0.08 for the M5 and M6 respectively., SpeX imaging of NLTT 20346 allowed us to measure the relative magnitude difference between components $\Delta$$J$ $\pm$ 0.02) and subsequent $J$ band magnitudes of $\pm$ 0.04 and $\pm$ 0.08 for the M5 and M6 respectively.797" From the SpeX spectrum, we classify the brighter of the two components as an M4+1 and the fainter as an M5+1 by comparing to the near- spectra of the M4 optical standard (αἱ 213 and the M5 optical standard Gl 51 respectively (see Figure 3))."," From the SpeX spectrum, we classify the brighter of the two components as an $\pm$ 1 and the fainter as an $\pm$ 1 by comparing to the near-IR spectra of the M4 optical standard Gl 213 and the M5 optical standard Gl 51 respectively (see Figure \ref{fig:near-IR}) )."798 'This is consistent within uncertainties with the optical spectral types., This is consistent within uncertainties with the optical spectral types.799" In the absence of a parallax measurement we computed a spectrophotometric distance to each component using the spectral type, individual J band magnitudes, and the spectrophotometric J band relation from Golimowski et al (2010 in prep)."," In the absence of a parallax measurement we computed a spectrophotometric distance to each component using the spectral type, individual $J$ band magnitudes, and the spectrophotometric $J$ band relation from Golimowski et al (2010 in prep)."800 We calculated component distances of 28435 pc and 33 + 5 for the M5 and M6 respectively resulting in a mean distance value to NLTT 20346 of 31+7 pc., We calculated component distances of $\pm$ 5 pc and 33 $\pm$ 5 for the M5 and M6 respectively resulting in a mean distance value to NLTT 20346 of $\pm$ 7 pc.801 The optical spectra of both components of NLTT 20346 show moderate Ha emission., The optical spectra of both components of NLTT 20346 show moderate $\alpha$ emission.802" We measured an Ha equivalent width of 4.20+0.06 and 3.64+0.08 from the MagE data for the M5 and M6, respectively."," We measured an $\alpha$ equivalent width of $\pm$ 0.06 and $\pm$ 0.08 from the MagE data for the M5 and M6, respectively."803 The upper Balmer series showing H8 through Hó as well as Ca II K and H+He are also seen in emission in both components (see Figure 2))., The upper Balmer series showing $\beta$ through $\delta$ as well as Ca II K and $\epsilon$ are also seen in emission in both components (see Figure \ref{fig:NLTT20346_spectra}) ).804" Combining the Ha equivalent width with the x parameter from ? yields the log(Lgo/Lso;j), a metric of magnetic activity and a statistical proxy for age."," Combining the $\alpha$ equivalent width with the $\chi$ parameter from \citet{2004PASP..116.1105W} yields the $_{H\alpha}$ $_{bol}$ ), a metric of magnetic activity and a statistical proxy for age."805" ? have found mean log(Lgo/Loo) values for active M5 and M6 dwarfs within 100 pc of the Sun Figure 5)) of 3.9+0.2 and -4.0+0.3, respectively."," \citet{2008AJ....135..785W} have found mean $_{H\alpha}$ $_{bol}$ ) values for active M5 and M6 dwarfs within 100 pc of the Sun (see Figure \ref{fig:Halpha}) ) of $\pm$ 0.2 and $\pm$ 0.3, respectively."806" (seeNLTT 20346A and B have log(Lia/Lbo1) values of -.94-Ε0.02 and -4.20+0.02 respectively, both within lo of typical active M dwarfs."," NLTT 20346A and B have $_{H\alpha}$ $_{bol}$ ) values of $\pm$ 0.02 and $\pm$ 0.02 respectively, both within $\sigma$ of typical active M dwarfs."807 ? estimate an activity lifetime for M5 and M6 dwarfs of 7.0+0.5 Gyr., \citet{2008AJ....135..785W} estimate an activity lifetime for M5 and M6 dwarfs of $\pm$ 0.5 Gyr.808 Using the age activity relation from ? yields consistent component ages of 6.3+1.0 and 6.5+1.0 Gyr for the M5 and M6 respectively., Using the age activity relation from \citet{2009IAUS..258..327W} yields consistent component ages of $\pm$ 1.0 and $\pm$ 1.0 Gyr for the M5 and M6 respectively.809 'The NLTT 20346 system is an X-ray source and the X-ray activity indicates a younger age than that calculated from the Ha activity., The NLTT 20346 system is an X-ray source and the X-ray activity indicates a younger age than that calculated from the $\alpha$ activity.810" 2XMMiJ085018.94-105644 (from the X-ray Multi Mirror 2nd Incremental Source Catalogue) is 2"" from the Mission(XMM)-Newtonposition of the source.", 2XMMiJ085018.9+105644 (from the X-ray Multi Mirror Mission(XMM)-Newton 2nd Incremental Source Catalogue) is $\arcsec$ from the position of the source.811" We computed the X-ray flux (fx) by combining the 0.2-0.5 keV, 0.5-1.0 keV, and 1.0-2.0 keV ranges in order to compare to equivalent X-ray detections of M dwarfs in the Rónntgen Satellite (ROSAT; ?)) catalog (~ 0.2-2.4 keV)."," We computed the X-ray flux $_{X}$ ) by combining the 0.2-0.5 keV, 0.5-1.0 keV, and 1.0-2.0 keV ranges in order to compare to equivalent X-ray detections of M dwarfs in the Rönntgen Satellite (ROSAT; \citealt{1999A&A...349..389V}) ) catalog $\sim$ 0.2-2.4 keV)."812" We used the f,/f; relation defined in ?:: log (f;/£;)=log(+0.47+6.30 to compute log (f,,/f£) for NLTT 20346 of fz)-2.5.", We used the $_{x}$ $_{J}$ relation defined in \citet{2009ApJS..181..444A}: log $_{x}$ $_{J}$ $f_{x}$ $J$ +6.30 to compute log $_{x}$ $_{J}$ ) for NLTT 20346 of -2.5.813" Note that the 2MASS J band magnitude for the combined light of the system was used to calculate log (f,/f;) since the components were not resolved in the XMM-Newton data.", Note that the 2MASS $J$ band magnitude for the combined light of the system was used to calculate log $_{x}$ $_{J}$ ) since the components were not resolved in the XMM-Newton data.814" Figure 6 compares this estimate to Hyades, Pleiades, Young (« 300 Myr) and thin-disk field M stars (?))."," Figure \ref{fig:xray} compares this estimate to Hyades, Pleiades, Young $<$ 300 Myr) and thin-disk field M stars \citealt{2009ApJ...699..649S}) )."815 The objects labeled Field Ms are from the? study., The objects labeled Field Ms are from the\citet{1999A&AS..135..319H} study.816 Several of these objects demonstrate large X-ray flux although they are regarded in ? as normal field objects (typically > 1 Gyr)., Several of these objects demonstrate large X-ray flux although they are regarded in \citet{2009ApJ...699..649S} as normal field objects (typically $>$ 1 Gyr).817" Possible explanations include flaring M dwarfs (? calculate a flare duty cycle for late M dwarfs of as much as 3%)), or undetected spectroscopic binaries (? found a contamination rate of SBs in their sample)."," Possible explanations include flaring M dwarfs \citealt{2010AJ....140.1402H} calculate a flare duty cycle for late M dwarfs of as much as ), or undetected spectroscopic binaries \citealt{2009ApJ...699..649S} found a contamination rate of SBs in their sample)."818AILOL. whose ULX phase was discovered in the 2000 March. oobservations (Penceοἱal.2001:Mukaiet 2003)..,"M101, whose ULX phase was discovered in the 2000 March observations \citep{Pea2001,Mea2003}. ."819 IXuntzetal.(2005). have discovered an optical counterpart ofULX-1.. with brightness and colors consistent with those of a D supergiant in M1OI. hence it is almost certainly a high-miass X-ray binary (ΠΔ).," \citet{Kea2005} have discovered an optical counterpart of, with brightness and colors consistent with those of a B supergiant in M101, hence it is almost certainly a high-mass X-ray binary (HMXB)."820" Also throughout. 2004. we carried out a series of oobservations totaling a million seconds of exposure time (hereafter ""Msec) for a comprehensive X-ray study of MIOL. including monitoring of bright individual sources."," Also throughout 2004, we carried out a series of observations totaling a million seconds of exposure time (hereafter “Msec”) for a comprehensive X-ray study of M101, including monitoring of bright individual sources."821 have analyzed a subset of these data and claim that reached a peak 0.37 keV luminositv of 3x10 iin July 2004. a claim which we reexamine in 83.3. after considering the long-term and variability in 83.1 and 33.2.D respectively.," \citet{KDY2004} have analyzed a subset of these data and claim that reached a peak 0.3–7 keV luminosity of $\times 10^{40}$ in July 2004, a claim which we reexamine in 3.3, after considering the long-term and short-term variability in 3.1 and 3.2, respectively."822 We (hen reassess (he nature of lin 84., We then reassess the nature of in 4.823 The Mec data set. as well as our reduction method. will be described fully in (2005).," The Msec data set, as well as our reduction method, will be described fully in \citet{K2005}."824. In addition. we have analvzed all archivalROSAT..Chandra. aud oobservations of MIOL to establish the long-term history ofULX-1.," In addition, we have analyzed all archival, and observations of M101 to establish the long-term history of."825. Ilere we present our detailed analvsis of the high state aand ddata., Here we present our detailed analysis of the high state and data.826 The relevant datasets are summarized in relhsdata.., The relevant datasets are summarized in \\ref{hsdata}.827 We do not analvze the low state data in detail: any effort to analvze them (e.g... ]xongetal. 2004)) is necessarily limited bv the poor statistics.," We do not analyze the low state data in detail; any effort to analyze them (e.g., \citealt{KDY2004}) ) is necessarily limited by the poor statistics."828 In addition. there is potential for source confusion in a low state. since we cannot rule oul a [aint contaminating source at huninosities up to 10!..," In addition, there is potential for source confusion in a low state, since we cannot rule out a faint contaminating source at luminosities up to $^{36}$."829 We have reconstructed the long-term light curve ofULX-I1., We have reconstructed the long-term light curve of.830. We compute the 0.32.5 keV luminosity using an absorbed blackbody plus power law model for the hieh signal-to-noise data (all data marked as “high state in Table 1as well as the 2000 October aand 2004 July, We compute the 0.3–2.5 keV luminosity using an absorbed blackbody plus power law model for the high signal-to-noise data (all data marked as “high state” in Table 1as well as the 2000 October and 2004 July831Table L.. aud listoerams for the first case are shown in Figure 3..,"Table \ref{tab:results}, and histograms for the first case are shown in Figure \ref{fig:biastest1}."832 First. the the upper section in Table 1 lists the mean aud standard deviation of the recovere paralucters for the posterior maximization alegoritlin.," First, the the upper section in Table \ref{tab:results} lists the mean and standard deviation of the recovered parameters for the posterior maximization algorithm."833" Recall that the input paraueters were (85.60.fu)(10OV, L8.0.1IIz). aud these are recovered pertectly in all cases. except for the one involving au unucorrectec eround template. as expected."," Recall that the input parameters were $(\sigma_0, \alpha, \fknee) =834(10^{-5}\textrm{V}, -1.8, 0.1\textrm{Hz})$ , and these are recovered perfectly in all cases, except for the one involving an uncorrected ground template, as expected."835" Second. in the bottom half we show the results frou he Cibbs samplue analyses. but this time in terms of jorinalized parameters on the form r=(CsGin)for: where 0. and σαν ave the mean aud standard deviation of the Cabbs chain for a given parameter (removing the fist of the samples for buru-in). auc 03, is the true input value."," Second, in the bottom half we show the results from the Gibbs sampling analyses, but this time in terms of normalized parameters on the form $r = (\theta_{\textrm{est}}-\theta_{\textrm{in}}) /836\sigma_{\textrm{est}}$, where $\theta_{\textrm{est}}$ and $\sigma_{\textrm{est}}$ are the mean and standard deviation of the Gibbs chain for a given parameter (removing the first of the samples for burn-in), and $\sigma_{\textrm{in}}$ is the true input value."837 If the Cübbs chain is both unbiased and has he correct dispersion. 7 should be Gaussian distributed with zero mean aud unit variauce.," If the Gibbs chain is both unbiased and has the correct dispersion, $r$ should be Gaussian distributed with zero mean and unit variance."838 As secu in Table 1.. his is indeed the case.," As seen in Table \ref{tab:results}, this is indeed the case."839 We also note that adding a €MD component to these siuulatious do uot bias the noise estimates. sinaply jecause the CMD is too weak to be detected on the time scales cousidered here.," We also note that adding a CMB component to these simulations do not bias the noise estimates, simply because the CMB is too weak to be detected on the time scales considered here."840 This coufirms the assumptiou uade by the QUIET team when estimating their noise xoperties: The QUIET observations are sufficiently roise dominated on a ouc-hour time scale that the CAIB can be safely neglected for noise estimation purposes., This confirms the assumption made by the QUIET team when estimating their noise properties: The QUIET observations are sufficiently noise dominated on a one-hour time scale that the CMB can be safely neglected for noise estimation purposes.841 To be practical. it is not sufficient trat a method is robust and accurate. but it nist also be computationally eficient.," To be practical, it is not sufficient that a method is robust and accurate, but it must also be computationally efficient."842 For the present aleorithiu the two most iuportant parameters for computationa speed are 1) the total unuuber of zuuples iu the time stream. à. aud 2) the uuniber of masked samples. a. while also the relative position of the nasked samples play an iuportaut role.," For the present algorithm the two most important parameters for computational speed are 1) the total number of samples in the time stream, $n$, and 2) the number of masked samples, $m$, while also the relative position of the masked samples play an important role."843 Iu Figure 1 we show the scaling of cach of the two algorithius (poserior maximization aud Cabbs sampling) as a functiou of both » (left panel) aud a (right xucel), In Figure \ref{fig:CPUtime} we show the scaling of each of the two algorithms (posterior maximization and Gibbs sampling) as a function of both $n$ (left panel) and $m$ (right panel).844 Iu the oft plot. i) was fixed at 1000. divided info fen gaps of 100 samples each. aud only the total cheth of the data stream was varied.," In the left plot, $m$ was fixed at 1000, divided into ten gaps of 100 samples each, and only the total length of the data stream was varied."845 In this case. we should expect t16 scaling of the overall algoritlian to be dominated by Fourier transforms. sugecsting an overall ywchavior οἼνοιι xw Ofnlogn).," In this case, we should expect the scaling of the overall algorithm to be dominated by Fourier transforms, suggesting an overall behavior given by $\mathcal{O}(n \log n)$."846 As seen in Figure L. this approxination holds to a very high degree. both for osterior nmaxiuization and Cabbs sampling.," As seen in Figure \ref{fig:CPUtime}, this approximation holds to a very high degree, both for posterior maximization and Gibbs sampling."847 Further. we see that the CPU time required to analyze a single 0000. sample data set with 1000. samples removed is 3 seconds for posterior maximization aud 21 secouds for Cübbs sample.," Further, we see that the CPU time required to analyze a single 000 sample data set with 1000 samples removed is 3 seconds for posterior maximization and 21 seconds for Gibbs sampling."848 Iu the middle panel. we fix à» at 1000000. and merease m by varvine the nuuber of gaps. each extending 100 siuuples.," In the middle panel, we fix $n$ at 000, and increase $m$ by varying the number of gaps, each extending 100 samples."849 Perlaps somewhat surprisingly. we see that the conrputiug time iu this case is nearlv independent of m.," Perhaps somewhat surprisingly, we see that the computing time in this case is nearly independent of $m$."850 The reason for this is simply that the nuuber of conjugate gradient iterations required for the gap filling xocedure is largely determined by condition uunuber (ic.," The reason for this is simply that the number of conjugate gradient iterations required for the gap filling procedure is largely determined by condition number (ie.,"851 he ratio between the lighest aud simallest cigenvalue) of he covariance matrix of a single gap., the ratio between the highest and smallest eigenvalue) of the covariance matrix of a single gap.852 Waving more gaps separated by more than one time-domain correlation cheth effectively corresponds to performing πα]τηρ]ο uatfrix inversious in parallel. aud the uet cost therefore do not increase significantly.," Having more gaps separated by more than one time-domain correlation length effectively corresponds to performing multiple matrix inversions in parallel, and the net cost therefore do not increase significantly."853 Tn the third panel we increase m by makiug one gap arecr. as opposed to adding many small gaps.," In the third panel, we increase $m$ by making one gap larger, as opposed to adding many small gaps."854 In this, In this855data) no significant. modulation of 20-70 keV. X-ray [lux at the orbital period is present at. the predicted: epochs.,data) no significant modulation of 20-70 keV X-ray flux at the orbital period is present at the predicted epochs.856 To do this we calculated an ephemeris for precise times at which this model predicts outbursts to occur., To do this we calculated an ephemeris for precise times at which this model predicts outbursts to occur.857 The orbital parameters were taken from Skinner (1982).. P=16.65cl. with a zeropoint TuEJD 3423.96 Maxima are expected at phase 0.9 in this scheme if the N-rays follow the optical variability.," The orbital parameters were taken from Skinner \shortcite{sk}, P=16.65d, with a zeropoint $_{0}$ =TJD 3423.96 Maxima are expected at phase 0.9 in this scheme if the X-rays follow the optical variability."858 “Phe long period. parameters from Alcock et al {1999) are under this scheme: P—420.82d.. with arbitrary zeropoint “PJD 9001.," The long period parameters from Alcock et al \shortcite{al}859 are under this scheme: P=420.82d, with arbitrary zeropoint TJD 9001."860 The long period minima occur at, The long period minima occur at861"If we define a as follows and since a>1 we can write x as We note that x is a monotonically decreasing function beyond x(0,0.7)=2.42.","If we define $\alpha$ as follows and since $\alpha > 1$ we can write $x$ as We note that $x$ is a monotonically decreasing function beyond $x(0, 0.7) = 2.42$."862 Wechoose the standard Robertson-Walker metric (Weinberg2008) as the metric. of the background space-time., Wechoose the standard Robertson-Walker metric \citep{Weinberg2008} as the metric of the background space-time.863" With usual notation, this is In the above space-time, we can use equation 5 to obtain r. A straightforward integration for a flat universe (k= 0) yields, This integral can be evaluated in terms of hypergeometric functions and related elliptic integrals."," With usual notation, this is In the above space-time, we can use equation \ref{eq:no3} to obtain $r$ A straightforward integration for a flat universe $k864= 0$ ) yields, This integral can be evaluated in terms of hypergeometric functions and related elliptic integrals."865" But here we take an alternate, simple approach by defining a new function, In the standard model the luminosity distance is defined as di αοτ(1--z)."," But here we take an alternate, simple approach by defining a new function, In the standard model the luminosity distance is defined as $d_L =866a_0 r (1+ z)$."867" Now we can use equation 13 to write the luminosity distance as Expanding V in a series expansion to the 4th order, we find that where Ψ(0)=—2.210."," Now we can use equation \ref{eq:no8} to write the luminosity distance as Expanding $\Psi$ in a series expansion to the 4th order, we find that where $\Psi(0) = -2.210$."868" Now, equation 14 reduces to the required expression for the luminosity distance as In order to compare the method of Pen99 to ours, lets define the absolute relative percentage error as follows."," Now, equation \ref{eq:no9} reduces to the required expression for the luminosity distance as In order to compare the method of Pen99 to ours, lets define the absolute relative percentage error as follows."869" Here d7""""* and dj"" are luminosity distance values calculated from approximate analytical methods and numerical method respectively."," Here $d_{L}^{\tiny \textrm{approx}}$ and $d_{L}^{\tiny870\textrm{num}}$ are luminosity distance values calculated from approximate analytical methods and numerical method respectively."871 A comparison of AF for both analytical methods for Qa=0.7 is shown in figure 1., A comparison of $\Delta E$ for both analytical methods for $\Omega_\Lambda = 0.7$ is shown in figure \ref{WickPenCompare}.872".Our method has a better absolute relative percentage error value for z< 1.0,"," .Our method has a better absolute relative percentage error value for $z < 1.0$ ,"873"related to the intrinsic [lux density S»,44 in the comoving [rame by the expression (Blandford&Ixónigl1979) where &=2 for a continuous jet anc &=3 for discrete ejections.","related to the intrinsic flux density $S_{\nu, \rm \: \rm rest}$ in the comoving frame by the expression \citep[][]{blandford79} where $k = 2$ for a continuous jet and $k=3$ for discrete ejections."874 The Doppler factor D is determined. using the Lorentz factor 5. clincnsionless velocity 3=efe ancl viewing angle to the jet &: For the FR 1 Bs. bulk Lorentz factors are tvpically —210 (Landtetal.2002.andreferencestherein)). and possibly higher for the BLRGs and RLQs (e.g.5~1014inAlullin&Llarcicastle 2009).," The Doppler factor $D$ is determined using the Lorentz factor $\gamma$, dimensionless velocity $\beta = v/c$ and viewing angle to the jet $\theta$: For the FR I RGs, bulk Lorentz factors are typically $\sim$ 2–10 \citep[][and references therein]{landt02}, and possibly higher for the BLRGs and RLQs \citep[e.g. $\gamma \sim$ $10$--$14$ in][]{mullin09}."875. Depending on the value of6 (in the range 0 907 for the jet/counterjet). the core emission could be boosted or deboosted.," Depending on the value of $\theta$ (in the range $0^{\circ}$ $90^{\circ}$ for the jet/counterjet), the core emission could be boosted or deboosted."876 For the PRL RCs. a fiducial viewing angle of —60 (e.g.Landtetal.2002.anclrefer-encestherein). could potentially [ead to a decrease in radio loudness of up to several dex. depending on how relativistic the emitting electrons are.," For the FR I RGs, a fiducial viewing angle of $\sim$ $^{\circ}$ \citep[e.g.][and references therein]{landt02} could potentially lead to a decrease in radio loudness of up to several dex, depending on how relativistic the emitting electrons are."877 The gap between the sequences for log(A)«2 might therefore be intrinsically larger., The gap between the sequences for $(\lambda) < -2$ might therefore be intrinsically larger.878 On the other hand. the viewing angles of several sources in the FRE RGs sample have been estimated by Ciovannini (2001).. and range from «19° to ~S5°.," On the other hand, the viewing angles of several sources in the FR I RGs sample have been estimated by \citet[][]{giovannini01}, and range from $<19^{\circ}$ to $\sim$ $^{\circ}$."879" Using the estimates of , and 3 that are also available from their study. there are some cases where we would expect the core to be deboosted. others where the core should be boosted. and several where the parameters are not constrained. sulliciently to allow us to cilferentiate between the two possibilities."," Using the estimates of $\gamma$ and $\beta$ that are also available from their study, there are some cases where we would expect the core to be deboosted, others where the core should be boosted, and several where the parameters are not constrained sufficiently to allow us to differentiate between the two possibilities."880 At a given value of A. a scatter of up to several dex in A? due to the ellects of beaming is therefore certainly possible for the FR LRGs. as well as the BLRGs and 1tLOs.," At a given value of $\lambda$, a scatter of up to several dex in $R$ due to the effects of beaming is therefore certainly possible for the FR I RGs, as well as the BLRGs and RLQs."881 Indeed. the range in the unbinned RC radio loucness residuals for case (iil) in ligure 2 is about 2.5 dex. for example.," Indeed, the range in the unbinned RG radio loudness residuals for case (iii) in Figure \ref{fig:plot2} is about 2.5 dex, for example."882 Bevond this. it is dillieult to make any concrete predictions: with our current data we cannot rule out that the gap between the tracks is intrinsically larger. nor smaller.," Beyond this, it is difficult to make any concrete predictions; with our current data we cannot rule out that the gap between the tracks is intrinsically larger, nor smaller."883" Another related. issue is that there might be velocity structure in the jet. for example a fast spine surrounded bv à slower sheath. with the core emission coming [rom the latter,"," Another related issue is that there might be velocity structure in the jet, for example a fast spine surrounded by a slower sheath, with the core emission coming from the latter."884 As one might expect. the magnitude. of the boosting/deboosting is smaller at lower values of 5.," As one might expect, the magnitude of the boosting/deboosting is smaller at lower values of $\gamma$."885 Such a scenario would reduce the importance of Doppler effects in the distribution of points in Figure 1.., Such a scenario would reduce the importance of Doppler effects in the distribution of points in Figure \ref{fig:plot1}.886 A further complication stems from evidence. that the nuclear optical (and. N-rav) emission in lower-power radio galaxies originates from a jet. instead. of from. the disc/accretion Low.," A further complication stems from evidence that the nuclear optical (and X-ray) emission in lower-power radio galaxies originates from a jet, instead of from the disc/accretion flow."887 For example. Chiaberge.Capetti&Celotti(1999). found a strong correlation between the racio ancl optical nuclear Dux. densities for a sample of FR 1 RGs. suggesting a svnchrotron origin for both (alsoseec.g.tle.Evans&Croston 2009).," For example, \citet*[][]{chiaberge99} found a strong correlation between the radio and optical nuclear flux densities for a sample of FR I RGs, suggesting a synchrotron origin for both \citep*[also see e.g.][]{chiaberge00,capetti00,hardcastle00,capetti02,hardcastle09}."888. Most. of the FR ERGs in that paper were included in the SSLOT ETt I RG subsample., Most of the FR I RGs in that paper were included in the SSL07 FR I RG subsample.889 The observed radio loudnesses will then depend additionally on the relative radio and optical Lorentz factors., The observed radio loudnesses will then depend additionally on the relative radio and optical Lorentz factors.890 However. more generally. the optical nuclear emission is potentially overestimated significantly (depencing on the extent of the beamine for any jet-relatecl emission).," However, more generally, the optical nuclear emission is potentially overestimated significantly (depending on the extent of the beaming for any jet-related emission)."891 About one-third. of the sources in the FRE RGs sample have upper limits only for Lg (see Table A4)): this fraction may in fact be much larger., About one-third of the sources in the FR I RGs sample have upper limits only for $L_{B}$ (see Table \ref{table: radio cores4}) ); this fraction may in fact be much larger.892 A decrease in Lg would cause the points in the ος) Iog(A) plane to move ciagonally to the upper left along lines with a gradient of 1., A decrease in $L_{B}$ would cause the points in the $R$ $\lambda$ ) plane to move diagonally to the upper left along lines with a gradient of $-1$.893 Therefore. the gap in radio loudness between the upper and. lower sequences would increase.," Therefore, the gap in radio loudness between the upper and lower sequences would increase."894 On the other hand. using infrared. data. SSLOT suggested that the accretion luminosities of some of the FR LRGs could in fact be underestimated by a factor of & 1 dex if the optical emission from the jet. originates from outside an obscuring torus. with the core itself hidden by the obscuring material (alsoseeCao&Rawlings2004).," On the other hand, using infrared data, SSL07 suggested that the accretion luminosities of some of the FR I RGs could in fact be underestimated by a factor of $\gtrsim$ 1 dex if the optical emission from the jet originates from outside an obscuring torus, with the core itself hidden by the obscuring material \citep[also see][]{cao04}."895. Correcting for this would result in the datapoints moving to the lower right along lines with a eracient of 1. closing rather than opening the gap between the sequences.," Correcting for this would result in the datapoints moving to the lower right along lines with a gradient of $-1$, closing rather than opening the gap between the sequences."896 For log(A) « the analysis in Section 77. implies that Figures 1 and 2 are essentially. comparisons between the radio loudnesses of RGs (mainly FR 1 Rs) and SCs/LINERs (mainly SCs) that tvpically have a significant extended: radio component which is associated. with the active nucleus. though less so in the latter case. especially as there may. also be contributions from starbursts.," For $\lambda$ ) $< -2$, the analysis in Section \ref{core_vs_lobe} implies that Figures \ref{fig:plot1} and \ref{fig:plot2} are essentially comparisons between the radio loudnesses of RGs (mainly FR I RGs) and SGs/LINERs (mainly SGs) that typically have a significant extended radio component which is associated with the active nucleus, though less so in the latter case, especially as there may also be contributions from starbursts."897 Moreover. the radio linear sizes of extended: Ss are typically much," Moreover, the radio linear sizes of extended SGs are typically much"898The evaluation of higher order perturbative terms has. however. shown that (his is not the case.,"The evaluation of higher order perturbative terms has, however, shown that this is not the case."899 InIrared divergences in finite temperature field theory limit calculations to a finite order in the coupling g [8]: for the pressure. the highest perturbatively caleulable order is q. and caleulations have now been extended to this order. [9]..," Infrared divergences in finite temperature field theory limit calculations to a finite order in the coupling $g$ \cite{Linde}; for the pressure, the highest perturbatively calculable order is $g^5$, and calculations have now been extended to this order \cite{Arnold94}."900" In relinikko.. we show theresult of expansions in different order g"" [or the pressurein 5U(3) gauge theory. normalized to the Stefan-Doltzmann |10].."," In \\ref{mikko}, we show theresult of expansions in different order $g^n$ for the pressurein $SU(3)$ gauge theory, normalized to the Stefan-Boltzmann \cite{Laine}."901 It is seen that in the temperature region of interest here. 7<107). the different orders lead to strong fluctuations: the final form. wp to and including O(qg?). still considerably undershoots the lattice results.," It is seen that in the temperature region of interest here, $T \leq 10~T_c$, the different orders lead to strong fluctuations; the final form, up to and including $O(g^5)$, still considerably undershoots the lattice results."902 Moreover. for an understanding of the interaction effects. a comparison of lattice ancl perturbation theory results for (he is in fact «uite misleading. since (he major part of the pressure is given by (he ideal gas component.," Moreover, for an understanding of the interaction effects, a comparison of lattice and perturbation theory results for the is in fact quite misleading, since the major part of the pressure is given by the ideal gas component."903 To concentrate on just the interaction effects. we return to the interaction measure .N(7). and here perturbation theory breaks down completely.," To concentrate on just the interaction effects, we return to the interaction measure $\Delta(T)$, and here perturbation theory breaks down completely."904 The next-to-leacding order (NLO) form for SU(3) gauge theory.," The next-to-leading order (NLO) form for $SU(3)$ gauge theory, ) g^4 - ] becomes positive only for $g^2 \gsim 0.27$ , which with the two-loop form of the coupling, _T) +"905measurements in a galaxy. i.e. (he rotation velocities al the bulge and bar radii.,"measurements in a galaxy, i.e. the rotation velocities at the bulge and bar radii."906 But to be sure that the velocities measured at (hese radii are not anomalous. we required good velocity coverage for the CO emission over a signilicant portion of the inner disk of these galaxies.," But to be sure that the velocities measured at these radii are not anomalous, we required good velocity coverage for the CO emission over a significant portion of the inner disk of these galaxies."907 Thus our sample size was limited by the eas distribution to a subsample of 13 barred galaxies from the BIMA SONG database (Table 1)., Thus our sample size was limited by the gas distribution to a subsample of 13 barred galaxies from the BIMA SONG database (Table 1).908 Dar morphology has an important effect on the gas inflow and star formation in galaxies (Martinet Friedli 1997. Aenerri 1999).," Bar morphology has an important effect on the gas inflow and star formation in galaxies (Martinet Friedli 1997, Aguerri 1999)."909 Dar strength ean be quantified either by measuring the bar axis ratio b/a (Martin 1995: Regan Elmeereen 1997: Chapelon. Contini. Davoust 1999). or alternatively bv determining the maximum of the ratio of the tangential force to the mean non-axisvmmnmetric radial force (Q5) in the bar (Buta Block 2001).," Bar strength can be quantified either by measuring the bar axis ratio $b/a$ (Martin 1995; Regan Elmegreen 1997; Chapelon, Contini, Davoust 1999), or alternatively by determining the maximum of the ratio of the tangential force to the mean non-axisymmetric radial force $(Q_b)$ in the bar (Buta Block 2001)."910 Recent studies have shown that bar ellipticity is roughly proportional to (Qy (Laurikainen. Salo Rantiainen 2002). and so ellipticity appears to be a good measure of the bar strength.," Recent studies have shown that bar ellipticity is roughly proportional to $Q_b$ (Laurikainen, Salo Rautiainen 2002), and so ellipticity appears to be a good measure of the bar strength."911 In our study we use optical and near-IR images (I. 1. ancl Ix bands) to determine the bar ellipticity. which we assume provides a reasonable estimate of the bar strength.," In our study we use optical and near-IR images (R, I, and K bands) to determine the bar ellipticity, which we assume provides a reasonable estimate of the bar strength."912 The Ix. aud I bands eenerallv trace the old stellar population in galaxies ancl thus follow the galactic potential., The K and I bands generally trace the old stellar population in galaxies and thus follow the galactic potential.913 We used Ix band images for NGC 3627 (Regan Elmeereen 1997) and NGC 6946 (Reean Vogel 1995). and 1 band images for NGC 2903. NGC 3351. NGC 4303. NGC 4569. NGC 5248. and NGC 5457.," We used K band images for NGC 3627 (Regan Elmegreen 1997) and NGC 6946 (Regan Vogel 1995), and I band images for NGC 2903, NGC 3351, NGC 4303, NGC 4569, NGC 5248, and NGC 5457."914 BR. band is not as good a tracer of old stars but was all that was available lor NGC 3726., R band is not as good a tracer of old stars but was all that was available for NGC 3726.915 For NGC 3184. NGC 3521. NGC 432] and NGC 5005 we used near-intrared (IX band) images from the 2\LASS survey (Jarrett et al.," For NGC 3184, NGC 3521, NGC 4321 and NGC 5005 we used near-infrared (K band) images from the 2MASS survey (Jarrett et al."916 2000)., 2000).917 The bar was identified [rom (he isophotes in the oplical/IR. image., The bar was identified from the isophotes in the optical/IR image.918 The isophotes were traced using the ellipse task in IRAF. which is based on the photometric technique developed by Jedrzejewski (1987).," The isophotes were traced using the $\tt{ellipse}$ task in IRAF, which is based on the photometric technique developed by Jedrzejewski (1987)."919 The bar-delining isophote was assumed to be where the position angle of the elliptical isophotes change direction and start tracing the disk of the ealaxy (Elmegreen et al., The bar-defining isophote was assumed to be where the position angle of the elliptical isophotes change direction and start tracing the disk of the galaxy (Elmegreen et al.920 1996: Lanrikainen Salo 2000)., 1996; Laurikainen Salo 2000).921 This isophote was used to determine the position angle and semimajor axis length of the bar., This isophote was used to determine the position angle and semimajor axis length of the bar.922 We also determined the intensity profile of the optical or near-IR emission along the bar axis and perpendicular to il. using the IRAF task pvector.," We also determined the intensity profile of the optical or near-IR emission along the bar axis and perpendicular to it, using the IRAF task $\tt{pvector}$."923 All the profiles have a characteristic peak at the center due to the bulge and usually a flat portion which represents the bar., All the profiles have a characteristic peak at the center due to the bulge and usually a flat portion which represents the bar.924 Such profiles have been used in previous studies to determine bar sizes ancl ellipticities (Elmegreen et al., Such profiles have been used in previous studies to determine bar sizes and ellipticities (Elmegreen et al.925 1996: Regan Elmegreen 1997)., 1996; Regan Elmegreen 1997).926 We have assumed that the bulge radius is the distance along the bar where the central, We have assumed that the bulge radius is the distance along the bar where the central927As our request. Dr. L. Girardi has kindly ealeulated isochrones of our filler svstem using the known DATC filler transmission curves and their Padova stellar evolutionary models (Girardietal.2000.2002).,"As our request, Dr. L. Girardi has kindly calculated isochrones of our filter system using the known BATC filter transmission curves and their Padova stellar evolutionary models \citep{gir00,gir02}."928. The Padova isochrone sets are computed will updated opacilies ancl equations of state. and a moderate amount of convective overshoot.," The Padova isochrone sets are computed with updated opacities and equations of state, and a moderate amount of convective overshoot."929 The results of Wuetal.(2002) proper motion and membership study of MAS. are used to determine members in this cluster., The results of \citet{wu} proper motion and membership study of M48 are used to determine members in this cluster.930 Stars with membership probabilities greater than 0.7 are considered to be members (Wuοἱal.2002)., Stars with membership probabilities greater than 0.7 are considered to be members \citep{wu}.931.. All stars considered as members based on (heir proper motions were used in our fitting., All stars considered as members based on their proper motions were used in our fitting.932 In our fitting procedure. the distances was chosen Irom 600 pe to 900 pe in intervals of 10 pe. E(B—V) om 0.00 to 0.10 in intervals of 0.01.," In our fitting procedure, the distances was chosen from 600 pc to 900 pc in intervals of 10 pc, $E(B-V)$ from 0.00 to 0.10 in intervals of 0.01."933 Theoretical isochrone models with metallicity Z= 0.08. 0.019. 0.030 and age log(/) from 8.0 to 9.0 in intervals of 0.05 were chosen.," Theoretical isochrone models with metallicity $Z=$ 0.08, 0.019, 0.030 and age $\log(t)$ from 8.0 to 9.0 in intervals of 0.05 were chosen."934 We find (hat. with a distance of 780 pc. reddening E(D—V)=0.04. the theoretical model with age of 0.32 Gvr and metallicity Z=0.019 give the smallest value of ¢ and best fit the observed SEDs.," We find that, with a distance of 780 pc, reddening $E(B-V)=0.04$, the theoretical model with age of 0.32 Gyr and metallicity $Z=0.019$ give the smallest value of $\zeta$ and best fit the observed SEDs."935 In Figure L.. we plot the best-fittàing results for some member stars.," In Figure \ref{sed}, we plot the best-fitting results for some member stars."936 The mass of each object in Padova models is labelled on the right of each corresponding curve in the unit of solar mass MM..., The mass of each object in Padova models is labelled on the right of each corresponding curve in the unit of solar mass $M_\sun$.937 In the top panel of Figure 1.. SEDs of 11 main sequence (AIS) stars with mass from 1.5662 Af. to 3.1878 AL. are plotted.," In the top panel of Figure \ref{sed}, , SEDs of 11 main sequence (MS) stars with mass from 1.5662 $M_\sun$ to 3.1878 $M_\sun$ are plotted."938 In the bottom panel of Figure 1.. the SED of a red eiant star is plotted.," In the bottom panel of Figure \ref{sed}, the SED of a red giant star is plotted."939 We can see Chat the observed SEDs of both MS stars and red eiat stars with the derived best-fitting parameters. can fit the theoretical ones verv well.," We can see that the observed SEDs of both MS stars and red giant stars with the derived best-fitting parameters, can fit the theoretical ones very well."940 In Figure 2.. we plot four representative CMDs [rom our data: (c— p) vs € gives us the widest pass-band colors: (e— €) vs e gives us the cleanest CMD: and (f— 7) vs f give us the deepest CMD.," In Figure \ref{cmd}, we plot four representative CMDs from our data: $c-p$ ) vs $c$ gives us the widest pass-band colors; $c-e$ ) vs $c$ gives us the cleanest CMD; and $f-i$ ) vs $f$ give us the deepest CMD."941 All of the CMDs have a well defined MS and. MS turnoll point., All of the CMDs have a well defined MS and MS turnoff point.942 All stars in(he field of MAS are plotted in each diagram., All stars inthe field of M48 are plotted in each diagram.943 Stars with known membership probabilities, Stars with known membership probabilities944observations of the hieh-enereyv tail in Comptonization spectra.,observations of the high-energy tail in Comptonization spectra.945 Dased on the data lor Cyve N-1 in the hard state. we have obtained the upper limits on the field strength at least an order of magnitude below both the value corresponding to equipartition (in the model of a two-temperature accretion disc) and the minimum value required bv dissipation of magnetic fields (in the model of active coronal regions).," Based on the data for Cyg X-1 in the hard state, we have obtained the upper limits on the field strength at least an order of magnitude below both the value corresponding to equipartition (in the model of a two-temperature accretion disc) and the minimum value required by dissipation of magnetic fields (in the model of active coronal regions)."946 Therefore. the latter model appears to be ruled out for the hard state of €vg X-1.," Therefore, the latter model appears to be ruled out for the hard state of Cyg X-1."947 We note that the presence of à strong correlation between reflection strength and the X-ray. spectral index. observed. in νο X-1 (Cilfanov et 1900). suggests that the CS emission is a negligible source of photons for Comptonization and thus the magnetic field strength must remain significantly: below the upper limits derived above.," We note that the presence of a strong correlation between reflection strength and the X-ray spectral index, observed in Cyg X-1 (Gilfanov et 1999), suggests that the CS emission is a negligible source of photons for Comptonization and thus the magnetic field strength must remain significantly below the upper limits derived above."948 The same correlation seen in other objects (Zdziarski ct 11990: Cilfanoy et 22000) implies that either the high-energy tails or the magnetic fields are weak enough for the CS process not to dominate the energy output., The same correlation seen in other objects (Zdziarski et 1999; Gilfanov et 2000) implies that either the high-energy tails or the magnetic fields are weak enough for the CS process not to dominate the energy output.949" In this work. we have assumed. for the sake of simplicity and. compatibility. with studies of eg... AleConnell et ((2000a). the electron distribution of the non-thermal electron tails to be-x5."" at any value of 5."," In this work, we have assumed, for the sake of simplicity and compatibility with studies of, e.g., McConnell et (2000a), the electron distribution of the non-thermal electron tails to be $\propto \gamma^{-p}$ at any value of $\gamma$."950" However. when he power-law tail extends down to non-relativistic energies. ud. the distributions expected from acceleration orocesses are power laws in either the kinetic energy or the momentum. x(1)"" for the former."," However, when the power-law tail extends down to non-relativistic energies, $\gamma_{\rm nth} \sim 1$, the distributions expected from acceleration processes are power laws in either the kinetic energy or the momentum, $\propto (\gamma-1)^{- p}$ for the former."951 Clearly. the smaller sain tthe larger 9). the larger the cdillerences oetween those distributions.," Clearly, the smaller $\gamma_{\rm nth}$ the larger $\delta$ ), the larger the differences between those distributions."952 Then. the actual shift. of the urnover [frequency at a given value of say would be somehow smaller.," Then, the actual shift of the turnover frequency at a given value of $\gamma_{\rm nth}$ would be somehow smaller."953" Also. the relation between 5,44, ane ó would change."," Also, the relation between $\gamma_{\rm nth}$ and $\delta$ would change."954 Nevertheless. the above effects: would moclify our results only quantitatively without allecting our conclusions.," Nevertheless, the above effects would modify our results only quantitatively without affecting our conclusions."955 The influence of a weak. non-thermal. component in the electron distribution on radiation spectra has also been independently considered by Ozzel. Psaltis Naravan (2000).," The influence of a weak, non-thermal, component in the electron distribution on radiation spectra has also been independently considered by Özzel, Psaltis Narayan (2000)."956 Their study has been devoted to the case of acdvection-dominated accretion Hows CXDALE). and their presented. spectra are integrated over all radii of the flow.," Their study has been devoted to the case of advection-dominated accretion flows (ADAF), and their presented spectra are integrated over all radii of the flow."957 In contrast to our results. they do not note any shift in the turnover frequency at the peak of the synchrotron spectrum.," In contrast to our results, they do not note any shift in the turnover frequency at the peak of the synchrotron spectrum."958 This appears to result. [rom their study being constrained to the XDAE model at. low acerction rates. in which case electrons in the innermost parts of the accretion [low reach rather high. temperatures. (at. which even thermal electrons reach relatively high Lorentz factors).," This appears to result from their study being constrained to the ADAF model at low accretion rates, in which case electrons in the innermost parts of the accretion flow reach rather high temperatures (at which even thermal electrons reach relatively high Lorentz factors)."959 Those temperatures are significantly higher than those we consider based on observational data from. luminous accreting black holes., Those temperatures are significantly higher than those we consider based on observational data from luminous accreting black holes.960 On the other hand. Ovzel et al. (," On the other hand, Özzel et al. ("9612000) [ind a significant excess non-thermal emission at frequencies well below the peak of the integrated svnchrotron spectrum.,2000) find a significant excess non-thermal emission at frequencies well below the peak of the integrated synchrotron spectrum.962 ‘This excess results [rom radiation emitted at large. racii where the electron. temperature. is. low. and where the svnchrotron emission. (both optically thick ancl optically thin) around the local turnover frequency can be strongly amplified by the presence of an electron tail. as illustrated in reffwidma above.," This excess results from radiation emitted at large radii, where the electron temperature is low, and where the synchrotron emission (both optically thick and optically thin) around the local turnover frequency can be strongly amplified by the presence of an electron tail, as illustrated in \\ref{f:widma} above."963 This research has been supported in part by the Foundation for Polish Science. and. WKBN grants. 2P03D01619.— and 2p03D00624., This research has been supported in part by the Foundation for Polish Science and KBN grants 2P03D01619 and 2P03D00624.964 We thank Marek Cierlifsski for providing us with his Monte-Carlo. Comptonization code ancl for help with its use., We thank Marek Gierlińsski for providing us with his Monte-Carlo Comptonization code and for help with its use.965 We are also grateful to Andrei Beloborodov. Joanna Mikolajewska anc Juri Poutanen for. valuable CLISCUSSLOLIS.," We are also grateful to Andrei Beloborodov, Joanna ajewska and Juri Poutanen for valuable discussions."966where A; is the modified: Bessel function of the second kind of order 7 and the argument AX is Substituting in this approximation and using (e.g.?).. the forcing function c becomes Finally. the total torque exerted by the planets on disces is calculated by llere. we cliscuss corotation torque and summarise its problems.,"where $K_i$ is the modified Bessel function of the second kind of order $i$ and the argument $\Lambda$ is Substituting in this approximation and using $K_0'=-K_1$ \citep[e.g.][]{as72}, the forcing function $\psi$ becomes Finally, the total torque exerted by the planets on discs is calculated by Here, we discuss corotation torque and summarise its problems."967" The corotation torque was originally derived. by (50,", The corotation torque was originally derived by GT80.968 The corotation resonances arise when the orbital frequeney of the gas © is identical to the orbital frequency of the planet £3., The corotation resonances arise when the orbital frequency of the gas $\Omega$ is identical to the orbital frequency of the planet $\Omega_p$.969 Phe analytical formula is where is one of the Oort constants or the vorticity of gas. and is the mth order Fourier component of the potential of the planets.," The analytical formula is where is one of the Oort constants or the vorticity of gas, and is the $m$ th order Fourier component of the potential of the planets."970 Thus. the sign of the corotation torque. is determined by the radial gradient of vorticity per unit surface censity. called: the vortensity.," Thus, the sign of the corotation torque is determined by the radial gradient of vorticity per unit surface density, called the vortensity."971 For the Ixeplerian discs. D.x.Og.," For the Keplerian discs, $B\propto \Omega_{Kep}$."972 Consequently. 1tnn vanishes with Voxrp V7.," Consequently, $\Gamma_m^C$ vanishes with $\Sigma \propto r^{-3/2}$ ."973 Unfortunately. this first. derived: analytical formula had a discrepaney with numerical caleulations (?)..," Unfortunately, this first derived analytical formula had a discrepancy with numerical calculations \citep{kp93}."974 Furthermore. the mechanism of the exchange. of angular momentum. between the planets and. the gaseous. clisces and its relation with the the gradient of the vortensity is yhvsically not clear.," Furthermore, the mechanism of the exchange of angular momentum between the planets and the gaseous discs and its relation with the the gradient of the vortensity is physically not clear."975" The ciserepaney between the analytical ancl numerical orques was resolved. by “PLWO2 by replacing 45, with Om|thn7. where qu; is the mth Fourier component of the enthalpy perturbation."," The discrepancy between the analytical and numerical torques was resolved by TTW02 by replacing $\phi_m^2$ with $|\phi_m+\eta _m|^2$, where $\eta_m$ is the $m$ th Fourier component of the enthalpy perturbation."976 This implies that the eas pressure or temperature around. the planet is crucial for a proper oescription of the corotation as well as the Lindblad torques since the enthalpy is defined by the pressure. divided: by density., This implies that the gas pressure or temperature around the planet is crucial for a proper prescription of the corotation as well as the Lindblad torques since the enthalpy is defined by the pressure divided by density.977 Phe revised full analytical formula of the corotation orque has recently been derived by 2..., The revised full analytical formula of the corotation torque has recently been derived by \citet{zl06}. .978 We call the torque discussed. above the linear. corotation torque since dU is derived from the linearized equations., We call the torque discussed above the linear corotation torque since it is derived from the linearized equations.979 7 derived the. corotation torque based. on a fundamentally cdillerent approach., \citet{ward91} derived the corotation torque based on a fundamentally different approach.980 Vhis corotation torque is often called. a horseshoc drag to distinguish. with the linear one., This corotation torque is often called a horseshoe drag to distinguish with the linear one.981 The horseshoe drag arises [rom the interaction between a planet and the uid element moving in the vicinity of it., The horseshoe drag arises from the interaction between a planet and the fluid element moving in the vicinity of it.982 When the Duid. clement encounters the planet. the orbital radius of the element is shifted from the inner to the outer one relative to the planetary orbit.," When the fluid element encounters the planet, the orbital radius of the element is shifted from the inner to the outer one relative to the planetary orbit."983 During this non-incar process. the fluid. clement gains angular momentunm. rom the planet ancl vice versa since angular. momentum of the disc increases with distance from the central star.," During this non-linear process, the fluid element gains angular momentum from the planet and vice versa since angular momentum of the disc increases with distance from the central star."984 When the orbital radius of the [uid element is shifted rom the outer to the inner orbits. the situation is the opposite.," When the orbital radius of the fluid element is shifted from the outer to the inner orbits, the situation is the opposite."985 As seen in numerical simulations (e.g.7).. these gaits result in a horseshoe orbit.," As seen in numerical simulations \citep[e.g.][]{m01}, these shifts result in a horseshoe orbit."986 That is why it is called 16 horseshoe drag., That is why it is called the horseshoe drag.987 Furthermore. adiabatic invariance forces 1e [uid to continue its circular motion (7).. which prohibits re excitation of density waves ancl possibly also produces saturation (that is. the horseshoe drag becomes negligible).," Furthermore, adiabatic invariance forces the fluid to continue its circular motion \citep{ward91}, which prohibits the excitation of density waves and possibly also produces saturation (that is, the horseshoe drag becomes negligible)."988 lt is very interesting that the horseshoe drag also epends on the radial gradient of the vortensity which is *xplained by mapping process of the area occupied by the Iuid element., It is very interesting that the horseshoe drag also depends on the radial gradient of the vortensity which is explained by mapping process of the area occupied by the fluid element.989 Note that there is no reason to identify the linear corotation torque with the horseshoe drag since they are derived. [rom cilferent approaches., Note that there is no reason to identify the linear corotation torque with the horseshoe drag since they are derived from different approaches.990 The formula of the horseshoe drag is where wry is the half width of the horseshoe region and is one of the Oort constants (?).., The formula of the horseshoe drag is where $x_s$ is the half width of the horseshoe region and is one of the Oort constants \citep{ward91}.991 Thus. the horseshoe drag strongly depends on urs although wy is treated. as a »uwameter in any numerical simulations (?7)..," Thus, the horseshoe drag strongly depends on $x_s$ although $x_s$ is treated as a parameter in any numerical simulations \citep{mdk06,pp09}."992 ltecentlv. 7? have reexamined the linear corotation orque and. horseshoe drag and. found. that the linear one is only valid. for the carly stage of numerical simulations or for discs with very high viscosity (a~ 0.1).," Recently, \citet{pp09a} have reexamined the linear corotation torque and horseshoe drag and found that the linear one is only valid for the early stage of numerical simulations or for discs with very high viscosity $\alpha \sim 0.1$ )."993 Except [or hese. the total torque is well-represented by the sum of the Lindblad torque and the horseshoe crag.," Except for these, the total torque is well-represented by the sum of the Lindblad torque and the horseshoe drag."994 With the proper choice of ες. the horseshoe drag is about 2-3 times larger (in magnitude) than the linear corotation torque. but it is still smaller than the Lindblad. one for discs with s<1. where Xx10.," With the proper choice of $x_s$, the horseshoe drag is about 2-3 times larger (in magnitude) than the linear corotation torque, but it is still smaller than the Lindblad one for discs with $s<1$, where $\Sigma \propto r^s$."995 A more complete treatment for the horseshoe drag including the ellecets of the pressure is done by 7. and confirms the same results., A more complete treatment for the horseshoe drag including the effects of the pressure is done by \citet{cm09} and confirms the same results.996 In the above studies. the temperature which may be a function of radius from the star is assumed to be fixed. during mass transfer.," In the above studies, the temperature which may be a function of radius from the star is assumed to be fixed during mass transfer."997 In. other words. discs are assumed. to be barotropic.," In other words, discs are assumed to be barotropic."998 In this case. the magnitude of the linear corotation torque or horseshoe drag is always smaller than the Lindblad. one (?)..," In this case, the magnitude of the linear corotation torque or horseshoe drag is always smaller than the Lindblad one \citep{kp93}."999 Therefore. one can safely assume both torques to be negligible even if it is not saturated.," Therefore, one can safely assume both torques to be negligible even if it is not saturated."1000 The situation. however. can change by relaxing the isothermal assumption (2)..," The situation, however, can change by relaxing the isothermal assumption \citep{pm06}. ."1001 For dises in which the energy conservation is fully considered. the linear corotation torque and horseshoe drag are determined not only by the racial eracicnt of the vortensity but also by the radial gradient of entropy (22)...," For discs in which the energy conservation is fully considered, the linear corotation torque and horseshoe drag are determined not only by the radial gradient of the vortensity but also by the radial gradient of entropy \citep{bm08,pp08}."1002 Ht is interesting that the entropy-related corotation torque. especially horseshoe drag. can dominate over the Lindblad one and control migration if discs have a large entropy gracicnt and. are considered. to be acliahatic.," It is interesting that the entropy-related corotation torque, especially horseshoe drag, can dominate over the Lindblad one and control migration if discs have a large entropy gradient and are considered to be adiabatic."1003 1n the region with a large (in magnitude). negative entropy eracient. planetsmigrate outwardsdue to the large. positive horseshoe drag.," In the region with a large (in magnitude), negative entropy gradient, planetsmigrate outwardsdue to the large, positive horseshoe drag."1004 The completeanalytical formulae in 2D, The completeanalytical formulae in 2D1005decline.,decline.1006 The sum of the contributions (2a) and (2b) well fit all the PSS data with po. a specific functions of Luminosity (see PSS).," The sum of the contributions (2a) and (2b) well fit all the PSS data with $\rho_0$ , $a^2$ specific functions of luminosity (see PSS)."1007 Let us remind that disk masses Ap of spirals were found in the range LAL. €Mp2.10H M..," Let us remind that disk masses $M_D$ of spirals were found in the range $10^9~$ $_\odot \leq M_D \leq 21008\times 10^{11}$ $_\odot$."1009 The URC for the purpose of this work matches well the individual RCs of late tvpe spirals (sce also Appendix for a discussion)., The URC for the purpose of this work matches well the individual RCs of late type spirals (see also Appendix for a discussion).1010 Lt is useful to express the URC paradigm in the following wav: at any chosen radius. the URC predicts the circular velocity of a (late type) spiral of Luminosity ane clisk scale-Iength. within an error that is one order of magnitude smaller than the variations it shows i) at cillerent radii and ii) at any radius. with respect to objects of different Luminosity.," It is useful to express the URC paradigm in the following way: at any chosen radius, the URC predicts the circular velocity of a (late type) spiral of luminosity and disk scale-length, within an error that is one order of magnitude smaller than the variations it shows i) at different radii and ii) at any radius, with respect to objects of different luminosity."1011 Let us remind that the Universal curve built in PSS holds out to #2). uses the luminosity as the galaxy identifier ancl the disk scale-Iength as a unit of measure for the radial coordinate.," Let us remind that the Universal curve built in PSS holds out to $R_l$, uses the luminosity as the galaxy identifier and the disk scale-length as a unit of measure for the radial coordinate."1012 We will label it as URC) to indicate it as the first step of a definitive function ofthe dark racial coordinate. able to reproduce the observed. RCs of spirals.," We will label it as ${_0}$ to indicate it as the first step of a definitive function of the dark radial coordinate, able to reproduce the observed RCs of spirals."1013 URC) provides funcamental knowledge on the mass distribution in spirals. while it sulfers from three limitations: 1) it strictly holds only in a region extended less than 5% the DM halo size (see below) 2) the velocity. profile of the halo component. valid out to Z4. cannot be extrapolated to radii of cosmological interest 3) it identifies objects by their luminosities. rather than by their virial masses.," $_0$ provides fundamental knowledge on the mass distribution in spirals, while it suffers from three limitations: 1) it strictly holds only in a region extended less than $5\%$ the DM halo size (see below) 2) the velocity profile of the halo component, valid out to $R_l$, cannot be extrapolated to radii of cosmological interest 3) it identifies objects by their luminosities, rather than by their virial masses."1014" Let us point out that the UC has been often and successfully used as an observational benchmark for theories. but this. only For 2«B, and alter that a relation between the halo mass and the galaxy. luminosity was assumed."," Let us point out that the $_0$ has been often and successfully used as an observational benchmark for theories, but this, only for $R<R_l$ and after that a relation between the halo mass and the galaxy luminosity was assumed."1015" On the other side. highresolution cosmological Νbody simulations have shown that. within the (A) Cold Dark Matter (CDAL) scenario. dark halos achieve a specific equilibrium density profile characterized by a universal shape and. in turn. anuniversal halo circular velocity (Navarro. Frenk White. 1997. NEW). VaraCAR.Ado) in which the virial mass M,;, and virial racius £2,;; are the galaxy identifier and racial coordinate."," On the other side, high–resolution cosmological N–body simulations have shown that, within the $\Lambda$ ) Cold Dark Matter (CDM) scenario, dark halos achieve a specific equilibrium density profile characterized by a universal shape and, in turn, anuniversal halo circular velocity (Navarro, Frenk White, 1997, NFW), $V_{\rm NFW}(R, M_{vir})$ in which the virial mass $M_{vir}$ and virial radius $R_{vir}$ are the galaxy identifier and radial coordinate."1016 where eDorfRey ds the radial coordinate. e is the concentration parameter. and gle)=In(1|e)ο16)]+," where $x\equiv r/R_{vir}$ is the radial coordinate, $c$ is the concentration parameter, and $g(c)= [\ln(1+c)-c/(1+c)]^{-1}$."1017" Phe parameter e is. found⋅ to be a weak function⋅. of the halo mass. given. by ez14(AL,]ΙΟΥΝ.}O13 (Bullock ct al. 2001. Dutton. 2006. Cinedin 2006)."," The parameter $c$ is found to be a weak function of the halo mass, given by $c\approx 14\, \left({M_{vir} / 10^{11}\, \rm M_{\odot}}1018\right)^{-0.13}$ (Bullock et al, 2001, Dutton, 2006, Gnedin 2006)."1019 This leads to with 15;=WV(Ro)., This leads to with $V_{vir}=V(R_{vir})$.1020 H is interesting to note that in this scenario the presentcay circular velocity. which also includes a barvonic component arranged in a disk. is predicted to be aCnéversad funetion of radius. tuned by few galaxy parameters (Mo. Mao White 1998).," It is interesting to note that in this scenario the present–day circular velocity, which also includes a baryonic component arranged in a disk, is predicted to be a function of radius, tuned by few galaxy parameters (Mo, Mao White 1998)."1021 However. it is well known that observations of spiral galaxies favor density concentrations lower than those predicted for CDM by Eq. (," However, it is well known that observations of spiral galaxies favor density concentrations lower than those predicted for CDM by Eq. ("1022a): DAL halos detected around spirals do not show the NEW central cusp in favor of a core-like structure (Gentile et 2005: van den Bosch Swaters 2001: Swaters et al.,3a): DM halos detected around spirals do not show the NFW central cusp in favor of a core-like structure (Gentile et 2005; van den Bosch Swaters 2001; Swaters et al.1023 2003: Welclrake et al., 2003; Weldrake et al.1024 2003: Simon et al., 2003; Simon et al.1025 2005: Donato et al. 2004: Gentile et al.," 2005; Donato et al, 2004; Gentile et al."1026 2007)., 2007).1027 Therefore. the reconstruction of the mass distribution of DAL halos from observations{οἱ with that emerging from N-bocly simulations is required not only as à normal scientific routine. but also in view of a theory-vs-observations Likely. disagreement.," Therefore, the reconstruction of the mass distribution of DM halos from observations with that emerging from N-body simulations is required not only as a normal scientific routine, but also in view of a theory-vs-observations likely disagreement."1028 As an alternative to the simulation method. we will support the URC paradigm by means of a set of proper observationa cata and we will derive an analytical form for this curve. valid from the galaxy center out to its virial racius and characterize by the halo mass as the galaxy identifier.," As an alternative to the simulation method, we will support the URC paradigm by means of a set of proper observational data and we will derive an analytical form for this curve, valid from the galaxy center out to its virial radius and characterized by the halo mass as the galaxy identifier."1029 In detail. we extend/improve the URC) in PSS a) by adopting a different halo prolile. proper to describe the halo distribution out to the virial radius. b) by using a number ofRCs substantially more extende than those in PSS and c) by exploiting the relationship between the disk mass Mp. and the virial galaxy mass M; recently obtained by Shankar et al. (," In detail, we extend/improve the $_0$ in PSS a) by adopting a different halo profile, proper to describe the halo distribution out to the virial radius, b) by using a number ofRCs substantially more extended than those in PSS and c) by exploiting the relationship between the disk mass $M_D$, and the virial galaxy mass $M_{vir}$, recently obtained by Shankar et al. ("10302006).,2006).1031" Phis will allow to build an “observational” Universal Curve. Vrzge(I:Md). extended out to £5, and having the virial mass as the galaxy icentifier."," This will allow to build an ""observational"" Universal Curve, $V_{URC}(R; M_{vir})$, extended out to $R_{vir}$ and having the virial mass as the galaxy identifier."1032 This curve is the observational counterpart of the universal ACT NEW N-body generated. profile., This curve is the observational counterpart of the universal $\Lambda$ CDM NFW N-body generated profile.1033 While pointing that the concept behind the Universal Rotation Curve may be valid also for galaxies of cilferent LEubble Types (see Salucci ancl Persic. 1997). but a number of issues are still open and will be dealt. elsewhere: i) Sa galaxies amount. by number. to less than of the whole spiral population. and are important objects in view of the dual nature of their stellar distribution.," While pointing that the concept behind the Universal Rotation Curve may be valid also for galaxies of different Hubble Types (see Salucci and Persic, 1997), but a number of issues are still open and will be dealt elsewhere: i) Sa galaxies amount, by number, to less than of the whole spiral population, and are important objects in view of the dual nature of their stellar distribution."1034 Thev show HC profiles with a clear svstematies with luminosity (Rubin ct al.," They show RC profiles with a clear systematics with luminosity (Rubin et al.,"1035 1985). but. not unexpectedly. with some dillerence from those of the y (Noordmoeer. 2007).," 1985), but, not unexpectedly, with some difference from those of the $_{0}$ (Noordmeer, 2007)."1036 ii) Dwarf spirals with Vou;«50/m/s are not well studied and included in the URC vet. also because in these objects the RCs do not coincide with the circular velocity. being significant the complex asymmetric drift correction.," ii) Dwarf spirals with $V_{opt}<50 km/s $ are not well studied and included in the URC yet, also because in these objects the RCs do not coincide with the circular velocity, being significant the complex asymmetric drift correction."1037 iii) The kinematical properties of spirals of very high stellar clisk mass are not presently investigated with a suitably large sample., iii) The kinematical properties of spirals of very high stellar disk mass are not presently investigated with a suitably large sample.1038 iv) A possible additional URC physical parameter (e.g. the surface stellar density) to take care of the (small) variance of the RCs profiles that scems to be unaccounted by the Luminosity., iv) A possible additional URC physical parameter (e.g. the surface stellar density) to take care of the (small) variance of the RCs profiles that seems to be unaccounted by the luminosity.1039" Finally. let us remind that. ina flat cosmology with matter density. parameter Oi;=0.27 and Hubble constant to at the present time. the halo virial radius #2.5,. ie. the size of the virialized cosmological perturbation of"," Finally, let us remind that, ina flat cosmology with matter density parameter $\Omega_M = 0.27$ and Hubble constant $H_0 = 71~1040\mathrm{km~s}^{-1}~\mathrm{Mpc}^{-1}$ , at the present time, the halo virial radius $R_{vir}$ , i.e. the size of the virialized cosmological perturbation of"1041aperture correction must be smaller than this level. and that both of the slopes found in our data fall within this range of a<|0.2]£0.06.,"aperture correction must be smaller than this level, and that both of the slopes found in our data fall within this range of $\alpha < \left|0.2\right| \pm 0.06$."1042 Our 50 orbit ACS observation of M87 shows no significant relation between the colors of the blue metal poor clusters and their huninositv. with a formal best fit of ZxM5 from 19.5</<24.5. ancl a conservative upper limit on the slope of any relation in the M87 elobular cluster population of a«0.20)£0.06 including systematic effects.," Our 50 orbit ACS observation of M87 shows no significant relation between the colors of the blue metal poor clusters and their luminosity, with a formal best fit of $Z \propto M^{0.08}$ from $19.51043< I < 24.5$, and a conservative upper limit on the slope of any relation in the M87 globular cluster population of $\alpha <1044\left|0.20\right| \pm 0.06$ including systematic effects."1045 A similarly small trend is found when the fitting is restricted (ο only the bright clusters above the luminosity function turnover (19.5<f 22.5)., A similarly small trend is found when the fitting is restricted to only the bright clusters above the luminosity function turnover $19.5 < I < 22.5$ ).1046 This absence of anv significant mass-metallicitv relation rules oul some earlier claims of such a trend from much shallower data., This absence of any significant mass-metallicity relation rules out some earlier claims of such a trend from much shallower data.1047 Some earlier work investigated (he mass metallicity relation of metal poor globular cluster populations in mach shallower images of nearly ellipticals. including single orbit data lor MIST ancl several other bright Vireo ellipticals (Straderetal.2006:Mieske2006).. single orbit pointines of NGC! 4594 (Spilleretal.2006).. ancl several distant. ellipücals with longer exposures ancl {hus similar signal to noise as (he nearby single orbit observations (Ilarrisetal.2006).," Some earlier work investigated the mass metallicity relation of metal poor globular cluster populations in much shallower images of nearly ellipticals, including single orbit data for M87 and several other bright Virgo ellipticals \citep{Strader,Mieske}, single orbit pointings of NGC 4594 \citep{Spitler}, and several distant ellipticals with longer exposures and thus similar signal to noise as the nearby single orbit observations \citep{Harris06}."1048". These shallower studies suggested (hat the metal poor globular cluster populations of some ol these galaxies. including AIST. had a blue tilt and inferred. a mass metallicity relation of about ZxAM""."," These shallower studies suggested that the metal poor globular cluster populations of some of these galaxies, including M87, had a blue tilt and inferred a mass metallicity relation of about $Z \propto M^{0.55}$."1049 These results are clearly not confirmed in our 50 orbit data. which places an upper limit on any mass-metallicitv relation (hat is much smaller (han this strong trend.," These results are clearly not confirmed in our 50 orbit data, which places an upper limit on any mass-metallicity relation that is much smaller than this strong trend."1050 There are also several ground based studies of the color-magnitude trends in globular cluster svstems that find a variety of results. including both blue tilts (Forte2008) as well as red (ills (Bassinoetal.," There are also several ground based studies of the color-magnitude trends in globular cluster systems that find a variety of results, including both blue tilts \citep{FFG,Wehner} as well as red tilts \citep{Bassino,Lee}."1051"2005:Lee2003).. Forte examined M8T. and found evidence lor mass-metallicitv relation of ZxAL!ΤΙ, which although smaller than the claims from space-based studies. is still inconsistent. with (he lack of a tlt in our much deeper data."," \citet{FFG} examined M87, and found evidence for mass-metallicity relation of $Z \propto M^{0.44}$, which although smaller than the claims from space-based studies, is still inconsistent with the lack of a tilt in our much deeper data."1052 This emphasizes the difficulty in accurately determining color tilts Irom data wilh low signal to noise and poor spatial resolution., This emphasizes the difficulty in accurately determining color tilts from data with low signal to noise and poor spatial resolution.1053 The clear absence of a significant mass metallicity effect in our data contrary to (he very strong effect in single orbit data for galaxies like AIST and in data with similar signal to noise ab larger distance. highlights the need for verv deep observations (o address (his question.," The clear absence of a significant mass metallicity effect in our data contrary to the very strong effect in single orbit data for galaxies like M87 and in data with similar signal to noise at larger distance, highlights the need for very deep observations to address this question."1054 ]vundu(2008) has imvestigated (his question in detail., \citet{Kundu08} has investigated this question in detail.1055 We do not reproduce (his extensive work here. but note that Ixundu(2008). identifies two major issues (hat arise in single orbit data or data with similar signal to noise for the bulk of the clusters.," We do not reproduce this extensive work here, but note that \citet{Kundu08} identifies two major issues that arise in single orbit data or data with similar signal to noise for the bulk of the clusters."1056 First. such data lacks the depth necessary to accurately follow the sizes of globular clusters will magnitude.," First, such data lacks the depth necessary to accurately follow the sizes of globular clusters with magnitude."1057 This lack of size discrimination will cause size dependent photometric errors., This lack of size discrimination will cause size dependent photometric errors.1058 Secondly. the error," Secondly, the error"1059around IRC+10216 could be formed chemically by Fischer-Tropsch eatalvsis on grain surfaces.,around IRC+10216 could be formed chemically by Fischer-Tropsch catalysis on grain surfaces.1060 While this mechanism is incapable of directly producing large amounts of formaldehyde (comparable to what we see in IRC+10216). Willacy suggests that the presence of formaldehyde could be explained separately by the photodissociation of methanol. which could be formed in large quantities by Fischer-Tropsch reactions.," While this mechanism is incapable of directly producing large amounts of formaldehyde (comparable to what we see in IRC+10216), Willacy suggests that the presence of formaldehyde could be explained separately by the photodissociation of methanol, which could be formed in large quantities by Fischer-Tropsch reactions."1061 Our failure to detect methanol in significant quantities rules oul this method of production of formaldehyde. ancl also suggests that grain cabalvsis is not (he source of the water vapor and OI around IRC+10216.," Our failure to detect methanol in significant quantities rules out this method of production of formaldehyde, and also suggests that grain catalysis is not the source of the water vapor and OH around IRC+10216."1062 Nevertheless. (here are plausible chemical production routes lor formaldehyde which we examine here.," Nevertheless, there are plausible chemical production routes for formaldehyde which we examine here."1063 There are al least (vo important reactions that are responsible for the production of formaldelivce around oxvgen-rich asymptotic giant branch stars. which may also operate around IRC+10216.," There are at least two important reactions that are responsible for the production of formaldehyde around oxygen-rich asymptotic giant branch stars, which may also operate around IRC+10216."1064 These are and In both oxvgen-rich stus and in IRC+10216. the Clie and Cl; would be produced bv the photodissociation of methane (ClI;).," These are and In both oxygen-rich stars and in IRC+10216, the $_2$ and $_3$ would be produced by the photodissociation of methane $_4$ )."1065 The source of OL around IC10216. and oxvgen-rich stars would also be the same. namely the photodissociation of water vapor.," The source of OH around IRC+10216 and oxygen-rich stars would also be the same, namely the photodissociation of water vapor."1066 The atomic oxvgen required [or the second reaction would come almost exclusively [rom the pholoclissociation of CO in the case of IC10216. but for oxvgen-rich stars. both the CO and OII will make a contribution.," The atomic oxygen required for the second reaction would come almost exclusively from the photodissociation of CO in the case of IRC+10216, but for oxygen-rich stars, both the CO and OH will make a contribution."1067 In both (vpes of stars atomic oxvgen will be available in the outermost reeions of the circumstellar envelope., In both types of stars atomic oxygen will be available in the outermost regions of the circumstellar envelope.1068 Clearly then. (he reactants are available around IRC+10216. and since (μον are themselves photodissociation products. thev. will result in an extended source for formaldehyde. consistent with our observations.," Clearly then, the reactants are available around IRC+10216, and since they are themselves photodissociation products, they will result in an extended source for formaldehyde, consistent with our observations."1069 We must therefore caleulate if chemical reactions will produce enough [ormaldehyde (ο match our observations., We must therefore calculate if chemical reactions will produce enough formaldehyde to match our observations.1070 A rough estimate of the expected formaldehyde abundance may be made by comparing ihe methane and water vapor abundances around RC10216 to that around oxveen-rich stars., A rough estimate of the expected formaldehyde abundance may be made by comparing the methane and water vapor abundances around IRC+10216 to that around oxygen-rich stars.1071 Willacy&Millar(1997) have modeled the chemistry of several oxygen-rich stars. including the reactions listed above for creating formaldehyde.," \citet{WM97} have modeled the chemistry of several oxygen-rich stars, including the reactions listed above for creating formaldehyde."1072 Thev (vpicallv find. [or assumed. abundances of (Πο)—3xLO! and (CHI)—3x10 7. a peak formaldehyde abundance of r(IbCO)~105.," They typically find, for assumed abundances of $x({\rm H_2O})=3\times 10^{-4}$ and $x({\rm CH_4})=3\times 10^{-5}$ , a peak formaldehyde abundance of $x({\rm H_2CO})\sim 10^{-6}$."1073 Since the observed r(1lsO) and (CHI) for IRC+10216 are down by factors of ~300 (Melnicketal.2001). and ~10 (heady&Ridgway1993).. respectively. ancl because (Π.Ο) is dependent on the product of e(EII3O0) and (CIL). we expect .e(II5CO) to be down by a factor of roughly 3000 relative to the models of (1997). or ΠΟ)3x10.1.," Since the observed $x({\rm H_2O})$ and $x({\rm CH_4})$ for IRC+10216 are down by factors of $\sim300$ \citep{mel01} and $\sim10$ \citep{KR93}, respectively, and because $x({\rm H_2CO})$ is dependent on the product of $x({\rm H_2O})$ and $x({\rm CH_4})$, we expect $x({\rm H_2CO})$ to be down by a factor of roughly 3000 relative to the models of \citet{WM97}, or $x({\rm H_2CO})\sim 3\times 10^{-10}$."1074 This is about 2 orders of magnitude less thanis observed in 1RC-2-10216. which does not make the chemical explanation look very promising.," This is about 2 orders of magnitude less thanis observed in IRC+10216, which does not make the chemical explanation look very promising."1075 (Bennett2007). ACDAL ACDM (Cathctal—1981).. 2001)...," \citep{bennett:2003, hinshaw:2007}, $\Lambda$ $\Lambda$ \citep{guth:1981}. ."1076 If hese effects are coufinned by the data from the Plauck experiment. various anisotropic uuiverse models should © seriously. considered.," If these effects are confirmed by the data from the Planck experiment, various anisotropic universe models should be seriously considered."1077 Iu order to investigate the properties of different inflationary inodels it is nuportaut uot only to o»ursue deviations from statistical isotropy. but also amy deviations from Gaussianity.," In order to investigate the properties of different inflationary models, it is important not only to pursue deviations from statistical isotropy, but also any deviations from Gaussianity."1078 Sinele-ficld inflation models usually predict a CAIB statistically close to Gaussian. but nore exotic models may give rise to a larger coutributiou of non-Catssianity.," Single-field inflation models usually predict a CMB statistically close to Gaussian, but more exotic models may give rise to a larger contribution of non-Gaussianity."1079 In this paper. we focus on a method or testing eeneral deviatious from Caussianity that are rot Obviously connected to inflationary ion(ταποσα," In this paper, we focus on a method for testing general deviations from Gaussianity that are not obviously connected to inflationary non-Gaussianity."1080 However. some effort has been made to use the localτν. curvatureto estimate the non-CGaussianity parameter fxg (Cabellaetal.2005).," However, some effort has been made to use the local curvatureto estimate the non-Gaussianity parameter $f_{NL}$ \citep{cabella2005}."1081. Doréetal(2003) presented a framework for investigating uon-Gaussianitics based on the properties of the local curvature of the CAIB temperature map., \cite{dore:2003} presented a framework for investigating non-Gaussianities based on the properties of the local curvature of the CMB temperature map.1082" By calculating the secoud-order derivatives. it is possible to classify cach pixel as a ""hill. ""lake or ""saddle based ou the eigeuvalues of the IHessiau matrix."," By calculating the second-order derivatives, it is possible to classify each pixel as a “hill”, “lake” or “saddle” based on the eigenvalues of the Hessian matrix."1083 If the map is first sinoothed with a Gaussian beam. it dis possible to extract the local curvature properties on scales given by the FWIHIAL of the beam.," If the map is first smoothed with a Gaussian beam, it is possible to extract the local curvature properties on scales given by the FWHM of the beam."1084 A temperature threshold 7; is iutroduced. where CAIB temperature values below a provided threshold are ignored.," A temperature threshold $T_{\textrm{t}}$ is introduced, where CMB temperature values below a provided threshold are ignored."1085 Starting with a negative temperature threshold. the fraction of Lill. lake aud saddle poiuts that have temperatures above the threshold are counted.," Starting with a negative temperature threshold, the fraction of hill, lake and saddle points that have temperatures above the threshold are counted."1086 By perforuuug this analysis ou sunulated isotropic Gaussian maps. it is possible to estimate what the fraction of hills. lakes aud saddle points should be for increasing 7;.," By performing this analysis on simulated isotropic Gaussian maps, it is possible to estimate what the fraction of hills, lakes and saddle points should be for increasing $T_{\textrm{t}}$ ."1087 This eraph isthen compared with a, This graph isthen compared with a1088points. illustrating the ecneralisation of the correlation in Fig.5 4..,"points, illustrating the generalisation of the correlation in Fig. \ref{probfns4}."1089 However. because the limits obtained [rom macro-models that. include. model uw? follow nearly the same correlation as combinations of models 7ar. the correlation mav be valid for combinations of ανσι and &g/sg other than those investigated.," However, because the limits obtained from macro-models that include model $xi$ follow nearly the same correlation as combinations of models $i-x$, the correlation may be valid for combinations of $\kappa_A/\gamma_A$ and $\kappa_B/\gamma_B$ other than those investigated."1090 Distributions oflux ratios vary with macro-mocel for fixed Rey., Distributions offlux ratios vary with macro-model for fixed $R_{BA}$.1091 Pherelore the correlation in Fig., Therefore the correlation in Fig.1092 5r is presumably due to the imposition of the optical Dux ratio., \ref{limits_single} is presumably due to the imposition of the optical flux ratio.1093 Phe following approximation demonstrates why this should be the case., The following approximation demonstrates why this should be the case.1094 Consider two microlensed. images ὁ and e., Consider two microlensed images $b$ and $a$.1095 Suppose that the magnificationmap for image e is uniform. while the magnification map for image 6 contains a single caustic but is otherwise uniform.," Suppose that the magnificationmap for image $a$ is uniform, while the magnification map for image $b$ contains a single caustic but is otherwise uniform."1096 Let the magnification of image e be fi., Let the magnification of image $a$ be $\mu^o_{a}$.1097" Furthermore. let the magnificationὃν of imageo 6 be comprised1 of the magnification due to critical images associated. with the caustic 5, in addition to the magnification from non-critical images 75."," Furthermore, let the magnification of image $b$ be comprised of the magnification due to critical images associated with the caustic $\mu^c_b$ in addition to the magnification from non-critical images $\mu^o_b$."1098" Phe resulting optical magnification ratio is where Z, is the theoretical [ux ratio.", The resulting optical magnification ratio is where $R_{ba}$ is the theoretical flux ratio.1099 Similarly. the largerD micd-LH source size has a magnification5 ratio Now: qnο.=μαheyf)oe by construction.. so hil1 for large mid-LHi sources.," Similarly, the larger mid-IR source size has a magnification ratio Now $\mu_{a}^{OPT,o}=\mu_{a}^{IR,o}\equiv\mu_{a}^o$ by construction, so $R_{ba}^{IR} \rightarrow R_{ba}$ for large mid-IR sources."1100" Consider a dillerent. moclel waving. both an increased. jr) and 47;Ωωτω“while . keeping. £2, constant."," Consider a different model having both an increased $\mu^o_{a}$ and $\mu_{b}^{OPT,o}$ while keeping $R_{ba}$ constant."1101 sLo maintainMEM the observed Beet.IPT itOPT.7 must be increased. either by increasing the caustic strength. (flux actor. see Witt (1990)). or by moving the optical source closer to the caustic.," To maintain the observed $R_{ba}^{OPT}$, $\mu_b^{OPT,c}$ must be increased, either by increasing the caustic strength (flux factor, see Witt (1990)), or by moving the optical source closer to the caustic."1102". In the former⋅ case 5/511 15MEN increasec w. the same fractionacti as ji,OPT.. thus the same source size. is required to produce the observed. flux ratio for dilleren models having the same ££."," In the former case $\mu_b^{IR,c}$ is increased by the same fraction as $\mu_b^{OPT,c}$, thus the same source size is required to produce the observed flux ratio for different models having the same $R_{ba}$."1103" In the second case. shifting the arger mid-Ilt. source relative to the caustic has a smaller ellect⋅ on 4/5Ht than on pr,OPT.. thus increasing⋠⋅⋠ jr,OPT. au OPT.a slightly lowers the resulting A240"," In the second case, shifting the larger mid-IR source relative to the caustic has a smaller effect on $\mu_b^{IR,c}$ than on $\mu_b^{OPT,c}$, thus increasing $\mu_b^{OPT,o}$ and $\mu_{a}^{OPT,o}$ slightly lowers the resulting $R_{ba}^{IR}$."1104 A larecr mid-Ht source is therefore required to reproduce the observed. mid-IR fux ratio. and hence the confidence for each (upper) limi is increased.," A larger mid-IR source is therefore required to reproduce the observed mid-IR flux ratio, and hence the confidence for each (upper) limit is increased."1105 The combination of these two elfects suggests an explanation for both the trend (of tighter constraints with higher mean mocdel magnification) shownin bie. 4..," The combination of these two effects suggests an explanation for both the trend (of tighter constraints with higher mean model magnification) shownin Fig. \ref{probfns4},"1106 and the correlation seen in Fig. 5.., and the correlation seen in Fig. \ref{limits_single}.1107 The left-hanel panels of Fig., The left-hand panels of Fig.1108" 6. show the probabilities (lower limits) that σε270.25n,. 91g0.55, and 95l.05, as a function of the macro-model fux ratio Ley."," \ref{limits} show the probabilities (lower limits) that $S_{IR}>0.25\eta_o$, $S_{IR}>0.5\eta_o$ and $S_{IR}>1.0\eta_o$ as a function of the macro-model flux ratio $R_{BA}$."1109 Similarlv. the right-hand 3 panels of Fig.," Similarly, the right-hand 3 panels of Fig."1110" 6 show the confidences (upper limits) that 975« L0. δε<5.0. ancl σερ 10.05,."," \ref{limits} show the confidences (upper limits) that $S_{IR}<1.0\eta_o$ , $S_{IR}<5.0\eta_o$ and $S_{IR}<10.0\eta_o$ ."1111" Points are shown representing the three assumptions for the optical source size. a uniform source Φορ=0.00254, (one pixel. dots). and 2 Gaussian sources Sopr=2a04054, (crosses) and Sop,=20601g. (squares)."," Points are shown representing the three assumptions for the optical source size, a uniform source $S_{OPT}=0.025\eta_o$ (one pixel, dots), and 2 Gaussian sources $S_{OPT}=2\sigma=0.05\eta_o$ (crosses) and $S_{OPT}=2\sigma=0.1\eta_o$ (squares)."1112 The confidences show some dependence on Sopr., The confidences show some dependence on $S_{OPT}$ .1113 Stronger limits are obtained if the optical source is larger, Stronger limits are obtained if the optical source is larger1114in (he previous paragraph are misleading for astrophivsies in general.,in the previous paragraph are misleading for astrophysics in general.1115 May [factors that. present obstacles for women's participation in sciences have been identified. including hidden gender biases in hiring and evaluation (Urry2008 ancl relerences therein). as well as discouragement of female undergraduates linked to the alorementioned lack of female role models (Xie&Shanman2003).," Many factors that present obstacles for women's participation in sciences have been identified, including hidden gender biases in hiring and evaluation \citealt{urry08} and references therein), as well as discouragement of female undergraduates linked to the aforementioned lack of female role models \citep{xie03}."1116. One major obstacle academics of both sexes frequently [ace is the tension between having a family and maintaining the compeltiüve curriculum vitae necessary [or allaining a desirable academic position., One major obstacle academics of both sexes frequently face is the tension between having a family and maintaining the competitive curriculum vitae necessary for attaining a desirable academic position.1117 This issue has become parücululyv acute for women in astrophvsies. as the standard duration of the postdoc position eradually creeps from three (o six or seven vears.," This issue has become particularly acute for women in astrophysics, as the standard duration of the postdoc position gradually creeps from three to six or seven years."1118 The conventional wisdoni has been to have children later in life after tenure has been achieved., The conventional wisdom has been to have children later in life after tenure has been achieved.1119 While (his may have been possible for previous generations. lor most families (his goal is now unrealistic.," While this may have been possible for previous generations, for most families this goal is now unrealistic."1120 llowever. having children during graduate school or a postdoc presents ils own set of challenges aud puts undue strain on families.," However, having children during graduate school or a postdoc presents its own set of challenges and puts undue strain on families."1121 Both the academic and biological clocks are licking. and [recently the biological clock precipitates one or both partners leaving academia.," Both the academic and biological clocks are ticking, and frequently the biological clock precipitates one or both partners leaving academia."1122 We would like to postulate. based on our own experiences and anecdotal evidence. (hat (his is one of the most significant issues driving women from the field.," We would like to postulate, based on our own experiences and anecdotal evidence, that this is one of the most significant issues driving women from the field."1123 For example. one of us. on her recent (rip to a highly ranked astronomy department. had an informal meeting with female graduate students. who at that time were nearly of the graduate students in the program.," For example, one of us, on her recent trip to a highly ranked astronomy department, had an informal meeting with female graduate students, who at that time were nearly of the graduate students in the program."1124 Despite their (unusually) hieh representation in the graduate student. population. every single woman at (his meeting idenüfied balancing bhunilv ad career as a daunting problem potentially (hreatening her [future participation in the field.," Despite their (unusually) high representation in the graduate student population, every single woman at this meeting identified balancing family and career as a daunting problem potentially threatening her future participation in the field."1125 Sociological research supports our assertion: We firmly believe that a significant improvement in women’s parlicipation in sciences can be reached if and only ifleave., Sociological research supports our assertion: We firmly believe that a significant improvement in women's participation in sciences can be reached if and only if.1126 While a lew simple low-cost adjustments nay provide some relie. a qualitative change in the situation will require [financial investment.," While a few simple low-cost adjustments may provide some relief, a qualitative change in the situation will require financial investment."1127 some individuals within (he astronomical community (sometimes will support of handing agencies) have been highlv effective in public outreach. programs encouraging participation of high-school and undergraduate female students. as well as in organizing meetings and publications to educate the members of the profession about the status of women.," Some individuals within the astronomical community (sometimes with support of funding agencies) have been highly effective in public outreach programs encouraging participation of high-school and undergraduate female students, as well as in organizing meetings and publications to educate the members of the profession about the status of women."1128 However. improvements in child care and parental leave policies cannot be easily achieved (hrough individual contributions. but. are," However, improvements in child care and parental leave policies cannot be easily achieved through individual contributions, but are"1129where the effects of the stress boundary. condition become important. we cannot use (his comparison method to estimate the magnitude of the retained heat.,"where the effects of the stress boundary condition become important, we cannot use this comparison method to estimate the magnitude of the retained heat."1130 Instead. we observe first that at the ISCO the mean Thomson optical depth through the disk in our simulation was ~50007. where i is the accretion rate in Eddington units.," Instead, we observe first that at the ISCO the mean Thomson optical depth through the disk in our simulation was $\simeq 500\dot m$, where $\dot m$ is the accretion rate in Eddington units."1131 The corresponding diffusion time is Ü.Ti orbits., The corresponding diffusion time is $\simeq 0.7\dot m$ orbits.1132" AC the same place. the inflow rate is 0.60=1.22/D.,4,."," At the same place, the inflow rate is $\simeq 0.6\Omega = 1.2\pi/P_{\rm orb}$."1133 Thus. the photon diffusion time near the ISCO in a real disk should be shorter than the inflow timeancl shorter (han our tov-model cooling time Q! for all accretion rates below Eddington.," Thus, the photon diffusion time near the ISCO in a real disk should be shorter than the inflow time—and shorter than our toy-model cooling time $\Omega^{-1}$ —for all accretion rates below Eddington."1134 A second standard of comparison max be derived from (he magnitude of (he retained heal., A second standard of comparison may be derived from the magnitude of the retained heat.1135 We found earlier that the accretion-weighted mean specilic enthalpy is c1+0.018 at r2244., We found earlier that the accretion-weighted mean specific enthalpy is $\simeq 1 + 0.018$ at $r\simeq 2M$.1136 That the retained heat is ~10% of the binding energy there is consistent with the fact that ~10% of the heat dissipatecl in the main disk body is left nuraciatecd., That the retained heat is $\simeq 10\%$ of the binding energy there is consistent with the fact that $\simeq 10\%$ of the heat dissipated in the main disk body is left unradiated.1137 Combining these two argumentis. we mieht expect that in the limit of truly complete radiation of dissipated heat. the efficiency. could have heen greater by as much as 0.02. rising perhaps to ~Q.1T. 20% above (he classical number as adjusted for photon capture.," Combining these two arguments, we might expect that in the limit of truly complete radiation of dissipated heat, the efficiency could have been greater by as much as 0.02, rising perhaps to $\simeq 0.17$, $20\%$ above the classical number as adjusted for photon capture."1138 Additional heat is created in the plunging region (the mean accreted specilic enthalpy rises from 1.02 at the ISCO to ~1.08 at the horizon). but. as we have already seen. the fraction of photons escaping from regions so close to the horizon to infinity is relatively small. so only a small part of the additional 0.01 in rest-mass equivalent is likelv to reach distant observers.," Additional heat is created in the plunging region (the mean accreted specific enthalpy rises from 1.02 at the ISCO to $\simeq 1.03$ at the horizon), but, as we have already seen, the fraction of photons escaping from regions so close to the horizon to infinity is relatively small, so only a small part of the additional 0.01 in rest-mass equivalent is likely to reach distant observers."1139 We might also ask what effect truly raciating all the heat would have on electromagnetic enerev I[luxes., We might also ask what effect truly radiating all the heat would have on electromagnetic energy fluxes.1140" To approach this question we begin bv considering it [rom (he point of view of the classical (NT) theory of accretion. where much attention is paid to (he r © component of the stress tensor 77. but little is said about other components except for the assumption that the stress tensor is orthogonal to the four-velocitv. 4,77=0."," To approach this question we begin by considering it from the point of view of the classical (NT) theory of accretion, where much attention is paid to the $r$ $\phi$ component of the stress tensor $T^\mu_\nu$, but little is said about other components except for the assumption that the stress tensor is orthogonal to the four-velocity, $u_\mu T^\mu_\nu = 0$."1141 As ?. pointed out. this assumption is consistent wilh the sort of stress NT had in mind. ie.. ordinary viscosity. bul nol necessarily with other physical stress mechanisms.," As \citet{2008arXiv0801.2974B} pointed out, this assumption is consistent with the sort of stress NT had in mind, i.e., ordinary viscosity, but not necessarily with other physical stress mechanisms."1142 In. particular. ib is inconsistent. with MBI-driven MUD turbulence: the electromagnetic stress tensor contains a term αρ. which is manilestlv.nef orthogonal to the four-velocity: in addition. the turbulence entails another (generally rather smaller) contribution to the stress tensor (phi4-διδημ. where ou is the fIuctuating part of the four-velocity.," In particular, it is inconsistent with MRI-driven MHD turbulence: the electromagnetic stress tensor contains a term $||b||^2 u^\mu u_\nu$, which is manifestly orthogonal to the four-velocity; in addition, the turbulence entails another (generally rather smaller) contribution to the stress tensor $(\rho h + ||b||^2)\delta u^\mu \delta u_\nu$, where $\delta u^\mu$ is the fluctuating part of the four-velocity."1143 Described in more «qualitative terms. the classical thieory accounts for the energv flow due to the work done bv the stress. but not the energv flow due to the advection. bv the mean flow. of an energy density associated with the stress mechanism.," Described in more qualitative terms, the classical theory accounts for the energy flow due to the work done by the stress, but not the energy flow due to the advection, by the mean flow, of an energy density associated with the stress mechanism."1144" As numerous numerical studies of the MRI-driven turbulence have shown. the ratio o4,=205,)/(0|b[||?)20.2 0.3 in the disk body. rising by [actors of a few in the plunging region (e.g. ?))."," As numerous numerical studies of the MRI-driven turbulence have shown, the fluid-frame ratio $\alpha_{\rm mag} \equiv 2\langle b^r b_\phi \rangle/\langle ||b||^2\rangle1145\simeq 0.2$ –0.3 in the disk body, rising by factors of a few in the plunging region (e.g. \cite{HK02}) )."1146 At the order of magnitude level. the ratio of the advected," At the order of magnitude level, the ratio of the advected"1147referenced to the z-axis of the system.,referenced to the z-axis of the system.1148 As part of the construction of these tages. the polarization vector of the photon must be rotated so that it is referenced to the y-axis of the image plane.," As part of the construction of these images, the polarization vector of the photon must be rotated so that it is referenced to the y-axis of the image plane."1149 The direct light surface brightucss mage is constructed usine where Fj! is the direct flux for the ath photon (see eq. 2)).," The direct light surface brightness image is constructed using where $F_0^\alpha$ is the direct flux for the $\alpha$ th photon (see eq. \ref{eq_fd}) ),"1150 Ὁμε is the surface area of pixel (C.7) iu steradiaus. and the sum over à is done only for photous whose birth position fall within pixel 6.7) when projected onto the sky.," $\Omega_{pixel}$ is the surface area of pixel $(i,j)$ in steradians, and the sum over $\alpha$ is done only for photons whose birth position fall within pixel $(i,j)$ when projected onto the sky."1151 The scattered light surface ποιον» image is constructed using where FY is the scattered flux for the wth scattering of the ath photon (see eqs., The scattered light surface brightness image is constructed using where $F_n^\alpha$ is the scattered flux for the $n$ th scattering of the $\alpha$ th photon (see eqs.1152 6 aud 17)). aud the sums over o and » are done ouly for photous aud scatterings of that photou whose scattering sites fall within pixel C.) when projected outo the kv.," \ref{eq_fs1} and \ref{eq_fsn}) ), and the sums over $\alpha$ and $n$ are done only for photons and scatterings of that photon whose scattering sites fall within pixel $(i,j)$ when projected onto the sky."1153 The inaages which describe the polarization state of the scattered light muage are coustructed by first rotating the 57 Stokes vector from the coordinated svstem referenced to the z-axis to a coordinate system referenced to the s-axis of the muage plane., The images which describe the polarization state of the scattered light image are constructed by first rotating the $S_n^\alpha$ Stokes vector from the coordinated system referenced to the z-axis to a coordinate system referenced to the y-axis of the image plane.1154" This is done using where S""ha is the augle which rotates the Stokes vector between the two coordinate svstems.", This is done using where $\beta^\alpha$ is the angle which rotates the Stokes vector between the two coordinate systems.1155 The O image. aud sinilarlv the U aud V images. are constructed using where the suis over à andy are done over the same limits as eq. 19..," The Q image, and similarly the U and V images, are constructed using where the sums over $\alpha$ and $n$ are done over the same limits as eq. \ref{eq_is_image}."1156 Of course. the suu of the direct and scattered elt images gives the image one would observe at a telescope.," Of course, the sum of the direct and scattered light images gives the image one would observe at a telescope."1157 The 2-dimenusioual absorbed euergy matrix is calculated usine where the stu over a and vv are only done over scatterings which happen im cell (7.7.4) and AS is the energv Which is absorbed the oth scattering site of the ath photon (see eqs.," The 3-dimensional absorbed energy matrix is calculated using where the sum over $\alpha$ and $n$ are only done over scatterings which happen in cell $(i,j,k)$ and $A_n^\alpha$ is the energy which is absorbed the $n$ th scattering site of the $\alpha$ th photon (see eqs."1158 5 aud 16))., \ref{eq_a1} and \ref{eq_an}) ).1159 The 3D absorbed eunergv matrix is what is ueeded to compute the dust enüssiou spectruni (Misseltetal.2000a)., The 3D absorbed energy matrix is what is needed to compute the dust emission spectrum \citep{mis00}.1160". Due to our use of photon weights. the uncertainties πι output quantities (νο, scattered intensity. polarizatio- ete.)"," Due to our use of photon weights, the uncertainties in output quantities (i.e., scattered intensity, polarization, etc.)"1161 can uot be computed directly frou the square root of the number of photous as is usually done when nou-weighted Monte Carlo techuiques are used., can not be computed directly from the square root of the number of photons as is usually done when non-weighted Monte Carlo techniques are used.1162 The ability to calculate uucertaimties is crucial when using Moute Carlo techniques as the accuracy of model results are depeudeut ou the number of photous run., The ability to calculate uncertainties is crucial when using Monte Carlo techniques as the accuracy of model results are dependent on the number of photons run.1163 Tf such uncertainties can be calculated durius the model gun. they can be used to cdyuanicallv set the uuuber of photons needed ii a model run to achieve a user input accuracy.," If such uncertainties can be calculated during the model run, they can be used to dynamically set the number of photons needed in a model run to achieve a user input accuracy."1164 We have adopted a siuple technique for computing the upper πιά» on the uncertainties in the output quantities., We have adopted a simple technique for computing the upper limits on the uncertainties in the output quantities.1165 If the output quantity is X. then where we) is the contribution of the nth scattering of the ath photon to .X. M is the total nuuber of ΠΡΟ photons or scatterings iu the model run and e is the average contribution each photou or scattering males to X.," If the output quantity is $X$, then where $x_n^\alpha$ is the contribution of the $n$ th scattering of the $\alpha$ th photon to $X$ , $M$ is the total number of number photons or scatterings in the model run, and $\bar{x}$ is the average contribution each photon or scattering makes to $X$."1166 Iu the case of the direct flux. the stim over η is dropped aud AJ=N.," In the case of the direct flux, the sum over $n$ is dropped and $M = N$."1167" The uncertainty in X is then where 0, is the standard deviation ofc.", The uncertainty in $X$ is then where $\sigma_x$ is the standard deviation of $\bar{x}$.1168" The value of σι, is calculated sine Again. in the case of the direct fiux. the sum over à» is dropped aud A=Ν."," The value of $\sigma_x$ is calculated using Again, in the case of the direct flux, the sum over $n$ is dropped and $M = N$."1169 The uncertainty oy is only au upper lait on the true uncertaintv since this quantity measures both the Moute Carlo noise associated with runing a finite nuuber of photous«nd the iutrinsic variation in the quantity., The uncertainty $\sigma_X$ is only an upper limit on the true uncertainty since this quantity measures both the Monte Carlo noise associated with running a finite number of photons the intrinsic variation in the quantity.1170 For example. the total scattered flux from a nebula can be computed bv directly suiuuinug every photons scattered weight.," For example, the total scattered flux from a nebula can be computed by directly summing every photon's scattered weight."1171" The uncertainty. oy. in this quantity has a contribution. frou the intrinsic variation of the scattered flux across the nebula as well as the Monte Carlo noise,"," The uncertainty, $\sigma_X$, in this quantity has a contribution from the intrinsic variation of the scattered flux across the nebula as well as the Monte Carlo noise."1172 An upper limit which would be closer to the true nucertaimty can be computed by computing the poiut-by- uncertainties iu an image of the nebula., An upper limit which would be closer to the true uncertainty can be computed by computing the point-by-point uncertainties in an image of the nebula.1173 The by-poiut uncertainties can be calculated using where AG.j) is the uuuber of scatterings coutributing to output quantitv iu pixel (6.7). the sum over o and » is only doue for those photous which contribute to the output quantitv in pixel (6.jJ. aud Αν) 1s calculated using eq. 18... 19..," The point-by-point uncertainties can be calculated using where $M(i,j)$ is the number of scatterings contributing to output quantity in pixel $(i,j)$, the sum over $\alpha$ and $n$ is only done for those photons which contribute to the output quantity in pixel $(i,j)$, and $X(i,j)$ is calculated using eq. \ref{eq_idij}, \ref{eq_is_image},"1174 or 21.., or \ref{eq_qij}.1175 Iu the case of the direct surface brightuess miase. the sin over » is dropped aud AZ(.j) is the uuuber of photous coutributiug to pixel (7.7).," In the case of the direct surface brightness image, the sum over $n$ is dropped and $M(i,j)$ is the number of photons contributing to pixel $(i,j)$."1176 The uncertainty in the quantity .X can then be calculated using Caleulatiug the uncertainty with eq., The uncertainty in the quantity $X$ can then be calculated using Calculating the uncertainty with eq.1177 27— will result in a lower value of the mucertainty because the mtrimsic variation of the quantity V(/.7) across the nebula will notbe inelidec in the uucertamty calculation.," \ref{eq_unc_image} will result in a lower value of the uncertainty because the intrinsic variation of the quantity $X(i,j)$ across the nebula will notbe included in the uncertainty calculation."1178 This calculation of the uncertainty is still only an upper Huit as the nucertaimty at a specific point in a nebula will still imelude a contribution from photons having iutrinsically cliffercut, This calculation of the uncertainty is still only an upper limit as the uncertainty at a specific point in a nebula will still include a contribution from photons having intrinsically different1179have been homogeneously provided for the 100 keV-1 MeV band.,have been homogeneously provided for the 100 keV–1 MeV band.1180 The hollow triangle point below the sensitivity curves corresponds to GRB 071010B. localized by Swift and observed at high energy by Suzaku-WAM (??)..," The hollow triangle point below the sensitivity curves corresponds to GRB 071010B, localized by Swift and observed at high energy by Suzaku-WAM \citep{Kira2007GCN6931,Golenetskii2007GCN6879}."1181 This GRB was not detected by MCAL. despite it being unocculted by the Earth and its incoming direction was just 41° off-axis. as expected from its spectral parameters and the MCAL sensitivity curve.," This GRB was not detected by MCAL, despite it being unocculted by the Earth and its incoming direction was just $41^\circ$ off-axis, as expected from its spectral parameters and the MCAL sensitivity curve."1182 Other GRBs in similar conditions are GRB 070704 (2?) and GRB 070724B (???)..," Other GRBs in similar conditions are GRB 070704 \citep{Kira2007GCN6616,Kira2007GCN6634} and GRB 070724B \citep{Feroci2007GCN6668,Endo2007GCN6672,Golenetskii2007GCN6671}."1183" GRB 070724B has been localized by SuperAGILE and was classified as ""No High Energy"" (?).."," GRB 070724B has been localized by SuperAGILE and was classified as ""No High Energy"" \citep{DelMonte2007}."1184 One of the main characteristics of MCAL is the broad energy range extending up to several MeV. To take full advantage of the extended spectral coverage. operation. with the on-board logic active is mandatory. as SRMs provide only a coarse spectral resolution.," One of the main characteristics of MCAL is the broad energy range extending up to several MeV. To take full advantage of the extended spectral coverage, operation with the on-board logic active is mandatory, as SRMs provide only a coarse spectral resolution."1185 Figure 4. shows two count spectra for GRB 080407 (trigger time 2008-04-07 20:42:05 UT). the highest fluence GRB triggered on-board by MCAL in the considered period.," Figure \ref{080407_spectra_SRM_TTE} shows two count spectra for GRB 080407 (trigger time 2008-04-07 20:42:05 UT), the highest fluence GRB triggered on-board by MCAL in the considered period."1186 One spectrum has been obtained from SRM data relative to the upper detection layer (filled triangles). the other is obtained from photon-by-photon data (crosses).," One spectrum has been obtained from SRM data relative to the upper detection layer (filled triangles), the other is obtained from photon-by-photon data (crosses)."1187 Photon-by-photon data obviously allow a much finer spectral reconstruction., Photon-by-photon data obviously allow a much finer spectral reconstruction.1188 Moreover these data are detected i1 the whole MCAL. while SRM spectra are obtained separately for the two detection layers. making the energy reconstructior more difficult at energies above a few MeV where Comptor scattering becomes more important and photons tend to produce multiple hits on different detection layers.," Moreover these data are detected in the whole MCAL, while SRM spectra are obtained separately for the two detection layers, making the energy reconstruction more difficult at energies above a few MeV where Compton scattering becomes more important and photons tend to produce multiple hits on different detection layers."1189 The total number of GRB events detected in photon-by-photon mode ts about twice that detected with SRM in a single detection layer., The total number of GRB events detected in photon-by-photon mode is about twice that detected with SRM in a single detection layer.1190 Figure 5. shows the MCAL effective area for different off-axis angles calculated. from Monte Carlo. simulations., Figure \ref{fig:Aeff} shows the MCAL effective area for different off-axis angles calculated from Monte Carlo simulations.1191 The estimated effective area is about 300cm- at | MeV. Although the effective area increases at higher energies. the limited thickness of the instrument prevents full containment of secondary particles in the pair conversion regime.," The estimated effective area is about $300~\mathrm{cm^2}$ at 1 MeV. Although the effective area increases at higher energies, the limited thickness of the instrument prevents full containment of secondary particles in the pair conversion regime."1192 At low energy. between 330 keV and about | MeV. the effective area is strongly dependent on the energy threshold of each detector’s bar.," At low energy, between 330 keV and about 1 MeV, the effective area is strongly dependent on the energy threshold of each detector's bar."1193 Moreover the error on energy estimation. based on weighing the signals from both photodiodes for each bar. becomes larger as the energy approaches the threshold. so the low energy response requires careful calibration.," Moreover the error on energy estimation, based on weighing the signals from both photodiodes for each bar, becomes larger as the energy approaches the threshold, so the low energy response requires careful calibration."1194 Details on the MCAL effectivearea and energy estimation algorithm are reported in ?.., Details on the MCAL effectivearea and energy estimation algorithm are reported in \citet{Labanti2008}. .1195where V is (he gravitational potential and II is the gas pressure integrated over the disk thickness.,where $V$ is the gravitational potential and $\Pi$ is the gas pressure integrated over the disk thickness.1196 The vertical component of the induction equation takes the form astuho]- zs) )) (2-6) where n is the electric resistivitv., The vertical component of the induction equation takes the form + = ] ) where $\eta$ is the electric resistivity.1197 Note that we ignore the viscous torque in the azimuthal component of the momentum equation (2-5)) because (he viscous timescale is much longer than the gravitational instability timescale., Note that we ignore the viscous torque in the azimuthal component of the momentum equation \ref{azimuth}) ) because the viscous timescale is much longer than the gravitational instability timescale.1198 Also. the azimuthal component of the magnetic field in the disk that arises from the stretching of the poloidal field by differential rotation averages to zero in the vertical integration.," Also, the azimuthal component of the magnetic field in the disk that arises from the stretching of the poloidal field by differential rotation averages to zero in the vertical integration."1199 The vacuum fields above anc below the disk are treated using the Green's [unetion technique (see. e.g.. Shu Li 1997).," The vacuum fields above and below the disk are treated using the Green's function technique (see, e.g., Shu Li 1997)."1200 Since D is current-Iree outside the disk. the magnetic lield can be derived [rom a scalar potential B=VVY.," Since ${\bf B}$ is current-free outside the disk, the magnetic field can be derived from a scalar potential =."

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