ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 We have moclified the second. order. symplectic integrator introduced. by (Duncanetal.1998)... also known as the democratic heliocentric method. so that it runs on a GPU.," We have modified the second order symplectic integrator introduced by \citep{duncan98}, also known as the democratic heliocentric method, so that it runs on a GPU."3 We have chosen the democratic heliocentric method because the force from the central body. is separated [rom the integration of the remainder of the particles and. the coordinates do not depend on the order of the particles., We have chosen the democratic heliocentric method because the force from the central body is separated from the integration of the remainder of the particles and the coordinates do not depend on the order of the particles.4 This increases the accuracy of the integrator when there are large mass dilferences and is particularly desirable when forced to work in lloating point single precision., This increases the accuracy of the integrator when there are large mass differences and is particularly desirable when forced to work in floating point single precision.5 When we obtain video cards that can compute in double precision the code will improve in precision., When we obtain video cards that can compute in double precision the code will improve in precision.6 The move to double precision will also allow us to extend the range of the planetesipal masses simulatecd., The move to double precision will also allow us to extend the range of the planetesimal masses simulated.7 In heliocentric coordinates ancl barycentric momenta (Wisdom.Holman&Touma1996). the Hamiltonian of the svstem can be written where is a linear drift term and Z5. are. thebarycentric momenta., In heliocentric coordinates and barycentric momenta \citep{wisdom96} the Hamiltonian of the system can be written where is a linear drift term and $P_i$ are thebarycentric momenta.8 Llere mo is the central particle mass., Here $m_0$ is the central particle mass.9 The second term ffx.) is the sum of Ixeplerian. Lamiltonians for all particles with respect to the central body. where Q; are the heliocentric coordinates and are conjugate to the barvcentric momenta.," The second term $H_{Kep}$ is the sum of Keplerian Hamiltonians for all particles with respect to the central body, where ${\bf Q}_i$ are the heliocentric coordinates and are conjugate to the barycentric momenta."10 Here m; is the mass of the th particle and €. is the gravitational constant., Here $m_i$ is the mass of the $i$ -th particle and $G$ is the gravitational constant.11 The interaction term contains all gravitational interaction terms except those to the central body. The second. order single timestep integrator advances with timestep 7 using evolution operators (es... Yoshida 19901) where we have reversed. the order. of the. Ixeplerian evolution and the interaction steps compared το that discussed. by (Duncan.etal.1998).," The interaction term contains all gravitational interaction terms except those to the central body, The second order single timestep integrator advances with timestep $\tau$ using evolution operators (e.g., \citealt{yoshida90}) ) where we have reversed the order of the Keplerian evolution and the interaction steps compared to that discussed by \citep{duncan98}."12.. We have done this to reduce the total number of computations per timestep., We have done this to reduce the total number of computations per timestep.13 The Weplerian advance requires. O(N) computations but interaction term. requires ON?) computations., The Keplerian advance requires $O(N)$ computations but interaction term requires $O(N^2)$ computations.14 The drift evolution operator requires computation of the sum of the momenta., The drift evolution operator requires computation of the sum of the momenta.15 We have implemented this using a parallel reduction sum algorithm available with the NVIDLA CUDA Software Development Wit (SDIN) 1.1 that is similar to the scan prefix sum algorithm (Llarrisetal.2008)., We have implemented this using a parallel reduction sum algorithm available with the NVIDIA CUDA Software Development Kit (SDK) 1.1 that is similar to the scan prefix sum algorithm \citep{harris08}.16. The Ixeplerian step was implemented. with f and g functions using the universal differential Ixepler's. equation (Prussing&Conway1993). so that. bound. and. unbound particles can both be integrated with the same routine., The Keplerian step was implemented with $f$ and $g$ functions using the universal differential Kepler's equation \citep{prussing93} so that bound and unbound particles can both be integrated with the same routine.17 The Ixeplerian evolution step is also done on the GPU with each thread computing the evolution for a separate particle., The Keplerian evolution step is also done on the GPU with each thread computing the evolution for a separate particle.18 The dominant source of error is in the Ixeplerian evolution step ancl is due to the single floating point precision., The dominant source of error is in the Keplerian evolution step and is due to the single floating point precision.19 Phese errors can cause à systematic radial drift that does not average to zero., These errors can cause a systematic radial drift that does not average to zero.20 To minimize errors caused. by the single precision computation during the Ixepler advances we chose f and g Functions that maintain angular momentum conservation across cach evolution step., To minimize errors caused by the single precision computation during the Kepler advances we chose $f$ and $g$ functions that maintain angular momentum conservation across each evolution step.21 The positions and. velocities at a later time can be written in terms of those at an earlier time The angular momentum at the later time. Ly can be written in terms of that at the earlier time. Lo. Conservation of angular momentum vields the condition We utilize this formula to solve for one of the 4 functions reducing the inward racial drift resulting by the single precision computation during the Ixeplerian advances.," The positions and velocities at a later time can be written in terms of those at an earlier time The angular momentum at the later time, $\vec{\bf L_1}$ can be written in terms of that at the earlier time, $\vec{\bf L_0}$, Conservation of angular momentum yields the condition We utilize this formula to solve for one of the 4 functions reducing the inward radial drift resulting by the single precision computation during the Keplerian advances."22 The interaction terms are computed on the GPU with all Απ. force. pairs evaluated: explicitly in. parallel., The interaction terms are computed on the GPU with all $N^2$ force pairs evaluated explicitly in parallel.23 The algorithm is based on the algorithm described by (NvIand. 2008)., The algorithm is based on the algorithm described by \citep{nyland08}.24. This algorithm takes advantage of fast shared. memory on board the GPU to simultaneously compute all forces in a pop tile of particle positions. where p ds the number of threads chosen for the computation (typically 256).," This algorithm takes advantage of fast shared memory on board the GPU to simultaneously compute all forces in a $p \times p$ tile of particle positions, where $p$ is the number of threads chosen for the computation (typically 256)."25 Phe total energy was evaluated with a kernel explicitly evaluating all N= pair potential enerey ternis. similar to that calculating all N= forces.," The total energy was evaluated with a kernel explicitly evaluating all $N^2$ pair potential energy terms, similar to that calculating all $N^2$ forces."26 Alter the change to heliocentric/barvcentric coordinates.— the position of the first coordinate corresponds to the center of mass and center. of momentum.," After the change to heliocentric/barycentric coordinates, the position of the first coordinate corresponds to the center of mass and center of momentum."27 The trajectory of this particle need not be integrated., The trajectory of this particle need not be integrated.28 Llowever it is convenient to calculate. the energy. using all. pair interactions including the central mass., However it is convenient to calculate the energy using all pair interactions including the central mass.29 The interaction term in the Weplerian part of. the Hamiltonian. can be computed at the same times as {τω if Qu is set to zero., The interaction term in the Keplerian part of the Hamiltonian can be computed at the same times as $H_{Int}$ if ${\bf Q}_0$ is set to zero.30 Consequently we set Qu=Po Oat the beginning of the computation., Consequently we set ${ \bf Q}_0 = {\bf P}_0 = 0$ at the beginning of the computation.31 Εις is equivalent to working in the center of mass and momentum reference frame., This is equivalent to working in the center of mass and momentum reference frame.32 Because we would like to be able to quickly check the total energy. we have chosen to keep the first particle corresponding to the center of mass and momentum as the first element in the position ancl velocity arravs.," Because we would like to be able to quickly check the total energy, we have chosen to keep the first particle corresponding to the center of mass and momentum as the first element in the position and velocity arrays."33 During computation of {τω we set my do zero so that force terms from the first particle are not computed., During computation of $H_{Int}$ we set $m_0$ to zero so that force terms from the first particle are not computed.34 These are already taken into account in the evolution term corresponding to {ων , These are already taken into account in the evolution term corresponding to $H_{Kep}$ .35Phe mass is restored during the energy sum computation as all potential energy terms must be calculated explicitly., The mass is restored during the energy sum computation as all potential energy terms must be calculated explicitly.36 The location of memory should. be considered: when running routines as data transler between the CPU, The location of memory should be considered when running routines as data transfer between the CPU37in these models need not be expected (o suffer major inward or outward migration prior to photoevaporation of (he outer disk. though clearly (this possibility is deserving of further study.,"in these models need not be expected to suffer major inward or outward migration prior to photoevaporation of the outer disk, though clearly this possibility is deserving of further study."38 The close-packing in seminmajor axis of the fragments in model 2.0 (Figures 9 and 15) makes it clear that these protoplanets will interact gravitationally with each other (as well as with the much more massive disk). resulting in mutual close encounters and scattering of proloplanets to orbits with larger and smaller semimajor axes (han (their initial values (Figure 15).," The close-packing in semimajor axis of the fragments in model 2.0 (Figures 9 and 15) makes it clear that these protoplanets will interact gravitationally with each other (as well as with the much more massive disk), resulting in mutual close encounters and scattering of protoplanets to orbits with larger and smaller semimajor axes than their initial values (Figure 15)."39 The evolution during (hiis subsequent phase is best described with a fixed-grid code by using the virtual protoplanet technique. where the [fragments are replaced by point mass objects that orbit and interact with the disk and each other (Boss 2005).," The evolution during this subsequent phase is best described with a fixed-grid code by using the virtual protoplanet technique, where the fragments are replaced by point mass objects that orbit and interact with the disk and each other (Boss 2005)."40 Models that continue the present models with the virtual protoplanet technique are now underway ancl will be presented in a future paper., Models that continue the present models with the virtual protoplanet technique are now underway and will be presented in a future paper.41 Most disk instability models have focused on forming giant. planets similar to those in our Solar Svstem. and hence have studied disks with outer radii of 20 AU (e.g.. Boss 2001: Maver et al.," Most disk instability models have focused on forming giant planets similar to those in our Solar System, and hence have studied disks with outer radii of 20 AU (e.g., Boss 2001; Mayer et al."42 2007)., 2007).43 Boss (2003) found that disk instability could lead to the formation of clumps with initial orbital semimajor axes of ~20 AU in disks with outer radii ol 30 AU., Boss (2003) found that disk instability could lead to the formation of self-gravitating clumps with initial orbital semimajor axes of $\sim 20$ AU in disks with outer radii of 30 AU.44 On the other hand. Boss (2006a) found no strong tendeney lor elump formation in disks extending from 100 AU to 200 AU.," On the other hand, Boss (2006a) found no strong tendency for clump formation in disks extending from 100 AU to 200 AU."45 In both cases these models assumed 1 AL. central protostars., In both cases these models assumed 1 $M_\odot$ central protostars.46 Model 1.0 in the present work shows (hat when the disk is assumed {ο extend [rom 20 AU to 60 AU. chuups are again expected to be able to form. with initial semimajor axes of ~ 30 AU to ~ 45 AU (Figure 15).," Model 1.0 in the present work shows that when the disk is assumed to extend from 20 AU to 60 AU, clumps are again expected to be able to form, with initial semimajor axes of $\sim$ 30 AU to $\sim$ 45 AU (Figure 15)."47 Taken together. these models imply that for à 1 AL. protostar at least. disk instability might be able to form gaseous proloplanels with initial semimajor axes anvwhere inside ~ 50 AU.," Taken together, these models imply that for a 1 $M_\odot$ protostar at least, disk instability might be able to form gaseous protoplanets with initial semimajor axes anywhere inside $\sim$ 50 AU."48 When multiple protoplanets form. as is likely to be the case for stus more massive than M dwarls. subsequent gravitational interactions are likely to result in at least a few protoplanets being kicked out to orbits with semimajor axes ereater than 50 AU.," When multiple protoplanets form, as is likely to be the case for stars more massive than M dwarfs, subsequent gravitational interactions are likely to result in at least a few protoplanets being kicked out to orbits with semimajor axes greater than 50 AU."49 Other authors have also considered the evolution of gravitationally unstable disks with outer radii much greater than 20 AU., Other authors have also considered the evolution of gravitationally unstable disks with outer radii much greater than 20 AU.50" Stamatellos Whitworth (2009a.b) used a smoothed particle hvdrodvnanmies (SPIL) eode with radiative transfer in the diffusion approximation {ο model the evolution of disk instabilities in disks with the same mass as (he central protostar: Af;=M,0.7M.."," Stamatellos Whitworth (2009a,b) used a smoothed particle hydrodynamics (SPH) code with radiative transfer in the diffusion approximation to model the evolution of disk instabilities in disks with the same mass as the central protostar: $M_d = M_s = 0.7 M_\odot$."51 The disks extended from 40 AU to 400 AU. with initial Toomre Q values οἱ 0.9 throughout. making them initially highlv gravitationally unstable.," The disks extended from 40 AU to 400 AU, with initial Toomre $Q$ values of 0.9 throughout, making them initially highly gravitationally unstable."52 As expected. these disks rapidly [ragmented into multiple chunps. which often grew to brown clwarl masses (1.e..," As expected, these disks rapidly fragmented into multiple clumps, which often grew to brown dwarf masses (i.e.,"53Copernicus and FUSE.,Copernicus and FUSE.54" The model values, which take into account UV pumping and H» excitation upon formation are also roughly an order of magnitude lower than the observations."," The model values, which take into account UV pumping and $\rm H_2$ excitation upon formation are also roughly an order of magnitude lower than the observations."55" Gryetal.(2002) and othersearlier (e.g. Draine&Katz,1986;Joulainetal.,1998;PineaudesForétsetal., 1986)) have proposed that this excited He traces warm gas in regions where kinetic energy is dissipated through shocks or vortices."," \cite{GBNPHF} and othersearlier (e.g. \citealp{DK86, Joulain98, Pineau86}) ) have proposed that this excited ${\rm H}_{2}$ traces warm gas in regions where kinetic energy is dissipated through shocks or vortices."56" Other authors have proposed that this warm Hg is the signature of molecular gas close to the star and thus exposed to a high UV field (e.g. Browningetal, 2003)).", Other authors have proposed that this warm ${\rm H}_{2}$ is the signature of molecular gas close to the star and thus exposed to a high UV field (e.g. \citealp{BTS}) ).57" The presence of CH* in quantities much larger than predicted by the PDR. model favors the former explanation (Falgaroneetal.,2005).", The presence of $^+$ in quantities much larger than predicted by the PDR model favors the former explanation \citep{Falga05}.58". To test this preference, we have used the PDR model to quantify the latter possibility in the specific case of HD 102065."," To test this preference, we have used the PDR model to quantify the latter possibility in the specific case of HD 102065."59" The ratio between the 100um brightness in the IRAS images and the visible extinction towards HD 102065 indicates that most of the matter is fairly distant from the star (Boulangeretal.,1994) and does not interact with it.", The ratio between the $100 \mu{\rm m}$ brightness in the IRAS images and the visible extinction towards HD 102065 indicates that most of the matter is fairly distant from the star \citep{BOUPREG} and does not interact with it.60" The 60 and 100 wm images only show a small brightness enhancement at the position of HD 102065, point-like at the IRAS resolution (angular size < 5’), and corresponding to a small fraction ( 107?) of the stellar luminosity (Boulangeretal.,1994)."," The 60 and 100 $\mu$ m images only show a small brightness enhancement at the position of HD 102065, point-like at the IRAS resolution (angular size $\leqslant$ 5'), and corresponding to a small fraction ( $^{-3}$ ) of the stellar luminosity \citep{BOUPREG}."61". If the absorbing matter occupies a solid angle 0 about the star, its UV/visible opacity is 107?x4-/0."," If the absorbing matter occupies a solid angle $\theta$ about the star, its UV/visible opacity is $10^{-3}\times 4\pi /\theta$."62" Combining the constraint on the source diameter (« 5’), and the star distance (170 pc), we derive an upper limit for the distance, from the star to the absorbing matter of 0.12pc."," Combining the constraint on the source diameter $< 5'$ ), and the star distance (170 pc), we derive an upper limit for the distance, from the star to the absorbing matter of $0.12\; {\rm pc}$."63" HD102065 is a B9IV star with a luminosity ~100Lo and an effective temperature of 11300 K. The stellar radiation field intensity is G,=0.2x(d/1pc)? in Draine units."," HD102065 is a B9IV star with a luminosity $\sim 100\,L_\odot$ and an effective temperature of $11300$ K. The stellar radiation field intensity is ${G_*= 0.2\times (d/1{\rm pc})^{-2}}$ in Draine units."64" For an extinction A,~10-? the gas is molecular only for large densities.", For an extinction $A_{\rm v} \sim 10^{-3}$ the gas is molecular only for large densities.65" To search for a more realistic solution, we assume that 0/4~0.1."," To search for a more realistic solution, we assume that $\theta/4\pi \sim 0.1$."66" To quantify with this assumption, the column density of warm H» that could be associated with the IRAS far-IR emission, we compute a grid of models with constant A,=10-7, varying the density ny from 10? to 3x109cm?, and the distance to the star from 0.1pc to 1107?pc (equivalent to G. from 20 to 2x 103)."," To quantify with this assumption, the column density of warm $_2$ that could be associated with the IRAS far-IR emission, we compute a grid of models with constant $A_{\rm v} = 10^{-2}$, varying the density $n_{\rm H}$ from $10^3$ to $3\times 10^6 {\rm cm^{-3}}$, and the distance to the star from $0.1 {\rm pc}$ to $1\; 10^{-2}\; {\rm pc}$ (equivalent to $G_*$ from 20 to $2\times 10^{3}$ )."67" Figure 15 shows the column densities of Hz(J=3), as a function of ny for various distances to the star."," Figure \ref{NH2exc_nh} shows the column densities of ${\rm H}_2\; (J=3)$, as a function of $n_{\rm H}$ for various distances to the star."68" As distance decreases, the radiation field increases, the H2 photo-dissociation rate rises, and higher densities are required to retain hydrogen in its molecular form."," As distance decreases, the radiation field increases, the $_2$ photo-dissociation rate rises, and higher densities are required to retain hydrogen in its molecular form."69" The stronger radiative pumping populates higher rotational levels, which accounts for the bell shape of the curves."," The stronger radiative pumping populates higher rotational levels, which accounts for the bell shape of the curves."70" The same trend occurs at higher rotational levels, for which the curve maxima are shifted towards higher densities."," The same trend occurs at higher rotational levels, for which the curve maxima are shifted towards higher densities."71" The observed excitation temperature of ~250K is reproduced for the correct column densities, in a range of models, as shown on Fig. 15.."," The observed excitation temperature of $\sim 250\; {\rm K}$ is reproduced for the correct column densities, in a range of models, as shown on Fig. \ref{NH2exc_nh}."72 One typical example is illustrated in Fig. 16.., One typical example is illustrated in Fig. \ref{H2_exc}.73 It can be clearly seen however that the J=4 point lags under the J=3—5 curve., It can be clearly seen however that the $J=4$ point lags under the $J=3-5$ curve.74 This is directly linked to the imposed ortho-to-para ratio on the formation on grains., This is directly linked to the imposed ortho-to-para ratio on the formation on grains.75" This is because the high radiation field results in a photodissociation time scale which is an order of magnitude larger than the conversion time scale from ortho-to-para Πο through reactive collisions, with either H or Ht."," This is because the high radiation field results in a photodissociation time scale which is an order of magnitude larger than the conversion time scale from ortho-to-para ${\rm H}_2$ through reactive collisions, with either ${\rm H}$ or ${\rm H}^+$."76 The only way to reproduce the J=4 column density is to assume a formation ortho-to-para ratio that is different from the statistical equilibrium value of 3., The only way to reproduce the $J=4$ column density is to assume a formation ortho-to-para ratio that is different from the statistical equilibrium value of 3.77 Fig., Fig.78 16 shows that an initial ratio of 1 provides robust results., \ref{H2_exc} shows that an initial ratio of 1 provides robust results.79 We are however unaware of any theoretical or experimental result that would support such an initial ratio., We are however unaware of any theoretical or experimental result that would support such an initial ratio.80" We conclude that a pure steady-state PDR model is able to reproduce the excitation of H5 at J> 2, observed"," We conclude that a pure steady-state PDR model is able to reproduce the excitation of ${\rm H}_2$ at $J>2$ , observed"81 (2>5). of high-redshift QSOs show a plethora of II I Lya absorption lines. the “Lye forest. as well as lines from a wide varicty of heavicr clements. all of which provide detailed information about the lhigh+vedshitt ICM. along he lince-ofsieht towards the QSO.," $z > 5$ of high-redshift QSOs show a plethora of H I $\alpha$ absorption lines, the $\alpha$ forest"", as well as lines from a wide variety of heavier elements, all of which provide detailed information about the high-redshift IGM along the line-of-sight towards the QSO."82 Around the QSOs heiselves. however. the ultraviolet fiux is so high that it vpically ionizes the surrounding eas.," Around the QSOs themselves, however, the ultraviolet flux is so high that it typically ionizes the surrounding gas."83 Thus QSOs are not ideal for stuckving the pervasive ICAL close to the QSO., Thus QSOs are not ideal for studying the pervasive IGM close to the QSO.84 lustead. we sugeest that brielt galaxies may provide setter probes for the study of ICAL coucditions in the wrontmuity of ligh-redshift objects. as these objects euüt ewer ultraviolet photous than QSOs do.," Instead, we suggest that bright galaxies may provide better probes for the study of IGM conditions in the proximity of high-redshift objects, as these objects emit fewer ultraviolet photons than QSOs do."85 The subject of this paper is the Lya forest in the spectrum of an unusually bright high-redshift salaxv at +=σος (Frve et al., The subject of this paper is the $\alpha$ forest in the spectrum of an unusually bright high-redshift galaxy at $z = 4.866$ (Frye et al.86 2002. 2007).," 2002, 2007)."87 The galaxy js situated behind the massive galaxy cluster Abell 1689 (2= 0.183). which magnifies the starlieht of this backeround object by a factor of 10.3 bv the effect of eravitational lensing (Droadhurst et al.," The galaxy is situated behind the massive galaxy cluster Abell 1689 $z = 0.183$ ), which magnifies the starlight of this background object by a factor of 10.3 by the effect of gravitational lensing (Broadhurst et al."88 2005)., 2005).89 Nulticolor IIubble Space Telescope (IST) imaging of one of the faint leused images. hereafter designated 1689.7.1. is shown in Figure 1.," Multicolor Hubble Space Telescope (HST) imaging of one of the faint lensed images, hereafter designated $A1689\_7.1$, is shown in Figure 1."90 We assume a cosinology for this paper of Hy— :01au + Mpe.ft. Ου=033. and Qu=0.7.," We assume a cosmology for this paper of $H_0 = 70$ km $^{-1}$ $^{-1}$, $\Omega_{m,0} = 0.3$, and $\Omega_{\Lambda,0} = 0.7$."91 Our spectrum of ALGS9_7.1 is made possible with present telescopes onlv by the combination of strong leuxiugend unusuall-loug observations., Our spectrum of $A1689\_7.1$ is made possible with present telescopes only by the combination of strong lensing unusually-long observations.92 We obtained the spectrum for ALGS9_7.1 in Ἐ hours at the Very Large Telescope (VLT) with the Focal Reducer aud low- Spectrograph (FORS2) iu 2001 June aud July and report a spectral resolution of R=A/AAz 5307., We obtained the spectrum for $A1689\_7.1$ in 14 hours at the Very Large Telescope (VLT) with the Focal Reducer and low-dispersion Spectrograph (FORS2) in 2001 June and July and report a spectral resolution of $R = \lambda/\Delta\lambda \approx 530$ .93The Sun rotates differentially (.e. the equatorial regions rotate faster than the polar regions) at the photosphere and chromosphere.,The Sun rotates differentially (i.e. the equatorial regions rotate faster than the polar regions) at the photosphere and chromosphere.94 The measurements of solar rotation have been carried out by two methods. namely. (1) Tracer Method - by tracing the passage of various features like sunspots. faculae. filaments etc..," The measurements of solar rotation have been carried out by two methods, namely, (i) Tracer Method - by tracing the passage of various features like sunspots, faculae, filaments etc.,"95 over the solar disk and (1) Doppler Method - by the spectroscopic observations of Doppler displacements of the core of the spectral lines., over the solar disk and (ii) Doppler Method - by the spectroscopic observations of Doppler displacements of the core of the spectral lines.96 The phenomenon of solar rotation is still to be understood clearly from the existing large volumes of data., The phenomenon of solar rotation is still to be understood clearly from the existing large volumes of data.97 On the other hand. the coronal rotation is observed through features like Fe XIV green lines. soft X-rays anc radio waves.," On the other hand, the coronal rotation is observed through features like Fe XIV green lines, soft X-rays and radio waves."98 The coronal rotation has been measured by two methods: (1) Tracer Method - basec on visual tracing of coronal features (XBPs) in consecutive images and (11) Automatic Method - relies on the IDL procedure “Regions Of Interest” segmentation which is used to identify anc follow them in the consecutive images.," The coronal rotation has been measured by two methods: (i) Tracer Method - based on visual tracing of coronal features (XBPs) in consecutive images and (ii) Automatic Method - relies on the IDL procedure ""Regions Of Interest"" segmentation which is used to identify and follow them in the consecutive images."99 However. in both the methods. there are advantages anc disadvantages.," However, in both the methods, there are advantages and disadvantages."100 The coronal rotation determination appears to be more complicated and even less understood. because the corona is optically thin across a wide range of observed wavelengths and the features are less distinct in duration and extent.," The coronal rotation determination appears to be more complicated and even less understood, because the corona is optically thin across a wide range of observed wavelengths and the features are less distinct in duration and extent."101 Solar coronal X-ray bright points (XBPs) were discovered using a soft X-ray telescope (SXT) on a sounding rocket and their nature has been an enigma since their discovery in late 1960°s (Vaiana et al., Solar coronal X-ray bright points (XBPs) were discovered using a soft X-ray telescope (SXT) on a sounding rocket and their nature has been an enigma since their discovery in late 1960's (Vaiana et al.102 1970)., 1970).103 Later. using Skylab and Yohkoh X-ray images. the XBPs were studied in great detail (Golub et al.," Later, using Skylab and Yohkoh X-ray images, the XBPs were studied in great detail (Golub et al."104 1974: Harvey 1996; Nakakubo Hara 1999 Longcope et al., 1974; Harvey 1996; Nakakubo Hara 1999; Longcope et al.105 2001: Hara Nakakubo 2003)., 2001; Hara Nakakubo 2003).106 It has been shown that the XBPs have a spatial correspondence with small-scale bipolar magnetic regions by comparing the ground-based magnetic field measurements with simultaneous space-born X-ray imaging observations (Krieger et al., It has been shown that the XBPs have a spatial correspondence with small-scale bipolar magnetic regions by comparing the ground-based magnetic field measurements with simultaneous space-born X-ray imaging observations (Krieger et al.107 1971: Golub et al., 1971; Golub et al.108 1977)., 1977).109 The number of XBPs (daily) found on the Sun varies from several hundreds upto a few thousands (Golub et al., The number of XBPs (daily) found on the Sun varies from several hundreds upto a few thousands (Golub et al.110 1974)., 1974).111 Zhang et al. (, Zhang et al. (1122001) found a,2001) found a113measured size corrected for luminosity dependence as part of this process.,measured size corrected for luminosity dependence as part of this process.114 In most cases these studies used the scaling of near-zone in proportion to luminosity to the one third power (e.g.??)..," In most cases these studies used the scaling of near-zone in proportion to luminosity to the one third power \citep[e.g.][]{fan2006,carilli2010}."115 As described above this value is appropriate if the near-zone is expanding into a neutral IGM., As described above this value is appropriate if the near-zone is expanding into a neutral IGM.116" On the other hand, a power of one half (B— 2) is more appropriate if the near-zone corresponds to a radius where resonant absorption in an ionized IGM results in the 10 per cent transmission (?).."," On the other hand, a power of one half $B=2$ ) is more appropriate if the near-zone corresponds to a radius where resonant absorption in an ionized IGM results in the 10 per cent transmission \citep[][]{bolton2007}."117 Thus the correct scaling between near-zone radius and quasar luminosity is uncertain., Thus the correct scaling between near-zone radius and quasar luminosity is uncertain.118 In this work we therefore treat the power-law index B as a free parameter in a 2-dimensional relation describing near-zone radius as a function of quasar luminosity and redshift., In this work we therefore treat the power-law index $B$ as a free parameter in a 2-dimensional relation describing near-zone radius as a function of quasar luminosity and redshift.119 We find that current near-zone data places strong constraints on the value of B., We find that current near-zone data places strong constraints on the value of $ B$.120" Moreover, rather than focus on the interpretation of the parameter A with respect to the end of hydrogen reionization, in this paper we concentrate instead on understanding the implications of the parameters B and FH»; for the EUV spectral index blueward of the Lyman limit for z~6 quasars."," Moreover, rather than focus on the interpretation of the parameter $A$ with respect to the end of hydrogen reionization, in this paper we concentrate instead on understanding the implications of the parameters $B$ and $R_{27}$ for the EUV spectral index blueward of the Lyman limit for $z\sim6$ quasars."121" We show that the near-zone relation offers a probe of the EUV spectrum of quasars at these early epochs, information that is otherwise concealed by the Lyman-limit absorption, and so has previously only been studied for quasars at redshifts of z51 (?).."," We show that the near-zone relation offers a probe of the EUV spectrum of quasars at these early epochs, information that is otherwise concealed by the Lyman-limit absorption, and so has previously only been studied for quasars at redshifts of $z\la1$ \citep[][]{telfer2002}."122 ? have assembled a sample of 25 z~6 quasars which have quality rest-frame UV spectra and redshift measurements (??)..," \citet{carilli2010} have assembled a sample of 25 $z\sim6$ quasars which have quality rest-frame UV spectra and redshift measurements \citep{fan2006,jiang2008}."123 Eight of the sample are detected (?) in CO., Eight of the sample are detected \citep{wang2010} in CO.124 Another nine have redshifts measured (77) from the Mg II line emission.," Another nine have redshifts measured \citep{kurk2007,jiang2007} from the Mg II line emission."125" For the other eight objects, ? adopt redshifts from the relevant discovery papers, which are mainly determined with the Lya+NV lines (?).."," For the other eight objects, \citet{carilli2010} adopt redshifts from the relevant discovery papers, which are mainly determined with the $\alpha$ +NV lines \citep{fan2006b}."126" The measurements are summarized in Table 1 of ?,, including the quasar absolute AB magnitude at 1450 (Mi4so), quasar redshifts (z), and near-zone size (Rp)."," The measurements are summarized in Table 1 of \citet{carilli2010}, , including the quasar absolute AB magnitude at 1450 $M_{1450}$ ), quasar redshifts $z$ ), and near-zone size $R_{\rm p}$ )."127" Three sources in the original sample (?) listed in Table 1 of ?,, J0353+ 0104, J1044—0125, and J10484-4637, are broad absorption line quasars (??),, while the source J1335+3533 has lineless (?) UV spectrum."," Three sources in the original sample \citep{wang2010} listed in Table 1 of \citet{carilli2010}, $J0353+0104$ , $J1044-0125$, and $J1048+4637$, are broad absorption line quasars \citep{jiang2008,fan2006b}, while the source $J1335+3533$ has a lineless \citep{fan2006b} UV spectrum."128 We exclude these quasars from aour analysis owing to the fundamentally different nature of their intrinsic spectra (??)..," We exclude these quasars from our analysis owing to the fundamentally different nature of their intrinsic spectra \citep{carilli2010,fan2006}."129 Thus the sample consists of 21 z~6 quasars which we use to analyse the near-zone relation., Thus the sample consists of 21 $z\sim6$ quasars which we use to analyse the near-zone relation.130 Near-zone sizes are plotted in Figure 1 as a function of both absolute magnitude and redshift., Near-zone sizes are plotted in Figure \ref{fig1} as a function of both absolute magnitude and redshift.131" Typical measurement errors (?) are 1.2 Mpc, 0.4 Mpc, and 0.1 Mpc in the estimated near-zone size Ry) introduced by UV, MglI, and CO-determined redshift uncertainties, respectively."," Typical measurement errors \citep{carilli2010} are 1.2 Mpc, 0.4 Mpc, and 0.1 Mpc in the estimated near-zone size $R_{\rm p}$ ) introduced by UV, MgII, and CO-determined redshift uncertainties, respectively."132 T'here are clear trends with both luminosity (7) and redshift (??)..," There are clear trends with both luminosity \citep{carilli2010} and redshift \citep{fan2006,carilli2010}."133" We note that quasar near-zone sizes have also been measured (??) for CFHQS J1509—1749, CFFQS J2329—0301 and CFHQS J0210—0456."," We note that quasar near-zone sizes have also been measured \citep{willott2007,willott2010} for CFHQS $1509-1749$, CFFQS $2329-0301$ and CFHQS $0210-0456$."134" Following ? we do not include these near-zones, which are drawn from a different data set, in our analysis."," Following \citet{carilli2010} we do not include these near-zones, which are drawn from a different data set, in our analysis."135" However as may be seen from Figure 1, these near-zones lie on the ? correlation, and we have checked that their addition does not significantly alter our results."," However as may be seen from Figure \ref{fig1}, these near-zones lie on the \citet[][]{carilli2010} correlation, and we have checked that their addition does not significantly alter our results."136" Our near-zone simulations combine a semi-analytical model for the evolving, density dependent photo-ionization rate in the biased regions surrounding quasars, with a radiative transfer implementation, and realistic density distributions drawn from a high resolution cosmological hydrodynamical simulation."," Our near-zone simulations combine a semi-analytical model for the evolving, density dependent photo-ionization rate in the biased regions surrounding quasars, with a radiative transfer implementation, and realistic density distributions drawn from a high resolution cosmological hydrodynamical simulation."137" 'These simulations are discussed in detail elsewhere (?),, and their description is not reproduced here."," These simulations are discussed in detail elsewhere \citep{bolton2010}, and their description is not reproduced here."138 However for completeness we show the evolution of the background photo-ionization rate for our fiducial simulations in the left hand panel of Figure 2.., However for completeness we show the evolution of the background photo-ionization rate for our fiducial simulations in the left hand panel of Figure \ref{fig2}.139" The grey curve shows the photo-ionization rate in the mean IGM, while the solid, dotted and dashed black curves show the mean and 1-sigma range of the photo-ionization rate in the biased regions within 5 Mpc of a 1015 Mo halo."," The grey curve shows the photo-ionization rate in the mean IGM, while the solid, dotted and dashed black curves show the mean and 1-sigma range of the photo-ionization rate in the biased regions within $5\,$ Mpc of a $10^{13}\,$ $_\odot$ halo."140" Importantly, we construct the absorption spectra using an ionizing background computed as a function of proper time along the trajectory of a photon emitted by the quasar, rather than at the proper time of the quasar."," Importantly, we construct the absorption spectra using an ionizing background computed as a function of proper time along the trajectory of a photon emitted by the quasar, rather than at the proper time of the quasar."141" This effect is appropriate if considering spectra at the end of the reionization era, when the ionizing background can evolvesignificantly during the light travel time across a quasar near-zone."," This effect is appropriate if considering spectra at the end of the reionization era, when the ionizing background can evolvesignificantly during the light travel time across a quasar near-zone."142 The right hand panel of Figure 2 illustrates the background, The right hand panel of Figure \ref{fig2} illustrates the background143"The dipole matrix eleicuts 47 πι mits of p are defined as. Lor aud pe denote au orbital im initial aud final state respectively,","The dipole matrix elements $d^{(q)}$ in units of $\hat\rho$ are defined as, $|m\nu\rangle$ and $|m'\nu'\rangle$ denote an orbital in initial and final state respectively."144 Using the orthonormality of Laudau functions. dipole matrix clements are evaluated as. The longitudinal wavefunction for the imitial aud the final states are uot quite orthogonal to cach other due to differing clectrou configurations.," Using the orthonormality of Landau functions, dipole matrix elements are evaluated as, The longitudinal wavefunction for the initial and the final states are not quite orthogonal to each other due to differing electron configurations."145 Nevertheless we evaluated oscillator strengths for the single clectrou transitions using only the dipole matrix clement of the transitioning electron., Nevertheless we evaluated oscillator strengths for the single electron transitions using only the dipole matrix element of the transitioning electron.146 The error caused by this truncation is insignificaut for one electron trausitions., The error caused by this truncation is insignificant for one electron transitions.147" Auexpansion of the single-particle Tamiltouian in terms of cvlindrical wavefuuctiousprovides accurate results when D»B,.", An expansion of the single-particle Hamiltonian in terms of cylindrical wavefunctionsprovides accurate results when $B>B_c$.148 As incutioned in rofatoimfractth? sisastater mentthatmagneticficldef feetsdominateover€ ‘oulomdfie heyprop., As mentioned in \\ref{atom_struct} this is a statement that magnetic field effects dominate over Coulomb field effects.149 VB fot Oerand. the perturbativctr ‘|.," On the other hand, the perturbative treatment of higher Landau levels is valid when $|\tilde h^{(1)}| < |\tilde h^{(0)}|$ ."150 Since the nuclear term in equation (20)) dominates he effective. potential term. the condition. Boo>D. is also sufficient to eusure the validity of a perturbative reatiment of the higher Landau levels.," Since the nuclear term in equation \ref{5.19}) ) dominates the effective potential term, the condition $B>B_c$ is also sufficient to ensure the validity of a perturbative treatment of the higher Landau levels."151" Therefore. P, sets a lower luit ou the magnetic field for which our method is valid for electrous (1.0. in state (i7.0))."," Therefore, $B_c$ sets a lower limit on the magnetic field for which our method is valid for electrons (i.e. in state $(m,0)$ )."152" Iu feure 2.. we plot B. for in=O3 assuming Z,y;=Zam or illustrative purposes."," In figure \ref{spinflip}, we plot $B_c$ for $m=0-3$ assuming $Z_{eff}\simeq153Z-m$ for illustrative purposes."154 Looscli-bouud electrons are well within the Landau τοσο due to their larger average distance to the nucleus., Loosely-bound electrons are well within the Landau regime due to their larger average distance to the nucleus.155 Therefore even at intermediate ποια streneths a cvliudrical expansion combined with erturbative treatineut of the higher Landau levels still xovides accurate results for most electrons., Therefore even at intermediate field strengths a cylindrical expansion combined with perturbative treatment of the higher Landau levels still provides accurate results for most electrons.156" The sharp decrease in 2B, with increasing a. secu in figure 2.. ueans that only those iuner electrous with m=Q3 will have significant configuration mixing."," The sharp decrease in $B_c$ with increasing $m$, seen in figure \ref{spinflip}, means that only those inner electrons with $m=0-3$ will have significant configuration mixing."157 At Neher quantuni state am. the Landau regime. with its weheible configuration mixing. is quickly recovered.," At higher quantum state $m$, the Landau regime, with its negligible configuration mixing, is quickly recovered."158 As the magnetic field ects smaller. spin-flip transitions can take place. obviating the validity of the FSP approximation.," As the magnetic field gets smaller, spin-flip transitions can take place, obviating the validity of the FSP approximation."159 The critical maguetic field streugths where spin-flip transitions take place (09) were recently studied or atonis up to Z=10 by Ivanov&Scluneleher(2000)., The critical magnetic field strengths where spin-flip transitions take place $B_{sf}$ ) were recently studied for atoms up to $Z=10$ by \citet{ivanov00}.160 Iu a fairly wide range of magnetic field they computed he erouud state energies of atoms in which the FSPapproximation was removed = the electron spins were unrestricted., In a fairly wide range of magnetic field they computed the ground state energies of atoms in which the FSPapproximation was removed – the electron spins were unrestricted.161" Using this study we found that By, could ο fit by a polvnomial function of Z.", Using this study we found that $B_{sf}$ could be fit by a polynomial function of $Z$ .162 At BBey the asstuuption of autisvuuuctrized total spatial wave function weaks down., At $B<B_{sf}$ the assumption of antisymmetrized total spatial wave function breaks down.163 This sets another restriction on the validity of our iiethod iu the phase space of (5.Z) (figure 2)).," This sets another restriction on the validity of our method in the phase space of $(B, Z)$ (figure \ref{spinflip}) )."164 Although the significance of the exehauge term ice he binding energv increases in the FSP approximatio (Schinelcheretal.1999). the exchange term can be reated perturbatively as long as it is simaller than the Oth order energy eigenvalues.. Le.. [eie](1)<lene].(O)," Although the significance of the exchange term in the binding energy increases in the FSP approximation \citep{schmelcher99}, the exchange term can be treated perturbatively as long as it is smaller than the 0th order energy eigenvalues, i.e. $|\epsilon^{(1)}_{m\nu}|<|\epsilon^{(0)}_{m\nu}|$."165 We- observed lis inequality was satisfied for amy single orbital iu all he configurations computed., We observed this inequality was satisfied for any single orbital in all the configurations computed.166 Iu the perturbation for the exchange teri we did uot perform calculations hieher thui Mth aud 18st order for the wavefunctions aud energy values jecause of the increasing colplesity of the calculations., In the perturbation for the exchange term we did not perform calculations higher than 0th and 1st order for the wavefunctions and energy values because of the increasing complexity of the calculations.167 Also the naive inclusion of a Ist order perturbation iuto he wavetfuuctious breaks the wavefuuctious orthogonality. requiring a further orthogonalization process for the sinele-orbital wavefunctions.," Also the naive inclusion of a 1st order perturbation into the wavefunctions breaks the wavefunctions orthogonality, requiring a further orthogonalization process for the single-orbital wavefunctions."168 The exact value of the wavefunction is not our primary concern. but rather the accuracy of the real physical observables such as energy values aud oscillator strengths.," The exact value of the wavefunction is not our primary concern, but rather the accuracy of the real physical observables such as energy values and oscillator strengths."169 For instance. errors on the energy levels caused by truncating the wavefunctions are actually sinall rofenerev)).," For instance, errors on the energy levels caused by truncating the wavefunctions are actually small \\ref{energy}) )."170{ We use au explicit procedure to quantitatively correct the oscillator streneths iu order to account for the deviation iutroduced by using Hartree rather than ILutrec-Fock wavefuuctious rofos))., We use an explicit procedure to quantitatively correct the oscillator strengths in order to account for the deviation introduced by using Hartree rather than Hartree-Fock wavefunctions \\ref{os}) ).171 lu realty the individual wavefunctions are not sviuuetrie but distorted by the Coulomb coupling with other electrons., In reality the individual wavefunctions are not symmetric but distorted by the Coulomb coupling with other electrons.172 The Dartree and Hartrec-Fock. methods do not include electrou correlation iu the Schróddiuser equation for cach orbital., The Hartree and Hartree-Fock methods do not include electron correlation in the Schröddinger equation for each orbital.173 However. as the magnetic field increases. the electron correlation becomes less relevant (Schanelcheretal.1999).," However, as the magnetic field increases, the electron correlation becomes less relevant \citep{schmelcher99}."174 The estimated error in our energies and oscillator streneths due to electron correlation is sienificantlv smaller than in the Laudau regine., The estimated error in our energies and oscillator strengths due to electron correlation is significantly smaller than in the Landau regime.175 The significance of relativistic effects is proportional to hepfine? or Epfine? where Ep is a binding energy.," The significance of relativistic effects is proportional to $\hbar\omega_B /176m_ec^2$ or $E_B / m_ec^2$ where $E_B$ is a binding energy."177 The former condition. trauslates to B/By. (B4=Lttx105 CQ. representing the deerce of relativistic effects iu the transverse motion of electrous.," The former condition translates to $B/B_{rel}$ $B_{rel}=4.414\times10^{13} \mbox { G}$ ), representing the degree of relativistic effects in the transverse motion of electrons."178 However. the shape of the Landau wavefuntion in the relativistic theory is the same as ta the non-relativistic theory (Lai 2000)...," However, the shape of the Landau wavefuntion in the relativistic theory is the same as in the non-relativistic theory \citep{lai00}. ."179" On the other haud. the electron relativistic along the magnetic field when Ep~me, become"," On the other hand, the electron becomes relativistic along the magnetic field when $E_B\sim m_ec^2$ ."180sHowever.the relativistic effects on the Coulomb binding cucreies remain uceligible even at maeuctic field. strengths of up to L7«1055 6 as determined bv nuuericalle solving Dirac’s equation," However,the relativistic effects on the Coulomb binding energies remain negligible even at magnetic field strengths of up to $4.7\times10^{13}$ G as determined by numerically solving Dirac's equation"181M87. established radiogalaxies as VHEy-ray emitters.,"M87, established radiogalaxies as VHE$\gamma$ -ray emitters."182show no spatial distinction from each other aud are spread throughout the entire observed region of the IIRS.,show no spatial distinction from each other and are spread throughout the entire observed region of the HRS.183 To quantify the likelihood of bianodalitv iu the redshift distribution. we first assess the likelihood that a single Caussian provides an adequate fit to the data.," To quantify the likelihood of bi-modality in the redshift distribution, we first assess the likelihood that a single Gaussian provides an adequate fit to the data."184 At cach PA. we determine the residual redshift of all galaxies from the svstematic position-redshift trend. and then we employ WAT statistics to assess the likelihood of a two-Ciuissiau versus a sinele-Caussian fit (Ashmanetal.1991).," At each PA, we determine the residual redshift of all galaxies from the systematic position-redshift trend, and then we employ KMM statistics to assess the likelihood of a two-Gaussian versus a single-Gaussian fit \citep{ash94}."185. ForeH position aneles.8 a conuuon covaudauce. two-Gaussian fit is preferred to a single Ciaussiun with a high degree of confidence (> ," For position angles, a common covariance, two-Gaussian fit is preferred to a single Gaussian with a high degree of confidence $>$ )."186The averageOo peak-to-peakm separation of the two components over the entire PA range is 3011 + 712. with the separation along the best-fit line (PA= sU*)) being 3003 + 171|.," The average peak-to-peak separation of the two components over the entire PA range is 3014 $\pm$ 712, with the separation along the best-fit line $=-$ ) being 3003 $\pm$ 174."187" Next, we utilize V? statistics to test the eooduess-offit for two Caussian distributions with differimg ENTIA asa fuuctiouof PA."," Next, we utilize $\chi ^2$ statistics to test the goodness-of-fit for two Gaussian distributions with differing FWHM as a function of PA."188" The reduced 4? values range from 0.95 to LOL with the best ft value at PAÀ-ο,", The reduced $\chi ^2$ values range from 0.95 to 4.91 with the best fit value at $=-$.189 In sunuuarv. the statistical tests confirm the bianodal nature of the TRS redshift distribution. with the clearest distinction between the two redshift commponcuts occurring along the principal spatialredshift axis of the supercluster.," In summary, the statistical tests confirm the bi-modal nature of the HRS redshift distribution, with the clearest distinction between the two redshift components occurring along the principal spatial-redshift axis of the supercluster."190 Finally. we have utilized the same WAIN statistical methods to assess the redshift distribution of clusters in the URS with kuown redshift.," Finally, we have utilized the same KMM statistical methods to assess the redshift distribution of clusters in the HRS with known redshift."191 For the clusters. the best fit correlation axis was fouud at PA=—507.," For the clusters, the best fit correlation axis was found at $=-$."192 However when considering the broad nature of the PA relations[umlp for clusters. we used the best fit line from the iuter-cluster galaxies at à PA of ((ct..," However when considering the broad nature of the $-$ PA relationship for clusters, we used the best fit line from the inter-cluster galaxies at a PA of $-$ (cf.,"193 Figure 7))., Figure \ref{f7}) ).194 We fitted the «ποιαο position-redshift trend of the Reealaxies aud fouik ie residual iean redshift for cach cluster from that treud., We fitted the systematic position-redshift trend of the galaxies and found the residual mean redshift for each cluster from that trend.195 The resulting histogram of cluster residual redshift was plotted iu Figure 9 (ight)., The resulting histogram of cluster residual redshift was plotted in Figure \ref{f9} (right).196 We then applied IKMM. statistics to the cluster histogram., We then applied KMM statistics to the cluster histogram.197 Unlike the test on the galaxies. the cluster histogram showed no clear signature of a bianodal redshift distribution.," Unlike the test on the galaxies, the cluster histogram showed no clear signature of a bi-modal redshift distribution."198 Specifically. the cluster redshifts fitted a biainodal distribution with confidence as compared to a single Gaussian distribution.," Specifically, the cluster redshifts fitted a bi-modal distribution with $\sim$ confidence as compared to a single Gaussian distribution."199 IToscever. as can be secu iu Figure 9 (right). the cluster redshift data were sparse aud little could be concluded. frou their redshift distribution.," However, as can be seen in Figure \ref{f9} (right), the cluster redshift data were sparse and little could be concluded from their redshift distribution."200 The IIRS is generally referred to as the second ]lugest supercluster within 200. Alpe. second ouly iu mass to the Shapley Supercluster (SSC) (IIudsonctal.1999).," The HRS is generally referred to as the second largest supercluster within 200 Mpc, second only in mass to the Shapley Supercluster (SSC) \citep{hud99}."201. Since the SSC is both well-studied. and the most comparable superchister in the local universe. we use it as a beuchinark for assessing the properties of the URS.," Since the SSC is both well-studied and the most comparable supercluster in the local universe, we use it as a benchmark for assessing the properties of the HRS."202 The conrparison between these two largest structures is somewhat hiudered by the fact that most of the SSC studies combine inter-cluster aud cluster ealaxies. while our GdF data for the IRS samples ouly the inter-cluster galaxies.," The comparison between these two largest structures is somewhat hindered by the fact that most of the SSC studies combine inter-cluster and cluster galaxies, while our 6dF data for the HRS samples only the inter-cluster galaxies."203 We beeiu by comparing the kincmatic extent of the IIRS (from 17.000 to 22.500 13) with that of the SSC.," We begin by comparing the kinematic extent of the HRS (from 17,000 to 22,500 ) with that of the SSC."204 The velocity bouudaries of the eutire SSC! are generally cited as exteuding from 8.000 to 18.000 citepquiüü.daiü£..," The velocity boundaries of the entire SSC are generally cited as extending from 8,000 to 18,000 \\citep{qui00,dri04}."205 To put the SSC ou the same quantitative footing as the IRS. we compare he cluster populations of the two superclusters.," To put the SSC on the same quantitative footing as the HRS, we compare the cluster populations of the two superclusters."206 Specifically. when compared with the 15 ACO clusters found iu the IIRS by ποσαetal.(1993).. he same authors find 21 ACO clusters in the SSC. while Einastoetal.(2001). find. 25.," Specifically, when compared with the 18 ACO clusters found in the HRS by \citet{zuc93}, the same authors find 24 ACO clusters in the SSC, while \citet{ein01} find 25."207" Hence the ΠΙΟΣ of clusters iu the SSC are comparable ο, perhaps slightly larger than. those iu the HRS."," Hence the numbers of clusters in the SSC are comparable to, perhaps slightly larger than, those in the HRS."208 For the 21 ACO clusters combined from hese studies. we used published. mean redshitt ata from Quintanaetal.(2000). to calculate a ‘oluparative kincmatic extent for the SSC.," For the 24 ACO clusters combined from these studies, we used published mean redshift data from \citet{qui00} to calculate a comparative kinematic extent for the SSC."209 We etermine the PWHAL of the redshift distribution of the SSC clusters to be —60004.. very similar to the ~5500 ffound for the IIRS.," We determine the FWHM of the redshift distribution of the SSC clusters to be $\sim$ 6000, very similar to the $\sim$ 5500 found for the HRS."210 As is discussed below. the redshift distribution of the SSC clusters is distinctly biauodal. thus the FWIIM. metric is rather au oversimplification of a complex environment.," As is discussed below, the redshift distribution of the SSC clusters is distinctly bi-modal, thus the FWHM metric is rather an oversimplification of a complex environment."211 However. the basic result is that the TRS aud SSC are similar in regard to their total uunuber of ACO clusters and overall kinematic extent.," However, the basic result is that the HRS and SSC are similar in regard to their total number of ACO clusters and overall kinematic extent."212 Next. we seek to make a valid) comparison between the iuter-chnuster overdeusitics of the SSC aud the URS.," Next, we seek to make a valid comparison between the inter-cluster overdensities of the SSC and the HRS."213 Three studies have examined, Three studies have examined214evolution.,evolution.215 The additional energy input due to the radioactive decay is shown in Fig. 9.., The additional energy input due to the radioactive decay is shown in Fig. \ref{fig:lc_source_dt}.216 With increasing time. the amount of energy input into the atmosphere decreases.," With increasing time, the amount of energy input into the atmosphere decreases."217 It also shows. that the additional energy is located in the inner part of the envelope. where the *°Ni has been produced.," It also shows, that the additional energy is located in the inner part of the envelope, where the $^{56}$ Ni has been produced."218 Fig., Fig.219 10 shows the energy loss due to the emission of radiation., \ref{fig:lc_rad_dt} shows the energy loss due to the emission of radiation.220 The temperature structures of the atmosphere for several moments in time are shown in Fig. I1.., The temperature structures of the atmosphere for several moments in time are shown in Fig. \ref{fig:lc_temp_dt}.221 Figure 12. shows the LTE SN Ia model light curve of the W7-based explosion model in the optical V band., Figure \ref{fig:lc_v_neb} shows the LTE SN Ia model light curve of the W7-based explosion model in the optical V band.222 The theoretical light curve accurately reproduces the observed light curves of two SNe Ia. The steep rise of the model light curve beginning at three days after explosion 15 1n agreement with the observed light curves., The theoretical light curve accurately reproduces the observed light curves of two SNe Ia. The steep rise of the model light curve beginning at three days after explosion is in agreement with the observed light curves.223 The maximum of the W7-based model light curve seems to be later than that of the observed light curves., The maximum of the W7-based model light curve seems to be later than that of the observed light curves.224 At 20 days after the explosion. the model light curve has its maximum. while the maximum of the observed light curves is around 17 days after the explosion.," At 20 days after the explosion, the model light curve has its maximum, while the maximum of the observed light curves is around 17 days after the explosion."225 After maximum. the decline of the light curve of the W7-based model well reproduces the observed light curve.," After maximum, the decline of the light curve of the W7-based model well reproduces the observed light curve."226 Even up to the later phase at 50 days after the explosion. where the atmosphere becomes significantly thinner. the fit to the observed light curves is quite accurate.," Even up to the later phase at 50 days after the explosion, where the atmosphere becomes significantly thinner, the fit to the observed light curves is quite accurate."227 The theoretical light curve in the ultraviolet U band ts shown in Fig. 13.., The theoretical light curve in the ultraviolet U band is shown in Fig. \ref{fig:lc_u}.228 Only an observed light curve of SN 1999ee Is available., Only an observed light curve of SN 1999ee is available.229 The observational data are scattered., The observational data are scattered.230 The rise in the beginning as well as the maximum phase is well represented by the model light curve., The rise in the beginning as well as the maximum phase is well represented by the model light curve.231 However. the decline of the theoretical light curve seems to be too steep.," However, the decline of the theoretical light curve seems to be too steep."232 This same effect is present ir the model ight curve of the B band. which is shown in Fig. H4..," This same effect is present in the model light curve of the B band, which is shown in Fig. \ref{fig:lc_b}."233 The first days of the model light curve are too bright comparec to both observed SN Ia light curves., The first days of the model light curve are too bright compared to both observed SN Ia light curves.234 The maximum phase of the model light curve is in good agreement with the observed ones., The maximum phase of the model light curve is in good agreement with the observed ones.235 At day 50. the model light curve becomes brighter thar the observed light curves.," At day 50, the model light curve becomes brighter than the observed light curves."236 In Fig. 15..," In Fig. \ref{fig:lc_r},"237 a plot of the model light curve of the R banc is shown., a plot of the model light curve of the R band is shown.238 The steep rise in the beginning and the maximum phase of the observed SN Ia light curves is well represented, The steep rise in the beginning and the maximum phase of the observed SN Ia light curves is well represented239of increasing variability: wilh redshilt. whether due to the more variable. hisher frequency photons redshifting into longer wavelength bandpasses ences(herein) or to actual evolutionary effects (e.g..Tooketal.1994:CristianiVandenBerketal. 2004).,"of increasing variability with redshift, whether due to the more variable, higher frequency photons redshifting into longer wavelength bandpasses \citep[e.g.,][and references therein]{Helfand01} or to actual evolutionary effects \citep[e.g.,][]{Hook94,Cristiani96,Vanden04}."240. To characterize anv differences in UV/optical luminosity between our variable ancl populations. we caleulated a 2500 [flux density for the 933 quasars.," To characterize any differences in UV/optical luminosity between our variable and non-variable populations, we calculated a 2500 flux density for the 933 quasars."241 2500 wwas chosen because il is a fairly clean region lor (vpical quasar spectra (Vanclen 2001)., 2500 was chosen because it is a fairly clean region for typical quasar spectra \citep{Vanden01}.242. Flux densities were calculated by convolving a redshifted composite quasar spectrum (VandenBerketal.2001) with the SDSS filter response curves. using elfective wavelengths from Yorketal.(2000).. and SDSS DR3 PSF magnitudes. corrected [or Galactic extinction and shifted to the AB magnitudesvstem!.," Flux densities were calculated by convolving a redshifted composite quasar spectrum \citep{Vanden01} with the SDSS filter response curves, using effective wavelengths from \citet{York00}, and SDSS DR3 PSF magnitudes, corrected for Galactic extinction and shifted to the AB magnitude."243. The huninosity values (in units of erg ! !) reported in include the median and quartile values for the entire quasar sample. for the variable population. and for the non-variable population.," The luminosity values (in units of erg $^{-1}$ $^{-1}$ ) reported in \\ref{props} include the median and quartile values for the entire quasar sample, for the variable population, and for the non-variable population."244 These data show that the median luminosity of our non-variable population is more than double that of our variable population. with overlapping lst-to-2rd quartile ranges.," These data show that the median luminosity of our non-variable population is more than double that of our variable population, with overlapping 1st-to-3rd quartile ranges."245 Non-variable quasars have a median value of while variable quasars have a median of 8.11x1055, Non-variable quasars have a median value of $1.63 \times 10^{31}$ while variable quasars have a median of $8.11 \times 10^{30}$.246 A Kohlnogorov-8S1irnov (KS) test shows that the two samples are rejected as coming from the same parent distribution to a level of significance of 0.001., A Kolmogorov-Smirnov (KS) test shows that the two samples are rejected as coming from the same parent distribution to a level of significance of 0.001.247 We interpret this result as a confirmation that the difference between (he median luminosity densities is statistically significant., We interpret this result as a confirmation that the difference between the median luminosity densities is statistically significant.248 This shows (hat selecting quasars based on likelihood of variability returns results consistent with trends seen in quasars ranked by amplitude of variability., This shows that selecting quasars based on likelihood of variability returns results consistent with trends seen in quasars ranked by amplitude of variability.249 The upper-left panel in refFIRSTQSO shows the variability likelihood of the known quasars. split into 2\TASS detections (N = 205) and non-detections (N = 723).," The upper-left panel in \\ref{FIRSTQSO} shows the variability likelihood of the known quasars, split into 2MASS detections (N = 205) and non-detections (N = 728)."250 Quasars which were detected by 2\TASS, Quasars which were detected by 2MASS251where |BUh\P denotes the average of [D(R)|? over spherical shells. and Bik)=fBlajyexp(ik:aya is the Fourier trausfoiin of D.,"where $|\tilde{B}(k)|^2$ denotes the average of $|\tilde{B}({\bm252k})|^2$ over spherical shells, and $\tilde{B}({\bm k}) = \int B({\bm253x}) \exp{(-i {\bm k} \cdot {\bm x})} d^3 {\bm x}$ is the Fourier transform of $B$."254 It is also iustructive to look at the Fourier traustori. of the induction equation., It is also instructive to look at the Fourier transform of the induction equation.255" Taking Fourier trausforius of the .c and y components of (3)) we find πο. μα and Sik, 1 ILE,"," Taking Fourier transforms of the $x$ and $y$ components of \ref{eq:induction}) ) we find = A_x + +, and = S + A_y + +."256 We will focus on these two components as they appear to be the most important for unuderstaudius the disk (LYALL., We will focus on these two components as they appear to be the most important for understanding the disk dynamo.257" The definitions of the terms on the right-hand sides of (123) and (13)) are S(k) = Re (Re) D, 2 ]|- E.) — Re whereαἶαι subscript / in A; refers to either the . or gy coordinate."," The definitions of the terms on the right-hand sides of \ref{eq:fourx}) ) and \ref{eq:foury}) ) are ) = Re ) B_x d^3 ], ) = -Re ) d^3 ], ) = Re d^3 ], ) = - Re d^3 ], ) = - Re d^3 ], and ) = Re d^3 ], where subscript $i$ in $A_i$ refers to either the $x$ or $y$ coordinate."258" The EMES are defined as €=0;«B. with Vw=vvy, and v= eydadz. where aud E. the size of the coniputational domain in the y £,aud :- direcfious."," The EMFs are defined as ${\bm \emf} = {\bm v_t} \times {\bf B}$, with ${\bm v_t} = {\bm v} - {\bm v_{\rm sh}}$ and = v_y y z, where $L_{y}$ and $L_{z}$ the size of the computational domain in the $y-$ and $z-$ directions."259" The 4, and A, terms are included for completeness. but they are generally niuchli sanaller than the other terms so we will not discuss them further."," The $A_x$ and $A_y$ terms are included for completeness, but they are generally much smaller than the other terms so we will not discuss them further."260 These relations are simular to the transfer functions used in Fromanege&Papaloizou(2007) and Simonct(2000)., These relations are similar to the transfer functions used in \citet{fp07} and \citet{shb09}. .261 Iu fact. our definition of S is ideutical ancl if we suu d; over all three spatial dimensions. it would equivalent to their definition of A.," In fact, our definition of $S$ is identical and if we sum $A_i$ over all three spatial dimensions, it would equivalent to their definition of $A$."262 These authors expand B)-(B-.)B. and perform simular Fourier analysis on the three right-hand side terms individually. labeling them 775. Tj. aud Tay. respectively:," These authors expand )=, and perform similar Fourier analysis on the three right-hand side terms individually, labeling them $T_{bv}$, $T_{bb}$, and $T_{\rm div}$, respectively."263" One drawhack of this expansion is that terms such as B,.0e)/00 are present. even though they do not contribute to the evolution of B. because they appear with opposites sigus in both Zi aud {νι"," One drawback of this expansion is that terms such as $B_x \partial264v_x/\partial x$ are present, even though they do not contribute to the evolution of ${\bm B}$, because they appear with opposites signs in both $T_{\rm div}$ and $T_{bv}$."265 Such terms cau be quite large. complicating the interpretation of Tj. Ty. aud Tg.," Such terms can be quite large, complicating the interpretation of $T_{bv}$, $T_{bb}$, and $T_{\rm266 div}$."267 We preter to leave the right haud sides in terms of the EXIFs., We prefer to leave the right hand sides in terms of the EMFs.268 For plotting purposes. we fud it useful to normalize the quautities on the right haud side of (12)) and (13)) with the power spectrum.," For plotting purposes, we find it useful to normalize the quantities on the right hand side of \ref{eq:fourx}) ) and \ref{eq:foury}) ) with the power spectrum."269 To differeutiate them frou the ununormnalized quautities. we will use lower case letters.," To differentiate them from the unnormalized quantities, we will use lower case letters."270 For example. ον)=218.)(BARPQ).," For example, $e_{y,z}(k) \equiv 2 E_{y,z}(k)/(|\tilde{B}_x(k)|^2 \Omega)$."271" This then constitutes the Fourier amplitude of the normalized rate of field production of 5, due to the vertical variation of £, Thefactor Q has been introduced to make the quautities dimenusionless rates.", This then constitutes the Fourier amplitude of the normalized rate of field production of $B_x$ due to the vertical variation of $\emf_y$ Thefactor $\Omega$ has been introduced to make the quantities dimensionless rates.272 Ourprimary goal is to test the robustness of sustained turbulence and angular momeutuni transport in stratified sheariug boxes with zero net flux. and in," Ourprimary goal is to test the robustness of sustained turbulence and angular momentum transport in stratified shearing boxes with zero net flux, and in"273have a period of at least ~3 years. making it unlikely to be caused by HAT-P-I3c.,"have a period of at least $\sim3$ years, making it unlikely to be caused by HAT-P-13c."274 Hence. ? conclude that the measured TTV may be the result of perturbations of another long-period companion.," Hence, \citet{Paletal11} conclude that the measured TTV may be the result of perturbations of another long-period companion."275 Interestingly. ? also point to the possibility of an additional body d in the system as their models of two Keplerian orbits give an unacceptable fit to the RV data while a model assuming a third companion with a longer orbital period is successful.," Interestingly, \citet{Winnetal10} also point to the possibility of an additional body d in the system as their models of two Keplerian orbits give an unacceptable fit to the RV data while a model assuming a third companion with a longer orbital period is successful."276 Furthermore. thinking about the origin of the HAT-P-13 system. ? ?.re.," Furthermore, thinking about the origin of the HAT-P-13 system, \citet{Mardling10} \citet{Mardling07}."277Gravitational wave astronomy could well make soon its first observations as the running earth-based facilities such àsLIGO!..VIRGO-..GEO600°.. and are up to reach the required high sensitivities.,"Gravitational wave astronomy could well make soon its first observations as the running earth-based facilities such as, and are up to reach the required high sensitivities."278 For à review on gravitational wave detection see e. g. (Hough&Rowan2007)., For a review on gravitational wave detection see e. g. \citep{lrr-2000-3}.279 The successful observation of gravitational waves (GW) would be a major breakthrough: it would open a new window to the universe. allowing us to observe electromagnetically hidden regions (Thorne1995)..," The successful observation of gravitational waves (GW) would be a major breakthrough: it would open a new window to the universe, allowing us to observe electromagnetically hidden regions \citep{1995pnac.conf..160T}."280 One of the most promising gravitational wave sources is the stellar core collapse leading to à supernova explosion., One of the most promising gravitational wave sources is the stellar core collapse leading to a supernova explosion.281 The observation of both. GW and the neutrino signal. from a galactic supernova would reveal hitherto hidden details about the explosion scenario and impose constraints on the nuclear and weak interaction physics under conditions that can not be obtained in terrestrial experiments.," The observation of both, GW and the neutrino signal, from a galactic supernova would reveal hitherto hidden details about the explosion scenario and impose constraints on the nuclear and weak interaction physics under conditions that can not be obtained in terrestrial experiments."282 As a core of a star of M>8M. reaches the end of its stellar evolution. it becomes gravitationally unstable as soon as thermonuclear burning produces a significant amount of iron group nuclei.," As a core of a star of $ M \geq 8M_{\odot} $ reaches the end of its stellar evolution, it becomes gravitationally unstable as soon as thermonuclear burning produces a significant amount of iron group nuclei."283 Next to photo-disintegration. electron captures on free protons and nuclei reduce the mostly electron supported pressure. and the core starts to collapse eventually.," Next to photo-disintegration, electron captures on free protons and nuclei reduce the mostly electron supported pressure, and the core starts to collapse eventually."284 The collapse continues untilnuclear densities of ~2x 104e/em* are reached. depending on the equation of state (EoS)," The collapse continues untilnuclear densities of $\sim2\times10^{14}$ $^{3}$ are reached, depending on the equation of state (EoS)."285 As soon as we enter this density regime. the core overshoots its equilibrium position and bouces back.," As soon as we enter this density regime, the core overshoots its equilibrium position and bounces back."286 A sound wave immediately forms and steepens into a shock wave that propagates outwards., A sound wave immediately forms and steepens into a shock wave that propagates outwards.287 However. the shock stalls within ~5 ms after core bounce due to the large energy loss caused by the dissociation of nuclei into free nucleons at a cost of ~8.8 MeV per nucleon and by neutrino emission connected to copious electron captures on the emerging free protons.," However, the shock stalls within $\sim5$ ms after core bounce due to the large energy loss caused by the dissociation of nuclei into free nucleons at a cost of $\sim8.8$ MeV per nucleon and by neutrino emission connected to copious electron captures on the emerging free protons."288 It continues to propagate outwards to radii around 100—200 km as standing accretion shock., It continues to propagate outwards to radii around 100-200 km as standing accretion shock.289 Hereafter. 1.0. some ms after the prompt explosion mechanism failed. a delayed explosion mechanism by neutrino heating ts thought to occur. e.g. (1990).," Hereafter, i.e. some ms after the prompt explosion mechanism failed, a delayed explosion mechanism by neutrino heating is thought to occur, e.g. \citet{Bethe1990}."290. The idea of reviving the stalled shock again via neutrino reactions behind and ahead of the shock has long been vestigated as possible explosion mechanism (Bethe&Wil-son1985:Jankaetal. 2001).," The idea of reviving the stalled shock again via neutrino reactions behind and ahead of the shock has long been investigated as possible explosion mechanism \citep{Bethe1985,Janka2001a}."291 In the dissociated matter behind the shock. electron-flavour neutrino captures are the dominant heating reactions. while in the accreting matter ahead of the shock. electron-neutrino absorption and neutrino-nucleon scattering are the dominant interactions that preheat the infalling unshocked material (Bruenn&Haxton1991).," In the dissociated matter behind the shock, electron-flavour neutrino captures are the dominant heating reactions, while in the accreting matter ahead of the shock, electron-neutrino absorption and neutrino-nucleon scattering are the dominant interactions that preheat the infalling unshocked material \citep{Bruenn1991}."292. In addition. neutrino-electron scattering and pair annihilatio=) may contribute to the heating as well.," In addition, neutrino-electron scattering and pair annihilation may contribute to the heating as well."293 However. the effects of pre-heating and neutrino-electron scattering on the shock revival are insignificantly small compared to the effect from the capture of neutrinos on free nucleons in the heating region below the shock.," However, the effects of pre-heating and neutrino-electron scattering on the shock revival are insignificantly small compared to the effect from the capture of neutrinos on free nucleons in the heating region below the shock."294 Equally as important as the neutrino heating is the neutrino cooling of matter that settles on the protoneutro=) star (PNS) (Janka2001)., Equally as important as the neutrino heating is the neutrino cooling of matter that settles on the protoneutron star (PNS) \citep{Janka2001}.295. As à core collapse supernova is likely to show aspherical features also close to its center (Leonardetal.2006).. where the matter assumes a high density. a tiny fraction of the released binding energy can be emitted via gravitational radiation.," As a core collapse supernova is likely to show aspherical features also close to its center \citep{2006Natur.440..505L}, where the matter assumes a high density, a tiny fraction of the released binding energy can be emitted via gravitational radiation."296 The following features have beer suggested as possible causes of the asymmetries in the energy-matter distribution necessary to emit GW: the rotational stellar core collapse. convection in the high-density protoneutror star. nonaxisymmetric rotational instabilities. fluid instabilities in the lower-density hot mantle surrounding it (possibly triggering neutron. star. oscillation modes). and an anisotropic neutrino emission (for recent reviews see e.g. (Kotakeetal.2006:Fryer&New 2006))).," The following features have been suggested as possible causes of the asymmetries in the energy-matter distribution necessary to emit GW: the rotational stellar core collapse, convection in the high-density protoneutron star, nonaxisymmetric rotational instabilities, fluid instabilities in the lower-density hot mantle surrounding it (possibly triggering neutron star oscillation modes), and an anisotropic neutrino emission (for recent reviews see e.g. \citep{2006RPPh...69..971K,Living Reviews in Relativity}) )."297 The understanding of GW emission from differentially rotating core collapse has evolved with time due to the improving input physics used in simulations., The understanding of GW emission from differentially rotating core collapse has evolved with time due to the improving input physics used in simulations.298 In 2D axisymmetric computations by Miiller(1982) Iron cores. a Newtonian hydrodynamics code and a tabulated finite temperature EoS were used.," In 2D axisymmetric computations by \citet{1982A&A...114...53M} iron cores, a Newtonian hydrodynamics code and a tabulated finite temperature EoS were used."299" The results allowed to recognise the link between rotation and the efficiency of GW emission,", The results allowed to recognise the link between rotation and the efficiency of GW emission.300 After having taken into account more micro-physics in Newtonian gravity. such as electron capture on protons and a simplified neutrino transport scheme (Moenchmeyer 199]).. one was able to distinguish two different," After having taken into account more micro-physics in Newtonian gravity, such as electron capture on protons and a simplified neutrino transport scheme \citep{1991A&A...246..417M}, , one was able to distinguish two different"301before formation of stellar BHs.,before formation of stellar BHs.302" This subsystem of massive stars can enter a phase of rapid collisions, and since the most massive object has the largest cross-section for further collisions, this object is expected to grow in a runaway fashion."," This subsystem of massive stars can enter a phase of rapid collisions, and since the most massive object has the largest cross-section for further collisions, this object is expected to grow in a runaway fashion."303 The resulting VMS eventually collapses to form an IMBH (??)..," The resulting VMS eventually collapses to form an IMBH \citep{PM02,304GU04}."305" As the time it takes for the most massive stars to turn into BHs is approximately 3Myr (?),, an IMBH is only formed through runaway merging if the cluster reaches core collapse within the first 3Myr of dynamical evolution."," As the time it takes for the most massive stars to turn into BHs is approximately $3\,{\rm Myr}$ \citep{MEMA00}, an IMBH is only formed through runaway merging if the cluster reaches core collapse within the first $3\,{\rm Myr}$ of dynamical evolution."306 This simple picture has a few important caveats., This simple picture has a few important caveats.307" First, the fate of such a massive merger remnant formed by a runaway is rather uncertain."," First, the fate of such a massive merger remnant formed by a runaway is rather uncertain."308" Direct monolithic collapse to a BH with no or little mass loss is a possible outcome, at least for sufficiently small metallicities (?).."," Direct monolithic collapse to a BH with no or little mass loss is a possible outcome, at least for sufficiently small metallicities \citep{HE02}."309" However, it has been suggested that mass loss from stellar winds could dominate the mass increase due to repeated mergers (?).."," However, it has been suggested that mass loss from stellar winds could dominate the mass increase due to repeated mergers \citep{GL09}."310 In this case it might be difficult to form a VMS at all., In this case it might be difficult to form a VMS at all.311" On the other hand, within the runaway phase, it has been shown that, for clusters like those studied here, the time between collisions is much shorter than the Kelvin-Helmholtz timescale of the collision product, so that the growing VMS must be out of thermal equilibrium."," On the other hand, within the runaway phase, it has been shown that, for clusters like those studied here, the time between collisions is much shorter than the Kelvin-Helmholtz timescale of the collision product, so that the growing VMS must be out of thermal equilibrium."312 Instead the calculations of ? were done assuming that each merger remnant behaves exactly like an ordinary massive star in thermal equilibrium., Instead the calculations of \citet{GL09} were done assuming that each merger remnant behaves exactly like an ordinary massive star in thermal equilibrium.313" The uncertainty in the final VMS (and IMBH) mass is further increased when considering that a stronger wind mass loss would also lead to a stronger expansion of the cluster core, decreasing the mass growth rate of the VMS by lowering the collision rate."," The uncertainty in the final VMS (and IMBH) mass is further increased when considering that a stronger wind mass loss would also lead to a stronger expansion of the cluster core, decreasing the mass growth rate of the VMS by lowering the collision rate."314" To address this problem, one would need to perform a fully self-consistent simulation coupling the stellar dynamics with detail radiation hydrodynamics of the stellar collisions and mass loss from merger remnants."," To address this problem, one would need to perform a fully self-consistent simulation coupling the stellar dynamics with detail radiation hydrodynamics of the stellar collisions and mass loss from merger remnants."315 This is clearly beyond the scope of this paper., This is clearly beyond the scope of this paper.316 The runaway collision scenario in globular clusters has been extensively investigated in Paper Iandin ?? using Monte Carlo (MC) simulations for a large variety of initial conditions.," The runaway collision scenario in globular clusters has been extensively investigated in Paper I and in \citet{freitag06,freitagrasio06} using Monte Carlo (MC) simulations for a large variety of initial conditions."317" Paper I focuses on the dependence of Ίος on the shape and the width of the IMF, the presence of a Galactic tidal field, and the cluster density profile."," Paper I focuses on the dependence of $t_{\rm cc}$ on the shape and the width of the IMF, the presence of a Galactic tidal field, and the cluster density profile."318" The key result is that for clusters with a broad range of masses, tee is set by the central relaxation time, ἔτε(θ), which means that for multi-mass clusters core collapse depends on the local conditions in the core while for single-mass clusters core collapse is a global phenomenon."," The key result is that for clusters with a broad range of masses, $t_{\rm cc}$ is set by the central relaxation time, $t_{\rm rc}(0)$, which means that for multi-mass clusters core collapse depends on the local conditions in the core while for single-mass clusters core collapse is a global phenomenon."319 Furthermore it is clear that tee depends only weakly on the external tidal field., Furthermore it is clear that $t_{\rm cc}$ depends only weakly on the external tidal field.320" It was also found that the dependence of t.. on the mass spectrum can be conveniently expressed by a single parameter m4544/(m), where ma is the maximum and (m) the average stellar mass."," It was also found that the dependence of $t_{\rm cc}$ on the mass spectrum can be conveniently expressed by a single parameter $m_{max}/\left<m\right>$, where $m_{max}$ is the maximum and $\left<m\right>$ the average stellar mass."321 For Mmax/(m)>50 the ratio tec/tre converges to a constant value z 0.15 for all IMFs and cluster density profiles., For $m_{max}/\left<m\right>\ > 50$ the ratio $t_{\rm cc}/t_{\rm rc}$ converges to a constant value $\approx$ $0.15$ for all IMFs and cluster density profiles.322" Combined with the requirement that te. be less than 3Myr, this relation provides a uniform criterion for runaway growth to occur for a large range of possible, unsegregated cluster configurations."," Combined with the requirement that $t_{\rm cc}$ be less than $3\,\rm Myr$, this relation provides a uniform criterion for runaway growth to occur for a large range of possible, unsegregated cluster configurations."323 ? performed similar simulations but also incorporating collisions explicitly., \citet{freitag06} performed similar simulations but also incorporating collisions explicitly.324" They quantified the dependence of the onset of the runaway on the initial collision time, and found that runaway growth happens earlier with respect to trn, the half-mass relaxation time for initially more collisional clusters."," They quantified the dependence of the onset of the runaway on the initial collision time, and found that runaway growth happens earlier with respect to $t_{\rm rh}$, the half-mass relaxation time for initially more collisional clusters."325" Thus, collisions extend the parameter space of initial cluster conditions for runaway to occur."," Thus, collisions extend the parameter space of initial cluster conditions for runaway to occur."326" However, as pointed out by the authors, for any standard IMF (Kroupa, Salpeter, Miller-Scalo) this effect is negligible for masses typical for globular clusters."," However, as pointed out by the authors, for any standard IMF (Kroupa, Salpeter, Miller-Scalo) this effect is negligible for masses typical for globular clusters."327" Thus, in this regime, the condition for runaway to occur reduces to the one found in Paper I, based on the central relaxation time alone."," Thus, in this regime, the condition for runaway to occur reduces to the one found in Paper I, based on the central relaxation time alone."328 The runaway collision scenario has also been verified numerically by direct N-body simulations., The runaway collision scenario has also been verified numerically by direct $N$ -body simulations.329 In ? runaway collisions were produced in sufficiently dense and highly concentrated clusters with only a few 104 stars initially., In \citet{PM02} runaway collisions were produced in sufficiently dense and highly concentrated clusters with only a few $10^4$ stars initially.330" ? modelled the evolution of MGG-11 with z10? and, in one case, with ~5x10? stars, and found that, similar to Paper I,only clusters with a short enough mass-segregation timescale, or, correspondingly, low enough typ, are likely to produce a runaway object."," \citet{P04} modelled the evolution of MGG-11 with $\approx 10^5$ and, in one case, with $\approx3315\times10^5$ stars, and found that, similar to Paper I,only clusters with a short enough mass-segregation timescale, or, correspondingly, low enough $t_{\rm rh}$ , are likely to produce a runaway object."332" However, their results also show that, in addition to a short t,4, these clusters must also be sufficiently concentrated, corresponding to King models with Wo>9, in order to trigger a runaway object."," However, their results also show that, in addition to a short $t_{\rm rh}$, these clusters must also be sufficiently concentrated, corresponding to King models with ${\rm W_0}\geq9$, in order to trigger a runaway object."333" This might be due to the fact that in the N-body simulations binaries formed by three-body interactions (?),, a process which is not included in the MC runs, and these binaries"," This might be due to the fact that in the $N$ -body simulations binaries formed by three-body interactions \citep{freitag06}, a process which is not included in the MC runs, and these binaries"334with the source (core) in VLBA observations by Paredesetal.(2000. 2002).. which were interpreted as emission from two opposite relativistic jets.,"with the source (core) in VLBA observations by \citet{Paredes2000, Paredes2002}, which were interpreted as emission from two opposite relativistic jets."335 Phe svstem was also identified with a very high. energy. (WILE) 5-ray. source found in the CGRO/DEGBRIZE (Paredes et al., The system was also identified with a very high energy (VHE) $\gamma$ -ray source found in the /EGRET (Paredes et al.336 2000) and HESS (Abaronian2005a) surveys., 2000) and HESS \citep{Aharonian2005a} surveys.337 The detection. of MeV-GeVΓον emission. placed LS 5039/10N 1826.2. 1450 into a class of unusual high-energy objects. the z-ray. binaries.," The detection of MeV-GeV/TeV emission placed LS 5039/RX $-$ 1450 into a class of unusual high-energy objects, the $\gamma$ -ray binaries."338 So far. only a handful of *-rav. binaries are known.," So far, only a handful of $\gamma$ -ray binaries are known."339 The others are PSR 63 (Aharonianetal.2005b).. LS L |61 303 2006:Acciarietal. 2008).. Cvenus X-1 (Albertctal. 2007).. Cygnus N-3 (Invanietal.2000).. and the recent candidate LIESS 0632|057 (Hintonetal.2009).," The others are PSR $-$ 63 \citep{Aharonian2005b}, LS I +61 303 \citep{Albert2006,Acciari2008}, Cygnus X-1 \citep{Albert2007}, Cygnus X-3 \citep{Tavani2009}, and the recent candidate HESS J0632+057 \citep{Hinton2009}."340. LS ΟΡΟΗΝ 1450 (hereafter. referred. to às LS 5039) has been classified as à high-mass X-ray binary in the catalogue compiled by Liu.vanParadijs&den (2006).," LS 5039/RX $-$ 1450 (hereafter, referred to as LS 5039) has been classified as a high-mass X-ray binary in the catalogue compiled by \cite{Liu2006}."341.. The. distance to the source is x2.5kpc (Casaresetal.2005)., The distance to the source is $\approx 2.5$ kpc \citep{Casares2005}.342.. Its primary is à bright (V= 11.2) massive O star (Clarkοἱd.2001:AleSwainetal.2001).. and its secondarv is a compact star.," Its primary is a bright $V = 11.2$ ) massive O star \citep{Clark2001, McSwain2001}, and its secondary is a compact star."343 It is still a matter of ebate whether the compact star in LS 5039 is a black hole or à neutron star., It is still a matter of debate whether the compact star in LS 5039 is a black hole or a neutron star.344 UV and optical spectroscopy established that the primary is à O6.5V((£)) star (MeSwainetal.2004)., UV and optical spectroscopy established that the primary is a O6.5V((f)) star \citep{McSwain2004}.345". -""he. presence of P. Cvgni. profiles in the UV. N AT240 and € AI550 lines (MeSwainetal.2004). indicates a strong wind outflow. whose rate has been estimated to be ~107 M. + or even higher (MeSwainetal.2004)."," The presence of P Cygni profiles in the UV N $\lambda$ and C $\lambda$ lines \citep{McSwain2004} indicates a strong wind outflow, whose rate has been estimated to be $\sim {\bf 10^{-7}}$ $_\odot$ $^{-1}$ or even higher \citep{McSwain2004}."346". From the radial velocities of the Ho and He lines. \leSwainetal.(2004). (hereafter. MOA) obtained. an orbital period P=(4.4267()+ 0.0005)d and f(m)=(0.0017)+0.0005) .. the orbital eccentricity e=O48+0.06 and e,sin;=M(1.36c 0.13)... where a, ds the semi-major axis of the primary’s orbit and i is orbital inclination."," From the radial velocities of the $\alpha$ and He lines, \citet{McSwain2004} (hereafter M04) obtained an orbital period $P=(4.4267\pm0.0005)$ d and $f(m) = (0.0017\pm0.0005)$ $_\odot$, the orbital eccentricity $e=0.48\pm0.06$ and $a_1 \sin i = (1.36\pm 0.13)$ $_\odot$ , where $a_1$ is the semi-major axis of the primary's orbit and $i$ is orbital inclination."347 Γον argued that the mass of the primary O star is in the range (20. 35)AL.. and the compact secondary is à neutron star which has a mass = 1.4M..," They argued that the mass of the primary O star is in the range $(20-35)$ $_\odot$, and the compact secondary is a neutron star which has a mass $\approx 1.4$ $_\odot$."348" Casaresal.(2005). (hereafter €C05) conducted a comprehensive analvsis of the optical LE Balmer and and lines and obtained P?=(3.906035 0.00017)d. ο=0.35+0.04. f(m)=(0.0053 20.0009)AL. and e,sin;=(1.42X 0.07)1t.."," \citet{Casares2005} (hereafter C05) conducted a comprehensive analysis of the optical H Balmer and and lines and obtained $P=(3.90603\pm0.00017)$ d, $e=0.35\pm0.04$, $f(m) = (0.0053\pm0.0009)$ $_\odot$ and $a_1 \sin i = (1.42\pm 0.07)$ $_\odot$."349" They derived that the orbital inclination /=(24.9+2.8) the primary O star has à mass A,=22.9 14M. and the compact star has a mass Mo=3.-1-- "," They derived that the orbital inclination $i =(24.9\pm2.8)^\circ$, the primary O star has a mass $M_1 = 22.9^{+3.4}_{-2.9}$ $_\odot$ and the compact star has a mass $M_2 =3.7^{+1.3}_{-1.0}$ $_\odot$."350Phe orbital period obtained. by C05 is shorter than that obtained. by AIO4., The orbital period obtained by C05 is shorter than that obtained by M04.351 Lt is however consistent with the modulations observed in the X-rays (Bosch-Ramonetal.2005:‘Takahashict2009) and 5-ravs a GeV. (Abdoοal.2009) ane TeV (Aharonianetal.20)6) energies.," It is however consistent with the modulations observed in the X-rays \citep{Bosch-Ramon2005,Takahashi2009} and $\gamma$ -rays at GeV \citep{Abdo2009} and TeV \citep{Aharonian2006} energies."352 Aragonaetal.(2009) (hereafter AOO) revisied radial velociv (RV) measurements ron optical spectra. confirming the 3.9c orbital period.," \citet{Aragona2009} (hereafter A09) revisited radial velocity (RV) measurements from optical spectra, confirming the 3.9d orbital period."353" Their refined orbital parameters. are P=(3.90608+ 00010)d. e=0.337i250.036. επι)=(0.00261£0.0003G6) AL. and e,sin;=(1.435d 0.066)R.."," Their refined orbital parameters are $P=(3.90608\pm0.00010)$ d, $e=0.337\pm0.036$, $f(m) = (0.00261\pm0.00036)$ $_\odot$ and $a_1 \sin i = (1.435\pm 0.066)$ $_\odot$."354 One major question about LS 5039 is the nature of he compact object., One major question about LS 5039 is the nature of the compact object.355 Dlack-hole binaries with a massive O-tvpe donor star are very rare. partly because of the extremely short life-spans of such systems.," Black-hole binaries with a massive O-type donor star are very rare, partly because of the extremely short life-spans of such systems."356 To date. (νο X-lL is the only known black-hole X-ray binary in the Milky Way with a massive O donor star.," To date, Cyg X-1 is the only known black-hole X-ray binary in the Milky Way with a massive O donor star."357 Phe presence of a black hole in LS 5039have significant implications not only on the formation of black-hole hieh-mass X-ray binaries and the population of such systems in the Milky Way. but also on how very high-cnerey (TeV) emission is produced. in οταν binaries (see c.g. Boseh-Ramon&Romero(2009))).," The presence of a black hole in LS 5039 significant implications not only on the formation of black-hole high-mass X-ray binaries and the population of such systems in the Milky Way, but also on how very high-energy (TeV) emission is produced in $\gamma$ -ray binaries (see e.g. \citet{Araudo2009}) )."358 The issue of the nature of the compact star associated with LS 5039 is far from being settled., The issue of the nature of the compact star associated with LS 5039 is far from being settled.359 Observationallv. Raboctal.(2008). found that changes in the morphology of the radio images were dillicult to reconcile with the micro-quasar (black-hole binary) scenario in which the radio emission. originates from. expanding plasmons.," Observationally, \citet{Ribo2008} found that changes in the morphology of the radio images were difficult to reconcile with the micro-quasar (black-hole binary) scenario in which the radio emission originates from expanding plasmons."360 The situation is further complicated by the fact that the temporal ancl spectral behaviour of the X-ray emission. (Bosch-Ramonetal.2007:Bosch-Ramon2009:Takahashietal.2009:Ixishishita2009) and properties of the TeV emission (Boseh-Ramonetal.2008:Khaneulvanetal.2008:Abdoct2009) indicate that the hieh-encrey radiation might originate [rom regions lar outside the binary orbit of LS 5039.," The situation is further complicated by the fact that the temporal and spectral behaviour of the X-ray emission \citep{Bosch-Ramon2007,Bosch-Ramon2009,Takahashi2009,Kishishita2009} and properties of the TeV emission \citep{Bosch-Ramon2008,Khangulyan2008,Abdo2009} indicate that the high-energy radiation might originate from regions far outside the binary orbit of LS 5039."361 We have been observing LS 5039 photometrically with eround-based telescopes at optical and near LR wavelengths to search for orbital modulation. but orbital variations have not been detected. in those data (to be reported elsewhere).," We have been observing LS 5039 photometrically with ground-based telescopes at optical and near IR wavelengths to search for orbital modulation, but orbital variations have not been detected in those data (to be reported elsewhere)."362 However. we have detected variations at the 20 numag level. especially in the Ze-band.," However, we have detected variations at the 20 mmag level, especially in the $I_{C}$ -band."363 This prompted. us to take a closer look at the optical photometric variations of LS 5039 from space with the Canadian. Alicrovariahility and Oscillations of Stars J) satellite., This prompted us to take a closer look at the optical photometric variations of LS 5039 from space with the Canadian Microvariability and Oscillations of Stars ) satellite.364 OurAJOST observations were made in July 2009. simultaneously with erounc-basecl optical spectroscopic observations from the Australian National University (ANU) 2.3m Telescope at Siding Spring Observatory. Australia.," Our observations were made in July 2009, simultaneously with ground-based optical spectroscopic observations from the Australian National University (ANU) 2.3m Telescope at Siding Spring Observatory, Australia."365 Here we report on the main findings. especially those concerning the masses of the component stars in LS 5039 and the nature of the compact star.," Here we report on the main findings, especially those concerning the masses of the component stars in LS 5039 and the nature of the compact star."366 This paper is organized as follows., This paper is organized as follows.367In Section 727. we describe the photometric observations with thespace telescope and the spectroscopic observations with the ANU 2.3m Telescope. which were mace simultaneously.,"In Section \ref{two} we describe the photometric observations with thespace telescope and the spectroscopic observations with the ANU 2.3m Telescope, which were made simultaneously."368 In Section 77. we describe the data analysis. present. the results on the system's orbital and other parameters. and discuss the implications of the nature of the compact object ancl the properties of the wind/outllow from the primary star.," In Section \ref{three} we describe the data analysis, present the results on the system's orbital and other parameters, and discuss the implications of the nature of the compact object and the properties of the wind/outflow from the primary star."369 The conclusions are summarized in Section ??.., The conclusions are summarized in Section \ref{four}. .370In ?.. it was pointed out that adjacent frequencies within a multiplet tend to pair up and come close together. except for the most retrograde mode 6=fm] sectoral mode).,"In \citet{Espinosa2004}, it was pointed out that adjacent frequencies within a multiplet tend to pair up and come close together, except for the most retrograde mode $\l = -|m|$ sectoral mode)."371 Lt was then suggested that this phenomena could explain the close frequency pairs observed in 7. (see also 7. and ?))., It was then suggested that this phenomena could explain the close frequency pairs observed in \citet{Breger2002} (see also \citealt{Breger2006} and \citealt{Breger2006b}) ).372 A similar pairing up of mocdes also occurs for the frequencies in? as well as the non-perturbative [frequencies presented here.," A similar pairing up of modes also occurs for the frequencies in \citet{Reese2006}373 as well as the non-perturbative frequencies presented here."374 In what follows. we will consider 2 Al. ZAMS models. as this is more representative of 9 Scuti stars.," In what follows, we will consider 2 $M_{\odot}$ ZAMS models, as this is more representative of $\delta$ Scuti stars."375 The second half of Table 1. gives the characteristics for a selection of these mocels., The second half of Table \ref{tab:models} gives the characteristics for a selection of these models.376 Figure 5 shows [our sets of (=2 multiplets calculated using— both perturbative ancl two-dimensional calculations., Figure \ref{fig:pairs} shows four sets of $\l=2$ multiplets calculated using both perturbative and two-dimensional calculations.377 As can be seen in the figures. only the two-dimensional calculations lead to this behaviour.," As can be seen in the figures, only the two-dimensional calculations lead to this behaviour."378 “Phe perturbative calculations produce. instead. spacings which decrease uniformly when going from the most retrograde to the most. prograde mode.," The perturbative calculations produce, instead, spacings which decrease uniformly when going from the most retrograde to the most prograde mode."379 However. the elfects of avoided crossings have not been included. in the perturbative calculations. so it remains to be seen whether including this ellect can also produce a pairing up of adjacent frequencies.," However, the effects of avoided crossings have not been included in the perturbative calculations, so it remains to be seen whether including this effect can also produce a pairing up of adjacent frequencies."380 It is then interesting to investigate whether this cllectcould explain the close frequency. pairs observed. in. 2.., It is then interesting to investigate whether this effectcould explain the close frequency pairs observed in \citet{Breger2006}.381 In Fie. 6..," In Fig. \ref{fig:pairs_count},"382 we compare the frequency. dilferences of mode pairs to à Írequency. separation of 0.1 cfd 1.1574 ΙΙ). a tvpical threshold. for observed frequeney. pairs.," we compare the frequency differences of mode pairs to a frequency separation of 0.1 c/d $1.1574\,\,\mu$ Hz), a typical threshold for observed frequency pairs."383 As can be seen from the upper panel. these dillerences remain larger on average than 0.1 cd. Phe lower panel shows the number of sullictently close frequencies as a function of the rotation rale.," As can be seen from the upper panel, these differences remain larger on average than 0.1 c/d. The lower panel shows the number of sufficiently close frequencies as a function of the rotation rate."384 As can be seen. this number is not very large [for any given rotation rate. except when the rotation rate is around or below 0.1 cd. However. 18 close frequency. pairs were observed in FC Vir (?2).. and its equatorial velocity is estimated. to be 664⋅⋅16⋅kms⊥7. as based on the modelling; of line profile variations (2)..," As can be seen, this number is not very large for any given rotation rate, except when the rotation rate is around or below 0.1 c/d. However, 18 close frequency pairs were observed in FG Vir \citep{Breger2006b}, and it's equatorial velocity is estimated to be $66\pm16\,\,\kms$, as based on the modelling of line profile variations \citep{Zima2006}."385 As a result. the pairing up of adjacent modes in frequeney multiplets do not seem to account for close frequency pairs in ὁ Scuti stars.," As a result, the pairing up of adjacent modes in frequency multiplets do not seem to account for close frequency pairs in $\delta$ Scuti stars."386 Of course. it is always possible to look at all of the requeney dillerences for a given spectrum.," Of course, it is always possible to look at all of the frequency differences for a given spectrum."387 This approach it been used by 2? to study 3 9 Seuti stars. including IG. Vir.," This approach has been used by \citet*{Lenz2008} to study 3 $\delta$ Scuti stars, including FG Vir."388 Here. we will push the analysis slightly further by ooking at how the number of close frequency. pairs depends on the rotation rate.," Here, we will push the analysis slightly further by looking at how the number of close frequency pairs depends on the rotation rate."389 Figure 7 shows the number of close requeney pairs as a function of the rotation rate. as well as where thev occur.," Figure \ref{fig:all_pairs} shows the number of close frequency pairs as a function of the rotation rate, as well as where they occur."390 The dashed line in the lower panel gives he expected number of pairs. Nex. as based on a Poisson cistribution: where Nude is the number of modes in the spectrum. Af the frequency span of the spectrum. and ὁ the target [requeney. separation 0.1 e£d).," The dashed line in the lower panel gives the expected number of pairs, $N_{\mathrm{exp.}}$, as based on a Poisson distribution: where $N_{\mathrm{mode}}$ is the number of modes in the spectrum, $\Delta f$ the frequency span of the spectrum, and $\delta f$ the target frequency separation 0.1 c/d)."391" At a sullicient. rotation rate. the average number of close frequency pairs matches Nesp, indicating that the spectrum is behaving like a Poisson distribution."," At a sufficient rotation rate, the average number of close frequency pairs matches $N_{\mathrm{exp.}}$ indicating that the spectrum is behaving like a Poisson distribution."392 As was pointed out by ? and 2.. the frequency spectrum of rapidly rotating stars is subcivided into classes of regular modes. such as these low degree modes. and chaotic modes. the frequencies of which follow Poisson and Wiener distributions respectively. provided. there are no selection effects.," As was pointed out by \citet{Lignieres2008} and \citet{Lignieres2009}, the frequency spectrum of rapidly rotating stars is subdivided into classes of regular modes, such as these low degree modes, and chaotic modes, the frequencies of which follow Poisson and Wigner distributions respectively, provided there are no selection effects."393 The number of close frequency. pairs is much higher han in the previous case and higher than the number of ours observed in EG. Vir., The number of close frequency pairs is much higher than in the previous case and higher than the number of pairs observed in FG Vir.394 However. Fig.," However, Fig."395 7 is based on 160 requencies. whereas there are 67 independent. [reequencies detected. in. FC: Vir.," \ref{fig:all_pairs} is based on 160 frequencies, whereas there are 67 independent frequencies detected in FG Vir."396 Applying Eq. (19) , Applying Eq. \ref{eq:Nexp}) )397to FG ιν requeney spectrum vields 10.4 close frequency pairs. which is slightly over half the number of observed. close frequency ours in this star.," to FG Vir's frequency spectrum yields 10.4 close frequency pairs, which is slightly over half the number of observed close frequency pairs in this star."398 Also. as pointed out in ?.. there are 7 frequeney pairs where the separation is below 0.01 cd. Equation (19)) would. vield. 1.12 very. close frequency: pairs or FO Vir.," Also, as pointed out in \citet{Lenz2008}, there are 7 frequency pairs where the separation is below 0.01 c/d. Equation \ref{eq:Nexp}) ) would yield 1.12 very close frequency pairs for FG Vir."399" Furthermore. according to ὃν, close [frequency »airs seem to cluster around radial modes. whereas a number ofpairs in Fig."," Furthermore, according to \citet{Breger2006b}, close frequency pairs seem to cluster around radial modes, whereas a number ofpairs in Fig."400 7. are close to the micdpoints between consecutive radial modes., \ref{fig:all_pairs} are close to the midpoints between consecutive radial modes.401 Hence. an astrophysical origin is still needed to account for this phenomena.," Hence, an astrophysical origin is still needed to account for this phenomena."402 An interesting feature appears in Fig. y.., An interesting feature appears in Fig. \ref{fig:all_pairs}.403 Between approximately 0.02Qy and 0.05Og. few frequency pairs are detected.," Between approximately $0.02\,\,\Omega_{\mathrm{K}}$ and $0.05\,\,\Omega_{\mathrm{K}}$, few frequency pairs are detected."404 A simple explanation is that the rotation rate is sullicicnt to keep individual multiplet components. far enough apart. but too small to cause frequency. multiplets to overlap.," A simple explanation is that the rotation rate is sufficient to keep individual multiplet components far enough apart, but too small to cause frequency multiplets to overlap."405 OL course. including modes. with higher { values would probably reduce this gap by introducing new multiplets into the frequeney spectrum.," Of course, including modes with higher $\ell$ values would probably reduce this gap by introducing new multiplets into the frequency spectrum."406 Llowever. as was pointed out by 2? and. ?.. cancellation. elects for such modes are more effective at lower rotation rates. where close frequencies pairs are lacking.," However, as was pointed out by \citet{Lignieres2006} and \citet{Lignieres2009}, cancellation effects for such modes are more effective at lower rotation rates, where close frequencies pairs are lacking."407 Table ο gives a list of 2 Scuti stars where close frequencies have been. reported., Table \ref{tab:stars_with_pairs} gives a list of $\delta$ Scuti stars where close frequencies have been reported.408 Interestingly.none of the stars fall in this gap.," Interestingly,none of the stars fall in this gap."409 Of course. a larger number of stars would need to be analysed to sce whether this gap remains or whether it is simply due to poor statistics.," Of course, a larger number of stars would need to be analysed to see whether this gap remains or whether it is simply due to poor statistics."410 Furthermore. some of the stars in Table 6.. such as BL CAL (?).. BY Cir (7). and 44 Tau (7).. are evolved.," Furthermore, some of the stars in Table \ref{tab:stars_with_pairs}, , such as BI CMi \citep{Breger2002b}, , BV Cir \citep*{Mantegazza2001} and 44 Tau \citep{Zima2007}, are evolved."411 Consequently. their. pulsation spectra are likely to contain acoustic. gravity (or gravito-inertial) ancl possibly mixed modes.," Consequently, their pulsation spectra are likely to contain acoustic, gravity (or gravito-inertial) and possibly mixed modes."412physical model is able to explain an array of observed properties of 5;—5.7 LAEs the Deep Survey (SNDS: Ouchietal.2008)). includiug spectra. morphology. apparent hnuuinositv function (LE). shape of the ultraviolet (UV)/ LF. and the distribution of equivalent width.,"physical model is able to explain an array of observed properties of $z\sim$ 5.7 LAEs the Deep Survey (SXDS; \citealt{Ouchi08}) ), including spectra, morphology, apparent luminosity function (LF), shape of the ultraviolet (UV) LF, and the distribution of equivalent width."413 The sclection inposed by the environment dependent radiative transter also introduces interesting new features in the clusterimg of LAEs (Zhengetal.2011.. hereafter Paper IT).," The selection imposed by the environment dependent radiative transfer also introduces interesting new features in the clustering of LAEs \citealt{Zheng11}, hereafter Paper II)."414 Iu the above radiative transfer model. while the uunuber of photons is couserved after they escape the ISM. the scatterings du the circumealactic aud interealactic media cause the enmüssou to spread spatially.," In the above radiative transfer model, while the number of photons is conserved after they escape the ISM, the scatterings in the circumgalactic and intergalactic media cause the emission to spread spatially."415 Therefore. one generic prediction of the model is an extended emission halo around a star-forming ealaxy.," Therefore, one generic prediction of the model is an extended emission halo around a star-forming galaxy."416 Observationallv. oulv a fraction of photons can be detected for an individual source. those included in the ceutral part of the extended cussion with lugh enough surface brightuess (tip of the icchere).," Observationally, only a fraction of photons can be detected for an individual source, those included in the central part of the extended emission with high enough surface brightness (tip of the iceberg)."417 The outskirts of the halo with low surface brightness is typically buried iu the sky. noise., The outskirts of the halo with low surface brightness is typically buried in the sky noise.418 Iu this paper. we show that it is possible to detect the bottom of the iceberg by stacking the narrowband images of a large number of sources to suppress the sky. noise.," In this paper, we show that it is possible to detect the bottom of the iceberg by stacking the narrowband images of a large number of sources to suppress the sky noise."419 We present the predictions of the exteuded emission in the stacked image from our radiative trausfer model and discuss what we can learn from dt., We present the predictions of the extended emission in the stacked image from our radiative transfer model and discuss what we can learn from it.420 Our radiative transfer modeling is performed for sources at i~5.7., Our radiative transfer modeling is performed for sources at $z\sim 5.7$.421 We study properties of surface rightuess profile from stacked images in Section 2., We study properties of surface brightness profile from stacked images in Section 2.422 Iu Section 3. we discuss the observational prospects.," In Section 3, we discuss the observational prospects."423 We sunuuarize our results in Section I., We summarize our results in Section 4.424" Throughout the paper. we adopt a spatially fiat ACDAL cosmiological model for our caleulatiouns. with a matter density parameter ©@,,=0.28 and a IIubble coustaut h=0.70 in units of LOOkustAIpeD"," Throughout the paper, we adopt a spatially flat $\Lambda$ CDM cosmological model for our calculations, with a matter density parameter $\Omega_m=0.28$ and a Hubble constant $h=0.70$ in units of $100\, \kms {\rm Mpc}^{-1}$."425 Distances are expressed in comoving units unless mentioned clearly otherwise., Distances are expressed in comoving units unless mentioned clearly otherwise.426 The radiative trauster calculation iu Paper I is performed in a simmlation box of 1007.1Mpe (comoving) on a side with the neutral hydrogen deusity. temperature. and peculiar velocity sampled with a 768? exid.," The radiative transfer calculation in Paper I is performed in a simulation box of $\hMpc$ (comoving) on a side with the neutral hydrogen density, temperature, and peculiar velocity sampled with a $^3$ grid."427 The cell size is therefore 130.25.tkpe (comoving). about the virial ciamoter of a Ls«10275.TAL. halo.," The cell size is therefore $\hkpc$ (comoving), about the virial diameter of a $1.8\times 10^{10}\hMsun$ halo."428" The star-forming reeion in a μοιτος] galaxy. where photos In our study originate. is only a few kpe (comoving) across (οιο,,Taniguehietal.2009)."," The star-forming region in a high-redshift galaxy, where photons in our study originate, is only a few kpc (comoving) across \citep[e.g.,][]{Taniguchi09}."429. So the initial Cluission is treated as a point source at the halo ceuter or the purpose of the radiative transfer calculation., So the initial emission is treated as a point source at the halo center for the purpose of the radiative transfer calculation.430" The size of the pixel for collecting photons is 5 ines finer. corresponding to 16:35.ως (comoving) or58"")."," The size of the pixel for collecting photons is 8 times finer, corresponding to $\hkpc$ (comoving) or."431 With the cell resolution. the gas distribution is uuifornmi inside the virial radius of small halos (below a few times LOMA TAL.) which would have some effect ou he surface brightuess profile.," With the cell resolution, the gas distribution is uniform inside the virial radius of small halos (below a few times $10^{10}\hMsun$ ), which would have some effect on the surface brightness profile."432 However. since photons are initially enuütted from a point source aud he dynamics of the iufall region around halos plavs a sjeuificaut role in determining the distribution of rotous (Paper ID. the resolution we use is sufficient or obtaining the eeueric features in the extended (nission.," However, since photons are initially emitted from a point source and the dynamics of the infall region around halos plays a significant role in determining the distribution of photons (Paper I), the resolution we use is sufficient for obtaining the generic features in the extended emission."433 We present a resolution test in 2.5. and the main results presented m this paper would remain valid with improved resolution.," We present a resolution test in 2.5, and the main results presented in this paper would remain valid with improved resolution."434 Our calculation does not address the effects of galactic wind aud dust. and we discuss these model wuneertaintics ii 2.l and 3.," Our calculation does not address the effects of galactic wind and dust, and we discuss these model uncertainties in 2.4 and 3."435 We start from the stacked image for sources residing iu halos of fixed mass. 1005tAL..," We start from the stacked image for sources residing in halos of fixed mass, $10^{11}\hMsun$."436 I our model. the ΗΕ huuinositv. which is the the total amount of ciission from the reprocessed. ionizing photous. is tightly correlated with the Lalo mass. therefore this stacking is basically for sources at fixed intrinsic bpuuunositv or UV Iuniünositv.," In our model, the intrinsic luminosity, which is the the total amount of emission from the reprocessed ionizing photons, is tightly correlated with the halo mass, therefore this stacking is basically for sources at fixed intrinsic luminosity or UV luminosity."437 Our radiative transfer model produces a threc-dimensional array. recording the spectra as a function of spatial position ou the sky.," Our radiative transfer model produces a three-dimensional array, recording the spectra as a function of spatial position on the sky."438" We construct the narrowband image from this array, with a filter width similar to that in the :~5.7 SNDS (see Paper D."," We construct the narrowband image from this array, with a filter width similar to that in the $z\sim 5.7$ SXDS (see Paper I)."439 Our simulation box has about the same arca as SNDS with a τομ depth three times larecr., Our simulation box has about the same area as SXDS with a redshift depth three times larger.440 So we are able to construct narrowband nuages for three SNDS-like fields., So we are able to construct narrowband images for three SXDS-like fields.441 Each nuage corresponds to au ideal case with perfect continui and sky. subtraction., Each image corresponds to an ideal case with perfect continuum and sky subtraction.442 Examples of amages of individual sources cau be found in Paper I (Fie.tl and Fie.5)., Examples of images of individual sources can be found in Paper I (Fig.4 and Fig.5).443 We stack all the source nuages together as would be done with the narrowhan¢l observation., We stack all the source images together as would be done with the narrowband observation.444 For each source. the tage includes the center and surrounding pixels (up to a radius of ~ 10h ?Mpe).," For each source, the image includes the center and surrounding pixels (up to a radius of $\sim$ $\hMpc$ )."445 The center pixel is chosen to be the one that coutaims the halo ceuter., The center pixel is chosen to be the one that contains the halo center.446 Ta other words. the ceuter corresponds to that in the UV baud.," In other words, the center corresponds to that in the UV band."447 It is evident that the surrounding pixels cau iuclude photons from other neighboring sources., It is evident that the surrounding pixels can include photons from other neighboring sources.448 For all the sources iu a narrow bin, For all the sources in a narrow bin449Accurately determined ages. metallicities and a-clement abundances of e@lobular cluster (CC). svstenis across the entire range of galaxy types can provide strong constraints for galaxy formation models.,"Accurately determined ages, metallicities and $\alpha$ -element abundances of globular cluster (GC) systems across the entire range of galaxy types can provide strong constraints for galaxy formation models."450 One example of such a constraint is the recently observed trend of decreasing afe ratios with increasing metallicity for extra-galactic GC systems (Puzia 2005: Pierce 2005a.b).," One example of such a constraint is the recently observed trend of decreasing $\alpha$ /Fe ratios with increasing metallicity for extra-galactic GC systems (Puzia 2005; Pierce 2005a,b)."451" ""his trend. restricts the allowable chemical enrichment histories. relative contribution of Tvpe la vs Type Hb supernova. and star formation timescales [or galasies well beyond the Local Group. where there is Little possibility of directly resolving stellar populations."," This trend restricts the allowable chemical enrichment histories, relative contribution of Type Ia vs Type II supernova, and star formation timescales for galaxies well beyond the Local Group, where there is little possibility of directly resolving stellar populations."452 To accurately measure ages. metallicitics ancl abundance ratios with Lick indices [rom low-resolution spectra requires a minimum S/N of ~30. which corresponds to an error of £0.34 ((Cardiel 2003).," To accurately measure ages, metallicities and abundance ratios with Lick indices from low-resolution spectra requires a minimum S/N of $\sim$ 30, which corresponds to an $\beta$ error of $\pm$ (Cardiel 2003)."453 With an integration. time of —S hours on an S-metre class telescope it is possible to obtain multi-object spectra to this depth for the brightest GCs of a rich GC svstem for galaxies within 20 Alpe of the Milky Way., With an integration time of $\sim$ 8 hours on an 8-metre class telescope it is possible to obtain multi-object spectra to this depth for the brightest GCs of a rich GC system for galaxies within $\sim$ 20 Mpc of the Milky Way.454 A major aim of most moderate to high S/N GC spectroscopy has been to measure ages and hence infer when GC formation occurred., A major aim of most moderate to high S/N GC spectroscopy has been to measure ages and hence infer when GC formation occurred.455 Spectroscopic follow-up. is a complimentary approach to recent. photometric results., Spectroscopic follow-up is a complimentary approach to recent photometric results.456 Rhode. Zepl Santos (2005) show that the mass-normalised number of blue GC's increases with host galaxy mass.," Rhode, Zepf Santos (2005) show that the mass-normalised number of blue GCs increases with host galaxy mass."457 This sugeests that the formation of blue CC's is allected by the mass of the host halo., This suggests that the formation of blue GCs is affected by the mass of the host halo.458 Phe observed. “blue tilt” correlation, The observed “blue tilt” correlation459VCC galaxy) and at least z200000 times fainter in terms of total radio power. despite the similar stellar mass.,"VCC galaxy) and at least $\gtrsim 200000$ times fainter in terms of total radio power, despite the similar stellar mass."460 This result emphasizes the probabilistic nature of the radio-optical bivariate law and that the optical luminosity of a given galaxy is not a good predictor of its level of radio emission., This result emphasizes the probabilistic nature of the radio-optical bivariate law and that the optical luminosity of a given galaxy is not a good predictor of its level of radio emission.461 From the analysis of the data-set ofHST images. Cotéetal.(2006) found that a large fraction of VCC early-type galaxies is nucleated. with a frequency of 66 - 82%.," From the analysis of the data-set of images, \citet{cote06} found that a large fraction of VCC early-type galaxies is nucleated, with a frequency of 66 - 82."462. Core galaxies do not follow this general rule. since they lack resolved stellar nuclei but. conversely. they often show unresolved optical nuclear sources (defined as nucleation class ID.," Core galaxies do not follow this general rule, since they lack resolved stellar nuclei but, conversely, they often show unresolved optical nuclear sources (defined as nucleation class II)."463 The origin of the nuclei in this class of galaxies. many of them associated with bright radio-sources. must be ascribed to the active nucleus and most likely they represent the synchrotron emission from the basis of their radio jets (Chiabergeetal.1999:Balmaverde&Capetti2006:Capettietal. 2007).," The origin of the nuclei in this class of galaxies, many of them associated with bright radio-sources, must be ascribed to the active nucleus and most likely they represent the synchrotron emission from the basis of their radio jets \citep{chiaberge:ccc,balmaverde06b,cccpol}."464 We examine the possible presence of a link between nucleation and radio emission., We examine the possible presence of a link between nucleation and radio emission.465 Leaving aside the core galaxies. we are left with only five galaxies with a radio detection and a Sérrsic profile.," Leaving aside the core galaxies, we are left with only five galaxies with a radio detection and a Sérrsic profile."466 There are two clear nuclei (classes Ia and Ib). two uncertain nuclei (class le and Id). and a dusty galaxy (VCCI030) that cannot be classified from the point of view of nucleation (class 0).," There are two clear nuclei (classes Ia and Ib), two uncertain nuclei (class Ic and Id), and a dusty galaxy (VCC1030) that cannot be classified from the point of view of nucleation (class 0)."467 In the whole sample of 100 VCC the breakdown in terms of nucleation is 62:15:12:6 in the classes La-b:le-d:IL:0 .., In the whole sample of 100 VCC the breakdown in terms of nucleation is 62:15:12:6 in the classes Ia-b:Ic-d:II:0 .468It is well known since the 80's that the spectra of low-mass binartes (LMXBs) hosting a neutron star (NS) can be described up to about 30 keV by a two-component model representing the contribution from different emitting regions of the system.,It is well known since the 80's that the spectra of low-mass binaries (LMXBs) hosting a neutron star (NS) can be described up to about 30 keV by a two-component model representing the contribution from different emitting regions of the system.469 However. the interpretation of the spectra is not unique às demonstrated using the variety of different models used across the years.," However, the interpretation of the spectra is not unique as demonstrated using the variety of different models used across the years."470 Before the aand eera. two concurring models were classically used to described X-ray emission in LMXBs.," Before the and era, two concurring models were classically used to described X-ray emission in LMXBs."471" In the so-called ""eastern model"" (Mitsudaetal.1984:Mitsuda1989) the spectra were fitted by the sum of a soft blackbody (BB) emission (actually modeled by a multi-colour disk BB spectrum) attributed to the accretion disk. plus a hotter simple or Comptonized BB claimed to originate close to the NS surface."," In the so-called “eastern model” \citep{mitsuda84, mitsuda89} the spectra were fitted by the sum of a soft blackbody (BB) emission (actually modeled by a multi-colour disk BB spectrum) attributed to the accretion disk, plus a hotter simple or Comptonized BB claimed to originate close to the NS surface."472" On the other hand. in the “western model"" interpretation (Whiteetal.1986;Whiteetal. 1988).. the direct BB component was attributed to the NS surface. while an unsaturated Comptonization spectrum was thought to originate from a hot corona above the inner accretion disk. which supplies most of the soft seed photons for Comptonization."," On the other hand, in the “western model” interpretation \citep{white86, white88}, the direct BB component was attributed to the NS surface, while an unsaturated Comptonization spectrum was thought to originate from a hot corona above the inner accretion disk, which supplies most of the soft seed photons for Comptonization."473 In fact. even after the advent of aandRXTE.. the persistent emission of NS LMXBs was described by the sum of a BB component plus a thermal Comptonization (TC) spectrum. usually described by the mmodel (Titarchuk1994:Hua&Titarchuk1995).," In fact, even after the advent of and, the persistent emission of NS LMXBs was described by the sum of a BB component plus a thermal Comptonization (TC) spectrum, usually described by the model \citep{t94, ht95}."474. Despite the significant improvement in our knowledge of the source spectral properties by means of the broad-band observations. the BB+TC model resulted and subjected to a dichotomy.," Despite the significant improvement in our knowledge of the source spectral properties by means of the broad-band observations, the BB+TC model resulted and subjected to a dichotomy."475" Indeed. both of the cases where the temperature of the direct BB spectrum ATi, 1s lower (e.g..DiSalvoetal.2000a.b.2001:al.2004;Paiziset2005) or higher (e.g..Paizisetal.2005: than that of the thermally Comptonized seed photons. &T.. provide in general equally acceptable good fits."," Indeed, both of the cases where the temperature of the direct BB spectrum $\ktbb$ is lower \citep[e.g.,][]{ds00a, ds00b, ds01, oosterbroek01, gd02, lavagetto04, paizis05} or higher \citep[e.g.,][hereafter F08]{paizis05, farinelli07, farinelli08} than that of the thermally Comptonized seed photons, $\kts$, provide in general equally acceptable good fits."476" The consequences of these results were the interpretation of the BB emission as due either to the accretion disk VT.) or to the NS surface (42),71).", The consequences of these results were the interpretation of the BB emission as due either to the accretion disk $\ktbb < \kts$ ) or to the NS surface $\ktbb > \kts$ ).477 Moreover. in addition to the persistent X-ray emission. citep[e.g..]||Kds0Ob.ds02. (D'Amicoetal.2001:DiSalvo2006) and later also citep[][hereafter.POG|paizisO6— allowed the possibility to discover in bright NS LMXBs a transient powerlaw (PL) X-ray emission above 30 keV. Motivated by the need to put some order and give an unified scenario in the different NS systems spectral states. Paizis et al. (," Moreover, in addition to the persistent X-ray emission, \\citep[e.g.,][]{ds00b,ds02} \citep{damico01, ds06} and later also \\citep[][hereafter P06]{paizis06} allowed the possibility to discover in bright NS LMXBs a transient powerlaw (PL) X-ray emission above 30 keV. Motivated by the need to put some order and give an unified scenario in the different NS systems spectral states, Paizis et al. ("4782006. hereafter PO6) performed a systematic observational campaign with the ((20-200 keV) monitor onborad/NTEGRAL.,"2006, hereafter P06) performed a systematic observational campaign with the (20-200 keV) monitor onborad."479. Using long-term average spectra and including former rresults on GX 354-0 (Falangaetal.2006).. PO6 classified NS LMXBs into four main states: thefard/PL..low/hard.. and soft.," Using long-term average spectra and including former results on GX 354–0 \citep{falanga06}, P06 classified NS LMXBs into four main states: the, and ."480. The high-energy (> 20 keV) spectra in different sources were interpreted by PO6 as the result of the interplay between thermal and bulk Comptonization processes whose relative efficiency is ultimately dictated by the mass accretion rate., The high-energy $>$ 20 keV) spectra in different sources were interpreted by P06 as the result of the interplay between thermal and bulk Comptonization processes whose relative efficiency is ultimately dictated by the mass accretion rate.481 At high energies (where the direct BB component ts negligible). the state spectra can be fitted with a simple PL component: the spectra by a TC spectrum of soft CS1 keV) BB-like photons off an electron population with KT.20230 keV and zyS3: the state spectra by TC spectrum with AZT.~305 keV and τηZ5 plus a PL component with photon index D—23 the state spectra by a TC component similar to the state but without the high-energy X-ray tail.," At high energies (where the direct BB component is negligible), the state spectra can be fitted with a simple PL component; the spectra by a TC spectrum of soft $\la 1$ keV) BB-like photons off an electron population with $\kte \sim 20-30$ keV and $\tau_0 \la 3$; the state spectra by TC spectrum with $\kte \sim 3-5$ keV and $\tau_0\ga 5$ plus a PL component with photon index $\Gamma \sim 2-3$; the state spectra by a TC component similar to the state but without the high-energy X-ray tail."482 From the observational point ofview. the quantities directly measurable in the data are the cut-off energy £L. of the dominating TC bump and the spectral slope. parametrized through the energy index α (2L 1).," From the observational point ofview, the quantities directly measurable in the data are the cut-off energy $E_c$ of the dominating TC bump and the spectral slope, parametrized through the energy index $\alpha$ $\Gamma -1$ )."483 For pure TC spectra. α is tightly correlated with the plasma temperature &7;. and optical depth 7; (Sunyaev&Titarchuk1980:TitarehukLyubarskij TL95).. while in the presence of a converging flow (bulk motion) the shape of the velocity field also determines the emerging spectral slope," For pure TC spectra, $\alpha$ is tightly correlated with the plasma temperature $\kte$ and optical depth $\tau_0$ \citep[][hereafter TL95]{st80, tl95}, , while in the presence of a converging flow (bulk motion), the shape of the velocity field also determines the emerging spectral slope"484in Figure 1 that model predictions for the line agree with those deduced from observations.,in Figure \ref{civew} that model predictions for the line agree with those deduced from observations.485" Conventional wisdom has been that the magnitude of line EW decreases in tandem with the equivalent width of as shown by Brinchmann,Pettini&Charlot(2008).", Conventional wisdom has been that the magnitude of line EW decreases in tandem with the equivalent width of as shown by \citet{brinchmann1}.486. This is because it is assumed that at lower metallicity there are fewer WR stars with shorter lifetimes to contribute to the spectral features., This is because it is assumed that at lower metallicity there are fewer WR stars with shorter lifetimes to contribute to the spectral features.487" However, as shown in Eldridge&Stanway(2009),, the inclusion of binaries make this predicted relation less clear-cut."," However, as shown in \citet{ES09}, the inclusion of binaries make this predicted relation less clear-cut."488" In Figure 2 we show how the EW, which does decrease with metallicity, relates to the line strength for our different model populations."," In Figure \ref{civheii} we show how the EW, which does decrease with metallicity, relates to the line strength for our different model populations."489" When only single star populations are considered, the strength of the line is largely independent of line strength, and, surprisingly, peaks at around Z=0.008 rather than at the highest (Solar and super-Solar) metallicity."," When only single star populations are considered, the strength of the line is largely independent of line strength, and, surprisingly, peaks at around $Z=0.008$ rather than at the highest (Solar and super-Solar) metallicity."490 This is because absorption lines in B star spectra decrease the apparent strength of at higher metallicity., This is because absorption lines in B star spectra decrease the apparent strength of at higher metallicity.491 Stellar populations including binaries reach higher EWs than the single star populations because of their greater number of WR stars (produced due to mass-transfer events in the binary systems)., Stellar populations including binaries reach higher EWs than the single star populations because of their greater number of WR stars (produced due to mass-transfer events in the binary systems).492" The highest EWs are only possible, however, when the effect of QHE is included in a binary population."," The highest EWs are only possible, however, when the effect of QHE is included in a binary population."493 The production of long lived hydrogen burning stars that are observed as WR stars boosts the line strength at the lowest metallicities., The production of long lived hydrogen burning stars that are observed as WR stars boosts the line strength at the lowest metallicities.494 The same trends are evident in Figure 3.., The same trends are evident in Figure \ref{modelew}.495 The highest EWs (i.e. strongest line emission) arise at later ages in QHE models than for the single star populations., The highest EWs (i.e. strongest line emission) arise at later ages in QHE models than for the single star populations.496 This is because the additional WR stars produced from binary evolution and QHE are typically from lower mass stars that would not normally become WR stars and take of order 107 years to evolve to this state., This is because the additional WR stars produced from binary evolution and QHE are typically from lower mass stars that would not normally become WR stars and take of order $^7$ years to evolve to this state.497 Also in Figure 3 we show how both and lines vary assuming an instantaneous burst of star formation., Also in Figure \ref{modelew} we show how both and lines vary assuming an instantaneous burst of star formation.498" This model may be more appropriate at the highest redshifts (z> 5) where the stellar populations appear to be short-lived, dramatic events with little fuel available for ongoing star formation (seeDaviesetal.2010).."," This model may be more appropriate at the highest redshifts $z>5$ ) where the stellar populations appear to be short-lived, dramatic events with little fuel available for ongoing star formation \citep[see][]{2010MNRAS.408L..31D}."499" In this instantaneous star formation case, larger EWs are possible for than in the constant star formation model."," In this instantaneous star formation case, larger EWs are possible for than in the constant star formation model."500 This is only because there are no younger stars contributing to the continuum and reducing the relative, This is only because there are no younger stars contributing to the continuum and reducing the relative50102 in the WTmodet.,0–2 in the WT.502. Source lighteurves and spectra were extracted with (v. 2.3)., Source lightcurves and spectra were extracted with (v. 2.3).503 We used a region of 40 40 pixels to extract source events from the WT data., We used a region of 40 $\times$ 40 pixels to extract source events from the WT data.504 A region of similar shape and size. positioned. on an empty part well outside the point spread. function of the source. was used for the background.," A region of similar shape and size, positioned on an empty part well outside the point spread function of the source, was used for the background."505 For the PC mode observations we used a circular region with a LO pixel radius to extract source photons., For the PC mode observations we used a circular region with a 10 pixel radius to extract source photons.506 An annulus with an inner (outer) radius of 75 (100) pixels. centred on the source position. served as the xckeround reference.," An annulus with an inner (outer) radius of 75 (100) pixels, centred on the source position, served as the background reference."507 We generated exposure maps with the ask and ancillary response files (ARE) were created withΧΗΜΙΚΑ., We generated exposure maps with the task and ancillary response files (ARF) were created with.508 The response matrix files (v. 11: UME) were obtained from the CALDD database., The response matrix files (v. 11; RMF) were obtained from the CALDB database.509 The spectra were grouped. using the FPOOL o contain bins with à minimum number of 20 photons., The spectra were grouped using the FTOOL to contain bins with a minimum number of 20 photons.510 We itted the spectra with in the 0.510 keV range., We fitted the spectra with in the 0.5–10 keV range.511 The C data of observation 311603000. was alfected by pile-up., The PC data of observation 311603000 was affected by pile-up.512 Following the aanalvsisthreads?.. we attempted to correct. for. the consequent effect on spectral shape and loss in source Hux bv using an annulus with an inner (outer) radius of 4 (10) pixels as the source extraction region.," Following the analysis, we attempted to correct for the consequent effect on spectral shape and loss in source flux by using an annulus with an inner (outer) radius of 4 (10) pixels as the source extraction region."513 We performed time-resolved spectroscopy of the fading tail of the X-ray burst using the XIXE observations of May 14 (both WE and PC mode data: LD 311603000)., We performed time-resolved spectroscopy of the fading tail of the X-ray burst using the XRT observations of May 14 (both WT and PC mode data; ID 311603000).514" ""Ehe first set of WE data was divided into 4 intervals of 20 s. each with a total of ~2000 counts per interval."," The first set of WT data was divided into 4 intervals of 20 s, each with a total of $\sim 2000$ counts per interval."515 We do not include the second. set o£. WE data in the analysis. since this Ss exposure collected only Lt source photons and the consecutive PC data provide better statistics.," We do not include the second set of WT data in the analysis, since this 8 s exposure collected only 14 source photons and the consecutive PC data provide better statistics."516 The ~2 ks PC mode observation consists of a single data segment. which was split into two intervals of similar length. containing ~500 counts cach after pile-up correction.," The $\sim 2$ ks PC mode observation consists of a single data segment, which was split into two intervals of similar length, containing $\sim 500$ counts each after pile-up correction."517 We searched. the —90 s lone WE observation of the X-rav burst for periodicities by means of Fast. Fourier ‘Transforms (ELITS) and applying the method described in Israel&Stella(1996)., We searched the $\sim90$ s long WT observation of the X-ray burst for periodicities by means of Fast Fourier Transforms (FFTs) and applying the method described in \citet{israel96}.518.. The analysed period range spans from ~3.5 ms up to 100 s (~262 0000 total period trials) and the Nyquist frequency is 283 Lz., The analysed period range spans from $\sim$ 3.5 ms up to 100 s $\sim$ 000 total period trials) and the Nyquist frequency is $\sim283$ Hz.519 No significant peaks were found., No significant peaks were found.520 Meaningful upper limits (< 100 per cent pulsed fraction) are obtained only for periods shorter than 5 s and range between 15 and ~20 per cent., Meaningful upper limits $<$ 100 per cent pulsed fraction) are obtained only for periods shorter than 5 s and range between $\sim$ 15 and $\sim$ 20 per cent.521 lo characterize the persistent. emission. we used. the data obtained from Alay 15. onwards (LDs 311603001 311603015).," To characterize the persistent emission, we used the data obtained from May 15 onwards (IDs 311603001– 311603015)."522 “Phe upper left. panel of Fig., The upper left panel of Fig.523 3. displays a summed. X-rav image of all PC mode observations of the post-burst epoch., \ref{fig:images} displays a summed X-ray image of all PC mode observations of the post-burst epoch.524 We obtained. another ΝΤ pointing in late July 2009 (LD 31446001) to investigate the state of the svstem more than a vear after the X-ray burst., We obtained another /XRT pointing in late July 2009 (ID 31446001) to investigate the state of the system more than a year after the X-ray burst.525 During that observation. iis detected at a count rate of ~0.11countss +.," During that observation, is detected at a count rate of $\sim 0.11~\cnts$ ."526 This is the same level as detected in 2008 MayAugust (see. also ‘Table 2)). which indicates that the svstem is still actively accreting (see Sections 3 and The UVO'T data of wwere obtained using a variety of filters. but. the source could only be detected in the broadband white filter(ML. ~1500.—8500 A)).," This is the same level as detected in 2008 May–August (see also Table \ref{tab:persistent}) ), which indicates that the system is still actively accreting (see Sections 3 and The UVOT data of were obtained using a variety of filters, but the source could only be detected in the broadband white filter, $\sim 1500-8500$ )."527 Phe upper right panel of Fig., The upper right panel of Fig.528 3 shows an UVO'T VW 7/-band image of the field around aand Fable 1. gives an overview of the UVOT observations obtained with this filter., \ref{fig:images} shows an UVOT $WH$ -band image of the field around and Table \ref{tab:obs} gives an overview of the UVOT observations obtained with this filter.529 Avoiding a nearby object (see Fig. 3)).," Avoiding a nearby object (see Fig. \ref{fig:images}) ),"530 we used a circular region with a radius of 2 aresee to extract source photons. and a source-free. region with a radius of 10 aresee as a background reference.," we used a circular region with a radius of 2 arcsec to extract source photons, and a source-free region with a radius of 10 arcsec as a background reference."531 Magnitudes were extracted using the tool uvOrsource.. taking into account aperture COLLCCLLONS.," Magnitudes were extracted using the tool , taking into account aperture corrections."532 During the X-ray burst decay. there were three intervals of UVOT observations using the V Z-filter.," During the X-ray burst decay, there were three intervals of UVOT observations using the $WH$ -filter."533 The bottom panel of Fig., The bottom panel of Fig.534 4. shows the evolution. of the magnitude during these intervals: there is a clear decay. visible (two magnitudes within two hours) simultaneous with the observed. fading in N-ravs.," \ref{fig:burst_fit} shows the evolution of the magnitude during these intervals; there is a clear decay visible (two magnitudes within two hours), simultaneous with the observed fading in X-rays."535 This provides strong evidence that the fading UVOT. source. represents the optical counterpart of the system. and allows for a sub-arcesecond localization of the burster (Israeletal.2008).., This provides strong evidence that the fading UVOT source represents the optical counterpart of the system and allows for a sub-arcsecond localization of the burster \citep{israel08}.536 All optical photometric observations discussed inthis sectionwere reduced using standard routines in, All optical photometric observations discussed inthis sectionwere reduced using standard routines in537The spectral characteristics are summarized in Figures 12-- 15.. Figures 12. and 13. compare the calculated. (solid Lines) and observed. (filled-cireles) phase-averagecd ancl phase-resolved. spectra. respectively.,"The spectral characteristics are summarized in Figures \ref{spec_3dis}- \ref{Gamma_Phi}.. Figures \ref{spec_3dis}538 and \ref{spec_pr} compare the calculated (solid lines) and observed (filled-circles) phase-averaged and phase-resolved spectra, respectively."539 By fitting calculated spectra with power law plus exponential eut-olf form. Figures 14 and 15 show the cut-olf energy. anc the photon index. respectively. as a function of the pulse phase.," By fitting calculated spectra with power law plus exponential cut-off form, Figures \ref{Ecut_Phi} and \ref{Gamma_Phi} show the cut-off energy and the photon index, respectively, as a function of the pulse phase."540 As we can see from Figure l4.. the present model can explain the observed cut-oll energy as a function of the pulse hase.," As we can see from Figure \ref{Ecut_Phi}, the present model can explain the observed cut-off energy as a function of the pulse phase."541 This can be explained as the cllect of the distribution olthe f. which decides the energies of the photons in the gap ον determining the value of the accelerating electric field.," This can be explained as the effect of the distribution of the $f$, which decides the energies of the photons in the gap by determining the value of the accelerating electric field."542 And the eut-olf energy of the spectrum is mainly determined ow the emission from the main acceleration region., And the cut-off energy of the spectrum is mainly determined by the emission from the main acceleration region.543 From Figure 5.. in the observable region from around 07 to 260° here are three peaks of f. which correspond to the three »eaks in Figure I4...," From Figure \ref{rp_phi}, in the observable region from around $^{\circ}$ to $^{\circ}$, there are three peaks of $f$, which correspond to the three peaks in Figure \ref{Ecut_Phi}."544 And the pulse phase of the middle peak in Figure 1H. is consistent with that of the third peak in the ight curve made by the distribution of f., And the pulse phase of the middle peak in Figure \ref{Ecut_Phi} is consistent with that of the third peak in the light curve made by the distribution of $f$.545 These two facts indicate that the distribution of f makes the caleulated cut-olf energies of the phase-resolved spectra consistent with the observed one., These two facts indicate that the distribution of $f$ makes the calculated cut-off energies of the phase-resolved spectra consistent with the observed one.546 Because the photon index is much more sensitive to the shape of the spectrum than the cut-olf energy. the Figure 15 is not so consistent with the observation. where the photon indices between pulse phase of 0.3 to 0.5 are dilferent. with the observed ones.," Because the photon index is much more sensitive to the shape of the spectrum than the cut-off energy, the Figure \ref{Gamma_Phi} is not so consistent with the observation, where the photon indices between pulse phase of 0.3 to 0.5 are different with the observed ones."547 As the spectrum of 0.315<c«0.324 in Figure 1:3 shows. the present model predicts a larger photon index at the pulse phase of 0.3-0.4 than the observations.," As the spectrum of $0.315<\psi<0.324$ in Figure \ref{spec_pr} shows, the present model predicts a larger photon index at the pulse phase of 0.3-0.4 than the observations."548 For the pulse phase-ü.4 to 0.5. as we can see [rom the energy dependent light curves (Figure 10)). the caleulatecl photons are more than those of the observation.," For the pulse phase=0.4 to 0.5, as we can see from the energy dependent light curves (Figure \ref{edlc_3dis}) ), the calculated photons are more than those of the observation."549 Consequently. the calculated: curvature radiation from the main acceleration region is too strong. leading the caleulated spectrum is hard with a photon index 1.," Consequently, the calculated curvature radiation from the main acceleration region is too strong, leading the calculated spectrum is hard with a photon index $\sim 1$."550 For the other pulse phases. as shown by the Figure. 13.. the πας and the shape of the spectra are close to the observed. ones. and the photon indices of these pulse phases can also explain the observed Ones.," For the other pulse phases, as shown by the Figure \ref{spec_pr}, the flux and the shape of the spectra are close to the observed ones, and the photon indices of these pulse phases can also explain the observed ones."551 In this paper. a three dimensional outer gap model is built to explain the energy dependent light curves of the Vela pulsar observed. by Fermi LAT (Abdo et ab.," In this paper, a three dimensional outer gap model is built to explain the energy dependent light curves of the Vela pulsar observed by $Fermi$ LAT (Abdo et al.,"552 2010b)., 2010b).553 In the present. two-laver model. the acceleration ancl emission region in the gap consist two parts. that is. the main acceleration region and the screening region.," In the present two-layer model, the acceleration and emission region in the gap consist two parts, that is, the main acceleration region and the screening region."554 In the main acceleration region. the charge density is much lower than the Goldreich-Julian charge density anc a strong electric Ποιά accelerates the particles to emit GeV photons via the curvature radiation process.," In the main acceleration region, the charge density is much lower than the Goldreich-Julian charge density and a strong electric field accelerates the particles to emit GeV photons via the curvature radiation process."555 In the screening region. the charge density is higher than the Goldreich-Julian. charge density to screen. out the accelerating electric. field.," In the screening region, the charge density is higher than the Goldreich-Julian charge density to screen out the accelerating electric field."556 We extend our. two-dimensional two-laver model in Wang et al. (, We extend our two-dimensional two-layer model in Wang et al. (557"2010) into a three-climensional one with the azimuthal structure of the fractional gap thickness Cf). ratio of the thicknesses of the primary ancl whole region (, /h3). and 1e number density in the main acceleration region (1gy).","2010) into a three-dimensional one with the azimuthal structure of the fractional gap thickness $f$ ), ratio of the thicknesses of the primary and whole region $h_1/h_2$ ), and the number density in the main acceleration region $(1-g_1)$."558 Using constant Log. fy/h» and f. although the caleulated ight curves can qualitatively explain the observations of 16 Vela pulsar. the energy dependent light curves can not jwe the third. peak.," Using constant $1-g_1$, $h_1/h_2$ and $f$, although the calculated light curves can qualitatively explain the observations of the Vela pulsar, the energy dependent light curves can not have the third peak."559 Therefore. we considered the possible vimuthal cistributions of these three parameters.," Therefore, we considered the possible azimuthal distributions of these three parameters."560 We found ju the distributions of 1σι and f make third-peak-ike structure in the bridge region of light curve of above rm GeV. while the distribution of fyfhe makes a bump in 10 bridge region of the light curves below 1 GeV. We also showed that the present model can reproduce the istribution of the eut-oll energy for cach rotation phase.," We found that the distributions of $1-g_1$ and $f$ make third-peak-like structure in the bridge region of light curve of above 1 GeV, while the distribution of $h_1/h_2$ makes a bump in the bridge region of the light curves below 1 GeV. We also showed that the present model can reproduce the distribution of the cut-off energy for each rotation phase."561significantly younger than in the globular clusters. and we therefore assume <Rec;PES0.2—0.4.,"significantly younger than in the globular clusters, and we therefore assume $<R_{GC/F}>\sim0.2-0.4$."562 As the fraction of globular clusters 1s small in the late-type galaxy part of the sample. Fijcc~0.1—0.3%.," As the fraction of globular clusters is small in the late-type galaxy part of the sample, $F_{M,GC}\sim0.1-0.3$."563". With these assumption we get a result of a,«75—450.", With these assumption we get a result of $\eta_{co}<75-450$.564 For the sample of early-type galaxies. the ages of the stars are similar to the ages of the globular clusters and therefore <RcGc;j;>~1.," For the sample of early-type galaxies, the ages of the stars are similar to the ages of the globular clusters and therefore $<R_{GC/F}>\sim1$."565 Furthermore. the globular cluster mass fraction is higher. and we assume an average value of 0.3—0.6%.," Furthermore, the globular cluster mass fraction is higher, and we assume an average value of $0.3-0.6$."566". This leads to à more constraining limit of 77,,,<37—73.", This leads to a more constraining limit of $\eta_{co}<37-73$.567 We have derived upper limits on the enhancement per unit stellar mass Πω of SNIae in. globular clusters., We have derived upper limits on the enhancement per unit stellar mass $\eta_{co}$ of SNIae in globular clusters.568 The limits are above the favoured theoretical expectations by almost an order of magnitude. but are well below the observed enhancement of LMXBs. Πενν>100.," The limits are above the favoured theoretical expectations by almost an order of magnitude, but are well below the observed enhancement of LMXBs, $\eta_{LMXB}>100$."569 We have discussed the effect of the decline of the SNIa DTD on the observations., We have discussed the effect of the decline of the SNIa DTD on the observations.570" Due to the older age of globular clusters compared to the field population in late type galaxies. this decreases the value of the parameter 77 (which can be seen as the average enhancement over the whole population of galaxies), which is usually used in the literature (see equation 3)."," Due to the older age of globular clusters compared to the field population in late type galaxies, this decreases the value of the parameter $\eta$ (which can be seen as the average enhancement over the whole population of galaxies), which is usually used in the literature (see equation \ref{eq:rate}) )."571 For this reason we find that the sample of SNlae in early-type galaxies is more constraming that the full sample. despite containing only <1/3 of the supernovae.," For this reason we find that the sample of SNIae in early-type galaxies is more constraining that the full sample, despite containing only $\lesssim$ 1/3 of the supernovae."572" As this effect of the DTD will be sample-dependent we believe that it is more appropriate to use 7,,,. which is the direct measure of the enhancement factor."," As this effect of the DTD will be sample-dependent we believe that it is more appropriate to use $\eta_{co}$, which is the direct measure of the enhancement factor."573" However. we note that it is possible that also 7, 1s time-dependent. as early and late SNIae progeritors are likely to have different evolutionary histories. and since the structure of globular clusters evolve."," However, we note that it is possible that also $\eta_{co}$ is time-dependent, as early and late SNIae progenitors are likely to have different evolutionary histories, and since the structure of globular clusters evolve."574 In this pilot study we have only included supernovae which had HST images available. and for which we were able to identify the position with high accuracy.," In this pilot study we have only included supernovae which had HST images available, and for which we were able to identify the position with high accuracy."575 This sample constitutes only a fraction of the total number of SNlae within distances at which it is possible to observe globular clusters (~100 Mpe)., This sample constitutes only a fraction of the total number of SNIae within distances at which it is possible to observe globular clusters $\sim$ 100 Mpc).576 As no globular clusters were detected at the position of the supernovae. and as we have managed to probe enough SNlae positions that we are starting to constrain theory. itis clearly interesting to extend the sample.," As no globular clusters were detected at the position of the supernovae, and as we have managed to probe enough SNIae positions that we are starting to constrain theory, it is clearly interesting to extend the sample."577 To reach the values currently favoured by theory. it will be necessary to expand the sample by a factor of few.," To reach the values currently favoured by theory, it will be necessary to expand the sample by a factor of few."578 There are several ways to proceed., There are several ways to proceed.579 As new supernovae are discovered continuously. and more galaxies are being observed with HST. it is possible to simply wait and let the sample expand.," As new supernovae are discovered continuously, and more galaxies are being observed with HST, it is possible to simply wait and let the sample expand."580 However. it is clear that from the current sample that only a few SNIae will be added every year. and it will therefore take decades before we can reach the goal of a factor of few more supernovae.," However, it is clear that from the current sample that only a few SNIae will be added every year, and it will therefore take decades before we can reach the goal of a factor of few more supernovae."581 Another option is to use archival data from other telescopes., Another option is to use archival data from other telescopes.582 As none of these are as sensitive to globular clusters as HST. it will only be possible to probe more nearby SNlae. but the advantage is that many more galaxies will be covered by useful observations.," As none of these are as sensitive to globular clusters as HST, it will only be possible to probe more nearby SNIae, but the advantage is that many more galaxies will be covered by useful observations."583 Such a study will be tedious. as data from many different telescopes will have to be processed. and it is unlikely that a factor of few can be reached.," Such a study will be tedious, as data from many different telescopes will have to be processed, and it is unlikely that a factor of few can be reached."584 A third option ts to make a dedicated obsertional program to observe the positions of known SNIae., A third option is to make a dedicated obsertional program to observe the positions of known SNIae.585 Enough are known that it will be possible to reach the goal of increasing the sample by a factor of few., Enough are known that it will be possible to reach the goal of increasing the sample by a factor of few.586 The most effective way of reaching it would be to make a joint program with a medium-sized ground-based telescope for the nearest SNIae. and HST for the more distant ones.," The most effective way of reaching it would be to make a joint program with a medium-sized ground-based telescope for the nearest SNIae, and HST for the more distant ones."587 Our experience from this pilot project tells us that it is very difficult to obtain useful limits for sources well inside the galaxies as the background there is bright and inhomogenous., Our experience from this pilot project tells us that it is very difficult to obtain useful limits for sources well inside the galaxies as the background there is bright and inhomogenous.588 While the number of SNlae will be lower if one excludes sources in the inner parts of the galaxies. it will be possible to be complete to larger distances. ~25—30 Mpe with telescopes and 100 Mpe with HST.," While the number of SNIae will be lower if one excludes sources in the inner parts of the galaxies, it will be possible to be complete to larger distances, $\sim25-30$ Mpc with ground-based telescopes and 100 Mpc with HST."589 From our results it can clearly be seen that targetting early-type galaxies will provide much stronger constraints due to the lower difference between the ages (and hence SNla rate) of the field and globular cluster populations. and this effect is being enhanced by the higher incidence of globular clusters in these galaxies.," From our results it can clearly be seen that targetting early-type galaxies will provide much stronger constraints due to the lower difference between the ages (and hence SNIa rate) of the field and globular cluster populations, and this effect is being enhanced by the higher incidence of globular clusters in these galaxies."590 By specifically targetting SNlae at larger radii. can further reduce the number of observations needed.," By specifically targetting SNIae at larger radii, can further reduce the number of observations needed."591 This is because the globular clusters have shallower radial density, This is because the globular clusters have shallower radial density592of general regularities that can be directly applied to galactic systems without further calculations.,of general regularities that can be directly applied to galactic systems without further calculations.593 Here are sole exaniples: l., Here are some examples: 1.594 As we saw already. MOND predicts that orbital velocities on circular orbits around a concentrated mass become independent of the orbital radius. for large radii (where the acceleration becomes siinaller than αρ).," As we saw already, MOND predicts that orbital velocities on circular orbits around a concentrated mass become independent of the orbital radius, for large radii (where the acceleration becomes smaller than $\az$ )."595 For dise galaxies. this meaus that the rotational velocity should become coustant with radius at large radi. as indeed it does (see Fig.5)).," For disc galaxies, this means that the rotational velocity should become constant with radius at large radii, as indeed it does (see \ref{rcs}) )."596 2., 2.597 We also saw that the coustant asvinptotic rotational velocity iu à galaxy should be proportional to the fourth root of the Ooealaxw’s mass., We also saw that the constant asymptotic rotational velocity in a galaxy should be proportional to the fourth root of the galaxy's mass.598 This is also in very Oogood aerecimentC» with observatious., This is also in very good agreement with observations.599 ὃν, 3.600 As sunumnarized in Fie... the mass discrepancy in galaxies should appear at a different radii for different galaxies. but always at the same value of the centrifugal acceleration. V2/R.=ay.," As summarized in \ref{pointmass}, the mass discrepancy in galaxies should appear at a different radii for different galaxies, but always at the same value of the centrifugal acceleration $V^2/R=\az$."601 Galaxies for which the acceleration is smaller than ej at all radii should show a discrepancy evervwhere.," Galaxies for which the acceleration is smaller than $\az$ at all radii, should show a discrepancy everywhere."602 All this is wuply born out by the observations., All this is amply born out by the observations.603 1., 4.604 MOND also predicts that an inflated. spleroid-like halo of dark matter. as is predicted by the cold dark matter paracigia. should not suffice to explain all the facets of the mass discrepancy in disc galaxy: an additional flat. disc-like component. with predictable properties. should be necessary.," MOND also predicts that an inflated, spheroid-like halo of dark matter, as is predicted by the cold dark matter paradigm, should not suffice to explain all the facets of the mass discrepancy in disc galaxy: an additional flat, disc-like component, with predictable properties, should be necessary."605 5., 5.606 MOND predicts that the discrepant acceleration in galactic svstenis eui never much exceed ay., MOND predicts that the discrepant acceleration in galactic systems can never much exceed $\az$.607 Quite a few more such predicted laws are known (e.g...o ones pertaining to elliptical galaxies and other such systems).," Quite a few more such predicted laws are known (e.g., ones pertaining to elliptical galaxies and other such systems)."608 They all conform well with the data., They all conform well with the data.609 Above aud bevoud such Nepler-like laws. the flagship of AIOND phenomenology is the full prediction of the exact rotation curves of individual dise ealaxies: MOND does this for each and every galaxy. given only the observed distribution of the normal mass in the galaxy.," Above and beyond such Kepler-like laws, the flagship of MOND phenomenology is the full prediction of the exact rotation curves of individual disc galaxies: MOND does this for each and every galaxy, given only the observed distribution of the normal mass in the galaxy."610 Over a πιάτο galaxies have been analyzed in this wav to date. with generally. τον good success;," Over a hundred galaxies have been analyzed in this way to date, with generally, very good success."611 We already saw one example shown in detail in Fig.3:: sole more are shown iu Fie.5.., We already saw one example shown in detail in \ref{1560}; some more are shown in \ref{rcs}.612 The fact that the initial motivation for DAT and MOND is simular. aud that they aim to account for simular phenomena. may eive the impression that they are simular paradienis that cau be tested by simular criteria.," The fact that the initial motivation for DM and MOND is similar, and that they aim to account for similar phenomena, may give the impression that they are similar paradigms that can be tested by similar criteria."613 This is anything but true: MOND is much more precictive. aud leuds itself to falsification to a far ereater degree then the CDM paradigm. to sav nothing of DM in eeueral.," This is anything but true: MOND is much more predictive, and lends itself to falsification to a far greater degree then the CDM paradigm, to say nothing of DM in general."614 MOND makes definite predictions on dynamics forZudividaal objects based on just the observed mass distribution., MOND makes definite predictions on dynamics for objects based on just the observed mass distribution.615 For CDM. predictions of this kind are impossible. with very few exceptions. as they would have to hinge ou understanding of the interrelations between normal aud dark matter iu a given svstem. which. in turn. would result frou complex formation aud evolution histories that cannot be known for a given object.," For CDM, predictions of this kind are impossible, with very few exceptions, as they would have to hinge on understanding of the interrelations between normal and dark matter in a given system, which, in turn, would result from complex formation and evolution histories that cannot be known for a given object."616 This is further complicated by the fact that normal matter aud DM follow very differeut evolution paths., This is further complicated by the fact that normal matter and DM follow very different evolution paths.617 CDAL is capable of waking some predictions on general properties of the bare CDM halos themselves. if we neelect the effects of normal matter ou the CDAL Using high power computer simulations. a wuifori. distribution of CDM. seeded with some initial ireeularitics. can be evolved to obtain somestatistical properties of CDM. halos at the preseut time.," CDM is capable of making some predictions on general properties of the bare CDM halos themselves, if we neglect the effects of normal matter on the CDM: Using high power computer simulations, a uniform distribution of CDM, seeded with some initial irregularities, can be evolved to obtain some properties of CDM halos at the present time."618 This includes population statistics. such as the distribution of total masses of these halos. and eeneral iutrinsic properties of the halos such as the form of the deusity distribution iu them.," This includes population statistics, such as the distribution of total masses of these halos, and general intrinsic properties of the halos such as the form of the density distribution in them."619 However CDM is almost completely di ou the expected properties of the normal, However CDM is almost completely dumb on the expected properties of the normal620universe at large radii.,universe at large radii.621 Usiug the parameters rg = 0.50 rogo aud p 1.5. the above Παςτοιal form srovides a good fit to the numerically determined density profiles for all epochs.," Using the parameters $r_S$ = 0.50 $r_{200}$ and $p$ = 1.8, the above functional form provides a good fit to the numerically determined density profiles for all epochs."622 Iu order t) natch he profile onto the background cleusity of the universe. the remaining[n]0 parameter ra nust scale according 00 ra=qaOP2) “vhere the preseut-day value Γρ = L7 190)-," In order to match the profile onto the background density of the universe, the remaining parameter $r_\infty$ must scale according to $r_\infty = r_{\infty(0)} a^{6/(3p+2)}$ , where the present-day value $r_{\infty(0)}$ = 4.7 $r_{200}$."623 The resuling fits o the density profiles are shown as the dashed curves in Figwe:, The resulting fits to the density profiles are shown as the dashed curves in Figure 2.624 ls ‘elatively simple function (eq. []), This relatively simple function (eq. \ref{eq:rhopro}] ])625 applies over a factor of 10 in halo mass scale. and Lisl je nuuerically calculated density »oliles over nearly 5 decades in radial scale. 11 decades in densitV. AllLa factor of 100 in the scale actor a.," applies over a factor of 10 in halo mass scale, and fits the numerically calculated density profiles over nearly 5 decades in radial scale, 11 decades in density, and a factor of 100 in the scale factor $a$."626 Over this range. the RMS departure of the fitted finelous (eq. ΠΠ)," Over this range, the RMS departure of the fitted functions (eq. \ref{eq:rhopro}] ])"627 from the composite averages is 0.13 in logyp Gwhich corresponds to differences of ~207Yay il p)., from the composite averages is 0.13 in $\log_{10} \rho$ (which corresponds to differences of $\sim 35 \%$ in $\rho$ ).628 |Sing the specilied foqn (eq. []]), Using the specified form (eq. \ref{eq:rhopro}] ])629 for the «eusity profile. we can now determine the line element ds? or the space-time wihin the horizon clistance ry [12].," for the density profile, we can now determine the line element $ds^2$ for the space-time within the horizon distance $r_H$ [12]."630 The center of the coordinate system is taker1to be at the center of the cluster (or galaxy) aud the inass distribution is assumed to be sphericaly svinmetric., The center of the coordinate system is taken to be at the center of the cluster (or galaxy) and the mass distribution is assumed to be spherically symmetric.631 We begin by writing the line element iu the form where we have explicitly separated out he the contribution due to the cosmological constau. which is set by the paraueter A?=(289/15UTATMis (whe'e tlie energy scaο Az 0.0003 eV for νο = 0.7).," We begin by writing the line element in the form ds^2 =- (1 - A(r) - ^2 r^2 ) dt^2 + (1 - B(r) - ^2 r^2 } dr^2 + r^2 ^2, where we have explicitly separated out the the contribution due to the cosmological constant, which is set by the parameter $\chi^2 \equiv 632(2 \pi^3/45)^{1/2} \Lambda^2/\mpl$ (where the energy scale $\Lambda 633\approx$ 0.0003 eV for $\vac$ = 0.7)."634" I iau ""empty"" universe coutailing ouly vacuum euergy. the liue element would have he above fori1 witli 4=0=5."," In an “empty” universe containing only vacuum energy, the line element would have the above form with $A=0=B$."635 Because of he vacuum contribution. the metric contains an outer i0rizon at ry—XL ," Because of the vacuum contribution, the metric contains an outer horizon at $r_H = \chi^{-1}$."636"This outer horizon sup»orts the emission of radiation through a Hawkiug-like nechanisin [1:3] and hence the future universe will be filled with a nearly thermal bath of racdiatiou with temperawe T—X.10"" eV and claracteristi€ wavelength: Ary12.600 Mpc."," This outer horizon supports the emission of radiation through a Hawking-like mechanism [13] and hence the future universe will be filled with a nearly thermal bath of radiation with temperature $T \sim \chi \sim 10^{-33}$ eV and characteristic wavelength $\lambda \sim r_H \sim 12,600$ Mpc."637" This ""adiatiou will become the domiuaut backgrounc racdiation field after about one trillion vears.", This radiation will become the dominant background radiation field after about one trillion years.638 The unctions Ar and B(r) take iuto account acditional ctrvature due to the mass distribution. whiC las a deusity proile given by equation []].," The functions $A(r)$ and $B(r)$ take into account additional curvature due to the mass distribution, which has a density profile given by equation \ref{eq:rhopro}] ]."639 If we adop nits in which e=1 (and hence G=iLol 7). the function Bor) can be written i he form COIT where the density profile p(r) is given by equaion. ΠΠ.," If we adopt units in which $c=1$ (and hence $G = \mpl^{-2}$ ), the function $B(r)$ can be written in the form B(r) = 2G = 8 G _0^r ) ^2, where the density profile $\rho (r)$ is given by equation \ref{eq:rhopro}] ]."640 Sluce we are Interestec iu tlie asymptotic form for the metric. we cau cousider late times for which the scale ra is st'etclied bevoud the horizon rg.," Since we are interested in the asymptotic form for the metric, we can consider late times for which the scale $r_\infty$ is stretched beyond the horizon $r_H$."641 Iu this limit. the functio1 B(r) can be simplified to the form sign ," In this limit, the function $B(r)$ can be simplified to the form B(r) = 4 G _0 r_S^2 _0 )."642"Iu the secoud equality. we have defined the j»aranueter yy=ImC'pgrz4Puls> whichn sets the ""strengthoE of the curvature aud the dimensionless function 25(£[«) which specilies the radial depeudeuce of the metric coefficient Gwhere£= r/rg)."," In the second equality, we have defined the parameter $\eta_0 = 4 \pi643G \rho_0 r_S^2$ which sets the “strength” of the curvature and the dimensionless function $\beta(\xi)$ which specifies the radial dependence of the metric coefficient (where $\xi = r/r_S$ )."644 For typical valies. the strength parameter jjj2LO”. indicating that the departure [rom flatuess is relativelysinall.," For typical values, the strength parameter $\eta_0 \approx 10^{-6}$, indicating that the departure from flatness is relativelysmall."645 The resulting function 2(£) is shown iu Figure 3., The resulting function $\beta(\xi)$ is shown in Figure 3.646 The function Ar) is related to the usual gravitational potential Φ through the definition er?=1—Afr) [12]. where the potential is defined through the source equation," The function $A(r)$ is related to the usual gravitational potential $\Phi$ through the definition ${\rm e}^{2 \Phi} \equiv 1-A(r)$ [12], where the potential is defined through the source equation = ."647OC Because of the scheduled. GLAST mission by NASA. there is strong scientific justification for preparation [or very exteusive blazar mouitoring iu the optical bauds to exploit the opportunity to learn about blazars through the correlation of variability of the @amuina-ray [fux with [lus at lower [requeucies.,".6cm Because of the scheduled GLAST mission by NASA, there is strong scientific justification for preparation for very extensive blazar monitoring in the optical bands to exploit the opportunity to learn about blazars through the correlation of variability of the gamma-ray flux with flux at lower frequencies."648 Current optical facilities do not provide the required capability., Current optical facilities do not provide the required capability.649Developments iu technology have euabled astronomers to readily deploy automatic telescopes.,Developments in technology have enabled astronomers to readily deploy automatic telescopes.650 The effort to create an Automatic Telescope Network (ATN) for blazar monitoring in the GLAST era is describe., The effort to create an Automatic Telescope Network (ATN) for blazar monitoring in the GLAST era is described.651 οσα The EGRET telescope aboard the as detected ~LL GeV emission from ~770 blazars (Hartman 11999. Mattox 1999a).," .6cm The EGRET telescope aboard the has detected 1 GeV emission from 70 blazars (Hartman 1999, Mattox 1999a)."652 The apparent uiinosity seen for the EGRET blazars is as much as one Πάνος times larger than that at all other wavelengths for some flaring EGRET blazars., The apparent luminosity seen for the EGRET blazars is as much as one hundred times larger than that at all other wavelengths for some flaring EGRET blazars.653 Variability of the ix from some blazars on a time-scale as short as | hours has been observed (Mattox 11997)., Variability of the flux from some blazars on a time-scale as short as 4 hours has been observed (Mattox 1997).654 This implies that the region of eeimission must be very compact., This implies that the region of emission must be very compact.655 Because the opacity [or ο ?—5 pair production with x-rays inust uot prevent 5-rays [rom escaping. relativistic beaming with a Lorentz factor of 110 for the bulk of material tu the jet is required (Mattox 11997).," Because the opacity for to $\gamma-\gamma$ pair production with x-rays must not prevent $\gamma$ -rays from escaping, relativistic beaming with a Lorentz factor of 10 for the bulk of material in the jet is required (Mattox 1997)."656 This couclusion is reinforced by the observation of a higli x-ray state during the 1996 flare of 3C 279 (Wehlrle 11995) whieh implies that the x-rays originate in the same volume as tlie 5-rays)., This conclusion is reinforced by the observation of a high x-ray state during the 1996 flare of 3C 279 (Wehrle 1998) which implies that the x-rays originate in the same volume as the s).657 With sibstantial accretion onto a pt&s M. blackhole. there is suflicieut. power to create the relativistic jets.," With substantial accretion onto a 8 $_\odot$ blackhole, there is sufficient power to create the relativistic jets."658 However. {1e plivsies involved in the conversion of gravitational potential to kinetic luminosity is not uuderstood.," However, the physics involved in the conversion of gravitational potential to kinetic luminosity is not understood."659 ]t is widely believed that this GeV emission is due to inverse-CouiMon scattering yy leptous within the relativistic jet., It is widely believed that this GeV emission is due to inverse-Compton scattering by shock-accelerated leptons within the relativistic jet.660 However. there is clisagree:uent over the origin of the 11 eV photons which are scattered.," However, there is disagreement over the origin of the 1 eV photons which are scattered."661 Some moclelers believe that they originate in the syichrotron emission of the leptous. so the 5-rays are a result of the svuchrotron seCCompton (SSC) process (Bloom Marscher 1993).," Some modelers believe that they originate in the synchrotron emission of the leptons, so the s are a result of the synchrotron self-Compton (SSC) process (Bloom Marscher 1993)."662to the shape. location. and racial profile of the ealaxy.,"to the shape, location, and radial profile of the galaxy."663 The maxinuun order of the sim iu (25)) determines the allowable complexity of the filter., The maximum order of the sum in \ref{nu2}) ) determines the allowable complexity of the filter.664 is the implementation of the methods described in the previous section., is the implementation of the methods described in the previous section.665 The code includes. classes to represent the vectors. trausformatious. and covariance lnatrices over quantities indexed by the iuteger pairs pq.," The code includes classes to represent the vectors, transformations, and covariance matrices over quantities indexed by the integer pairs $pq$."666 To fit to a single galaxy. the code requires as nut: The procedure for shape determination has the following steps:," To fit to a single galaxy, the code requires as input: The procedure for shape determination has the following steps:"667iowever. still missing.,"however, still missing."668 In Szeidlet.al.us--.Paper1). we collected. all the photometric data of in order ο study the period changes of RR Lyrac stars., In \citet[Paper I]{oc} we collected all the photometric data of M5 variables in order to study the period changes of RR Lyrae stars.669 “Phese data are utilized here to detect and study Blazhko variables., These data are utilized here to detect and study Blazhko variables.670 The homogenized (see section 2.3 of Paper E) light curves of the RRab stars in ALS were carefully examined to identity variables showing light-curve instability., The homogenized (see section 2.3 of Paper I) light curves of the RRab stars in M5 were carefully examined to identify variables showing light-curve instability.671 Due to crowding problems. this was not possible for all the λα stars in our sample.," Due to crowding problems, this was not possible for all the RRab stars in our sample."672 Variables Iving in too crowded areas and/or having close bright companions could not be measured. accurately enough to detect light-curve variability without doubt., Variables lying in too crowded areas and/or having close bright companions could not be measured accurately enough to detect light-curve variability without doubt.673 This was especially true if no CCD observation of the variable was available., This was especially true if no CCD observation of the variable was available.674 From the 65 Rab stars for which phase variation diagrams were constructed in Paper L this was the case for 15 stars (V6. V13. V17. V25. V26. V36. VAT. V54. VT4. V8S3. V85. V90. VOL. V92 and V96).," From the 65 RRab stars for which phase variation diagrams were constructed in Paper I, this was the case for 15 stars (V6, V13, V17, V25, V26, V36, V37, V54, V74, V83, V85, V90, V91, V92 and V96)."675 These stars were denoted by the letter  in the ‘Remarks’ column of Table 4 in Paper 1. Fhe combined. photographic and CCD D light curves of the remaining 50 Ritab stars were studied: using cilferent methods in order to detect. light-curve variations and to determine modulation periods if it was possible., These stars were denoted by the letter $d$ ' in the `Remarks' column of Table 4 in Paper I. The combined photographic and CCD $B$ light curves of the remaining 50 RRab stars were studied using different methods in order to detect light-curve variations and to determine modulation periods if it was possible.676 When CCD V observations from different sources were also available. these data were investigatecl separately.," When CCD $V$ observations from different sources were also available, these data were investigated separately."677 Dilerent segments of the data were checked and analvsed., Different segments of the data were checked and analysed.678 LE light-curve variability was suspected. in any part of the data. Fourier analyses of the light curves and the maximum brightness/maximum timing data were also applied.," If light-curve variability was suspected in any part of the data, Fourier analyses of the light curves and the maximum brightness/maximum timing data were also applied."679 The maximum brightness/phase cata of elobular-cluster variables are. however. very sparse (one-two data per season if any). and give uscable information only in very few cases (e.g. in V19).," The maximum brightness/phase data of globular-cluster variables are, however, very sparse (one-two data per season if any), and give useable information only in very few cases (e.g. in V19)."680 We searched. for modulation-frequeney. signals in the vicinity of the low-order pulsation frequency components (ουδx d) ¢srresponding to the same modulation frequeney (fia).," We searched for modulation-frequency signals in the vicinity of the low-order pulsation frequency components $kf_0, k<4$ ) corresponding to the same modulation frequency $f_{\mathrm{m}}$ )."681" T16 modulation period (I4,=Lf fia) was then determined. by a non-linear process that fitted the pulsation and some of the modulation frequencies (&fo.&<S and ο+fu.< 4) and their amplitudes ancl phases simultaneously to the data."," The modulation period $P_{\mathrm{m}}=1/f_{\mathrm{m}}$ ) was then determined by a non-linear process that fitted the pulsation and some of the modulation frequencies $kf_0, k<8$ and $kf_0\pm f_{\mathrm{m}}, k<4$ ) and their amplitudes and phases simultaneously to the data."682luminosity of the AGN was found to be ~4x107s7!..,luminosity of the AGN was found to be $\sim 4\times 10^{42}$.683 Due to the limited energy bandpass of XMM-Newton. this observation did not allow us to directly see the intrinsic continuum. thus to measure the absorbing column density and the intrinsic X-ray luminosity of IRAS 19254-7245.," Due to the limited energy bandpass of XMM-Newton, this observation did not allow us to directly see the intrinsic continuum, thus to measure the absorbing column density and the intrinsic X-ray luminosity of IRAS 19254-7245."684 Here we present the analysis of a deep Suzaku observation (150 ksec) of this system. which allowed us for the first time to constrain the intrinsic power of the AGN hosted in19254-7245.. as well as to investigate in detail the properties of the Fe line complex.," Here we present the analysis of a deep Suzaku observation $\sim 150$ ksec) of this system, which allowed us for the first time to constrain the intrinsic power of the AGN hosted in, as well as to investigate in detail the properties of the Fe line complex."685 In Sec., In Sec.686 2 we present the Suzaku data analysis and results. while in Sec.," 2 we present the Suzaku data analysis and results, while in Sec."687 3 we discuss the overall scenario for X-ray emission of7245., 3 we discuss the overall scenario for X-ray emission of.688". Throughout this paper. the current popular cosmology is assumed with Hy=73 km s! Mpe7!. ον=0.27 and Q,=0.73."," Throughout this paper, the current popular cosmology is assumed with $H_0=73$ km $^{-1}$ $^{-1}$, $\Omega_{\rm{M}}=0.27$ and $\Omega_\lambda=0.73$."689 Suzaku (Mitsudaetal.. 2007)) is the fifth Japanese X-ray satellite. which carries on board four sets of X-ray mirrors. with a X-ray CCD (XIS: three front illuminated. FI. and one back illuminated. BI Koyamaetal.. 2007)) at their focal plane. and a non imaging hard X-ray detector (HXD. Takahashiet. 2007)).," Suzaku \citealp{Mitsuda}) ) is the fifth Japanese X-ray satellite, which carries on board four sets of X-ray mirrors, with a X-ray CCD (XIS; three front illuminated, FI, and one back illuminated, BI \citealp{XISref}) ) at their focal plane, and a non imaging hard X-ray detector (HXD, \citealp{Takahashi}) )."690 The latter is composed by 2 main instruments: the Si PIN photodiodes and the GSO scintillator counter., The latter is composed by 2 main instruments: the Si PIN photodiodes and the GSO scintillator counter.691 Altogether the XIS and the HXD-PIN cover the 0.5-10 keV and 12-70 keV bands Suzaku observed IRASI9254-7245 for a total exposure time of about 150 ksec: the observation was performed at the beginning of November 2005. when all the 4 XIS were still Cleaned event files from the version 2 of the Suzaku pipeline processing were used with the standardsereening.," Altogether the XIS and the HXD-PIN cover the 0.5–10 keV and 12–70 keV bands Suzaku observed IRAS19254-7245 for a total exposure time of about 150 ksec; the observation was performed at the beginning of November 2005, when all the 4 XIS were still Cleaned event files from the version 2 of the Suzaku pipeline processing were used with the standard."692. The net exposure times are 97.9 ksee for each of the XIS and 142.1 ksec for the HXD-PIN., The net exposure times are $97.9$ ksec for each of the XIS and $142.1$ ksec for the HXD-PIN.693 The XIS source spectra were extracted from a circular region of 2.9’ radius ( which correspond to an energy encircled fraction of 2008-04.pdf)) centered on the source., The XIS source spectra were extracted from a circular region of $'$ radius ( which correspond to an energy encircled fraction of ) centered on the source.694 Background spectra were extracted from two circular regions of 2.4’ radius offset from the source and the calibration sources., Background spectra were extracted from two circular regions of $'$ radius offset from the source and the calibration sources.695 The XIS response (rmfs) and ancillary response (arfs) files were produced. using the latest calibration files available. with the tasks and respectively.," The XIS response (rmfs) and ancillary response (arfs) files were produced, using the latest calibration files available, with the tasks and respectively."696 The net 0.5-10 keV count rates are: (1.67+0.07)x107 cts/s. (1.57+0.06)x107 cts/s. (1.55+0.06)x1077 ets/s and (1.84+0.09)x107 cts/s for the XISO. XIS2. XIS3 and XISI respectively.," The net 0.5–10 keV count rates are: $(1.67\pm6970.07)\times 10^{-2}$ cts/s, $(1.57\pm 0.06)\times 10^{-2}$ cts/s, $(1.55\pm 0.06)\times69810^{-2}$ cts/s and $(1.84\pm 0.09)\times 10^{-2}$ cts/s for the XIS0, XIS2, XIS3 and XIS1 respectively."699 The source spectra from the three Fl CCDs were then combined. while the BI (the XISI) spectrum was kept separate and fitted simultaneously.," The source spectra from the three FI CCDs were then combined, while the BI (the XIS1) spectrum was kept separate and fitted simultaneously."700 The net XIS source spectra were then binned in order to have a minimum S/N of 4 in each energy bin and y statistics have been used., The net XIS source spectra were then binned in order to have a minimum S/N of 4 in each energy bin and $\chi^2$ statistics have been used.701 For the HXD-PIN data reduction and analysis we followed the latest Suzaku data reduction guide (the ABC guide Version 2y°., For the HXD-PIN data reduction and analysis we followed the latest Suzaku data reduction guide (the ABC guide Version .702. For the analysis we used the rev2 data. which include all 4 cluster units. and the best background available (Fukazawaetal..2009).. which account for the instrumental background (NXB: Takahashietal..2007;Kokubun 2007)).," For the analysis we used the rev2 data, which include all 4 cluster units, and the best background available \citep{fukazawa}, which account for the instrumental background (NXB; \citealp{Takahashi,kokubun}) )."703" We then simulated a spectrum for the cosmic X-ray background counts (Boldt.1987:Gruberetal..1999) and added it to the instrumental At the time of the writing two different instrumental background files have been released (background A or ""quick"" background and the background D or ""tuned"" background: Mizuno et al :Fukazawaetal. 2009)."," We then simulated a spectrum for the cosmic X-ray background counts \citep{Boldt,Gruber} and added it to the instrumental At the time of the writing two different instrumental background files have been released (background A or “quick” background and the background D or “tuned” background; Mizuno et al. \citealt{fukazawa}) )."704 We tested both the instrumental backgrounds and we included a x105€ uncertainty in the level of the CXB., We tested both the instrumental backgrounds and we included a $\pm 10\%$ uncertainty in the level of the CXB.705 The inspection of the net spectrum shows that the source is detected in the 15—30 keV with both the two background files., The inspection of the net spectrum shows that the source is detected in the 15–30 keV with both the two background files.706 The net count rate in the 15-30 keV using background A and D are respectively 1.59+0.14x107 cts κ) and 148x0.14107 ets s! and the corresponding background count rates are 0.25+0.004 ets «παπα 0.26+0.003 cts ο. We then decided to use the latest release (background D). which is affected by lower systematic uncertainties (of about at lo). which correspond to about half of the first release ftp://legacy.gsfe.nasa.gov/suzaku/doe/xrt/suzakumemoef the NXB.," The net count rate in the 15–30 keV using background A and D are respectively $1.59\pm0.14\times10^{-2}$ cts $^{-1}$ and $1.48\pm0.14\times10^{-2}$ cts $^{-1}$ and the corresponding background count rates are $0.25\pm 0.004$ cts $^{-1}$ and $0.26\pm 0.003$ cts $^{-1}$ We then decided to use the latest release (background D), which is affected by lower systematic uncertainties (of about at $\sigma$ ), which correspond to about half of the first release of the NXB."707 Using this background iis detected in the 15-30 keV band at~5.5% above the background (a total of ~ 2000 net counts have been collected). corresponding to a signal-to noise ratio S/N.=10.8.," Using this background is detected in the 15–30 keV band at$\sim 5.5$ above the background (a total of $\sim$ 2000 net counts have been collected), corresponding to a signal-to noise ratio $S/N\simeq 10.8$."708 The dominant component in the background ts the instrumental one with a count rate of 0.24+ 0.001cts s!. while the CXB count rate ranges from [4x107 to 1.6x107 when we include the 410% uncertainty on its level.," The dominant component in the background is the instrumental one with a count rate of $0.24\pm 0.001$ cts $^{-1}$, while the CXB count rate ranges from $1.4 \times 10^{-2}$ to $1.6 \times 10^{-2}$ when we include the $\pm 10\%$ uncertainty on its level."709 If we then assume a higher CXB level the source is still detected at 5.0% above the background (mean count rate in the 15-30 keV is 1.35£0.14x107 ets s! ) with S/N 9.7. thus the detection of iis not dependent on the CXB absolute level.," If we then assume a higher CXB level the source is still detected at $5.0$ above the background (mean count rate in the 15–30 keV is $1.35\pm0.14\times10^{-2}$ cts $^{-1}$ ) with $\simeq 9.7$ , thus the detection of is not dependent on the CXB absolute level."710 As a furthercheck, As a furthercheck711choudrules formed.,chondrules formed.712 These include: (1) the increased rate of collisions between plastic and molten chondrules to formu adhering pairs (?).. (2) the seeding of melted choudrules with dust eraius (?).. (3) the O/T ratio well above the solar value (?).. and (1) the improved absorption efficiency of x-ravs and 5-ravs by the precursor dust balls.," These include: (1) the increased rate of collisions between plastic and molten chondrules to form adhering pairs \cite{was:1993}, (2) the seeding of melted chondrules with dust grains \cite{ch:1995}, (3) the O/H ratio well above the solar value \cite{fp:1985}, and (4) the improved absorption efficiency of x-rays and $\gamma$ -rays by the precursor dust balls."713 Tho rims ou chondrules iudicate time spent in dusty regions., The rims on chondrules indicate time spent in dusty regions.714 The formation of the Sun aud planets has been the subje of extensive study aud is now particularly importa- because of the recent detections of Jupiter like plaucts around solar type stars that are inferred to be eiau planets (7:?:?)..," The formation of the Sun and planets has been the subject of extensive study and is now particularly important because of the recent detections of Jupiter like planets around solar type stars that are inferred to be giant planets \cite{mq:1995,bs:1996,LLD:1998}."715 The main model for planetary formation in the solar svsteni is that planets are the end resul of a bottonrup assembly process begmning with the acciunulatiou of interstellar eraius iuto wullimeter aux centimeter sized objects that fori iu the disk are eventuav settle to the midplane where they are brought ogether to form kilometer sized objects (2:2).," The main model for planetary formation in the solar system is that planets are the end result of a bottom-up assembly process beginning with the accumulation of interstellar grains into millimeter and centimeter sized objects that form in the disk and eventually settle to the midplane where they are brought together to form kilometer sized objects \cite{miz:1980,bl1:1995}."716 These so called planctesimals proceed through a runaway accretion xocess to form bodies of Imax size that are eventually accumulated to form the terrestrial planets., These so called planetesimals proceed through a runaway accretion process to form bodies of lunar size that are eventually accumulated to form the terrestrial planets.717 Iu the«case of he elant and icy outer planets the process is different (?).., In the case of the giant and icy outer planets the process is different \cite{phb:1996}.718 A planetary core accretes until a critical mass of about LO ALI is reached., A planetary core accretes until a critical mass of about 10 $\oplus$ is reached.719 At this point the erowing core is unable ο sustain an equilibriun atmosphere and a very rapid accretion of uchular eas occurs that eives a eiaut planet., At this point the growing core is unable to sustain an equilibrium atmosphere and a very rapid accretion of nebular gas occurs that gives a giant planet.720 The total mass ofthe nebula between 0.35 AU and 36 AU is O.OL ALS aud is cousidered the minima necessary to form the preseut planets., The total mass of the nebula between 0.35 AU and 36 AU is 0.01 $\odot$ and is considered the minimum necessary to form the present planets.721 There are perceived difficulties with this model with regard to timescales because the predominantly II aud Πο composition of Jupiter aud Saturn predates the dispersal of the solar nebula (?).., There are perceived difficulties with this model with regard to timescales because the predominantly H and He composition of Jupiter and Saturn predates the dispersal of the solar nebula \cite{cam2:1978}.722 A uwnnber of models have been proposed for distribution of surface densities of dust materials and gases in a preplauetary solar nebula. which is iu thermal aud eravitational equilibriun.," A number of models have been proposed for distribution of surface densities of dust materials and gases in a preplanetary solar nebula, which is in thermal and gravitational equilibrium."723 According to Cameron (7) the nebula surface density as a function of radial distance frou ↑∐↸∖⊱∏∐↖↖↽⋜↧↴∖↴∑∶∑⋃↥⋅↓⊳∪∶↴∙⊾↸⊳⋯−↖∏↑∐⋜↧∐∪↥⋅↕⊔⋜↧∐↴∖↴∐↓∶↴⋁↖↽⋜↧↕⋯∖ >. ⋅⋅ of = 125.10? at y = 1 AU.," According to Cameron \cite*{cam3:1995} the nebula surface density as a function of radial distance from the Sun was $\Sigma =724\Sigma_{0}$ $^{-1.0}$ g $^{-2}$ with a normalising value of = 4.25 at r = 1 AU."725" The abundance by mass of rocky aud inetallie materials was 0.0013 aud 0.0137 for icy materials (Πο. CIE, aud. NIT;). that occur bevoud i:bout 3 AU."," The abundance by mass of rocky and metallic materials was 0.0043 and 0.0137 for icy materials $_{2}$ O, $_{4}$ and $_{3}$ ), that occur beyond about 3 AU."726 There are many complicated processes that occur in the evolution of the solar nebula from essentially interstcllay erains to planetesinials and planets (e.g. (2)))., There are many complicated processes that occur in the evolution of the solar nebula from essentially interstellar grains to planetesimals and planets (e.g. \cite{cam3:1995}) ).727 Particle radii vary over 11 orders of maguitude from wicron sized interstellar particles to planctesimals., Particle radii vary over 11 orders of magnitude from micron sized interstellar particles to planetesimals.728 It seclus likely that planctesimal formation involved at least an carly stage of collisional sticking aud coagulation of articles., It seems likely that planetesimal formation involved at least an early stage of collisional sticking and coagulation of particles.729 This process depended ou poorly constrained xoperties of the nebula such as turbulence and of the articles themselves such as stickiness aud composition., This process depended on poorly constrained properties of the nebula such as turbulence and of the particles themselves such as stickiness and composition.730 The process of particle accumulation and coagulation is strongly influenced by turbulence which keeps the articles in constant random motion with respect to the eas and many sinulatiouns on particle coagulation have con. carried out for silicate and icy eras (2:2:7)...," The process of particle accumulation and coagulation is strongly influenced by turbulence which keeps the particles in constant random motion with respect to the gas and many simulations on particle coagulation have been carried out for silicate and icy grains \cite{cam3:1995,weid:1980,wc:1993}."731 Tn he GRD-clondrule scenario. the choucrules reflect the size distribution of the precursor erains.," In the GRB-chondrule scenario, the chondrules reflect the size distribution of the precursor grains."732 It is interesting hat they have an approximate lognormal distribution., It is interesting that they have an approximate lognormal distribution.733 This distribution is generated by particle exindiug and collisions and iuplv these conditions prevailed iu the jicbula at the time of the CRB (?).., This distribution is generated by particle grinding and collisions and imply these conditions prevailed in the nebula at the time of the GRB \cite{ab:1957}.734 Uistorically the oenornmal distribution was developed to account for the size distribution of graius of sand., Historically the lognormal distribution was developed to account for the size distribution of grains of sand.735 Turbuleuce is known to xoduce structure on mnauv scales and hence the particle distribution iu the nebula was probably quite chuupy., Turbulence is known to produce structure on many scales and hence the particle distribution in the nebula was probably quite clumpy.736 To uake progress we assume the particles aud gas werewell uixed and of solar composition., To make progress we assume the particles and gas werewell mixed and of solar composition.737 The GRD shouk have xocducec a laver of 0.15 ο ? of choudrules or 27 MI out tor = 36 AU axd LOO NET aif IT and We were depleted uniforiulv by a factor of 3., The GRB should have produced a layer of 0.18 g $^{-2}$ of chondrules or 27 $\oplus$ out to r = 36 AU and 100 $\oplus$ if H and He were depleted uniformly by a factor of 3.738 Iu the latter use. three )Oycolr and ten percent of the dust is conver5 to chondrules a r-—] AU aud r 2 10 AU respectively.," In the latter case, three percent and ten percent of the dust is converted to chondrules at r = 1 AU and r = 10 AU respectively."739 The eas may no rave been depletec uuiforiulv across the nebula at the nue ofthe CRB., The gas may not have been depleted uniformly across the nebula at the time of the GRB.740 The compositions of Jupiter aud Satur reveal that they formed before the uebula was depleted of II and Ue 1Y more than about a factor of 5., The compositions of Jupiter and Saturn reveal that they formed before the nebula was depleted of H and He by more than about a factor of 5.741 The terrestria anuets aud eiut icy outer planets; Urauus aud Neptune. colpleted their formation after eas depletion from the jebula.," The terrestrial planets and giant icy outer planets, Uranus and Neptune, completed their formation after gas depletion from the nebula."742 The gas depletion from the immer uebula probably occurred over about 10' wears by strong solar winds during the FU Orionis aud T-Tauri phase of the Sun and from the outer nebula bevoud about 9 AU by photo evaporation (7). , The gas depletion from the inner nebula probably occurred over about $^{7}$ years by strong solar winds during the FU Orionis and T-Tauri phase of the Sun and from the outer nebula beyond about 9 AU by photo evaporation \cite{sjh:1993}. .743Iu this scenario the chondrules formed almost sinmultaucouslv across the side of the nebula, In this scenario the chondrules formed almost simultaneously across the side of the nebula744composition high above the Galactic plane.,composition high above the Galactic plane.745 Phe upper panel of depicts the iron. abundance distributions of the stars at cdillerent heights above the plane., The upper panel of depicts the iron abundance distributions of the stars at different heights above the plane.746 Both tails of the clistribution are strengthened as one moves away [rom the plane., Both tails of the distribution are strengthened as one moves away from the plane.747 “Phe growth in the proportion of metal-rich stars with |z| is at first unexpected. but is a natural consequence of the higher vertical velocity. dispersion. of stars in the inner disc.," The growth in the proportion of metal-rich stars with $|z|$ is at first unexpected, but is a natural consequence of the higher vertical velocity dispersion of stars in the inner disc."748 Notwithstanding the growth of the metal-rich wing of the metallicity distribution. the mean metallicity falls with increasing |;| by more than 0.2dex. while the dispersion increases from below 0.3dex to 0.5dex.," Notwithstanding the growth of the metal-rich wing of the metallicity distribution, the mean metallicity falls with increasing $|z|$ by more than $0.2 \dex$, while the dispersion increases from below $0.3\dex$ to $0.5\dex$."749 We expect the model. however. to underestimate the vertical metallicity eracient on account of our assumption that a star inherits the velocity dispersion of the galacetocentrie radius at which it was born.," We expect the model, however, to underestimate the vertical metallicity gradient on account of our assumption that a star inherits the velocity dispersion of the galactocentric radius at which it was born."750 X better model would take account of the actual migration paths of stars how long cach star spent with its guiding centre at cach —raciius., A better model would take account of the actual migration paths of stars – how long each star spent with its guiding centre at each radius.751 It would. predict. smaller scale heights for populations of stars born in the inner disc., It would predict smaller scale heights for populations of stars born in the inner disc.752 Thus the model might predict too high a fraction of metallicity stars to high altitudes., Thus the model might predict too high a fraction of high-metallicity stars to high altitudes.753 The metallicity distribution at high altitudes depends on the weakly constrained carly evolution of the clise and on details of mixing. so comparisons with observational data would provide valuable constraints on these less secure aspects of the model.," The metallicity distribution at high altitudes depends on the weakly constrained early evolution of the disc and on details of mixing, so comparisons with observational data would provide valuable constraints on these less secure aspects of the model."754 Unfortunately. such. comparisons are not feasible at present.," Unfortunately, such comparisons are not feasible at present."755 In. particular. we cannot compare with the SDSS data of Ivezieetal.(2008) because their metallicity determination breaks down above ο)-—0.5dex.," In particular, we cannot compare with the SDSS data of \cite{Ivezic08} because their metallicity determination breaks down above $\feh \sim -0.5 \dex$ ."756 Phe model however has a constant mean rotational velocity in the metallicity range probed by the SDSS survey. in line with the data of Ivezicetal.(2008).," The model however has a constant mean rotational velocity in the metallicity range probed by the SDSS survey, in line with the data of \cite{Ivezic08}."757. The lower panel of shows the O/Fe] distributions at cillerent heights., The lower panel of shows the $\ofe$ distributions at different heights.758 Lt reveals the bimodal structure that motivates the division. of the disc into two., It reveals the bimodal structure that motivates the division of the disc into two.759 The exact garape of the two peaks as well as the number of stars in between depend on assumptions about gas enrichment. and 10 behaviour of SNIa. but the bimocalitv ofthe distribution is à fundamental prediction of the model. as was shown in 1f appendix of SBOO.," The exact shape of the two peaks as well as the number of stars in between depend on assumptions about gas enrichment and the behaviour of SNIa, but the bimodality of the distribution is a fundamental prediction of the model, as was shown in the appendix of SB09."760 Phe increasing bias to high ages as >| increases is reflected in the growing strength of the high Οο peak relative to the low O/Fe] peak associated with 10 thin cise., The increasing bias to high ages as $|z|$ increases is reflected in the growing strength of the high $\ofe$ peak relative to the low $\ofe$ peak associated with the thin disc.761 There are principally two strategies by which the disc has classically been dissected: by kinematies and by chemistry., There are principally two strategies by which the disc has classically been dissected: by kinematics and by chemistry.762 We caution that. dillerent. selection. procedures do. viek intrinsically different. samples and that in general these are not equivalent., We caution that different selection procedures do yield intrinsically different samples and that in general these are not equivalent.763 We shall see that these selection cilferences. which account for the spread. by almost. an order of magnitude in estimates of the relative local densities. of the thick ane thin dises. are readily understood. in. the context of our model.," We shall see that these selection differences, which account for the spread by almost an order of magnitude in estimates of the relative local densities of the thick and thin discs, are readily understood in the context of our model."764" In each scheme criteria are set tha define both thin and thick disc components. while stars tha meet neither criterion are here assigned to an ""intermediate population”."," In each scheme criteria are set that define both thin and thick disc components, while stars that meet neither criterion are here assigned to an “intermediate population”."765 We turn first to chemical selection and then in the light of this assess the quality and elfects of kinematica criteria., We turn first to chemical selection and then in the light of this assess the quality and effects of kinematical criteria.766 The dots and crosses in the upper panel of show a realisation of a GCS-like sample of stars in the model., The dots and crosses in the upper panel of show a realisation of a GCS-like sample of stars in the model.767 The ridge of the thin disc is evident. as is a ridge of metal-poor uick-cise stars at Fell]z0.65 and O/Fe]~0.6.," The ridge of the thin disc is evident, as is a ridge of metal-poor thick-disc stars at $\feh\lta-0.65$ and $\ofe\sim0.6$."768 We consider the thin dise to consist of all stars that lie within the black lines around this ridge., We consider the thin disc to consist of all stars that lie within the black lines around this ridge.769 Less clear is the extent of the ick discat Κο)0.6., Less clear is the extent of the thick disc at $\feh\gta-0.6$.770 Guidance is provided by plotting in green the locations of those stars in the realisation that satisfy the kinematic selection criteria of Bensbv o belong to the thick disc.," Guidance is provided by plotting in green the locations of those stars in the realisation that satisfy the kinematic selection criteria of \cite{Bensby03}771 to belong to the thick disc."772 A few of these stars lie in the region reserved for the thin disce: this phenomenon illustrates 1e inability of any kinematic selection criteria to separate ‘leanly the thin and thick discs — see refsec:kinsel below., A few of these stars lie in the region reserved for the thin disc; this phenomenon illustrates the inability of any kinematic selection criteria to separate cleanly the thin and thick discs – see \\ref{sec:kinsel} below.773" la light. of the distribution of green ‘rosses inὃν, we define the thick disc to consist of all stars that [ie either above the horizontal line at 0.56 or to the right ofthe sloping line. which has the equation The lower panel of shows the chemical compositions of stars in three large observational programs."," In light of the distribution of green crosses in, we define the thick disc to consist of all stars that lie either above the horizontal line at $\ofe=0.56$ or to the right of the sloping line, which has the equation The lower panel of shows the chemical compositions of stars in three large observational programs."774 ‘These studies used. dilferent. selection criteria )onsby.et kinematically selected. for thick-clise stars. while," These studies used different selection criteria – \cite{Bensby05} kinematically selected for thick-disc stars, while"775Tlence. the static kink is a stable structure.,"Hence, the static kink is a stable structure."776 Our studies show (hat strong pinning of vortex lines is likely (ο occur especially when the average direction of a vortex line is parallel or approximately parallel to. the major axis of a crvstal lattice ancl (the Magnus force is nol so strong., Our studies show that strong pinning of vortex lines is likely to occur especially when the average direction of a vortex line is parallel or approximately parallel to the major axis of a crystal lattice and the Magnus force is not so strong.777 The orientation of a crystal lattice varies [rom one domain to another in a polvervstalline structure., The orientation of a crystal lattice varies from one domain to another in a polycrystalline structure.778 The pinning strength decreases in the domain where the major axis of a crvstal lattice is not close to the vortex line., The pinning strength decreases in the domain where the major axis of a crystal lattice is not close to the vortex line.779 ILowever. as long as the equilibrium vortex conligurations are represented bv the kink solutions. pinning of a vortex line in a polvervstalline structure would be still strong enough to explain the large glitches (see the subsection 3.7).," However, as long as the equilibrium vortex configurations are represented by the kink solutions, pinning of a vortex line in a polycrystalline structure would be still strong enough to explain the large glitches (see the subsection 3.7)."780 We have shown that the equilibrium configuration of a vortex line consists of straight and kink parts when the rotation axis of the star is approximately aliened with the major axis of a crystal lattice and (he Magnus force is weak., We have shown that the equilibrium configuration of a vortex line consists of straight and kink parts when the rotation axis of the star is approximately aligned with the major axis of a crystal lattice and the Magnus force is weak.781 The straight part is much longer than the kink part., The straight part is much longer than the kink part.782 Furthermore. (he straight parts pass through nearly all of iuclei along the major axis. whereas (he kink parts lie mostly in space between the lattice planes.," Furthermore, the straight parts pass through nearly all of nuclei along the major axis, whereas the kink parts lie mostly in space between the lattice planes."783 The vortex line is strongly pinned to (he lattice nuclei in the straight part. while not in the kink part.," The vortex line is strongly pinned to the lattice nuclei in the straight part, while not in the kink part."784 We have found from the perturbation analvses (hal there exist two modes. rotational and helical (kelvin). lor oscillations excited on a vortex line.," We have found from the perturbation analyses that there exist two modes, rotational and helical (Kelvin), for oscillations excited on a vortex line."785 The vortex oscillations are possible onlv above a minimum frequency (Link.Epstein.&ανα1993). and the phase velocity ol oscillations varies with wave number., The vortex oscillations are possible only above a minimum frequency \citep{lin93} and the phase velocity of oscillations varies with wave number.786 We find no unstable mode that grows with time., We find no unstable mode that grows with time.787 These [acts lead to the conclusion that the vortex configuration with kinks may be stable and vield (he stronely pinned state especially when the vortex line is close to the main axis ol a ervstal lattice., These facts lead to the conclusion that the vortex configuration with kinks may be stable and yield the strongly pinned state especially when the vortex line is close to the main axis of a crystal lattice.788 Jones (1997. 1993) argues that pinning is not strong enough to explain the large elitches adopting a kink motion in a polvervstalline structure.," Jones (1997, 1998) argues that pinning is not strong enough to explain the large glitches adopting a kink motion in a polycrystalline structure."789 Our studies show that the static kink is a stable structure and the kink motion is less likelv., Our studies show that the static kink is a stable structure and the kink motion is less likely.790 If the kinks do not move along a vortex line. the conclusion made by Jones is not. guaranteed.," If the kinks do not move along a vortex line, the conclusion made by Jones is not guaranteed."791 Nuclei in the crust may be in a polvervstalline structure., Nuclei in the crust may be in a polycrystalline structure.792 The orientation of a crvstal lattice varies from one domain to another., The orientation of a crystal lattice varies from one domain to another.793 The pinning strength decreases in the domain where the major axis of a crvstal lattice is not close to the vortex line., The pinning strength decreases in the domain where the major axis of a crystal lattice is not close to the vortex line.794 However. as long as the equilibrium vortex configurations are represented by (he kink solutions. pinning of a vortex line in a polverystalline structure would be still strong enough to explain the large elitches.," However, as long as the equilibrium vortex configurations are represented by the kink solutions, pinning of a vortex line in a polycrystalline structure would be still strong enough to explain the large glitches."795Each of these two methods is similar to dilfusion dy-means. but both have critical drawbacks.,"Each of these two methods is similar to diffusion $K$ -means, but both have critical drawbacks."796 works similarly to. cdilfusion A -moeans (Algorithm 1) except that A-means is performed. on the projection of the normalized SSP spectra into (PC) space. not dilfusion space.," works similarly to diffusion $K$ -means (Algorithm 1) except that $K$ -means is performed on the projection of the normalized SSP spectra into (PC) space, not diffusion space."797 For an example of the application of principal components analysis to SSP spectra see Ronen.Aragón-Salamanca&Lahay(1999)., For an example of the application of principal components analysis to SSP spectra see \citet{Ron1999}.798.. Phe main drawback to PC A-moeans is its assumption that the SSP spectra lie on a linear subspace of the original pLO? dimensional space., The main drawback to PC $K$ -means is its assumption that the SSP spectra lie on a linear subspace of the original $p\gtrsim 10^3$ dimensional space.799 If the SSPs actually lie on a non-linear manifold. then the A prototypes may poorly capture the intrinsic variation of the original SSPs because the non-linear structure will have been inappropriately collapsed on to a linear space by the principal components projection.," If the SSPs actually lie on a non-linear manifold, then the $K$ prototypes may poorly capture the intrinsic variation of the original SSPs because the non-linear structure will have been inappropriately collapsed on to a linear space by the principal components projection."800 is also similar to Algorithm 1. except that A-means is performed. in the original Ny= dimensional space: Le... no reduction in dimensionality is done before running A-means.," is also similar to Algorithm 1, except that $K$ -means is performed in the original $N_{\lambda}\simeq 10^3$ dimensional space; i.e., no reduction in dimensionality is done before running $K$ -means."801 Vhere are two obvious drawbacks to this procedure., There are two obvious drawbacks to this procedure.802 First. the algorithm generally is slow because distance computations are cumbersome in high dimensions and A -moeans usually takes more iterations to converge.," First, the algorithm generally is slow because distance computations are cumbersome in high dimensions and $K$ -means usually takes more iterations to converge."803 For comparison. the dimensionality of the spaces used by dilfusion and PC A-moeans are cach ©10. a [actor of 100 smaller than p.," For comparison, the dimensionality of the spaces used by diffusion and PC $K$ -means are each $\lesssim 10$, a factor of 100 smaller than $p$."804 Second. and more importantly. Uppropriate prototype spectra are. dillieult. to. find. by standard A -moeans because Euclidean distances. used by A-means to define clusters. are only physically meaningful over short distances.," Second, and more importantly, appropriate prototype spectra are difficult to find by standard $K$ -means because Euclidean distances, used by $K$ -means to define clusters, are only physically meaningful over short distances."805 Diffusion A -moeans avoids this problem by clustering in diffusion space. in which Euclidean distance i»proximates diffusion distance. à measure that has physical meaning on all scales.," Diffusion $K$ -means avoids this problem by clustering in diffusion space, in which Euclidean distance approximates diffusion distance, a measure that has physical meaning on all scales."806 The result is that standard. A -moeans inappropriately relates SSPs that are not physically similar., The result is that standard $K$ -means inappropriately relates SSPs that are not physically similar.807 In Fig. 3.," In Fig. \ref{prototZ},"808 we plot logZ versus log! for. Av —150 prototypes in Ανατ and cilfusion. standard. and. PC A-," we plot $\log Z$ versus $\log t$ for $K$ =150 prototypes in Asa07 and diffusion, standard, and PC $K$ -means."809 Notably. dillusion. A-moeans finds a much higher density of prototypes with high logZ or high log. rellecting the complicated manner in which SSPs with those properties vary with respect to Z and /.," Notably, diffusion $K$ -means finds a much higher density of prototypes with high $\log Z$ or high $\log t$, reflecting the complicated manner in which SSPs with those properties vary with respect to $Z$ and $t$."810 At the other extreme. the AsaQ7 prototypes reside on a regular grid. and thus include many prototvpe spectra that are essentially identical and also exclude prototypes that have unique spectral properties.," At the other extreme, the Asa07 prototypes reside on a regular grid, and thus include many prototype spectra that are essentially identical and also exclude prototypes that have unique spectral properties."811 The standard. and PC A-means. prototypes also. estimate more high logZ and high log/ prototvpes than a regular eid., The standard and PC $K$ -means prototypes also estimate more high $\log Z$ and high $\log t$ prototypes than a regular grid.812 The methods. introduced above use only the observable properties of SSPs to choose representative prototypes., The methods introduced above use only the observable properties of SSPs to choose representative prototypes.813 Lt mav be the case that we want to incorporate other information that we have about the SSPs ancl their relationship with the galaxies we are fitting., It may be the case that we want to incorporate other information that we have about the SSPs and their relationship with the galaxies we are fitting.814 For instance. we might know that a SSP with à particular age and metallicity is generally. found in the types of galaxies we are trying to fit. and hence will want to include in our basis a prototype with characteristics closely matching those of this SSP.," For instance, we might know that a SSP with a particular age and metallicity is generally found in the types of galaxies we are trying to fit, and hence will want to include in our basis a prototype with characteristics closely matching those of this SSP."815 This information can casily be incorporated with the framework introduced above by defining an weight. e;20 for cach SSP in our database. where higher weights signifv more importance of the SSP.," This information can easily be incorporated with the framework introduced above by defining an weight, $w_i \ge 0$ for each SSP in our database, where higher weights signify more importance of the SSP."816 ὃν moclifving the definition. of the cilfusion map ecometric centroid (7)) to be and altering the A-moeans algorithm to minimize insteac of V in (6)). we choose a basis that rellects both," By modifying the definition of the diffusion map geometric centroid \ref{centroid}) ) to be and altering the $K$ -means algorithm to minimize instead of $V$ in \ref{kmeans}) ), we choose a basis that reflects both"817models considered in this work.,models considered in this work.818 Consistently with what found in previous studies. at high redshifts ες~2.5) all the coupled dark energy models show a larger number of halos with respect to ACDM over the whole mass range covered by our numerical sample.," Consistently with what found in previous studies, at high redshifts $z\sim 2.5$ ) all the coupled dark energy models show a larger number of halos with respect to $\Lambda $ CDM over the whole mass range covered by our numerical sample."819 The enhancement in the halo number density reaches a factor of ~20 at AL~1.0.1013 M.//h for the most extreme standard coupled dark energy scenario. while the SUGRA cDE model shows an enhancement of a factor ~45 at the same mass.," The enhancement in the halo number density reaches a factor of $\sim 20$ at $M\sim 1.0\times 10^{14}$ $_{\odot}/h$ for the most extreme standard coupled dark energy scenario, while the SUGRA cDE model shows an enhancement of a factor $\sim 4-5$ at the same mass."820 Furthermore. the enhancement has a clear mass dependence and increases towards larger masses. suggesting that the effect might be significantly larger at masses not covered by the halo sample of our simulations.," Furthermore, the enhancement has a clear mass dependence and increases towards larger masses, suggesting that the effect might be significantly larger at masses not covered by the halo sample of our simulations."821 The subsequent evolution of the halo mass function clearly displays the fundamental difference between the standard coupled dark energy models based on a monotonic self-interaction potential and the bouncing coupled dark energy scenarios. as the SUGRA cDE proposed here.," The subsequent evolution of the halo mass function clearly displays the fundamental difference between the standard coupled dark energy models based on a monotonic self-interaction potential and the bouncing coupled dark energy scenarios, as the SUGRA cDE proposed here."822 At >~1.6. in fact. all the models still feature a significant excess of massive halos as compared to ACDM. although the SUGRA cDE model has reduced. its enhancement factor much more significantly than the other coupled dark energy models.," At $z\sim 1.6$, in fact, all the models still feature a significant excess of massive halos as compared to $\Lambda $ CDM, although the SUGRA cDE model has reduced its enhancement factor much more significantly than the other coupled dark energy models."823 Finally. at >=0 the SUGRA cDE model fully recovers the standard ACDM mass function over the whole mass range of our sample. while the other coupled dark energy models still show a large excess of massive halos. especially in the range of very massive galaxy clusters. being therefore potentially in tension with available constraint on the cluster number counts.," Finally, at $z=0$ the SUGRA cDE model fully recovers the standard $\Lambda $ CDM mass function over the whole mass range of our sample, while the other coupled dark energy models still show a large excess of massive halos, especially in the range of very massive galaxy clusters, being therefore potentially in tension with available constraint on the cluster number counts."824 This result. which represents the main outcome of the present paper. demonstrates for the first time by means of large and fully self-consistent N-body simulations that coupled dark energy models with a suitable choice of the self-interaction potential can simultaneously account for the detection of anomalously massive clusters at high redshifts and for the observed halo mass function at low redshifts.," This result, which represents the main outcome of the present paper, demonstrates for the first time by means of large and fully self-consistent N-body simulations that coupled dark energy models with a suitable choice of the self-interaction potential can simultaneously account for the detection of anomalously massive clusters at high redshifts and for the observed halo mass function at low redshifts."825 Such peculiar evolution could not arise in other types of models that have been recently invoked as a possible explanation of the unexpected detection of massive clusters at high redshifts. as non-Gaussian cosmological scenarios. where an enhanced number density of halos at high redshifts necessarily implies a corresponding enhancement at low redshifts.," Such peculiar evolution could not arise in other types of models that have been recently invoked as a possible explanation of the unexpected detection of massive clusters at high redshifts, as non-Gaussian cosmological scenarios, where an enhanced number density of halos at high redshifts necessarily implies a corresponding enhancement at low redshifts."826" To conclude. we have studied a new class of interacting dark energy cosmologies characterized by a ""bounce"" of the dark energy scalar field that is allowed to invert its direction of motion during the cosmic expansion."," To conclude, we have studied a new class of interacting dark energy cosmologies characterized by a “bounce"" of the dark energy scalar field that is allowed to invert its direction of motion during the cosmic expansion."827 We have shown by means of linear and nonlinear numerical treatments that this new class of models could be simultaneously consistent with observational constraints at CMB and at the present epoch. while allowing for significant deviations from the standard ACDM scenario at intermediate redshifts.," We have shown by means of linear and nonlinear numerical treatments that this new class of models could be simultaneously consistent with observational constraints at CMB and at the present epoch, while allowing for significant deviations from the standard $\Lambda $ CDM scenario at intermediate redshifts."828 In particular. we have shown this class of models to possess the (so far) unique feature of simultaneously accounting for unexpected detections of very massive clusters at high redshifts and for the standard cluster abundance at the present time.," In particular, we have shown this class of models to possess the (so far) unique feature of simultaneously accounting for unexpected detections of very massive clusters at high redshifts and for the standard cluster abundance at the present time."829 Such behavior is a direct consequence of a non-trivial dynamics of dark energy at relatively recent cosmological epochs. and therefore represents a specitic observational signature of a possible dynamical origin of the accelerated expansion of the Universe.," Such behavior is a direct consequence of a non-trivial dynamics of dark energy at relatively recent cosmological epochs, and therefore represents a specific observational signature of a possible dynamical origin of the accelerated expansion of the Universe."830" This work has been supported by the DFG Cluster of Excellence “Origin and Structure of the Universe"" and by the TRR33 Transregio Collaborative Research Network on the ""Dark Universe"".", This work has been supported by the DFG Cluster of Excellence “Origin and Structure of the Universe” and by the TRR33 Transregio Collaborative Research Network on the “Dark Universe”.831 I am deeply thankful to Valeria Pettorino for useful discussions on the models., I am deeply thankful to Valeria Pettorino for useful discussions on the models.832 All the numerical simulations have been performed on the Power6 cluster at the RZG computing centre in Garching., All the numerical simulations have been performed on the Power6 cluster at the RZG computing centre in Garching.833Tn Figure 2. we show f(>:) together with the cüffereutial distribution (df/d:) for the two star formation histories of Figure 1.,"In Figure 2, we show $f(>z)$ together with the differential distribution $({\rm d}f/{\rm d} z)$ for the two star formation histories of Figure 1."834 It is evideut that a significant fraction of all bursts is predicted to occur at hüiehli redshifts. niuncly Fl.=5)>50%. and that a few percent of all bursts occur at redshifts as lich as +—20.," It is evident that a significant fraction of all bursts is predicted to occur at high redshifts, namely $f(z\ge 5)\ga 50\%$, and that a few percent of all bursts occur at redshifts as high as $z\sim 20$."835 Evaluating the mean redshift for GRBs using the distributions of Figure 2. we find 2~5 in the case of atomic cooling and +~& for molecular cooling.," Evaluating the mean redshift for GRBs using the distributions of Figure 2, we find $\bar{z}\sim 5$ in the case of atomic cooling and $\bar{z}\sim 8$ for molecular cooling."836 Cirrently. only ~20 bursts have known redshifts (kulkarni et al.," Currently, only $\sim 20$ bursts have known redshifts (Kulkarni et al."837 x2000: Djorgovski et al., 2000; Djorgovski et al.838 20016: (ακοή 2001). and we include this simall observed sauiple in Figure 2.," 2001c; Ghisellini 2001), and we include this small observed sample in Figure 2."839 The fact that the data points lie below our theoretical prediction could be due to sinall-umubor statistics as well as due to a redshiftdependent incompletcuess bias., The fact that the data points lie below our theoretical prediction could be due to small-number statistics as well as due to a redshift–dependent incompleteness bias.840 Wo stress that equation (2) cives the fraction of trausieut events observed ou the sky. aud not the fraction of all baryous that have been incorporated ito stars by a redshift 2 relative to the same fraction today.," We stress that equation (2) gives the fraction of transient events observed on the sky, and not the fraction of all baryons that have been incorporated into stars by a redshift $z$ relative to the same fraction today."841 This latter quautity is elven by and is shown iu Figure 2 for the case of atomic cooling., This latter quantity is given by and is shown in Figure 2 for the case of atomic cooling.842 As can be seen. the fraction of all stars that are formed at iom Sis~I5.," As can be seen, the fraction of all stars that are formed at $z\ga 5$ is $\sim 15$."843 Tt is iuportant to eimipliasize that the analysis presentec here pertains toal bursts. regardless of whether existing or previous instruments have actually been able to detect them.," It is important to emphasize that the analysis presented here pertains to bursts, regardless of whether existing or previous instruments have actually been able to detect them."844" If the horizon of previous iustrumieuts was limited to 24, then our predictions provide important motivation for the coustruction of more-scusitive mstrunents that would triggerao on GRBs out to the highest redshifts."," If the horizon of previous instruments was limited to $z\ll 5$, then our predictions provide important motivation for the construction of more-sensitive instruments that would trigger on GRBs out to the highest redshifts."845 The fraction of all bursts that were detected by any even dustrunient depends on the /iustrunent-spoecitic flux seusitivitv threshold aud ou the poorly-deterimined huninosity function (LF) of GRBs (see e.g.. Schacter. Dene. Daud 2001: Schiuidt 2001: Norris 2002).," The fraction of all bursts that were detected by any given instrument depends on the instrument-specific flux sensitivity threshold and on the poorly-determined luminosity function (LF) of GRBs (see e.g., Schaefer, Deng, Band 2001; Schmidt 2001; Norris 2002)."846 It is nevertheless iustructive to ascertain what existiug or planned Παςποιές like DATSE audSwift ave expected to fud., It is nevertheless instructive to ascertain what existing or planned instruments like BATSE and are expected to find.847 To this extent. we modify the CRB event rate to have Tere. pCL) is the GRB LF with £ being the intrinsic photon huninosity (in units ofphotouss 1).," To this extent, we modify the GRB event rate to have Here, $p(L)$ is the GRB LF with $L$ being the intrinsic photon luminosity (in units of photons $^{-1}$ )."848" Lf fij, denotes the sensitivity threshold of a eiven instrument Gu photons ston P? ). then ΕΕmnΠΕ luminosity.+ is+ This expression is derived with a spectral index of à=2 for Lxrv"" (Band ot al."," If $f_{\rm lim}$ denotes the sensitivity threshold of a given instrument (in photons $^{-1}$ $^{-2}$ ), then the minimum luminosity is This expression is derived with a spectral index of $\alpha=2$ for $L\propto849\nu^{-\alpha}$ (Band et al."850 1993)., 1993).851 For definiteness. we assunie a loe-norimal distribution functiou (e.g... Woods Loeb 1995) where σ and Ly are the width aud the average huninosity. respectively.," For definiteness, we assume a log-normal distribution function (e.g., Woods Loeb 1995) where $\sigma$ and $L_{0}$ are the width and the average luminosity, respectively."852" Receutlv. Sethi Bhareavi (2001) have shown that both the observed number couutflux relation as well as the existing afterelow redshift data are consistent with a log-normal LF for best-fit paramcters (taking iuto account the effect of beaming): v»=2 and Ly=2< los1, and we adopt these values in the following analysis."," Recently, Sethi Bhargavi (2001) have shown that both the observed number count–flux relation as well as the existing afterglow redshift data are consistent with a log-normal LF for best-fit parameters (taking into account the effect of beaming): $\sigma=2$ and $L_{0}=2\times85310^{56}$ $^{-1}$, and we adopt these values in the following analysis."854 To determine the expected redshift distribution as observed by BATSE andSwift. we use equation (2) together with the CRB rate eiven in equation (7).," To determine the expected redshift distribution as observed by BATSE and, we use equation (2) together with the GRB rate given in equation (7)."855" The fiux thresholds are fi,=0.2 and 0.01 photous s1 ? for DATSE andSwift. respectively (Lam Reichart 2000. and references therein)."," The flux thresholds are $f_{\rm lim}=0.2$ and 0.04 photons $^{-1}$ $^{-2}$ for BATSE and, respectively (Lamb Reichart 2000, and references therein)."856 In Figure 3. we show the same quantities as in Figure 2. but now comparing the distributions for DATSE audSwift with our theoretical prediction for atomic lue cooling.," In Figure 3, we show the same quantities as in Figure 2, but now comparing the distributions for BATSE and with our theoretical prediction for atomic line cooling."857 It can be seen that in the case of BATSE a fraction of f(.>z104 of all bursts originates from high redshifts. whereas the corresponding fraction forο is f(-ν ," It can be seen that in the case of BATSE a fraction of $f(z\ge 5)\ga 10$ of all bursts originates from high redshifts, whereas the corresponding fraction for is $f(z\ge 5)\ga 25$ ."858We cmphasize again that these nunibers are uncertain due to the poorly-kuown CRB LF., We emphasize again that these numbers are uncertain due to the poorly-known GRB LF.859 Figure 3 micely demonstrates the asviuptotic character of our heoretical prediction. pertaining to a future “ultimately-sensitive’ instrument.," Figure 3 nicely demonstrates the asymptotic character of our theoretical prediction, pertaining to a future `ultimately-sensitive' instrument."860 Tuceed. using the LF above. we estimate that an dustrunent with a seusitivity of ~50 nues better thanSwift would be able to detect the full heoretically-possible szuuple of bursts from zz5.," Indeed, using the LF above, we estimate that an instrument with a sensitivity of $\sim 50$ times better than would be able to detect the full theoretically-possible sample of bursts from $z\ga 5$."861" The detectability of :z5 GRBs is also a crucial ingredient iu estinatius the fraction of all well-localized musts that have uo detectable optical afterelow. the so-called ""dark GRBs""."," The detectability of $z\ga 5$ GRBs is also a crucial ingredient in estimating the fraction of all well-localized bursts that have no detectable optical afterglow, the so-called “dark GRBs”."862 Various authors have used the raction of dark bursts in the currently observed sample of GRBs to coustrain the amount of dust obscured star formation (e.g... Djorgovski et al.," Various authors have used the fraction of dark bursts in the currently observed sample of GRBs to constrain the amount of dust obscured star formation (e.g., Djorgovski et al."863 2001b)., 2001b).864 The resulting fraction of dark GRBs estimated for differcut redshifts depends on the. presently unknown. level of incompleteness in the observed sample.," The resulting fraction of dark GRBs estimated for different redshifts depends on the, presently unknown, level of incompleteness in the observed sample."865 Iu the context. of, In the context of866phenomenological approach to understanding the assembly of SALBUs involves optical data from both high and low redshifts.,phenomenological approach to understanding the assembly of SMBHs involves optical data from both high and low redshifts.867 These data are used as a starting point to construct à consistent picture that fits within the larger framework of the erowth ancl evolution of structure in the Universe (727?7?7)..," These data are used as a starting point to construct a consistent picture that fits within the larger framework of the growth and evolution of structure in the Universe \citep{haehnelt98,haiman98,kauffmann00,kauffmann02,wyithe02,volonteri03,dimatteo03}."868 Current modeling is grounded in the framework of the standard: paradigm that involves the erowth of structure via gravitational amplification of small perturbations in a CDAL Universea model that has independent. validation. most recently from (AWALAP) measurements of the anisotropies in the cosmic microwave background (22)..," Current modeling is grounded in the framework of the standard paradigm that involves the growth of structure via gravitational amplification of small perturbations in a CDM Universe—a model that has independent validation, most recently from (WMAP) measurements of the anisotropies in the cosmic microwave background \citep{spergel03,page03}."869 Structure formation is tracked in cosmic time by keeping a census of the number of collapsed clark matter halos of a given mass that form: these »ovide the sites for harboring black holes., Structure formation is tracked in cosmic time by keeping a census of the number of collapsed dark matter halos of a given mass that form; these provide the sites for harboring black holes.870 Phe computation of the mass Function of dark matter halos is done using either he Press-Schechter (2). or the extended: Press-Schechter heory (?).. or Monte-Carlo. realizations of merger trees (777) or. in some cases. directly [rom cosmological N-body simulations (7?)..," The computation of the mass function of dark matter halos is done using either the Press-Schechter \citep{press74} or the extended Press-Schechter theory \citep{lacey93}, or Monte-Carlo realizations of merger trees \citep{kauffmann00,volonteri03,bromleysomerville04} or, in some cases, directly from cosmological N-body simulations \citep{dimatteo03,dimatteo05}."871 In particular ? have presented a detailed: merger-t rmasecl scenario to trace the growth of black holes from theree earliest epochs to the present day., In particular \citet{volonteri03} have presented a detailed merger-tree based scenario to trace the growth of black holes from the earliest epochs to the present day.872 Monte-Carlo merger trees are created for present day halos and. propagatecl back in ime to a redshift of ~ 20., Monte-Carlo merger trees are created for present day halos and propagated back in time to a redshift of $\sim$ 20.873 With the merging history thus determined. the initial halos at z20 are then populated with seed black holes whieh are assumed. to be remnants of the first stars that form in the Universe.," With the merging history thus determined, the initial halos at $z \sim 20$ are then populated with seed black holes which are assumed to be remnants of the first stars that form in the Universe."874 The masses of these so-called. Population HIE stars are not accurately known. however numerical simulations by various. groups (77) suggest that they are skewed to high masses of the order of a few hundred: solar masses.," The masses of these so-called Population III stars are not accurately known, however numerical simulations by various groups \citep{abel00,bromm02} suggest that they are skewed to high masses of the order of a few hundred solar masses."875 Seeded with the end ooducts of this first population. the merger sequence is ollowecd and black holes are assumed to grow with every major merecr episode.," Seeded with the end products of this first population, the merger sequence is followed and black holes are assumed to grow with every major merger episode."876 An accretion episode is assumed to occur às a consequence of every merger. event., An accretion episode is assumed to occur as a consequence of every merger event.877 Following he growth and mass assembly. of these. black holes. it is required that the model is in consonance with the observed ocal Apg—c relation.," Following the growth and mass assembly of these black holes, it is required that the model is in consonance with the observed local $M_{\rm BH} - \sigma$ relation."878 The luminosity function of quasars is predicted. by these models and. can. be compared. to observations., The luminosity function of quasars is predicted by these models and can be compared to observations.879 Volonteri et. al., Volonteri et al.880 fine that not every halo at vigh redshift needs to be populated with a black hole seed in order to satisly the observational constraints at z=0., find that not every halo at high redshift needs to be populated with a black hole seed in order to satisfy the observational constraints at $z = 0$.881 These models do not automatically reproduce the required abundance of supermassive black holes. inferred to power the observed 2>6 SDSS quasars., These models do not automatically reproduce the required abundance of supermassive black holes inferred to power the observed $z > 6$ SDSS quasars.882 In order to match the observation ancl produce SAIBLISs roughly 1: Gar after the Big Bang. it is required that black holes undergo brief. but extremely strong growth episodes during which the accretion rate onto them is well in excess of the Exldington rate (?2)..," In order to match the observation and produce SMBHs roughly 1 Gyr after the Big Bang, it is required that black holes undergo brief, but extremely strong growth episodes during which the accretion rate onto them is well in excess of the Eddington rate \citep{volonteri05b,begelman06}."883 Lt is the existence of these SMDBlIIS powering quasars at z26 that has prompted work on alternate channels to explain their mass build-up., It is the existence of these SMBHs powering quasars at $z > 6$ that has prompted work on alternate channels to explain their mass build-up.884 In order to alleviate the problem of explaining the existence of SMDBlIIs in place by 2~6. roughly 1 vr alter the Bie Bang. in this paper we examine the possibility of using a well motivated. high. redshift seed black hole mass function as the initial black hole population at the highest redshifts.," In order to alleviate the problem of explaining the existence of SMBHs in place by $z \sim 6$, roughly 1 Gyr after the Big Bang, in this paper we examine the possibility of using a well motivated high redshift seed black hole mass function as the initial black hole population at the highest redshifts."885 We investigate the clleet of populating carly dark matter halos with massive black hole seeds. preclieted in a mocel proposed by ??..," We investigate the effect of populating early dark matter halos with massive black hole seeds predicted in a model proposed by \citet{LN06,LN07}. ."886Phis model predicts a mass function or black holes that results from the direct. collapse of pre-galactic gas disces., This model predicts a mass function for black holes that results from the direct collapse of pre-galactic gas discs.887 We study the implications of the use of his seed mass function versus that of the Population LLL remnants. in particular the difference in predictions at Ξ0 or the massive seed mocdoels.," We study the implications of the use of this seed mass function versus that of the Population III remnants, in particular the difference in predictions at $z = 0$ for the massive seed models."888 In Section 2. we briellv outline he high redshift DII seed. formation. model. in Section 3 we evolve this model with redshift using the merger-tree ormalism. developed. by 2..," In Section 2, we briefly outline the high redshift BH seed formation model, in Section 3 we evolve this model with redshift using the merger-tree formalism developed by \citet{volonteri03}."889 The results are. presented. in section +4. followed by a discussion. of implications in the inal section.," The results are presented in Section 4, followed by a discussion of implications in the final section."890 In this paper. we track the formation of seed black holes in an ab-initio model and follow their mass assembly down to >=0.," In this paper, we track the formation of seed black holes in an ab-initio model and follow their mass assembly down to $z = 0$."891 This is done in two separate phases - starting with the high redshift seeds and tracing their subsequent growth., This is done in two separate phases - starting with the high redshift seeds and tracing their subsequent growth.892 At high redshift (z215). we assume the intergalactic medium has not been significantly enriched by metals. and therefore the eas cooling timescales are long.," At high redshift $z>15$ ), we assume the intergalactic medium has not been significantly enriched by metals, and therefore the gas cooling timescales are long."893 Under these conditions. many authors (?7?7) have shown that pre-galactic discs can cllicicnthy transport matter into their innermost regions through the development and. amplification of non-axisvmmetric gravitational instabilities. offen without fragmentation and star formation taking place (see below).," Under these conditions, many authors \citep{koushiappas04,begelman06,LN06,LN07}894 have shown that pre-galactic discs can efficiently transport matter into their innermost regions through the development and amplification of non-axisymmetric gravitational instabilities, often without fragmentation and star formation taking place (see below)."895 This is the main seed formation phase. wherein massive seeds with ALzz10710A4. can form.," This is the main seed formation phase, wherein massive seeds with $M\approx89610^5-10^6M_{\odot}$ can form."897" At lower redshifts. cooling becomes more ellicient and we assume that further accretion occurs via a ""merger driven scenario. described in more detail in Section 3."," At lower redshifts, cooling becomes more efficient and we assume that further accretion occurs via a `merger driven scenario' described in more detail in Section 3."898 In this section we provide simple. analytical estimates of the amount of mass that we expect o be assembled in the form of massive DII seeds. based on he above scenario. as a function of the key dark matter halo xwanmeters.," In this section we provide simple, analytical estimates of the amount of mass that we expect to be assembled in the form of massive BH seeds, based on the above scenario, as a function of the key dark matter halo parameters."899 Here we refer in particular to the model by 2.. who considered the evolution of pre-galactic disesby self-consistently taking into account gravitational stability anc ragmentation. thereby providing a detailed inventory of the ate of the gas.," Here we refer in particular to the model by \citet{LN06}, who considered the evolution of pre-galactic discsby self-consistently taking into account gravitational stability and fragmentation, thereby providing a detailed inventory of the fate of the gas."900 Consider a dark matter halo of mass Al ancl viria enperature Zi. Containing gas mass Af=mad (we also assume that the barvon fraction is roughly implying my= 0.05). of primordial composition. i.e. gas not enrich o» metals. for which the cooling function. is dominate w hwdrogen.," Consider a dark matter halo of mass $M$ and virial temperature $T_{\rm901vir}$, containing gas mass $M_{\rm gas}=m_{\rm d}M$ (we also assume that the baryon fraction is roughly implying $m_{\rm d}=0.05$ ), of primordial composition, i.e. gas not enriched by metals, for which the cooling function is dominated by hydrogen."902" The other main parameter characterizing a dark matter halo that is relevant to the fate of the gas is ls spin parameter A (=AyE,.GALs where J), is the otal angular momentum and £), is the binding energy)"," The other main parameter characterizing a dark matter halo that is relevant to the fate of the gas is its spin parameter $\lambda$ $\equiv J_h E_h^{1/2}/903GM_h^{5/2}$, where $J_h$ is the total angular momentum and $E_h$ is the binding energy)."904" The distribution of spin parameters for dark matter halos measured in numerical simulations is well fit by a lognormal distribution in Asi. with mean Aii,=0.05 and standard deviation e=0.5: This function has been shown to provide a good fit to the N-bocly results of several investigations (e.g.. 2277))."," The distribution of spin parameters for dark matter halos measured in numerical simulations is well fit by a lognormal distribution in $\lambda_{\rm spin}$, with mean $\bar \lambda_{\rm spin}=0.05$ and standard deviation $\sigma_\lambda=0.5$: This function has been shown to provide a good fit to the N-body results of several investigations (e.g., \citealt{warren92,cole96,bullock01,bosch02}) )."905 If the virial temperature of the halo Zu sus the gas collapses and forms a rotationally supported. clisc.," If the virial temperature of the halo $T_{\rm vir}>T_{\rm gas}$ , the gas collapses and forms a rotationally supported disc."906 For low values of the spin parameter A the resulting disc can be compact ancl dense ancl issubject to gravitational, For low values of the spin parameter $\lambda$ the resulting disc can be compact and dense and issubject to gravitational907The virial theorem shows that a star deprived of any euergv sources will slits aud its kinetic energy will erow which normally implies it will eet hotter.,The virial theorem shows that a star deprived of any energy sources will shrink and its kinetic energy will grow which normally implies it will get hotter.908 In the 1920's Eddineton (1926) was puzzled as to how a star could ever cool down aud end its life., In the 1920's Eddington (1926) was puzzled as to how a star could ever cool down and end its life.909 This problem. together with the mystery of white cdawarts such as Sirius D. was beautifully solved bx BR. IL. Fowler (1926) who realised that the clectrous would become degenerate. as in a metal. so the star could then be supported by the degeneracy pressure which is an inevitable cousequeuce ofthe zero-point energy combined with the Pauli exclusion principle.," This problem, together with the mystery of white dwarfs such as Sirius B, was beautifully solved by R. H. Fowler (1926) who realised that the electrons would become degenerate, as in a metal, so the star could then be supported by the degeneracy pressure which is an inevitable consequence of the zero-point energy combined with the Pauli exclusion principle."910 Even bodies of zero temperature have such a pressure which supports the white dwarfs against eravity., Even bodies of zero temperature have such a pressure which supports the white dwarfs against gravity.911 Stoner (1929) mace early models of white cavarts to coupare their densities with the theory but Audersou (1929) rightlv criticised lim for not :dlowiug for the rclativistic motions of electrous forced to very high deusities., Stoner (1929) made early models of white dwarfs to compare their densities with the theory but Anderson (1929) rightly criticised him for not allowing for the relativistic motions of electrons forced to very high densities.912 Πο showed that when this was allowed for. there would be a limiting mass beyond which no cold white dwarf models could exist.," He showed that when this was allowed for, there would be a limiting mass beyond which no cold white dwarf models could exist."913 Tis estimate of the mniΠιο mass was not vorv good. but Stoner (1930) then modified his own calculations aud. calculated the Iit for homogencous models which eave au auswer «eoodL to©," His estimate of the limiting mass was not very good, but Stoner (1930) then modified his own calculations and calculated the limit for homogeneous models which gave an answer good to."914 Meamwhile. Chandrasclhar {L931) had devolo]xxl the theory independently starting frou Fowler's work.," Meanwhile, Chandrasekhar (1931) had developed the theory independently starting from Fowler's work."915 He realised that the linütius coiieuration wouk be au 9=3 polvtrope aud gave the first accurate determination of the Chandrasclshay linuit., He realised that the limiting configuration would be an $n=3$ polytrope and gave the first accurate determination of the Chandrasekhar limit.916 Alore detailed models of white dwar* were eivon by Salpeter (1967) who derived conditions for their solidification aud determined properties of the lattice., More detailed models of white dwarfs were given by Salpeter (1967) who derived conditions for their solidification and determined properties of the lattice.917 Shapiro and Teukolsky in their book give a definitive account of how all this extends to neuron stars., Shapiro and Teukolsky in their book give a definitive account of how all this extends to neutron stars.918(e.g.. Grindlay1993;Kundu.\laecarone.&Zepf 2002)).,"(e.g., \citealt{grind93,kund02}) )."919 Also. there is a preponderance for clusters hosting LAINBs to lie within 4 kpc of the center of the Milky Way (Figure 5).," Also, there is a preponderance for clusters hosting LMXBs to lie within 4 kpc of the center of the Milky Way (Figure 8)."920 This mav be due to the tidal influence of the bulge causing the bulee population of clusters to evolve more rapidly., This may be due to the tidal influence of the bulge causing the bulge population of clusters to evolve more rapidly.921 Alternatively. this bulge cluster population may simply have formed more compact svstenis initially.," Alternatively, this bulge cluster population may simply have formed more compact systems initially."922 These results are interpreted within the context of models. which have advanced greatly in (he last decade. but are not vet complete in the sense of having a cstandard model to use.," These results are interpreted within the context of models, which have advanced greatly in the last decade, but are not yet complete in the sense of having a “standard model” to use."923 Consequently. we will interpret our results in terms of the generic features of present models. relving most heavily on (hose of Fregeauetal.(2003).. and in particular. those with King proliles (Wy= 7).," Consequently, we will interpret our results in terms of the generic features of present models, relying most heavily on those of \citet{freg03}, and in particular, those with King profiles $_{{\rm 0}}$ = 7)."924 These models include binaries with dillerent amounts of initial binary fractions from and they caleulate the time variation of various binary properties. such as their destruction and their hardness distribution.," These models include binaries with different amounts of initial binary fractions from and they calculate the time variation of various binary properties, such as their destruction and their hardness distribution."925" These models show that as the cluster evolves dynamically, (he binaries are hardened. (auc destroved). a process that delays core collapse."," These models show that as the cluster evolves dynamically, the binaries are hardened (and destroyed), a process that delays core collapse."926 The binary fraction decreases (but hardens) by about half in LO-20 (444 lies. which we consider a characteristic time.," The binary fraction decreases (but hardens) by about half in 10-20 $_{{\rm h,relax}}$ times, which we consider a characteristic time."927 This implies that when tyreas 10? vr. the cluster has significantly modified the initial binary population. possibly causing close binaries (hat form into LAINBs. in general agreement with our findings.," This implies that when $_{{\rm h,relax}}$ $\lesssim$ $^{{\rm 9}}$ yr, the cluster has significantly modified the initial binary population, possibly causing close binaries that form into LMXBs, in general agreement with our findings."928 The initial predictor of close binary formation from the rate of binary collisions should then be modified by the time needed [or a cluster to begin evolving. relative to ils age.," The initial predictor of close binary formation from the rate of binary collisions should then be modified by the time needed for a cluster to begin evolving, relative to its age."929 The original rate (proportional to re might be modified by a term such as )]- where jj zz 5-10.," The original rate (proportional to $r_{h}^{2.5}$ might be modified by a term such as )), where $\eta$ $\approx$ 5-10."930 Provided that the cluster does not become disrupted. (he number of binaries eventually decreases to the level at which it can no longer prevent core collapse (about binary fraction).," Provided that the cluster does not become disrupted, the number of binaries eventually decreases to the level at which it can no longer prevent core collapse (about binary fraction)."931 The core collapses and oscillates even as rj hardly changes (e.g.. the binary fraction model of Fregeau).," The core collapses and oscillates even as $_{{\rm h}}$ hardly changes (e.g., the binary fraction model of Fregeau)."932 During this process. some binaries still exist ancl are extremely hard and therefore likely to become mass transler svstems during the course of stellar evolution.," During this process, some binaries still exist and are extremely hard and therefore likely to become mass transfer systems during the course of stellar evolution."933 At these high densities. direct collisions between neutron stars ancl τοῦ giants can produce LMXDs as well (Ivanovaetal.2005).," At these high densities, direct collisions between neutron stars and red giants can produce LMXBs as well \citep{ivan05}."934". llalf of the LAINB clusters are designated as core collapse svstems (compare to one-fifth for the non-LMXD clusters). where the definition of a core collapse object is that it has a power-law optical surface brightness distribution into the center with no apparent core radius (Lor objects labeled as ""possible core collapse’. it is difficult to be certain of the power-law"," Half of the LMXB clusters are designated as core collapse systems (compare to one-fifth for the non-LMXB clusters), where the definition of a core collapse object is that it has a power-law optical surface brightness distribution into the center with no apparent core radius (for objects labeled as “possible core collapse”, it is difficult to be certain of the power-law"935of 20.0 Jyο,of 20.0 Jy.936", For KK98 251. the iuteerated flux is 10.6+1.0 Jvον, the systemic velocity is 130.2+ stand Wsy is 51.7+18b."," For KK98 251, the integrated flux is $10.6\pm 1.0$ Jy, the systemic velocity is $130.2\pm1.7$ and $_{50}$ is $51.7\pm1.8$."937 Again. the systolic velocity is iu reasonable agreement with the value of 126.042.0 lobtaiued from single dis[um observations (IIuchtiucierctal. 1997)). but the integrated Hix aud Wo are considerably smaller than the single dis[um values of1 1L6 Jv tand 6L0 respectively.," Again, the systemic velocity is in reasonable agreement with the value of $126.0 \pm2.0$ obtained from single dish observations \cite{hucht97}) ), but the integrated flux and $_{50}$ are considerably smaller than the single dish values of 14.6 Jy and $64.0$ respectively."938 The GMBT ftuxes could be lower than those obtained roni single dish measurements either )ocause of (d) a calibration error or (11) a large fraction of the III being in an extended distribution that is resolved out., The GMRT fluxes could be lower than those obtained from single dish measurements either because of (i) a calibration error or (ii) a large fraction of the HI being in an extended distribution that is resolved out.939 However. he flux of the poiut sources secu in the CAIRT image are in good agreement with those listed in NVSS. indicating hat our calibration is not at fault.," However, the flux of the point sources seen in the GMRT image are in good agreement with those listed in NVSS, indicating that our calibration is not at fault."940 Further. from our vast experience in III imagine of galaxies (with sizes siuilar to ΠΙΟΣ 250 aud KIN98 251) with the CAIRT. it secs unlikely that we have resolved out a large raction of the total flux.," Further, from our past experience in HI imaging of galaxies (with sizes similar to KK98 250 and KK98 251) with the GMRT, it seems unlikely that we have resolved out a large fraction of the total flux."941 Interestingly. a large discrepancy vetween the interferometric fluxes and the single dish fluxes was also secu in the DRAO images of these galaxies (Pisano&Wilcots2000) ). although the comparison iu hat case is complicated by the very poor signal to noise ratio of the DRAO data.," Interestingly, a large discrepancy between the interferometric fluxes and the single dish fluxes was also seen in the DRAO images of these galaxies \cite{pisano00}) ), although the comparison in that case is complicated by the very poor signal to noise ratio of the DRAO data."942 Finally. we uote that for both the ealaxies there is a strong local HIT cinission at velocities very close to the systemic velocities.," Finally, we note that for both the galaxies there is a strong local HI emission at velocities very close to the systemic velocities."943 Ieuce. it is likely that the sinele dish inteerated flux measurenients were contaminated by bleuding of the TT cussion from the ealaxies with that of the galactic ciission due to bot[um the coarse velocity resolution (10.0. ο as well as nmuperfeet subtraction of the foreground. emission iu the position switching mode used iu those observations.," Hence, it is likely that the single dish integrated flux measurements were contaminated by blending of the HI emission from the galaxies with that of the galactic emission due to both the coarse velocity resolution $\sim$ 10.0 ), as well as imperfect subtraction of the foreground emission in the position switching mode used in those observations."944 If we asstune that the total fluxes are those measured at the GMBRT. then the IIT mass of IKI&98 250 is aud Min/Ly~12.," If we assume that the total fluxes are those measured at the GMRT, then the HI mass of KK98 250 is and $\rm{M_{\rm{HI}}/L}_{\rm{B}}\sim 1.2$."945 For KK98 251. the corresponding umubers are 7.8EOF«105AL. αμα 1.6.," For KK98 251, the corresponding numbers are $7.8\pm0.7 \times{10}^{7}~\rm{M_\odot}$ and $1.6$ ."946 Fig., Fig.947" 2 shows the iutegrated III cussion from KI&98 250 aud ντος 251 at 26""421"" resolution. overlaved ou the digitized sky survey (DSS) nuage."," \ref{fig:ov} shows the integrated HI emission from KK98 250 and KK98 251 at $''\times21''$ resolution, overlayed on the digitized sky survey (DSS) image."948 Although ος 250 may be mildly warped. there is no clear signature of interaction between the two galaxies.," Although KK98 250 may be mildly warped, there is no clear signature of interaction between the two galaxies."949 For KIx98 251. two lugh density peaks are seen near the center.," For KK98 251, two high density peaks are seen near the center."950" Ax estimate of the morphological ceuter. position angle (PA) anc inclination (assuming an intrinsic thickuess ratio qy=0.2) of the galaxies were obtained by fitting elliptical aunuli o the 137&38"", 26""21"" and 16”«11"" resolution iuteerated IIT column density maps."," An estimate of the morphological center, position angle (PA) and inclination (assuming an intrinsic thickness ratio $q_0 = 0.2$ ) of the galaxies were obtained by fitting elliptical annuli to the $''\times38''$, $''\times21''$ and $''\times14''$ resolution integrated HI column density maps."951" For Ίος 250. the inclination aud PA were ound to be 80c£1 aud 267+3 deerees respectively,"," For KK98 250, the inclination and PA were found to be $80\pm 4$ and $267\pm3$ degrees respectively."952" Due to the high deusity clamps iu the ceuter. ellipse fitting for KI&98 25] was restricted to the outer coutours of the 133a aud 26421"" resolution images."," Due to the high density clumps in the center, ellipse fitting for KK98 251 was restricted to the outer contours of the $''\times38''$ and $''\times21''$ resolution images."953 The inclination and PA of the IT disk were found to be 62£4 and 220+5 degrees respectively., The inclination and PA of the HI disk were found to be $62\pm 5$ and $220\pm5$ degrees respectively.954 For cach ealaxy. the value of the PA aud inclination estimated frou different. resolution iuages match within the error bars.," For each galaxy, the value of the PA and inclination estimated from different resolution images match within the error bars."955 For KI&98 250. the estimated parameters are also i good aereemoeut with the values obtained from the optical nuage.," For KK98 250, the estimated parameters are also in good agreement with the values obtained from the optical image."956 Another input that we require for estimating the pressure support of the III disk is the deprojected III radial surface deusitv profile., Another input that we require for estimating the pressure support of the HI disk is the deprojected HI radial surface density profile.957 For highly inclined ealaxies. deprojection using ellipse fittingdoes not lead to reliable estimates for the surface deusitv.," For highly inclined galaxies, deprojection using ellipse fittingdoes not lead to reliable estimates for the surface density."958 Hence. in the case of," Hence, in the case of"959" οἱLac20.3 οταν 2155.BOL +-rav-loud 5-rav‘bias 5-rav οταν a,=0,710.50. 5-ray. ταν ee -rav ", $E>$ $\gamma$ $2155-304$ $\gamma$ $\gamma$ $\gamma$ $\gamma$ $\alpha_{rx}=0.74<0.80$ $\gamma$ $\gamma$ $\gamma$ 960 The results are plotted in Figure 3..., The results are plotted in Figure \ref{fig:err}.961 Firstly. it should bο noted that the fits to spin frequency and. frequency derivaive were by far the most alfected by the GWB as can be xcon in ‘Tables 1. and 2..," Firstly, it should be noted that the fits to spin frequency and frequency derivative were by far the most affected by the GWB as can be seen in Tables \ref{tab:0437} and \ref{tab:1713}."962 However. these parameters are not potted here as this is expected since the spin frequency. and requencey derivative it out a linear trend. and. a (quadratic trend respectively. hereby absorbing the lowest frequency (highest power) part of the GWD spectrum.," However, these parameters are not plotted here as this is expected since the spin frequency and frequency derivative fit out a linear trend and a quadratic trend respectively, thereby absorbing the lowest frequency (highest power) part of the GWB spectrum."963 We see. that the orbital period derivative. £4. is allected more for PSt J1713]0747 than or PSR 04374715.," We see that the orbital period derivative, $\dot{P}_{\rm b}$, is affected more for PSR J1713+0747 than for PSR J0437–4715."964 This is likely due to the cillerence of orbital periods for these pulsars (5.7 ancl 67.8 days for SR J04374715 and PSR. J1713|0747. respectively).," This is likely due to the difference of orbital periods for these pulsars (5.7 and 67.8 days for PSR J0437–4715 and PSR J1713+0747, respectively)."965 The arecr orbital period for PSIUJ1713|0747 allows for lower requeney power to be absorbed resulting in a larger overall ellect by Equation 2.., The larger orbital period for PSR J1713+0747 allows for lower frequency power to be absorbed resulting in a larger overall effect by Equation \ref{eq:power}.966 Finally. it is also important to note that. for both pulsars. the increase in uncertainty of these parameters is approximately linear in CAVB amplitude over the region of interest of 1:10τςc5.H.," Finally, it is also important to note that, for both pulsars, the increase in uncertainty of these parameters is approximately linear in GWB amplitude over the region of interest of $1\times 10^{-15}\le A \le 5\times 10^{-14}$."967 As discussed in Section 1.. many papers have been published dealing with calculation of upper limits on the stochastic CAVB amplitude.," As discussed in Section \ref{intro}, many papers have been published dealing with calculation of upper limits on the stochastic GWB amplitude."968 While some caleulate this upper limit using a method that is designed to detect the background (?7).. others use a statistic that is exclusively designed. [or putting limits on the background (?)..," While some calculate this upper limit using a method that is designed to detect the background \citep{vlm+09,hlj+11}, others use a statistic that is exclusively designed for putting limits on the background \citep{jhs+06}."969 For example. Jenet et al.," For example, Jenet et al."970 use à statistic that is sensitive to à red power spectrum., use a statistic that is sensitive to a red power spectrum.971 By design. this method relies on the noise having a very white power spectrum and thus any deviation from Gaussian noise is a problem for this test.," By design, this method relies on the noise having a very white power spectrum and thus any deviation from Gaussian noise is a problem for this test."972 Since some non-Caussian noise may occur in timing data. especially in lone data sets. this method is limited in applicability.," Since some non-Gaussian noise may occur in timing data, especially in long data sets, this method is limited in applicability."973 However. it has thus [ar produced the most stringent published. limits.," However, it has thus far produced the most stringent published limits."974 The method discussed in this paper is also not a suitable candidate for detection. but it does produce. independen upper limits that are consistent with previously. publishe imits., The method discussed in this paper is also not a suitable candidate for detection but it does produce independent upper limits that are consistent with previously published limits.975 Before discussing specifie methods. Figure 4. shows some general results of this method.," Before discussing specific methods, Figure \ref{fig:detection} shows some general results of this method."976 To obtain these plots. we run the simulation as described in Section. 2.3.— a ren take the output at cach GAVB amplitude and make a lstogram as shown in Figure 2..," To obtain these plots, we run the simulation as described in Section \ref{sec:extended} and then take the output at each GWB amplitude and make a histogram as shown in Figure \ref{fig:gauss}."977 We calculate an upper limi sing this scheme by finding the amplitude for which of 1¢ simulations vield parameter values that lic outside of the mal 0 errors on that parameter., We calculate an upper limit using this scheme by finding the amplitude for which of the simulations yield parameter values that lie outside of the formal $\sigma$ errors on that parameter.978 Note here again tha le proper motion is significantly alfected for both pulsars., Note here again that the proper motion is significantly affected for both pulsars.9794.2. While this analysis could be seen as providing a limit on the CGWD amplitude. it depends on the timing value of these parameters. which is not fully independent of the simulated values.," While this analysis could be seen as providing a limit on the GWB amplitude, it depends on the timing value of these parameters, which is not fully independent of the simulated values."980 Therefore. we require an independent estimate of a timing parameter. as can be provided by VLBI. for example.," Therefore, we require an independent estimate of a timing parameter, as can be provided by VLBI, for example."981 With the parallax method we repeat the procedure described in the previous section for the timing parallax. but. instead of comparing against the unperturbecl timing. value. and uncertainty. we use the VLBI parameter and parallax.," With the parallax method we repeat the procedure described in the previous section for the timing parallax, but instead of comparing against the unperturbed timing value and uncertainty, we use the VLBI parameter and parallax."982 To accomplish this. we define an offset. parameter where zynüpp and wre are the VLBI and simulation values of parallax. respectively anc the denominator is the stun of the formal uncertainties on the parameters.," To accomplish this, we define an offset parameter where $\pi_{\rm VLBI}$ and $\pi_{\rm T2}$ are the VLBI and simulation values of parallax, respectively and the denominator is the sum of the formal uncertainties on the parameters."983 While previous work has shown that a stochastic CWB will allect astrometric parameters. (2???) nmieasured by VLBI such as parallax. it is known that the angular dellections expected. are on the order of the characteristic strain amplitude (seee.g.2)..," While previous work has shown that a stochastic GWB will affect astrometric parameters \citep{gep+97,ksg+99,jaf04} measured by VLBI such as parallax, it is known that the angular deflections expected are on the order of the characteristic strain amplitude \citep[see e.g.][]{bf10}."984" Because typical amplitudes are ~10D"" these οσον are fer less than the typica uncertainties on these astrometric parameters.", Because typical amplitudes are $\sim 10^{-15}$ these effects are far less than the typical uncertainties on these astrometric parameters.985 Thus. we can treat VLBI measurements as unallectec by the stochastic GWLB.," Thus, we can treat VLBI measurements as unaffected by the stochastic GWB."986 To place a limit. we determine the CWB amplitude in which of the realisations result in offset. values in excess of 2.," To place a limit, we determine the GWB amplitude in which of the realisations result in offset values in excess of 2."987 The factor of 2 is to ensure a false negative rate., The factor of 2 is to ensure a false negative rate.988 Phe results from this method are shown in Table 3.., The results from this method are shown in Table \ref{tab:amp}.989 It is clear from the table that the upper limits obtained from PSH. 04374715 are more stringent than those obtained from PSR. J1713|0747., It is clear from the table that the upper limits obtained from PSR J0437–4715 are more stringent than those obtained from PSR J1713+0747.990 This is to be expected. because the background does not corrupt the values of parallax as much," This is to be expected, because the background does not corrupt the values of parallax as much"991sell-shielded from the starlight and located closer to the galactic center.,self-shielded from the starlight and located closer to the galactic center.992 The far-infrared excess is especially prominent in radio galaxies (Golombeketal.1988:Knappοἱ1990).," The far-infrared excess is especially prominent in radio galaxies \citep{gol88,kna90}."993. llowever. as (he origin aud spatial distribution of this radiation is unknown. and also as the fav-infrarecl emission shows significant variations from galaxy to galaxy. we do not discuss ils contribution to the kpc-scale jet inverse-Compton enission.," However, as the origin and spatial distribution of this radiation is unknown, and also as the far-infrared emission shows significant variations from galaxy to galaxy, we do not discuss its contribution to the kpc-scale jet inverse-Compton emission."994" In Appendix C. following TsaiandMathews(1995).. we estimate (he enerey density of the starlight (slar) photons to be Uy,~10? erg/em? at the distance ~1 kpe [rom ihe center of the typical giant elliptical galaxy."," In Appendix C, following \citet{tsa95}, we estimate the energy density of the starlight $star$ ) photons to be $U_{star} \sim 10^{-9}$ $^3$ at the distance $\sim 1$ kpc from the center of the typical giant elliptical galaxy."995 Assuming lor simplicity an approximately isotropic distribution of the stellar emission at (his scale. in the jet comoving frame one has (Appendix D). with a characteristic starlight frequency νο“star~10!P Hz.," Assuming for simplicity an approximately isotropic distribution of the stellar emission at this scale, in the jet comoving frame one has (Appendix B), with a characteristic starlight frequency $\nu'_{star} \sim996 10^{14} \, \Gamma$ Hz."997 The galactic dust emission (dus!) is distributed analogously to the stellar radiation and hence its energy density. in. the jet. rest frameB is. also amplifiedPM approximately. bv a factorB I7.L7, The galactic dust emission $dust$ ) is distributed analogously to the stellar radiation and hence its energy density in the jet rest frame is also amplified approximately by a factor $\Gamma^2$.998 In this. paper we lake ab piu~3:10T Hz.," In this paper we take at $\nu'_{dust} \sim 3 \cdot 10^{13} \, \Gamma$ Hz."999" Finally. for redshifts z«1 an analogous energy density of the blackbody CMD is equal to where α=τοῦ.10© ces and the observed. CMB temperature is Tea);—2.7 Ix. The appropriate characteristic CMD photon frequency is vey),c2+10HT Hz."," Finally, for redshifts $z1000 \ll 1$ an analogous energy density of the blackbody CMB is equal to where $a = 7.53 \cdot 10^{-15}$ cgs and the observed CMB temperature is $T_{CMB}1001 = 2.7$ K. The appropriate characteristic CMB photon frequency is $\nu'_{CMB}1002 \sim 2 \cdot 10^{11}\, \Gamma$ Hz."1003 With the evaluated. photon fields in the emitting region rest frame. U'κος one can estimate (he observed break luminosity of the appropriate inverse-Comptlon (/e(seed)) emission in the Thomson regime as Presence of an additional factor οί.90) is connected with the possible anisotropy οἱ the external radiation fields within the jet comoving frame. in cases of its relativistie bulk," With the evaluated photon fields in the emitting region rest frame, $U'_{seed}$, one can estimate the observed break luminosity of the appropriate inverse-Compton $ic(seed)$ ) emission in the Thomson regime as Presence of an additional factor $f_{\pm / iso}(\Gamma, \theta)$ is connected with the possible anisotropy of the external radiation fields within the jet comoving frame, in cases of its relativistic bulk"1004follow the behavior of the other variables.,follow the behavior of the other variables.1005 This would confirm early suggestions that SU Cas (see. e.g.. Gieren 1932: Evans 1991: Fernie οἱ al.," This would confirm early suggestions that SU Cas (see, e.g., Gieren 1982; Evans 1991; Fernie et al."1006 1995; Andrievsky οἱ al., 1995; Andrievsky et al.1007 2002¢) and EV Set (Tammann et al., 2002c) and EV Sct (Tammann et al.1008 2003: Groenewegen et al., 2003; Groenewegen et al.1009 2004) mieht be FO pulsators., 2004) might be FO pulsators.1010 However. these two objects need to be haaxdled with care. since SU Cas is connected with a reflection nebula (van den Dergh 1966) and EV Sct appears to show an unusual line profile structure (Ixovtvukh el al.," However, these two objects need to be handled with care, since SU Cas is connected with a reflection nebula (van den Bergh 1966) and EV Sct appears to show an unusual line profile structure (Kovtyukh et al."1011 2003)., 2003).1012 For the remaining Cepheids which are. according to Fernie οἱ al. (," For the remaining Cepheids which are, according to Fernie et al. ("10131995). fundamental pulsators. we plot in the top panel of Fig.,"1995), fundamental pulsators, we plot in the top panel of Fig."1014" 9 the ratio AL,/ALpiο as a function of the pulsation period."," 9 the ratio $M_p/M_{e,can}$ as a function of the pulsation period."1015 Note (hat. in order to minimize (he effects of uncertainties on (he adopted reddening (see Table 6). we consider only the pulsation and evolutionary mass estimates based on PECΔΝ) and VCL(VI) relations. respectively.," Note that, in order to minimize the effects of uncertainties on the adopted reddening (see Table 6), we consider only the pulsation and evolutionary mass estimates based on $PLC(VK)$ and $MCL(VK)$ relations, respectively."1016" Current results suggest that the ALM,uu; ralio decreases from long-period to short-period variables. thus supporting earlier sugeestions by BOL and Gieren (1989)."," Current results suggest that the $M_p/M_{e,can}$ ratio decreases from long-period to short-period variables, thus supporting earlier suggestions by B01 and Gieren (1989)."1017" Data plotted in the bottom panel of the same figure show that (he inclusion of mild convective core overshooting (i.e.. by adopting logL/L,,—0.2) does not alfect the pulsation masses. but vields svstematically smaller evolutionary masses. with the unfortunate consequence of several variables showing AL,>1M,,,."," Data plotted in the bottom panel of the same figure show that the inclusion of mild convective core overshooting (i.e., by adopting $L/L_{can}$ =0.2) does not affect the pulsation masses, but yields systematically smaller evolutionary masses, with the unfortunate consequence of several variables showing $M_p>M_{e,over}$."1018" By the way. (his result allows us to drop the hypothesis of noncanonical luninosity levels. so as to solve (he mild discrepaney between. AM,(V) and Mu(A) values discussed in Section 3."," By the way, this result allows us to drop the hypothesis of noncanonical luminosity levels, so as to solve the mild discrepancy between $M_{e,can}(V)$ and $M_{e,can}(K)$ values discussed in Section 3."1019 In order to test the dependence of current findings on the adopted ML relation. we also adopted the ALL relation provided by GOO ancl based on canonical evolutionary computations with Z=0.019. Y=0.273. and stellar masses in (he range 4-5...," In order to test the dependence of current findings on the adopted $ML$ relation, we also adopted the $ML$ relation provided by G00 and based on canonical evolutionary computations with $Z$ =0.019, $Y$ =0.273, and stellar masses in the range $M_{\odot}$."1020 The top panel of Fig., The top panel of Fig.1021 10 shows the comparison between (he average Iuminosity. predicted by GOO for canonical central ]Ie-burning models (solid line) ancl the Iuminosity given by equation (2) (dashed line)., 10 shows the comparison between the average luminosity predicted by G00 for canonical central He-burning models (solid line) and the luminosity given by equation (2) (dashed line).1022 The two sels of models present different slopes of the VL relation (see also Fig., The two sets of models present different slopes of the $ML$ relation (see also Fig.1023 5 in BBIN). in particular the GOO models appear Inter for stellar masses <5.M. and brighter for masses >5M. than predictions based on BO computations.," 5 in BBK), in particular the G00 models appear fainter for stellar masses $<5M_{\odot}$ and brighter for masses $>5M_{\odot}$ than predictions based on B0 computations."1024" As a consequence. (see the bottom panel in (he same ligure) the adoption of the GOO canonical models leads (o a steeper dependence of the MM.uu, ratio on the Cepheid period. and to an increased number of variables with M,>Mou."," As a consequence, (see the bottom panel in the same figure) the adoption of the G00 canonical models leads to a steeper dependence of the $M_p/M_{e,can}$ ratio on the Cepheid period, and to an increased number of variables with $M_p>M_{e,can}$."1025" The inclusion of mild convective core overshooting makes the situation even worse: owing to the increased. Iuminositv for any. [fixed mass. all the M,pi/AM. ratios become svslematically larger ancl almost all the Cepheids would have evolutionary masses smaller (han (he pulsation ones."," The inclusion of mild convective core overshooting makes the situation even worse: owing to the increased luminosity for any fixed mass, all the $M_p/M_e$ ratios become systematically larger and almost all the Cepheids would have evolutionary masses smaller than the pulsation ones."1026 The discussion of the evolutionary models is bevond the purpose of the present paper: however. the results presented in Fie.," The discussion of the evolutionary models is beyond the purpose of the present paper; however, the results presented in Fig."1027 9 and Fig., 9 and Fig.1028 10 show that the current. evolutionary scenario is affected not only bv the assumptions on the efficiency. of overshooting. bul also bv sizable differences (e.g.. the equation of state) in the canonical models.," 10 show that the current evolutionary scenario is affected not only by the assumptions on the efficiency of overshooting, but also by sizable differences (e.g., the equation of state) in the canonical models."1029 Here. relvine," Here, relying"1030The Sloan Lens ACS Survey (SLACS:Boltonctal.2006) is a large sample of strong gravitational lenses derived from the Sloan Digital Sky Survey (SDSS).,The Sloan Lens ACS Survey \citep[SLACS;][]{bolton} is a large sample of strong gravitational lenses derived from the Sloan Digital Sky Survey (SDSS).1031 The lens sample has proved to be particularly useful due to the high quality of the data: all of the SLACS lenses have known lens and source redshifts. stellar velocity dispersions for the lensing galaxies have been measured from the SDSS spectra. all of the systems have (LIST) ACS imaging in two bands for accurate non-parametric lens mocdelling. and all of the sources are extended and therefore. provide additional constraints on the mass profile of the lensing ealaxy.," The lens sample has proved to be particularly useful due to the high quality of the data; all of the SLACS lenses have known lens and source redshifts, stellar velocity dispersions for the lensing galaxies have been measured from the SDSS spectra, all of the systems have ) ACS imaging in two bands for accurate non-parametric lens modelling, and all of the sources are extended and therefore provide additional constraints on the mass profile of the lensing galaxy."1032 Furthermore. the density of background. sources in theST imagine allows a weak lensing analysis of the ensemble saniple of lenses (Gavazzietal.2007):: the major drawback of the lens sample is that it is unlikely to find any variable sources that woul provide time delays.," Furthermore, the density of background sources in the imaging allows a weak lensing analysis of the ensemble sample of lenses \citep{gavazzi}; the major drawback of the lens sample is that it is unlikely to find any variable sources that would provide time delays."1033 Ixoopmansetal.(20063 have used the SLACS lenses to show that earlv-type ealaxics have isothermal total inner density profiles wih VOEV little intrinsic scatter (approximately G per cent) assuming a uniformity in the environments of the lenses that has not. been rigorously testect., \citet{koopmansSLACS} have used the SLACS lenses to show that early-type galaxies have isothermal total inner density profiles with very little intrinsic scatter (approximately 6 per cent) assuming a uniformity in the environments of the lenses that has not been rigorously tested.1034 While the SLACS lenses seem to le on the Fundamental Plane (Boltonοἱal.2006:Treu3oltonοἱal.2007) and clo not diller noticeably from other SDSS ealaxies with similar luminosities and stellar velocity clispersions. the local environments of the lenses might alfect the mass profiles of the lensing galaxies (e.g...Rusinetal.102;Dobkeetal.2007:Augerct 2007b).," While the SLACS lenses seem to lie on the Fundamental Plane \citep{bolton,treu,bolton07} and do not differ noticeably from other SDSS galaxies with similar luminosities and stellar velocity dispersions, the local environments of the lenses might affect the mass profiles of the lensing galaxies \citep[e.g.,][]{rusin,dobke,augerb}."1035. 1£ some of the lenses are being perturbed by neighbouring galaxies the intrinsic scatter of the density slope forisofafed carly-type ealaxies might be even smaller than 6 per cent., If some of the lenses are being perturbed by neighbouring galaxies the intrinsic scatter of the density slope for early-type galaxies might be even smaller than 6 per cent.1036 Furthermore. it has been suggested that line-of-sight (LOS) contamination significantly allects the SLACS lenses (Guimaraes&Sodré2007) and the density. slope might be. expected το be shallower than originally reported.," Furthermore, it has been suggested that line-of-sight (LOS) contamination significantly affects the SLACS lenses \citep{guimaraes} and the density slope might be expected to be shallower than originally reported."1037 We report on a spectroscopic and photometric evaluation of the environments and lines of sight of the 15 SLACS lenses investigated by Koopmansetal.(2006)., We report on a spectroscopic and photometric evaluation of the environments and lines of sight of the 15 SLACS lenses investigated by \citet{koopmansSLACS}.1038. A weighting scheme is used to determine the ellective number of potential perturbing companions to each lens galaxy., A weighting scheme is used to determine the effective number of potential perturbing companions to each lens galaxy.1039 We also characterize the ‘richness’ of the global environment of each lens field and quantify the number of galaxies along the LOS to the ens., We also characterize the `richness' of the global environment of each lens field and quantify the number of galaxies along the LOS to the lens.1040 Throughout this paper the term ‘global environment is used to describe the group. cluster. or field in which the lens resides while the ‘local environment describes the environment within =I00 kpe of the lensing galaxy.," Throughout this paper the term `global environment' is used to describe the group, cluster, or field in which the lens resides while the `local environment' describes the environment within $\approx 100$ kpc of the lensing galaxy."1041" A ACDAL cosmicAogv with ο=0.27 and Ὃν=0.73 is used to determine al physical distances. which are measured in ""units."," A $\Lambda$ CDM cosmology with $\Omega_M = 0.27$ and $\Omega_\Lambda = 0.73$ is used to determine all physical distances, which are measured in units."1042 Our primacy intent is to investigate a correlation between the inner density profile of the lensing galaxy ancl the, Our primary intent is to investigate a correlation between the inner density profile of the lensing galaxy and the1043form stars.,form stars.1044" This value for nin is the maximum density gas can reach using gravity, 32Myas/e>."," This value for $n_{th}$ is the maximum density gas can reach using gravity, $32M_{gas}/\epsilon{^3}$."1045" Such gas is converted to stars according to the equation Here, AM, is the mass of the star particle formed, At is the timestep between star formation events, 0.8 Myrs in these simulations, Ms; is the mass of the gas particle and tayn is the gas particle's dynamical time."," Such gas is converted to stars according to the equation Here, $\Delta M_\star$ is the mass of the star particle formed, $\Delta t$ is the timestep between star formation events, 0.8 Myrs in these simulations, $M_{gas}$ is the mass of the gas particle and $t_{dyn}$ is the gas particle's dynamical time."1046" c, is the efficiency of star formation, in other words, the fraction of gas that will be converted into stars during tayn."," $c_\star$ is the efficiency of star formation, in other words, the fraction of gas that will be converted into stars during $t_{dyn}$."1047 Stars feed energy back into the interstellar medium gas where they formed., Stars feed energy back into the interstellar medium gas where they formed.1048" Two types of energetic feedback are considered in these simulations, supernovae and stellar radiation."," Two types of energetic feedback are considered in these simulations, supernovae and stellar radiation."1049 Supernova feedback is implemented using the blastwave formalism described in ? and deposit 10?! erg of energy into the surrounding medium., Supernova feedback is implemented using the blastwave formalism described in \citet{stinson06} and deposit $10^{51}$ erg of energy into the surrounding medium.1050" Since this gas is dense, the energy would be quickly radiated away due to the efficient cooling."," Since this gas is dense, the energy would be quickly radiated away due to the efficient cooling."1051" For this reason, cooling is disabled for particles inside the blast region R and for the length of time t—10655g9:3250340yr given in ?.."," For this reason, cooling is disabled for particles inside the blast region $R = 10^{1.74}E_{\rm 51}^{0.32}n_0^{-0.16}\tilde{P}_{\rm 04}^{-0.20} {\rm pc}$ and for the length of time $t = 10^{6.85}E_{\rm 51}^{0.32}n_0^{0.34}\tilde{P}_{\rm 04}^{-0.70} {\rm yr}$ given in \cite{mckee77}."1052" Here, E3;=10°! erg, no is the ambientp hydrogen density, and Pos=10Pk! where Po is the ambient pressure and k is the Boltzmann constant."," Here, $E_{\rm 51}=10^{51}$ erg, $n_0$ is the ambient hydrogen density, and ${P}_{\rm 04} = 10^{-4}P_0k^{-1}$ where $P_0$ is the ambient pressure and k is the Boltzmann constant."1053 Both no and Po are calculated using the SPH kernel for the gas particles surrounding the star., Both $n_0$ and $P_0$ are calculated using the SPH kernel for the gas particles surrounding the star.1054" Metals are ejected from type II supernovae (SNII), type Ia supernovae (SNIa), and the stellar winds driven from asymptotic giant branch (AGB) stars."," Metals are ejected from type II supernovae (SNII), type Ia supernovae (SNIa), and the stellar winds driven from asymptotic giant branch (AGB) stars."1055 EEjected mass and metals are distributed to the nearest neighbour gas particles using the smoothing kernal., ÊEjected mass and metals are distributed to the nearest neighbour gas particles using the smoothing kernal.1056 Details of the manner in which metals are incorporated into the code are found in ?.., Details of the manner in which metals are incorporated into the code are found in \citet{stinson06}.1057 The prescribed SNII and SNIa yields have been updated in this study., The prescribed SNII and SNIa yields have been updated in this study.1058 EThe SNII oxygen and iron use fits to ?.., ÊThe SNII oxygen and iron use fits to \citet{woosley95}.1059" É For SNIa, we use the W7 yields from Table 1 in ?.."," Ê For SNIa, we use the W7 yields from Table 1 in \citet{nomoto97}."1060" Metal diffusion is also included, such that unresolved turbulent mixing is treated as a shear-dependent diffusion term, as described in ?.."," Metal diffusion is also included, such that unresolved turbulent mixing is treated as a shear-dependent diffusion term, as described in \cite{shen10}."1061 'The allows proximate gas particles to mix their metals., The allows proximate gas particles to mix their metals.1062 Metal cooling is calculated based on the diffused metals., Metal cooling is calculated based on the diffused metals.1063 The effects of stellar radiation have only recently begun to be considered in galaxy simulations (?).., The effects of stellar radiation have only recently begun to be considered in galaxy simulations \citep{hopkins11}.1064" Here, we model the luminosity of stars using the 7? mass-luminosity relationship."," Here, we model the luminosity of stars using the \citet{bressan93} mass-luminosity relationship."1065" Typically, this relationship leads to 10?? ergs of energy being released from the high mass stars over the course of the 0.8Myr between star formation calculations."," Typically, this relationship leads to $10^{53}$ ergs of energy being released from the high mass stars over the course of the 0.8Myr between star formation calculations."1066 These photons do not couple efficiently with the surrounding ISM (?).., These photons do not couple efficiently with the surrounding ISM \citep{freyer06}.1067 We thus do not want to couple all of this energy to the surrounding gas in the simulation., We thus do not want to couple all of this energy to the surrounding gas in the simulation.1068" To mimic this highly inefficient energy coupling, we inject of the energy as thermal energy in the surrounding gas, and cooling is turned off for this form of energy input."," To mimic this highly inefficient energy coupling, we inject of the energy as thermal energy in the surrounding gas, and cooling is turned off for this form of energy input."1069 It is well established that such thermal energy injection is highly inefficient at the spatial and temporal resolution of the type of cosmological simulations used here (7)., It is well established that such thermal energy injection is highly inefficient at the spatial and temporal resolution of the type of cosmological simulations used here \citep{katz92}.1070 This is primarily due to the characteristic cooling timescales in the star forming regions being lower than the step time of the simulations., This is primarily due to the characteristic cooling timescales in the star forming regions being lower than the step time of the simulations.1071" The dynamical effect of this feedback is negligible, as is the overall coupling of energy to the ISM, but high mass star radiation feedback does reduce star formation in the region immediately surrounding a recently formed star particle (full details of this radiative feedback will be presented in a separate paper, Stinson et al."," The dynamical effect of this feedback is negligible, as is the overall coupling of energy to the ISM, but high mass star radiation feedback does reduce star formation in the region immediately surrounding a recently formed star particle (full details of this radiative feedback will be presented in a separate paper, Stinson et al."1072 in prep)., in prep).1073raciative transfer simulations with N=64.,radiative transfer simulations with $N_c=64^3$.1074 Phe resulting evolution ofr. is shown in Fig., The resulting evolution of $x_v$ is shown in Fig.1075 S. bv asterisks., \ref{fig08} by asterisks.1076" From this ligure it is evident that the grid resolution does not greatly aleet the final results: the value of c, never dillers in the two runs by more than 10 or 20%. although the case with ANS=64% produces slightly higher values.", From this figure it is evident that the grid resolution does not greatly affect the final results; the value of $x_v$ never differs in the two runs by more than 10 or $20\%$ although the case with $N_c=64^3$ produces slightly higher values.1077" IN,7»128? is not allowed by the mass resolution of our N-body simulation. as sampling Iluctuations in the density field then become large."," $N_c>128^3$ is not allowed by the mass resolution of our N-body simulation, as sampling fluctuations in the density field then become large."1078 As mentioned. above. small mass objects. although negligible for ionizing photon production. are important because small-scale clumping can enhance recombination.," As mentioned above, small mass objects, although negligible for ionizing photon production, are important because small-scale clumping can enhance recombination."1079 Simulations which co not include such objects may ancerestimate the actual number of ionizing photons needed to reionize the IGM., Simulations which do not include such objects may underestimate the actual number of ionizing photons needed to reionize the IGM.1080 To mimic clumping on unresolved scales. aso called clumping factor. C'. is often introduced.," To mimic clumping on unresolved scales, a so called clumping factor, $C$ , is often introduced."1081 lt is defined as Co=<nτσ«onD where n is the density.," It is defined as $C=<n^2>/<n>^2$, where $n$ is the density."1082 The TSC€ technique. used. to. derive our densitv distributions will lead us to underestimate the ‘lumping factor., The TSC technique used to derive our density distributions will lead us to underestimate the clumping factor.1083 Phe TSC interpolation has the advantage of producing smoothed density values at the positions of the erid cells. as required for the radiative transfer computation.," The TSC interpolation has the advantage of producing smoothed density values at the positions of the grid cells, as required for the radiative transfer computation."1084 However. this technique is not adaptive. Like an SPLL kernel for example. and density variations on sub-gricl scales are smoothed out. reducing the contrast. of the DAL density peaks where our sources are positioned.," However, this technique is not adaptive, like an SPH kernel for example, and density variations on sub-grid scales are smoothed out, reducing the contrast of the DM density peaks where our sources are positioned."1085 This results in an underestimate of the recombination rate ancl thus Laster reionization., This results in an underestimate of the recombination rate and thus faster reionization.1086 dn order to address the importance of this elect we have measured densities at the particle positions using both the “PSC interpolation and a 32-particle SPILL smoothing kernel., In order to address the importance of this effect we have measured densities at the particle positions using both the TSC interpolation and a 32-particle SPH smoothing kernel.1087" Phe result of this comparison for ""M3 at redshifts z=10 and z=6 is shown in Fig. 9..", The result of this comparison for `M3' at redshifts $z=10$ and $z=6$ is shown in Fig. \ref{fig09}.1088 Phe overall agreement for low and intermediate densities is reasonable. but the smoothing of the PSC scheme is clearly visible at the high densities.," The overall agreement for low and intermediate densities is reasonable, but the smoothing of the TSC scheme is clearly visible at the high densities."1089 This is especially true at 2=6., This is especially true at $z=6$.1090 An estimate of the error introduced. can be quantified. by the ratio of the total recombination rate derived. with the two different schemes. rspa/irsct.," An estimate of the error introduced can be quantified by the ratio of the total recombination rate derived with the two different schemes, $r_{SPH}/1091r_{TSC}$."1092 Vhis ratio is equal to 6.24 (20.87) αἱ =10 (6). suggesting that we are substantially underestimating the recombination rate in the high density regions surrounding the sources.," This ratio is equal to 6.24 (20.87) at $z=10$ (6), suggesting that we are substantially underestimating the recombination rate in the high density regions surrounding the sources."1093 We are interested. primarily in the higher redshifts. where agreement is somewhat better.," We are interested primarily in the higher redshifts, where agreement is somewhat better."1094 Since almost all the high density regions where the above corrections are important host sources. the error in the recombination rate can be considered part of the uncertainty on our adopted escape fraction (see below).," Since almost all the high density regions where the above corrections are important host sources, the error in the recombination rate can be considered part of the uncertainty on our adopted escape fraction (see below)."1095 Moreover. the ellect of clumping is alleviated by photoevaporation. which tends to weaken the effect. of eas on unresolved. scales as ionization precedes (Shapiro ct al.," Moreover, the effect of clumping is alleviated by photoevaporation, which tends to weaken the effect of gas on unresolved scales as ionization precedes (Shapiro et al."1096 2003)., 2003).1097 The number of available ionizing. photons. depends on the choice of the stellar. spectrum. EME ancl escape fraction.," The number of available ionizing photons depends on the choice of the stellar spectrum, IMF and escape fraction."1098 As the first. stars form out of gas of. primordial composition. they are thought to be very massive. resulting in a higher ionizing photon emission.when compared. withhigher metallicity stars (e.g. Larson 1998).," As the first stars form out of gas of primordial composition, they are thought to be very massive, resulting in a higher ionizing photon emission,when compared withhigher metallicity stars (e.g. Larson 1998)."1099 For example.," For example,"1100Granulation forms (he instantly recognisable “patchwork” pattern of the solar photosphere and dominates quiet Sun regions.,Granulation forms the instantly recognisable “patchwork” pattern of the solar photosphere and dominates quiet Sun regions.1101 The dark intergranular lanes are formed as a result. of convective downllows and are the regions where magnetic bright points (AIBPs) can be observed., The dark intergranular lanes are formed as a result of convective downflows and are the regions where magnetic bright points (MBPs) can be observed.1102 It is the horizontal transler of magnetic [hix from the centre of granules. and into (he lanes. that foris MDPs.," It is the horizontal transfer of magnetic flux from the centre of granules, and into the lanes, that forms MBPs."1103 In the MBPs. the magnetic flux clumps together to form small magnetic concentrations with field strengths of the order of a kiloGiauss 1993).," In the MBPs, the magnetic flux clumps together to form small magnetic concentrations with field strengths of the order of a kiloGauss \citep{Sten85, Solan93}."1104. These are some of the smallest features currently observable on the solar surface. ancl due to their dvnanic nature. can provide a conduit for the transfer of kinetic enerey into the upper solar atmosphere (deWijnetal.2009).," These are some of the smallest features currently observable on the solar surface, and due to their dynamic nature, can provide a conduit for the transfer of kinetic energy into the upper solar atmosphere \citep{deWi09}."1105. Due to the increased computational power available in recent vears. significant progress ias been made in understanding the complex interplay between convective energy. transport and radiation in these concentrated magnetic elements.," Due to the increased computational power available in recent years, significant progress has been made in understanding the complex interplay between convective energy transport and radiation in these concentrated magnetic elements."1106 \IBPs are best observed as strong intensity enhancements in G-band intensity images (Muller&Rouclier1934:Berger1996) which have intensity peaks between 0.8—1.5 limes the mean photospheric intensity (SánchezAlmeidaetal.2004:Langhans2002).," MBPs are best observed as strong intensity enhancements in G-band intensity images \citep{Mull84, Ber96} which have intensity peaks between $0.8-1.8$ times the mean photospheric intensity \citep{San04, Lan02}."1107. These enhancements are due (o an increase in continuum intensitv. caused by (the continuum formation laver being depressed into the deeper. hotter lavers of the solar photosphere. where regions of strong magnetic field concentrations and reduced CLL abundances exist (Steineretal.2001:Shelvagοἱ2004).," These enhancements are due to an increase in continuum intensity, caused by the continuum formation layer being depressed into the deeper, hotter layers of the solar photosphere, where regions of strong magnetic field concentrations and reduced CH abundances exist \citep{Stein01, Shel04}."1108. The significance of MBPs on solar atmospheric energy. (rausport and dvnanmices has led lo several studies on their area coverage and size distribution., The significance of MBPs on solar atmospheric energy transport and dynamics has led to several studies on their area coverage and size distribution.1109 found that MBPs have a minor axis of 135 km. while Wiehretal.(2004) determined a predominant diameter of 1602E20 kin.," \citet{San04} found that MBPs have a minor axis of 135 km, while \citet{Wie04} determined a predominant diameter of $160 \pm 20$ km."1110 In a recent study. Crockettοἱal.(2010) utilised hieh spatial resolution observations and magneto-hydrodvnamic (MIID) simulations to conclude that the MBP area distribution peaks at 2245000 kn. with a sharp decrease in occurrence for smaller surface areas.," In a recent study, \citet{Croc10} utilised high spatial resolution observations and magneto-hydrodynamic (MHD) simulations to conclude that the MBP area distribution peaks at $\approx$ 45000 $^2$, with a sharp decrease in occurrence for smaller surface areas."1111 The area of the smallest \IBPs is defined by the width of the lanes. which is in turn limited bv the balance of radiative and convective energies in the magneto-convective processes.," The area of the smallest MBPs is defined by the width of the inter-granular lanes, which is in turn limited by the balance of radiative and convective energies in the magneto-convective processes."1112 MBP velocities are induced by (he expansion of granules. ancl are (vpically in the range o[1—3 ! (Berger&Title1996:Utzetal.2010).," MBP velocities are induced by the expansion of granules, and are typically in the range of $1-3$ $^{-1}$ \citep{Ber96, Utz10}."1113. It has been shown by οἱal.(1993). that magnetic footpoints with velocities greater than ~2 + can excite maegnelo-sonic kink waves. which can transport sufficient energy to heat the localisecl quiet corona. under a two laver atmospheric approximation.," It has been shown by \citet{Choud93} that magnetic footpoints with velocities greater than $\sim$ 2 $^{-1}$ can excite magneto-sonic kink waves, which can transport sufficient energy to heat the localised quiet corona, under a two layer atmospheric approximation."1114 Also. recent observations al.2008:Weclemever-Bolin&RouppevanderVoort2009) and simulations suggest the presence of vortex motions in the photosphere. with a possible connection to (he spiral tracks of MDPs and chromospheric swirls.," Also, recent observations \citep{Bon08, Wed09} and simulations \citep{Shel11} suggest the presence of vortex motions in the photosphere, with a possible connection to the spiral tracks of MBPs and chromospheric swirls."1115 Very recent studies by, Very recent studies by1116equations: ancl Now. the Af outsicle the braces becomes M(r). but the M inside the braces does not change.,"equations: and Now, the $M$ outside the braces becomes $M(r)$, but the $M$ inside the braces does not change."1117 Therefore. for given values of ry. Ady and Af (the total mass of the svstem) the expression inside the braces depends only on r..," Therefore, for given values of $r_0$, $M_0$ and $M$ (the total mass of the system) the expression inside the braces depends only on $r$."1118 Asstunine centrifugal equilibrium and a given mass distribution. i.e. M(r). DM model their rotation curves.," Assuming centrifugal equilibrium and a given mass distribution, i.e. $M(r)$, BM model their rotation curves."1119 Also. note that. Ecuation (4)) obevs the superposition principle. which is an essential property if one intends (to make use of N-body simulations.," Also, note that Equation \ref{moffat_aceleration2}) ) obeys the superposition principle, which is an essential property if one intends to make use of $N$ -body simulations."1120 We note [rom the above equations that the Mollatian gravity. can be adjusted to a laree range of lengths and masses. bv means of the parameters ry anc AM. that depend on the svslem under investigation.," We note from the above equations that the Moffatian gravity can be adjusted to a large range of lengths and masses, by means of the parameters $r_0$ and $M_0$, that depend on the system under investigation."1121 IIence. (hey coukl. in principle. explain many plivsieal effects that the canonical theory attributes to the dark matter: galaxy rotation curves. galactic cluster masses and so on. because the DMs parameters depend on the total mass of the svslem under stucs.," Hence, they could, in principle, explain many physical effects that the canonical theory attributes to the dark matter: galaxy rotation curves, galactic cluster masses and so on, because the BM's parameters depend on the total mass of the system under study."1122 DM apply their modified gravity to explain the rotation curves of a sample of observed spiral galaxies ancl vield the following set of parameters. namely. Mj=96x10!A. and ro=13.96 kpe (Brownstein&Molfat.200Ga).," BM apply their modified gravity to explain the rotation curves of a sample of observed spiral galaxies and yield the following set of parameters, namely, $M_0 = 96 \times 10^{10} M_{\odot}$ and $r_0 = 13.96 $ kpc \citep{bm2006a}."1123. As usual in this kind of study. they consider centrifugal equilibrium. which means in (he end that their galaxy. model is “static.”," As usual in this kind of study, they consider centrifugal equilibrium, which means in the end that their galaxy model is “static."""1124 It is well known. from the N-body simulation studies. (hat disks built with," It is well known, from the $N$ -body simulation studies, that disks built with"1125where IN.(7.[) is the total number of electrons of kinetic energy £L present within the SNR at time /. b(/7)—diedl is the energy loss rate and q(/7) is the source term which. in our case. is the rate at which CR electrons are injected downstream of the shock.,"where $N_e(E,t)$ is the total number of electrons of kinetic energy $E$ present within the SNR at time $t$, $b(E)=-dE/dt$ is the energy loss rate and $q_e(E)$ is the source term which, in our case, is the rate at which CR electrons are injected downstream of the shock."1126 We believe that Eq. (, We believe that Eq. (11271) represents a valid approximation at least for energies up to around 10 TeV for which the typical acceleration timescale is less than LOO yr (Sturner et al.,1) represents a valid approximation at least for energies up to around $10$ TeV for which the typical acceleration timescale is less than $\sim 100$ yr (Sturner et al.1128 1997)., 1997).1129 In Eq. , In Eq. (1130"CL. we consider the energy loss of the electrons to be due to synchrotron and inverse compton interactions which is true forenergies ££=LO GeV. Therefore. we take in the Thompson regime with @=LOl10J'""(ej,|we) ! +. where wy, and wy are the energy densities of the radiation fields and the magnetic field respectively in eV .","1), we consider the energy loss of the electrons to be due to synchrotron and inverse compton interactions which is true for energies $E\gtrsim 10$ GeV. Therefore, we take in the Thompson regime with $a=1.01\times 10^{-16}(w_{ph}+w_B)$ $^{-1}$ $^{-1}$, where $w_{ph}$ and $w_B$ are the energy densities of the radiation fields and the magnetic field respectively in eV $^{-3}$ ."1131" With this. we detine the radiative energy loss timescale for the electrons as /;,,,(/7) l/(adlz)."," With this, we define the radiative energy loss timescale for the electrons as $t_{loss}(E)=1/(aE)$ ."1132 Now. for the source spectrum taken as power-law of the form. the solution of Eq. (," Now, for the source spectrum taken as power-law of the form, the solution of Eq. ("1133"1) at time / can be written as (Kardashev 1962. Gratton 1972) where fy=l/(al) is the energy at which the energy loss time /;,,,; becomes equal to time /.","1) at time $t$ can be written as (Kardashev 1962, Gratton 1972) where $E_0=1/(at)$ is the energy at which the energy loss time $t_{loss}$ becomes equal to time $t$ ."1134 Eq. (, Eq. (1135"4) shows that for energies ILox dey. the electron spectrum still reflects the source spectrum because of their large /;,,,. ie. IN(IE)xEUs","4) shows that for energies $E\ll E_0$ , the electron spectrum still reflects the source spectrum because of their large $t_{loss}$, i.e. $N_e(E)\propto E^{-\Gamma}$."1136 However. for electrons with energies £>Ly. their spectrum is quite steeper due to their faster energy loss rate and follows IN.(47)xLeqon," However, for electrons with energies $E\gg E_0$, their spectrum is quite steeper due to their faster energy loss rate and follows $N_e(E)\propto E^{-(\Gamma+1)}$."1137" For the CR primary nuclei. the spectrum inside the SNR can be described by where (4.7) is the total number of particles of kinetic energy per nucleon ££ at time /. jj is the matter density in the SNR. c Is the velocity of light and e, is the spallation cross-section of the primary nuclei assumed to be independent of energy."," For the CR primary nuclei, the spectrum inside the SNR can be described by where $N_p(E,t)$ is the total number of particles of kinetic energy per nucleon $E$ at time $t$, $\eta^{\prime}$ is the matter density in the SNR, $c$ is the velocity of light and $\sigma_p$ is the spallation cross-section of the primary nuclei assumed to be independent of energy."1138 In Eq. (, In Eq. (11395). we assume that the source term qu(/7)=hyde has the same index as those of the electrons.,"5), we assume that the source term $q_p(E)=k_pE^{-\Gamma}$ has the same index as those of the electrons."1140 The solution of Eq. (, The solution of Eq. (1141"5) can be obtained as For time much less than the nuclear spallation time. i.e. cm,). Eq. (","5) can be obtained as For time much less than the nuclear spallation time, i.e. $t\ll 1/(\eta^{\prime}c\sigma_p)$ , Eq. ("11426) becomes INC.1)zzquiEM.,"6) becomes $N_p(E,t)\approx q_p(E) t$."1143 During the time when primary CRs are confined within the SNRs. they interact with matter and produce secondary nuclei of almost the same Kinetic energy per nucleon as their primaries.," During the time when primary CRs are confined within the SNRs, they interact with matter and produce secondary nuclei of almost the same kinetic energy per nucleon as their primaries."1144 These secondaries can also be described by an equation similar to Eq. (, These secondaries can also be described by an equation similar to Eq. (1145"5) by replacing the source term by ico,NC.E) where o, is the total fragmentation crossection of primary to secondary.","5) by replacing the source term by $\eta^{\prime}c\sigma_{ps}N_p(E,t)$ where $\sigma_{ps}$ is the total fragmentation crossection of primary to secondary."1146 The solution for these secondaries is then obtained by where. In Eq. (," The solution for these secondaries is then obtained by where, In Eq. ("1147"7). 0, represents the spallation cross-section of the secondary nuclei.","7), $\sigma_s$ represents the spallation cross-section of the secondary nuclei."1148 Now. taking /=7° which is the CR confinement time inside the SNR. we can use Eqs. (," Now, taking $t=T$ which is the CR confinement time inside the SNR, we can use Eqs. ("1149+4). (6) & (7) to calculate the spectrum of CR electrons and the spectra of primary and secondary CR nuclei finally injected into the ISM from a single SNR.,"4), (6) $\&$ (7) to calculate the spectrum of CR electrons and the spectra of primary and secondary CR nuclei finally injected into the ISM from a single SNR."1150 Then. knowing the rate of supernova explosion per unit volume in the Galaxy. we can calculate the rate at which CRs are injected per unit volume in the Galaxy.," Then, knowing the rate of supernova explosion per unit volume in the Galaxy, we can calculate the rate at which CRs are injected per unit volume in the Galaxy."1151 CRs after escaping from the SNRs undergo diffusive propagation in the Galaxy due to scattering either by magnetic field irregularities or by self excited Alfven and hydromagnetie waves., CRs after escaping from the SNRs undergo diffusive propagation in the Galaxy due to scattering either by magnetic field irregularities or by self excited Alfven and hydromagnetic waves.1152 For the present work. we assume the diffusion region as a cylindrical disk of infinite radius with finite half-thickness // and that the sources as well as the matter are distributed uniformly and continuously in the Galactic disk with half-thickness / and radius 77. where f?>><> fh.," For the present work, we assume the diffusion region as a cylindrical disk of infinite radius with finite half-thickness $H$ and that the sources as well as the matter are distributed uniformly and continuously in the Galactic disk with half-thickness $h$ and radius $R$, where $R\gg H\gg h$ ."1153 The details of the geometry are described in Thoudam 2008., The details of the geometry are described in Thoudam 2008.1154 During the propagation. high energy electrons interact with the background radiation and the magnetic tields and lose their energies.," During the propagation, high energy electrons interact with the background radiation and the magnetic fields and lose their energies."1155 On the other hand. CR nuclei undergo nuclear spallation interactions with the interstellar matter and produce lighter nuclear species.," On the other hand, CR nuclei undergo nuclear spallation interactions with the interstellar matter and produce lighter nuclear species."1156 As already mentioned in section |. the assumption of a continuous source distribution may not be fully appropriate for high energy electrons particularly those in the TeV region because of their faster energy loss rate.," As already mentioned in section 1, the assumption of a continuous source distribution may not be fully appropriate for high energy electrons particularly those in the TeV region because of their faster energy loss rate."1157 Electrons with energies greater than 1 TeV cannot travel distances more than ~1 kpe in the Galaxy through diffusive propagation before they lost all their energies., Electrons with energies greater than $1$ TeV cannot travel distances more than $\sim 1$ kpc in the Galaxy through diffusive propagation before they lost all their energies.1158 Therefore. high energy electrons from distant and old sources may not reach the Earth effectively and TeV electrons that we observe can be mostly dominated by those produced by few young local sources.," Therefore, high energy electrons from distant and old sources may not reach the Earth effectively and TeV electrons that we observe can be mostly dominated by those produced by few young local sources."1159 The effect of this can be that the spectrum at high energies can be quite complex because of its strong dependence on the local source parameters (Delahaye et al., The effect of this can be that the spectrum at high energies can be quite complex because of its strong dependence on the local source parameters (Delahaye et al.1160 2010)., 2010).1161 Moreover. it may even show up features related to the stochastic nature of the local sources in space and time (see e.g.. Pohl & Esposito 1998).," Moreover, it may even show up features related to the stochastic nature of the local sources in space and time (see e.g., Pohl $\&$ Esposito 1998)."1162 In our study. our main focus is to explore the possibility of explaining the break in the electron spectrum as an effect of CR continement in the downstream region of SNRs and at the same time. following the standard model of CR propagation in the Galaxy.," In our study, our main focus is to explore the possibility of explaining the break in the electron spectrum as an effect of CR confinement in the downstream region of SNRs and at the same time, following the standard model of CR propagation in the Galaxy."1163 Such an effect of continement within the sources are generally not considered in CR propagation studies and we believe that they may exist if. SNRs are the main sources of galactic CRs., Such an effect of confinement within the sources are generally not considered in CR propagation studies and we believe that they may exist if SNRs are the main sources of galactic CRs.1164 Therefore. we do not intend to focus on a detailed source distribution and in what follows. we adopt the continuous and stationary source distribution for calculating the CR spectrum inthe Galaxy.," Therefore, we do not intend to focus on a detailed source distribution and in what follows, we adopt the continuous and stationary source distribution for calculating the CR spectrum inthe Galaxy."1165"Under the diffusion model. the propagation of high energy electrons in the Galaxy can be described by where n,(r.£2) is the electronnumber density in the Galaxy.","Under the diffusion model, the propagation of high energy electrons in the Galaxy can be described by where $n_e(\textbf{r},E)$ is the electronnumber density in the Galaxy,"1166eravitation cannot be considered complete.,gravitation cannot be considered complete.1167 The eravitational poteutials as defined viaο) carry an idepeudeut physical siguificauce iu the quantum realin. a situation that is reminiscent on the significance of the gauge potential in clectrodyuamiics as revealed by the Alaronoy-Boluu effect.," The gravitational potentials as defined via$g_{\mu\nu}(\vec r)$ carry an independent physical significance in the quantum realm, a situation that is reminiscent on the significance of the gauge potential in electrodynamics as revealed by the Aharonov-Bohm effect."1168"” The statement on the iucompleteness of ecneral relativitv is best illustrated ou the example of a “favor-oscillation clock.” Iu the linear superposition of the mass cigcustates we assume(only for simplicity) that both η) and ο) carry vanishingly small three momentum (1.0, are at rest)."," \cite{AB}1169 The statement on the incompleteness of general relativity is best illustrated on the example of a “flavor-oscillation \cite{grf96}1170 In the linear superposition of the mass eigenstates we assume for simplicity) that both $\vert m_1\rangle$ and $\vert1171m_2\rangle$ carry vanishingly small three momentum (i.e. are at rest)."1172" By studying the time-oscillation between the flavor states |Fi,) aud |Fp) one discovers that this system can be characterized bv the favor-oscillatiou frequeucyv? = The superscript on Oc|, is to identity this frequeney. with a clock at the spatial infinity from the eravitational sources uuder consideration (see below)."," By studying the time-oscillation between the flavor states $\vert1173F_a\rangle$ and $\vert F_b\rangle$ one discovers that this system can be characterized by the flavor-oscillation \cite{grf97}1174 = The superscript on $\Omega^\infty_{a\rightleftharpoons b}$ is to identify this frequency with a clock at the spatial infinity from the gravitational sources under consideration (see below)."1175 Now consider this davor-oscillation clock to be iunersed into the eravitational potential prt)., Now consider this flavor-oscillation clock to be immersed into the gravitational potential $\varphi_E(r)$.1176 Then each of the mass eigeustates picks up a phase because the eravitational interaction is of the formasger).," Then each of the mass eigenstates picks up a phase because the gravitational interaction is of the form $m \times1177\varphi_E(r)$."1178" Asa result. one finds that the new flavor-oscillation frequency. denoted by. Οἱος, is given bs? = ία| On This equation is valid for an observer fixed in the global coordinate system. attached to the Earth."," As a result, one finds that the new flavor-oscillation frequency, denoted by $\Omega^\prime_{a\rightleftharpoons b}$, is given \cite{grf97}1179 = ( 1+ ) This equation is valid for an observer fixed in the global coordinate system attached to the Earth."1180 Equation (3)) would have been the standard gravitational red shift expression if the τί] was replaced by of(r)., Equation \ref{red}) ) would have been the standard gravitational red shift expression if the $\varphi_E(\vec r)$ was replaced by $\phi_E(\vec r)$.1181 Freely falling frames (C£) do not carry fastest moving clocks. they carry clocks that are sensitive to potentials of the type oci.," Freely falling frames $(\cal F)$ do not carry fastest moving clocks, they carry clocks that are sensitive to potentials of the type $\phi_{GA}$."1182 A freely falling frame in Earth's eravity ouly iumuls the exadieuts of the exavitational potential while preserving all its constant pieces stich as Οι., A freely falling frame in Earth's gravity only annuls the gradients of the gravitational potential while preserving all its constant pieces such as $\phi_{GA}$ .1183" In denoting by OF4, the frequency asmecastred im a frecly falling frame ou Earth. one is led to"," In denoting by $\Omega^{\cal F}_{a\rightleftharpoons b}$ the frequency asmeasured in a freely falling frame on Earth, one is led to"1184muuch higher than iu the halo or the disk.,much higher than in the halo or the disk.1185 These eccentric binaries. however. could provide a unique opportuuitv for learning about white dwarf structure with (Willemsetal.2007).," These eccentric binaries, however, could provide a unique opportunity for learning about white dwarf structure with \citep{Wil07}."1186. For yp=1l in a 10?ML. halo. we obtain 1.5«10° white dwarfs (single aud binary): 500ον10° binary white dwarfs aud out of these 27.5«10° binary white dwarfs.," For $\eta_{\rm B}=1$ in a $10^9 \msun$ halo, we obtain $1.5 \times 10^{9}$ white dwarfs (single and binary); $500 \times 10^6$ binary white dwarfs and out of these $27.5 \times 10^6$ binary white dwarfs."1187 Oulv 5.5% of double white dwarts have periods shorter than 5.6 hr., Only $5.5\%$ of double white dwarfs have periods shorter than 5.6 hr.1188 Obviously. the above numbers scale down linearly with jp.," Obviously, the above numbers scale down linearly with $\eta_{\rm B}$."1189 Chemo-dynaimical simulations of the Milkv. Wax (Brooketal.2003) have demonstrated that a white dwarf dominated halo that is evolved from a white dwarf progenitor-donuünated initial nass function (Chabrieretal.1996) at early times would lead to an overproduction of carbon aud nitrogen when compared to observed abundances. so the py=1 model is unrealistic.," Chemo-dynamical simulations of the Milky Way \citep{Bro03} have demonstrated that a white dwarf dominated halo that is evolved from a white dwarf progenitor-dominated initial mass function \citep{CSM96} at early times would lead to an overproduction of carbon and nitrogen when compared to observed abundances, so the $\eta_{\rm B}=1$ model is unrealistic."1190 For a realistic upper lait on the white dwarf halo contribution we choose gp=0.3 based ou Lasserreet &5).. and this vields 8.3«109 double white dwarfs inthe halo.," For a realistic upper limit on the white dwarf halo contribution we choose $\eta_{\rm B}=0.3$ based on \citet[][their figure 2; also 1191Brook et al. (2003) their \S\,5]{Las00}, , and this yields $8.3 \times119210^{6}$ double white dwarfs in the halo."1193" Fora Galactic | bulge with a total stellar uass of Gs1019NT, foroll stella types (IKIvpinetal. 2002).. we predict a total of ~1.6«1P white dwarts: 550s10° double white dwarfs. out of which ouly 8% are ‘ound within the baud: LLD5«109 (see RBBLW 3)."," For a Galactic $+$ bulge with a total stellar mass of $6 \times 10^{10} \msun$ for stellar types \citep{klypin:2002:mwmass}, we predict a total of $\sim 1.6 \times 10^{9}$ white dwarfs; $550 \times 10^{6}$ double white dwarfs, out of which only $8\%$ are found within the band: $44.5 \times 10^{6}$ (see RBBLW 3)."1194 Note that the halo is presiued. to include a specific yaction of mass in white dwarts (gp). therefore the xedieted nmuubers of white dwarfs are a direct result of the7) adopted halo mass andE caleulated (with »»pulatiou svuthesis) mass aud period distributions for ido white dwarf binaries with the assumed biuurv yaction.," Note that the halo is presumed to include a specific fraction of mass in white dwarfs $\eta_{\rm B}$ ), therefore the predicted numbers of white dwarfs are a direct result of the adopted halo mass and calculated (with population synthesis) mass and period distributions for halo white dwarf binaries with the assumed binary fraction."1195 For the rest of the Calaxy. in addition to he calculation of double white dwarf properties. we dave computed the white chwarf mass fraction with the adopted Galactic field initial mass fuuctiou (for details see RBBLW).," For the rest of the Galaxy, in addition to the calculation of double white dwarf properties, we have computed the white dwarf mass fraction with the adopted Galactic field initial mass function (for details see RBBLW)."1196 In other words the | diskbulee model results iu a true white dwart formation efficiency per unit mass. While in the halo model this efficicney is iuposed a prioi (through the straight forward application of observational constraints. e.g... MACTIOs).," In other words the $+$ bulge model results in a true white dwarf formation efficiency per unit mass, while in the halo model this efficiency is imposed a priori (through the straight forward application of observational constraints, e.g., MACHOs)."1197 The disk and halo double white dwarf populatious differ significantv dn numbers and physical properties. due to the different environments under which stellar evolution proceeds Guetallicitv. age. star formation history).," The disk and halo double white dwarf populations differ significantly in numbers and physical properties, due to the different environments under which stellar evolution proceeds (metallicity, age, star formation history)."1198" For example. typical average double white chwart chirp masses GV—CUM)/(AL,|ALY. where Af, and M, vepreseut the first formed aud secoud formed white chwarf masses. respectively) of halo svstems are 0.13AD. as compared to 0.19AL. for the disk."," For example, typical average double white dwarf chirp masses ${\cal M} = \left(M_{\rm p}M_{\rm s}\right)^{3/5}/\left(M_{\rm p}+M_{\rm s}\right)^{1/5}$, where $M_{\rm p}$ and $M_{\rm s}$ represent the first formed and second formed white dwarf masses, respectively) of halo systems are $0.13 \msun$ as compared to $ 0.19 \msun$ for the disk."1199 Also. there are relatively few short period double white dwarts in the halo vs. for the | buleec) since this population is older aud a larger number of short period systems have mereec.," Also, there are relatively few short period double white dwarfs in the halo vs. for the $+$ bulge) since this population is older and a larger number of short period systems have merged."1200 Iu particular. some double white dwarf systems form on rather short orbits (c.g. hybrid white with carbou-oxveen white cwart companions). aud none of these svsteiis are found im our 13 Cr old halo population (see below).," In particular, some double white dwarf systems form on rather short orbits (e.g., hybrid white with carbon-oxygen white dwarf companions), and none of these systems are found in our 13 Gyr old halo population (see below)."

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