ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" This simple expression, which accounts exactly for all results that we have obtained to date with the Meudon PDR model (Le Petit et al."," This simple expression, which accounts exactly for all results that we have obtained to date with the Meudon PDR model (Le Petit et al."3" 2006; Goicoechea Le Bourlot 2007), assumes only that H.O* is produced by reaction of OH* with Hb, is destroyed by dissociative recombination or reaction with Ho, and has reached a steady-state abundance."," 2006; Goicoechea Le Bourlot 2007), assumes only that $_2$ $^+$ is produced by reaction of $^+$ with $_2$, is destroyed by dissociative recombination or reaction with $_2$, and has reached a steady-state abundance."4" For the six absorption components in which the OH* and H;O* column densities are well determined, the resultant abundance ratios range from ~3—15, requiring f(H2) in the range ~0.02—0.08."," For the six absorption components in which the $^+$ and $\rm H_2O^+$ column densities are well determined, the resultant abundance ratios range from $\sim 3 - 15 $ , requiring $f({\rm H}_2)$ in the range $\sim 50.02 - 0.08$."6" Since the largest plausible fractional ionization in a neutral gas cloud is ~1.4x107, corresponding to the complete ionization of carbon, the OH* ions must reside primarily within clouds of low molecular fraction."," Since the largest plausible fractional ionization in a neutral gas cloud is $\sim 1.4 \times 10^{-4},$ corresponding to the complete ionization of carbon, the $^+$ ions must reside primarily within clouds of low molecular fraction."7 The derived molecular fraction is given in Table 2 for each absorption component., The derived molecular fraction is given in Table 2 for each absorption component.8" Our conclusion that OH* resides primarily in clouds that are predominantly atomic — a result obtained previously by Gerin et ((2010) for the sight-line to G10.6—0.4 — is strongly corroborated by the observed distribution of absorbing material in velocity space 22, bottom panel)."," Our conclusion that $^+$ resides primarily in clouds that are predominantly atomic – a result obtained previously by Gerin et (2010) for the sight-line to G10.6–0.4 – is strongly corroborated by the observed distribution of absorbing material in velocity space 2, bottom panel)."9" The distribution of H,O+ (in green) and OH* (blue) is similar to that of atomic hydrogen, as determined by 21 cm observations reported by Fish et ((2003; black), strikinglydissimilar from that of H250 (red), which has been observed by HIFI and reported by Sonnentrucker et ((2010)."," The distribution of $_2$ $^+$ (in green) and $^+$ (blue) is similar to that of atomic hydrogen, as determined by 21 cm observations reported by Fish et (2003; black), strikingly from that of $_2$ O (red), which has been observed by HIFI and reported by Sonnentrucker et (2010)."10" Whereas water and other molecules detected previously toward W49N appear to reside primarily in clouds of relatively narrow velocity width, OH*, H,O* and H are more broadly distributed in velocity space."," Whereas water and other molecules detected previously toward W49N appear to reside primarily in clouds of relatively narrow velocity width, $\rm OH^+$, $\rm H_2O^+$ and H are more broadly distributed in velocity space."11" In Table 2, we present the abundances of OH* and H50* relative to atomic hydrogen in two velocity ranges considered previously by Godard et ((2010)."," In Table 2, we present the abundances of $\rm OH^+$ and $\rm H_2O^+$ relative to atomic hydrogen in two velocity ranges considered previously by Godard et (2010)."12" Here we adopt the estimates of N(H) derived by Godard et ffrom the HI 21 cm spectra of Fish et ((2003) As discussed by Gerin et (2010), the OH* to atomic hydrogen ratio probes the cosmic ray ionization rate, Zu, defined here as the total rate of ionization per hydrogen atom."," Here we adopt the estimates of $N({\rm H})$ derived by Godard et from the HI 21 cm spectra of Fish et (2003) As discussed by Gerin et (2010), the $^+$ to atomic hydrogen ratio probes the cosmic ray ionization rate, $\zeta_{\rm H}$, defined here as the total rate of ionization per hydrogen atom."13" The presence of OH* in clouds of small molecular fraction was anticipated by Liszt (2007), in his investigation of the time-scale for Hz formation in diffuse atomic clouds."," The presence of $^+$ in clouds of small molecular fraction was anticipated by Liszt (2007), in his investigation of the time-scale for $_2$ formation in diffuse atomic clouds."14" In his models, the hydrogen molecular fraction approaches steady state only after 107 yr."," In his models, the hydrogen molecular fraction approaches steady state only after $10^7$ yr."15 His predicted formation rate of OH* at £y23Χ10-16 s! is sufficient to attain (OH*)/ng=5x10% in clouds at nj~50 cm? when the cloud age is in the range 2 to 10 million yr., His predicted formation rate of $^+$ at $\zeta_H=3\times 10^{-16}$ $^{-1}$ is sufficient to attain $n({\rm OH}^+)/n_{H}=5\times 10^{-8}$ in clouds at $n_H\sim 50$ $^{-3}$ when the cloud age is in the range 2 to 10 million yr.16" Defining e as the ratio of theOH* production rate to the cosmic ray ionization rate, assuming that OH* is destroyed by reaction with H» and dissociative recombination at a rate equal"," Defining $\epsilon$ as the ratio of the$^+$ production rate to the cosmic ray ionization rate, assuming that $^+$ is destroyed by reaction with $_2$ and dissociative recombination at a rate equal"17"plane but well away from the bulge, see Table 1) and the number of objects present with K<7.8 in a series of regions of radii 1-10 deg centered around the star (measured population in this zone of the sky), is very small, ~10-9.","plane but well away from the bulge, see Table 1) and the number of objects present with $K<7.8$ in a series of regions of radii 1-10 deg centered around the star (measured population in this zone of the sky), is very small, $\sim 10^{-6}$."18 Thus it is likely that the candidate companion is physically associated with ε Cephei., Thus it is likely that the candidate companion is physically associated with $\epsilon$ Cephei.19" However, astrometry and/or spectroscopy will be needed to confirm this."," However, astrometry and/or spectroscopy will be needed to confirm this."20" Assuming the candidate companion is bound to ε Cephei, we will derive its physical properties based on an evolutionary model."," Assuming the candidate companion is bound to $\epsilon$ Cephei, we will derive its physical properties based on an evolutionary model."21 We will also discuss the consequence of this discovery on the interpretation of near-infrared and far-infrared excesses., We will also discuss the consequence of this discovery on the interpretation of near-infrared and far-infrared excesses.22 An interesting question one could then ask is why this second source has largely remained undetected so far., An interesting question one could then ask is why this second source has largely remained undetected so far.23" According tothe BCAH98 evolutionary model al. 1998),, and following the age estimation in Rheeetal.(2007) the candidate companion would have a mass of ~0.5 Mgun, and a temperature of 3650 K 2)."," According tothe BCAH98 evolutionary model \citep{Baraffe1998}, and following the age estimation in \citet{Rhee2007} the candidate companion would have a mass of $\sim 0.5$ $M_{\rm Sun}$, and a temperature of 3650 K (Table 2)."24 The stellar type of the candidate companion is thus (Tablelikely to be at the transition between late-type K stars and early M stars., The stellar type of the candidate companion is thus likely to be at the transition between late-type K stars and early M stars.25" This result is fairly independent of the age between 200 Myr up to well above 1 Gyr, making this mass determination quite robust even with big error bars (Figure 2))."," This result is fairly independent of the age between 200 Myr up to well above 1 Gyr, making this mass determination quite robust even with big error bars (Figure \ref{baraffe}) )."26" The interferometrically detected near-infrared excess is likely due to the companion, and not hot dust."," The interferometrically detected near-infrared excess is likely due to the companion, and not hot dust."27" However, the candidate companion would only contribute ~5% additional flux at 60 µ."," However, the candidate companion would only contribute $\sim 5\%$ additional flux at 60 $\mu$."28" It thus cannot account for the large excess detected in the[ΠΑΟ beam, which was interpreted as thermal emission from cold dust at a separation of ~62 AU (Rheeetal.2007)."," It thus cannot account for the large excess detected in the beam, which was interpreted as thermal emission from cold dust at a separation of $\sim 62$ AU \citep{Rhee2007}."29". In this picture, the cold dust belt would thus likely be circumbinary which is not unprecedented, see for instance the case of GG Tau (Kristetal.2005)."," In this picture, the cold dust belt would thus likely be circumbinary which is not unprecedented, see for instance the case of GG Tau \citep{Krist2005}."30". However, as mentioned earlier, e Cephei lies away from the galactic bulge but still on the galactic plane (b=+0.4 deg, see Table 1), which raises the possibility of source confusion given the large beam size ofIRAS (~25"" at 60 µ)."," However, as mentioned earlier, $\epsilon$ Cephei lies away from the galactic bulge but still on the galactic plane $b=+0.4$ deg, see Table 1), which raises the possibility of source confusion given the large beam size of $\sim 25\arcsec$ at 60 $\mu$ )."31" To confirm the excess emission, the star was observed with Spitzer/MIPS on 2009 Feb 20 (PI: George "," To confirm the excess emission, the star was observed with Spitzer/MIPS on 2009 Feb 20 (PI: George Rieke)."32The MIPS 70 µ BCD Rieke).(Basic Calibrated Data) image retrieved from the Spitzer Heritage Archive (see, The MIPS 70 $\mu$ BCD (Basic Calibrated Data) image retrieved from the Heritage Archive (see33"In other words, where ooperates on a single residual image, kkeeps a set of residual images, one image per scale size defined.","In other words, where operates on a single residual image, keeps a set of residual images, one image per scale size defined."34" The peak subtraction is performed on all of these images, but only the one subtracted component and its scale size are stored in the ccomponent table."," The peak subtraction is performed on all of these images, but only the one subtracted component and its scale size are stored in the component table."35" The restoration is then an addition of the appropriately scaled, positioned and convolved components subtracted at each iteration on top of the final residual image."," The restoration is then an addition of the appropriately scaled, positioned and convolved components subtracted at each iteration on top of the final residual image."36 We refer to for a technical description of the algorithm., We refer to for a technical description of the algorithm.37" For practical reasons, any implementation of wwill have purelyan iteration limit built in ?)."," For purely practical reasons, any implementation of will have an iteration limit built in ."38. The design of the algorithm is to iteratively find and remove the strongest point sources; the number of iterations is therefore one of the factors that defines how deep wwill go in terms of the flux level., The design of the algorithm is to iteratively find and remove the strongest point sources; the number of iterations is therefore one of the factors that defines how deep will go in terms of the flux level.39" Eventually, noise peaks will start to be cleaned away as well, as the algorithm cannot distinguish them from faint real signals."," Eventually, noise peaks will start to be cleaned away as well, as the algorithm cannot distinguish them from faint real signals."40 The number of components will therefore start to increase dramatically., The number of components will therefore start to increase dramatically.41 This can easily spiral out of control as aapproaches the noise limit and leads to a diverging total flux (?)., This can easily spiral out of control as approaches the noise limit and leads to a diverging total flux .42". All of this illustrates the necessity of imposing a hard limit on the number of iterations, either directly or through a flux threshold."," All of this illustrates the necessity of imposing a hard limit on the number of iterations, either directly or through a flux threshold."43" However, despite its usefulness in placing a practical constraint onCLEAN,, the iteration limit is not without its disadvantages."," However, despite its usefulness in placing a practical constraint on, the iteration limit is not without its disadvantages."44 It is a compromise between cleaning as deeply as possible and avoiding most of the noise., It is a compromise between cleaning as deeply as possible and avoiding most of the noise.45" As mentioned in the introduction, this is a particularly important point for extended sources (such as the THINGS galaxies), which wwill to model with a number of point sources."," As mentioned in the introduction, this is a particularly important point for extended sources (such as the THINGS galaxies), which will attempt to model with a large number of point sources."46" In contrast, practical results show that rremoves attemptlarge-scale structure largebefore finer details 3."," In contrast, practical results show that removes large-scale structure before finer details ."472)mainBodyCitationEnd1963|msclean. This provides a useful advantage over iin most cases: the prior removal of underlying extended emission will reduce the strength of small-scale emission peaks that will remain., This provides a useful advantage over in most cases: the prior removal of underlying extended emission will reduce the strength of small-scale emission peaks that will remain.48" This means that when bbegins to remove the small-scale structure, it will require fewer iterations to do so."," This means that when begins to remove the small-scale structure, it will require fewer iterations to do so."49" The lack of this scale-size advantage in classical mmeans it is required to slowly cut down sources.MSCLEAN,"," The lack of this scale-size advantage in classical means it is required to slowly cut down sources.,"50", with its convergence from large to small scales, does not spend its final cycles slowly removing a large amount of extended emission in small increments."," with its convergence from large to small scales, does not spend its final cycles slowly removing a large amount of extended emission in small increments."51 Classical mmust also use low loop gains (typically 10% or less) to improve the reconstruction of extended emission., Classical must also use low loop gains (typically $10$ or less) to improve the reconstruction of extended emission.52" Using a high loop gain would be more efficient, especially for extended sources, but can easily lead to instabilities(?)."," Using a high loop gain would be more efficient, especially for extended sources, but can easily lead to instabilities."53. Furthermore the gain is one parameter of tthat has a large effect on the final ssolution(??)., Furthermore the gain is one parameter of that has a large effect on the final solution.54. iis much less on the and is able to use much values(?)., is much less dependent on the gain and is able to use much higher values.55". This means that each sscale has the ability to dependentremove a gainmuch larger portion of the flux in highereach individual iteration, again reducing the overall number of iterations required compared toCLEAN."," This means that each scale has the ability to remove a much larger portion of the flux in each individual iteration, again reducing the overall number of iterations required compared to."56. The problem whereby ppoorly models extended emission is further compounded by the interpolation for the missing spacing information., The problem whereby poorly models extended emission is further compounded by the interpolation for the missing spacing information.57" Generally, in interferometric observations, the extremely short or zero spacings, which measure the largest structure on the sky, are missing."," Generally, in interferometric observations, the extremely short or zero spacings, which measure the largest structure on the sky, are missing."58" In other words, the innermost part of the uv--plane is not (well) sampled."," In other words, the innermost part of the -plane is not (well) sampled."59 In these cases the total flux of an source ccontaining structures at scales larger than sampled by the shortest baseline) cannot be recovered., In these cases the total flux of an source containing structures at scales larger than sampled by the shortest baseline) cannot be recovered.60" Together with the strong side-lobes present in the dirty beam and the pedestal of uncleaned flux, this leads to **bowT': the source sits in a region with a negative background."," Together with the strong side-lobes present in the dirty beam and the pedestal of uncleaned flux, this leads to a `bowl': the source sits in a region with a negative background."61 This bbowl will cause skewed noise and flux estimates., This bowl will cause skewed noise and flux estimates.62" The higher efficiency of iin removing extended structures means it can approach the noise limit more easily thanCLEAN,, with the result that the presence of the bbowl is also greatly reduced yielding a noise-like residual background."," The higher efficiency of in removing extended structures means it can approach the noise limit more easily than, with the result that the presence of the bowl is also greatly reduced yielding a noise-like residual background."63" A subtle, but important limitation of llies in the reconstruction of the oor restored image from the final residual image and the ccomponents."," A subtle, but important limitation of lies in the reconstruction of the or restored image from the final residual image and the components."64" The restored image is an addition of two separate flux scales, a residual map with the units and a ccomponent map with unitsbeam."," The restored image is an addition of two separate flux scales, a residual map with the units and a component map with units."65". As the extent of the dirty beam is always larger than that of the best-fitting bbeam, using the bbeam to determine the flux of the residuals will always lead to an overestimate of this flux."," As the extent of the dirty beam is always larger than that of the best-fitting beam, using the beam to determine the flux of the residuals will always lead to an overestimate of this flux."66 As such a correction factor needs, As such a correction factor needs67(2009).,.68. This local BHMF encompasses the range of several estimates of BHMF with different methods (Belletal.Ford2005;Tundoetal.2007;Hopkins 2007a)..," This local BHMF encompasses the range of several estimates of BHMF with different methods \citep*{2003ApJ...585L.117B,2004MNRAS.351..169M,2004MNRAS.354.1020S,692005SSRv..116..523F,2007ApJ...663...53T,2007ApJ...669...45H}."70" We find that the final results are insensitive to the initial conditions at Zmax, because the fraction of local black hole mass accreted at very high redshifts can be neglected."," We find that the final results are insensitive to the initial conditions at $z_{\rm max}$, because the fraction of local black hole mass accreted at very high redshifts can be neglected."71 The results for the evolution of the total BHMFs and AGN BHMFs with redshift z are plotted in Fig., The results for the evolution of the total BHMFs and AGN BHMFs with redshift $z$ are plotted in Fig.72 4 for different values of the model parameters., \ref{fig_bhmf_b} for different values of the model parameters.73" In Fig. 5,,"," In Fig. \ref{fig_dutycyc},"74 the duty cycles 6 of AGNs are plotted as functions of black hole mass Msn at different redshifts z., the duty cycles $\delta$ of AGNs are plotted as functions of black hole mass $M_{\rm bh}$ at different redshifts $z$.75" In this work, the AGNs accreting at >merit are referred as bright AGNs, in which radiative efficiently accretion disks are present."," In this work, the AGNs accreting at $\ge \dot{m}_{\rm crit}$ are referred as bright AGNs, in which radiative efficiently accretion disks are present."76 We plot the radiative efficiency evolving with redshift in Fig. 6.., We plot the radiative efficiency evolving with redshift in Fig. \ref{fig_eta}.77" lcm Our estimates of the lower limits on the Eddington ratios of AGNs show that Amin increases with redshift z, which implies that the mean ratio is higher at redshifts."," 1cm Our estimates of the lower limits on the Eddington ratios of AGNs show that $\lambda_{\rm min}$ increases with redshift $z$, which implies that the mean Eddington ratio is higher at high redshifts."78" At high redshifts, the Eddingtonquasar life timescale is highcomparable with (or even shorter than) the age of the universeΤο at redshift z, and most of the AGNs are therefore still very luminous (i.e., at rates)."," At high redshifts, the quasar life timescale $\tau_{\rm Q}$ is comparable with (or even shorter than) the age of the universe at redshift $z$, and most of the AGNs are therefore still very luminous (i.e., accreting at high rates)."79 The mean Eddington ratios for these AGNs accretingare relativelyhigh higher than those at low redshifts., The mean Eddington ratios for these AGNs are relatively higher than those at low redshifts.80" The estimates of the Eddington ratios for AGNs show that the mean Eddington ratio increases with z (e.g.,McLure&Dunlop2004;Warneretal. 2004),, which is qualitatively consistent with our results."," The estimates of the Eddington ratios for AGNs show that the mean Eddington ratio increases with $z$ \citep*[e.g.,][]{2004MNRAS.352.1390M,2004ApJ...608..136W}, which is qualitatively consistent with our results."81" Unlike most of the previous works (e.g.,Yu&Tremaine2002;Marconietal.2004;Shankar 2004),, in which a single mean Eddington ratio is adopted as a free parameter, we use an Eddington ratio distribution in our calculations."," Unlike most of the previous works \citep*[e.g.,][]{2002MNRAS.335..965Y,2004MNRAS.351..169M,2004MNRAS.354.1020S}, in which a single mean Eddington ratio is adopted as a free parameter, we use an Eddington ratio distribution in our calculations."82" Such a power-law Eddington ratio distribution for AGNs is the black hole model (Silkexpected&Rees1998;byHopkinsself-regulatedetal. 2005a),, which is growthalso supported by the Eddington ratio estimates for AGNs2009)."," Such a power-law Eddington ratio distribution for AGNs is expected by the self-regulated black hole growth model \citep{1998A&A...331L...1S,2005ApJ...630..716H}, , which is also supported by the Eddington ratio estimates for AGNs."83". lcm There are three free parameters, πιαϱ» £j, and Apeak, in our calculations on the evolution of massive black holes."," 1cm There are three free parameters, $\eta_{\rm rad,0}$, $\beta_l$, and $\lambda_{\rm peak}$, in our calculations on the evolution of massive black holes."84 The resultant local BHMF for the AGN relics is sensitive to the value of the peak luminosity of AGNs., The resultant local BHMF for the AGN relics is sensitive to the value of the peak luminosity of AGNs.85" It is found that the measured local BHMF can be well reproduced the BHMF of the AGN relics at z=0 calculated in this bywork, if the three parameters: =0.11, 5;=0.3, and Apeak= 2.5, are adopted (see Fig. 3)). MadoHopkins&Her"," It is found that the measured local BHMF can be well reproduced by the BHMF of the AGN relics at $z=0$ calculated in this work, if the three parameters: $\eta_{\rm rad,0}=0.11$, $\beta_l=0.3$, and $\lambda_{\rm peak}=2.5$ , are adopted (see Fig. \ref{fig_bhmf_a}) )."86"nquist(2009) suggested that £8;c0.3—0.8 based on their self-regulated black hole growth model calculations, and our calculations also provide a useful constraint on the value of 6;."," \citet{2009ApJ...698.1550H} suggested that $\beta_l\simeq 0.3-0.8$ based on their self-regulated black hole growth model calculations, and our calculations also provide a useful constraint on the value of $\beta_l$."87" Our results show that the peak Eddington ratio ofAGNs ~2.5 is required for modeling the local BHMF, which implies that a small fraction ofAGNs are accreting at slightly super-Eddingtonrates."," Our results show that the peak Eddington ratio ofAGNs $\sim 2.5$ is required for modeling the local BHMF, which implies that a small fraction ofAGNs are accreting at slightly super-Eddingtonrates."88" This is consistent with the estimates for different samples of AGNs (e.g.,Warner 2010).. "," This is consistent with the estimates for different samples of AGNs \citep*[e.g.,][]{2004ApJ...608..136W,2009MNRAS.398.1905W,2010ApJ...716L..31A,2010arXiv1006.1342W}. ."89lcm, 1cm90Ceres and Vesta are the largest and most massive members of à vast population of small bodies located between Mars and Jupiter commonly called the asteroid Main Belt.,Ceres and Vesta are the largest and most massive members of a vast population of small bodies located between Mars and Jupiter commonly called the asteroid Main Belt.91 Several numerical models (e.g. Bottke et al. 2005a.2005b::," Several numerical models (e.g. Bottke et al. \cite{Bottke2005a, Bottke2005b};"92 ΟBrien Greenberg 2005:: de Elfaa Brunini 2007)) indicate that the size distribution of the Main Belt asteroids is determined primarily by collisional processes., O'Brien Greenberg \cite{OBrien2005}; de a Brunini \cite{deElia2007}) ) indicate that the size distribution of the Main Belt asteroids is determined primarily by collisional processes.93 In fact. these studies suggest that most of the largest objects (D.z 120 km) have never been disrupted. while many smaller asteroids are byproducts of fragmentation events among the largest bodies.," In fact, these studies suggest that most of the largest objects $D \gtrsim$ 120 km) have never been disrupted, while many smaller asteroids are byproducts of fragmentation events among the largest bodies."94 While Ceres and Vesta have not been targets of catastrophic collisions. they have been exposed to cratering impacts over the age of the Solar System.," While Ceres and Vesta have not been targets of catastrophic collisions, they have been exposed to cratering impacts over the age of the Solar System."95 In fact. the existence of the Vesta family (Binzel Xu 1993)) is clear evidence that this object has undergone large cratering impacts over time.," In fact, the existence of the Vesta family (Binzel Xu \cite{Binzel1993}) ) is clear evidence that this object has undergone large cratering impacts over time."96 Cratering is one of the most important processes that determine the morphology of the surface of a Solar System object., Cratering is one of the most important processes that determine the morphology of the surface of a Solar System object.97 The understanding and quantification of the impactor source population onto an object and the observation of the object surface help for understanding the dynamical and physical history of both the impactor population and the target., The understanding and quantification of the impactor source population onto an object and the observation of the object surface help for understanding the dynamical and physical history of both the impactor population and the target.98 Launched in September 2007. NASA’s Dawn Mission was captured in orbit by Vesta on July 15. 2011. and it should reach the vicinities of Ceres in February 2015.," Launched in September 2007, NASA's Dawn Mission was captured in orbit by Vesta on July 15, 2011, and it should reach the vicinities of Ceres in February 2015."99 The theoretical predictions of producing of craters may be compared with observations of Ceres and Vesta., The theoretical predictions of producing of craters may be compared with observations of Ceres and Vesta.100 This will help. on the one hand. for identifying the souree of craters and. on the other hand. accounting for the geological processes that have acted on the surfaces of those bodies.," This will help, on the one hand, for identifying the source of craters and, on the other hand, accounting for the geological processes that have acted on the surfaces of those bodies."101" Then. it is very mportant to study all the possible sources of crater production on Ceres and Vesta in order to estimate the total crater production and to contrast them with observations,"," Then, it is very important to study all the possible sources of crater production on Ceres and Vesta in order to estimate the total crater production and to contrast them with observations."102 In this paper we evaluate the impactor flux and cratering on Vesta and Ceres due to the collisional and dynamical evolution of the asteroid Main Belt., In this paper we evaluate the impactor flux and cratering on Vesta and Ceres due to the collisional and dynamical evolution of the asteroid Main Belt.103 To do this. we constructed a statistical code based on the collisional model developed by Bottke et al. (2005a))," To do this, we constructed a statistical code based on the collisional model developed by Bottke et al. \cite{Bottke2005a}) )"104 with some dynamical considerations from Bottke et al. (2005b))., with some dynamical considerations from Bottke et al. \cite{Bottke2005b}) ).105 A comparison between our study and data obtained from the Dawn Mission may be relevant for the structure and evolution of the early Solar System., A comparison between our study and data obtained from the Dawn Mission may be relevant for the structure and evolution of the early Solar System.106 Bottke et al. (2005a)), Bottke et al. \cite{Bottke2005a}) )107 developed a collistonal model capable of tracking the evolution of the asteroid Main Belt over the Solar System history., developed a collisional model capable of tracking the evolution of the asteroid Main Belt over the Solar System history.108 At each timestep. this statistical. algorithm calculates the total number of catastrophic collisions between objects residing in different size bins. using parameters such as the mean impact velocity (V). the intrinsic collision probability (Pj). and the impact energy required for dispersal Ορ.," At each timestep, this statistical algorithm calculates the total number of catastrophic collisions between objects residing in different size bins, using parameters such as the mean impact velocity $\langle V \rangle$, the intrinsic collision probability $\langle P_{\text{i}} \rangle$, and the impact energy required for dispersal $Q_{D}$."109 From this. the code computes how many objects are catastrophically fragmented and removed from each size bin. as well as the number of fragments resulting from those collisions. which are distributed i the different bins according to their sizes.," From this, the code computes how many objects are catastrophically fragmented and removed from each size bin, as well as the number of fragments resulting from those collisions, which are distributed in the different bins according to their sizes."110 This model assumes that all breakups occur close to the catastrophic disruption threshold and neglects cratering events. which produce much less ejecta over time than catastrophic disruption events. and highly-energetie catastrophic disruption events. which are relatively uncommon.," This model assumes that all breakups occur close to the catastrophic disruption threshold and neglects cratering events, which produce much less ejecta over time than catastrophic disruption events, and highly-energetic catastrophic disruption events, which are relatively uncommon."111 The algorithm developed by Bottke et al. (2005a)), The algorithm developed by Bottke et al. \cite{Bottke2005a}) )112 includes the effects of an intense period of collisional evolution i1 the early massive Main Belt., includes the effects of an intense period of collisional evolution in the early massive Main Belt.113 Using numerical simulations. the authors found that the net collisional activity in the Mair Belt over its lifetime is the equivalent of ~ 7.5 - 9.5 Gyr of collisional activity in the current Main Belt.," Using numerical simulations, the authors found that the net collisional activity in the Main Belt over its lifetime is the equivalent of $\sim$ 7.5 - 9.5 Gyr of collisional activity in the current Main Belt."114" This ""pseudo-time approximation"" means that the Main Belt population required ~ L5-2 times the degree of comminution than it would have experienced if it were hot initially much more massive.", This “pseudo-time approximation” means that the Main Belt population required $\sim$ 1.5 - 2 times the degree of comminution than it would have experienced if it were not initially much more massive.115 It is worth noting that this model assumes that the collisional history of the Main Belt has been dominated by the same intrinsic collision probabilities and impact velocities as are found in the current Main Belt., It is worth noting that this model assumes that the collisional history of the Main Belt has been dominated by the same intrinsic collision probabilities and impact velocities as are found in the current Main Belt.116 Based on Petit et al. (2001. 2002)).," Based on Petit et al. \cite{Petit2001, Petit2002}) ),"117 Bottke et al. (2005a)), Bottke et al. \cite{Bottke2005a}) )118 consider that the dynamical removal phase of the Main Belt was short and owing to that the high velocity impacts did not play an important role in the collisional history of the Main Belt., consider that the dynamical removal phase of the Main Belt was short and owing to that the high velocity impacts did not play an important role in the collisional history of the Main Belt.119 From this. the collisional model from Bottke et al. (2005a))," From this, the collisional model from Bottke et al. \cite{Bottke2005a}) )"120 uses the current values of (Pj) and (V) throughout the whole simulation., uses the current values of $\langle P_{\text{i}} \rangle$ and $\langle V \rangle$ throughout the whole simulation.121The main difference between most of the IMFs proposed (e.g. Salpeter 1955: Miller Scalo 1979; Kroupa. Tout Gilmore 1993; Chabrier 2003) lies in the relative contribution from stars with masses M.«M..,"The main difference between most of the IMFs proposed (e.g. Salpeter 1955; Miller Scalo 1979; Kroupa, Tout Gilmore 1993; Chabrier 2003) lies in the relative contribution from stars with masses $M< M_\odot$."122 Since these stars have a large M/L ratio. stellar populations born with either IMF feature very similar spectral energy distributions. albeit with a different normalization for a given stellar mass (see e.g. Bruzual Charlot 2003).," Since these stars have a large $M/L$ ratio, stellar populations born with either IMF feature very similar spectral energy distributions, albeit with a different normalization for a given stellar mass (see e.g., Bruzual Charlot 2003)."123 Therefore. a photo-spectroscopic analysis cannot be used reliably to constrain the IMF at the low- end.," Therefore, a photo-spectroscopic analysis cannot be used reliably to constrain the IMF at the low-mass end."124 Instead. we will use the available photometry from our sample and compute the stellar mass content corresponding to either a Salpeter or a Chabrier IMF.," Instead, we will use the available photometry from our sample and compute the stellar mass content corresponding to either a Salpeter or a Chabrier IMF."125 These two mass distributions represent a robust range of possible values between the unphysically high M/L imposed by a simple power law extrapolated to low masses and a more realistic distribution., These two mass distributions represent a robust range of possible values between the unphysically high $M/L$ imposed by a simple power law extrapolated to low masses and a more realistic distribution.126 The age and metallicity distribution can be constrained by a comparison of the photometry with a simple model of star formation., The age and metallicity distribution can be constrained by a comparison of the photometry with a simple model of star formation.127 We assume a 3-parameter model which reduces the description of the stellar populations to a single metallicity (Z.). a formation epoch (frog). and a formation timescale (75)-). so that at any given time the star formation rate is ο)κexp(—Ar/ rs). with Ar2£—7:0&.," We assume a 3-parameter model which reduces the description of the stellar populations to a single metallicity $Z_\star$ ), a formation epoch $t_{\rm FOR}$ ), and a formation timescale $\tau_{\rm128SF}$ ), so that at any given time the star formation rate is $\psi(t)\propto\exp (-\Delta t/\tau_{\rm SF})$ , with $\Delta t=t-t_{\rm129FOR}$."130 Each choice of parameters (Z..fyoR.TS) represents a possible formation scenario. and can be convolved with simple stellar populations (SSP) in order to generate a composite model from which various. photo-spectroscopic observables can be retrieved.," Each choice of parameters $(Z_\star ,t_{\rm FOR},\tau_{\rm SF})$ represents a possible formation scenario, and can be convolved with simple stellar populations (SSP) in order to generate a composite model from which various photo-spectroscopic observables can be retrieved."131 We use the Bruzual Charlot (2003) population synthesis models., We use the Bruzual Charlot (2003) population synthesis models.132 We use the published photometry of the lenses from the CASTLeS group (Rusin et al., We use the published photometry of the lenses from the CASTLeS group (Rusin et al.133 2003) which was obtained from HST/WFPC2+NICMOS images after carefully subtracting the contribution from the sources., 2003) which was obtained from HST/WFPC2+NICMOS images after carefully subtracting the contribution from the sources.134 Each set of measurements correspond to a number of colours (from | to 5) which is used in order to constrain the parameter space described above., Each set of measurements correspond to a number of colours (from $1$ to $5$ ) which is used in order to constrain the parameter space described above.135 We use their radial fits to generate the profile of the stellar component., We use their radial fits to generate the profile of the stellar component.136 Galactic reddening was included in the analysis by using the E(B—V) values from Rusin et al. (, Galactic reddening was included in the analysis by using the $E(B-V)$ values from Rusin et al. (1372003) and applying a dust correction according to the R=3.1 curve of Fitzpatrick (1999).,2003) and applying a dust correction according to the R=3.1 curve of Fitzpatrick (1999).138 The best fit for each lens was obtained using an adaptive grid in the 3-dimensional parameter space that describes all possible star formation histories 1n our model. and using à Metropolis algorithm (see e.g.. Binney et al.," The best fit for each lens was obtained using an adaptive grid in the 3-dimensional parameter space that describes all possible star formation histories in our model, and using a Metropolis algorithm (see e.g., Binney et al."139 1992. or Saha 2003) to find the uncertainties which are quoted with respect to the 5th-95th percentiles confidence interval) throughout the paper.," 1992, or Saha 2003) to find the uncertainties which are quoted with respect to the 5th-95th percentiles confidence interval) throughout the paper."140" The stellar mass content is computed for the best fit. with respect to the light inside the half-light radius (p,)."," The stellar mass content is computed for the best fit, with respect to the light inside the half-light radius $r_e$ )."141" Figure 1. shows the mass profiles (stellar and total) for four galaxies. two with M,,,«10'M.. Gef) and two with M,,,>10'°°-M.. (right)."," Figure \ref{fig:profile} shows the mass profiles (stellar and total) for four galaxies, two with $\Mtot \ll 10^{12}M_\odot$ ) and two with $\Mtot\gtrsim 10^{12}M_\odot$ )."142 The result is striking: the low-mass galaxies have little or no dark matter at all observed radi., The result is striking: the low-mass galaxies have little or no dark matter at all observed radii.143" The high- galaxies have little or no dark matter inside of ~r,. but at large radii they are dominated by dark matter."," The high-mass galaxies have little or no dark matter inside of $r\sim\re$, but at large radii they are dominated by dark matter."144 Here we have a clear indication that massive galaxies have a gradient in their dark-matter fraction., Here we have a clear indication that massive galaxies have a gradient in their dark-matter fraction.145 Rather than presenting mass profiles for all the galaxies in our sample. we will summarize the profiles in two ways: first by comparing stellar and total mass at a chosen radius. and then by quantifying the dark-matter gradient.," Rather than presenting mass profiles for all the galaxies in our sample, we will summarize the profiles in two ways: first by comparing stellar and total mass at a chosen radius, and then by quantifying the dark-matter gradient."146 In Figure 2. and Table |) we show three derived aperture masses: the total mass derived from lensing. the stellar mass derived assuming a Salpeter IMF. and the stellar mass derived assuming a Chabrier IMF.," In Figure \ref{fig:mass} and Table \ref{tab1} we show three derived aperture masses: the total mass derived from lensing, the stellar mass derived assuming a Salpeter IMF, and the stellar mass derived assuming a Chabrier IMF."147 Uncertainties are at confidence., Uncertainties are at confidence.148" The aperture radius in all cases is a quantity we call 754, and it is the largest radius at which the lensing mass is well-constrained."," The aperture radius in all cases is a quantity we call $\rl$, and it is the largest radius at which the lensing mass is well-constrained."149" In general. 7j, represents the radius over which there is lensing information. and is roughly the radius of the outermost image."," In general, $\rl$ represents the radius over which there is lensing information, and is roughly the radius of the outermost image."150 From Figure 2. it is apparent that the dark-matter fraction increases with mass. and the trend is compatible with the observed tilt of the NIR fundamental plane (Mobasher et al.," From Figure \ref{fig:mass} it is apparent that the dark-matter fraction increases with mass, and the trend is compatible with the observed tilt of the NIR fundamental plane (Mobasher et al."151 1999: Ferreras Silk 2000)., 1999; Ferreras Silk 2000).152" Additionally. we see that M, 1s estimated as more than M,,, in a few cases for the Salpeter IMF. but never for the Chabrier IMF: while it would be cavalier to argue"," Additionally, we see that $\Mstel$ is estimated as more than $\Mtot$ in a few cases for the Salpeter IMF, but never for the Chabrier IMF; while it would be cavalier to argue"153Figure 1 also demonstrates that the inclined sources tend to be the most reddened. which indicates that the reddening is primarily associated with dust in the plane of the host ealaxy.,"Figure 1 also demonstrates that the inclined sources tend to be the most reddened, which indicates that the reddening is primarily associated with dust in the plane of the host galaxy."154 Similar correlations have been found in previous studies., Similar correlations have been found in previous studies.155 Cheng. Danese. de Zot (1983) found that the optical colors D-V aud U—D of Sevlert 1 nuclei increase (i.e. become redder) with decreasing axial ratio (i.e.. increasing inclination).," Cheng, Danese, de Zotti (1983) found that the optical colors $-$ V and $-$ B of Seyfert 1 nuclei increase (i.e, become redder) with decreasing axial ratio (i.e., increasing inclination)."156 De Zotti Gaskell (1985) found that the Balmer decrement Io /IL? of the broad lines increases with decreasing axial ratio. and the narrow-line decrement shows a similar. though less significant. behavior.," De Zotti Gaskell (1985) found that the Balmer decrement $\alpha$ $\beta$ of the broad lines increases with decreasing axial ratio, and the narrow-line decrement shows a similar, though less significant, behavior."157 We point out the advantage of using the UV color for this wpe of correlation is (hat it is very sensitive to reddening. since reddening curves tend to be steep in the UV.," We point out the advantage of using the UV color for this type of correlation is that it is very sensitive to reddening, since reddening curves tend to be steep in the UV."158 In Figure 2. we have replotted the UV color against inclination angle for the entire sample. flageing those sources for which the presence or absence of intrinsic UV. absorption is known.," In Figure 2, we have replotted the UV color against inclination angle for the entire sample, flagging those sources for which the presence or absence of intrinsic UV absorption is known."159 The correlation between UV color and inclination is well established in (his sample., The correlation between UV color and inclination is well established in this sample.160 The dispersion in UV colors at low inclinations is due in large part to (he intrinsic dispersion in spectral energy. distributions. since the UV color of even an individual Sevfert can vary significantlv.," The dispersion in UV colors at low inclinations is due in large part to the intrinsic dispersion in spectral energy distributions, since the UV color of even an individual Seyfert can vary significantly."161 For example. based on theUE fluxes of Fairall 9 in Courvoisier Paltani (1992). FUV — NUV varied from —0.3 to —1.0 as it went through a [actor of £30 variation in [flux at 1350 (wilh more negative colors corresponding to larger Hluxes).," For example, based on the fluxes of Fairall 9 in Courvoisier Paltani (1992), FUV $-$ NUV varied from $-$ 0.3 to $-$ 1.0 as it went through a factor of $\sim$ 30 variation in flux at 1350 (with more negative colors corresponding to larger fluxes)."162 Other sources of dispersion al all inelinations could be: 1) different amounts of dust in the lines of sight through the host ealaxies (due to intrinsic variations in dust content or chlumpiness). 2) different recldenine curves (see Crenshaw el al.," Other sources of dispersion at all inclinations could be: 1) different amounts of dust in the lines of sight through the host galaxies (due to intrinsic variations in dust content or clumpiness), 2) different reddening curves (see Crenshaw et al."163 2001b). or 3) additional components of dusty gas that are nol coplaner with the host galaxy. (see 84).," 2001b), or 3) additional components of dusty gas that are not coplaner with the host galaxy (see 4)."164 The use of the 2400 rregion (instead of 2200 A)) for theZUE spectra introduces only a small amount of scatter., The use of the 2400 region (instead of 2200 ) for the spectra introduces only a small amount of scatter.165" From the STIS spectrum of NGC 4151. which has a relatively huge ""little blue bump"" (Crenshaw et al."," From the STIS spectrum of NGC 4151, which has a relatively large “little blue bump"" (Crenshaw et al."166 2001a). we find that the Fe II emission in this region increases FUV—NUV bv only +0.10. whereas the use of the continuum fit at 2400 (ie. i NGC 4151 had no emission bump) decreases FUV—NUV by only —0.09.," 2001a), we find that the Fe II emission in this region increases $-$ NUV by only $+$ 0.10, whereas the use of the continuum fit at 2400 (i.e., if NGC 4151 had no emission bump) decreases $-$ NUV by only $-$ 0.09."167 The Sevlert 1 &alaxies in Figure 1 with intrinsic absorption are distributed thoughout the ull range of inclination angle., The Seyfert 1 galaxies in Figure 1 with intrinsic absorption are distributed thoughout the full range of inclination angle.168 This is not surprising. since many of (hese absorbers are known to be associated with the active nuclei (and not the host galaxies). due to their high outflow velocities. variability. or less (han one covering [actors (Crenshaw et al.," This is not surprising, since many of these absorbers are known to be associated with the active nuclei (and not the host galaxies), due to their high outflow velocities, variability, or less than one covering factors (Crenshaw et al."169 1999)., 1999).170 [lowever. it is interesting that absorption-free Sevlert 1 galaxies are completely lacking al high inclination angles.," However, it is interesting that absorption-free Seyfert 1 galaxies are completely lacking at high inclination angles."171 We suggest (hat (he reason for this is (hat sources in this area of the plot tend to be reddened. and a column of dusty gas which causes even marginally detectable reddening will produce detectable UV absorption lines. unless very highly ionized.," We suggest that the reason for this is that sources in this area of the plot tend to be reddened, and a column of dusty gas which causes even marginally detectable reddening will produce detectable UV absorption lines, unless very highly ionized."172 For example. we have eeneraled a set of models using the photoionization code CLOUDYO0 (Ferland et al.1993) and the form of the ionizing continuum described in Kraemer et al. (," For example, we have generated a set of models using the photoionization code CLOUDY90 (Ferland et al.1998) and the form of the ionizing continuum described in Kraemer et al. ("1732000).,2000).174 We varied the, We varied the175to the DDNOLI moclel (more details can be found in. the Appencix A)).,to the DDN01 model (more details can be found in the Appendix \ref{gaapp}) ).176 Considering that the GA nomenclature can. be misplaced in the astrophysical context. we first present the translation from one field to another.," Considering that the GA nomenclature can be misplaced in the astrophysical context, we first present the translation from one field to another."177" Apercaneler (e.g. disc raclius). corresponcs to the concept ofa ""gene. and aperameler is a “mutation”."," A (e.g. disc radius), corresponds to the concept of a “gene”, and a is a “mutation”."178 X that vields to a possible solution corresponds to a “chromoson, A that yields to a possible solution corresponds to a “chromosome”.179" An ""individual is a5ofulion. that is composed. by one parameters set and two. additional. CX. control variables."," An “individual” is a, that is composed by one parameters set and two additional GA control variables."180" One of these variables is V7. which means the ""adaptation? level."," One of these variables is $\chi^2$, which means the “adaptation” level."181 The other control variable is 9. the genetic operator described in Sect. 3.1.2..," The other control variable is $\Phi$, the genetic operator described in Sect. \ref{sectopers}."182" The term “generation” means “all the individuals"" (or sofulions) present in a given iteration.", The term “generation” means “all the individuals” (or ) present in a given iteration.183 The LLABdisk code uses the same parameters of FitCCPlus. which are: AL. Ryo. 0. Mp and p.," The HABdisk code uses the same parameters of FitCGPlus, which are: $M_{\star}$, $R_D$, $\theta$, $M_D$ and $p$ ."184 On the other hand. we decided to allow τν to be variable.," On the other hand, we decided to allow $T_{rim}$ to be variable."185" Phe stellar parameters d. L, and T,. are adopted from observations (see Sect. 4.2))."," The stellar parameters $d$, $L_{\star}$ and $T_{\star}$, are adopted from observations (see Sect. \ref{sectinputpar}) )."186" Essentially, the GA) method. presented. herein implements à X7 minimisation of the SED— fitting provided bv the DDNOI model."," Essentially, the GA method presented herein implements a $\chi^2$ minimisation of the SED fitting provided by the DDN01 model."187 Phere are three main advantages in using GA for this task: (4) the CX method. potentially browses the whole permitted parameter. space. better avoiding the “traps” of local minima: (ii) the method is not allected by changes in the model: (ui) the Cid implementation does not need. to compute the derivatives of S7. (like ὃνΟρ for example) required. by the usual methods.," There are three main advantages in using GA for this task: (i) the GA method potentially browses the whole permitted parameter space, better avoiding the “traps” of local minima; (ii) the method is not affected by changes in the model; (iii) the GA implementation does not need to compute the derivatives of $\chi^2$ (like $\partial \chi^2 / \partial R_D$ for example) required by the usual methods."188 This fact simplifies the code. ancl minimises computer errors due to gradient. caleulations., This fact simplifies the code and minimises computer errors due to gradient calculations.189" The main structures used to manipulate the data are linked lists containing the solutions (parameters set. the adaptation level. v7. and the genetic operator. ;). expressed by where 9; means the ‘th solution. and 7; is the /th 55, Following Coldberg(1980). the code starts with the construction of the first generation. where all parameters are randomly chosen within an allowed range (for example. 50:Ry<1000 AUD."," The main structures used to manipulate the data are linked lists containing the solutions (parameters set, the adaptation level, $\chi^2_i$, and the genetic operator, $\Phi_i$ ), expressed by where $S_i$ means the $i$ th solution, and $T_i$ is the $i$ th $T_{rim}$ Following \cite{Goldberg89} the code starts with the construction of the first generation, where all parameters are randomly chosen within an allowed range (for example, $50 \leq R_D \leq 1000$ AU)."190 In the present work. the number ofdillerent parameter sets in the first generation is assumed to be 100.," In the present work, the number of different parameter sets in the first generation is assumed to be 100."191 In the next step the evaluation function runs the DDNOI model for cach solution. ancl compares the synthetic SLD withthe observed data to find the X7. using the expression eiven by Pressetal.(1995): where [Nds the number of observed. data points. f°) is the observed ux at wavelength Aj; and ó;; is the calculated Ες for the solution ;.," In the next step the evaluation function runs the DDN01 model for each solution, and compares the synthetic SED withthe observed data to find the $\chi^2$, using the expression given by \cite{Press95}: where $N$ is the number of observed data points, $F_j$ is the observed flux at wavelength $\lambda_j$ and $\phi_{ij}$ is the calculated flux for the solution $S_i$."192 The smallest 47 corresponds to the eoocdness-ol-itting. or gof.," The smallest $\chi^2$ corresponds to the goodness-of-fitting, or $gof$."193 As the evaluation function has been applied to all solutions. the judgementH procedure sorts the listH bv increasingH 2X7. and sets to 9; one of the genetic operators: copy. crossover (also called. recombination). mutation or termination.," As the evaluation function has been applied to all solutions, the judgement procedure sorts the list by increasing $\chi^2$, and sets to $\Phi_i$ one of the genetic operators: copy, crossover (also called recombination), mutation or termination."194 Each @ is attributed to a fraction of the generation following the values suggested. by Koza(1994)... Bentley&Corne(2002) ane references therein.," Each $\Phi$ is attributed to a fraction of the generation following the values suggested by \cite{Koza94}, \cite{Bentley02} and references therein."195 The next generation is constructed by applying the correspondent genetic operators., The next generation is constructed by applying the correspondent genetic operators.196 The copy uses an olitis selection. since the solutions with the smallest 47 are copie to the next generation.," The copy uses an elitist selection, since the solutions with the smallest $\chi^2_i$ are copied to the next generation."197 The crossover operator randomly mixes parameters from two different solutions., The crossover operator randomly mixes parameters from two different solutions.198" For example: MΞdip..B,.Mp.pa-1] and 5,=dip.B.Alou.pe.d can give S,=Ros.60.Mpa.pe.τω]."," For example: $S_a = \left[R_D{}_a, \theta_a, M_D{}_a, p_a, T_a \right]$ and $S_b = \left[R_D{}_b, \theta_b, M_D{}_b, p_b, T_b \right]$ can give $S_c = \left[R_D{}_b, \theta_a, M_D{}_a, p_b, T_a \right]$."199 Mutation reproduces the same original solution. except for one of the parameters that is randomly changed.," Mutation reproduces the same original solution, except for one of the parameters that is randomly changed."200 The method continues to build new generationsuntil the end condition is reached. as illustrated by the schematic view shown in Figure Al. ," The method continues to build new generationsuntil the end condition is reached, as illustrated by the schematic view shown in Figure \ref{stepsGA}. ."201‘Phe distribution of 47 for a sequence of 50 generations in the SED fitting of AB Aur is presented in Figure 4.., The distribution of $\chi^2$ for a sequence of 50 generations in the SED fitting of AB Aur is presented in Figure \ref{figgenerations}..202reprocessing olf the blobs or the periodic reprocessing olf material in the outer disc as the blobs intermittently absorb the X-rays from the central object.,reprocessing off the blobs or the periodic reprocessing off material in the outer disc as the blobs intermittently absorb the X-rays from the central object.203 We have determined that. in velocity. the QPO ranges between the expected. rotational velocity of the outer disc and the overllow impact site (paper 1).," We have determined that, in velocity, the QPO ranges between the expected rotational velocity of the outer disc and the overflow impact site (paper )."204 Although this distribution of ΟΡΟ power is consistent with the proposed mechanism. it is more cdillicult to reconcile the bLIue-shifted bias of power in terms of the overllow mocdel (Fig.," Although this distribution of QPO power is consistent with the proposed mechanism, it is more difficult to reconcile the blue-shifted bias of power in terms of the overflow model (Fig."205 10)., 10).206Thus static stars can stably support magnetic fields.,Thus static stars can stably support magnetic fields.207 Our field is hiddeu iuside tlie star. but it seetus likely that a poloidal component which sticks through the surface of the star can be added without causing auiiustability. at least a component with a sinall enough amplitude.," Our field is hidden inside the star, but it seems likely that a poloidal component which sticks through the surface of the star can be added without causing an instability, at least a component with a small enough amplitude."208 This is because the minimur-euergy state that we have presented forbids any deformations of the magnetized region other than motious aloug the maeuetic surlaces., This is because the minimum-energy state that we have presented forbids any deformations of the magnetized region other than motions along the magnetic surfaces.209 Therefore. adding a weak uet. poloidal flux. which eoes through the surface of the star aud through the center of the star is likely to cause just a small deformation of our equilibrium — oue cannot kill this poloidal component y the motious aloug the magnetic surfaces.," Therefore, adding a weak net poloidal flux which goes through the surface of the star and through the center of the star is likely to cause just a small deformation of our equilibrium – one cannot kill this poloidal component by the motions along the magnetic surfaces."210 Lthank Peter Goldreich. Jeremy Coodiman. Aucrew MacFacdyveu aud Boris Iwhesin for clisceussions.," I thank Peter Goldreich, Jeremy Goodman, Andrew MacFadyen and Boris Khesin for discussions."211 This work was supported by the David aud Lucile Packard founuclation., This work was supported by the David and Lucile Packard foundation.212 Take R= 1.py=6. po=0.," Take $R=1$ ,$\rho _1=6$, $\rho _2=0$."213 Then the gravitational potential is where «. b are constants. Y are the spherical factions.," Then the gravitational potential is where $a$, $b$ are constants, $Y$ are the spherical functions."214 From continuity of the potential aud its derivative across the bouudary r— 1+. we get. to first order in e. where Note that ορ Is a second order quantity — [rom volume conservation. to secoud order in v. To secoud order in e. the continuity of the potentialgives which gives," From continuity of the potential and its derivative across the boundary $r=1+\psi$ , we get, to first order in $\psi$, where Note that $\psi _0$ is a second order quantity – from volume conservation, to second order in $\psi$, To second order in $\psi$ the continuity of the potentialgives which gives"215While substantial progress has been done iu recent vears towards a better description of the formation of low-mass stars. much remains to be understood of their lnassive counterparts.,"While substantial progress has been done in recent years towards a better description of the formation of low-mass stars, much remains to be understood of their massive counterparts."216" Iu fact. several problems hiuder the study of higlianass star formation: massive stars (AL=10 AL.) ave nore distant. interact more strongly with their chviromment. aud have shorter evolution timescales,"," In fact, several problems hinder the study of high-mass star formation: massive stars $M\geq 10~M_\odot$ ) are more distant, interact more strongly with their environment, and have shorter evolution timescales."217 After the protostellar pliase. they reach the ZAMS auc create an iregion in the οποιατοαν medium before the accretion phase is finished.," After the protostellar phase, they reach the ZAMS and create an region in the circumstellar medium before the accretion phase is finished."218 When the star is very vouug (ie. 10? yr). this ionised region is small (ie. €0.1 pe for an O star) with respect to the typical diameter of an rregion associated with a more evolved OB star (1.6. —1 10 pe). and is iuued ultracompact (UC) iregion.," When the star is very young (i.e. $\leq10^{5}$ yr), this ionised region is small (i.e. $\leq0.1$ pc for an O star) with respect to the typical diameter of an region associated with a more evolved OB star (i.e. $\sim$ 1--10 pc), and is named ultracompact (UC) region."219 Caven the strong interaction between carly type stars and their swroundines. it is muüportant to have knowledge of the physical characteristics of their parcutal molecular clouds.," Given the strong interaction between early type stars and their surroundings, it is important to have knowledge of the physical characteristics of their parental molecular clouds."220" With this in ήπια, Churclavell et al. ("," With this in mind, Churchwell et al. ("2211990). Cesaroui et al. (,"1990), Cesaroni et al. ("2221991). and Tofuer et al. (,"1991), and Hofner et al. ("223"2000) observed respectively NIT;. CS, and CO towards a few UC iregions. thus assessing the existence of molecular clips surrounding such UC rregions.","2000) observed respectively $_3$, $^{34}$ S, and $^{17}$ O towards a few UC regions, thus assessing the existence of molecular clumps surrounding such UC regions."224" Thev estimated masses of 107. 104AL... densities of 104 10 7, and diameters of 0.11 pe."," They estimated masses of $10^3$ $10^4~M_\odot$, densities of $10^4$ $10^5$ $^{-3}$, and diameters of 0.4–1 pc."225 In another study. Ohnui ot al (," In another study, Olmi et al. ("2261993) detected. various ον rotational lines iu a limited sample of UC iregious. Which demonstrated the existence of even hotter. deuser cores inside the more extended clumps observed in the CHS lines.,"1993) detected various $_3$ CN rotational lines in a limited sample of UC regions, which demonstrated the existence of even hotter, denser cores inside the more extended clumps observed in the $^{34}$ S lines."227 Notwithstanding these results. a robust temperature cstimate for he aolectlar chuups surrounding UC rregious was still missing.," Notwithstanding these results, a robust temperature estimate for the molecular clumps surrounding UC regions was still missing."228 In fact. on the one hand tracers such as NIL; and CO xovide temperature estinates based on 23 transitions ouly aud hence prone to relatively large uncertainties: on the other. CIT4CN is au excolleut “thermometer” but arises from a region much smaller aud deuser than the 1 pe ehuups seen ii C?!S aud ClO. Hence. the main goal of the present study was to derive a good temperature estimate for the medium density molecular surroundings of UC PYCCIOUS.," In fact, on the one hand tracers such as $_3$ and $^{17}$ O provide temperature estimates based on 2–3 transitions only and hence prone to relatively large uncertainties; on the other, $_3$ CN is an excellent “thermometer” but arises from a region much smaller and denser than the 1 pc clumps seen in $^{34}$ S and $^{17}$ O. Hence, the main goal of the present study was to derive a good temperature estimate for the medium density molecular surroundings of UC regions."229 The sxpecies is especially suitable to our purposes., The species is especially suitable to our purposes.230 This is a svuunetrie-ctop molecule (see Townes Schawlow 1975) with a small dipole momen (p—0.75 Debye. Dubrulle ot al.," This is a symmetric-top molecule (see Townes Schawlow 1975) with a small dipole moment $\mu=0.75$ Debye, Dubrulle et al."231" 1978). which makes thermatlisation easy even at densities as low as LO! 2,"," 1978), which makes thermalisation easy even at densities as low as $^4$ $^{-3}$."232" We thus expect tto be in ""local thermocdvuamical ο (LTE) conditions iu the clamps found by Cesaroni ct al. (", We thus expect to be in “local thermodynamical equilibrium” (LTE) conditions in the clumps found by Cesaroni et al. (2331991) around the UC rregious.,1991) around the UC regions.234 Moreover. the large uumber of trausitious observable in the same bandwidth makes the temperature estimate very accurate.," Moreover, the large number of transitions observable in the same bandwidth makes the temperature estimate very accurate."235 For instance. Berein oet al. (," For instance, Bergin et al. ("2361991) successfully used this method to measure the temperature of dense cores in giaut molecular clouds. deriving temperatures of ~10 EK. Iu Sect.,"1994) successfully used this method to measure the temperature of dense cores in giant molecular clouds, deriving temperatures of $\sim 40$ K. In Sect."237 2 we describe the observations and data reduction procedure. iu Sect.," \ref{sobs} we describe the observations and data reduction procedure, in Sect."238 3. we stuumarise the observational results aud derive the plysical parameters of the chumps. in Sect.," \ref{sres} we summarise the observational results and derive the physical parameters of the clumps, in Sect."239 L we discuss the duplications ofthe results obtained.," \ref{sdisc}240 we discuss the implications of the results obtained."241 The conchisions are draxvu in Sect. 5.., The conclusions are drawn in Sect. \ref{sconc}.242 The data from the IRAM. 30-1 telescope were obtained iu the period from Aueust 21 to 29. 1997.," The data from the IRAM 30-m telescope were obtained in the period from August 24 to 29, 1997."243 The source list is shown in Table 1., The source list is shown in Table 1.244 The velocity of each source listed in Table 1 is taken from previous observations of various molecular transitions. aud it is onlv an indicative value of the real velocity of the eas from which the Hines arise.," The velocity of each source listed in Table 1 is taken from previous observations of various molecular transitions, and it is only an indicative value of the real velocity of the gas from which the lines arise."245 We simultaneously observed the (65). (87)," We simultaneously observed the (6–5), (8–7)"246(cosmologv-independent) LIST Ixev. project. value. discussed earlier.,(cosmology-independent) HST Key project value discussed earlier.247 In this section we present posterior distributions for our SES model parameters inferred. (rom each of the cosmological probes described in Section 3., In this section we present posterior distributions for our SFS model parameters inferred from each of the cosmological probes described in Section 3.248 For ease of presentation we have computed a series of slices’ through the 2-dimensional conditional distribution of the parametersn and yo at given values of the non-standardicity parameter ὃν, For ease of presentation we have computed a series of `slices' through the 2-dimensional conditional distribution of the parameters$n$ and $y_0$ at given values of the non-standardicity parameter $\delta$.249" We adopted uniform priors for à» and. yo over the intervals 1n<2 and O«yoLI respectively, on the theoretical grounds discussed in Section 2."," We adopted uniform priors for $n$ and $y_0$ over the intervals $1 < n < 2$ and $0 < y_0 < 1$ respectively, on the theoretical grounds discussed in Section 2."250 Thus. for these uniform. priors. the mode of the posterior distribution function. for cach ‘slice’ in ὁ was coincident with the maximum of the conditional likelihood function.," Thus, for these uniform priors, the mode of the posterior distribution function, for each `slice' in $\delta$ was coincident with the maximum of the conditional likelihood function."251 For the case of the SNe la data. as noted in Section 3 we computed the posterior distribution after first marginalising over the Llubble constant.," For the case of the SNe Ia data, as noted in Section 3 we computed the posterior distribution after first marginalising over the Hubble constant."252 Lt follows straightforwardly [rom Baves’ theorem that: where {ο}. represents our prior information on the IIubble constant., It follows straightforwardly from Bayes' theorem that: where $p(H_0)$ represents our prior information on the Hubble constant.253 Thus for the SNe la case we computed1 pln.μυ) Following eq. (," Thus for the SNe Ia case we computed $p(n,y_0 | \delta)$ following eq. ("25422). adopting a Gaussian prior for llo with a mean value of 74.2 and a standard deviation of 3.6. in accordance with the results of the LIS Key Project.,"22), adopting a Gaussian prior for $H_0$ with a mean value of 74.2 and a standard deviation of 3.6, in accordance with the results of the HST Key Project."255 We computed. posterior. cüstributions adopting both a regular grid of (n.go) values over the 2-dimensional parameter space and a simple MCXMCC-hbased approach using the Metropolis algorithm.," We computed posterior distributions adopting both a regular grid of $(n,y_0)$ values over the 2-dimensional parameter space and a simple MCMC-based approach using the Metropolis algorithm."256 Both methods gave very similar results. although the latter approach is more practical when exploring more general parameter spaces with larger numbers ofparameters.," Both methods gave very similar results, although the latter approach is more practical when exploring more general parameter spaces with larger numbers ofparameters."257 We will consider such cases further in à subsequent. paper., We will consider such cases further in a subsequent paper.258 ligs., Figs.2593 -5 present contour plots showing the Bayesian crecible regions (evaluated at the GS per cent. 95 per cent and 99 per cent level) for n and yo. computed. for each of our cosmological probes at a series of fixed. values of 8.," \ref{fig3} - \ref{fig5} present contour plots showing the Bayesian credible regions (evaluated at the 68 per cent, 95 per cent and 99 per cent level) for $n$ and $y_0$, computed for each of our cosmological probes at a series of fixed values of $\delta$."260 In each figure we show separately contours for each of the six cosmological probes we have considered. labelled (a) (0) respectivelv.," In each figure we show separately contours for each of the six cosmological probes we have considered, labelled (a) – (f) respectively."261" These probes are: (a) the SNe Ia redshilt- relation: (b) the CALB shift parameter. 2: (c) the CAIB acoustic scale. £,: (d) the BAO distance. parameter. (e) the present-day value of the Hubbleconstant. {ος (f£) the present age of the universe. fy."," These probes are: (a) the SNe Ia redshift-magnitude relation; (b) the CMB shift parameter, $R$; (c) the CMB acoustic scale, $l_a$; (d) the BAO distance parameter, $A$ ; (e) the present-day value of the Hubbleconstant, $H_0$; (f) the present age of the universe, $t_0$."262 Fig., Fig.263 3. shows results for &=0.7., \ref{fig3} shows results for $\delta = -0.7$.264 For larger (i.e. less negative) values οἱ 8 the posterior. distributions for most of the probes were qualitatively similar: significantly. however. the predicted value of the shift parameter was such that no credible region for the SES mocdel parameters was found at the 99 per cent level.," For larger (i.e. less negative) values of $\delta$ the posterior distributions for most of the probes were qualitatively similar; significantly, however, the predicted value of the shift parameter was such that no credible region for the SFS model parameters was found at the 99 per cent level."265 We return to this point below., We return to this point below.266 One can clearly see from Fig., One can clearly see from Fig.267 3. that there is no part of the (n.go) plane where the credible regions for the six cosmological probes overlap. for this value of a.," \ref{fig3} that there is no part of the $(n,y_0)$ plane where the credible regions for the six cosmological probes overlap, for this value of $\delta$."268 There is substantial overlap between the SNe la and BAO contours: this is not surprising given that both probes are sensitive to the £(z) function over a similar range of recdshilts., There is substantial overlap between the SNe Ia and BAO contours; this is not surprising given that both probes are sensitive to the $E(z)$ function over a similar range of redshifts.269 The age of the universe constraint (£) is rather weak. rellecting the large uncertainty on the observed. value. and only a small region of the (n.go) plane. on the upper left of Fig. (," The age of the universe constraint (f) is rather weak, reflecting the large uncertainty on the observed value, and only a small region of the $(n,y_0)$ plane, on the upper left of Fig. \ref{fig3}( ("2700. is excluded: at the 95 per cent. level: these parameter values are already strongly excluded by all other probes.,"f), is excluded at the 95 per cent level; these parameter values are already strongly excluded by all other probes."271 In Fig. 3((, In Fig. \ref{fig3}( (272b) we have magnified the shift. parameter contours for greater clarity.,b) we have magnified the shift parameter contours for greater clarity.273 Note. however. that the münimum X value for the shift parameter in this plot is already 21.35. (corresponding to a predicted: value. of R=1.641) which is unacceptably laree ic. the likelihood function (and hence the posterior probability) for the SE: model parameters is everywhere vanishinglv small for the shift parameter at this value of 0.," Note, however, that the minimum $\chi^2$ value for the shift parameter in this plot is already 21.35 (corresponding to a predicted value of $R=1.641$ ) which is unacceptably large – i.e. the likelihood function (and hence the posterior probability) for the SFS model parameters is everywhere vanishingly small for the shift parameter at this value of $\delta$."274 Similar behaviour was observed for larger values of 8: indeed the minimum X7 value becomes progressively higher as 9 increases., Similar behaviour was observed for larger values of $\delta$; indeed the minimum $\chi^2$ value becomes progressively higher as $\delta$ increases.275 Hence we do not show contour plots for 0ο0.7., Hence we do not show contour plots for $\delta > -0.7$.276 ]t is interesting to note from panels (b) and (c) in Fig., It is interesting to note from panels (b) and (c) in Fig.277" 3 that the two CALB constraints £ and /, produce credible regions which do not in fact show overlap at the 99 per cent level.", \ref{fig3} that the two CMB constraints $R$ and $l_a$ produce credible regions which do not in fact show overlap at the 99 per cent level.278 Εις illustrates the importance of the point mace by Wang and Mukherjee. as noted earlier. that one should use CIB probes in order to better constrain (or indeed. as ds the case here. to reject) a given model. since these probes are sensitive to the model parameters in. cillerent wavs.," This illustrates the importance of the point made by Wang and Mukherjee, as noted earlier, that one should use CMB probes in order to better constrain (or indeed, as is the case here, to reject) a given model, since these probes are sensitive to the model parameters in different ways."279 Moreover we also see that the credible regions for /? ancl { do not share a common overlap with any of the other four probes either., Moreover we also see that the credible regions for $R$ and $l_a$ do not share a common overlap with any of the other four probes either.280 Hence a fit to the SES model parameters is strongly. excluded for this value of 9., Hence a fit to the SFS model parameters is strongly excluded for this value of $\delta$.281 lies., Figs.282 4 and 5. present credible regions for two further values of 9. in order to illustrate the pattern of behaviour exhibited by the various probes as 9 decreases.," \ref{fig4} and \ref{fig5} present credible regions for two further values of $\delta$, in order to illustrate the pattern of behaviour exhibited by the various probes as $\delta$ decreases."283 Firstly Fie., Firstly Fig.284 shows results for à=., \ref{fig4} shows results for $\delta=-1$.285 We can see that. as before. there appears to be overlap between the credible regions for SNe. BAO distance parameter. Hubble constant and age of the universe: indeed the contours for these probes have shifted only slightly [rom their position in Fig. 3..," We can see that, as before, there appears to be overlap between the credible regions for SNe, BAO distance parameter, Hubble constant and age of the universe; indeed the contours for these probes have shifted only slightly from their position in Fig. \ref{fig3}."286 However all four show no overlap at the 99 per cent level with either of the CAB probes. which in turn. continue to show no overlap with each other.," However all four show no overlap at the 99 per cent level with either of the CMB probes, which in turn continue to show no overlap with each other."287 Finally. Fig.," Finally, Fig."288 5. shows the credible regions for à=Ia, \ref{fig5} shows the credible regions for $\delta=-1.5$.289 llere we can see that the contours follow more or less the same shapes as in the previous figures., Here we can see that the contours follow more or less the same shapes as in the previous figures.290" There is still. no overlap between A and £,. and neither CALB probe overlaps with any of the other probes. again at the 99 per cent level."," There is still no overlap between $R$ and $l_a$ , and neither CMB probe overlaps with any of the other probes, again at the 99 per cent level."291 Note. moreover. that while the general appearance of the credible regions is similar to Fig. 4..," Note, moreover, that while the general appearance of the credible regions is similar to Fig. \ref{fig4},"292" the contours for the acoustic scale. /,. in Fie. 5(("," the contours for the acoustic scale, $l_a$, in Fig. \ref{fig5}( ("293e) have shifted. slightly downwards and appear to be approaching the lower limit of yo.,c) have shifted slightly downwards and appear to be approaching the lower limit of $y_0$.294 As 9 ds decreased further this trend continues and hence no fit is obtained., As $\delta$ is decreased further this trend continues and hence no fit is obtained.295 To emphasize that indeed the contours display no overlap with one another. we show in Fig.," To emphasize that indeed the contours display no overlap with one another, we show in Fig."296" 6. the most important contours of SNe Ia. CMD shift. parameter. R. CAB acoustic scale. /, and BAO distance parameter superimposed. for values of 8. previously considered in bigs."," \ref{fig6} the most important contours of SNe Ia, CMB shift parameter, $R$ , CMB acoustic scale, $l_a$ and BAO distance parameter superimposed for values of $\delta$ previously considered in Figs."297 3 - 5. One can see clearly in these figures that while the SNe Ia data are consistent with an SES occurring in the very near future. asshown by Dabrowskietal. (2007).. the same SES parameters would not give a fit to the CMD data.," \ref{fig3} - \ref{fig5}.. One can see clearly in these figures that while the SNe Ia data are consistent with an SFS occurring in the very near future, asshown by \citet{b9}, , the same SFS parameters would not give a fit to the CMB data."298 Note that for the purpose of straightforward illustration, Note that for the purpose of straightforward illustration299with those of the steady state solution of Atovan&Aharonian(1996).,with those of the steady state solution of \citet{aa96}.300. Secondly. we show the spectral evolution of the Crab Nebula in our model with the use of the determined parameters.," Secondly, we show the spectral evolution of the Crab Nebula in our model with the use of the determined parameters."301 Through the evolutions of the magnetic field aud the particle distribution. we explain how the behavior of the spectral evolution can be understood.," Through the evolutions of the magnetic field and the particle distribution, we explain how the behavior of the spectral evolution can be understood."302 We also show that our spectral evolution model is in a reasonably g00d agreement with the observations of the racio/optical flux decreases., We also show that our spectral evolution model is in a reasonably good agreement with the observations of the radio/optical flux decreases.303 Thirdly. we give a simple argument to see the dependences on the fraction parameter 7 of the spectral evolution.," Thirdly, we give a simple argument to see the dependences on the fraction parameter $\eta$ of the spectral evolution."304 Dased on the general properties of PWNe in (his simple argument. we can apply (this to other PWNe in future works.," Based on the general properties of PWNe in this simple argument, we can apply this to other PWNe in future works."305 Finally. we discuss about the fitted parameters other than the fraction parameter 5. which characterize (he injection spectrum (equation (4))).," Finally, we discuss about the fitted parameters other than the fraction parameter $\eta$, which characterize the injection spectrum (equation \ref{eq4}) ))."306 The Crab pulsar has the period 3.31x10.7s. its time derivative 4.21x10.Ms-s! and braking index 2.51.," The Crab pulsar has the period $3.31 \times 10^{-2}\rm s$, its time derivative $4.21 \times 10^{-13} \rm {s} \cdot \rm {s}^{-1}$ and braking index 2.51."307 The progenitor supernova is SNI054. which means (he age of the Crab Nebula /44;7950vr.," The progenitor supernova is SN1054, which means the age of the Crab Nebula $t_{\rm age} \sim 950\rm yr$."308 Because all the necessary pulsar parameters are known. the evolution of the spin-down power in equation (2)) is fixed. as 7)~TOON and Ly—3.4xI0eres-s.!.," Because all the necessary pulsar parameters are known, the evolution of the spin-down power in equation \ref{eq2}) ) is fixed, as $\tau_0 \sim 700 \rm yr$ and $L_0 = 3.4 \times 10^{39} \rm ergs \cdot s^{-1}$."309 The distance to the Crab Nebula 2kpe is used to convert the luminosity into the isotropic flux., The distance to the Crab Nebula $2\rm kpc$ is used to convert the luminosity into the isotropic flux.310 The Crab svnchrotron Nebula is roughly an elliptical shape with a major axis of 4.4pc¢ and a minor axis of 2.9pc., The Crab synchrotron Nebula is roughly an elliptical shape with a major axis of $4.4\rm pc$ and a minor axis of $2.9\rm pc$.311 Here. we regardthat the Crab Nebula is a sphere of the diameter ~3.5pc.," Here, we regardthat the Crab Nebula is a sphere of the diameter $\sim 3.5\rm pc$."312 Combining with fase950vr. the constant expansion velocity becomes CewvN~I800km/s. which is close to the observed expansion velocity of the Crab Nebula.," Combining with $t_{\rm age} \sim 950\rm yr$, the constant expansion velocity becomes $v_{\rm PWN} \sim 1800 \rm km/s$, which is close to the observed expansion velocity of the Crab Nebula."313 Fieure 1. shows calculated current spectrum of the Crab. Nebulawith the current observational data., Figure \ref{f1} shows calculated current spectrum of the Crab Nebulawith the current observational data.314 The adopted parameters are shown in Table 1.., The adopted parameters are shown in Table \ref{tbl-1}. .315 As seen in Figure 1.. the," As seen in Figure \ref{f1}, , the"316a function of ther D. R color.,a function of their B – R color.317 Note as the broad line ACN are relatively well separated frou the narrow liue ACN in the diagram. althoueh the scatter in both BR and (S-ID/(S|ID) is lavee for both class of ACN (also see Table 0).," Note as the broad line AGN are relatively well separated from the narrow line AGN in the diagram, although the scatter in both B – R and (S-H)/(S+H) is large for both class of AGN (also see Table 1)."318 Both (S-ID/(S|ID) and B R of broad ine AGN are different (at the ~360 level) from that o[narrow line ACN. which. «on average. have a lower (ΕΠ)|IT). aud are therefore likely to be more N-rayv absorbed. and an higher Bo OR. and are therefore subjeced to a greater extinction. (," Both (S-H)/(S+H) and B – R of broad line AGN are different (at the $\sim3\sigma$ level) from that of narrow line AGN, which, on average, have a lower (S-H)/(S+H), and are therefore likely to be more X-ray absorbed, and an higher B – R, and are therefore subjected to a greater extinction. ("319S-ID/(S1ID) is plotte Las a function of the redshift iu figure. 3 for the 53 identified sources detected far from the berilliun strougback supporting the MECS window.,S-H)/(S+H) is plotted as a function of the redshift in figure 3 for the 53 identified sources detected far from the berillium strongback supporting the MECS window.320 The dotted lines 1Cpresen the expectation of unabsorbed power law with ag(ht and 0.8., The dotted lines represent the expectation of unabsorbed power law with $\alpha_E=0.4$ and 0.8.321" The dashed lines represeut the expectations of a power law absorbed by coluuus of 5\391077. gs107"" and 5«on107 57 respectively.⋅ iu. the source frame."," The dashed lines represent the expectations of a power law absorbed by columns of $5\times10^{22}$, $10^{23}$ and $5\times10^{23}$ $^{-2}$ respectively, in the source frame."322 Note that fhe softuess ratios of constai column density models stronelv iicreases with the redslüft., Note that the softness ratios of constant column density models strongly increases with the redshift.323 Most of the 1marrow Li16 AGN have (S-ID/(S|TD) inconsistent with that expected from a power law model with agλα , Most of the narrow line AGN have (S-H)/(S+H) inconsistent with that expected from a power law model with $\alpha_E=0.4$ .324Absorbing columns. of the order of 1tjo0Jac7507 »C. are inost Like.‘ly implied.," Absorbing columns, of the order of $10^{22.5-23.5}$ $^{-2}$, are most likely implied."325 Note also tha sole of ie broad line ACN have (GS-ID/(S|IT) iuconsiscut with tha expected for απ ασL8 power law. iu particular at lieh redshif.," Note also that some of the broad line AGN have (S-H)/(S+H) inconsistent with that expected for a $\alpha_E=0.8$ power law, in particular at high redshift."326 The (S-ID/(SID) of the 2 broad litιο ACUNS is nuugiually. auticorrelated with z (Spouiuui ruik correlation cocfiicent of -0.361 for 22 degrees of freedom. corresponding to a probability of 925433.," The (S-H)/(S+H) of the 24 broad line AGNs is marginally anticorrelated with z (Spearman rank correlation coefficent of -0.364 for 22 degrees of freedom, corresponding to a probability of )."327 The nuujor of sources ds rot large enough ο reach a definite conclusion. but it is interesting to note that this correlation goes iu the opposite lirection than expectec.," The number of sources is not large enough to reach a definite conclusion, but it is interesting to note that this correlation goes in the opposite direction than expected."328 In fact. the ratio of the optical deth iu the optical baud. due to dus extinction. to theut in the Nav baid. clue to ohotoeectric absorption. should scale as (L1:," In fact, the ratio of the optical depth in the optical band, due to dust extinction, to that in the X-ray band, due to photoelectric absorption, should scale as $(1+z)^4$."329 Iliehy N-ray obscured broad line blue continui quasar can exist only if their dust to gas ratio or their dust composition strougly differs from the Galactic oue (also see Maiolimo. this mcetiic).," Highly X-ray obscured broad line blue continuum quasar can exist only if their dust to gas ratio or their dust composition strongly differs from the Galactic one (also see Maiolino, this meeting)."330 Similar results have been receutlv found iu ASCA samples w Akbuuna ct al. (, Similar results have been recently found in ASCA samples by Akiyama et al. (3311999) aand Della Ceca et al. (,1999) and Della Ceca et al. (332this mecting).,this meeting).333 NADENewton axd Chaney‘a follow-up observation may easily. confirm or disregard a significant absorbing column in hese ligh z broad line quasars., XMM-Newton and Chandra follow-up observation may easily confirm or disregard a significant absorbing column in these high z broad line quasars.334 Figure tL shows the hard N-rax (5-10 keV) to optical (R baud) fux ratio as a function ofthe N-rav flux for the idetified TELLAS sources and a sample of relatively bright. nearby ACN observed by BeppoSAN (Sevfert 1 ealaxies. Sevfert 2 galaxies. PG quasars with z<0.1).," Figure 4 shows the hard X-ray (5-10 keV) to optical (R band) flux ratio as a function of the X-ray flux for the identified HELLAS sources and a sample of relatively bright, nearby AGN observed by BeppoSAX (Seyfert 1 galaxies, Seyfert 2 galaxies, PG quasars with $<$ 0.4)."335 The N-rav to optical ratio of the IIELLAS sources is similar to that of the N-rav brightest objects in the local universe (with the exception of ταν selected blazars. like the NBL. which have higher N-ax to optical ratio. but also a relatively strong radio elwission).," The X-ray to optical ratio of the HELLAS sources is similar to that of the X-ray brightest objects in the local universe (with the exception of X-ray selected blazars, like the HBL, which have higher X-ray to optical ratio, but also a relatively strong radio emission)."336 While supporting the robustuess of our identifications. this sugeess tha roughly oue third of the hard N-xav. background is due to sources similar to localSevferts and quasars.," While supporting the robustness of our identifications, this suggests that roughly one third of the hard X-ray background is due to sources similar to localSeyferts and quasars."337population of discrete sources existing below the flux Limit of current surveys.,population of discrete sources existing below the flux limit of current surveys.338 This issue was further examined. by Singalctal.(2010)., This issue was further examined by \citet{Singal10}.339". Taking into account that a class of low Hux sources must extend to ~ 10""μον (at L4Cllz). they concluded that this emission could primarily be coming from ordinary star-forming galaxies at 2 > Lif the radio to far-intrared observed Hux ratio increases with recshilt."," Taking into account that a class of low flux sources must extend to $\sim$ $10^{-2}$$\mu$ Jy (at $1.4\,$ GHz), they concluded that this emission could primarily be coming from ordinary star-forming galaxies at $z$ $>$ 1 if the radio to far-infrared observed flux ratio increases with redshift."340 3efore looking for radical causes of this emission. it is worth reexamüning the observed radio source data to sce if the ARCADE 2 result really does. cliffer from. what. is expected.," Before looking for radical causes of this emission, it is worth reexamining the observed radio source data to see if the ARCADE 2 result really does differ from what is expected."341 To do this we derive new estimates of the source-integrated CRB at. various frequencies and. derive. formal error estimates for each., To do this we derive new estimates of the source-integrated CRB at various frequencies and derive formal error estimates for each.342 In Section 2. we describe the source count cata used. together with our procedure and results for fitting the observed radio data.," In Section \ref{sec:method} we describe the source count data used, together with our procedure and results for fitting the observed radio data."343 In Section 3. we present our estimates for the background sky temperature contributions and the analvsis of the uncertainties associated with these estimates., In Section \ref{sec:temp} we present our estimates for the background sky temperature contributions and the analysis of the uncertainties associated with these estimates.344 La Section 4. we compare our results to those obtained bv the ARCADE 2 and PRIS collaborations., In Section \ref{sec:discussion} we compare our results to those obtained by the ARCADE 2 and TRIS collaborations.345 Radio source counts at lower frequencies have been available since the 1960s., Radio source counts at lower frequencies have been available since the 1960s.346 There are many compilations of radio source counts available. particularly in the last decade (e.g. Fomalontetal.2002:Bone2003:Hopkinsal..2003:Prandonietal.. 2006)).," There are many compilations of radio source counts available, particularly in the last decade (e.g. \citealp{Fomalont02, Bondi03, Hopkins03, Prandoni06}) )."347 More recently deep continuum surveys at. higher frequencies have become available. and with the use of newer technologies. have cramatically increased the amount and. quality of data.," More recently deep continuum surveys at higher frequencies have become available, and with the use of newer technologies, have dramatically increased the amount and quality of data."348 The cata used in this paper are from continuum surveys carried out from 1979 to 2009 (see De Zotti et al., The data used in this paper are from continuum surveys carried out from 1979 to 2009 (see De Zotti et al.349 2009. Sirothia et al.," 2009, Sirothia et al."350 2009)., 2009).351 We used source count distributions from 150 MllIz to S400 Mllz. with the individual frequencies covered. being vo = 150 MIIz. 325 MlIz. 408 MlIz. 610 MllIz. 1.43 Hz. 4.8 Cillz and S.A llIz.," We used source count distributions from 150 MHz to 8400 MHz, with the individual frequencies covered being $\nu$ = $150\,$ MHz, $325\,$ MHz, $408\,$ MHz, $610\,$ MHz, $1.4\,$ GHz, $4.8\,$ GHz and $8.4\,$ GHz."352 References for all number counts used can be found in Table 1.., References for all number counts used can be found in Table \ref{tbl:references}.353 For fitting the source count data we opted. to use a fifth order polvnomial., For fitting the source count data we opted to use a fifth order polynomial.354 X third. order. polynomial was used in source count fitting by Ixatgertetal.(1988). ancl a sixth order polvnomial fit to the 1.4 CGllz data was used hy llopkinsetal.(2003).. while Ciervasietal.(2008)— used simple power-Iaw fitting.," A third order polynomial was used in source count fitting by \citet{Katgert88} and a sixth order polynomial fit to the 1.4 GHz data was used by \citet{Hopkins03}, while \citet{Gervasi08} used simple power-law fitting."355 Polvnomial fits are simpler than some other choices of function. but still allow for fitting of different features in the data. such as the upturn at the low lux end seen at some of the frequencies (where we note hat an additional sub-miJdw peak could make a substantial contribution to the background).," Polynomial fits are simpler than some other choices of function, but still allow for fitting of different features in the data, such as the upturn at the low flux end seen at some of the frequencies $($ where we note that an additional sub-mJy peak could make a substantial contribution to the $)$."356 We chose a filth order xilvnomial as it is high enough order to account Lor the eatures seen in the 1.4 Gllz data.," We chose a fifth order polynomial as it is high enough order to account for the features seen in the $1.4\,$ GHz data."357 Going to higher orders creates unneccesary extra. parameters while not improving he 247 bv a significant> amount., Going to higher orders creates unneccesary extra parameters while not improving the $\chi^2$ by a significant amount.358 Our empirical [its are xerformed on the Euclidean-normalized counts. Le. iOS)ST(ΑΝ dS). with S being the Dux density in Jv. using the polynomial with parameters The fitting is. initially performed. using ai Y minimization routine.," Our empirical fits are performed on the Euclidean-normalized counts, i.e. $F(S)=S\textsuperscript{2.5}(dN/dS)$ , with $S$ being the flux density in Jy, using the polynomial with parameters The fitting is initially performed using a $\chi^2$ minimization routine."359 The  minima are then used as starting points in à Monte Carlo Markov Chain. or SICALC approach (Lewis&Dridle.2002).. which is used to refine he fits and obtain estimates of uncertainty.," The $\chi^2$ minima are then used as starting points in a Monte Carlo Markov Chain, or MCMC approach \citep{Lewis02}, which is used to refine the fits and obtain estimates of uncertainty."360 More details on he MCMC method can be found in section 3.2.., More details on the MCMC method can be found in section \ref{sec:mcmc}.361 The best it values for all the parameters at. cach of the frequency mands can be found in Table 2 along with X7 values for each it., The best fit values for all the parameters at each of the frequency bands can be found in Table \ref{tbl:chi} along with $\chi^2$ values for each fit.362 The data and the best fit lines are plotted in Fig. 1..," The data and the best fit lines are plotted in Fig. \ref{fig:best_fit},"363 which shows the Euclidean normalized data. as well as the 57 normalized results.," which shows the Euclidean normalized data, as well as the $S^2$ normalized results."364 Phese S7(LN/d8) (surface brightness scr logarithmic interval in flux density) plots are included o show where the peak contributions to the background arises., These $S^2(dN/dS)$ (surface brightness per logarithmic interval in flux density) plots are included to show where the peak contributions to the background arises.365 The right-hand panels in Fig., The right-hand panels in Fig.366 1. show that the bulk of he background. comes from relatively bright radio sources. with S ~ I Jv at the lowest frequencies to tens of my at the highest. frequencies.," \ref{fig:best_fit}367 show that the bulk of the background comes from relatively bright radio sources, with $S$ $\sim$ 1 Jy at the lowest frequencies to tens of mJy at the highest frequencies."368 But there is a significant. ancl still poorly characterized. contribution from much fainter SOULCCS.," But there is a significant, and still poorly characterized, contribution from much fainter sources."369 ‘Table 2 shows that the 472 values of the fits are generally good. with all but one of the reduced x72 values being below 2.," Table \ref{tbl:chi} shows that the $\chi^2$ values of the fits are generally good, with all but one of the reduced $\chi^2$ values being below 2."370 The exception is for the L4 ClLz data set. with a X7 of over 20 per degree of freedom.," The exception is for the $1.4\,$ GHz data set, with a $\chi^2$ of over 20 per degree of freedom."371 To obtain anything like a reasonable yo we would have to increase the errors by a [actor of four., To obtain anything like a reasonable $\chi^2$ we would have to increase the errors by a factor of four.372 Lt is worrisome that the 1.4 CllIz compilation is the one with the most available data.," It is worrisome that the $1.4\,$ GHz compilation is the one with the most available data."373 As can be seen in the plot. there are many data points that are inconsistent with each other. even with the relatively large error bars.," As can be seen in the plot, there are many data points that are inconsistent with each other, even with the relatively large error bars."374 Vhere are clearly systematic dillerences between different surveys at 14 GHz. particularly at the faint end.," There are clearly systematic differences between different surveys at $1.4\,$ GHz, particularly at the faint end."375 La the gJv range it is dillicult to obtain reliable counts. as this range is close to the natural confusion limit of most racio surveys (Condon&Mitchell.1984:Windhorstetal. 1985)) and hence the level of incompleteness may be incorrectly estimated in some surveys.," In the $\mu$ Jy range it is difficult to obtain reliable counts, as this range is close to the natural confusion limit of most radio surveys \citealp{Condon84,Windhorst85}) ) and hence the level of incompleteness may be incorrectly estimated in some surveys."376 Moreover. at the bright end there are significant and. systematic sources of error introduced when attempting to correct for source extension and surface brightness limitations (sce discussion in Singaletal.. 2010)).," Moreover, at the bright end there are significant and systematic sources of error introduced when attempting to correct for source extension and surface brightness limitations (see discussion in \citealp{Singal10}) )."377 In addition to these effects. sampling variance (enhanced by source clustering) can lead to dilferences in counts [or small fieles.," In addition to these effects, sampling variance (enhanced by source clustering) can lead to differences in counts for small fields."378 All of these svstematic ellects make it. eüllicult to assess robustly the uncertainties in the derived. CRB. as we discuss in the next section.," All of these systematic effects make it difficult to assess robustly the uncertainties in the derived CRB, as we discuss in the next section."379 We integrate best-fit polynomials to obtain the contribution from the sources to the sky brightness., We integrate best-fit polynomials to obtain the contribution from the sources to the sky brightness.380 To do this we integrate the function S(dN/dS) for cach data set only in the range where data are available., To do this we integrate the function $S(dN/dS)$ for each data set only in the range where data are available.381 We make this conservative choice to avoid extrapolating at the very low and. high llux density ends., We make this conservative choice to avoid extrapolating at the very low and high flux density ends.382 Beeause of this our estimates of the sky brightness should be seen as lower limits., Because of this our estimates of the sky brightness should be seen as lower limits.383 Thus to estimate, Thus to estimate38430 aresec the iudividual coumponcuts (or subsystems with separatious below 10 arcsec} could be observed as sinele stars. again avoiding signal distortion from the IFOV edges.,"30 arcsec the individual components (or subsystems with separations below 10 arcsec) could be observed as single stars, again avoiding signal distortion from the IFOV edges."385 ILowever. syvsteis with intermediate separatious (210 to 30 arcsec) could not be observed without some adverse effects of the TFOV edees;," However, systems with intermediate separations $\simeq 10$ to 30 arcsec) could not be observed without some adverse effects of the IFOV edges."386 Tn order to allow at least sole useful astrometric iuformation to be extracted for such systems. cach component (or subsystem) received a separate poutine.," In order to allow at least some useful astrometric information to be extracted for such systems, each component (or subsystem) received a separate pointing."387 For example. HIP. 70 and TIP 71 formed such a fwo-poiuting svsteni with a separation of about 15 arcsec.," For example, HIP 70 and HIP 71 formed such a two-pointing system with a separation of about 15 arcsec."388 When pointing at the brighter star (UP 71. fpz s.l) the other component (IIIP 70. Πρ~ 10.6) would be just at the edge of the TFOV aud a (variable) yaction of its signal was added to that of the brighter star.," When pointing at the brighter star (HIP 71, $Hp\simeq 8.4$ ), the other component (HIP 70, $Hp\simeq 10.6$ ) would be just at the edge of the IFOV and a (variable) fraction of its signal was added to that of the brighter star."389 Conversely. when pointing at the famter conrponeut. some fraction of the brighter stars signal would be added.," Conversely, when pointing at the fainter component, some fraction of the brighter star's signal would be added."390 Proper reduction of such svstenis. iust consider the uutual (aud possibly distorted) influence of each component upon the other. as was mdeed doue in the Hipparcos data reductions.," Proper reduction of such systems must consider the mutual (and possibly distorted) influence of each component upon the other, as was indeed done in the Hipparcos data reductions."391 In some multiple systems three differeut poiutiugs were ueeded., In some multiple systems three different pointings were needed.392 The situation is further complicated by the fact that the targeted position of the IPOV was souetimes updated in the course of the mission. usually because the original (eround-based) »osition was found to be wrong by several arcsec.," The situation is further complicated by the fact that the targeted position of the IFOV was sometimes updated in the course of the mission, usually because the original (ground-based) position was found to be wrong by several arcsec."393 Knowledge o: both the original and the updated »ositiou. and the time of upd:ing. iav then be necessary or proper interpretation of he observations.," Knowledge of both the original and the updated position, and the time of updating, may then be necessary for proper interpretation of the observations."394 Iu order to cope with two- aud three-poiutiug svstenis as well as updated positions. the concept of “tarec yositions was introduced in the TD.," In order to cope with two- and three-pointing systems as well as updated positions, the concept of `target positions' was introduced in the TD."395 For a set of TD referring to a articular double or multiple syste. tarec »ositious are defined by their offse coordinates (Zo.Ad) roni the adopted reference voit. rounded to the neares arcsec.," For a set of TD referring to a particular double or multiple system, target positions are defined by their offset coordinates $(\Delta\alpha*,\Delta\delta)$ from the adopted reference point, rounded to the nearest arcsec."396 Iu inmost cases there is just one target position. coinciding with the reference point [offset coordinates = (0.0)].," In most cases there is just one target position, coinciding with the reference point [offset coordinates $=(0,0)$ ]."397 For inultiple-poiuting svstenis there is at leas oue target position for each pointing. with a differen HIP προ attached to cach pointing.," For multiple-pointing systems there is at least one target position for each pointing, with a different HIP number attached to each pointing."398 For objects whose coordinates relative to he reference poiut changed iu the course of the niission. a jew target position was mtroduced whenever the offset coordinates changed bv iore than l aresec.," For objects whose coordinates relative to the reference point changed in the course of the mission, a new target position was introduced whenever the offset coordinates changed by more than 1 arcsec."399 To within the errors of the realtime attitude determination (norinallv 1.2 aresec rnm) it can therefore be assumed tha the IFOV was poiuted to the specified target position., To within the errors of the real-time attitude determination (normally 1–2 arcsec rms) it can therefore be assumed that the IFOV was pointed to the specified target position.400 In the TD the results frou cüffereut poiutiugs pertaiulus to the sane svstenu have been collected together and expressed relative to a como reference point., In the TD the results from different pointings pertaining to the same system have been collected together and expressed relative to a common reference point.401" This has Όσοι done for all svsteuis deemed. to be ""difficult! iu the seuse explained above. but uot for very wide systems where the umtual infiuence of the couponeut signals was negligible."," This has been done for all systems deemed to be `difficult' in the sense explained above, but not for very wide systems where the mutual influence of the component signals was negligible."402 The TD 1ioreover contains the bookkeeping data necessuy to calculate the actual tireet positions in cach transit., The TD moreover contains the bookkeeping data necessary to calculate the actual target positions in each transit.403 This section gives a rather detailec description of the contents of the TD files. conrpleuentius the formal description in Vol.," This section gives a rather detailed description of the contents of the TD files, complementing the formal description in Vol."404 1 of ESA (1997)) and providing additional explanation of the data items., 1 of ESA \cite{hip}) ) and providing additional explanation of the data items.405 All relevant data are contained in two ASCII files. both located on Disk 6 in Vol.," All relevant data are contained in two ASCII files, both located on Disk 6 in Vol."406 17 of ESA (1997)): the TD iudex file (hip_jj-ids. ~| Mb) aud the TD file (hip.jjdat. ~553 Mb).," 17 of ESA \cite{hip}) ): the TD index file j.idx, $\simeq 1$ Mb) and the TD file j.dat, $\simeq 553$ Mb)."407 A sumnunuurv of the couteuts of the two files is in Table I.. while iiportaut relations amoue the data are illustrated in Fig. 2..," A summary of the contents of the two files is in Table \ref{tab:sum}, while important relations among the data are illustrated in Fig. \ref{fig:idx}."408 The TD iudex file is included to facilitate accessing the TD file., The TD index file is included to facilitate accessing the TD file.409 It coutaius a poiuter from the WIP umber to the correspouding record in the TD file where data on that, It contains a pointer from the HIP number to the corresponding record in the TD file where data on that410In reledens we show (he temperature behavior of (he energy density for (he cases of 2. 24-1 and 3 light quark flavors δις here 22-1: means one heavy and two light quarks.,"In \\ref{edens} we show the temperature behavior of the energy density for the cases of 2, 2+1 and 3 light quark flavors \cite{KLP}; here 2+1 means one heavy and two light quarks."411 The sudden junp corresponding to the latent heat of deconfinement is «quite evident., The sudden jump corresponding to the latent heat of deconfinement is quite evident.412 It is found to occur αἱ a critical temperature of about. 160 - 150 MeV. and the energy density at that point is around 0.5 to 1.0 /[nr*.," It is found to occur at a critical temperature of about 160 - 180 MeV, and the energy density at that point is around 0.5 to 1.0 $^3$."413" To relate this ""jump more specifically to some form of critical behavior. we consider the corresponding order parameters for deconfinement and for chiral svyaumetry. restoration."," To relate this “jump” more specifically to some form of critical behavior, we consider the corresponding order parameters for deconfinement and for chiral symmetry restoration."414 such parameters signal the onset of the new phase., Such parameters signal the onset of the new phase.415 For deconfinement. (he order parameter is given by (he average value of the Polvakov loop where Foo(T) denotes the [ree energy. of a static QQ pair at infinite separation.," For deconfinement, the order parameter is given by the average value of the Polyakov loop \cite{Larry}, L(T) , where $F_{Q\bar Q}(T)$ denotes the free energy of a static $\Q$ pair at infinite separation."416 In a confining medium. this diverges (Fog(r.T)~ or). while in a deconfined medium. screening prevents communication between (he Q and the Q bevond a certain distance. so that Fog remains finite.," In a confining medium, this diverges $F_{Q\bar Q}(r,T)417 \sim \sigma r$ ), while in a deconfined medium, screening prevents communication between the $Q$ and the $\bar Q$ beyond a certain distance, so that $F_{Q\bar Q}$ remains finite."418 As a result. LUC) defines the deconfinement temperature 77.," As a result, L(T) defines the deconfinement temperature $T_L$."419 Actually. CL(P)) vanishes exactly for T'<Ty onlv in the case of infinitely heavy quarks: lor finite quark mass. the string binding Q anc," Actually, $\langle L(T) \rangle$ vanishes exactly for $T < T_L$ only in the case of infinitely heavy quarks; for finite quark mass, the string binding $Q$ and"420 Actually. CL(P)) vanishes exactly for T'<Ty onlv in the case of infinitely heavy quarks: lor finite quark mass. the string binding Q ancl," Actually, $\langle L(T) \rangle$ vanishes exactly for $T < T_L$ only in the case of infinitely heavy quarks; for finite quark mass, the string binding $Q$ and"421the multiple data points from most sources tend to spread throughout the plot.,the multiple data points from most sources tend to spread throughout the plot.422 In contrast. there are 9 measurements of ὃςτο (the source most frequently observed) in the first bin alone. 5 measurements of OJ287. between 30°60: and 6 measurements of 3€345. between 60907. which inlluence the concentration of data points in these areas.," In contrast, there are 9 measurements of 3C279 (the source most frequently observed) in the first bin alone, 5 measurements of OJ287 between $30\degr - 60\degr$ and 6 measurements of 3C345 between $60\degr - 90\degr$, which influence the concentration of data points in these areas."423 The data available on the LPQs (15 measurements) come from 3 different sources. but 3€23 contributes with LO entries and 4€39.25 with 4.," The data available on the LPQs (15 measurements) come from 3 different sources, but 3C273 contributes with 10 entries and 4C39.25 with 4."424" Ehe distributions of P and |Ayre, for this class are therefore strongly biased by the characteristics of a single source and thus any comparison with the other classes must be treated with care.", The distributions of $P$ and $\mid\theta_{VLBI} - \chi\mid$ for this class are therefore strongly biased by the characteristics of a single source and thus any comparison with the other classes must be treated with care.425 Although all orientations of the magnetic field have been observed at least once in this group. there is a concentration of measurements close to direction parallel to the jet.," Although all orientations of the magnetic field have been observed at least once in this group, there is a concentration of measurements close to direction parallel to the jet."426 Also. half of the polarisation meastwements are in the <34 bin and none have been obtained aboveSA.," Also, half of the polarisation measurements are in the $< 3\%$ bin and none have been obtained above."427. A Ίντο test of the P? parameter between BL Lacs and LIPQs gives a Ix-8 statistic of 0.12 with significance level of 16 per cent. indicating that the two samples being compared could have been obtained from a single population of objects.," A K-S test of the $P$ parameter between BL Lacs and HPQs gives a K-S statistic of 0.14 with significance level of 16 per cent, indicating that the two samples being compared could have been obtained from a single population of objects."428 A very similar result is obtained on the |65g;x parameter (0.13 with 11 per cent significance) and in a 2-dimensional Ix-S test combining these two parameters (0.16 with 21 per cent significance)., A very similar result is obtained on the $\mid\theta_{VLBI} - \chi\mid$ parameter (0.13 with 11 per cent significance) and in a 2-dimensional K-S test combining these two parameters (0.16 with 21 per cent significance).429 Similar tests carried out between either of these two classes and the LPQs all give Ix-8 statistics >0.5 with significance levels of 299 per cent. clearly ΤΗΠΜ between them.," Similar tests carried out between either of these two classes and the LPQs all give K-S statistics $> 0.5$ with significance levels of $> 99$ per cent, clearly differentiating between them."430 We therefore. find no evidence of any significant dilference in the properties of the magnetic field. (degree of order and orientation) between BL Lacs and. LPQs on the scales sampled. by millimetre/submillimetre measurements., We therefore find no evidence of any significant difference in the properties of the magnetic field (degree of order and orientation) between BL Lacs and HPQs on the scales sampled by millimetre/submillimetre measurements.431 However. there is some evidence that the magnetic field in the inner jets of LPQs may be generally. less-ordered and be preferentially aligned with the jet. although this needs to be confirmed by increasing the number of dilferent LPOs in the sample.," However, there is some evidence that the magnetic field in the inner jets of LPQs may be generally less-ordered and be preferentially aligned with the jet, although this needs to be confirmed by increasing the number of different LPQs in the sample."432 Pannels (c) and (d) of Figuree 7 summarise the, Pannels (c) and (d) of Figure 7 summarise the433"the collapse of halos with Zu,>10!R. or Ativan>105|(.1:)/11].82AL. (Ostriker Cuedin 1996. Haiuau. Rees Loeb 1997. Ciardi et al 2000. Abel Taian 2000. Ricotti. Guedin Shull 20012. 20015).","the collapse of halos with $T_{\rm vir} > 10^4$ K, or $M_{\rm halo} > 10^8434[(1+z)/11]^{-3/2} \, {\rm M_\odot}$ (Ostriker Gnedin 1996, Haiman, Rees Loeb 1997, Ciardi et al 2000, Abel Haiman 2000, Ricotti, Gnedin Shull 2001a, 2001b)."435 These halos do not rely ou the presence of Πω molecules. since they cau cool via recombination aud collisional excitation of neutral atolls.," These halos do not rely on the presence of ${\rm H_2}$ molecules, since they can cool via recombination and collisional excitation of neutral atoms."436" The goal of this paper is to critically examine the xevailius assuniptious of efficient eas cooling and star ormation iu metal free halos with Ty,>104 K. To date. he details of gas cooling aud chemistry iu these halos ive not been studied with the same care aud attention devoted to lower mass halos."," The goal of this paper is to critically examine the prevailing assumptions of efficient gas cooling and star formation in metal free halos with $T_{\rm vir} > 10^4$ K. To date, the details of gas cooling and chemistry in these halos have not been studied with the same care and attention devoted to lower mass halos."437 Since the majority of stars and/or quasars which reionized the universe. aud polluted he interealactic medimm (CAD) with metals. are expected ο fori iu such halos. it is Important to study the evolution of the gas in these halos in detail.," Since the majority of stars and/or quasars which reionized the universe, and polluted the intergalactic medium (IGM) with metals, are expected to form in such halos, it is important to study the evolution of the gas in these halos in detail."438 It is ecuerally taken for erauted that Lya cooling of jieutral atomic hwdrogen allows rapid contraction of gas until it becomes selteravitatius at the center of the xoteutial well and fragiments to form: stars (ideas tracing ak to Rees Ostriker 1977: White Rees 1978)., It is generally taken for granted that $\alpha$ cooling of neutral atomic hydrogen allows rapid contraction of gas until it becomes self-gravitating at the center of the potential well and fragments to form stars (ideas tracing back to Rees Ostriker 1977; White Rees 1978).439 ILowever. it is also known that significant contraction is required for this fragmentation to result im stellaruass fragments.," However, it is also known that significant contraction is required for this fragmentation to result in stellar--mass fragments."440 If only Lwo cooling operates. the gas retains at a temperature of ~ 10!K due to the sharp cutoff in the (equilibriun) cooling function aud the Jeaus nass is exceedingly high. even at high densities: Af)zmLos/105WyF(aem2) PALL.," If only $\alpha$ cooling operates, the gas remains at a temperature of $\sim 10^4$ K due to the sharp cutoff in the (equilibrium) cooling function and the Jeans mass is exceedingly high, even at high densities: $M_{\rm J}\approx 10^{8} (T/10^4~{\rm441K})^{3/2} (n/1~{\rm cm^{-3}})^{-1/2} \, \msolar$ ."442" Even if the gas cane sclferavitating. unless the gas can contract to extremely hieh densities. 5»>10!27eὉ, fragmentation o lower Jeans masses AL~100ML.. cannot proceed."," Even if the gas became self-gravitating, unless the gas can contract to extremely high densities, $n > 10^{12} {\rm cm^{-3}}$, fragmentation to lower Jeans masses $M \sim 100 {\rm M_\odot}$ cannot proceed."443 However. the gas cannot cool to arbitrarily high deusities. nit eventually mist fori a rotationally supported disk: at he temperatures allowed by Lya cooling. we shall show hat the majority of such disks are locally gravitationally stable.," However, the gas cannot cool to arbitrarily high densities, but eventually must form a rotationally supported disk; at the temperatures allowed by $\alpha$ cooling, we shall show that the majority of such disks are locally gravitationally stable."444 Thus. an additional coolant is needed to lower the eas cluperature. both to eusure eravitational instability aud o lower the Jeans mass by several orders of magnitude.," Thus, an additional coolant is needed to lower the gas temperature, both to ensure gravitational instability and to lower the Jeans mass by several orders of magnitude."445 Iu the absence of metals. IH formation and cooling is herefore still critical to star formation in Zi> LO‘ wos. aud cannot be ignored.," In the absence of metals, ${\rm H_2}$ formation and cooling is therefore still critical to star formation in $T_{\rm vir} > 10^4$ K halos, and cannot be ignored."446" Iu this paper. we study > ormation in shockheated eas. aud show that a universal IT, fraction of ry,~103 forms in gas that cools from an initial temperature of T> LOK. Similar behavior as already. been noted im previous studies of pregalactic shocks (Shapiro Kang 1987. ang Shapio 1992)."," In this paper, we study ${\rm H_2}$ formation in shock–heated gas, and show that a universal ${\rm H_2}$ fraction of $x_{\rm H_2} \approx 10^{-3}$ forms in gas that cools from an initial temperature of $T > 10^4$ K. Similar behavior has already been noted in previous studies of pregalactic shocks (Shapiro Kang 1987, Kang Shapiro 1992)."447 Tere we study the unou-equilibriu IT» formation in the Tay.> WOES halos of interest. examine the robustuess of this mechanisi to variations in density. temperature. aud radiation feld. and show that the asviuptotic abundance can be understood iu terms of timescale arguineuts.," Here we study the non-equilibrium ${\rm H_2}$ formation in the $T_{\rm vir}448> 10^4$ K halos of interest, examine the robustness of this mechanism to variations in density, temperature, and radiation field, and show that the asymptotic abundance can be understood in terms of timescale arguments."449 These arguments reveal that over a wide rauge of deusities. the cooling gas follows a universal track in the Ge.D) plane.," These arguments reveal that over a wide range of densities, the cooling gas follows a universal track in the $(x_{\rm450e},T)$ plane."451 This paper is organized as follows., This paper is organized as follows.452 Iu vetdisk.. we study the equilibria structure of isothermal disks embedded i dark matter halos. aud show that I> cooling is needed. to promote eravitational iustabilitv iu most disks.," In \\ref{disk}, we study the equilibrium structure of isothermal disks embedded in dark matter halos, and show that ${\rm H_2}$ cooling is needed to promote gravitational instability in most disks."453 In refeool. wei use senianalytic amethods aud lon chemistry to investigate I5 formation aud radiative cooling in halos with virial temperatures 1011. aud avenue that the Πο abundance buikls up to a universal value of egcLO quder most realistic conditious.," In \\ref{cool}, we use semi–analytic methods and non--equilibrium chemistry to investigate ${\rm H_2}$ formation and radiative cooling in halos with virial temperatures K, and argue that the ${\rm H_2}$ abundance builds up to a universal value of $x_{\rm H_2}\approx45410^{-3}$ under most realistic conditions."455 Iu roffeedback.. we study the effects of Πο destruction bv internal and external sources of UV radiation and show that feedback processes are much less efficient in TQ>10K halos than in their smaller counterparts. primarily because in the larger halos. eas can be compressed to high densities bv initial atomic Lue cooling.," In \\ref{feedback}, we study the effects of ${\rm H_{2}}$ destruction by internal and external sources of UV radiation and show that feedback processes are much less efficient in $T_{\rm vir} > 10^{4}$ K halos than in their smaller counterparts, primarily because in the larger halos, gas can be compressed to high densities by initial atomic line cooling."456 We also examine whether opacity aud radiatiou pressure effects can halt the collapse or fragmoeutation., We also examine whether opacity and radiation pressure effects can halt the collapse or fragmentation.457 Although we conclude that this is unlikely. we argue that it could affect the efficiency of star formation.," Although we conclude that this is unlikely, we argue that it could affect the efficiency of star formation."458 In reftcouclusious.. we summarize our conclusious and the inplicatious of this work.," In \\ref{conclusions}, we summarize our conclusions and the implications of this work."459" Du all nuucerical estimates. we asstune a cold dark matter cosmology with a cosinological ‘oustaut CXCDALD (QuiOY.Qu?h.m,i)(0.3.0.7.0.019.0.7.1.0) (see. e.g.. Balicall et al."," In all numerical estimates, we assume a cold dark matter cosmology with a cosmological constant $\Lambda$ CDM) $(\Omega_{\rm m},\Omega_{\Lambda},\Omega_{\rm b}h^{2},h,\sigma_{8460h^{-1}})=(0.3,0.7,0.019,0.7,1.0)$ (see, e.g., Bahcall et al."461 1999 for a review of these choices)., 1999 for a review of these choices).462" Let us first consider the cooling aud collapse of au initially spherical coufiguratiou of gas in a typical halo with T,>I0! K. The discussion presented in this section serves two purposes: if will hiehlieht the importance of IL» molecules for the larger halos. aud. will also vield the physically appropriate range of deusity. temperature and ionization fractions under which to cousider Πο formation and cooling in later sections."," Let us first consider the cooling and collapse of an initially spherical configuration of gas in a typical halo with $T_{\rm vir} >46310^4$ K. The discussion presented in this section serves two purposes: it will highlight the importance of ${\rm H_2}$ molecules for the larger halos, and will also yield the physically appropriate range of density, temperature and ionization fractions under which to consider ${\rm H_2}$ formation and cooling in later sections."464 The wellknown condition for ruuswav coutraction of eas is fooolXανα<feo (see Rees Ostriker 1977). which is typically satisfied for hydrogen atomic line cooling.," The well–known condition for runaway contraction of gas is $t_{\rm465cool} < t_{\rm dyn} < t_{\rm sc}$ (see Rees Ostriker 1977), which is typically satisfied for hydrogen atomic line cooling."466 Since cooling due to Lva has a very sharp cutoff at T10! FK. the cooling time is a very scusitive function of teniperature. Increasing rapidly by several orders of mmaenitucde i a very murow temperature range below ~104K (Spitzer 1978).," Since cooling due to $\alpha$ has a very sharp cutoff at $T < 10^4$ K, the cooling time is a very sensitive function of temperature, increasing rapidly by several orders of magnitude in a very narrow temperature range below $\sim 10^{4}$ K (Spitzer 1978)."467 This is because the free electron fraction able to excite atomic line cooling drops very rapidly iu this temperature range., This is because the free electron fraction able to excite atomic line cooling drops very rapidly in this temperature range.468" Thus. the condition tego<fay, nmuplies that the collapse is nearly isothermal."," Thus, the condition $t_{\rm cool} < t_{\rm dyn}$ implies that the collapse is nearly isothermal."469" If the eas cools below ~ WK. the eas reconibiues. the cooling time rapidly lnereases until tego)2fag. and further contraction of the gas is close to adiabatic. with the gas heating up due to the contraction until the hydrogen atoms are collisionally redomized aud the condition tooo)<fag, Is satisfied ouce again."," If the gas cools below $\sim47010^4$ K, the gas recombines, the cooling time rapidly increases until $t_{\rm cool} > t_{\rm dyn}$, and further contraction of the gas is close to adiabatic, with the gas heating up due to the contraction until the hydrogen atoms are collisionally re–ionized and the condition $t_{\rm cool} < t_{\rm dyn}$ is satisfied once again."471" In the absence of any other effects. this thermostatic mcchanisia would allow the gas ina Ta,> 10! halo to cool and coutract to arbitrarily high clensities."," In the absence of any other effects, this thermostatic mechanism would allow the gas in a $T_{\rm vir} > 10^{4}$ K halo to cool and contract to arbitrarily high densities."472 Iu practice. however. the eas has some initial aueular 1ionieutuim. aud must therefore eventually become rotationally supported.," In practice, however, the gas has some initial angular momentum, and must therefore eventually become rotationally supported."473 After a contraction by a factor of A|~20 in radius (where A=JIE)ο is the spinparameter. and J. E. and Af are the total angular momentum. cucrey aud uass of the halo). this results in rotationally supported disk at the ceuter of the halo (Mo. Mao White 1998. jereafter MONI).," After a contraction by a factor of $\lambda^{-1}\sim 20$ in radius (where $\lambda \equiv J |E|^{1/2}/G474M^{5/2}$ is the spin–parameter, and $J$, $E$, and $M$ are the total angular momentum, energy and mass of the halo), this results in rotationally supported disk at the center of the halo (Mo, Mao White 1998, hereafter MMW)."475 It is possible that some fragmentation akes place as the eas collapses toward a disk. however. lis is Likely to be inefücieut due to the slow erowth of density fluctuations in a rapidly contracting iiedium (e.g. Iashliuskv Rees 1983).," It is possible that some fragmentation takes place as the gas collapses toward a disk, however, this is likely to be inefficient due to the slow growth of density fluctuations in a rapidly contracting medium (e.g., Kashlinsky Rees 1983)."476 We therefore assume that most raenientation must take place in the disk itself., We therefore assume that most fragmentation must take place in the disk itself.477 We shall show that if ouly atomic line cooling operates. the disk will 0 stable to fragmentation in the majority of cases.," We shall show that if only atomic line cooling operates, the disk will be stable to fragmentation in the majority of cases."478 For, For479"grains exceed electron abundance, and m/n,4 reaches about 1000 at the disk midplane.","grains exceed electron abundance, and $\bar{n}/n_e$ reaches about $1000$ at the disk midplane."480" The large value of implies strong suppresion of AD and the Hall effect n/n,according to equation (16)).", The large value of $\bar{n}/n_e$ implies strong suppresion of AD and the Hall effect according to equation \ref{eq:eta_AD}) ).481" To see its significance, we also show the electron (thus ion) abundance in the grain-free calculation as the red dash-dotted line in the Figure."," To see its significance, we also show the electron (thus ion) abundance in the grain-free calculation as the red dash-dotted line in the Figure."482" Clearly, we seethat neg<m for z€2H."," Clearly, we seethat $n_{e0}<\bar{n}$ for $z\lesssim2H$."483" According to equation (17)), this means that when tiny grains are present, the AD coefficient is even smaller than that in the grain-free case!"," According to equation \ref{eq:criterion}) ), this means that when tiny grains are present, the AD coefficient is even smaller than that in the grain-free case!"484" Seemingly counterintuitive, one can qualitatively understand this result as follows."," Seemingly counterintuitive, one can qualitatively understand this result as follows."485" Near the disk midplane, we see that ng,>ng.=I mne."," Near the disk midplane, we see that $n_{\rm gr}\gg n_{\rm gr}^{\pm}\gtrsim n_i\gg n_e$ ."486" In this regime, the electrons produced from Πο ionization is quickly swallowed by the grains."," In this regime, the electrons produced from $_2$ ionization is quickly swallowed by the grains."487" Similarly, the ions exchange charge with neutral grains to produce positively charged grains."," Similarly, the ions exchange charge with neutral grains to produce positively charged grains."488" Therefore, ionization effectively takes place on the grains: 2 gr — gr* + gr with the same ionization rate ¢.¢."," Therefore, ionization effectively takes place on the grains: 2 gr $\rightarrow$ $^+$ + $^-$, with the same ionization rate $\zeta_{\rm eff}$."489" The dominant recombination, channel is simply its inverse reaction, withrecombination rate given by equation (3) of Umebayashi&Nakan"," The dominant recombination channel is simply its inverse reaction, withrecombination rate given by equation (3) of \citet{UN90}."490"o For recombination between two equal sized tiny grains (1990)..(e?/akT> 1), it reduces to where pg=3 g cm-! is the grain mass density, k is the Boltzmann constant, T' is the temperature."," For recombination between two equal sized tiny grains $e^2/akT\gg1$ ), it reduces to where $\rho_d=3$ g $^{-1}$ is the grain mass density, $k$ is the Boltzmann constant, $T$ is the temperature."491" In the second equation a, denotes grain size normalized to 1 nm, and Tioo= K. As long as charged grain recombination is the dominantΤ/100 recombination process, the abundance of charged grains can be approximately given by where Geg,17 is the ionization rate normalized to 10717s-1, ngo is the number density of the hydrogen atoms normalized to 1010cm-?."," In the second equation $a_1$ denotes grain size normalized to 1 nm, and $T_{100}=T/100$ K. As long as charged grain recombination is the dominant recombination process, the abundance of charged grains can be approximately given by where $\zeta_{\rm eff, -17}$ is the ionization rate normalized to $10^{-17}\ {\rm s}^{-1}$, $n_{H, 10}$ is the number density of the hydrogen atoms normalized to $10^{10}\ {\rm cm}^{-3}$."492" Plugging in the numbers relevant to Figure 2 at midplane, we find nz./mng~1.1x10719, "," Plugging in the numbers relevant to Figure \ref{fig:nsp} at midplane, we find $n_{\rm gr}^{\pm}/n_H\approx1.1\times10^{-10}$ ."493"Our chemistry calculation gives 6.5x10- for the averaged abundance of charged grains, which is slightly smaller due to small contributions from other recombination channels, but is within a factor of 2 from the analytical estimate."," Our chemistry calculation gives $6.5\times10^{-11}$ for the averaged abundance of charged grains, which is slightly smaller due to small contributions from other recombination channels, but is within a factor of 2 from the analytical estimate."494 Our chemistry calculations further reveal that ng./nj increases weakly with total grain abundance ng; (or zpAg) and approaches the asymptotic value (19))., Our chemistry calculations further reveal that $n_{\rm gr}^{\pm}/n_H$ increases weakly with total grain abundance $n_{\rm gr}$ (or $x_{\rm PAH}$ ) and approaches the asymptotic value \ref{eq:ngrpm}) ).495" In the grain-free case, the electron abundance neo is determined by the balance between ionization and multiple recombination channels, dominated by dissociative recombinations."," In the grain-free case, the electron abundance $n_{e0}$ is determined by the balance between ionization and multiple recombination channels, dominated by dissociative recombinations."496" Typical electron-ion dissociative recombination rate coefficients are on the order of 10-7 s-! cm-? at 100K, which is a factor of several higher than the grain recombination coefficient (18))."," Typical electron-ion dissociative recombination rate coefficients are on the order of $10^{-7}$ $^{-1}$ $^{-3}$ at $100$ K, which is a factor of several higher than the grain recombination coefficient \ref{eq:rcbrate}) )."497" The higher recombination rate leads to smaller ionization level than our estimate (19)), which explains why neo<n in the presence of abundant tiny grains."," The higher recombination rate leads to smaller ionization level than our estimate \ref{eq:ngrpm}) ), which explains why $n_{e0}<\bar{n}$ in the presence of abundant tiny grains."498 We note that the value of Περ depends on the choice of chemical reaction network., We note that the value of $n_{e0}$ depends on the choice of chemical reaction network.499 Simple reaction network (such as Oppenheimer&Dalgarno 1974)) generally produces larger neo mainly because of the lack of recombination channels., Simple reaction network (such as \citealp{OD74}) ) generally produces larger $n_{e0}$ mainly because of the lack of recombination channels.500" In our complex (and presumably more realistic) network, we find that the dominant recombination process is due to NHj and CH3CNH™ in this particular case, giving neo/ng to be about 3.2x10711."," In our complex (and presumably more realistic) network, we find that the dominant recombination process is due to $_4^+$ and $_3$ $^+$ in this particular case, giving $n_{e0}/n_H$ to be about $3.2\times10^{-11}$."501" As a result, we obtain ri/neo©4 in the midplane, which leads to a substantial net reduction of the AD coefficient."," As a result, we obtain $\bar{n}/n_{e0}\approx4$ in the midplane, which leads to a substantial net reduction of the AD coefficient."502 The fact that n>neo implies that tiny grains may facilitate the MRI by suppressing AD., The fact that $\bar{n}>n_{e0}$ implies that tiny grains may facilitate the MRI by suppressing AD.503" To see this more explicitly, we calculate the non-ideal MHD diffusion coefficients and apply the criteria (20) in Bai(2011) to identify the MRI-active regions in our adopted PPD model."," To see this more explicitly, we calculate the non-ideal MHD diffusion coefficients and apply the criteria (20) in \citet{Bai11a} to identify the MRI-active regions in our adopted PPD model."504" Briefly, for the MRI to operate, the Ohmic Elsasser number A=v4/7oQ has to be greater than unity, where v4=B/,/4xp is the Alfvénn velocity."," Briefly, for the MRI to operate, the Ohmic Elsasser number $\Lambda\equiv v_A^2/\eta_O\Omega$ has to be greater than unity, where $v_A=B/\sqrt{4\pi\rho}$ is the Alfvénn velocity."505" Moreover, the magnetic field has to be weaker than some critical value, which is set by 8>Bi, (Am)."," Moreover, the magnetic field has to be weaker than some critical value, which is set by $\beta\geq\beta_{\rm min}(Am)$ ."506" Here plasma B is the ratio of gas to magnetic pressure (not to be confused with the Hall parameter), Am=v3/n4Q is the AD Elsasser number, and f,(Αι) is given by (Bai& which increases with decreasing Am."," Here plasma $\beta$ is the ratio of gas to magnetic pressure (not to be confused with the Hall parameter), $Am\equiv v_A^2/\eta_A\Omega$ is the AD Elsasser number, and $\beta_{\rm min}(Am)$ is given by \citep{BaiStone11a}507 which increases with decreasing $Am$ ."508" For the number density profile given in Figure 2,, the result is shown in Figure 3.."," For the number density profile given in Figure \ref{fig:nsp}, , the result is shown in Figure \ref{fig:constrain}. ."509Differential PSF photometry of the QSO components relative to Al was available from the ALLSTAR analysis reftab:phot)).,Differential PSF photometry of the QSO components relative to A1 was available from the ALLSTAR analysis \\ref{tab:phot}) ).510" Flux calibration was established separately using simple aperture photometry (aperture diameter was 976 for and 7""5 for K,).", Flux calibration was established separately using simple aperture photometry (aperture diameter was $9\farcs 6$ for and $7\farcs 5$ for $K_s$ ).511 Standard stars from the 1149 field (Landolt 1992)) served to obtain colour terms and photometric zeropoints 1n the optical. while 99106 (Persson et citepersson*98)) was used for the NIR photometry.," Standard stars from the 149 field (Landolt \cite{landolt*92}) ) served to obtain colour terms and photometric zeropoints in the optical, while 9106 (Persson et \\cite{persson*98}) ) was used for the NIR photometry."512 The total magnitudes thus measured are listed in the first line of Table 2.. with uncertainty estimates as given in the DAOPHOT output.," The total magnitudes thus measured are listed in the first line of Table \ref{tab:phot}, with uncertainty estimates as given in the DAOPHOT output."513 We have also determined aperture magnitudes for 14 nearby stars in the field that may be useful to serve as reference stars in future monitoring., We have also determined aperture magnitudes for 14 nearby stars in the field that may be useful to serve as reference stars in future monitoring.514 A list with these measurements is available on The relative photometry confirms that Al. A2. and B have very similar optical-NIR colours although B appears slightly redder than Al and A2.," A list with these measurements is available on The relative photometry confirms that A1, A2, and B have very similar optical-NIR colours although B appears slightly redder than A1 and A2."515 C and D are much redder. on the other hand. so neither can correspond to a single unobscured fourth QSO image.," C and D are much redder, on the other hand, so neither can correspond to a single unobscured fourth QSO image."516 Because of the apparent positional shift between the bands. we computed a second model with fixed positions imposed from the / band image. fitting only the PSF scaling factors.," Because of the apparent positional shift between the bands, we computed a second model with fixed positions imposed from the $I$ band image, fitting only the PSF scaling factors."517 The resulting colours are slightly bluer for components B and C. and even much redder for D. However. inspection of the PSF-subtracted images indicated that the fit quality of these restricted models was much poorer. leaving. residuals significant on the 2-36 level.," The resulting colours are slightly bluer for components B and C, and even much redder for D. However, inspection of the PSF-subtracted images indicated that the fit quality of these restricted models was much poorer, leaving residuals significant on the $\sigma$ level."518 While in double QSOs there 1s always the possibility that a true binary system is being observed. a configuration like that seen in HE 2130 is almost certainly best explained as a lensed system. even without spectroscopic evidence.," While in double QSOs there is always the possibility that a true binary system is being observed, a configuration like that seen in HE $-$ 2130 is almost certainly best explained as a lensed system, even without spectroscopic evidence."519 Although we do not yet have spectra of all components. the available data allow nevertheless to confirm the lens hypothesis beyond all reasonable doubt: (1) The total spectrum reffig:spedanish)) contains no trace of absorption features that would be expected if Al was a star or a galaxy.," Although we do not yet have spectra of all components, the available data allow nevertheless to confirm the lens hypothesis beyond all reasonable doubt: (1) The total spectrum \\ref{fig:spcdanish}) ) contains no trace of absorption features that would be expected if A1 was a star or a galaxy."520 We conclude that Al and A2 have most probably very similar spectra. given the broad-band colours. (," We conclude that A1 and A2 have most probably very similar spectra, given the broad-band colours. ("5212) A2 and B have both very similar QSO spectra. apart from the slit loss effects.,"2) A2 and B have both very similar QSO spectra, apart from the slit loss effects."522 Figure + shows that the emission line centroids agree within the measurement accuracy. the line widths are equal. and also the strong ‘associated’ (Zap;7 Sem) absorption system ts clearly present in both components.," Figure \ref{fig:spcntt} shows that the emission line centroids agree within the measurement accuracy, the line widths are equal, and also the strong `associated' $z_{\mathrm{abs}} \simeq z_{\mathrm{em}}$ ) absorption system is clearly present in both components."523 A curious feature. however. are the significant residuals detected in the difference spectrum A2-B(scaled). indicating," A curious feature, however, are the significant residuals detected in the difference spectrum A2–B(scaled), indicating"524The solar global field has a distinct paritv: the poloidal field is a dipole. ie. anlisvinmmelric about the equator.,"The solar global field has a distinct parity: the poloidal field is a dipole, i.e., antisymmetric about the equator."525 The polar fields almost always have the clilferent sien between hemispheres. even though they show the occasional weak north-south asvinnmeltry in phase and amplitude.," The polar fields almost always have the different sign between hemispheres, even though they show the occasional weak north-south asymmetry in phase and amplitude."526 In addition. Hale's polarity law states (hat the sunspots between hemispheres are nearly always anlisvuunetric about the equator (ILale1905)..," In addition, Hale's polarity law states that the sunspots between hemispheres are nearly always antisymmetric about the equator \citep{1908ApJ....28..315H}."527" It can then be interpreted that the toroidal fields (42,) below the surface are antisvyiumetric about the equator.", It can then be interpreted that the toroidal fields $B_\phi$ ) below the surface are antisymmetric about the equator.528 This interesting feature is. however. not axiomatically explained bv the flux transport dvnamo model since this model significantly depends on three [ree parameters. i.e.. the a-elfect. the meridional flow. and the turbulent diffisivitv.," This interesting feature is, however, not axiomatically explained by the flux transport dynamo model since this model significantly depends on three free parameters, i.e., the $\alpha$ -effect, the meridional flow, and the turbulent diffusivity."529 lt has been suggested that the a-elfect around the base of the convection zone leads to the generation of the global dipolar magnetic field. (Dikpati&Gilman2001:Bonannoet2002:Chatterjeeetal. 2004)..," It has been suggested that the $\alpha$ -effect around the base of the convection zone leads to the generation of the global dipolar magnetic field. \citep{2001ApJ...559..428D,2002A&A...390..673B,2004A&A...427.1019C}."530 The existence of the poloidal fields around the tachocline and the coupling of these fields between hemispheres are significant [actors for the generation ol the dipole field., The existence of the poloidal fields around the tachocline and the coupling of these fields between hemispheres are significant factors for the generation of the dipole field.531 A detailed explanation of this process is given in the next paragraph., A detailed explanation of this process is given in the next paragraph.532 Chatterjeeetal.(2004) also suggested. however. that the dipole field can be obtained with the strong diffusivity in the convection zone without the presence of the the a-effect around the (achocline.," \cite{2004A&A...427.1019C} also suggested, however, that the dipole field can be obtained with the strong diffusivity in the convection zone without the presence of the the $\alpha$ -effect around the tachocline."533 Hence the exact necessity of the a-elfect in generating the dipole field is still inconclusive., Hence the exact necessity of the $\alpha$ -effect in generating the dipole field is still inconclusive.534 The dependence of (he parity on these parameters can be explained when we understaud the role of the turbulent diffusivity in the solar magnetic parity issue., The dependence of the parity on these parameters can be explained when we understand the role of the turbulent diffusivity in the solar magnetic parity issue.535 Lf (he elobal magnetic Ποια is anlisvinmetric. ie. is a dipole like our sun. the ó component of the magnetic vector potential in each hemisphere has the same sien (Fig.," If the global magnetic field is antisymmetric, i.e. is a dipole like our sun, the $\phi$ component of the magnetic vector potential in each hemisphere has the same sign (Fig."536 laa)., \ref{explain}a a).537 When the cyclic phase in one hemisphere sliehtly differs from the other. the coupling effect by the turbulent. diffusivity of the poloidal field distinguishes the phase difference in the vector potential and causes the maenetic field to be a dipole.," When the cyclic phase in one hemisphere slightly differs from the other, the coupling effect by the turbulent diffusivity of the poloidal field distinguishes the phase difference in the vector potential and causes the magnetic field to be a dipole."538 On the other hand. when (he magnetic Ποιά is svyiumetric. 1.e..," On the other hand, when the magnetic field is symmetric, i.e.,"539with observations presented by ισα»oetal.(2002).,with observations presented by \citet{ingalls02}.540". The ISO LAWS observations of the !| Lynn line have a resolution of 71"".", The ISO LWS observations of the $^{\rm +}$ ] $\mu$ m line have a resolution of $\arcsec$.541" The FIR data are based on IRAS ISSA maps with a resolution of 5,"," The FIR data are based on IRAS ISSA maps with a resolution of $4-5\,\arcmin$."542 We assunie the cells of our models have an angular size of 0.25% and the computed. (CTI and FIR maps are convolved to the resolution of the observations.," We assume the cells of our models have an angular size of $\arcmin$, and the computed [CII] and FIR maps are convolved to the resolution of the observations."543 For cach model the FUV. absorption aud the FIR intensity. Jgpjg are calculated towards three directions perpendicular to the faces of the density field data cubes.," For each model the FUV absorption and the FIR intensity, $I_{\rm FIR}$ are calculated towards three directions perpendicular to the faces of the density field data cubes."544" Since the FUY absorption is asstuued to be equivalent to the [CTI] line intensity, Loy. divided by the efficiency. €. in the following we will refer to the quantitv [οε (vith € still uukuown) instead of the computed FUY absorption."," Since the FUV absorption is assumed to be equivalent to the [CII] line intensity, $I_{\rm CII}$, divided by the efficiency, $\epsilon$ , in the following we will refer to the quantity $I_{\rm CII}/\epsilon$ (with $\epsilon$ still unknown), instead of the computed FUV absorption."545 Fig., Fig.546 1 shows the distribution of the ratio Τετε(εἶμιν) in the three models.," \ref{fig:map.y} shows the distribution of the ratio $I_{\rm547CII}/(\epsilon I_{\rm FIR})$ in the three models."548" The figure is obtained at the original resolution «250 pixels). and ucither Igy, nor {οιε ave spatially convolved."," The figure is obtained at the original resolution $\times$ 250 pixels), and neither $I_{\rm FIR}$ nor $I_{\rm CII}/\epsilon$ are spatially convolved."549 Model Ais based ou a flow with subsonic turbulence. with only small density fluctuations.," Model $A$ is based on a flow with subsonic turbulence, with only small density fluctuations."550 This is reflected in the top panel of Fi, This is reflected in the top panel of Fig.551"e. l showing a smooth distribution of ""mL/GÍgig) in model A.", \ref{fig:map.y} showing a smooth distribution of $I_{\rm CII}/(\epsilon I_{\rm FIR})$ in model $A$.552 The density coutrast increases with increasing Au., The density contrast increases with increasing $M_{\rm S}$.553 Model DB. with Avy=2.5. shows a more chuupy distribution of {ο(εἶπιι) GQuiddle panel of Fig. 1)).," Model $B$, with $M_{\rm S}=2.5$, shows a more `clumpy' distribution of $I_{\rm CII}/(\epsilon I_{\rm FIR})$ (middle panel of Fig. \ref{fig:map.y}) )."554 Model €. with Ma=10. has clearly the most inhomoecncous and filameutary distribution (bottom) panel of Fig. 1)).," Model $C$ with $M_{\rm S}=10$, has clearly the most inhomogeneous and filamentary distribution (bottom panel of Fig. \ref{fig:map.y}) )."555 Iu the case of the nearly homogeneous cloud <A. both [μμ aud Zegqj/e are determined mainly bv the distance to the cloud surface.," In the case of the nearly homogeneous cloud $A$, both $I_{\rm FIR}$ and $I_{\rm CII}/\epsilon$ are determined mainly by the distance to the cloud surface."556 Since Zeq1/6 ds assumed to be equivalent to the PUV absorption. loge depends only on photous iu the energv range 613.6 eV. while [μμ depeuds on a iuch wider wavelength rauge responsible for heating the dust grains.," Since $I_{\rm CII}/\epsilon$ is assumed to be equivalent to the FUV absorption, $I_{\rm CII}/\epsilon$ depends only on photons in the energy range 6–13.6 eV, while $I_{\rm FIR}$ depends on a much wider wavelength range responsible for heating the dust grains."557 The dust extinction increases towards shorter wavelengths. aud this leads to a reductio- in the ratio Zeqp/(e£gpg) inside the clouds.," The dust extinction increases towards shorter wavelengths, and this leads to a reduction in the ratio $I_{\rm CII}/(\epsilon I_{\rm FIR})$ inside the clouds."558 At tlicloud surface the ratio Zeqi/t(efgig) is above onc. and it decreases to ιδ inside the cloud.in all three models.," At thecloud surface the ratio $I_{\rm CII}/(\epsilon I_{\rm FIR})$ is above one, and it decreases to $\la$ 0.8 inside the cloud,in all three models."559 The total range of values is wider i-, The total range of values is wider in560aand ddata. πο detected low-frequency noise fro astroplivsical fares im the count rates of individual sources stich as preanaein-sequence stars. ando from backeround flares that our filtering algorithlun failed to remove.,"and data, we detected low-frequency noise from astrophysical flares in the count rates of individual sources such as pre-main-sequence stars, and from background flares that our filtering algorithm failed to remove."561 From AACIS. we detected signals from sources that fell near chip bouudares. at the harmonics and beat periods of the satellite dither (700s in the «direction. 1000s in the y).," From ACIS, we detected signals from sources that fell near chip boundaries, at the harmonics and beat periods of the satellite dither (700s in the $x$ -direction, 1000s in the $y$ )."562 Fox the EEPIC. particularly the pu. we found signals with a range of periods that appeared to be related to hot cohuuus aud chip boundaries. particularly in observations with high particle background.," For the EPIC, particularly the pn, we found signals with a range of periods that appeared to be related to hot columns and chip boundaries, particularly in observations with high particle background."563 We are uot certain of the origin of these signals from the EPIC., We are not certain of the origin of these signals from the EPIC.564 The spurious signals introduced by the detector eenerallv shared the feature that they could be found in multiple sources at the exact same frequency during an observation., The spurious signals introduced by the detector generally shared the feature that they could be found in multiple sources at the exact same frequency during an observation.565 Therefore. we have removed from consideration auv signals that appeared in two or more sources on the same detector in the same observation.," Therefore, we have removed from consideration any signals that appeared in two or more sources on the same detector in the same observation."566 After removing such signals. we found 358 sources with candidate signals in the oobservations. aud 12380 sources (some of which are duplicates) with signals fromNewton.," After removing such signals, we found 358 sources with candidate signals in the observations, and 1380 sources (some of which are duplicates) with signals from."567.. These signals still turned out to be dominated bv low-frequency noise and detector artifacts. which could be quickly determined by visually inspecting the power spectrum.," These signals still turned out to be dominated by low-frequency noise and detector artifacts, which could be quickly determined by visually inspecting the power spectrum."568 Therefore. for the final step. we scrutinized 1700 power spectra by eve to remove the remaimine examples that were clearly uodlsv. aud to remove sources that appeared to be detector artifacts.," Therefore, for the final step, we scrutinized $\approx$ 1700 power spectra by eye to remove the remaining examples that were clearly noisy, and to remove sources that appeared to be detector artifacts."569 We defined a sienal as significant if it had a power πμ 232.8 ina single observation or had a power larger than the sinele-observation threshold iu two or more observations., We defined a signal as significant if it had a power $P_{\rm meas}$$>$ 32.8 in a single observation or had a power larger than the single-observation threshold in two or more observations.570 We found a few sources with siguificant periodic signals that we could uot attribute to noise or detector artifacts., We found a few sources with significant periodic signals that we could not attribute to noise or detector artifacts.571 We describe the previoush-known anc new sources separately below., We describe the previously-known and new sources separately below.572 Most of the signals were from previously-icentified pulsars., Most of the signals were from previously-identified pulsars.573 These confirmed that our algorithin worked as iuteuded., These confirmed that our algorithm worked as intended.574 Iu our oobservations. we ideutified the high-mass N-rav binary (IINEIND) IU 1115619 (Whitectal.1978:etal. 2005). CNOU J161710.2(55216 (Munoetal. 2006). and two sources toward the Calactic center (CNOCJL71532.3290251andGNOCCJ171532.7200552:Munoetal. 2003)..," In our observations, we identified the high-mass X-ray binary (HMXB) 4U 1145–619 \citep{whi78,rut05}, CXOU J164710.2–455216 \citep{mun06}, and two sources toward the Galactic center \citep[CXOC~J174532.3--290251 and GXOGC~J174532.7--290552;][]{mun03}. ."575" In the oobservations. we identified the pulsus Ceminea (Halpern&Πο.1992:JacksonUalperm2005) and PSR —J15135908 (Seward&Ihunudeu1982). the TIAINB Sct N-1. (Novamactal.1991:Kaplanetal. 2007).. and the maenetars LE 10151.5937 (Seward.Charles.&Stale1986:Tieugoetal. 2005).. IRNS J170819.000010 (Sueizakictetal. 2005). SCR 1506-20 (Alwakamictal.L991:Mereeghettietal. 2005).. SCR 1900,LE (ITurlev.etal.1999:Moreghettictal. 2006a). ATE 51ο197 in outburst (Ioralinnetal.200£ITalperu&Cotthelf2005).. aud LE 2259|586 (Fahhuan&Caegory1981)."," In the observations, we identified the pulsars Geminga \citep{hh92,jh05} and PSR J1513–5908 \citep{sh82}, the HMXB Sct X-1 \citep{koy91,kap07}, and the magnetars 1E 1048.1–5937 \citep{scs86,tie05}, , 1RXS J170849.0–400910 \citep{sug97,rea05}, SGR 1806-20 \citep{mur94,mer05}, SGR 1900+14 \citep{hur99,mer06}, XTE J1810–197 in outburst \citep{ibr04,hg05}, and 1E 2259+586 \citep{fg81}."576. The list above imcludes 7 of the 12 confined. magnuetars in the Galaxy., The list above includes 7 of the 12 confirmed magnetars in the Galaxy.577 It is notable. however. that several maguctars were uot detected m our search. despite being the targets of archival aand observations.," It is notable, however, that several magnetars were not detected in our search, despite being the targets of archival and observations."578" Ποσο, we sunnuuize the difficulties icountered ideutifviug several examples: was not idoutifid with ο it saturated the detector durius an imagine observation."," Here, we summarize the difficulties encountered identifying several examples: was not identified with because it saturated the detector during an imaging observation."579 and400910 were not identified with bbecause they were ouly observed with the eratines m place., and were not identified with because they were only observed with the gratings in place.580 These cases are not a serious concern. because sucli bright sources are rare. and so almost never are fouud sereudipitously in the fields of aandNewton.," These cases are not a serious concern, because such bright sources are rare, and so almost never are found serendipitously in the fields of and."581.. aud were not identified by wwhile in quiescence., and were not identified by while in quiescence.582 Although their signals were preseut in the data. their powers were below our search threshold.," Although their signals were present in the data, their powers were below our search threshold."583 All of the above sources were ideutified withNewton., All of the above sources were identified with.584 was not identified with either. oor, was not identified with either or.585 This is partly because the source had a smallNewton... pulse fraction ris). but also because of the detector modes with which the source was observed.," This is partly because the source had a small pulse fraction rms), but also because of the detector modes with which the source was observed."586 With tthe source either saturated the detector duiug niaeiug observations. or was observed with the exatings in place.," With the source either saturated the detector during imaging observations, or was observed with the gratings in place."587" WithXAZAM-Newton.. oulv the MOS2 camera was active. and the maeuetar only produced a signal above the siugle-observation threshold (D,,4,:718) im oue of the two observations."," With, only the MOS2 camera was active, and the magnetar only produced a signal above the single-observation threshold $P_{\rm meas}$$>$ 18) in one of the two observations."588" That sienal (2,221.27) was below the threshold for our cutive search. aud so can nof be considered a detection as part of our bliud search."," That signal $P_{\rm meas}$ =24.7) was below the threshold for our entire search, and so can not be considered a detection as part of our blind search."589 llowever. had that source been observed with the pu active. we would have identified it.," However, had that source been observed with the pn active, we would have identified it."590 also was not ideutified with oorNewton., also was not identified with or.591. With a fractional rius amplitude of rans. it did not produce a sienificaut signal iu the ddata.," With a fractional rms amplitude of rms, it did not produce a significant signal in the data."592 The oobservatious of this source were too short (<10 ks) to be included in our search., The observations of this source were too short $<$ 10 ks) to be included in our search.593 A longer oobservation would almost certaily have ideutified this source.4," A longer observation would almost certainly have identified this source.,"5941.0258. aud197 in quiescence were all too faint to produce detectable pulsations. even in searches targeted at thei knowu or suspected spin periods (Gotthelfctal.2001:Tametal.2006:Mereghoetti 2006b).," and in quiescence were all too faint to produce detectable pulsations, even in searches targeted at their known or suspected spin periods \citep{got04, tam06, mer06b}."595". These objects. aud possibly the newlyidentified magnetar LE 1517.0-5Los. represent a class of maguetars frou, which pulsatious could ouly be detected iuteiitteutlv. or perliaps not at all. in a search like ours."," These objects, and possibly the newly-identified magnetar 1E 1547.0-5408, represent a class of magnetars from which pulsations could only be detected intermittently, or perhaps not at all, in a search like ours."596 Four sources produced periodic signals that have not been previously reported., Four sources produced periodic signals that have not been previously reported.597 Iu Table 1 we lave listed basic information abouteach source andsignal., In Table \ref{tab:signals} we have listed basic information abouteach source andsignal.598 Figures 2 and { contain the Fourier power spectra in which the candidate signals were discovered., Figures \ref{fig:cxcfft} and \ref{fig:xmmfft} contain the Fourier power spectra in which the candidate signals were discovered.599 The power spectra, The power spectra600Frail et al. [2001])).,Frail et al. \nocite{fksd01}) ).601 Why. if bists are all of roughly equal total energy. should more luminous bursts such as 9990125 tend to lave much narrower openiue angles than less Iuninous bursts such as 9970508?," Why, if bursts are all of roughly equal total energy, should more luminous bursts such as 990123 tend to have much narrower opening angles than less luminous bursts such as 970508?"602 Also. why is there a dearth of very narrow opening aneles (ie. less than 3 degrees)?," Also, why is there a dearth of very narrow opening angles (i.e. less than 3 degrees)?"603 Iu the next two sections we will assuue that bursts are produced by jets that are verv similar in nature. Le. we will απο a generic (sinele) morphology.," In the next two sections we will assume that bursts are produced by jets that are very similar in nature, i.e. we will assume a generic (single) morphology."604 Asstuine. as discussed in Section 3.. that the relation of Fig.," Assuming, as discussed in Section \ref{modelsection}, that the relation of Fig."605 { las a kinematic origiu (i.c. Equ. 5)).," \ref{tjvtlag} has a kinematic origin (i.e. Eqn. \ref{tdeltaeqn}) ),"606 then the observed variation amoue GRBs originates from variation in D (Eqn. 1j), then the observed variation among GRBs originates from variation in ${\cal D}$ (Eqn. \ref{deltaeqn}))607 which depends on two variables: 0 and 5., which depends on two variables; $\theta$ and $\gamma$.608 Iu more realistic jets two effects will likely play a role., In more realistic jets two effects will likely play a role.609 The first is where the variation in GRD properties is due to variation of viewing angle. 0. aud. the second is where the variation in CRB properties is due to the velocity structure of the jet. ic. 2.," The first is where the variation in GRB properties is due to variation of viewing angle, $\theta$, and, the second is where the variation in GRB properties is due to the velocity structure of the jet, i.e. $\gamma$."610 In reality both viewing augle aud velocity profile may be important. m which case the conibiue effect needs to be taken mto account.," In reality both viewing angle and velocity profile may be important, in which case the combined effect needs to be taken into account."611 This is bevoud the scope of this paper., This is beyond the scope of this paper.612 It was receutly sueeested by Joka&Nakamura(2001) that the lag-huninosity relationship (equ. 7)), It was recently suggested by \citet{in01} that the lag-luminosity relationship (Eqn. \ref{jpnlageqn}) )613 could be explained by variation iu observer anele. 0.. from the axis of the jet.," could be explained by variation in observer angle, $\theta_v$, from the axis of the jet."614 Tere we have a sinple jet. where the Loreutz factor 5= const.," Here we have a simple jet, where the Lorentz factor $\gamma = $ const."615 for 0κ0j and 5=0 for 0> 0;.," for $\theta <616\theta_j$ and $\gamma = 0$ for $\theta > \theta_j$ ."617" However. now the observer is not looking at the ceuter of the jet. but is slightly offanis (0,4 0)."," However, now the observer is not looking at the center of the jet, but is slightly off-axis $\theta_v \neq 0$ )."618" The lags derive from the difference iu time-offielt of the near aud far edees of an cutting internal shock disk of finite size. AfxD1, and the luminosity is defined as L= coust."," The lags derive from the difference in time-of-flight of the near and far edges of an emitting internal shock disk of finite size, $\Delta t \propto {\cal D}^{-1}$, and the luminosity is defined as $L \approx $ const."619" for (0,<< 0;) aud asyiuptotically varies as LxD? for (0,> 0j). Toka&N"," for $\theta_v <620\theta_j$ ) and asymptotically varies as $L \propto {\cal D}^{3}$ for $\theta_v > \theta_j$ )."621"akamura(2001) calculate that bursts observe: at aneles 0, a few times 0; would peak iu X ravs (possibly X rav rich GRBs) while for 0.~0; they would peak in eununa rays.", \citet{in01} calculate that bursts observed at angles $\theta_v$ a few times $\theta_j$ would peak in X rays (possibly X ray rich GRBs) while for $\theta_v \sim \theta_j$ they would peak in gamma rays.622" Using this model aud 6,zm0j. Ίοκα&Nakamura(2001) were able to adequately reproduce the observed lag-Iuninosity relationship (Equ. 7)):"," Using this model and $\theta_v \approx623\theta_j$, \citet{in01} were able to adequately reproduce the observed lag-luminosity relationship (Eqn. \ref{jpnlageqn}) );"624 this includes 9950125. (Calamaetal1998) which has very low luminosity. very laree spectral lag and very low variability.," this includes 980425 \citep{gvv+98} which has very low luminosity, very large spectral lag and very low variability."625 The simplicity of this model allows for a demonstration of its predicted adherence to the relationship of Equ. (1))., The simplicity of this model allows for a demonstration of its predicted adherence to the relationship of Eqn. \ref{t_jeqn}) ).626" The observed jet-break tie. defined here as the time when +=1/6;. will occur at a radius: rjX527/7x0;265Cad thus will: vary with observer angle 0, from the jet axis as Thus oue sees that if 5z1/0; one gets the relation simular to Equ. (1))."," The observed jet-break time, defined here as the time when $\gamma \equiv6271/\theta_j$, will occur at a radius $r_j \propto \gamma^{-2/3} \propto628\theta_j^{2/3}$ and thus will vary with observer angle $\theta_v$ from the jet axis as Similarly the pulse lag will vary as Thus one sees that if $\gamma \approx 1/\theta_j$ one gets the relation similar to Eqn. \ref{t_jeqn}) )."629 In this model. the relation observed in Fig.," In this model, the relation observed in Fig."630 bois a natural result of the ranec of off-axis views. 0. of a narrow jet.," \ref{tjvtlag} is a natural result of the range of off-axis views, $\theta_v$, of a narrow jet."631 Note that Eq. (10)), Note that Eq. \ref{tauj}) )632 relates to the afterglow phase. whereas Eq. (11))," relates to the afterglow phase, whereas Eq. \ref{deltat}) )"633 relates to the CRB phase., relates to the GRB phase.634 Two predictions can be made:2) 521/0; to within a factor of a ew lest the curve deviate from the straight line of Fie. L.," Two predictions can be made: $\gamma \approx6351/\theta_j$ to within a factor of a few lest the curve deviate from the straight line of Fig. \ref{tjvtlag}."636 So the afterglow Leltcurve breaks while noving at a substantial fraction of the original Loreutz factor., So the afterglow lightcurve breaks while moving at a substantial fraction of the original Lorentz factor.637 Since the ratio of naxinunmn to uinum lag aud that of jet-break times shown in Fie., Since the ratio of maximum to minimum lag and that of jet-break times shown in Fig.638 1 is about 30. and assuimiug hat 6. is neeleable for the bursts with the shortest iuescales (0.8. 9990510 and 9971211). he implied maxiuun timescale Gu particular 9970508) derives frou a viewing angle (οpporzosusi~ 6/5.," \ref{tjvtlag} is about 30, and assuming that $\theta_v$ is negligable for the bursts with the shortest timescales (e.g. 990510 and 971214), the implied maximum timescale (in particular 970508) derives from a viewing angle $\theta_{v(GRB\,970508)} \sim \sqrt{30}/\gamma \sim 6/\gamma$ ."639" For example. letting 1/0;=25/2 aud defining rz;=0.601|[235(0).0,37) and At=Qld[5(0,.0,3) over the rauge 0κs(0.—0,;)<GO. oue gets an acceptable fit to the data in Fig. l.."," For example, letting $1/\theta_j = 2 \gamma/3$ and defining $\tau_j =6400.6 (1 + [2/3 \gamma (\theta_v - \theta_j)]^2)$ and $\Delta t = 0.01641(1 + [\gamma (\theta_v - \theta_j)]^2)$ over the range $0 < \gamma642(\theta_v -\theta_j) < 6$, one gets an acceptable fit to the data in Fig. \ref{tjvtlag}. ."643" A difficulty with this model is that (deipozosos ~ήis viewed well outside the beaming angle 1 and thus we expect the afterglow decay to be steeper than the E,x#12 that is typically observed."," A difficulty with this model is that $\theta_{v(GRB\,970508)}$ $ \sim6446/\gamma$is viewed well outside the beaming angle $1/\gamma$ and thus we expect the afterglow decay to be steeper than the $F_{\nu} \propto645t^{-1.2}$ that is typically observed."646 That is. the afterglow decay curve mist already have broken.," That is, the afterglow decay curve must already have broken."647 We then also expect to observe a steeper luuinosity versus spectral lag curve, We then also expect to observe a steeper luminosity versus spectral lag curve648First we relate the total energy in photons between the comoving aud stationary frames.,First we relate the total energy in photons between the comoving and stationary frames.649 The differential nuunuber of photous NV.(¢..Q.) per unit enerev and solid angle trausforiis as Nie...)=ON(εἰ.Ol). as is easily secon by calculating the Jacobian of the transformation. or by noting that e.bdN/dedQ—eIN(e.Q) is au invariaut.," The differential number of photons $N_*(\e_*,\Omega_*)$ per unit energy and solid angle transforms as $N_*(\e_*,\Omega_*) = \delta N^\prime (\ep, \Omega^\prime)$, as is easily seen by calculating the Jacobian of the transformation, or by noting that $\e^{-1}dN/d\e d\Omega \equiv \e^{-1} N(\e,\Omega)$ is an invariant."650 For an isotropic. monochromatic photou spectrum iu the comoving frame. lx. aud the total photon energy in the comoving frame is just EG=Noeg (in units of the electron rest mass).," For an isotropic, monochromatic photon spectrum in the comoving frame, $N^\prime (\ep,651\Omega^\prime)= N_0 \delta(\ep - \ep_0)/4\pi$ , and the total photon energy in the comoving frame is just $E^\prime_0 = N_0 \ep_0$ (in units of the electron rest mass)."652" The differcutial photon spectrum in the stationary frame is therefore IN.(e;0.)=dNydle./8ej)lz =οNode,δει)Ix. so that This result is obvious by noting the sviunetrv of the traustormetion equation e;=Τε|oy’) with respect toμ”."," The differential photon spectrum in the stationary frame is therefore $N_*(\e_*,\Omega_*) = \delta N_0653\delta(\e_* /\delta -\ep_0)/4\pi$ $ = \delta^2 N_0654\delta(\e_*-\delta\ep_0)/4\pi$, so that This result is obvious by noting the symmetry of the transformation equation $\e_* = \Gamma \ep(1+\beta \mu^\prime)$ with respect to$\mu^\prime$."655" BecausePf=Lf)lads. boy definition""EM of the Inuinosity.κ distance. dr. the fucuce lids. where &) and 0.25 ave times of reception aud emission in the observer aud stationary "," Because$\Phi_E = L/4\pi d_L^2$, by definition of the luminosity distance $d_L$, the fluence $\varphi = \Phi_E\langle t \rangle = L_*656\langle t \rangle/4\pi d_L^2 = L_* \langle t_* \rangle (1+z) /4\pi657d_L^2$ , where $\langle t \rangle$ and $\langle t_*\rangle$ are times of reception and emission in the observer and stationary frame, respectively."658"A simple estimate rclating comoving eucrgy density et with eucrgy flux 9r is obtained by noting that the stationary+ frame. huuiositv+ of. a blast wave is- given. by L.=dE,/dt.DUL'. where fe)."," Using \ref{E*}) ) gives A simple estimate relating comoving energy density $u^\prime_0$ with energy flux $\Phi_E$ is obtained by noting that the stationary frame luminosity of a blast wave is given by $L_*= dE_*/dt_* = \Gamma^2659L^\prime $, where $L^\prime = dE^\prime /d\tp \cong u_0^\prime 4\pi660r^2 \Delta r^\prime/(\Delta r^\prime/c)$ ."661 Thus: 9g=esta2pl fd]. giviugHM κ (2)).," Thus $\Phi_E \cong662cr^2 u_0^\prime\Gamma^2/d_L^2$ , giving \ref{phie}) )."663 If: the variability:⋅⋅ is. produced by. curvature effects accordingAn to (1). then Note that the same basic dependence. though with E replaced by à. is derived for a (comoving) spherical blob geometry.," If the variability is produced by curvature effects according to \ref{r}) ), then Note that the same basic dependence, though with $\Gamma$ replaced by $\delta$, is derived for a (comoving) spherical blob geometry."664" Tn this. case. Pr=EM81L'/2bed]. and L'=2.πρὸς with: blob radius: 17,=ctu-,12)."," In this case, $\Phi_E \cong \delta^4 L^\prime/4\pi d_L^2$, and $L^\prime \cong 4\pi r_b^{\prime 2} c u_0^\prime/3$, with blob radius $r_b^\prime = c \delta t_{var}/(1+z)$."665 Starting with ((5)). we approximate Nonualiziug to the comoving energy LE of a pulse inuplies that The integrals can now be performed.," Starting with \ref{fet2}) ), we approximate Normalizing to the comoving energy $E_p^\prime$ of a pulse implies that The integrals can now be performed."666 First note the subtlety that |drfdr’|=6. whereas Ar’=TAr in equation (6)).," First note the subtlety that $|dr/dr^\prime| = \delta$, whereas $\Delta r^\prime = \Gamma \Delta667 r$ in equation \ref{uep}) )."668 Imposing the limits over + in equation (9)) recoversthe 6 factor in the umuerical integration of equation (11)) performed im Section 2., Imposing the limits over $r$ in equation \ref{r1}) ) recoversthe $\delta$ factor in the numerical integration of equation \ref{fet3}) ) performed in Section 2.669 Furthermore noting that ty2ry/Te. aud defining e;=(1| τ)ε. we obtain The final proportionality holds providedthat f. is in the rauge satisfing the Hoeaviside function.," Furthermore noting that $\tp_0 = r_0/\beta670\Gamma c$, and defining $\e_z = (1+z)\e$ , we obtain The final proportionality holds providedthat $t_z$ is in the range satisfying the Heaviside function."671" When a =). corresponding to eiiission at the peak of the j£, spectrum. fi(0)Xfx eoe"," When $a = 0$ , corresponding to emission at the peak of the $\nu F_\nu$ spectrum, $f_{\e_{pk}}(t)\propto t_z^{-3}\propto \e_{pk}^3$ ."672 This follows because, This follows because673shocl-leaing.,shock-heating.674 The imoclels in Dobbs-Dixonetal.(2010) do include artificial viscosity aud so should be able to correctly treat any gejeration of APE from shocks., The models in \citet{DobbsDixon2010} do include artificial viscosity and so should be able to correctly treat any generation of APE from shocks.675 In. principle the clillerences between tiese models could demonstrate the impact of standing shocks on the euergetics of the circulation. but there are ohe‘important cdiffereuces between these modeling approaches aud it is difficult to disentaugle the johwsis.," In principle the differences between these models could demonstrate the impact of standing shocks on the energetics of the circulation, but there are other important differences between these modeling approaches and it is difficult to disentangle the physics."676 Fially. recent work iiles that the atmospheres of hot Jupiters may be weakly thermally jionized ad subject to interaction with he planetary magnetic field (BatveinPeηlaοἱal. 2010a).," Finally, recent work implies that the atmospheres of hot Jupiters may be weakly thermally ionized and subject to interaction with the planetary magnetic field \citep{Batygin2010,Perna2010a}."677. In. particular. the mostly neutral [flow may be draggedMD by the interaction beween ου charges and tle uaguetic field.," In particular, the mostly neutral flow may be dragged by the interaction between free charges and the magnetic field."678 This mechanism is strongly allected by as relates to the orient:lo Lol the magnetic field ane due to coucductivity dillereuces between the hot ¢ayside aud cold. utelsicle—aας Pernaetal.(2010a) estimate that the amount of drag COU dlye strong enough to siguilicantly alter the momentu1 of the flow., This mechanism is strongly affected by geometry---both as relates to the orientation of the magnetic field and due to conductivity differences between the hot dayside and cold nightside—and \citet{Perna2010a} estimate that the amount of drag could be strong enough to significantly alter the momentum of the flow.679 The drag is associated witli al iudiced. maguetic field. itself sustained by electric currents which will dissipate olumically in a nou-lo¢wal way.," The drag is associated with an induced magnetic field, itself sustained by electric currents which will dissipate ohmically in a non-local way."680 The result. of this complex interaction between the fIuid aud the maguetic field is that tl kinetic energy dissipated will not be locally deposited as heating., The result of this complex interaction between the fluid and the magnetic field is that the kinetic energy dissipated will not be locally deposited as heating.681 Nevertheless. tlie energy tay ‘eturnecl to the flow i a way that alters the eiergeties of the οἱreulation.," Nevertheless, the energy may be returned to the flow in a way that alters the energetics of the circulation."682 A full MHD sliion nay be required to fully uudeStand how this process cau afect the atinospheric flow., A full MHD simulation may be required to fully understand how this process can affect the atmospheric flow.683 The'e are also numerical sources of dissipation. alhough these are usually not well characterized and will vary from code to code. depeding on the exact scheme used.," There are also numerical sources of dissipation, although these are usually not well characterized and will vary from code to code, depending on the exact scheme used."684 A known issue with elobal sinulatious is the build up of noise )l sla] scales and a couunon techuique is to use livperclissipaion (or hypercilUsion) to remove power [rom the simalles scales (seeThrastarsou&Cho2011.fo‘astudyofhowhisaffectstekiteticeiereyspectrumhe flow).., A known issue with global simulations is the build up of noise on small scales and a common technique is to use hyperdissipation (or hyperdiffusion) to remove power from the smallest scales \citep[see][for a study of how this affects the kinetic energy spectrum of the flow]{Thrastarson2011}.685 Hypercissipatiou is applied in order to fix au aAificial resu of the nuijerical simulation auc in principle should wot have an errojeous ellect on the APE eene‘allo1, Hyperdissipation is applied in order to fix an artificial result of the numerical simulation and in principle should not have an erroneous effect on the APE generation.686 However. αν sclieme hat alters the wind aud/or lemperature profiles. as this ¢oes. lias tlie poteitial to change both the johysical dissipation. as well as the ellicieicy with which tiat. would be tur1ος into reheating.," However, any scheme that alters the wind and/or temperature profiles, as this does, has the potential to change both the physical dissipation, as well as the efficiency with which that would be turned into reheating."687 Iu order to evaluate the impo‘tance of various possible drag mechanisms iu the context. of strongly forced. atinospheres we need expressious [or the local energetics., In order to evaluate the importance of various possible drag mechanisms in the context of strongly forced atmospheres we need expressions for the local energetics.688 In this section we will borrow from the derivation of avaiable potential enthalpy in Marquet(1991).. but extended to explicitly track dissipation aud frictional heating.," In this section we will borrow from the derivation of available potential enthalpy in \citet{Marquet}, but extended to explicitly track dissipation and frictional heating."689 For a steady kleal flow. witlioit any net heatinsef)j‘cooling or dissipation of kinetic energy. we can use Bernoulli's theorem to defie a set of locally couserved euergies (see.e.g.Vallis 2006)::," For a steady ideal flow, without any net heating/cooling or dissipation of kinetic energy, we can use Bernoulli's theorem to define a set of locally conserved energies \citep[see, e.g.][]{Vallis}: :"690We estimate (hat the final relative error in (he quantities along the equilibrium sequence is of the order of some parts times 10. [or M and Q and some parts times 10? for E.,We estimate that the final relative error in the quantities along the equilibrium sequence is of the order of some parts times $10^{-4}$ for $\hat M$ and $\hat Q$ and some parts times $10^{-5}$ for $\hat E$.691 The total energy is less sensitive to the finite radius truncation error. due to its 1/I? convergence.," The total energy is less sensitive to the finite radius truncation error, due to its $1/R^{2}$ convergence."692 The propagation of these errors leads to the error bars plotted in Fig.1," The propagation of these errors leads to the error bars plotted in Fig.,"693. where (he entropy σ is the more difficult to determine with good accuracy., where the entropy $\sigma$ is the more difficult to determine with good accuracy.694"we obtain Fix;<ταν, ","we obtain $R_{\rm695Ni} \lsim 4700$ km."696Within this Ry. ouly 1.54. is enclosed. (Figure 1)). so that only 0.211. ONT can be ejected.," Within this $R_{\rm Ni}$ , only $M_\odot$ is enclosed (Figure \ref{fig:mvsr}) ), so that only $M_\odot$ $^{56}$ Ni can be ejected."697" From this. we exclude the models less massive than 25AL.. in thei main sequence because they caunot eject enough ο να,"," From this, we exclude the models less massive than $M_\odot$ in their main sequence because they cannot eject enough $^{56}$ Ni."698 This aretunent above is further evideuce that the progenitor of SNLOOSAw is a massive star., This argument above is further evidence that the progenitor of SN1998bw is a massive star.699 Since the progenitor of another hwperuova candidate SNI9970f also secius to be massive (Iviunoto et al., Since the progenitor of another hypernova candidate SN1997ef also seems to be massive (Iwamoto et al.700 2000). we consider only relatively massive progenitor models (8 - 16 AL. We core models) iu the following for uucleosvuthesis calculations of hivperuovac.," 2000), we consider only relatively massive progenitor models (8 - 16 $M_\odot$ He core models) in the following for nucleosynthesis calculations of hypernovae."701 Ihperunovae are characterized. bv explosion energies arger than E~1077 eves.," Hypernovae are characterized by explosion energies larger than $E \sim70210^{52}$ ergs."703 Such an euergetie stellar explosion nav be associated with the formation of a dack hole as has been discussed in the context of the GRB-SNe counection. (Wooslev 1993: Paczvuski 1998: Iwamoto et al., Such an energetic stellar explosion may be associated with the formation of a black hole as has been discussed in the context of the GRB-SNe connection (Woosley 1993; Paczynski 1998; Iwamoto et al.704 1998: MacFadyeu Woosley 1999)., 1998; MacFadyen Woosley 1999).705 Iu these uodels. the eravitational energy. or the rotational energy would be released via pair-neutrio annuihilation or the Dlaudford-Zuajek mechanis (Blaudford Zuajek 1977).," In these models, the gravitational energy, or the rotational energy would be released via pair-neutrino annihilation or the Blandford-Znajek mechanism (Blandford Znajek 1977)."706 Alternatively. larec maguetic enereies are released from a xossible magnetar CNaleuunura 1998: Wheeler et al.," Alternatively, large magnetic energies are released from a possible magnetar (Nakamura 1998; Wheeler et al."707 2000)., 2000).708 The explosion may also be aspherical (IHHóffich. Wheeler. Wane 1999: MacFadyeu Woosley 1999: Khokhlov et al.," The explosion may also be aspherical (Höfflich, Wheeler, Wang 1999; MacFadyen Woosley 1999; Khokhlov et al."709 1999)., 1999).710 Tlowever. the actual explosion mniechauisui and the degree of asphericity in the ejecta are still quite uncertain.," However, the actual explosion mechanism and the degree of asphericity in the ejecta are still quite uncertain."711 For the preseut paper. therefore. we investigate nucleosvuthesis iu προ explosions as au extreme case.," For the present paper, therefore, we investigate nucleosynthesis in spherical explosions as an extreme case."712 Iu a next step. we will exploreΊσα] aspherical explosion models (Alaeda et al.," In a next step, we will explore aspherical explosion models (Maeda et al."713 2000: also Nagataki ct al., 2000; also Nagataki et al.714 1997)., 1997).715 Our caleulatious are performed in the same wav as studies of supernova uucleogvuthnesis (e.g... Uashimoto et al.," Our calculations are performed in the same way as studies of supernova nucleosynthesis (e.g., Hashimoto et al."716 1989: Thiclemann. IHashiuoto. Nomoto 1990: Iashuunoto 1995: Thiclemann. Nomoto. IlLashinoto 1996: Nalguuura et al.," 1989; Thielemann, Hashimoto, Nomoto 1990; Hashimoto 1995; Thielemann, Nomoto, Hashimoto 1996; Nakamura et al."717 1999)., 1999).718" First. the hydrodyuimuical siuulatious are performed with a one dimensional PPM (piecewise parabolic method) code (Colella Woodward 1981). which includes a small nuclear reaction network that coutaius ouly 13 alpha nuclei (Πο, ο, 190, 29 Ne, 2IN[e, 2857, 97S, 06 Ag, θα, TL 9ου, PF Fe. and CONT) in order to take into account the eucrev release due to unclear reactions."," First, the hydrodynamical simulations are performed with a one dimensional PPM (piecewise parabolic method) code (Colella Woodward 1984), which includes a small nuclear reaction network that contains only 13 alpha nuclei $^{4}$ He, $^{12}$ C, $^{16}$ O, $^{20}$ Ne, $^{24}$ Mg, $^{28}$ Si, $^{32}$ S, $^{36}$ Ar, $^{40}$ Ca, $^{44}$ Ti, $^{48}$ Cr, $^{52}$ Fe, and $^{56}$ Ni) in order to take into account the energy release due to nuclear reactions."719 We eeucrate a shock wave by depositing thermal cherey below the mass cut. which divides the central conrpact object aud the ejecta.," We generate a shock wave by depositing thermal energy below the mass cut, which divides the central compact object and the ejecta."720 Next. post-processing calculations are performed at each mesh point of the lvcdvodvuamical model with an extended reaction network of 293 isotopes (ITix Thiclemann 1996. 1999) to provide precise total vields (even for minor abundances}.," Next, post-processing calculations are performed at each mesh point of the hydrodynamical model with an extended reaction network of 293 isotopes (Hix Thielemann 1996, 1999) to provide precise total yields (even for minor abundances)."721 The progenitor models are taken from Nomoto Tashimeto (1988). Hashimoto (1995) aud Nomoto et al. (," The progenitor models are taken from Nomoto Hashimoto (1988), Hashimoto (1995) and Nomoto et al. ("7221997).,1997).723 We make use of the GAL... SAL... OAL... aud L6OAL.. We core models. which correspoucd approximately to the main sequence masses of 20M... 25447... 3042... aud 103... respectively.," We make use of the $M_{\odot}$, $M_{\odot}$, $M_{\odot}$, and $M_{\odot}$ He core models, which correspond approximately to the main sequence masses of $M_{\odot}$, $M_{\odot}$, $M_{\odot}$, and $M_{\odot}$, respectively."724 In order to compare uicleosvuthesis in hvpernovae with ordinary supernovae and also to investigate the dependence ou the explosion cuerey. we study explosion eucreies of E= 100. 30. 10. and 1 & 1074 eres.," In order to compare nucleosynthesis in hypernovae with ordinary supernovae and also to investigate the dependence on the explosion energy, we study explosion energies of $E725=$ 100, 30, 10, and 1 $ \times$ $ 10^{51}$ ergs."726 The mass cuts are sumunarized in Table 1.., The mass cuts are summarized in Table \ref{tab:masscuthn}.727 We chose these mass cuts to be as small as they can. but prevent O/Fe of the ejecta from being much less than the solar value (8?77)).," We chose these mass cuts to be as small as they can, but prevent O/Fe of the ejecta from being much less than the solar value \ref{sec:alpha}) )."728" Figure 2 shows uucleosvuthesis iu hwperuovae aud typical supernovae for £= 100 (top loft). 30 (top right). 10 (bottom left). aud 1 (bottom right) « 1075 eres,"," Figure \ref{fig:donehn} shows nucleosynthesis in hypernovae and typical supernovae for $E =$ 100 (top left), 30 (top right), 10 (bottom left), and 1 (bottom right) $ \times$ $ 10^{51}$ ergs."729 The progenitor is 1637.. We core model., The progenitor is $M_{\odot}$ He core model.730 Frou this figure. we note the following characteristics of uucleosvutliesis with very large explosion energies.," From this figure, we note the following characteristics of nucleosynthesis with very large explosion energies."731 Tables 20 - 9 stuumarize the nucleosvuthesis products of hvperuovae (and normal supernovae) before and after radioactive decays for various explosion energies., Tables \ref{doneisohn16a} - 9 summarize the nucleosynthesis products of hypernovae (and normal supernovae) before and after radioactive decays for various explosion energies.732 Major radioactive elements are summarized in table 10.., Major radioactive elements are summarized in table \ref{doneisohn}.733 The progenitors are Πο stars of OAL... 107... SAL... and GAZ...," The progenitors are He stars of $M_{\odot}$, $M_{\odot}$, $M_{\odot}$, and $M_{\odot}$."734 Products from the πο euvelope are not included., Products from the H-rich envelope are not included.735 Note that the amount of the clements produced iu the complete Si-buruiug region depends ou the mass cut., Note that the amount of the elements produced in the complete Si-burning region depends on the mass cut.736 Tere we choose the mass cuts shown in Table 1.., Here we choose the mass cuts shown in Table \ref{tab:masscuthn}.737 Figure 5 displays the abundances of stable isotopes relative to their solar values for£= 100 (top left). 30 (top welt). 10 (bottom left). aud 1 (bottom right) \ lot eres," Figure \ref{fig:vssolarhn} displays the abundances of stable isotopes relative to their solar values for$E =$ 100 (top left), 30 (top right), 10 (bottom left), and 1 (bottom right) $ \times$ $ 10^{51}$ ergs."738" The progenitor is a 1011, Πο star.", The progenitor is a $M_{\odot}$ He star.739 The isotopic ratios relative to 19O with respect to the solar values are shown., The isotopic ratios relative to $^{16}$ O with respect to the solar values are shown.740 The uucleosvuthesis is characterized bv laree abundance ratios of iutermecdiate mass nuclei, The nucleosynthesis is characterized by large abundance ratios of intermediate mass nuclei741"to fit the observed trend, without overfitting.","to fit the observed trend, without overfitting."742" The usage of the window function introduces a calibration factor, which is compensated by the P"" term."," The usage of the window function introduces a calibration factor, which is compensated by the $P^\gamma$ term."743 This implies that stellar terms must be computed and fitted with the same value of ϐ used for each galaxy (?).., This implies that stellar terms must be computed and fitted with the same value of $\theta$ used for each galaxy \citep{Hoekstra98}.744" An alternative approach, not based on a constant (and somehow arbitrary) order polynomial, is given e.g. by Generalized Additive Models: we found that the implementation in R (function in the mgcv library) provides good results."," An alternative approach, not based on a constant (and somehow arbitrary) order polynomial, is given e.g. by Generalized Additive Models: we found that the implementation in R (function in the mgcv library) provides good results."745 Fig., Fig.746" 7 shows fitting and residuals of the anisotropic PSF component: from the comparison between the results obtained with polynomial and GAM fitting we see that in the latter case we obtain lower residuals, in particular in the borders of the image."," \ref{fig:psfmap} shows fitting and residuals of the anisotropic PSF component: from the comparison between the results obtained with polynomial and GAM fitting we see that in the latter case we obtain lower residuals, in particular in the borders of the image."747" To quantify the improvement compared to the usage of the polynomial, we obtain (éaniso,1)=(1+5)x 1075, (eaniso.2)=(72£9)x107 with a polynomial of order 3, (€aniso,1)=(2£4)x1077, (eaniso.2)=(1£7)x107 with the GAM algorithm."," To quantify the improvement compared to the usage of the polynomial, we obtain $\left\langle e_{\rm aniso,1} \right\rangle = (1 \pm 5) \times 10^{-4}$ , $\left\langle e_{\rm aniso,2} \right\rangle = (-2 \pm 9) \times 10^{-4} $ with a polynomial of order 3, $ \left\langle e_{\rm aniso,1}\right\rangle = (2 \pm 4) \times 10^{-4} $, $\left\langle e_{\rm aniso,2}\right\rangle = (1 \pm 7) \times 10^{-4} $ with the GAM algorithm."748" The values of the fitted terms p and q at the positions of the galaxies are predicted byGAM,, that also provides an estimate of the standard errors of the predictions, Ap and Aq."," The values of the fitted terms $p$ and $q$ at the positions of the galaxies are predicted by, that also provides an estimate of the standard errors of the predictions, $\Delta p$ and $\Delta q$."749" From error propagation, the uncertainty on 6ιεο was computed as: where (Aeaniso)”=(Aeops)”+(PS™Ap) and (APY)?=(P*™ Aq)’; uncertainties on the measured values of P?? and P*h were not considered."," From error propagation, the uncertainty on $e_{\rm iso}$ was computed as: where $(\Delta e_{\rm aniso})^2 = (\Delta e_{\rm obs})^2 + (P^{\rm sm} \Delta p)^2$ and $(\Delta P^\gamma)^2 = (P^{\rm sm} \Delta q)^2$ ; uncertainties on the measured values of $P^{\rm sm}$ and $P^{\rm sh}$ were not considered."750" For each galaxy, a weight is defined as: where Aeg~0.3 is the typical intrinsic rms of galaxy ellipticities."," For each galaxy, a weight is defined as: where $\Delta {e_0} \sim 0.3$ is the typical intrinsic rms of galaxy ellipticities."751 Stars and galaxies were separated in the magnitude (MAG_AAUTO) vs. size plot., Stars and galaxies were separated in the magnitude AUTO) vs. size plot.752" Instead of using e.g. FLUX_RRADIUS as the estimator of size, we used the quantity 6=MU_MMAX-MAG_AAUTO, where MU.MMAX is the peak surface brightness above background."," Instead of using e.g. RADIUS as the estimator of size, we used the quantity $\delta$ AUTO, where MAX is the peak surface brightness above background."753" Saturated stars were found in the locus of sources with constant MU.MMAX; in the 6 vs. MAG.AAUTO plot, stars are identified as sources in the vertical branch."," Saturated stars were found in the locus of sources with constant MAX; in the $\delta$ vs. AUTO plot, stars are identified as sources in the vertical branch."754 Sources with ó lower than stars were classified as spurious detections., Sources with $\delta$ lower than stars were classified as spurious detections.755" In addition, we rejected those sources for which 6 is ~2σ larger than the median value."," In addition, we rejected those sources for which $\delta$ is $\sim 2\sigma$ larger than the median value."756" This is to exclude from the sample of stars used to compute the PSF correction terms, those sources for which the shape measurement may be wrong due to close blended sources, noise, etc."," This is to exclude from the sample of stars used to compute the PSF correction terms, those sources for which the shape measurement may be wrong due to close blended sources, noise, etc."757" We further excluded those galaxies with w«1 or SNe «5, for which the ellipticity measurement is not meaningful."," We further excluded those galaxies with $w<1$ or SNe $<5$, for which the ellipticity measurement is not meaningful."758" In the case of faint galaxies used for the weak lensing analysis, theellipticity is underestimated due to noise."," In the case of faint galaxies used for the weak lensing analysis, theellipticity is underestimated due to noise."759" Such effect is not included in the PY term, which can be only computed on stars with high signal to noise ratio."," Such effect is not included in the $P^\gamma$ term, which can be only computed on stars with high signal to noise ratio."760" ? proposed the following parametrization for such bias, as a function of the signal to noise: where e,, and e; are the ellipticities before and after the correction respectively."," \citet{schrabback10} proposed the following parametrization for such bias, as a function of the signal to noise: where $e_m$ and $e_k$ are the ellipticities before and after the correction respectively."761" Such parameters were derived using the STEP1 (?) and STEP2 (?) simulations, where both PSF and shear are constant for each simulated image."," Such parameters were derived using the STEP1 \citep{step1} and STEP2 \citep{step2} simulations, where both PSF and shear are constant for each simulated image."762" We obtain a=—0.l and b= —0.45, which corresponds to a bias m "," We obtain $a=-0.1$ and $b=-0.45$ , which corresponds to a bias $m$ "763line (see Figure 11)).,line (see Figure \ref{fig:xoratio}) ).764" The median value for the optically extended sources lies further above the f,= line. but the scatter is large enough that the median value is still consistent with f£;= f,."," The median value for the optically extended sources lies further above the $f_x=f_o$ line, but the scatter is large enough that the median value is still consistent with $f_x=f_o$ ."765 In Figure 12.. we illustrate how the extended sources have a larger mean X-ray to optical flux ratio than the point sources.," In Figure \ref{fig:xohist}, we illustrate how the extended sources have a larger mean X-ray to optical flux ratio than the point sources."766 A KS-test (2). shows that the X-ray to optical flux ratio distributions of the two populations are drawn from a different underlying distribution at a 799.956 significance., A KS-test \citep{pre92} shows that the X-ray to optical flux ratio distributions of the two populations are drawn from a different underlying distribution at a $>$ significance.767 This i$ probably due to the fact that for the extended sources. the optical emission is from the stellar population (1.e.. the host galaxy light dominates either because it is optically brighter or because the central AGN is completely optically obscured) whereas in the case of the point sources. the optical emission is dominated by an optically less obscured AGN.," This is probably due to the fact that for the extended sources, the optical emission is from the stellar population (i.e., the host galaxy light dominates either because it is optically brighter or because the central AGN is completely optically obscured) whereas in the case of the point sources, the optical emission is dominated by an optically less obscured AGN."768" One must be careful because the optical classification may be unreliable at R >23 (see Figure 9)) and this may affect the classification of sources with f/f, =5.", One must be careful because the optical classification may be unreliable at $R>$ 23 (see Figure \ref{fig:stel}) ) and this may affect the classification of sources with $f_x/f_o\ge$ 5.769 However. our conclusions still hold when considering only R <23 sources (albeit with larger uncertainties).," However, our conclusions still hold when considering only $R<$ 23 sources (albeit with larger uncertainties)."770" We define the 773 sources with f./f,,> 10 as our candidates for an optically obscured AGN population (we have omitted the 26 sources that are not truly optically blank: see Section 5.4)).", We define the 773 sources with $f_x/f_o>$ 10 as our candidates for an optically obscured AGN population (we have omitted the 26 sources that are not truly optically blank; see Section \ref{sec:nomatch}) ).771 The population consists of 510 sources that are detected in R. 217 that are only detected in another optical band. and 47 that are optically non-detected in all optical bands to the limits of our survey.," The population consists of 510 sources that are detected in $R$, 217 that are only detected in another optical band, and 47 that are optically non-detected in all optical bands to the limits of our survey."772" All of the non-detected sources have f/f, —10.", All of the non-detected sources have $f_x/f_o>$ 10.773" The majority of the f./f,> 10 sources (643/773) have extended optical emission (stellarity <0.7). suggesting that the optical light is dominated by the stars in the host galaxy (re. the optical emission from the AGN is heavily obscured)."," The majority of the $f_x/f_o>$ 10 sources (643/773) have extended optical emission (stellarity $<$ 0.7), suggesting that the optical light is dominated by the stars in the host galaxy (i.e. the optical emission from the AGN is heavily obscured)."774 This is also true for the R <23 sources (37/47 are optically extended).suggesting that the," This is also true for the $R<$ 23 sources (37/47 are optically extended),suggesting that the"775"the Nearby Galaxies Survey (NGS,GildePazal. 2007).","the Nearby Galaxies Survey \citep[NGS,][]{gildepaz07}."776". The image covers a square region on the skyof size —5760"" x5760""., i.e., much larger than the extent of the optical disk of3627,, with 1.55 pixels."," The image covers a square region on the skyof size $\sim$ $\times$, i.e., much larger than the extent of the optical disk of, with 5 pixels."777" As the image was reduced with the data pipeline, it is already expressed in intensity units and skysubtracted."," As the image was reduced with the data pipeline, it is already expressed in intensity units and skysubtracted."778" The total FUV calibrated magnitude is 16.34+0.02, corresponding to a FUV flux density of 1057419 py."," The total FUV calibrated magnitude is $\pm$ 0.02, corresponding to a FUV flux density of $\pm$ 19 $\mu$ Jy."779" The observations performed with the A and B receivers of the IRAM mm telescope in the two !CO lines covered the inner —50"".,, corresponding to the central ~2.5 kpc (in diameter)"," The observations performed with the A and B receivers of the IRAM m telescope in the two $^{12}$ CO lines covered the inner $\sim$ , corresponding to the central $\sim$ 2.5 kpc (in diameter)"780((2007) were taken from the Web site provided by Riess.,(2007) were taken from the Web site provided by Riess.781 The distance moduli aud redshifts for the ESSENCE supernovae were extracted from Table 9 in the Latex file for astro-ph/O70L0LL 22007)., The distance moduli and redshifts for the ESSENCE supernovae were extracted from Table 9 in the Latex file for astro-ph/0701041 (Wood-Vasey 2007).782 Typically different groups analyze supernovae with different asstunptious about the Hubble constant or equivalently the absolute magnitude Mf of a canonical SN la with a nominal decay rate., Typically different groups analyze supernovae with different assumptions about the Hubble constant or equivalently the absolute magnitude ${\cal M}$ of a canonical SN Ia with a nominal decay rate.783 In order to combine the new supernovae from ESSENCE with the Riess ssatuple. it was necessary to check the relative normalization of the two data sets using the 93 objects they have in common.," In order to combine the new supernovae from ESSENCE with the Riess sample, it was necessary to check the relative normalization of the two data sets using the 93 objects they have in common."784 Figure 1. shows the comparisou., Figure \ref{fig:ESSENCEtab9-Riess} shows the comparison.785 The scatter in the clilferential distance moduli is 0.2 mag le. which seems unusually high. and the median difference in ge is 0.022 mae which is consistent. with the staucdard deviation of the mean given the scatter.," The scatter in the differential distance moduli is $0.2$ mag $\sigma$, which seems unusually high, and the median difference in $\mu$ is 0.022 mag which is consistent with the standard deviation of the mean given the scatter."786 Objects which are uot in the Riess ssaunple but which had successful fits with 4? per degree of freedom <7 were added to the Riess ssample. with the 0.022 mag added to p. and an intrinsic scatter of 0.10 mag added in quadrature to σµ.," Objects which are not in the Riess sample but which had successful fits with $\chi^2$ per degree of freedom $< 7$ were added to the Riess sample, with the 0.022 mag added to $\mu$, and an intrinsic scatter of $0.10$ mag added in quadrature to $\sigma_\mu$."787 Lhis gives a total sample of 358 SNe., This gives a total sample of 358 SNe.788 I have binned the SNe into bius containing «24Nyy/10 objects aud widths less than 0.1 in redshift., I have binned the SNe into bins containing $< 2+N_{tot}/10$ objects and widths less than 0.1 in redshift.789 An empty Universe model (the Milne model) was first subtracted from the ge values., An empty Universe model (the Milne model) was first subtracted from the $\mu$ values.790 The binned values are listed in Table 1.., The binned values are listed in Table \ref{tab:SNall}.791 A Hubble constant of 63.8 kin/sec/Mpc was used when computing the Milne model. but this value has no effect ou the," A Hubble constant of 63.8 km/sec/Mpc was used when computing the Milne model, but this value has no effect on the"792In the past vears. an increasing number of observational studies have focused their ellort. in. probing kinematic. photometric ancl stellar. population properties at. large ealactocentric radii of earlv-tvpe. galaxies. (ee. Lau& 2006: Spolaorctal. 2009a:: Proctoretal.2009:: Weijmansetal. 2009: Fosterctal. 20092).,"In the past years, an increasing number of observational studies have focused their effort in probing kinematic, photometric and stellar population properties at large galactocentric radii of early-type galaxies (e.g., \citealt{hau06}; ; \citealt{spolaor09a}; ; \citealt{proctor09}; \citealt{weijmans09}; \citealt{foster09}) )."793 This interest is motivated by the fact that nuclear regions are indicative of only 15 percent of the total stellar mass and of less than 10 percent of the angular momentum ofa galaxy (i.c.. assuming a de Vaucouleurs r7 light profile and a Dat rotation prolile).," This interest is motivated by the fact that nuclear regions are indicative of only $\sim$ 15 percent of the total stellar mass and of less than 10 percent of the angular momentum of a galaxy (i.e., assuming a de Vaucouleurs $^{1/4}$ light profile and a flat rotation profile)."794 In numerical simulations. the elliciencv of galaxy formation mechanisms are predicted to vary with raclius leaving measurable changes at cillerent galactocentric radii.," In numerical simulations, the efficiency of galaxy formation mechanisms are predicted to vary with radius leaving measurable changes at different galactocentric radii."795 The spatial distribution of these observed. stellar properties. and their relationship to galaxy structura parameters. provide unique clues to constrain competing galaxy formation processes.," The spatial distribution of these observed stellar properties, and their relationship to galaxy structural parameters, provide unique clues to constrain competing galaxy formation processes."796 A specific cxample is the mass-metallicity gracicon relation found. by Spolaoretal.(2009a)., A specific example is the mass-metallicity gradient relation found by \cite{spolaor09a}.797. Phe correlation shows a sharp change in slope at a dynamical mass of ~ ü . ∆∫≻⊳⋅↱≻↓∪↓↳∖↓⋅↿∖⊓⋅↦⇀∪≿⇡∿↓≤∩⋡∐↥∢⋅⊔↓∢⋅⇂⋜↧∐⊔↛∐∙∖⇁⋏∙≟↓⋅⋯⇂⊓⋅⊔↿≱∖∪ qs," The correlation shows a sharp change in slope at a dynamical mass of $\sim$ $\times 10^{10}$ $_{\odot}$ (i.e., $M_{B} \sim -19$ )."798 un . ⊔↓∪↓⋅∢⊾⊔↓⋜↧⊳∖⊳∖⊀↓∖⇁∢⊾⋏∙≟⋜↧↓⋜∟∖⊀⊓⊾⊳∖↿∖⊲⊔⋅↦↓↥⊲↓⋏∙≟↓↕−↓⊔⊔↓⊀↓⊔∪⊳∖⊀∐∙∖⇁⋏∙≟⋜↧↓⋜∟∖⊲⊓⊾⊳∖⊐∐∥↿⋖⋅⊔ with increasing mass. perhaps due to the progressively larger number of mergers that these galaxies undergo to assemble their mass.," The metallicity gradients of more massive galaxies (i.e., high-luminosity galaxies) flatten with increasing mass, perhaps due to the progressively larger number of mergers that these galaxies undergo to assemble their mass."799 In the remnants. the eradients are. partially regenerated if à central burst of star formation is induced bv the merger.," In the remnants, the gradients are partially regenerated if a central burst of star formation is induced by the merger."800 In low-mass (ie... low-Iuminositv). galaxies. an early star-forming collapse with a varving star formation ellicieney. is required. in order to explain the steepening of eradients with increasing mass.," In low-mass (i.e., low-luminosity) galaxies, an early star-forming collapse with a varying star formation efficiency is required in order to explain the steepening of gradients with increasing mass."801The depthof the galaxy,The depthof the galaxy802ΚΙ) where projects objects onto a plane orthogonal to the wavevector k. P(X) is the magnetic power spectrum and in the interests of simplicity I have neglected an antisymmetric. helical component.,"') where projects objects onto a plane orthogonal to the wavevector $\mathbf{k}$ , $\mathcal{P}_B(k)$ is the magnetic power spectrum and in the interests of simplicity I have neglected an antisymmetric, helical component."803 H(x) 1s the Heaviside function. which ts defined to vanish for x«0 and to be unity for x>0.," $H(x)$ is the Heaviside function, which is defined to vanish for $x<0$ and to be unity for $x\geq 0$."804" The power spectrum is defined as The analyticity of PyPop, requires 25>2. corresponding to magnetic fields generated by causal processes (?).."," The power spectrum is defined as The analyticity of $\mathcal{P}_BP_{ab}$ requires $n_B\geq 2$, corresponding to magnetic fields generated by causal processes \citep{Durrer:2003ja}."805 Inflation can produce fields with jg——3. corresponding to near seale-invariance.," Inflation can produce fields with $n_B\rightarrow -3$, corresponding to near scale-invariance."806 Some current constraints (generally based on the two-point moments) constrain the spectral index to 5«—0.12 ? at confidence and rp=-23745 at l-c., Some current constraints (generally based on the two-point moments) constrain the spectral index to $n_B<-0.12$ \cite{Paoletti:2010rx} at confidence and $n_B=-2.37^{+0.88}_{-0.73}$ at $1$ $\sigma$.807 The amplitude of the power spectrum Αμ can be normalised to observation either by the mean square field (22??.forexample) or more commonly by the field smoothed on a scale ο] (see for example ?.. CFPRO9 and BIO) but this choice is widely prevalent in the literature).," The amplitude of the power spectrum $A_B$ can be normalised to observation either by the mean square field \citep[for example]{Finelli:2008xh,Paoletti:2008ck,Caprini:2009vk,Bonvin:2010nr} or more commonly by the field smoothed on a scale $\lambda$ (see for example \citet{Mack:2001gc}, CFPR09 and B10) but this choice is widely prevalent in the literature)."808 In this paper we do not make contact with observation and leave Αρ unfixed., In this paper we do not make contact with observation and leave $A_B$ unfixed.809 Note. though. that the normalisation requires 5>—3 to keep the integration finite.," Note, though, that the normalisation requires $n_B\geq -3$ to keep the integration finite."810 The magnetic field contributes to the Euler and Einstein equations through the stress-energy tensor r(K)., The magnetic field contributes to the Euler and Einstein equations through the stress-energy tensor $\tau^\mu_\nu(\mathbf{k})$.811 As the Poynting vector vanishes to first order and the magnetic energy density is equivalent to the isotropic pressure it Is sufficient to consider the stress tensor τρ). T!5(K)). is the self-convolution of the magnetic field.," As the Poynting vector vanishes to first order and the magnetic energy density is equivalent to the isotropic pressure it is sufficient to consider the stress tensor $\tau^a_b(\mathbf{k})$, ), is the self-convolution of the magnetic field."812 The stress tensor can be separated into the isotropic pressure (scalar trace). anisotropic pressure (traceless scalar). vector and transverse-traceless (TT) tensor components. which we denote by r. rs. r] and τa͵ respectively.," The stress tensor can be separated into the isotropic pressure (scalar trace), anisotropic pressure (traceless scalar), vector and transverse-traceless (TT) tensor components, which we denote by $\tau$, $\tau_S$, $\tau_a^V$ and $\tau_{ab}^T$ respectively."813 For more details see BO6., For more details see B06.814 The magnetic field also contributes through the Lorentz force and this has been studied in BO6 and (?2):: however. here we focus on the statistics of the stresses themselves.," The magnetic field also contributes through the Lorentz force and this has been studied in B06 and \citep{Paoletti:2008ck,Paoletti:2010rx}; however, here we focus on the statistics of the stresses themselves."815" Magnetic fields have been separated into ""ultra-violet and “infra-red” cases by the behaviour of their stress power spectra: the power spectra for 7,>—3/2 are dominated by the damping scale and referred to as “ultra-violet” fields. while the spectra for 5<—3/2 are independent of &.(77) across a wide range of scales and referred to as fields."," Magnetic fields have been separated into “ultra-violet” and “infra-red” cases by the behaviour of their stress power spectra; the power spectra for $n_B\geq -3/2$ are dominated by the damping scale and referred to as “ultra-violet” fields, while the spectra for $n_B<-3/2$ are independent of $k_c(\eta)$ across a wide range of scales and referred to as ``infra-red'' fields."816" It was noted in ? (hereafter BIQ) that this has consequences for the ""coherence"" of the stresses.", It was noted in \citet{Brown:2010ms} (hereafter B10) that this has consequences for the “coherence” of the stresses.817 Since the damping scale is time-dependant. the statistics induced by à magnetic field on the matter perturbations are in principle also time-dependant.," Since the damping scale is time-dependant, the statistics induced by a magnetic field on the matter perturbations are in principle also time-dependant."818" In that paperI identified a coherence scale ου below which the stresses are ""decoherent and the standard techniques for evaluating CMB signals is suspect.", In that paperI identified a coherence scale $k_\mathrm{Coh}$ below which the stresses are “decoherent” and the standard techniques for evaluating CMB signals is suspect.819 The coherence scale is of the order of the damping, The coherence scale is of the order of the damping8202008).,.821. However. several authors have reported the detectious of the TPE through the observations ou the Ilelk rather than IIL Lye forest or metal absorption lines2008).," However, several authors have reported the detections of the TPE through the observations on the He, rather than H, $\alpha$ forest or metal absorption lines."822. Those detections suggest that the QSO lifetime should be zLO'vr., Those detections suggest that the QSO lifetime should be $\ga10^7\yr$.823 Currently it is still unclear whether that apparent contradiction is due to some selection effects in observations or the complications imtroduced bv other factors. such as. the deusity enhancement iu the QSO near zones or the anisotropic radiation frou QSOs.," Currently it is still unclear whether that apparent contradiction is due to some selection effects in observations or the complications introduced by other factors, such as, the density enhancement in the QSO near zones or the anisotropic radiation from QSOs."824 Iu this paper. we study the LOSPE aud the TPE of QSOs. with taking into account the deusity eublaucemen in the QSO proximity region. their anisotropic UV radiation. and their lifetime: aud the purpose is no oulv to solve the apparent contradiction among the observational constraints on the QSO lifetime from current TPE observations. but also to demonstrate tha the LOSPE and the TPE combine to put coustraiuts on both the QSO lifetime and the opening angle of torus associated with QSOs sinultaucouslv.," In this paper, we study the LOSPE and the TPE of QSOs, with taking into account the density enhancement in the QSO proximity region, their anisotropic UV radiation, and their lifetime; and the purpose is not only to solve the apparent contradiction among the observational constraints on the QSO lifetime from current TPE observations, but also to demonstrate that the LOSPE and the TPE combine to put constraints on both the QSO lifetime and the opening angle of torus associated with QSOs simultaneously."825 The paper is organized as follows., The paper is organized as follows.826 Ta Section ??.. we illustrate the ecometiy of the proximity region of a QSO in the observer's rest frame that can be affected by UV photons cmutted from the QSO.," In Section \ref{sec:Geom}, we illustrate the geometry of the proximity region of a QSO in the observer's rest frame that can be affected by UV photons emitted from the QSO."827 Accounting the PE of (fe)QSOs. we use a Monte-C'arlo method to generate a large umber of Lva forest spectra of feOSOs aud beQSOs as described in Section 3.. based on some statistical distributions of the III column density. the Doppler factor of Lya absorption lines. and the redshift distribution of the ΠΙΠΜΟΟ density of these lines2009).," Accounting the PE of (fg)QSOs, we use a Monte-Carlo method to generate a large number of $\alpha$ forest spectra of fgQSOs and bgQSOs as described in Section \ref{sec:MCsimu}, based on some statistical distributions of the HI column density, the Doppler factor of $\alpha$ absorption lines, and the redshift distribution of the number density of these lines."828. With these svuthetic Lya forest spectra. we illustrate both the optical depth decrease due to the LOSPE aud the TPE of QSOs and then compare them with current observational results on type 1 QSOs in Section ??..," With these synthetic $\alpha$ forest spectra, we illustrate both the optical depth decrease due to the LOSPE and the TPE of QSOs and then compare them with current observational results on type 1 QSOs in Section \ref{sec:results}."829 Considering that future N-rav observations potentially discover a large umber of type 2 QSOs. the TPE of type 2 QSOs is also investigated in Section ??..," Considering that future X-ray observations potentially discover a large number of type 2 QSOs, the TPE of type 2 QSOs is also investigated in Section \ref{sec:results}."830 Our simmiation results demoustrate that the density chhancement near the QSOs. the QSO lifetime. aud the opening anele of the tori associated with the QSOs can be simultaneously constrained through measurements on both the LOSPE aud the TPE.," Our simulation results demonstrate that the density enhancement near the QSOs, the QSO lifetime, and the opening angle of the tori associated with the QSOs can be simultaneously constrained through measurements on both the LOSPE and the TPE."831 Discussious and conclusious are given in Section ??.., Discussions and conclusions are given in Section \ref{sec:conclusion}.832" Iu the paper. We adopt the IIubble constant Tlkuis aud the cosinological parameters (0,,,004)(0.27.0.73) 2009)."," In the paper, We adopt the Hubble constant $H_0=71\kms$ and the cosmological parameters $(\Omega_{\rm m},\Omega_{\Lambda})=(0.27,0.73)$ ."833. Iu this section. we illustrate how the geometry of the xoxinuitv region of a feQsSO iu the distant observers rane ds affected by the age of the QSO aud the anisotropic feature of its radiation," In this section, we illustrate how the geometry of the proximity region of a fgQSO in the distant observer's frame is affected by the age of the QSO and the anisotropic feature of its radiation."834" Iu general. we describe the region near a ο by the plivsical distance ofa point from the QSO R and its polar angle 0 measured roni the observer's LOS ιο, OC in Figure 1))."," In general, we describe the region near a fgQSO by the physical distance of a point from the QSO $R$ and its polar angle $\theta$ measured from the observer's LOS (i.e., OC in Figure \ref{fig:f1}) )."835 From Livan forest spectra. the distant observer deduces he proxinitv region which can be affected bw the eOSO radiation through the light passing by the region.," From $\alpha$ forest spectra, the distant observer deduces the proximity region which can be affected by the fgQSO radiation through the light passing by the region."836 Considering the finite speed of the light. the combination of the helt traveling time from the affected region to the observer and the time of the feQSO lieht. traveling frou. its location to its affected region should not be longer than the light traveling time from the feQsO to the observer by the QSO age.," Considering the finite speed of the light, the combination of the light traveling time from the affected region to the observer and the time of the fgQSO light traveling from its location to its affected region should not be longer than the light traveling time from the fgQSO to the observer by the QSO age."837 That is. in the distaut observers rest frame. photons emitted from the QSO can reach a plivsical distance of at most R.(7..)=|OA| from the QSO as shown iu Figure 1. and (1cosd.)στο. where 0. is the angle of OA from the observers LOS OC. zy is the QSO age. aud © is the speed of light.," That is, in the distant observer's rest frame, photons emitted from the QSO can reach a physical distance of at most $R_*(\theta_*)=|{\rm838OA}|$ from the QSO as shown in Figure \ref{fig:f1}, and $R_*(1-\cos\theta_*)=c\tauq$, where $\theta_*$ is the angle of OA from the observer's LOS OC, $\tauq$ is the QSO age, and $c$ is the speed of light."839 The RAO.) gives the apparent time-delay cuvelope within which the ionization state of (hydrogen) atoms can be possibly affected by UV radiation from the QSO., The $R_*(\theta_*)$ gives the apparent time-delay envelope within which the ionization state of (hydrogen) atoms can be possibly affected by UV radiation from the QSO.840 Considering a beQSO of which the LOS to the observer is separated from the feQSO by a transverse proper distance of R4. the intersection point of the heQsSO LOS with the time-delay cuvelope (point A in Figure 1)) is given by 0.=Ri).," Considering a bgQSO of which the LOS to the observer is separated from the fgQSO by a transverse proper distance of $R_{\perp}$, the intersection point of the bgQSO LOS with the time-delay envelope (point A in Figure \ref{fig:f1}) ) is given by $\theta_*=2\arctan( c\tauq/R_{\perp})$."841" The Lye forest iu the spectrum of the2arctau(czo/ beOSO may be then affected by the feQSO at observational waveleneth Ax121GA(1|za). where τι is the redshift of the interaction point A. We have zaig—(0b|ptgοRyase. where ty. ds tho redshitt of the feQSO. Πιν=eten is the the plivsical distance from A to DB shown in Figure 1.. poiut D is located on the LOS to the beQSO aud has the same distance/redshift to the observer as the feQSO. aud £(:)-2Il,L5)|Og."," The $\alpha$ forest in the spectrum of the bgQSO may be then affected by the fgQSO at observational wavelength $\lambda\leq1216{\rm \AA}(1+z_A)$, where $z_A$ is the redshift of the interaction point A. We have $z_A\simeq z_{\rm fg}-(1+z_{\rm fg})E(z_{\rm842fg})R_{\parallel,\rm A}/c$, where $z_{\rm fg}$ is the redshift of the fgQSO, $R_{\parallel,\rm A}=\frac{\cos\theta_*}{1- \cos\theta_*}c\tauq$ is the the physical distance from A to B shown in Figure \ref{fig:f1}, point B is located on the LOS to the bgQSO and has the same distance/redshift to the observer as the fgQSO, and $E(z)=H_0\sqrt{\Omega_{\rm m}(1+z)^3+\Omega_{\Lambda}}$."843 The photoionization chhancement atVIENI a particular point on the LOS to the beQSO due to the feQSO can be characterized by the ratio of i;=Poso/Trvp. where Poso d the photoionization rate due to the QSO UV radiation and Dvspds the photoionization rate due to the cosmic UVB.," The photoionization enhancement at a particular point on the LOS to the bgQSO due to the fgQSO can be characterized by the ratio of $\omega\equiv\Gamma_{\rm844QSO}/\Gamma_{\rm UVB}$, where $\Gamma_{\rm QSO}$ is the photoionization rate due to the QSO UV radiation and $\Gamma_{\rm UVB}$ is the photoionization rate due to the cosmic UVB."845 The latest constraints on the cosine UWB show that Τον is roughly a constant over redshift from 2 to 1 e605510Ds1 du2008a.. ~1L3«10Es on 2005.. sce also 2005)).," The latest constraints on the cosmic UVB show that $\Gamma_{\rm UVB}$ is roughly a constant over redshift from 2 to 4 (e.g., $\sim8460.5\times 10^{-12}{\rm s}^{-1}$ in, $\sim 1-1.3\times 10^{-12}847{\rm s}^{-1}$ in , see also )."848 In this paper. we choose Trypcm10Ds1," In this paper, we choose $\Gamma_{\rm UVB}\simeq 10^{-12}{\rm s}^{-1}$."849" The Toso ata distance & from the f5Q50VOSGO Isτω nfLosolah?elf)or)hidi, where Logo(00) is the huninosity of the QSO per unit frequeney at its intrinsic frequeney v enütted at time t=TeBR(1cos@)fe since its nuclear activity is triggered. vy is the Lyman μπιτ frequency. ayp(7)wv5m is the IIT photoionization cross-section 1989).. aud R can be approximated as the correspondiug hnuninuosityv distance as long as it is xunall enough."," The $\Gamma_{\rm850QSO}$ at a distance $R$ from the fgQSO is $\int^{\infty}_{\nu_0} \frac{L_{\rm851QSO,\nu}(t)}{4\pi R^2}\frac{\sigma_{\rm HI}(\nu)}{h\nu}d\nu$, where $L_{\rm852QSO,\nu}(t)$ is the luminosity of the QSO per unit frequency at its intrinsic frequency $\nu$ emitted at time $t=\tauq-R(1-\cos\theta)/c$ since its nuclear activity is triggered, $\nu_0$ is the Lyman limit frequency, $\sigma_{\rm853HI}(\nu)\propto \nu^{-3}$ is the HI photoionization cross-section , and $R$ can be approximated as the corresponding luminosity distance as long as it is small enough."854" Iu this paper. we assume LosouwX(viéry) "". "," In this paper, we assume $L_{\rm855QSO,\nu}\propto (\nu/\nu_0)^{-0.5}$ ."856Due to the time delay. we have Toso=0 and w= Oat those points with R»R.(0).," Due to the time delay, we have $\Gamma_{\rm QSO}=0$ and $\omega=0$ at those points with $R>R_*(\theta)$."857 Iu the AGN unification model1995).. however. the UV. radiation. from a QSO cau be highly anisotropic depending ou whether the torus associated with the QSO blocks its radiation along the LOS to the observer. and this ecometrical effect results in the observational differences between type 1 aud type 2 QSOs.," In the AGN unification model, however, the UV radiation from a QSO can be highly anisotropic depending on whether the torus associated with the QSO blocks its radiation along the LOS to the observer, and this geometrical effect results in the observational differences between type 1 and type 2 QSOs."858 The anisotropic radiation of QSOs leads to different ionization states of itssurrounding ICM in different directions and thus we may have ciffereut observational PEs for type 1 aud tvpe 2 QSOs as follows., The anisotropic radiation of QSOs leads to different ionization states of itssurrounding IGM in different directions and thus we may have different observational PEs for type 1 and type 2 QSOs as follows.859irradiated σας giant.,irradiated gas giant.860 These (wo characteristics may or may not be related: the obvious next test would be to extend these observations to a much lareer saniple of planets to determine which. if any. of the other 21 known transiting planets show similar temperature inversions.," These two characteristics may or may not be related; the obvious next test would be to extend these observations to a much larger sample of planets to determine which, if any, of the other 21 known transiting planets show similar temperature inversions."861 The very bright 3.0 flux from the core-dominated planet ID 149026b 2007) indicates Chat this planet may. also have a temperature inversion. as predicted by Fortneyetal.(2006b):: this result should be confirmed by observations at additional wavelengths in the near fiture.," The very bright 8.0 flux from the core-dominated planet HD 149026b \citep{har07} indicates that this planet may also have a temperature inversion, as predicted by \citet{fort06b}; this result should be confirmed by observations at additional wavelengths in the near future."862 Given (he imminent depletion of ervogen. al which point only the 3.6 and 4.5 channels will be functioning. it is worth noting that the best evidence for the temperature inversion in IID 209458b's atmosphere comes [rom observations in these two shorter-waveleneth channels.," Given the imminent depletion of cryogen, at which point only the 3.6 and 4.5 channels will be functioning, it is worth noting that the best evidence for the temperature inversion in HD 209458b's atmosphere comes from observations in these two shorter-wavelength channels."863 provides the optimal platorm for this type of measurement. and it would be relatively straightforward. to survey. all of the known bright. transiting svslenis as part of the post-crvogenicmission!.," provides the optimal platform for this type of measurement, and it would be relatively straightforward to survey all of the known bright transiting systems as part of the post-cryogenic."864. Such a survey has the potential to provide a definitive answer to the question of what properties of the planet or parent star lead to these temperature inversions. and perhaps shed light on the nature of the clouds or other upper-at(mosphere optical absorbers that. are needed to produce (he temperature inversion.," Such a survey has the potential to provide a definitive answer to the question of what properties of the planet or parent star lead to these temperature inversions, and perhaps shed light on the nature of the clouds or other upper-atmosphere optical absorbers that are needed to produce the temperature inversion."865" This work is based on observations made with theTelescope.. which is operated by the Jet Propulsion. Laboratory. California Institude of Technology. wider contract to NASA,"," This work is based on observations made with the, which is operated by the Jet Propulsion Laboratory, California Institude of Technology, under contract to NASA."866 Support for this work was provided hy NASA through an award issued by JPL/Caltech., Support for this work was provided by NASA through an award issued by JPL/Caltech.867 ITAL was supported by a National Science Foundation Graduate Research Fellowship., HAK was supported by a National Science Foundation Graduate Research Fellowship.868 AB would like to acknowledge support from NASA under grants NNGOA4GL22G and NNNOTAGSOG and through the NASA Astrobiology Institute under Cooperative Agreement No., AB would like to acknowledge support from NASA under grants NNG04GL22G and NNX07AG80G and through the NASA Astrobiology Institute under Cooperative Agreement No.869 CAN-02-OS8-02 issued through the Olfice of Space Science., CAN-02-OSS-02 issued through the Office of Space Science.870 We would also like to thank J. Matthews for sharing MOST results in advance of publication., We would also like to thank J. Matthews for sharing MOST results in advance of publication.871solar mass (Chabrier2001:Kroupa2002).,"solar mass \citep{chabrier01,kroupa02}."872. However. this is a consequence of our limited mass resolution. which prevents us from forming stars less massive than 0.5 M. and hence biases our mean mass towards higher values. (," However, this is a consequence of our limited mass resolution, which prevents us from forming stars less massive than 0.5 $_{\odot}$, and hence biases our mean mass towards higher values. ("873We return to this point in Section 3.3. below).,We return to this point in Section \ref{resn} below).874 In run D. we again lind a greater dillerence in behaviour. but even in this case. the mean stellar mass remains relatively small. at roughly 2AL..," In run B, we again find a greater difference in behaviour, but even in this case, the mean stellar mass remains relatively small, at roughly 2 $_{\odot}$."875 H therefore appears that the presence or absence of molecules does not strongly allect either the star formation rate of the clouds or the mass function of the stars that form within them., It therefore appears that the presence or absence of molecules does not strongly affect either the star formation rate of the clouds or the mass function of the stars that form within them.876 Conspicuous by its absence [rom our discussion so far das been run A. the run in which we assumed that the gas remained optically thin throughout the simulation.," Conspicuous by its absence from our discussion so far has been run A, the run in which we assumed that the gas remained optically thin throughout the simulation."877 In his run. we find a very dillerent outcome.," In this run, we find a very different outcome."878 Star formation is strongly suppressed. and the first star does not form until Ξ1.9 Myr. or roughly three global free-Lall times after the einning of the simulation.," Star formation is strongly suppressed, and the first star does not form until $t = 7.9$ Myr, or roughly three global free-fall times after the beginning of the simulation."879 The results of this run suggest hat it is the ability of the cloud to shield itself from the elfects. of the interstellar radiation field. rather than the ormation of molecules within the cloud. that plavs the most important role in regulating star formation within the cloud.," The results of this run suggest that it is the ability of the cloud to shield itself from the effects of the interstellar radiation field, rather than the formation of molecules within the cloud, that plays the most important role in regulating star formation within the cloud."880 (ef.Ixrumholz.Leroy&Melxee2011) 1n order to understand. why molecular gas appears to be of only very limited. importance in determining the star formation rate. it is useful to look at the thermal state of the gas in the dillerent runs at the point at which they begin forming stars.," \citep[c.f.][]{klm11}881 In order to understand why molecular gas appears to be of only very limited importance in determining the star formation rate, it is useful to look at the thermal state of the gas in the different runs at the point at which they begin forming stars."882 This is illustrated in Figure 2 for runs D. C. Di and D2.," This is illustrated in Figure \ref{tphase} for runs B, C, D1 and D2."883 For comparison. we also show the temperature distribution of the gas in run A at /=2.3Myr aat a similar time to the other four runs. albeit roughly 5.6 Myr before run A itself begins to form stars).," For comparison, we also show the temperature distribution of the gas in run A at $t = 2.3 \: {\rm Myr}$ at a similar time to the other four runs, albeit roughly 5.6 Myr before run A itself begins to form stars)."884 “Phe first point to note is the basic similarity of the temperature distribution in most of the runs., The first point to note is the basic similarity of the temperature distribution in most of the runs.885 In runs D. C. D1 and D2. the temperature decreases [rom roughly LOO Ix at ο—I0cm to 10 [x at n=10em! and 8 Ix at ο210em7.," In runs B, C, D1 and D2, the temperature decreases from roughly 100 K at $n \sim 10 \: {\rm cm^{-3}}$ to 10 K at $n = 10^{5} \: {\rm cm^{-3}}$ and 8 K at $n = 10^{6} \: {\rm cm^{-3}}$."886" This corresponds o a relationship between temperature and density that can νο approximated as Toxp""7 at p<Loem"". or a relationship between pressure. and. density Pxo. in good agreement with the relationship Pxp'? proposed Larson(1985.2005)."," This corresponds to a relationship between temperature and density that can be approximated as $T \propto \rho^{-0.25}$ at $n < 10^{5} \: {\rm cm^{-3}}$, or a relationship between pressure and density $P \propto \rho^{0.75}$, in good agreement with the relationship $P \propto \rho^{0.73}$ proposed by \citet{larson85,larson05}."887. The fact that the elfective equation of state of the gas is significantly softer than isothermal Σοκ p) means that the local Jeans mass decreases rapidly with increasing density within the cloud. a factor which is known to greatly assist gravitational fragmentation (seee.g.Clover&Ixlessen2008:Dopckeetal. 2011).," The fact that the effective equation of state of the gas is significantly softer than isothermal $P \propto \rho$ ) means that the local Jeans mass decreases rapidly with increasing density within the cloud, a factor which is known to greatly assist gravitational fragmentation \citep[see e.g.][]{li03,jappsen05,clark08,dopcke11}."888. In run A. on he other hand. there is a brief. period of cooling at. low densities. but the σας then begins to reheat at. densities n500em and the temperature in the densest gas is uigher than the temperature at the edge of the eloud.," In run A, on the other hand, there is a brief period of cooling at low densities, but the gas then begins to reheat at densities $n > 500 \: {\rm cm^{-3}}$, and the temperature in the densest gas is higher than the temperature at the edge of the cloud."889 Lt is herefore not surprising that gravitational fragmentation is strongly suppressed in this run., It is therefore not surprising that gravitational fragmentation is strongly suppressed in this run.890 Η we look in more detail at the relationship between emperature and density in the four runs that. do. show significant cooling. then several adcditional features become apparent.," If we look in more detail at the relationship between temperature and density in the four runs that do show significant cooling, then several additional features become apparent."891" First. all of the runs show a significant degree of scatter in the relationship at densities between nον100cm and n~107em (in run B) or pn—LO""emE (in the other runs). but this scatter abruptly. vanishes at ugher densities."," First, all of the runs show a significant degree of scatter in the relationship at densities between $n \sim 100 \: {\rm cm^{-3}}$ and $n \sim 10^{4} \: {\rm cm^{-3}}$ (in run B) or $n \sim 10^{5} \: {\rm cm^{-3}}$ (in the other runs), but this scatter abruptly vanishes at higher densities."892 This pronounced change in behaviour is due in part to a change in the dominant. coolant within he clouds., This pronounced change in behaviour is due in part to a change in the dominant coolant within the clouds.893 At low densities. gas-phase coolants (primarily Cand CO) dominate. while at. higher densities. energy ransfer between gas ancl dust becomes the dominant process regulating the gas temperature.," At low densities, gas-phase coolants (primarily $^{+}$ and CO) dominate, while at higher densities, energy transfer between gas and dust becomes the dominant process regulating the gas temperature."894 In the regime dominated w gas-phase cooling. the local cooling rate depends on the ocal value of the optical depth in the appropriate cooling inc. and hence on the local details of the velocity structure of the cloud.," In the regime dominated by gas-phase cooling, the local cooling rate depends on the local value of the optical depth in the appropriate cooling line, and hence on the local details of the velocity structure of the cloud."895 In the dust-cominated regime. on the other iuxd. the gas temperature quickly converges to the dust emperature. which is determined. largely. by continuum emission and absorption and which is thus insensitive to the velocity structure of the cloud.," In the dust-dominated regime, on the other hand, the gas temperature quickly converges to the dust temperature, which is determined largely by continuum emission and absorption and which is thus insensitive to the velocity structure of the cloud."896 In addition. another elfect contributing to the scatter at low densities is the sensitivity of the photoclectric heating rate to the visual extinction.," In addition, another effect contributing to the scatter at low densities is the sensitivity of the photoelectric heating rate to the visual extinction."897 We know from previous work that the mean visual extinction within a given fluid element. in a turbulent cloud. is only ουν correlated with the volume density of the cloud (Cloveretal.2010).. and hence the value of the photoelectric jeating rate shows a significant scatter at any given density.," We know from previous work that the mean visual extinction within a given fluid element in a turbulent cloud is only poorly correlated with the volume density of the cloud \citep{g10}, and hence the value of the photoelectric heating rate shows a significant scatter at any given density."898 Ad low densities. photoclectric heating is the dominant jw source (see Section 3.2.4. below). and so this scatter in the heating rate helps to create a significant scatter in the gas temperature.," At low densities, photoelectric heating is the dominant heat source (see Section \ref{dom_therm} below), and so this scatter in the heating rate helps to create a significant scatter in the gas temperature."899 At higher densities. photoelectric wating becomes far less important. and so the scatter in he photoelectric heating rate has much less effect on the emperature.," At higher densities, photoelectric heating becomes far less important, and so the scatter in the photoelectric heating rate has much less effect on the temperature."900 A second. feature to note is the pronounced. παρ in the temperature-density. düstribution. roughly centered at T—20 Ix and n~2107cm° that is present in runs C and D1. but absent in runs D and D2.," A second feature to note is the pronounced “hump” in the temperature-density distribution, roughly centered at $T \sim 20$ K and $n \sim 2 \times 10^{4} \: {\rm cm^{-3}}$, that is present in runs C and D1, but absent in runs B and D2."901" This [eature is caused bv LH» formation heating: we assume (followingTakahashi&Uehara2001) that Ll, molecules form on dust. grains with a high degree of rotational and vibrational excitation. and at densities above a few thousand. particles per cubic centimetre. much of this energv. is converted. into thermal energv by collisional de-cxcitation of the newly-formed LL» molecules."," This feature is caused by $_{2}$ formation heating: we assume \citep[following][]{tu01}902 that $_{2}$ molecules form on dust grains with a high degree of rotational and vibrational excitation, and at densities above a few thousand particles per cubic centimetre, much of this energy is converted into thermal energy by collisional de-excitation of the newly-formed $_{2}$ molecules."903 This does not occur in run B because no IL» is allowed to form in that run. and it does not occur in run D2 because the hydrogen starts in fully molecular form. ancl although some is subsequently. dissociated. the atomic hydrogen fraction at the appropriate densities remains small (see Figure 4)).," This does not occur in run B because no $_{2}$ is allowed to form in that run, and it does not occur in run D2 because the hydrogen starts in fully molecular form, and although some is subsequently dissociated, the atomic hydrogen fraction at the appropriate densities remains small (see Figure \ref{rhoh2}) )."904 Finally. the inlluence. of the CO in runs DI. and D2 is clear if we look at the temperature clistribution of the gas at densities of around 10* to 10+em7.," Finally, the influence of the CO in runs D1 and D2 is clear if we look at the temperature distribution of the gas at densities of around $10^{3}$ to $10^{4} \: {\rm cm^{-3}}$."905 ‘The münimum. gas temperature reached in the runs with CO is approximately 5 Ix. roughly half the size of the minimum temperature reached in the runs that must rely on cooling.," The minimum gas temperature reached in the runs with CO is approximately 5 K, roughly half the size of the minimum temperature reached in the runs that must rely on $^{+}$ cooling."906 Llowever. despite the fact that the gas is able to reach lower temperatures in the runs with CO cooling. very little of it does so: most of the gas at these densities has a temperature that is close to 10 Ix. implving that the difference in the mean temperature of the gas is much smaller than the difference in the minimum temperature.," However, despite the fact that the gas is able to reach lower temperatures in the runs with CO cooling, very little of it does so: most of the gas at these densities has a temperature that is close to 10 K, implying that the difference in the mean temperature of the gas is much smaller than the difference in the minimum temperature."907 Given the similarity between the temperature distribution in run DB. and. that in runs C. D1 and 039. it may at first seem odd that star formation in the former is," Given the similarity between the temperature distribution in run B and that in runs C, D1 and D2, it may at first seem odd that star formation in the former is"908Galaxy eroups are ubiquitous. intermediate density structures. spamuine the range between isolated field ealaxies aud rich clusters (Coller&Uuchra1983:Tully1987:Eleetal.2001:Tago 2010)..,"Galaxy groups are ubiquitous, intermediate density structures, spanning the range between isolated field galaxies and rich clusters \citep{1983ApJS...52...61G,1987ApJ...321..280T,2004MNRAS.348..866E,2010A&A...514A.102T}."909 According to the hierarchical scenario of the formation of larec-scale structure. groups are the building blocks of rich clusters of galaxies (Douéetal.2008:MeCGoo2009)..," According to the hierarchical scenario of the formation of large-scale structure, groups are the building blocks of rich clusters of galaxies \citep{2008A&A...489...11B,2009MNRAS.400..937M}."910 Thus. understanding the physical properties of clusters and their member galaxies requires knowledge of the extent to which galaxy evolution occurs m the group environment.," Thus, understanding the physical properties of clusters and their member galaxies requires knowledge of the extent to which galaxy evolution occurs in the group environment."911 The effectiveness of pliasical processes that may be responsible for this evolution. like ranpressure stripping aud strangulation. is a function of the density of intergalactic gas.," The effectiveness of physical processes that may be responsible for this evolution, like ram-pressure stripping and strangulation, is a function of the density of intergalactic gas."912 There are ouly a handful of wavs to detect this gas. namely X-ray observations which are linited to the more massive groups aud UV absorption line studies which probe gas with a limuted telperature range.," There are only a handful of ways to detect this gas, namely X-ray observations which are limited to the more massive groups and UV absorption line studies which probe gas with a limited temperature range."913 We discuss here a complementary method. applicable in even low mass groups. which cau determine the intergalactic eas density using beut-double radio sources.," We discuss here a complementary method, applicable in even low mass groups, which can determine the intergalactic gas density using bent-double radio sources."914 Groups are likely to contain a significant fraction of the barvous iu the local universe (Fukugitaetal.1998:Mulcliaey. 2000).," Groups are likely to contain a significant fraction of the baryons in the local universe \citep{1998ApJ...503..518F,2000ARA&A..38..289M}."915 Attempts to reconcile the barvou content of the local universe with the barvon deusitv seen at high redshift have failed to locate the majority of barvous (Fukueita&Peebles2001).., Attempts to reconcile the baryon content of the local universe with the baryon density seen at high redshift have failed to locate the majority of baryons \citep{2004ApJ...616..643F}.916 Specifically. the birvou deficit appears to scale with poteutial well depth such that the barvon content of massive clusters Is nearly as expected while groups aud individual galaxies are lacking (Belletal.2003:Dai2010)..," Specifically, the baryon deficit appears to scale with potential well depth such that the baryon content of massive clusters is nearly as expected while groups and individual galaxies are lacking \citep{2003ApJ...585L.117B, 2010ApJ...719..119D}."917 These ocallv “uuissing barvous are predicted by simulations ο exist in a warn-hot interealactic ποπα (WIIIMO hat pervades Lhuge-cale structures (Con&Ostriker1999:Davéetal. 2001).," These locally “missing baryons” are predicted by simulations to exist in a warm-hot intergalactic medium (WHIM) that pervades large-scale structures \citep{1999ApJ...514....1C,2001ApJ...552..473D}."918 Iu παος this gas Is shock heated during structure formation. leacing to emperatures in the range 107<T«105 K and a woad deusity distribution that is peaked at 10—20 ines the critical density of the universe (Cen&Oxriker 2006)..," In simulations this gas is shock heated during structure formation, leading to temperatures in the range $10^5 < T < 10^7$ K and a broad density distribution that is peaked at $10-20$ times the critical density of the universe \citep{2006ApJ...650..560C}."919 Ultraviolet (UV) aud N-ray absorption line detections certainly confirm the existence of the highly ionized WIITM (see the review by Bregman (2007))) but he spatial distribution of this gas inside aud outside of ealaxies is still wncoustrained., Ultraviolet (UV) and X-ray absorption line detections certainly confirm the existence of the highly ionized WHIM (see the review by \citet{2007ARA&A..45..221B}) ) but the spatial distribution of this gas inside and outside of galaxies is still unconstrained.920 We explore the potential iupact of the presence of a widespread intergalactic medium with with densities ~10°10bem? by looking at the fate of the gas content of dwarf spheroidal galaxies., We explore the potential impact of the presence of a widespread intergalactic medium with with densities $\sim 10^{-3}-10^{-4} \cmc$ by looking at the fate of the gas content of dwarf spheroidal galaxies.921 Dwarf spheroidal (dSph) galaxies are darkauatter domunated. eas poor. low surface brightness. aud have stellar populatious with old to intermediate ages.," Dwarf spheroidal (dSph) galaxies are dark-matter dominated, gas poor, low surface brightness, and have stellar populations with old to intermediate ages."922 Evideuce for the role of environnient iu the evolution of dSpls is seem in the morphologv-deusitv relations which exist for the Local Croup and nearby eroups (vandeuDereh1991:x 2009):: dSplis are prefereutially found near large galaxies.," Evidence for the role of environment in the evolution of dSphs is seen in the morphology-density relations which exist for the Local Group and nearby groups \citep{1994AJ....107.1328V,2009AJ....138.1037C,2003AJ....125..593S,2009AJ....137.3038B}; dSphs are preferentially found near large galaxies."923 Their progeuitors are thought to be similar to chart iregular (dav) galaxies which were processed bv their euvironnient. causing angular moment loss and σας stripping (Grebeletal.2003:Maver2010)...," Their progenitors are thought to be similar to dwarf irregular (dIrr) galaxies which were processed by their environment, causing angular moment loss and gas stripping \citep{2003AJ....125.1926G,2010AdAst2010E..25M}."924 This Is supported by the observation that structurally. wheu conrpariue surface briglhtuess profile shapes. dSplis. cars. and ealaxy disks formu: a family that is distinct from," This is supported by the observation that structurally, when comparing surface brightness profile shapes, dSphs, dIrrs, and galaxy disks form a family that is distinct from"925 Ifa fixed fraction ey; (pi for ‘pair instability) of the mass converted into sstars ds expelled. ino pair-instability supernovae. the nucleosvnthetic viel calculation. from. Leger Woosley (2002) mav be used to determine the contribution from sstars to the metallicity of the ΓΔ.,"If a fixed fraction $\epsilon_{\mathrm pi}$ (`pi' for `pair instability') of the mass converted into stars is expelled in pair-instability supernovae, the nucleosynthetic yield calculation from Heger Woosley (2002) may be used to determine the contribution from stars to the metallicity of the IGM."926 bor where ; is à species and f; and f; are the mass fractions of species £ in the Universe and Sun. respectively.," For where $i$ is a species and $f^U_i$ and $f^\odot_i$ are the mass fractions of species $i$ in the Universe and Sun, respectively."927" Similarly. if we denote the ejected mass fraction of species 7 by f£. then and where £5;—fFff, is the production factor of species i."," Similarly, if we denote the ejected mass fraction of species $i$ by $f^E_i$, then and where $P_i\equiv f^E_i/f^\odot_i$ is the production factor of species $i$."928 dleger Woosley (2002. table 4) calculated. 2; for many isotopes and stellar masses.," Heger Woosley (2002, table 4) calculated $P_i$ for many isotopes and stellar masses."929 We here take ~200M. as a fiducial mass for a pair-instability supernova progenitor., We here take $\sim 200~\msun$ as a fiducial mass for a pair-instability supernova progenitor.930 A few values of interest. from their table are /5(;=When MO 21A 778i το)=(13.2.45.8.85.7353. 49.8).," A few values of interest from their table are $P_i(i=931\mbox{$ $},\mbox{$ $},932\mbox{$ $},\mbox{$ $},933\mbox{$ $})934=(13.2,45.8,85.7,353,49.8)$ ."935 In t ," In general, the highest values of $P_i$ are for the alpha elements."936becomes, Observations of the abundance of species $i$ in the high-redshift universe are sometimes quoted in slightly different notation from [i].937," Assuming $\epsilon_{\mathrm938pi}\Omega_{\mathrm{III}}\ll\Omega_{\mathrm{B}}$, $[i/\mathrm{H}]\simeq[i]$."939values £5 we e," Using tabulated values for $f^E_i$ (Heger Woosley 2002, table 3), it is straightforward to calculate $\Omega_{i}=f^U_i \Omega_{\mathrm B}$."940xpect the jtepalocnet ‘nebula," With assumptions about the mixing of the ejecta from stars, measurements of metals in the IGM at high redshifts (or the metallicities of stars formed at high redshifts) can place a limit on a combination of the IMF of stars (which we simplify into the parameter $\epsilon_{\mathrm pi}$ ) and $\Omega_{\mathrm III}$."941:cont{ervationsadn of th," For example, if $\epsilon_{\mathrm pi}=1$ and $f_{\mathrm B}\equiv\Omega_{\mathrm III}/\Omega_{\mathrm942B}\simeq3\times10^{-3}$, then stars would, in the mean, enrich the Universe to the solar abundance of silicon already at a redshift $\ga 7$."943e ab ," In contrast, if $\epsilon_{\mathrm pi}=0$, then metallicity measurements place no constraints on the abundance of stars."944‘To compare our models. we present the SER as a function of redshift in1.," To compare our models, we present the SFR as a function of redshift in."945. We assume that sstar formation shuts oll at τω27: this may. be due o photoevaporation of low-mass haloes due to reionization (Barkana&Loeb19990) or some other process.," We assume that star formation shuts off at $z_{\mathrm end}\simeq7$; this may be due to photoevaporation of low-mass haloes due to reionization \cite{bar99}946 or some other process."947 shows the SERs normalized toy= OA., shows the SFRs normalized to $\eta=0.4$ .948 The curves are abelled with the corresponding value of fis., The curves are labelled with the corresponding value of $f_{\mathrm B}$.949" shows 41,762) for the SERs of1.", shows $\Omega_{\mathrm III}(z)$ for the SFRs of.950. The iorizontal lines are explained in refelisesec.., The horizontal lines are explained in \\ref{discsec}.951 Aletal-free very massive stars have spectra similar to a ~LOW blackbody spectrum (Brommetal.2001b).," Metal-free very massive stars have spectra similar to a $\sim95210^5~\kelvin$ blackbody spectrum \cite{bro01c}."953.. Most of the energy. is then racliatecl in photons with energies -13.6eV., Most of the energy is then radiated in photons with energies $>13.6~\ev$.954 There are also many photons produced capable of ionizing ((but see Schaerer 2002)., There are also many photons produced capable of ionizing (but see Schaerer 2002).955 Phe specific luminosity per solar mass of very massive stars is almost independent of stellar mass (Brommetal.2001b)., The specific luminosity per solar mass of very massive stars is almost independent of stellar mass \cite{bro01c}.956.. We will therefore take the spectrum of a 1000AL. star as our fiducial input sstellar spectrum., We will therefore take the spectrum of a $1000~\msun$ star as our fiducial input stellar spectrum.957" a {minors the ithost lo general.eas ""gr1enot highest.Incorporated olinto stars:are Torwe call this gas the s."," When a star becomes luminous, we expect the host halo to contain gas not incorporated into stars; we call this gas the `nebula.'"958 Werefer to the gas outside the collapsed halo as the IGM., Werefer to the gas outside the collapsed halo as the IGM.959 The physical environment ofsstar formation will likely undergo a transition from dense, The physical environment ofstar formation will likely undergo a transition from dense960processing.,processing.961 For GP Com and CE 315 the puzzle is the absence of heavy elements such as Mg. Si. Ca and Fe that would be expected.," For GP Com and CE 315 the puzzle is the absence of heavy elements such as Mg, Si, Ca and Fe that would be expected."962 This led to suggest a low metallicity for the progenitor and leaves the question of where the abundant N has come from., This led to suggest a low metallicity for the progenitor and leaves the question of where the abundant N has come from.963 In any case the high N/C (assuming the UV estimate in GP Com indeed is a lower limit) points to a helium white dwarf donor (Fig. L9. ," In any case the high N/C (assuming the UV estimate in GP Com indeed is a lower limit) points to a helium white dwarf donor (Fig. \ref{fig:Nratios}) ),"964while in that case the high N/O ratio points towards a progenitor of the helium white dwarf on the high mass side., while in that case the high N/O ratio points towards a progenitor of the helium white dwarf on the high mass side.965 A similar conclusion can be drawn for the most recently discovered AM CVn star (SDSS JO804+16) for which N/C > 10 and N/O 10 have been derived(2)., A similar conclusion can be drawn for the most recently discovered AM CVn star (SDSS J0804+16) for which N/C $>$ 10 and N/O $\gtrsim$ 10 have been derived.966. Some limits have been derived from the X-ray spectra of AM CVn stars., Some limits have been derived from the X-ray spectra of AM CVn stars.967" derives detailed abundances for GP Com of Noo—09.Xy=LT107.YXo2.25""Ny.107Ne2237,Xj,8«10"" andalimiton C No2:010%."," derives detailed abundances for GP Com of $X_{\rm He} = 0.99,968X_N = 1.7\, \times 10^{-2}, X_{\rm O} = 2.2\, \times 10^{-3}, X_{\rm969 Ne} = 3.7\, \times 10^{-3},X_{\rm S} = 2.3\,970\times 10^{-4}, X_{\rm Fe} = 8\, \times 10^{-5}$ and a limit on C $971X_{\rm C} < 2\, \times 10^{-3}$."972 This is roughly consistent with the results from the optical spectra. except for a lower N/O ratio of about 8.," This is roughly consistent with the results from the optical spectra, except for a lower N/O ratio of about 8."973" find slightly higher values Xy—ὃ102.Xo6«""a ratio of N/O=5."," find slightly higher values $974X_{\rm N} = 3\,975\times 10^{-2}, X_{\rm O} = 6\, \times 10^{-3}$, a ratio of $\rm N/O =9765$."977" find. in addition. evidence for enhanced N in AM CVn. HP Lib. CR Boo. SDSS J1240-01 and CE 315. as expected from the He-rich optical spectrum,"," find, in addition, evidence for enhanced N in AM CVn, HP Lib, CR Boo, SDSS J1240-01 and CE 315, as expected from the He-rich optical spectrum."978 For the other AM CVn systems. the determination of the donor type is not so clear.," For the other AM CVn systems, the determination of the donor type is not so clear."979 Prominent N lines manifest themselves in the red part of the spectrum and that is also where the strongest C and O lines would show up. if they would be present.," Prominent N lines manifest themselves in the red part of the spectrum and that is also where the strongest C and O lines would show up, if they would be present."980 However. most studies of AM CVn stars have been made in the blue part of the spectrum.," However, most studies of AM CVn stars have been made in the blue part of the spectrum."981 For SDSS J1240-01 there is a red spectrum in which indeed the N lines. as well as quite strong Si lines are detected but no sign of C or O lines(2).," For SDSS J1240-01 there is a red spectrum in which indeed the N lines, as well as quite strong Si lines are detected but no sign of C or O lines."982. Although no detailed calculations have been made. a simple estimate. with the same LTE model that was used by2.. and suggest thatN/€71 without doubt.," Although no detailed calculations have been made, a simple estimate, with the same LTE model that was used by, and suggest that $\rm N/C > 1$ without doubt."983 This rules out hvbrind white dwarf donors and helium star donors. except the least evolved ones.," This rules out hybrind white dwarf donors and helium star donors, except the least evolved ones."984 In table | we also list the detected elements in UCXBs., In table \ref{tab:abundances} we also list the detected elements in UCXBs.985 These come rom X-ray. UV and optical spectroscopy. as well as abundances inferred from the properties of type I X-ray bursts.," These come from X-ray, UV and optical spectroscopy, as well as abundances inferred from the properties of type I X-ray bursts."986 Unfortunately in many cases the detection of elements is uncertain and. even in he cases where the detections are solid. it is typically impossible ο derive meaningful abundance ratios because model spectra are not yet very realistic22).," Unfortunately in many cases the detection of elements is uncertain and, even in the cases where the detections are solid, it is typically impossible to derive meaningful abundance ratios because model spectra are not yet very realistic."987. The extremely short orbital period of 4U 1820-30 led to he suggestion that the transferred material in this system must be hydrogen-deficient22)., The extremely short orbital period of 4U 1820-30 led to the suggestion that the transferred material in this system must be hydrogen-deficient.988 The properties of type I X-ray bursts has led to the conclusion that the transferred material in jU 1820-30 is indeed helium. possibly with a small amount of H(??).. This is consistent with an evolved main-sequence donor if H really is present. or with a helium white dwarf or helium star donor if not.," The properties of type I X-ray bursts has led to the conclusion that the transferred material in 4U 1820-30 is indeed helium, possibly with a small amount of H. This is consistent with an evolved main-sequence donor if H really is present, or with a helium white dwarf or helium star donor if not."989 However. have shown that. even with full magnetie braking. this scenario can be discarded because it requires very finely tuned initial parameters and predicts many systems with 10«Piπα60 for each observed mmin binary.," However, have shown that, even with full magnetic braking, this scenario can be discarded because it requires very finely tuned initial parameters and predicts many systems with $10 <990P_\mathrm{orb}/{\rm min} < 60$ for each observed min binary."991 For many other Systems there are now optical spectra tha show no evidence or any H tor He in many cases) while al longer period low-mass X-ray binaries aways show strong H lines.," For many other systems there are now optical spectra that show no evidence for any H (or He in many cases), while all longer period low-mass X-ray binaries always show strong H lines."992 However. the accreion dise spectral nqodels of suggest tha amounts up to pper cent of H and He could remain undetected.," However, the accretion disc spectral models of suggest that amounts up to per cent of H and He could remain undetected."993 The best constraints are founc for 4U 1626-67 anc 4U 0614409. for wich optical spectra exclude large amounts of H or He and show C and O lines(222).," The best constraints are found for 4U 1626-67 and 4U 0614+09, for which optical spectra exclude large amounts of H or He and show C and O lines."994. The X-ray spectrum of 4U 1626-67 shows double peaked O and Ne emission lines(?).. while its UV spectrum shows strong C and O lines but not the usual He and N lines.," The X-ray spectrum of 4U 1626-67 shows double peaked O and Ne emission lines, while its UV spectrum shows strong C and O lines but not the usual He and N lines."995 This all suggests evolved helium stars or hybrid white dwarfs as donors for these two systems., This all suggests evolved helium stars or hybrid white dwarfs as donors for these two systems.996 show that the optical spectrum of 4U 1543-62 is similar to that of JU 061409., show that the optical spectrum of 4U 1543-62 is similar to that of 4U 0614+09.997 This suggests a C/O rich donor too., This suggests a C/O rich donor too.998 The low S/N spectra of 28 0918-54. XTE 0929-314 and A 1246-58 are difficult to classify. although À 1246-58 shows some hints of detected C and O lines but not He lines(2).," The low S/N spectra of 2S 0918-54, XTE 0929-314 and A 1246-58 are difficult to classify, although A 1246-58 shows some hints of detected C and O lines but not He lines."999. Now suggest. based on the type I bursts. that the donor of 28 0918-54 is more likely helium rich.," Now suggest, based on the type I X-ray bursts, that the donor of 2S 0918-54 is more likely helium rich."1000 The optical spectrum of 4U 1916-05 does not show strong He lines but is still best fitted with a He/N mixture., The optical spectrum of 4U 1916-05 does not show strong He lines but is still best fitted with a He/N mixture.1001 Finally. the broadband UV spectrum of MIS X-2 is consistent with quite strong emission lines of C and/or He(?).," Finally, the broadband UV spectrum of M15 X-2 is consistent with quite strong emission lines of C and/or He."1002. We therefore conclude that there is evidence for at least two helium star or hybrid donors (4U 1626-67 and 4U 0614409) but more detailed observations are needed to classify the rest of the observed systems., We therefore conclude that there is evidence for at least two helium star or hybrid donors (4U 1626-67 and 4U 0614+09) but more detailed observations are needed to classify the rest of the observed systems.1003 Several populationV I hydrogen-rich dwarf novae are known to apparently have periods significantly below mmin The SU UMa type dwarf nova IRXS J232953.9+062814 has an orbital period of mmin(22)., Several population I hydrogen-rich dwarf novae are known to apparently have periods significantly below min The SU UMa type dwarf nova 1RXS J232953.9+062814 has an orbital period of min.1004 report for this system an Ila to He I A6678 ratio of 3.6. by at least factor 2 lower than typical for SU UMa stars.," report for this system an ${\mathrm H\alpha}$ to He I $\lambda$ 6678 ratio of 3.6, by at least factor 2 lower than typical for SU UMa stars."1005 According to this system also has an anomalously high flux ratio., According to this system also has an anomalously high flux ratio.1006 For V485 Cen. found an orbital period of mmin This period is even shorter than the period minimum estimate for population II hydrogen-rich cataclysmic binaries2).," For V485 Cen, found an orbital period of min This period is even shorter than the period minimum estimate for population II hydrogen-rich cataclysmic binaries."1007. We may suspect that these stars belong to the evolved CV family. with an expected Voz0.1. 3&0.9. see Fig.," We may suspect that these stars belong to the evolved CV family, with an expected $X \approx 0.1$, $Y \approx10080.9$, see Fig."1009 6. but have to defer any firm conclusions until sufficient observational data have been obtained., \ref{fig:pre_min} but have to defer any firm conclusions until sufficient observational data have been obtained.1010 We have computed the ranges of abundances (assuming initial Solar metallicity) in possible donor stars of ultra-compact binaries for the three different proposed formation channels. the white dwarf channel. the helium star channel and the evolved main-sequence star channel.," We have computed the ranges of abundances (assuming initial Solar metallicity) in possible donor stars of ultra-compact binaries for the three different proposed formation channels, the white dwarf channel, the helium star channel and the evolved main-sequence star channel."101112).. First. the presence of hydrogen unambiguously points to an evolved main-sequence donor and rules out all other channels and vice versa.," First, the presence of hydrogen unambiguously points to an evolved main-sequence donor and rules out all other channels and vice versa."1012 Secondly. if no H is detected. absence of He and N may point to a hybrid white dwarf.," Secondly, if no H is detected, absence of He and N may point to a hybrid white dwarf."1013 Then if N is detected. the N/C ratio is an effective discriminant between helium white dwarf donors and helium star donors.," Then if N is detected, the N/C ratio is an effective discriminant between helium white dwarf donors and helium star donors."1014 The difference between He white dwarfs and He stars is that the former transfer matter with equilibrium N/C which mildly depends on the mass of the progenitor of the white dwarf (Fig. 33) , The difference between He white dwarfs and He stars is that the former transfer matter with equilibrium N/C which mildly depends on the mass of the progenitor of the white dwarf (Fig. \ref{fig:abund_HeWD1}) )1015and is always about 100. while in the latter N/C has to be diminished unless He didn't burn at all.," and is always about $100$, while in the latter N/C has to be diminished unless He didn't burn at all."1016 This is unlikely., This is unlikely.1017 Once this distinction is made. the N/O and N/He ratios can give further information on the main-sequence progenitor mass for the helium white dwarfs or the initial post-common-envelope period of the helium star binary.," Once this distinction is made, the N/O and N/He ratios can give further information on the main-sequence progenitor mass for the helium white dwarfs or the initial post-common-envelope period of the helium star binary."1018 If O or C is detected. the O/C ratio and the O/He ratio tor at least their limits) are effective to distinguish," If O or C is detected, the O/C ratio and the O/He ratio (or at least their limits) are effective to distinguish"1019We have thus [ar assumed all heavy elements to lie within a ceitral core.,We have thus far assumed all heavy elements to lie within a central core.1020 I1 order to see how the results are cleyendent ou this assumption. we compare our previous model with a 60MM ice core to a similar uodel with a Ice coὁ and ai envelope which is enricied by of ices.," In order to see how the results are dependent on this assumption, we compare our previous model with a $_\oplus$ ice core to a similar model with a $_\oplus$ ice core and an envelope which is enriched by $_\oplus$ of ices."1021 For the ices n tlie envelope. we use the EOS described by Saunon&Cuilot(2001).," For the ices in the envelope, we use the EOS described by \citet{SG04}."1022. Figure 2. she»ws the results of the calcul:vious in the two cases: (i) wihu ichauged opacities i.e. as calculated for a solar-coimposition mixlure) aud (ii) with 30 times larger opacities to mimic je efTect of the euichiuent of heavy elements in the envelope.," Figure \ref{fig:evol_opa} shows the results of the calculations in the two cases: (i) with unchanged opacities (i.e., as calculated for a solar-composition mixture) and (ii) with 30 times larger opacities to mimic the effect of the enrichment of heavy elements in the envelope."1023 Basically. when using zu uuchanged pacity table (tlie dotted line). iere is very Litle dillerence between a planet that has all its heavy ements in tlie coὁ aud a plauet that has teim mixed throughout its euvelope.," Basically, when using an unchanged opacity table (the dotted line), there is very little difference between a planet that has all its heavy elements in the core and a planet that has them mixed throughout its envelope."1024 However. large diferences arise when the opacities are allected proportionally to the amount of heavy. elemeuts 1lat are minec (the dashed liie).," However, large differences arise when the opacities are affected proportionally to the amount of heavy elements that are mixed (the dashed line)."1025 Iu that case. the cooling ancl contractjon timescale. which is dominated by radiative transport in the outer radiative zone. becomes loug. aud preveuts the rapid contraction of the planet.," In that case, the cooling and contraction timescale, which is dominated by radiative transport in the outer radiative zone, becomes long, and prevents the rapid contraction of the planet."1026 These results coufirur again that our estinates of the amount of heavy elenents in HDI19026b are lower limits aud that the panet iudeed must contain a significant amoult of heavy elements., These results confirm again that our estimates of the amount of heavy elements in HD149026b are lower limits and that the planet indeed must contain a significant amount of heavy elements.1027 If most of the leavy elevents are located bek»w the radiative zone. which is not unlikely. then we expect our constraints to be relatively accurate.," If most of the heavy elements are located below the radiative zone, which is not unlikely, then we expect our constraints to be relatively accurate."1028 On the other hand. if the maerial is minxecl in the outer radiative zoue. we expect that its Interior contains more heavy elemeus by up to ~20M than calculated 1lere.," On the other hand, if the material is mixed in the outer radiative zone, we expect that its interior contains more heavy elements by up to $\sim 20\,\rm M_\oplus$ than calculated here."1029 We have used a rather stinplifiecl approac1 for the caleulatious of the interior structure., We have used a rather simplified approach for the calculations of the interior structure.1030 Ou the other hand. reality is without doubt more couiplex.," On the other hand, reality is without doubt more complex."1031 However. this should not affect. significantly the global coustiants that are derived in Taje 1..," However, this should not affect significantly the global constraints that are derived in Table \ref{tab:constraints}."1032" First. the two extreme compositions used for the heavy. elemeus (σος andd ""rocks?) enswe that most variations due to improved EOS. lor example. are likely to fall in between the range of values that are cousicderecd."," First, the two extreme compositions used for the heavy elements (“ices” and “rocks”) ensure that most variations due to improved EOS, for example, are likely to fall in between the range of values that are considered."1033 Qur externa boundary coudition is extretrely simplified., Our external boundary condition is extremely simplified.1034 Although it agrees with more cetailec atinosphlierie. noclels. one has to account. for he fact that the atinospheric temperatures may be higher. in partictar iL the atinospleye is itself enriched i heavy elements (seeFortiusevetal.2006).," Although it agrees with more detailed atmospheric models, one has to account for the fact that the atmospheric temperatures may be higher, in particular if the atmosphere is itself enriched in heavy elements \citep[see][]{Fortney06}."1035. A higher atmosperic temperature leads to a slightly larger radius. everything else )elug tlie saine.," A higher atmospheric temperature leads to a slightly larger radius, everything else being the same."1036 However. given te decrease of the opacity with increasii temperature in that regime. the radius increase is very |nited.," However, given the decrease of the opacity with increasing temperature in that regime, the radius increase is very limited."1037 Other [actors point toward a slightly larger amour ol heavy elements than calculated. here: (1) as cliscussed. tie likely increase of the opacities in an enriched envelope: (ii) the presence of any other energy source such as the one that is required to reproduce the radius of HD209[58b: (iii)," Other factors point toward a slightly larger amount of heavy elements than calculated here: (i) as discussed, the likely increase of the opacities in an enriched envelope; (ii) the presence of any other energy source such as the one that is required to reproduce the radius of HD209458b; (iii)"1038"Adding all of the above uncertainties (18 us from the optical template, 8 us from the radio template, 6 us from DM uncertainty, 4 us from the fit to the offset between the radio and optical TOAs) linearly we obtain a total uncertainty of 36 µς. This is likely to be an overestimate of the total uncertainty since all individual deviations have to be in the same direction to end up at this value.","Adding all of the above uncertainties (18 $\mu$ s from the optical template, 8 $\mu$ s from the radio template, 6 $\mu$ s from DM uncertainty, 4 $\mu$ s from the fit to the offset between the radio and optical TOAs) linearly we obtain a total uncertainty of 36 $\mu$ s. This is likely to be an overestimate of the total uncertainty since all individual deviations have to be in the same direction to end up at this value."1039" Adding all uncertainties in quadrature yields a final uncertainty of 21 ys. From reffig:results we conclude that the variation in the optical-radio delay is substantially larger than the individual uncertainties on the TOAs (which are between 1.4 and 2.1 ys, Ισ)."," Adding all uncertainties in quadrature yields a final uncertainty of 21 $\mu$ s. From \\ref{fig:results} we conclude that the variation in the optical-radio delay is substantially larger than the individual uncertainties on the TOAs (which are between 1.4 and 2.1 $\mu$ s, $\sigma$ )."1040 The average value of the delays obtained during the first and second night differ by 6 us (only 1.4 us when one excludes the deviant point in the second night)., The average value of the delays obtained during the first and second night differ by 6 $\mu$ s (only 1.4 $\mu$ s when one excludes the deviant point in the second night).1041" The observed scatter during the first night and the possible difference between the two nights, suggests that small variations (less than about 10 ys) exist."," The observed scatter during the first night and the possible difference between the two nights, suggests that small variations (less than about 10 $\mu$ s) exist."1042" For this relative comparison the uncertainties introduced by determining phase zero on both the radio and optical templates (which each amount to 8 ws) should not be considered, since they affect all data points in the same way."," For this relative comparison the uncertainties introduced by determining phase zero on both the radio and optical templates (which each amount to 8 $\mu$ s) should not be considered, since they affect all data points in the same way."1043" We consider it unlikely that this night-to-night variation is solely caused by variations in the DM, since a variation of ~1 times that of typical monthly variations is needed in 1 day."," We consider it unlikely that this night-to-night variation is solely caused by variations in the DM, since a variation of $\sim$ 1 times that of typical monthly variations is needed in 1 day."1044" Variations in the peak position on time scales of days and shorter are studied in more detail by Karpov et ((2007)), who find, during one observation, variations at the ~150 ps-level."," Variations in the peak position on time scales of days and shorter are studied in more detail by Karpov et \cite{karpov:2007}) ), who find, during one observation, variations at the $\sim$ 150 $\mu$ s-level."1045 In total 927 Giant radio pulses were detected during the radio observations., In total 927 Giant radio pulses were detected during the radio observations.1046 The rate of GPs was much higher during the second night where we have optical data (on average 1 per 6.6 s) than the first night (1 per 29.5 s)., The rate of GPs was much higher during the second night where we have optical data (on average 1 per 6.6 s) than the first night (1 per 29.5 s).1047 Following the method by Shearer et ((2003)) we have selected the optical data coincident with Giant Pulses (GPs) detected in the radio observations., Following the method by Shearer et \cite{shearer:2003}) ) we have selected the optical data coincident with Giant Pulses (GPs) detected in the radio observations.1048" The barycentric arrival times of the GPs were computed usingTEMPO2, while the event time tags were corrected using our barycentering code."," The barycentric arrival times of the GPs were computed using, while the event time tags were corrected using our barycentering code."1049 We checked that these corrections are consistent to better than 15 µς and that therefore this procedure provides the required accuracy., We checked that these corrections are consistent to better than 15 $\mu$ s and that therefore this procedure provides the required accuracy.1050" We find, in total, 603 GPs coincident with optical data."," We find, in total, 603 GPs coincident with optical data."1051 We made sure that these GPs occurred near the main peak of the profile and selected data half a phase range before and half a phase range after the main peak (in the radio)., We made sure that these GPs occurred near the main peak of the profile and selected data half a phase range before and half a phase range after the main peak (in the radio).1052 The data was then folded to obtain a pulse profile coincident with radio GPs., The data was then folded to obtain a pulse profile coincident with radio GPs.1053 A reference profile was also constructed from data spanning 80 cycles around (but not including) this cycle., A reference profile was also constructed from data spanning 80 cycles around (but not including) this cycle.1054 This was done since changes in sky background and airmass force us to select data close to the cycle coincident with the GP., This was done since changes in sky background and airmass force us to select data close to the cycle coincident with the GP.1055" Several different ranges were tried and all gave similar results, with obviously better statistics as the number was increased."," Several different ranges were tried and all gave similar results, with obviously better statistics as the number was increased."1056" We settled for 80 cycles, since this gives a very good reference profile and yet it still only spans 2.7 s of data."," We settled for 80 cycles, since this gives a very good reference profile and yet it still only spans 2.7 s of data."1057 We ensured that no optical data was missing during these periods (e.g. at the end of an observation)., We ensured that no optical data was missing during these periods (e.g. at the end of an observation).1058 We present the obtained results in Fig. 6.., We present the obtained results in Fig. \ref{fig:gp}.1059 As can be seen from this figure no clear excess is present., As can be seen from this figure no clear excess is present.1060 Depending on the choice of phase range this excess amounts to about 2.lc., Depending on the choice of phase range this excess amounts to about $\sim2.1\sigma$.1061 We view this a confirmation of the result of Shearer et ((2003)) and shows that their dataset has a much better statistical quality given the longer exposure times and larger telescope aperture., We view this a confirmation of the result of Shearer et \cite{shearer:2003}) ) and shows that their dataset has a much better statistical quality given the longer exposure times and larger telescope aperture.1062" In order to investigate whether we are able to detect a delay between the pulse profiles obtained at different wavelengths we divided the photons obtained during the observations described above in three adjacent bands, each containing approximately"," In order to investigate whether we are able to detect a delay between the pulse profiles obtained at different wavelengths we divided the photons obtained during the observations described above in three adjacent bands, each containing approximately"1063the heating shell where the energy. is well determined.,the heating shell where the energy is well determined.1064 We integrate through the critical point by using a first order Tavlor expansion and appropriate limit(s). although this introduces a small discrepancy between the steady state and time-dependent results in this region (Figure 4)).," We integrate through the critical point by using a first order Taylor expansion and appropriate limit(s), although this introduces a small discrepancy between the steady state and time-dependent results in this region (Figure \ref{fig:nrsteadysoln}) )."1065 Having determined the energy. ancl heating gradient at cach point in the wind we integrate (11)) both inwards and outwards from the chosen. point above the heating shell using a fourth order Runge-hutta integrator (scaling (11)) to the units described in refscesscaling))., Having determined the energy and heating gradient at each point in the wind we integrate \ref{eq:machno}) ) both inwards and outwards from the chosen point above the heating shell using a fourth order Runge-Kutta integrator (scaling \ref{eq:machno}) ) to the units described in \\ref{sec:scaling}) ).1066 The velocity profile is then given by (07=Λο where The resulting steady. wind solution is shown in Figure 4 along with the time-dependent solution., The velocity profile is then given by $v^2 = M^2 c_s^2$ where The resulting steady wind solution is shown in Figure \ref{fig:nrsteadysoln} along with the time-dependent solution.1067 The two profiles are in excellent agreement. proving the validity of our time-dependent numerical solution and the assumption that the wind is in a steady state.," The two profiles are in excellent agreement, proving the validity of our time-dependent numerical solution and the assumption that the wind is in a steady state."1068 The steady solution thus provides an accurate estimate of the velocity at arbitrarily large radii (although as pointed out. previously this is set by the value of the steady state Bernoulli energy), The steady solution thus provides an accurate estimate of the velocity at arbitrarily large radii (although as pointed out previously this is set by the value of the steady state Bernoulli energy).1069 Using the steady wind extrapolation of the time-dependent solution. we can determine the relationship between the heating rate and the terminal wind velocities.," Using the steady wind extrapolation of the time-dependent solution, we can determine the relationship between the heating rate and the terminal wind velocities."1070 In. order to make a useful comparison between the heating rates used in both the Newtonian and the relativistic regimes. we need to define a local canonical heating rate κ) valid in both sets of regimes.," In order to make a useful comparison between the heating rates used in both the Newtonian and the relativistic regimes, we need to define a local canonical heating rate $\Lambda_c(r)$ valid in both sets of regimes."1071 In dimensional terms the heating rate Αλ) corresponds to an input energy. per unit mass per unit time., In dimensional terms the heating rate $\Lambda(r)$ corresponds to an input energy per unit mass per unit time.1072 Thus we need to define the local canonical heating rateas for some relevant energy A‘ and some relevant timescale 2M., Thus we need to define the local canonical heating rateas for some relevant energy $\Delta E$ and some relevant timescale $\Delta t$.1073 ‘There are clearly many different wavs in which we might define a canonical heating rate., There are clearly many different ways in which we might define a canonical heating rate.1074 We find. however. that our results are not sensitive to the particular choice we make.," We find, however, that our results are not sensitive to the particular choice we make."1075 We shall make use of a definition which draws on the physical processes we expect to be behind the jet acceleration. process., We shall make use of a definition which draws on the physical processes we expect to be behind the jet acceleration process.1076 Even though the processes by which this occurs are still obscure. we expect the energy for the jet to be provided fundamentally by liberation of energy in a rotating Dow.," Even though the processes by which this occurs are still obscure, we expect the energy for the jet to be provided fundamentally by liberation of energy in a rotating flow."1077 Thus. with this physical motivation in mind. we take the canonical energy. per unit mass. AL. to be the energy. released locally by. bringing to rest a particle of unit mass which is orbiting in a circular orbit at radius r.," Thus, with this physical motivation in mind, we take the canonical energy per unit mass, $\Delta E$, to be the energy released locally by bringing to rest a particle of unit mass which is orbiting in a circular orbit at radius $r$."1078 In the Newtonian regime this is simply the kinetic energy of a circular orbit (An alternative possibility. for example. would be to take AL to be the energy. released by dropping a particle [rom infinity and bringing it to rest at racius r. which would correspond to the escape energy from that racius. G@AL/r.)," In the Newtonian regime this is simply the kinetic energy of a circular orbit (An alternative possibility, for example, would be to take $\Delta E$ to be the energy released by dropping a particle from infinity and bringing it to rest at radius $r$, which would correspond to the escape energy from that radius, $GM/r$ .)"1079" By similar reasoning. we take the canonical timescale on which the energy. is released to be the orbital timescale at radius r. that is AL0,4. where Using this. we are now in a position to define a local canonical heating rate as For intercomparison of our various wind computations both in the Newtonian and in the relativistic regimes. we now use the canonical heating rate derived above to define a cimensionless heating rate for cach wind computation."," By similar reasoning, we take the canonical timescale on which the energy is released to be the orbital timescale at radius $r$, that is $\Delta t = \Omega_o^{-1}$, where Using this, we are now in a position to define a local canonical heating rate as For intercomparison of our various wind computations both in the Newtonian and in the relativistic regimes, we now use the canonical heating rate derived above to define a dimensionless heating rate for each wind computation."1080 Because heat is aclded over a range of radii. we need to define the cimensionless heating rate CV as an appropriate volume average.," Because heat is added over a range of radii, we need to define the dimensionless heating rate $\langle \Lambda1081\rangle$ as an appropriate volume average."1082 We shall define where Muss is the radius at which the heating rate A(r) takes its maximum value and ry and re are the lower and upper bounds of the heating shell respectively., We shall define where $r_{\rm max}$ is the radius at which the heating rate $\Lambda(r)$ takes its maximum value and $r_1$ and $r_2$ are the lower and upper bounds of the heating shell respectively.1083 The relation between this average dimensionless heating rate and the terminal wind velocity is shown in Figure 5.., The relation between this average dimensionless heating rate and the terminal wind velocity is shown in Figure \ref{fig:nrrates}.1084 Phe wind velocities are plotted in units of the escape velocity ee ab Ze; and solutions are computed for wind. velocities of up to  Bee.," The wind velocities are plotted in units of the escape velocity $v_{\rm1085esc}$ at $R_*$ and solutions are computed for wind velocities of up to $\sim 3v_{\rm esc}$ ."1086 Phe important point in the present analysis is that the heating rate can be meaningfully compared to the relativistic results (see below)., The important point in the present analysis is that the heating rate can be meaningfully compared to the relativistic results (see below).1087"We also study the star-formation effects in a single, dense region: viz.,","We also study the star-formation effects in a single, dense region: viz.,"1088" the central 30 kpc of galaxy A, presented in Fig. 6.."," the central 30 kpc of galaxy A, presented in Fig. \ref{fig:sfr-gal-A100}."1089" Here there is little effect on the initial peak, which we expect since this region should have a short cooling time due to its overdensity."," Here there is little effect on the initial peak, which we expect since this region should have a short cooling time due to its overdensity."1090" However, star formation below z=1 is enhanced: of the stellar mass within 30kpc is formed after z=1 in the New UV case, compared to for Old UV (and for FG UV)."," However, star formation below $z=1$ is enhanced: of the stellar mass within 30kpc is formed after $z=1$ in the New UV case, compared to for Old UV (and for FG UV)."1091 The bump in New UV centered at ~7 Gyr ago matches well with the merger-event peak in gas accretion we saw centered at ~8 Gyr ago in Fig 4.., The bump in New UV centered at $\sim$ 7 Gyr ago matches well with the merger-event peak in gas accretion we saw centered at $\sim$ 8 Gyr ago in Fig \ref{fig:cgasacc-A100}.1092 This results in the New UV version of galaxy A actually having stars at the present within the 30 kpc radius compared to Old UV; FG UV has only a increase (again see Table 2))., This results in the New UV version of galaxy A actually having stars at the present within the 30 kpc radius compared to Old UV; FG UV has only a increase (again see Table \ref{tab:stars}) ).1093" New UV+X has a very late burst of star formation 0.5 Gyr ago which is due to a the infall of warm gas that cools in situ, but this is not enough to make up for the earlier deficit, and it has slightly less stellar mass within 30 kpc than Old UV; of the stellar mass is formed after z—1."," New UV+X has a very late burst of star formation 0.5 Gyr ago which is due to a the infall of warm gas that cools in situ, but this is not enough to make up for the earlier deficit, and it has slightly less stellar mass within 30 kpc than Old UV; of the stellar mass is formed after $z=1$."1094" Finally, we convert these star-formation histories into present luminosities via the code of assuming a Salpeter IMF and solar metallicity; (2003),,bolometric magnitude and color results for Galaxy A are presented in Table 3.."," Finally, we convert these star-formation histories into present luminosities via the code of, assuming a Salpeter IMF and solar metallicity; bolometric magnitude and color results for Galaxy A are presented in Table \ref{tab:obs}."1095 No dust extinction effects were included., No dust extinction effects were included.1096" In brief, we see that compared to Old UV, New UV has only a slight increase in bolometric luminosity (0.13 mag) and blueness (0.09 mag), and FG UV has even less change, while New UV-+X is 1.3 mag or 3.25 times brighter, and 0.28 mag bluer in U-B, thanks to its late burst of star formation."," In brief, we see that compared to Old UV, New UV has only a slight increase in bolometric luminosity (0.13 mag) and blueness (0.09 mag), and FG UV has even less change, while New UV+X is 1.3 mag or 3.25 times brighter, and 0.28 mag bluer in U-B, thanks to its late burst of star formation."1097" These results, like those for the gas, are dependent on the environment of the galaxy."," These results, like those for the gas, are dependent on the environment of the galaxy."1098" For example, with the Galaxy E simulations the New UV+X model has an decrease in total stellar mass compared to Old UV, but has stellar mass in the central 30kpc from enhanced gas accretion. ("," For example, with the Galaxy E simulations the New UV+X model has an decrease in total stellar mass compared to Old UV, but has stellar mass in the central 30kpc from enhanced gas accretion. ("1099New UV with no X-rays produces less total stellar mass and an increase within 30 kpc.),New UV with no X-rays produces less total stellar mass and an increase within 30 kpc.)1100 There is also a correspondingly stronger effect on the mean stellar age for galaxy E: the fraction of stellar mass within 30kpc formed after z=1 increases from for Old UV to with New UV+X. See refsect:disc for discussion of these differences., There is also a correspondingly stronger effect on the mean stellar age for galaxy E: the fraction of stellar mass within 30kpc formed after $z=1$ increases from for Old UV to with New UV+X. See \\ref{sect:disc} for discussion of these differences.1101" In addition to affecting the mass and hydrodynamic properties of the stars and gas in the simulations, the"," In addition to affecting the mass and hydrodynamic properties of the stars and gas in the simulations, the"1102The late-time acceleration of the expansion of the Universe has been one of the most exciting cosmological discoveries in recent years (Riessetal.1998:Perlmutter1999).,"The late-time acceleration of the expansion of the Universe has been one of the most exciting cosmological discoveries in recent years \citep{riess98,perlmutter99}."1103. Understanding the nature of this acceleration is one of the main challenges facing cosmologists., Understanding the nature of this acceleration is one of the main challenges facing cosmologists.1104 One of the key observational methods that will be used to help meet this challenge involves using Baryonie Acoustic Oscillations (BAO) in the 2-point galaxy clustering signal as a standard ruler to make precise measurements of cosmological expansion., One of the key observational methods that will be used to help meet this challenge involves using Baryonic Acoustic Oscillations (BAO) in the 2-point galaxy clustering signal as a standard ruler to make precise measurements of cosmological expansion.1105 The acoustic signature has now been convincingly detected (Percivaletal.2001:Cole2005:Eisenstein2005) using the 2dF Galaxy Redshift Survey (2dFGRS: etal. 2003)) and the Sloan Digital Sky Survey (SDSS: Yorketal. 20003).," The acoustic signature has now been convincingly detected \citep{percival01,cole05,eisenstein05}1106 using the 2dF Galaxy Redshift Survey (2dFGRS; \citealt{colless03}) ) and the Sloan Digital Sky Survey (SDSS; \citealt{york00}) )."1107 The detection has subsequently been refined using more data and better techniques. and is now producing interesting constraints on cosmological models (Percivaletal.2007a.b:Gaz-tanagaetal.2008:Sanchez2009:Percival 2009).," The detection has subsequently been refined using more data and better techniques, and is now producing interesting constraints on cosmological models \citep{percival07a,percival07b,gaztanaga08,sanchez09,percival09}."1108. Some of the next generation of sky surveys. including the Dark Energy Survey (DES the Panoramic Survey Telescope and Rapid Response System (PanSturs starrs.ita.hawaii.cctu). and the Large Synoptic Survey Telescope (LSST will use photometric techniques to estimate galaxy redshifts. rather than more precise estimates from spectroscopic emission lines.," Some of the next generation of sky surveys, including the Dark Energy Survey (DES ), the Panoramic Survey Telescope and Rapid Response System (PanStarrs ), and the Large Synoptic Survey Telescope (LSST ), will use photometric techniques to estimate galaxy redshifts, rather than more precise estimates from spectroscopic emission lines."1109 The larger uncertainties on galaxy redshifts induce errors on inferred distances in the radial direction., The larger uncertainties on galaxy redshifts induce errors on inferred distances in the radial direction.1110 The amplitude of the power spectrum and correlation function is reduced in the radial direction by this smoothing. removing information.," The amplitude of the power spectrum and correlation function is reduced in the radial direction by this smoothing, removing information."1111 In this scenario. where little information remains from fluctuations in the radial direction. it makes sense to use the projected 2-pt functions in photometric-redshift slices as the statistics to compare with models (Padmanabhanetal.2007:Blake2007).," In this scenario, where little information remains from fluctuations in the radial direction, it makes sense to use the projected 2-pt functions in photometric-redshift slices as the statistics to compare with models \citep{padmanabhan07,blake07}."1112. The projection does not completely remove problems caused by inferring distances from velocity data (.e. working in redshift-space)., The projection does not completely remove problems caused by inferring distances from velocity data (i.e. working in redshift-space).1113 The distribution of galaxies that we observe in sky surveys. where we measure radial distances from spectroscopic or photometric redshifts. is not a true 3D picture.," The distribution of galaxies that we observe in sky surveys, where we measure radial distances from spectroscopic or photometric redshifts, is not a true 3D picture."1114 We observe an apparent clustering pattern. in.redshifi-space. which is systematically different from the true distribution in. because redshifts of galaxies are altered from their Hubble flow values by peculiar velocities.," We observe an apparent clustering pattern in, which is systematically different from the true distribution in because redshifts of galaxies are altered from their Hubble flow values by peculiar velocities."1115 For example. on large scales. the," For example, on large scales, the"1116Models of magnetic reconnection. from (he very earliest. have assigned particular significance {ο points where (he magnetic fiekl vanishes: magnetic null points (Dungey1958:Sweet1955).,"Models of magnetic reconnection, from the very earliest, have assigned particular significance to points where the magnetic field vanishes: magnetic null points \citep{Dungey1958,Sweet1958}."1117. In two-dimensional reconnection models. null points (also called neutral points) are natural locations to change magnetic field line topology.," In two-dimensional reconnection models, null points (also called neutral points) are natural locations to change magnetic field line topology."1118 While three cimensions offer alternatives for topological change (Greene1988:HesseandSchindler1933).. null points are still natural locations for current intensification (Craig.FablingandLenton1995:RickarclanclTitov1996:GalseaardandNordlund1997:PontinGalsgaard2007) and for focusing of magnetosonic waves (Ilassam1992:CraigandMeClvimont1993:MeLbaughlinHood2004).," While three dimensions offer alternatives for topological change \citep{Greene1988,Hesse1988}, null points are still natural locations for current intensification \citep{Craig1995,Rickard1996,Galsgaard1997,Pontin2007} and for focusing of magnetosonic waves \citep{Hassam1992,Craig1993,McLaughlin2004}."1119. Dissipation of magnetic energv al magnetic null points is (therefore a potential source of heat in (he quiet sun corona., Dissipation of magnetic energy at magnetic null points is therefore a potential source of heat in the quiet Sun corona.1120 The effectiveness of this dissipation for heating the entire corona will depend. in part. in how null points are distributed throughout its field.," The effectiveness of this dissipation for heating the entire corona will depend, in part, in how null points are distributed throughout its field."1121 Coronal jets are taken as another observational manilestation of coronal null points., Coronal jets are taken as another observational manifestation of coronal null points.1122 Observations in EUV and X-rays show that jets. will (heir characteristic apex cusp efαἱ. 1996).. appear to be more common in coronal holes and the quiet sun than previously believed (Culhanee£a£.2007;Cirtainef2007).," Observations in EUV and X-rays show that jets, with their characteristic apex cusp \citep{Shibata1992,Shimojo1996}, appear to be more common in coronal holes and the quiet Sun than previously believed \citep{Culhane2007,Cirtain2007}."1123. Theoretical mocels of jets invoke magnetic reconnection occurring al a null point many meganieters above the photospheric surface (YokovamaandShibata1996:Moreno-Insertis.Urra 2008)..," Theoretical models of jets invoke magnetic reconnection occurring at a null point many megameters above the photospheric surface \citep{Yokoyama1996,MorenoInsertis2007}."1124 In order that such a model apply to the large number of jets observed it would be necessary Chat magnetic null points are relatively common at the altitudes of observed Cusps., In order that such a model apply to the large number of jets observed it would be necessary that magnetic null points are relatively common at the altitudes of observed cusps.1125 In many models. coronal null points occur above a photospheric field consisting of one magnetic element completely surrounded by a ring of opposing polarity (Antiochos1998:Moreno-Inserlis.GalseaardandUgarte-Urra 2008).," In many models, coronal null points occur above a photospheric field consisting of one magnetic element completely surrounded by a ring of opposing polarity \citep{Antiochos1998,MorenoInsertis2007}."1126". The null point will persist even if the continuous surrounding ring is broken. but il remains necessary that opposing polarity be founcl on ""all sides” of the central element (Seehaler1986:Deveridge. 2004)."," The null point will persist even if the continuous surrounding ring is broken, but it remains necessary that opposing polarity be found on “all sides” of the central element \citep{Seehafer1986,Beveridge2004}."1127. This suggests that coronal null points occur only under special circumstances which are likely to be found infrequently in (he actual solar photosphere. ancl raises once more the question of how common null points might be in the actual coronal magnetic field.," This suggests that coronal null points occur only under special circumstances which are likely to be found infrequently in the actual solar photosphere, and raises once more the question of how common null points might be in the actual coronal magnetic field."1128 One recent investigation by Réggnier. Parnell and Waynes (2008) [ound 80 magnetic null points over a 102Mmx116Mam patch of quiet Sun.," One recent investigation by Réggnier, Parnell and Haynes (2008) \nocite{Regnier2008} found 80 magnetic null points over a $102\,{\rm Mm}\times116\,{\rm Mm}$ patch of quiet Sun."1129 A potential field was extrapolated onto a rectilinear grid from a magnetogram made by Hinode's NF] instrument., A potential field was extrapolated onto a rectilinear grid from a magnetogram made by Hinode's NFI instrument.1130 The algorithm of Havnes and Parnell (2007) was then applied to the gridded field to locate all points where an interpolated field would vanish., The algorithm of Haynes and Parnell (2007) \nocite{Haynes2007} was then applied to the gridded field to locate all points where an interpolated field would vanish.1131" This revealed (hat. at least over that region at that time. there was a column of IN,=6.7x107 null points per square megameter. about half above a height of 2=1 Man."," This revealed that, at least over that region at that time, there was a column of $N_n=6.7\times 10^{-3}$ null points per square megameter, about half above a height of $z=1$ Mm."1132 Close. Parnell and Priest (2004) extrapolating from high-resolution," Close, Parnell and Priest (2004) \nocite{Close2004b} extrapolating from high-resolution"1133temperatures below 10? K on typical length scales of ~107 em (see 1991). emit the optical moving? lines at distances ~10 em. show strong radio emission (2 0.5So Jy at 5GHz with spectral index «—-0.6 ) on scales from 107—10! em (c.f.,"temperatures below $10^5$ K on typical length scales of $\sim 10^{12}$ cm (see ), emit the optical 'moving' lines at distances $\sim 10^{15}$ cm, show strong radio emission $\ga$ 0.5 Jy at 5GHz with spectral index $\alpha$ =-0.6 ) on scales from $^{14} - 10^{17}$ cm (c.f."1134" Vermeulen 1993. for a review ). then remain visible"" until they show up in X-rays again ~ 15 aremin from SS433. ie. at distances =6.5x10! cm."," Vermeulen 1993, for a review ), then remain 'invisible' until they show up in X-rays again $\sim$ 15 arcmin from SS433, i.e., at distances $\ga 6.5\times 10^{19}$ cm."1135 An insight into the physical mechanisms leading to this transfer of the kinetic energy of the jets into radiation of different frequencies. at different distances from the source. is certainly of great interest for our understanding of the jet phenomenon in general.," An insight into the physical mechanisms leading to this transfer of the kinetic energy of the jets into radiation of different frequencies, at different distances from the source, is certainly of great interest for our understanding of the jet phenomenon in general."1136 Using the procedures mentioned before for the production of overlaid pictures we created images in various energy ranges and formed an RGB - image. shown in reffig:rgbl..," Using the procedures mentioned before for the production of overlaid pictures we created images in various energy ranges and formed an RGB - image, shown in \\ref{fig:rgb1}. ."1137" The “red” energy band was 0.5-IkkeV. the ""green"" band 1.0—2.0 kkeV and the ""blue"" band covered the energies 2.0— kkeV. (See reffig:;jetl-s-h for the individual ""soft. and ""hard? images.)"," The “red” energy band was $-$ keV, the “green” band $-$ keV and the “blue” band covered the energies $-$ keV. (See \\ref{fig:jet1-s-h}1138 for the individual `soft' and `hard' images.)"1139 The lenticular structure of the bright spot is clearly hard emission and this hard emission extends further to the right. towards 4433.," The lenticular structure of the bright spot is clearly hard emission and this hard emission extends further to the right, towards 433."1140 At lower energies the bright spot becomes diffuse. losing its well-defined shape and filling a large part of the central image (red colors).," At lower energies the bright spot becomes diffuse, losing its well-defined shape and filling a large part of the central image (red colors)."1141 At the lowest energies the jet emission on the right side disappears., At the lowest energies the jet emission on the right side disappears.1142 Also visible is the clearly reduced emissior region in the north-eastern part of the image. the region outside the radio contours of W50.," Also visible is the clearly reduced emission region in the north-eastern part of the image, the region outside the radio contours of W50."1143 The emission filling the interior of the radio remnant ts rather soft: at energies 2 kkeV the separation of the surface brightness between inside and outside W50 disappears., The emission filling the interior of the radio remnant is rather soft; at energies $\ga$ keV the separation of the surface brightness between inside and outside W50 disappears.1144 However. the low statistics of the signal at higher energies does not permit any quantitative analysts.," However, the low statistics of the signal at higher energies does not permit any quantitative analysis."1145 Por the spectral fits we first extracted for all detectors the source photons from an ellipsoidal region comeiding with the brightest lenticular part in reffig:rgbl.., For the spectral fits we first extracted for all detectors the source photons from an ellipsoidal region coinciding with the brightest lenticular part in \\ref{fig:rgb1}.1146 Background spectra were extracted from the recast. renormalized blank-sky backgrounds as detailed above in Sect.," Background spectra were extracted from the recast, renormalized blank-sky backgrounds as detailed above in Sect."1147 2., 2.1148 Previous spectral analyses of this region favored a non-thermal power law spectrum (Yamauchi 1994. ID.," Previous spectral analyses of this region favored a non-thermal power law spectrum (Yamauchi 1994, I)."1149 reffig:pn-hard shows the result of a simultaneous fit of the PN and MOS detectors with an absorbed power lawin the 0.6-8 keV energy band.," \\ref{fig:pn-hard}1150 shows the result of a simultaneous fit of the PN and MOS detectors with an absorbed power lawin the $-$ 8 keV energy band."1151 The fit resulted in a slope of '=2.17x0.02. an absorbing column density of Ny=(0.56x0.01)10°? cm with a reduced Uu = |.085 for 852 d.o.f.," The fit resulted in a slope of $\Gamma = 2.17\pm0.02$, an absorbing column density of $_{\rm H} = (0.56\pm0.01)\times10^{22}$ $^{-2}$ with a reduced $\chi^2_{\rm red}$ = 1.085 for 852 d.o.f."1152 However. a fit with similar quality was achieved by a bremsstrahlung continuum model.," However, a fit with similar quality was achieved by a bremsstrahlung continuum model."1153" The best fit parameters were kT = 3.98+0.11 keV. Ny=(0.4140.01)%10°? em7 with a reduced y7,, = 1.076 (852 d.o.f.)."," The best fit parameters were kT = $\pm$ 0.11 keV, $_{\rm H} = (0.41\pm0.01)\times10^{22}$ $^{-2}$ with a reduced $\chi^2_{\rm red}$ = 1.076 (852 d.o.f.)."1154 In both cases there were small residuals resembling weak emission lines in the soft energy band. for example 2 0.9kkeV ILX or XXIX) in reffig:pn-hard..," In both cases there were small residuals resembling weak emission lines in the soft energy band, for example $\ma$ keV IX or XIX) in \\ref{fig:pn-hard}."1155 We therefore repeated the fit. first fitting a power law to the 2-8 keV band data only.," We therefore repeated the fit, first fitting a power law to the $-$ 8 keV band data only."1156 The extrapolation of the model showed some weak excess emission at low energies., The extrapolation of the model showed some weak excess emission at low energies.1157 We then fixed the power law parameters and fitted the total spectrum by adding a thermal (MEKAL) emission model., We then fixed the power law parameters and fitted the total spectrum by adding a thermal ) emission model.1158 The fit resulted in a Uu = 1.038 (for 853 d.o.£.), The fit resulted in a $\chi^2_{\rm red}$ = 1.038 (for 853 d.o.f.)1159" with best fit parameters of [=2.41+ 0.09. kT=0.2040.02 keV and thegalactic absorption increased to Ny=(1.07£0.24)*1077 em""."," with best fit parameters of $\Gamma = 2.41\pm0.09$ , $\pm$ 0.02 keV and thegalactic absorption increased to $_{\rm H} =1160(1.07\pm0.24)\times10^{22}$ $^{-2}$ ."1161" The contribution of the thermal component to the 0.2-2 kkeV flux with ~9.9x107 cem"" s! is of the same magnitude as the power law component of ~6.6x107 cem"" sl."," The contribution of the thermal component to the $-$ keV flux with $\sim11629.9\times10^{-12}$ $^{-2}$ $^{-1}$ is of the same magnitude as the power law component of $\sim 6.6\times10^{-12}$ $^{-2}$ $^{-1}$ ."1163"a smaller number of low-mass galaxies as compared with high-mass galaxies (9 galaxies with total stellar mass 105—10? Mo, 40 galaxies with total stellar mass 10?—10!?Mo, and 207 galaxies with total stellar mass 10!?—10! Mo).","a smaller number of low-mass galaxies as compared with high-mass galaxies (9 galaxies with total stellar mass $10^8-10^9 \rm{~M}_\odot$ , 40 galaxies with total stellar mass $10^9-10^{10} \rm{~M}_\odot$, and 207 galaxies with total stellar mass $10^{10}-10^{11} \rm{~M}_\odot$ )."1164 We now cross-correlate our sample with the morphologically classified bright galaxy catalogue of Fukugitaetal.(2007)., We now cross-correlate our sample with the morphologically classified bright galaxy catalogue of \citet{Fuku07}.1165. Their catalogue contains 2275 galaxies classified by visual inspection of SDSS images in the g-band., Their catalogue contains 2275 galaxies classified by visual inspection of SDSS images in the $g$ -band.1166 We find 283 objects overlapping between the two samples., We find 283 objects overlapping between the two samples.1167" The small overlap is partly due to the fact that around half of the objects in Fukugitaetal.(2007) are early-type galaxies (RC3 type T« 1), and partly since it is essentially the overlap between the LEDA sample and that of Fukugitaetal.(2007)."," The small overlap is partly due to the fact that around half of the objects in \citet{Fuku07} are early-type galaxies (RC3 type $T<1$ ), and partly since it is essentially the overlap between the LEDA sample and that of \citet{Fuku07}."1168". Moreover, our sample has an upper limit for the galaxy sizes due to our preferred strategy for using SkyView (see section 2.1))."," Moreover, our sample has an upper limit for the galaxy sizes due to our preferred strategy for using SkyView (see section \ref{sec:sample}) )."1169" From this sample of 283 galaxies, only 45 galaxies have been accurately classified (their T error < 1) in Fukugitaetal. (2007)."," From this sample of 283 galaxies, only 45 galaxies have been accurately classified (their T error $\le 1$ ) in \citet{Fuku07}."1170". For these objects, we find weak correlation between the morphological classification from LEDA and those from Fukugitaetal.(2007)."," For these objects, we find weak correlation between the morphological classification from LEDA and those from \citet{Fuku07}."1171". In a similar fashion to Shimasakuetal.(2001), we define the ""inverse"" concentration parameter as the ratio between the radii containing and of the Petrosian flux respectively, rso/roo provided by the SDSS services."," In a similar fashion to \citet{Shimasaku01}, we define the concentration parameter as the ratio between the radii containing and of the Petrosian flux respectively, $r_{50}/r_{90}$ provided by the SDSS services."1172" As a consistency check, we ensure that we reproduce Fig."," As a consistency check, we ensure that we reproduce Fig."1173" 10 of Shimasakuetal.(2001), i.e., that morphological classification provided by LEDA correlates with concentration parameter."," 10 of \citet{Shimasaku01}, i.e., that morphological classification provided by LEDA correlates with concentration parameter."1174" Furthermore, we find that although the vast majority of our sample have very large morphological classification uncertainties (T error > 1), the concentration parameters that we calculate for all 30374 galaxies indicate that, in agreement with Shimasaku (2001),, they are disk galaxies."," Furthermore, we find that although the vast majority of our sample have very large morphological classification uncertainties (T error $\ge 1$ ), the concentration parameters that we calculate for all 30374 galaxies indicate that, in agreement with \citet{Shimasaku01}, they are disk galaxies."1175" Regarding the correlation of the concentration parameter with morphological type, for the 309 well-classified galaxies 91=0.31, and for the full sample R*=0.16."," Regarding the correlation of the concentration parameter with morphological type, for the 309 well-classified galaxies $\mathfrak{R^2} = 0.31$, and for the full sample $\mathfrak{R^2} = 0.16$."1176" Although we find these values unconvincing as firm correlations, we acknowledge a clear trend that concentration parameter is increasing with galaxy morphological type."," Although we find these values unconvincing as firm correlations, we acknowledge a clear trend that concentration parameter is increasing with galaxy morphological type."1177" Likewise, the spread of points in asymmetry-type and velocity dispersion-type diagrams are very large, and the coefficients of determination even lower than that of the concentration parameter, however, here also the trend is acknowledged."," Likewise, the spread of points in asymmetry-type and velocity dispersion-type diagrams are very large, and the coefficients of determination even lower than that of the concentration parameter, however, here also the trend is acknowledged."1178" Given that robust morphological classification is known only for a very small subset of our entire sample, we invoke other parameters in order to be able to furtherinvestigate the scale lengths for the full sample."," Given that robust morphological classification is known only for a very small subset of our entire sample, we invoke other parameters in order to be able to furtherinvestigate the scale lengths for the full sample."1179" Following the above arguments, and their consistency with the previous findings"," Following the above arguments, and their consistency with the previous findings"1180with the Sagittarius dwarf. which are plotted as crosses in Figure6.. appear to be distributed similarly to other globular clusters at fec19 Κρο.,"with the Sagittarius dwarf, which are plotted as crosses in Figure\ref{f:rhvsmv}, appear to be distributed similarly to other globular clusters at $R_{\rm{gc}} > 15$ kpc."1181" Figure 7. shows a plot of the distribution of the globular clusters in the LMC. the SMC and the Fornax dwarf in the //;, vs. Ady plane."," Figure \ref{f:rhvsmvexternal} shows a plot of the distribution of the globular clusters in the LMC, the SMC and the Fornax dwarf in the $R_h$ vs. $M_V$ plane."1182 This figure shows that these external globular clusters also fall below the line defined by Eq. |.," This figure shows that these external globular clusters also fall below the line defined by Eq. \ref{e:cutoff},"1183 inhabiting a comparable region of the plane to that occupied by the globular clusters in the outer Galactic halo., inhabiting a comparable region of the plane to that occupied by the globular clusters in the outer Galactic halo.1184" The LMC Reticulum cluster is the most extended object in the external sample. with 7/7,=19.3 pe."," The LMC Reticulum cluster is the most extended object in the external sample, with $R_h = 19.3$ pc."1185 The resemblance between the external globular clusters and those in the outer Galactic halo may suggest a similar origin — Le. in dwarf spheroidal-like galaxies.," The resemblance between the external globular clusters and those in the outer Galactic halo may suggest a similar origin – i.e., in dwarf spheroidal-like galaxies."1186 It is presently not clear why the most luminous. and hence oresumably most massive. globular clusters have the smallest radii.," It is presently not clear why the most luminous, and hence presumably most massive, globular clusters have the smallest radii."1187 This conclusion appears to hold true both for Galactic globular clusters and for those associated with the Magellanie Clouds and he dwarf spheroidal companions of the Milky Way., This conclusion appears to hold true both for Galactic globular clusters and for those associated with the Magellanic Clouds and the dwarf spheroidal companions of the Milky Way.1188 It is noted hat in the case of a constant cluster mass-to-light ratio. Eq.," It is noted that in the case of a constant cluster mass-to-light ratio, Eq."1189 | implies that the upper limit to globular cluster sizes in the outer qalo Cexcluding NGC 2419) is detined by where A is cluster mass., \ref{e:cutoff} implies that the upper limit to globular cluster sizes in the outer halo (excluding NGC 2419) is defined by where $M$ is cluster mass.1190" In form. this is perhaps reminiscent to the correlation 2,xAL°°? noted by Ostriker Gnedin (1997) for clusters with 5[ex00 kpe."," In form, this is perhaps reminiscent to the correlation $R_h \propto M^{-0.63}$ noted by Ostriker Gnedin \shortcite{ostriker:97} for clusters with $5 < R_{\rm{gc}} < 60$ kpc."1191 The majority of clusters in Figures 6 and 7 appear to follow a similar correlation. running approximately parallel to the line detined by Eq. I..," The majority of clusters in Figures \ref{f:rhvsmv} and \ref{f:rhvsmvexternal}1192 appear to follow a similar correlation, running approximately parallel to the line defined by Eq. \ref{e:cutoff}."1193 McLaughlin (2000) defines a fundamental plane for globular clusters using observations of clusters at all Galactocentrie radii., McLaughlin \shortcite{mclaughlin:00} defines a fundamental plane for globular clusters using observations of clusters at all Galactocentric radii.1194 Although he only finds a very weak correlation between luminosity (mass) and half-light radius. it seems plausible that the cut-off we observe in the present work is related to the presence of a undamental plane for globular clusters.," Although he only finds a very weak correlation between luminosity (mass) and half-light radius, it seems plausible that the cut-off we observe in the present work is related to the presence of a fundamental plane for globular clusters."1195 McLaughlin argues that he characteristics of the fundamental plane were set by the cluster ormation process., McLaughlin argues that the characteristics of the fundamental plane were set by the cluster formation process.1196 The fact that NGC 2419 and c Centauri fall above our cut-off and away from all other globular clusters seems ikely to place them away from the fundamental plane., The fact that NGC 2419 and $\omega$ Centauri fall above our cut-off and away from all other globular clusters seems likely to place them away from the fundamental plane.1197 If this iypothesis is correct then it would imply a formation scenario or NGC 2419 and w Centauri different from that for the rest of he Galactic globular clusters., If this hypothesis is correct then it would imply a formation scenario for NGC 2419 and $\omega$ Centauri different from that for the rest of the Galactic globular clusters.1198 One such scenario is that these two objects are not true globular clusters. but rather the remaining cores of now defunct dwarf galaxies.," One such scenario is that these two objects are not true globular clusters, but rather the remaining cores of now defunct dwarf galaxies."1199" Finally. it is informative to place the ""faint fuzzy"" clusters discovered in the lenticular galaxies NGC 1023 and 3384 by Larsen Brodie (2000) and. Larsen et al."," Finally, it is informative to place the “faint fuzzy” clusters discovered in the lenticular galaxies NGC 1023 and 3384 by Larsen Brodie \shortcite{larsen:00} and Larsen et al."1200 (2001). on our logf? vs. Ay plot., \shortcite{larsen:01} on our $\log R_h$ vs. $M_V$ plot.

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