ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Tn this paper. we show results from) a detailed nerical study of the effects that magnetic fields nav have on the dyvuamical birauode iustabilitv in differentially rotating inagnetized neutron stars.," In this paper, we show results from a detailed numerical study of the effects that magnetic fields may have on the dynamical bar-mode instability in differentially rotating magnetized neutron stars."3 In articular. we investigate how scusitive the onset aud development of the instability is to the presence of imagnetie fields. as well as the role plaved by he magnetorotational instability (MBRI) aud magnetic waking mechanisius to alter the augular momentum distribution in the star and possibly suppress the bar-uode instability.," In particular, we investigate how sensitive the onset and development of the instability is to the presence of magnetic fields, as well as the role played by the magnetorotational instability (MRI) and magnetic braking mechanisms to alter the angular momentum distribution in the star and possibly suppress the bar-mode instability."4 Our study is motivated by the poteutia astrophivsical iuplicatious that the presence of strong naenetic fields iiw have for post-bounce core collapse dvuaiics and. in turn. for gravitational wave astronomy.," Our study is motivated by the potential astrophysical implications that the presence of strong magnetic fields may have for post-bounce core collapse dynamics and, in turn, for gravitational wave astronomy."5 The uncertainty of the streneth aud distribution of naenetic fields in collapse progenitors is reflectec ii our somewhat oad hoc parameterization of he field configuration through ai large sample of equilibrium models of rapidly and highly differcutially rotating mneutrou stars., The uncertainty of the strength and distribution of magnetic fields in collapse progenitors is reflected in our somewhat ad hoc parameterization of the field configuration through a large sample of equilibrium models of rapidly and highly differentially rotating neutron stars.6 Our sample of Newtonian naenetohydrodvuamical (MITID) simulations is base upon the set of purely hydrodynamical models previously analyzed by Newetal.(2000)., Our sample of Newtonian magnetohydrodynamical (MHD) simulations is based upon the set of purely hydrodynamical models previously analyzed by \citet{new00}.7. The simulations are oerformed using the covariant (aud adaptive imesh refinement) code {Auninos&Fragile2003:Auninosetal.2003.2005:Fragile2005) which allows us to perform three-dimensional simulations ou a logarithmically scaled cylindrical erid at hieh resolution.," The simulations are performed using the covariant (and adaptive mesh refinement) code \citep{anninos03a,anninos03b,anninos05,fragile05} which allows us to perform three-dimensional simulations on a logarithmically scaled cylindrical grid at high resolution."8 A umber of equilibrium models of rapidly rotating stars with different values of the rotational instability parameter (3=T/|IV|) aud magnetic plasina beta (op=PfPp). aud differcut polvtropic equatious of state are constructed. introducing also cdiffercut configurations for the maenetic field distribution (of both poloidal aud toroidal varieties) aud field streueths.," A number of equilibrium models of rapidly rotating stars with different values of the rotational instability parameter $\beta=T/|W|$ ) and magnetic plasma beta $\beta_B=P/P_B$ ), and different polytropic equations of state are constructed, introducing also different configurations for the magnetic field distribution (of both poloidal and toroidal varieties) and field strengths."9 The equilibrimm models are perturbed by seceding small random perturbations in order to initiate the onset of the bar-mode deformation., The equilibrium models are perturbed by seeding small random perturbations in order to initiate the onset of the bar-mode deformation.10 The organization of the paper is as follows., The organization of the paper is as follows.11 Section 2 jscusses our basic formalism. nunerical methods. diagnostics. aud the construction of initial data: Section 3 preseuts our results iu two subsectious. oue for initially toroidal ficld configurations aud one for poloidal.," Section \ref{sec:methods} discusses our basic formalism, numerical methods, diagnostics, and the construction of initial data; Section \ref{sec:results} presents our results in two subsections, one for initially toroidal field configurations and one for poloidal."12 We conclude with a sununary and discussion of our results in Section L.., We conclude with a summary and discussion of our results in Section \ref{sec:conclusion}.13 Although the code now inchides options ) solve the full radiative and conductive MIID. equations for Newtoulan svstenis plus multi-species chemical aud unclear reaction networks. we onlv include here the subset of those equations necessuv for the current work.," Although the code now includes options to solve the full radiative and conductive MHD equations for Newtonian systems plus multi-species chemical and nuclear reaction networks, we only include here the subset of those equations necessary for the current work."14 However. see Auninosetal.(2003). for a more complete description of the Newtouian options includiug radiation. or Aunninosetal.(2005) for the general relativistic foriuulation and a discussion of the various enerev formulation options available iu the code.," However, see \citet{anninos03b} for a more complete description of the Newtonian options including radiation, or \citet{anninos05} for the general relativistic formulation and a discussion of the various energy formulation options available in the code."15 In the xeseut study. we use the internal euergy. (and artificial viscosity. A.V.) foxinulatiou due to the robustness of the uethod in tracking adiabats across thin kinematically dominated stellar atinospheres.," In the present study, we use the internal energy (and artificial viscosity, $A.V.$ ) formulation due to the robustness of the method in tracking adiabats across thin kinematically dominated stellar atmospheres."16 The relevant equatious are sutiicicutly different than those published iu our xevious papers (simplified to Newtoniau form aud eeneralized to covariant curvilinear grids) that we write heim out here for convenieuce: 0; =O/OCrepresents covariaut derivatives in eeueralized coordinates £. and J/g is the determinant of the spatial 3-metric g;; defining the coordinate syvstcm (cvlndzrical for this work. with a logarithmically scaled radius to achieve greater resolution iu the stars interior).," The relevant equations are sufficiently different than those published in our previous papers (simplified to Newtonian form and generalized to covariant curvilinear grids) that we write them out here for convenience: where $\partial_i \equiv \partial/\partial\xi^i$ represents covariant derivatives in generalized coordinates $\xi^i$, and $\sqrt{g}$ is the determinant of the spatial 3-metric $g_{ij}$ defining the coordinate system (cylindrical for this work, with a logarithmically scaled radius to achieve greater resolution in the star's interior)."17" Also. p is the fiuid density. V* is the coutravariant fluid velocity. 5,=pl) is the covariant monienutuni. « is the fluid internal energy density. ο is the artificial"," Also, $\rho$ is the fluid density, $V^k$ is the contravariant fluid velocity, $S_k = \rho V_k$ is the covariant momentum, $e$ is the fluid internal energy density, $Q^i_j$ is the artificial"18r+ ( )r.. where V is the svstemic part of the velocity Ποιά as a function of the position vector Pr.,") + ( ), where $\vec{V}$ is the systemic part of the velocity field as a function of the position vector $\vec{r}$."19 It is assumed in the following that positions are determined with respect to Che solar svstem barveenter: any shift of the coordinate svstem origin results in an additional constant translation term., It is assumed in the following that positions are determined with respect to the solar system barycenter; any shift of the coordinate system origin results in an additional constant translation term.20 For convenience. the matrix of transformation is split into the svuunetric (shear) part M. and the antisvyimnietric (raceless (votation) part £.," For convenience, the matrix of transformation is split into the symmetric (shear) part $M$ and the antisymmetric traceless (rotation) part $L$."21 It is reaclily seen that the malrix A describes (he eradient-tvpe distortions of the field. and (he £ part represents rigid rotations. or spins. around (he three coordinate axes.," It is readily seen that the matrix $M$ describes the gradient-type distortions of the field, and the $L$ part represents rigid rotations, or spins, around the three coordinate axes."22 After à small manipulation. the tangential velocity components are Comparing these equations with the (rigonometric expressions [or low-degree vector spherical harmonies (Appendix A). the following relations of proportionality are established where ο. Alo2).," After a small manipulation, the tangential velocity components are Comparing these equations with the trigonometric expressions for low-degree vector spherical harmonics (Appendix A), the following relations of proportionality are established where ); )."23 After à small manipulation. the tangential velocity components are Comparing these equations with the (rigonometric expressions [or low-degree vector spherical harmonies (Appendix A). the following relations of proportionality are established where ο. Alo2).(," After a small manipulation, the tangential velocity components are Comparing these equations with the trigonometric expressions for low-degree vector spherical harmonics (Appendix A), the following relations of proportionality are established where ); )."24 After à small manipulation. the tangential velocity components are Comparing these equations with the (rigonometric expressions [or low-degree vector spherical harmonies (Appendix A). the following relations of proportionality are established where ο. Alo2).(B," After a small manipulation, the tangential velocity components are Comparing these equations with the trigonometric expressions for low-degree vector spherical harmonics (Appendix A), the following relations of proportionality are established where ); )."25 After à small manipulation. the tangential velocity components are Comparing these equations with the (rigonometric expressions [or low-degree vector spherical harmonies (Appendix A). the following relations of proportionality are established where ο. Alo2).(B3," After a small manipulation, the tangential velocity components are Comparing these equations with the trigonometric expressions for low-degree vector spherical harmonics (Appendix A), the following relations of proportionality are established where ); )."26 After à small manipulation. the tangential velocity components are Comparing these equations with the (rigonometric expressions [or low-degree vector spherical harmonies (Appendix A). the following relations of proportionality are established where ο. Alo2).(B3)," After a small manipulation, the tangential velocity components are Comparing these equations with the trigonometric expressions for low-degree vector spherical harmonics (Appendix A), the following relations of proportionality are established where ); )."27since many surveys have revealed that the bulk of the field binary sdB population has periods of approximately P=1 d. systems with P> 5d constituting only the tail end of the period distribution?).,"since many surveys have revealed that the bulk of the field binary sdB population has periods of approximately $P \approx 1$ d, systems with $P \geq 5$ d constituting only the tail end of the period distribution."28. Using the calculated detection probability. we estimated the closebinary fraction fp.34 among EHB stars as in?.. assuming a flat distribution of periods. and the successful detection of one binary out of 41 targets.," Using the calculated detection probability, we estimated the closebinary fraction $f_{P\leq 5\,{\rm d}}$ among EHB stars as in, assuming a flat distribution of periods, and the successful detection of one binary out of 41 targets."29 We calculated fp.s4 assuming a Gaussian distribution in logP. as in?) and?.. which better represents the period distribution for field sdBs—but the results do not differ noticeably.," We calculated $f_{P\leq 5\,{\rm d}}$ assuming a Gaussian distribution in $\log P$, as in and, which better represents the period distribution for field sdBs—but the results do not differ noticeably."30 The derived. probability. distribution peaks atf=4%., The derived probability distribution peaks at $f = 4\%$.31 It is markedly non-Gaussian. but it falls below for f>16%.," It is markedly non-Gaussian, but it falls below for $f\geq 16\%$."32 We conclude that the best estimate (1.e.. the most likely value) for fp.sq is4%.. and that fp.sq<16% at the confidence level.," We conclude that the best estimate (i.e., the most likely value) for $f_{P\leq 5\,{\rm d}}$ is, and that $f_{P\leq 5\,{\rm d}}\leq$ at the confidence level."33 Our derived upper limit is 1n perfect agreement with the one that was found for fp<jog by?.," Our derived upper limit is in perfect agreement with the one that was found for $f_{P\leq 10\,{\rm d}}$ by."34. We note that these results are at variance with the preliminary ones previously obtained by?.. who claimed the detection of many close binaries among the EHB stars in the same cluster.," We note that these results are at variance with the preliminary ones previously obtained by, who claimed the detection of many close binaries among the EHB stars in the same cluster."35 The reader ts referred to for a discussion of this discrepancy., The reader is referred to for a discussion of this discrepancy.36 Using an independent dataset. a sample more than twice as large as in2.. and a resolution in RV variations that is higher by almost a factor of two. for the first time we were able to find a good binary candidate among the EHB stars in6752.," Using an independent dataset, a sample more than twice as large as in, and a resolution in RV variations that is higher by almost a factor of two, for the first time we were able to find a good binary candidate among the EHB stars in."37. That notwithstanding. our results confirm. that the corresponding (close) binary fraction f is very small in6752.. with a most likely value of f=4% and an upperlimit of f=16% at the confidence level.," That notwithstanding, our results confirm that the corresponding (close) binary fraction $f$ is very small in, with a most likely value of $f = 4\%$ and an upperlimit of $f = 16\%$ at the confidence level."38 There are hints that a small f£ is not a peculiarity of6732.. but could also be a characteristic of other globular clusters(2).," There are hints that a small $f$ is not a peculiarity of, but could also be a characteristic of other globular clusters."39. This is in sharp contrast with the situation for field sdB stars. where close binaries are at least a factor of ten more frequent. comprising up to of the entire sdB populationreview).," This is in sharp contrast with the situation for field sdB stars, where close binaries are at least a factor of ten more frequent, comprising up to of the entire sdB population."40. There is however no knowledge about cluster EHB stars in long-period binaries. or with à close low-mass companion. because no survey has investigated their role yet.," There is however no knowledge about cluster EHB stars in long-period binaries, or with a close low-mass companion, because no survey has investigated their role yet."41 These kind of systems are known to exist among field sdBs. but are just a minor population. and their presence in GCs would not alleviate the striking contrast with field results.," These kind of systems are known to exist among field sdBs, but are just a minor population, and their presence in GCs would not alleviate the striking contrast with field results."42 What is the origin of this startling difference betwee=) field and cluster EHB stars?, What is the origin of this startling difference between field and cluster EHB stars?43 We believe that it may not be completely unexpected: there should be a relation between th[27 close binary fraction and the mean age of a sdB population. as à consequence of the different efficiency of binary channels responsible for EHB star formation.," We believe that it may not be completely unexpected: there should be a relation between the close binary fraction and the mean age of a sdB population, as a consequence of the different efficiency of binary channels responsible for EHB star formation."44 Theoretical arguments strongly suggest that sdB stars in close binary systems should have undergone at least one common envelope (CE) phase., Theoretical arguments strongly suggest that sdB stars in close binary systems should have undergone at least one common envelope (CE) phase.45 Although found an upper limit for the initial mass of the sdB progenitor in this scenario. they also pointed out that within the permitted values a higher initial mass favors the CE channel. and leads to sdB binaries with shorter periods.," Although found an upper limit for the initial mass of the sdB progenitor in this scenario, they also pointed out that within the permitted values a higher initial mass favors the CE channel, and leads to sdB binaries with shorter periods."46 In facet. a higher mass implies a more tightly-bound envelope. which requires a greater amount of (orbital) energy to be released.," In fact, a higher mass implies a more tightly-bound envelope, which requires a greater amount of (orbital) energy to be released."47 On the other hand. explored the stable Roche Lobe Overflow (RLOF) scenario. and found that a higher initial progenitor mass makes it harder for the RLOF to be stable (see their Table 3). because the minimum mass of the companion increases with increasing. progenitor mass.," On the other hand, explored the stable Roche Lobe Overflow (RLOF) scenario, and found that a higher initial progenitor mass makes it harder for the RLOF to be stable (see their Table 3), because the minimum mass of the companion increases with increasing progenitor mass."48 For higher values. fewer MS and white dwarf (WD) secondaries are sufficiently massive for the activation of this channel (sdB's with neutron star companions are indeed very rare).," For higher values, fewer MS and white dwarf (WD) secondaries are sufficiently massive for the activation of this channel (sdB's with neutron star companions are indeed very rare)."49 The progeny of systems that underwent stable RLOF. that is wide binaries with very long periods. is therefore generated primarily by progenitors of lower initial mass.," The progeny of systems that underwent stable RLOF, that is wide binaries with very long periods, is therefore generated primarily by progenitors of lower initial mass."50 In light of these results. a relation between f and the mean initial mass of the sdB progenitors could be naturally expected. hence implying a relationship between f and (mean) age.," In light of these results, a relation between $f$ and the mean initial mass of the sdB progenitors could be naturally expected, hence implying a relationship between $f$ and (mean) age."51 More specifically. one may naturally expect that field sdB's formed from progenitors with a wide spectrum of initial masses (up to about 2 Mc). whereas in an old population (such as in globular clusters) only the progeny of less massive stars are currently found on the EHB. those of more massive ones having long evolved away from the He-burning phase.," More specifically, one may naturally expect that field sdB's formed from progenitors with a wide spectrum of initial masses (up to about $2\,M_{\sun}$ ), whereas in an old population (such as in globular clusters) only the progeny of less massive stars are currently found on the EHB, those of more massive ones having long evolved away from the He-burning phase."52 The stable RLOF is an efficient channel for sdB formation in the old case. while the CE one is not—and the CE itself would be released at earlier stages. before the orbits shrink substantially.," The stable RLOF is an efficient channel for sdB formation in the old case, while the CE one is not—and the CE itself would be released at earlier stages, before the orbits shrink substantially."53 Therefore. in old populations we should expect to find predominantly wide binaries. or/and single EHB stars formed through other channels discussion).," Therefore, in old populations we should expect to find predominantly wide binaries, or/and single EHB stars formed through other channels ."54. In fact. WD mergers. the third binary channel studied by ?.. can form (single)," In fact, WD mergers, the third binary channel studied by , can form (single)"55Figure 6 plots the relation between circularity and eccentricity for orbits near the solar radius (5.0 kpc) in the disk.,Figure \ref{fig:ecc_circ} plots the relation between circularity and eccentricity for orbits near the solar radius $8.0\kpc$ ) in the disk.56 Cireularity is related to eccentricity via the particle's radial and vertical energies as well as its orbital inclination (since JJ. is a projected quantity)., Circularity is related to eccentricity via the particle's radial and vertical energies as well as its orbital inclination (since $J_z$ is a projected quantity).57 Orbits in the midplane of the disk have the highest circularity for a given eccentricity., Orbits in the midplane of the disk have the highest circularity for a given eccentricity.58" Shaded regions in Figure 6 show the 95'"" and 99!"" percentile circularity as a function of eccentricity at the solarradius.", Shaded regions in Figure \ref{fig:ecc_circ} show the $95^{th}$ and $99^{th}$ percentile circularity as a function of eccentricity at the solarradius.59 For reference in interpreting Figure 5. and subsequent figures. it is worth noting that changes of ~0.02 in ttypically correspond to quite noticeable changes in eccentricity.," For reference in interpreting Figure \ref{fig:lindblad} and subsequent figures, it is worth noting that changes of $\sim 0.02$ in typically correspond to quite noticeable changes in eccentricity."60 The boundaries of these regions are not smooth due to binning and small number statistics for initially high eccentricity particles., The boundaries of these regions are not smooth due to binning and small number statistics for initially high eccentricity particles.61 Returning to Figure 5.. we see that the two isolated disks show markedly different evolution of their circularity distributions.," Returning to Figure \ref{fig:lindblad}, we see that the two isolated disks show markedly different evolution of their circularity distributions."62 In the isolated thin disk. the fraction of stars with | trightmost bin) drops from 0.38 to 0.26. and the median ddrops from 0.980 to 0.955.," In the isolated thin disk, the fraction of stars with $\sim1$ (rightmost bin) drops from $0.38$ to $0.26$, and the median drops from $0.980$ to $0.955$."63 Particles in the bar predominantly populate the newly formed low circularity tail., Particles in the bar predominantly populate the newly formed low circularity tail.64 In the thick isolated disk. on the other hand. the ddistribution is nearly identical to the initial disks. with median ddropping onlywt 0.002.," In the thick isolated disk, on the other hand, the distribution is nearly identical to the initial disk's, with median dropping only $0.002$."65 This lack of evolution in the circularity distribution is fully consistent with CR scattering., This lack of evolution in the circularity distribution is fully consistent with CR scattering.66 As described by SBO2. individual stars may exchange angular momentum across CRs (churning) while the overall distribution would remain unchanged.," As described by SB02, individual stars may exchange angular momentum across CRs (churning) while the overall distribution would remain unchanged."67 However. our results from Section ο show that the Delta R distribution of this model. which reflects individual particles and their orbits. is nearly identical to that expected from observing the particles’ initially elliptical orbits.," However, our results from Section \ref{sec:radmix} show that the Delta R distribution of this model, which reflects individual particles and their orbits, is nearly identical to that expected from observing the particles' initially elliptical orbits."68 The circularity distribution of the isolated. thick disk combined with its Delta R distribution imply that. on average. individual particle guiding centers are not significantly modified.," The circularity distribution of the isolated, thick disk combined with its Delta R distribution imply that, on average, individual particle guiding centers are not significantly modified."69 The circularity distributions of the perturbed disks are demonstrably altered from their isolated counterparts but are similar to one another., The circularity distributions of the perturbed disks are demonstrably altered from their isolated counterparts but are similar to one another.70 The most common circularities are now in the range 0.96.x«0.98 in both disks. with a decrease for (40.98," The most common circularities are now in the range $0.96\leq71\cir \leq 0.98$ in both disks, with a decrease for $>0.98$."72 Thelhindiskstariswilh | particles because of its smaller moreorbital inclinations. and its cireularity distribution evolves more strongly. with median ddropping from 0.980 to 0.936 vs. 0.963 to 0.929 for the perturbed thick disk.," The thin disk starts with more $\sim 1$ particles because of its smaller orbital inclinations, and its circularity distribution evolves more strongly, with median dropping from $0.980$ to $0.936$ vs. $0.963$ to $0.929$ for the perturbed thick disk."73 Notably. the perturbed thin and thick disks evolve to similar (Figure 3)) and ddistributions despite starting with different scale heights.," Notably, the perturbed thin and thick disks evolve to similar (Figure \ref{fig:perdisks}) ) and distributions despite starting with different scale heights."74 Figure 7 tracks the changes of selected individual particles in the (A. J.) space of the Lindblad diagram.," Figure \ref{fig:lindzoom} tracks the changes of selected individual particles in the $E$, $J_z$ ) space of the Lindblad diagram."75" While { and JJ. are not individually conserved in the presence of a non-axisymmetric perturbation. the Jacobi invariant £=fFQ,./. is. where ©), is the pattern speed of the perturbation. assumed to be static and small (SBO2: Sellwood 20103)."," While $E$ and $J_z$ are not individually conserved in the presence of a non-axisymmetric perturbation, the Jacobi invariant $I=E-\Omega_b J_z$ is, where $\Omega_b$ is the pattern speed of the perturbation, assumed to be static and small (SB02; \citealt{Sellwood10}) )."76 If Ad=0. then AJ./ALzOy.," If $\Delta I= 0$, then $\Delta J_z / \Delta E \approx \Omega_b$."77" The SBO2 mechanism operates at the corotation resonance of the star/particle and the spiral wave. requiring that Q,,=O,,."," The SB02 mechanism operates at the corotation resonance of the star/particle and the spiral wave, requiring that $\Omega_b=\Omega_\mathrm{rot}$."78 Thus. in the galaxy. particles should move parallel to the line that is tangent to the circular orbit curve at their binding energy prior to scattering.," Thus, in the galaxy, particles should move parallel to the line that is tangent to the circular orbit curve at their binding energy prior to scattering."79 In other words. the SBO2 mechanism requires that changes in energy be accompanied by changes in angular momentum that preserve the orbital shape. modulo differences in the slope of the circular orbit curve over the range zi.£1] of a given particle.," In other words, the SB02 mechanism requires that changes in energy be accompanied by changes in angular momentum that preserve the orbital shape, modulo differences in the slope of the circular orbit curve over the range $[E_\mathrm{i}, E_\mathrm{f}]$ of a given particle."80 Figure 7. zooms in on the area of the Lindblad diagram designated by the two small boxes drawn on the initial state diagrams in Figure 5.., Figure \ref{fig:lindzoom} zooms in on the area of the Lindblad diagram designated by the two small boxes drawn on the initial state diagrams in Figure \ref{fig:lindblad}. .81 We randomly select ten particles within the, We randomly select ten particles within the82]t is assumed that the AMI is constant over the orbital fit interval.,It is assumed that the AMR is constant over the orbital fit interval.83 A default value of 0.02 nzkg.+ is selected. which corresponds to an AMIR: value of a standard GPS satellite. in case the AMI parameter is not estiniated but kept fixed in the orbit. determination.," A default value of 0.02 $\text{m}^2\text{kg}^{-1}$ is selected, which corresponds to an AMR value of a standard GPS satellite, in case the AMR parameter is not estimated but kept fixed in the orbit determination."84 For ILAMIS objects always an AAR value is estimated., For HAMR objects always an AMR value is estimated.85 The shadow. paths of the orbit are modeled. under the assumption of a spherical earth. on a mean circular orbit: the boundary between sunlit and eclipsed part is assumed to be evlindrical. no distinction. between penumbra anc umbra is mace. earth atmosphere is For a long term investigation of the orbits and the AMI values. different comparable orbits have to be determined.," The shadow paths of the orbit are modeled, under the assumption of a spherical earth on a mean circular orbit; the boundary between sunlit and eclipsed part is assumed to be cylindrical, no distinction between penumbra and umbra is made, earth atmosphere is For a long term investigation of the orbits and the AMR values, different comparable orbits have to be determined."86 Only sparse observations are available. which are unequally. spaced in time.," Only sparse observations are available, which are unequally spaced in time."87 A normalized setup is developed. tested with two low AMI objects and two of the LLAMIR objects of the AIUD catalog and applied for the ereation of comparable orbits for the investigation of the ILXMI objects.," A normalized setup is developed, tested with two low AMR objects and two of the HAMR objects of the AIUB catalog and applied for the creation of comparable orbits for the investigation of the HAMR objects."88 Four representative GEO objects from the internal catalogue of the AIUB were chosen. they have been Followed: over longer time periods ancl are not listed. in the USSTRATCOAL catalogue.," Four representative GEO objects from the internal catalogue of the AIUB were chosen, they have been followed over longer time periods and are not listed in the USSTRATCOM catalogue."89 Those objects are clearly space debris. since no maneuvers could be detected. in the data.," Those objects are clearly space debris, since no maneuvers could be detected in the data."90 The IUD clid not have information what those objects actually were before. becoming debris., The AIUB did not have information what those objects actually were before becoming debris.91 From the apparent magnitude it can be concluded: that those are all fragmentation pieces., From the apparent magnitude it can be concluded that those are all fragmentation pieces.92 They represent. typical objects Found in GEO surveys., They represent typical objects found in GEO surveys.93 Fheir properties are listed in Tab. L.., Their properties are listed in Tab. \ref{prop}.94 Two of the objects have low area to mass ratios. two objects qualify as ILXMIU objects with an MIU. value larger than κο.," Two of the objects have low area to mass ratios, two objects qualify as HAMR objects with an AMR value larger than $m^2/kg$."95 Lhe optical angle-ouly observations are obtained with ZIAILAT (Zimmerwalel. Switzerland). and ISASDT (lLenerife. Spain). supplemented. by some observations of the ISON network provided by the Ixeldvsh Institute of Applied: Mathematics. Moscow. Russia.," The optical angle-only observations are obtained with ZIMLAT (Zimmerwald, Switzerland), and ESASDT (Tenerife, Spain), supplemented by some observations of the ISON network provided by the Keldysh Institute of Applied Mathematics, Moscow, Russia."96 The latter observations were obtained from. clillerent sites. of the ISON network. in these particular cases. all located in Eastern All orbits were determined. from. two observation sets only. using a priori orbital elements.," The latter observations were obtained from different sites of the ISON network, in these particular cases, all located in Eastern All orbits were determined from two observation sets only, using a priori orbital elements."97 A maximum of eight observations are allowed per set., A maximum of eight observations are allowed per set.98 An observation set. may consist. of more than one tracklet., An observation set may consist of more than one tracklet.99 But the observations within the sets should not be distributed over more than three days., But the observations within the sets should not be distributed over more than three days.100 Orbits were determined. for dillerent spacings of two observation sets stemming a) from one observation site only and b) from cilferent sites., Orbits were determined for different spacings of two observation sets stemming a) from one observation site only and b) from different sites.101 In the first case. the observations either stem from ZIMLAT or from ESASDT only.," In the first case, the observations either stem from ZIMLAT or from ESASDT only."102 In the second case. not only the observations of ZIAILAT and ESASD'T were combined but also observations of the ISON network. if available.," In the second case, not only the observations of ZIMLAT and ESASDT were combined but also observations of the ISON network, if available."103 When observations from cdillerent sites are used in orbit determination. the distribution is either that the first set of observations stenis [rom one site and the second from another. or that there are observations from different sites at similar epochs used within the first and/or the last set of observations or a mixture of those options.," When observations from different sites are used in orbit determination, the distribution is either that the first set of observations stems from one site and the second from another, or that there are observations from different sites at similar epochs used within the first and/or the last set of observations or a mixture of those options."104 In the figures the label is applied. when observations of ZIAILAT (labeled ZLAZ)). the ESASD'T and of the ISON network are combined: the label is applied. if only the observations of ZIAILAT and the ESASDT are used.," In the figures the label is applied, when observations of ZIMLAT (labeled ), the ESASDT and of the ISON network are combined; the label is applied, if only the observations of ZIMLAT and the ESASDT are used."105 The distances between the observations and. the ephemoerides of the predicted orbits of the four objects for à prediction interval of 50 days after the last observation used for orbit determination were determined., The distances between the observations and the ephemerides of the predicted orbits of the four objects for a prediction interval of 50 days after the last observation used for orbit determination were determined.106 The distances were averaged and a mean value ancl standard. deviation was calculated., The distances were averaged and a mean value and standard deviation was calculated.107 Between six and 50 single distances between ephemerides and observations were The predicted. ephemeris positions are compared. to the optical angle-only observations. which were not used in orbit determination.," Between six and 50 single distances between ephemerides and observations were The predicted ephemeris positions are compared to the optical angle-only observations, which were not used in orbit determination."108 Angular distances are determined on the celestial sphere., Angular distances are determined on the celestial sphere.109 Phe observation used. for. the comparison stem from ZIMLAT and ISASDT and serve as erouncl truth., The observation used for the comparison stem from ZIMLAT and ESASDT and serve as ground truth.110 Calibration measurements with high accuracy ephemerides of Global Navigation Satellite System (GNSS) satellites provided. by International. GNSS Service. (GS) showed an accuracy of the measurements of ZIAILAT and ESASDT of below one aresecond., Calibration measurements with high accuracy ephemerides of Global Navigation Satellite System (GNSS) satellites provided by International GNSS Service (IGS) showed an accuracy of the measurements of ZIMLAT and ESASDT of below one arcsecond.111 That the further observations in fact belong to the same object is validated via an orbit determination with both the observations used. in the original sparse data orbit determination and the observations. which they were compared. to.," That the further observations in fact belong to the same object is validated via an orbit determination with both the observations used in the original sparse data orbit determination and the observations, which they were compared to."112 An orbit determination with a root-mean-square of below two areseconds is a reliable tool to associate observations of this accuracy of the same object to cach other. as shown with cluster observations in ?..," An orbit determination with a root-mean-square of below two arcseconds is a reliable tool to associate observations of this accuracy of the same object to each other, as shown with cluster observations in \citet{Musci05b}."113 In Fig., In Fig.114 1 the angular distance between predicted: and observed. position are. cisplaveck as a function of the time interval between the first and the last observation. which were used in orbit. determination.," \ref{resE03174A} the angular distance between predicted and observed position are displayed as a function of the time interval between the first and the last observation, which were used in orbit determination."115 Displayed are the mean values and the standard deviations of the angular distances of the single orbits., Displayed are the mean values and the standard deviations of the angular distances of the single orbits.116 Phe mean value and standard deviations are determined with the single angular distances of predicted: position to observed. ones. all within 50r clays since orbit Figure 1 shows that the angular distances are in general very small.," The mean value and standard deviations are determined with the single angular distances of predicted position to observed ones, all within 50 days since orbit Figure \ref{resE03174A} shows that the angular distances are in general very small."117 “Phe vast majority of the determined. orbits even produce distances smaller than 0.6 degrees., The vast majority of the determined orbits even produce distances smaller than 0.6 degrees.118 Except, Except119next innermost component (GabuzdaandCawthorne2000:Homanetal.2002).,"next innermost component \citep{gab00,hom02}."120. Clearly. flix and polarization monitoring al well-selectecd [frequencies remains an essential tool [or probing the detailed changes in the jet flow and unraveling the complex opacitv-dependent effects within it.," Clearly, flux and polarization monitoring at well-selected frequencies remains an essential tool for probing the detailed changes in the jet flow and unraveling the complex opacity-dependent effects within it."121 IIopefully. a combination of imaging and monitoring of both blazars ancl other (vpes of extragalactic objects will ultimately lead (ο a more complete understanding ol their origin and evolution.," Hopefully, a combination of imaging and monitoring of both blazars and other types of extragalactic objects will ultimately lead to a more complete understanding of their origin and evolution."122 Finally. while we continue to believe thal the features of the variability apparent in our data can most readily be explained within the standard picture of relativistic jet. Lows containing passive magnetic fields aud (he naturallv-«developing instabilities within them. we nole (hat an alternative picture has recently been proposed by Blancllord(2003) based on dvnaimo models and ensuing currents.," Finally, while we continue to believe that the features of the variability apparent in our data can most readily be explained within the standard picture of relativistic jet flows containing passive magnetic fields and the naturally-developing instabilities within them, we note that an alternative picture has recently been proposed by \citet{blan03} based on dynamo models and ensuing currents."123 Once detailed predictions of the fIux and polarization are available for (his class of model. it will be most interesting to compare them with the range of behaviors discussed here.," Once detailed predictions of the flux and polarization are available for this class of model, it will be most interesting to compare them with the range of behaviors discussed here."124 Our main results are as follows: 1., Our main results are as follows: 1.125 Weidentilv variability in steep spectrum objects (ssc and ed classes by radio morphology) which is characterized by infrequent events or longterm monotonic changes., We identify variability in steep spectrum objects (ssc and cd classes by radio morphology) which is characterized by infrequent events or longterm monotonic changes.126 This group includes 3C 147 and calls into question its use as a secondary Εις standard., This group includes 3C 147 and calls into question its use as a secondary flux standard.127 2., 2.128 We have tentatively identified small-aumplitude variations in several lobe-dominated sources including 3C 179. 3C 236. and 3C 390.3.," We have tentatively identified small-amplitude variations in several lobe-dominated sources including 3C 179, 3C 236, and 3C 390.3."129 These variations are consistent with information on core strengths and the ratio of core to total flux known from radio maps ol those objects., These variations are consistent with information on core strengths and the ratio of core to total flux known from radio maps of those objects.130 3., 3.131 We have provided evidence in support of our view that variability is a pervasive phenomenon in extragalactic objects. and that the majority of extragalactic objects exhibit aclivitv which can be identilied [rom integrated light curves over time periods of order 1-2 decades.," We have provided evidence in support of our view that variability is a pervasive phenomenon in extragalactic objects, and that the majority of extragalactic objects exhibit activity which can be identified from integrated light curves over time periods of order 1-2 decades."132 This long time range is crucial for the case of the steep spectrum objects where large events are required for detection because of the dominant contribution from extended structure., This long time range is crucial for the case of the steep spectrum objects where large events are required for detection because of the dominant contribution from extended structure.133 4., 4.134 We lind no strong evidence for periodicity for any sample members based on a Scarele periodogram analysis of our total Πας densitv data. nor are we able to identify the signature ol precession in the temporal evolution of the EVPAs.," We find no strong evidence for periodicity for any sample members based on a Scargle periodogram analysis of our total flux density data, nor are we able to identify the signature of precession in the temporal evolution of the EVPAs."135 5., 5.136 We find a range of behavior in the polarization spectra of the steep-spectrum objects., We find a range of behavior in the polarization spectra of the steep-spectrum objects.137 The flat-to-inverted. spectra. we find in several source members is consistent. wilh Faraday depolarization by a Faraday. screen., The flat-to-inverted spectra we find in several source members is consistent with Faraday depolarization by a Faraday screen.138 6., 6.139 We find loneterm EVPA stability in many objects indicative of a persistent. dominant," We find longterm EVPA stability in many objects indicative of a persistent, dominant"140is greater than a certain chosen value is given bv the formula: with standard deviation of the amplitude: In cases of testing η and p angles we can pul = insteacl of zz.,is greater than a certain chosen value is given by the formula: with standard deviation of the amplitude: In cases of testing $\eta$ and $p$ angles we can put $=$ instead of $\approx$.141 This test was originally introduced by Lawley&Peebles(1975). and substantially mocdified by Gocllowski(1993.1994).," This test was originally introduced by \citet{h4} and substantially modified by \citet{g2,g3}."142. In the paper Gocllowski(1994) the case with higher Fourier modes taken into account was discussed: Amplitude A it i$ now the function for all four A;; coefficients., In the paper \citet{g3} the case with higher Fourier modes taken into account was discussed: Amplitude $\Delta$ it is now the function for all four $\Delta_{ij}$ coefficients.143 Generally. when we take into consideration both Fourier modes 28 and 49. the formulas are complicated and (his was discussed in details in Godlowski(1994).5.," Generally, when we take into consideration both Fourier modes $2\theta$ and $4\theta$, the formulas are complicated and this was discussed in details in \citet{g3}144."145" From the sign of Ay, coefficient one can deduce the direction of departure from isotropy.", From the sign of $\Delta_{11}$ coefficient one can deduce the direction of departure from isotropy.146" If Ay,<0. then the excess of the galaxies with 9 angle near 90° is observed."," If $\Delta_{11}<0$, then the excess of the galaxies with $\theta$ angle near $90^o$ is observed."147" [It indicates for example that in the case of the position angles (6= p) Ay,<0 means that the excess of ealaxies wilh position angles near 90"" (parallel to main plane of (he coordinate svstem) is observed.", It indicates for example that in the case of the position angles $\theta \equiv p$ ) $\Delta_{11}<0$ means that the excess of galaxies with position angles near $90^o$ (parallel to main plane of the coordinate system) is observed.148" HL Ay,270 then the excess of objects with position angles perpendicular to the main plane of the coordinate svstem is observed.", If $\Delta_{11}>0$ then the excess of objects with position angles perpendicular to the main plane of the coordinate system is observed.149" Therefore. for Ay,>0 the rotation axis projections tends to be parallel to (he main plane."," Therefore, for $\Delta_{11}>0$ the rotation axis projections tends to be parallel to the main plane."150of the anisotropic distribution of the plasma in velocity space. 1.9. a loss-cone distribution.,"of the anisotropic distribution of the plasma in velocity space, i.e. a loss-cone distribution."151 The plasma including a loss-cone distribution ts unstable: instability arises very quickly from such a distribution., The plasma including a loss-cone distribution is unstable; instability arises very quickly from such a distribution.152 A large amount of free energy can be released via the instability and converted to electromagnetic waves - see ?. for a review of the process., A large amount of free energy can be released via the instability and converted to electromagnetic waves - see \citet{Dulk85} for a review of the process.153 An external magnetic-field-aligned electric field (222) induced by à time-varying external current source (?) would further modify the plasma velocity distribution to shell or horseshoe form. leading to an enhanced ECMI emission.," An external magnetic-field-aligned electric field \citep{Cattell98,Zarka98,Ergun00} induced by a time-varying external current source \citep{Omura03} would further modify the plasma velocity distribution to shell or horseshoe form, leading to an enhanced ECMI emission."154 In this paper. we assume for simplicity that the ECMI emission from UCDs ts driven by the loss-cone distribution.," In this paper, we assume for simplicity that the ECMI emission from UCDs is driven by the loss-cone distribution."155 The existence of the electric field and its effect will be addressed in future work., The existence of the electric field and its effect will be addressed in future work.156 In a loss-cone region where the ECMI operates. the maser radiation is concentrated on the surface of a hollow cone as discussed by ? (see Fig.," In a loss-cone region where the ECMI operates, the maser radiation is concentrated on the surface of a hollow cone as discussed by \citet{Melrose82} (see Fig."157 1. top panel)., \ref{fig_ucdspot} top panel).158 The half-angle ao of the hollow cone depends on the ratio of the velocity of the plasma electrons to the speed of light. i.e. cosag=v/c.," The half-angle $\alpha_{0}$ of the hollow cone depends on the ratio of the velocity of the plasma electrons to the speed of light, i.e. $\alpha_{0}=v_{p}/c$."159" For example. if v,/c=0.5. we have ag=60°."," For example, if $v_{p}/c=0.5$, we have $\alpha_{0}=60^{\circ}$."160 The surface of the cone should be very thi with Aw=vy/c., The surface of the cone should be very thin with $\Delta\alpha\approx v_{p}/c$.161 The naser emission in the loss-cone region can be observed if the line of sight i5 located within a thin conical sheet with thickness Aa., The maser emission in the loss-cone region can be observed if the line of sight is located within a thin conical sheet with thickness $\Delta\alpha$.162 For a low magnetic loop with a small angle between the magnetic field and the surface of the UCD. the maser emission can be seen when the emission ts near the top of the loop.," For a low magnetic loop with a small angle between the magnetic field and the surface of the UCD, the maser emission can be seen when the emission is near the top of the loop."163 The maser emission from near the foot-point (where the magnetic field is almost perpendicular to the surface of UCD) can be seen when the loop is near the limb., The maser emission from near the foot-point (where the magnetic field is almost perpendicular to the surface of UCD) can be seen when the loop is near the limb.164 However. for a large scale. the maser emission could have an angular distribution.," However, for a large scale, the maser emission could have an angular distribution."165 In our calculation. we assume we can observe the maser emission in each flux tube in the active region.," In our calculation, we assume we can observe the maser emission in each flux tube in the active region."166 By analogy to the solar coronal radio emission. powered by two populations of plasma from the Sun with different velocity. we propose there be similar active regions on UCDs.," By analogy to the solar coronal radio emission powered by two populations of plasma from the Sun with different velocity, we propose there be similar active regions on UCDs."167 We note that. however. an alternative mechanism. where the hot plasma beam could result from the interaction of a close-in companion of the UCD. re. magnetized or non-magnetized satellites resulting in auroral emission. similar to Io-Jupiter system (???).. is possible.," We note that, however, an alternative mechanism, where the hot plasma beam could result from the interaction of a close-in companion of the UCD, i.e. magnetized or non-magnetized satellites resulting in auroral emission, similar to Io-Jupiter system \citep{Queinnec98,Saur04,Zarka05}, , is possible."168 ECM emission has been detected in compact objects. such as white dwarfs (??) or neutron stars (?)..," ECM emission has been detected in compact objects, such as white dwarfs \citep{Willes04,Willes05} or neutron stars \citep{Wolszczan92}."169 We are not able to rule out this model and the competition between the two models should be investigated in further work., We are not able to rule out this model and the competition between the two models should be investigated in further work.170 The fine structure and time interval of the observations described in $2 indicate that the radio-emitting region on TVLM 513 would consist of complex substructures., The fine structure and time interval of the observations described in \ref{sec_tvlm} indicate that the radio-emitting region on TVLM 513 would consist of complex substructures.171" The detected flux density S may be the sum of several small sources where S; 1s the flux density for a small source which can be determined by the relation (?) where 7), is the brightness temperature of a source. kg is the Boltzmann constant. f is the observed frequency. c is the speed of light. dQ is the differential solid angle."," The detected flux density $\tilde{S}$ may be the sum of several small sources where $S_{\rm i}$ is the flux density for a small source which can be determined by the relation \citep{Dulk85}172 where $T_{\rm b}$ is the brightness temperature of a source, $k_{\rm B}$ is the Boltzmann constant, $f$ is the observed frequency, $c$ is the speed of light, $\Omega$ is the differential solid angle."173 If we assume that the radiation is isotropic. the differential solid angle should depend on the radius of the flux tube “ype of the small source and its distance from the observer.," If we assume that the radiation is isotropic, the differential solid angle should depend on the radius of the flux tube $r_{\rm tube}$ of the small source and its distance from the observer."174 The flux density $; can be expressed as For simplicity. we assume that the active region has a symmetric shape. and the small sources are randomly distributed within the region.," The flux density $S_{i}$ can be expressed as For simplicity, we assume that the active region has a symmetric shape, and the small sources are randomly distributed within the region."175 The number of small sources (2) may be determined by rotation of the UCD., The number of small sources $\tilde{n}(t)$ may be determined by rotation of the UCD.176 We set the time t=0 to be the moment when the first active region emerges in the field of view of the observer; this is also the onset time of a radio pulse., We set the time $t=0$ to be the moment when the first active region emerges in the field of view of the observer; this is also the onset time of a radio pulse.177 With the rotation of the UCD. the area of the active region seen by the observer increases until it reaches a maximum. and then it decreases and disappears from the field of view of the observer.," With the rotation of the UCD, the area of the active region seen by the observer increases until it reaches a maximum, and then it decreases and disappears from the field of view of the observer."178 The maximum number of small sources is where Tucp is the rotation period. R’ is the height of the active region. & is the latitude of the active region and Ar is the time interval from the beginning of a pulse to the maximum flux.," The maximum number of small sources is where $T_{\rm UCD}$ is the rotation period, $R'$ is the height of the active region, $\theta$ is the latitude of the active region and $\Delta t$ is the time interval from the beginning of a pulse to the maximum flux."179 The time duration of a pulse would be 2A; for a symmetric shape., The time duration of a pulse would be $\Delta t$ for a symmetric shape.180 We assume that the radio emission is from a thin shell of the active region near the surface of the UCD. so that we can take y=2 and A'=Rucp where Rucp is the radius of the UCD.," We assume that the radio emission is from a thin shell of the active region near the surface of the UCD, so that we can take $\gamma\approx2$ and $R'\approx R_{\rm UCD}$ where $R_{\rm UCD}$ is the radius of the UCD."181 The brightness temperature of small sources depends strongly on the growth rate of the ECM emission and. incoherent radiation of the background plasma., The brightness temperature of small sources depends strongly on the growth rate of the ECM emission and incoherent radiation of the background plasma.182" If we assume the maser emission is operated by the loss-cone distribution of a population of hot plasma expressed by a Maxwellian multiplied by the function sin""(e/o,-7/2) and an isotropic Maxwellian distribution of a cold background plasma. the brightness temperature can be determined by the parameters of these two types of plasma."," If we assume the maser emission is operated by the loss-cone distribution of a population of hot plasma expressed by a Maxwellian multiplied by the function $\sin^{N}(\alpha/\alpha_{\rm c}\cdot \pi/2)$ and an isotropic Maxwellian distribution of a cold background plasma, the brightness temperature can be determined by the parameters of these two types of plasma."183 We adopt the quasi-linear theory developed by ? to determine the growth rate and the efficiency of energy conversion., We adopt the quasi-linear theory developed by \citet{Aschwanden90a} to determine the growth rate and the efficiency of energy conversion.184 Here. we summarize the basic assumptions and the effects of several free parameters.," Here, we summarize the basic assumptions and the effects of several free parameters."185 The quasi-linear code of ? describes the evolution of the ECM instability and the wave-particle interactions by solving the kinetic wave-particle equations in a locally homogeneous plasma., The quasi-linear code of \citet{Aschwanden90b} describes the evolution of the ECM instability and the wave-particle interactions by solving the kinetic wave-particle equations in a locally homogeneous plasma.186 The wave equation includesinduced gyroresonance emission/absorption (for the X-. O-. Z-," The wave equation includesinduced gyroresonance emission/absorption (for the X-, O-, Z-"187he observed and underlying ratios of DNS binaries to DIS.,the observed and underlying ratios of DNS binaries to DRPs.188 This can be summarized by the expression where ron. is the observed ratio of DNS binaries to DIS. μμ is the underlying (intrinsic) ratio and fans is a correction factor which takes account of observational selection ellects.," This can be summarized by the expression where $r_{\rm obs}$ is the observed ratio of DNS binaries to DRPs, $r_{\rm int}$ is the underlying (intrinsic) ratio and $f_{\rm obs}$ is a correction factor which takes account of observational selection effects."189 As we discuss in Section ??.. we find that rons~l.," As we discuss in Section \ref{sec:sample}, , we find that $r_{\rm obs} \sim 1$."190 dn Sections ?77. and 4. we use state-of-the-art binary population synthesis models to explore the possible predicted ranges of kr.," In Sections \ref{sec:simulation} and 4, we use state-of-the-art binary population synthesis models to explore the possible predicted ranges of $r$."191 We investigate observational selection ellects in radio pulsar survevs to evaluate fi; in Section ?7.., We investigate observational selection effects in radio pulsar surveys to evaluate $f_{\rm obs}$ in Section \ref{sec:selfx}.192" Finally. in Section ο οι, we summarize the main findings of this study."," Finally, in Section \ref{sec:conclusions}, , we summarize the main findings of this study."193 Table 1. summarizes the observational cata for the known DNS binaries and DRPs in the Galactic disk., Table \ref{tab:dnsdrp} summarizes the observational data for the known DNS binaries and DRPs in the Galactic disk.194 In Piel. we present an updated version of the magnetic Ποιάperiod (5 DP) diagram from Lorimer et al. (," In \ref{fig:bp}, we present an updated version of the magnetic field–period $B-P$ ) diagram from Lorimer et al. ("1952004) showing both samples of objects.,2004) showing both samples of objects.196 Phere are. currently nine DNS binaries which can be identified: based. on their orbital parameters where measurements of multiple post-Keplerian parameters (see. e.g. Lorimer 2008) suggest. the presence of two neutron. stars in each svstem.," There are currently nine DNS binaries which can be identified based on their orbital parameters where measurements of multiple post-Keplerian parameters (see, e.g. Lorimer 2008) suggest the presence of two neutron stars in each system."197 For the purposes of this paper. where the focus is on recycled pulsars produced curingbinary evolution. we do not select PSK J1906|0746(Lorimeretal.2006) where the observed," For the purposes of this paper, where the focus is on recycled pulsars produced duringbinary evolution, we do not select PSR J1906+0746\citep{lsf+06} where the observed"198mountains in Fig. 6)).,mountains in Fig. \ref{fig:schematic}) ).199" The hydrostatic pressure gradients for both EOSs are comparable at characteristic accreted masses, because the magnetic field lines are bent by a similar angle for all modelsat Ma&M. [since u(Mc) is EOS-independent]."," The hydrostatic pressure gradients for both EOSs are comparable at characteristic accreted masses, because the magnetic field lines are bent by a similar angle for all modelsat $M_{\mathrm{a}} \approx M_{\mathrm{c}}$ [since $\mu(M_{\textrm{c}})$ is EOS-independent]."200" This can be expressed equivalently in terms of the comparable width of the equatorial magnetic belt of both mountains, since comparable deformation angles of the magnetic field lines result in corresponding widths of the magnetic belt."," This can be expressed equivalently in terms of the comparable width of the equatorial magnetic belt of both mountains, since comparable deformation angles of the magnetic field lines result in corresponding widths of the magnetic belt."201" Referring to the bottom panel of Fig. 6,,"," Referring to the bottom panel of Fig. \ref{fig:schematic},"202" the hydrostatic pressure gradient at the base of the accreted layer is greater for adiabatic mountains than isothermalones at an equivalent M4, because Mc;4>MopMe;cMos, where the subscripts A-D denote the models in Table 1 (see Section 4.1))."," the hydrostatic pressure gradient at the base of the accreted layer is greater for adiabatic mountains than isothermalones at an equivalent $M_{\mathrm{a}}$, because $M_{\mathrm{c}; \mathrm{A}} >203M_{\mathrm{c}; \mathrm{D}} > M_{\mathrm{c}; \mathrm{C}} > M_{\mathrm{c}; \mathrm{B}}$, where the subscripts A–D denote the models in Table \ref{table:eos} (see Section \ref{section_4:dipole_moment}) )."204" Hence, magnetic-field lines of an adiabatic mountain are more deformed than those of an isothermal one to counteract this."," Hence, magnetic-field lines of an adiabatic mountain are more deformed than those of an isothermal one to counteract this."205" This decreases the lateral extent of the magnetic belt and, by magnetic flux conservation, |B|max increases as the belt shrinks."," This decreases the lateral extent of the magnetic belt and, by magnetic flux conservation, $|\bmath{B}|_{\mathrm{max}}$ increases as the belt shrinks."206" This explains why the point where |.B|max is reached moves equatorward as Ma increases, and why |B|max is greater for an adiabatic rather than an isothermal mountain for the same M,."," This explains why the point where $|\bmath{B}|_{\mathrm{max}}$ is reached moves equatorward as $M_{\mathrm{a}}$ increases, and why $|\bmath{B}|_{\mathrm{max}}$ is greater for an adiabatic rather than an isothermal mountain for the same $M_{\mathrm{a}}$."207" The compressed magnetic field can surpass the yield strength of the crust, at which point the magnetic stresses break the Coulomb lattice as the field deforms."," The compressed magnetic field can surpass the yield strength of the crust, at which point the magnetic stresses break the Coulomb lattice as the field deforms."208" Taking the breaking strain of the neutron star crust to be z0.1 from recent molecular dynamics simulations (?),, the magnetic field strength at which the crustal matter yields (?) is where Z and A are the mean atomic and mass numbers, respectively."," Taking the breaking strain of the neutron star crust to be $\approx2090.1$ from recent molecular dynamics simulations \citep{horowitz2009a}, the magnetic field strength at which the crustal matter yields \citep{romani1990} is where $Z$ and $A$ are the mean atomic and mass numbers, respectively."210 We evaluate Byicia at the base of a mountain of mass M4 from the nuclides present at base pressure (??7)..," We evaluate $B_{\mathrm{yield}}$ at the base of a mountain of mass $M_{\mathrm{a}}$ from the nuclides present at base pressure \citep{haensel1990b, haensel1990a, chamel2008}."211 The results are plotted as curves in Fig., The results are plotted as curves in Fig.212 5 for the models in Table 1.., \ref{fig:mag_mass} for the models in Table \ref{table:eos}.213" In an isothermal mountain, we find |Blmax«Byiaa, so that the accreted matter does not crack and remains polycrystalline, with a frozen-in magnetic field."," In an isothermal mountain, we find $|\bmath{B}|_{\mathrm{max}}214< B_{\mathrm{yield}}$, so that the accreted matter does not crack and remains polycrystalline, with a frozen-in magnetic field."215" As the substrate of an isothermal mountain does not spread significantly, « and M. are larger."," As the substrate of an isothermal mountain does not spread significantly, $\epsilon$ and $M_{\mathrm{c}}$ are larger."216" Indeed, strictly speaking, crustal freezing should be included in the boundary conditions of an isothermal mountain calculation (implemented dynamically at the depth where it first occurs)."," Indeed, strictly speaking, crustal freezing should be included in the boundary conditions of an isothermal mountain calculation (implemented dynamically at the depth where it first occurs)."217" On the other hand, adiabatic mountains compress the magnetic field in excess of Byicia for Μα3x10""Ma and Μα=6x for models D and respectively, while Byicia is 10-°Mosurpassed for all accreted Cmasses in the case of model B. This suggests that the accreted matter continuously cracks or flows plastically at most depths (?),, validating the fluid approximation for models with [I>4/3."," On the other hand, adiabatic mountains compress the magnetic field in excess of $B_{\mathrm{yield}}$ for $M_{\mathrm{a}} \gtrsim 3 \times 10^{-7} \mathrm{M}_{\sun}$ and $M_{\mathrm{a}} \gtrsim 6 \times 10^{-9}218\mathrm{M}_{\sun}$ for models D and C respectively, while $B_{\mathrm{yield}}$ is surpassed for all accreted masses in the case of model B. This suggests that the accreted matter continuously cracks or flows plastically at most depths \citep{horowitz2009a}, , validating the fluid approximation for models with $\Gamma \geq 4/3$."219 The maximum density at the base of a magnetic mountain is reached at the magnetic pole (see Section 4.5))., The maximum density at the base of a magnetic mountain is reached at the magnetic pole (see Section \ref{section_4:hydromagnetic_structure}) ).220" We extract the maximum density pmax(Rin,0) as a function of M4 from the simulated models listed in Table 1 and graph the results in Fig. 7.."," We extract the maximum density $\rho_{\mathrm{max}}(R_{\mathrm{in}}, 0)$ as a function of $M_{\mathrm{a}}$ from the simulated models listed in Table \ref{table:eos} and graph the results in Fig. \ref{fig:rho_mass}."221" A deficiency of isothermal mountains, noted by PM04, is the unrealistically high density at the base, which exceeds the neutron drip pyp&6x10!!gcm""? at relatively small accreted masses of 109M (cf."," A deficiency of isothermal mountains, noted by PM04, is the unrealistically high density at the base, which exceeds the neutron drip $\rho_{\mathrm{ND}} \approx 6222\times 10^{11} \ \mathrm{g} \ \mathrm{cm}^{-3}$ at relatively small accreted masses of $\sim 10^{-8} \mathrm{M}_{\sun}$ (cf."223 Ma~10!Mc in a typical LMXB)., $M_{\mathrm{a}} \sim 10^{-1} \mathrm{M}_{\sun}$ in a typical LMXB).224" In contrast, Fig."," In contrast, Fig."225 7 shows that pmax is several orders of magnitude lower for an adiabatic EOS; none of the adiabatic mountains surpass pnp for MaSΜο.," \ref{fig:rho_mass} shows that $\rho_{\mathrm{max}}$ is several orders of magnitude lower for an adiabatic EOS; none of the adiabatic mountains surpass $\rho_{\mathrm{ND}}$ for $M_{\mathrm{a}} \lesssim226M_{\mathrm{c}}$."227" At accreted masses approaching Ma~10-°Mo, models C and D attain crust-core pco&2x1014gcm? at their bases."," At accreted masses approaching $M_{\mathrm{a}} \sim 10^{-2} \mathrm{M}_{\sun}$, models C and D attain crust–core $\rho_{\mathrm{CC}} \approx 2 \times 10^{14} \ \mathrm{g} \ \mathrm{cm}^{-3}$ at their bases."228" These models are good approximations to the EOS of the neutron star crust at p>10?gcm? and p>10?gcmὁ, respectively (see Section 5))."," These models are good approximations to the EOS of the neutron star crust at $\rho \gtrsim 10^{9} \ \mathrm{g} \ \mathrm{cm}^{-3}$ and $\rho \gtrsim22910^{13} \ \mathrm{g} \ \mathrm{cm}^{-3}$, respectively (see Section \ref{section_5}) )."230" On the other hand, model B does not reach the crust-core interface because it is too stiff and approximates the true crustal EOS only at low densities 10°<p/(gcm?)«10”."," On the other hand, model B does not reach the crust–core interface because it is too stiff and approximates the true crustal EOS only at low densities $10^{5} < \rho/(\mathrm{g} \ \mathrm{cm}^{-3}) <23110^{7}$."232" In the isothermal mountain (model A), Pmax exceeds pcc for Μα210-°Mo."," In the isothermal mountain (model A), $\rho_{\mathrm{max}}$ exceeds $\rho_{\mathrm{CC}}$ for $M_{\mathrm{a}} \gtrsim 10^{-5} \mathrm{M}_{\sun}$."233" A meridional cross-section of the magnetic mountain produced by models A-D in Table 1 is displayed in Fig. 8, "," A meridional cross-section of the magnetic mountain produced by models A–D in Table \ref{table:eos} is displayed in Fig. \ref{fig:magnetic_mountain}, ,"234"for M,= M..", for $M_{\mathrm{a}} = M_{\mathrm{c}}$ .235" The magnetic field lines and isodensity contours are graphed as solid and dashed curves, respectively; the shading also representsthe density and is included to guide the eye."," The magnetic field lines and isodensity contours are graphed as solid and dashed curves, respectively; the shading also representsthe density and is included to guide the eye."236 Note that the vertical scale changes dramatically from panel to panel., Note that the vertical scale changes dramatically from panel to panel.237 Adiabatic mountains stand 10!—10? times higher than an isothermal mountain for Ma—M. (see also Section 4.1))., Adiabatic mountains stand $10^{1}-10^{2}$ times higher than an isothermal mountain for $M_{\mathrm{a}} = M_{\mathrm{c}}$ (see also Section \ref{section_4:dipole_moment}) ).238" Moreover,"," Moreover,"239azimuthally average results of the four GBT measurements in the envelope.,azimuthally average results of the four GBT measurements in the envelope.240" We strongly disagree with this heart of their argument (hat (his is a ""flaw (hat leads to completely incorrect results.", We strongly disagree with this heart of their argument – that this is a “flaw” that leads to completely incorrect results.241 The issue is whether this spatial variation is what dominates the plivsies. or whether the azimuthallvy-averaged radial variation of observed parameters captures the important physics.," The issue is whether this spatial variation is what dominates the physics, or whether the azimuthally-averaged radial variation of observed parameters captures the important physics."242" AT theorists have argued that such small-scale structure produced perhaps bv turbulence is not central to the physics of star formation: in testing the ""idealized AD models. we follow their lead."," AT theorists have argued that such small-scale structure produced perhaps by turbulence is not central to the physics of star formation; in testing the “idealized” AD models, we follow their lead."243" MIT show a cartoon of the possible morphology of magnetic field lines around a single core. another cartoon with (visting and reversing field direction between four cores in a flux tube. aud discuss these cartoons qualitatively,"," MT show a cartoon of the possible morphology of magnetic field lines around a single core, another cartoon with twisting and reversing field direction between four cores in a flux tube, and discuss these cartoons qualitatively."244 These qualitative complications give the lreedom to explain virtually anv observational test of the AD model: if (his assertion is accepted. AD models of star formation are not testable by experiment or observation (he essence of the scientific method.," These qualitative complications give the freedom to explain virtually any observational test of the AD model; if this assertion is accepted, AD models of star formation are not testable by experiment or observation – the essence of the scientific method."245 Further. many investigators have implicitly agreed that azimuthal averaging is valid — [or example. in measuring the radial profiles of cores for comparison wilh Donner-Ebert profiles.," Further, many investigators have implicitly agreed that azimuthal averaging is valid – for example, in measuring the radial profiles of cores for comparison with Bonner-Ebert profiles."246" If such azimuthal averaging were agreed to be a ""flawed approach. many of (he analvzes in the literature. would have to be so judged."," If such azimuthal averaging were agreed to be a “flawed” approach, many of the analyzes in the literature would have to be so judged."247 When one spatially resolves such objects. one always finds small-scale structure. particularly as vou go to observational probes of higher densities.," When one spatially resolves such objects, one always finds small-scale structure, particularly as you go to observational probes of higher densities."248 We (along with apparently the remainder of the astronomy community aside [rom MT) argue that it is meaningful to use mean values and the uncertainties in (hose mean values to study astrophysical phenomena., We (along with apparently the remainder of the astronomy community aside from MT) argue that it is meaningful to use mean values and the uncertainties in those mean values to study astrophysical phenomena.249" As we clearly stated. CHT tested the published. quantitative models. not. ""models? with ad hoc qualitative complications."," As we clearly stated, CHT tested the published, quantitative models, not “models” with ad hoc qualitative complications."250 The central point is whether or not it is valid to test «quantitative theoretical models that presumably capture the important physics. or whether il is an appropriate scientific method to add ad hoc. qualitative complications that make the theory untestable.," The central point is whether or not it is valid to test quantitative theoretical models that presumably capture the important physics, or whether it is an appropriate scientific method to add ad hoc, qualitative complications that make the theory untestable."251 We now discuss one bv one the specilic “flaws” listed bv MT., We now discuss one by one the specific “flaws” listed by MT.252" We have ""synthesized"" a toroidal beam with parameters chosen to match the sampling scale defined bv the published AD models.", We have “synthesized” a toroidal beam with parameters chosen to match the sampling scale defined by the published AD models.253 There are (wo wavs to produce tliis svuthesis., There are two ways to produce this synthesis.254 One is to fit for the magnetic field al each position aud then arithmetically average the, One is to fit for the magnetic field at each position and then arithmetically average the255Including radiative transfer (RT) into three dimensional simulations ofthe first structures and galaxy formation has proven {ο be extremely challenging.,Including radiative transfer (RT) into three dimensional simulations of the first structures and galaxy formation has proven to be extremely challenging.256 This is mostly because of the non-locality of radiation physics., This is mostly because of the non-locality of radiation physics.257 Although many different aspects of RT can be accounted for by various approximations (e.g.. space-averaged field. sell-shielding. diffusion approximation). so Lar most calculations have not been able to include details of the spatially inhomogeneous 3D transfer of radiation.," Although many different aspects of RT can be accounted for by various approximations (e.g., space-averaged field, self-shielding, diffusion approximation), so far most calculations have not been able to include details of the spatially inhomogeneous 3D transfer of radiation."258 Of particular interest is studying the effects of radiative feedback from the first luminous structures in (he universe. which is (he focus of the present stu.," Of particular interest is studying the effects of radiative feedback from the first luminous structures in the universe, which is the focus of the present study."259 Photons [rom these early objects heated ancl ionized (he intergalactie medium (IGM). altering the dvnamies of barvons on a wide range of scales.," Photons from these early objects heated and ionized the intergalactic medium (IGM), altering the dynamics of baryons on a wide range of scales."260 Intviguinely. the process through which the ionized regions percolated (he Universe mav be directly observable in the spectra of the most distant quasars (BeckerοἱDjorgovskietal. 2001).," Intriguingly, the process through which the ionized regions percolated the Universe may be directly observable in the spectra of the most distant quasars \citep{becker01,djorgovski01}."261. In order to use such observations to understand. early structure formation it is important to model the relevant. physics as reliably as possible., In order to use such observations to understand early structure formation it is important to model the relevant physics as reliably as possible.262 For this purpose accurate treatment of the radiation is crucial., For this purpose accurate treatment of the radiation is crucial.263" The RT equation in the expanding Universe is given by which is (hie conservation law for the specific intensity Z, propagating in the direction n. with // being the expansion rate. a=1/(12-z) the cosmological scale factor ancl e, ancl a, the enussion and absorption coellicients. respectively,"," The RT equation in the expanding Universe is given by which is the conservation law for the specific intensity $I_\nu$ propagating in the direction ${\bf n}$, with $H$ being the expansion rate, $a=1/(1+z)$ the cosmological scale factor and $\epsilon_\nu$ and $\kappa_\nu$ the emission and absorption coefficients, respectively."264 Unfortunately. full solution of this seven dimensional ((ühree in space. two angles. frequency and time) equation is sUll well bevond our computational capabilities.," Unfortunately, full solution of this seven dimensional (three in space, two angles, frequency and time) equation is still well beyond our computational capabilities."265 Although in many astrophysical situations it is possible to reduce the dimensionality of (his equation. transfer in the cliampy IGM has proved to be one of the most difficult problems. since it does not provide us with anv obvious spatial svinnmetries.," Although in many astrophysical situations it is possible to reduce the dimensionality of this equation, transfer in the clumpy IGM has proved to be one of the most difficult problems, since it does not provide us with any obvious spatial symmetries."266 For this reason. a great deal of effort has been put into solution of the spatially and clirectionally averaged. RT equation (laardt&Alacdau1996:ChinValageas&Silk 1999).," For this reason, a great deal of effort has been put into solution of the spatially and directionally averaged RT equation \citep{haardt96,chiu00,valageas99}."267. In (hese models (he UV background is computed using the properties of an average cosmological volume. such as (he mean liminosity function per unit volume for the source term and (he statistical properties of absorbing clouds (often in the form of the chuupineg factor) for the recombination term.," In these models the UV background is computed using the properties of an average cosmological volume, such as the mean luminosity function per unit volume for the source term and the statistical properties of absorbing clouds (often in the form of the clumping factor) for the recombination term."268 This part of the ealeulation is sufficiently simple (hat it is (hen possible to estimate in great. detail the spectrum of the background radiation (laardt Macau 2001)., This part of the calculation is sufficiently simple that it is then possible to estimate in great detail the spectrum of the background radiation (Haardt Madau 2001).269 ILowever. these models fail to address «questions related to the time-dependent. propagation of radiation fronts and therefore cannot. predict. what," However, these models fail to address questions related to the time-dependent propagation of radiation fronts and therefore cannot predict what"270below. appears to be the LQG.,"below, appears to be the LQG."271 At the other linkage scale considered in the binary chop. 90 Alpe. the LQG does not appear at the specified minimum cluster size of 10 members.," At the other linkage scale considered in the binary chop, 90 Mpc, the LQG does not appear at the specified minimum cluster size of 10 members."272 The apparent linkage scale of 100 Alpe thus means that the LOC is unlikely to be fragmenting at the true mean nearest- separation  τὸ Alpe. (, The apparent linkage scale of 100 Mpc thus means that the LQG is unlikely to be fragmenting at the true mean nearest-neighbour separation $\sim$ 73 Mpc. (273Note that this scale. of 100 Alpe is between the two scales [100h.7+. 200f+ Alpe diameters. equivalent to 71. 143 Ape for spherical filtering used by Milleretal.2004. to find LQGs.),"Note that this scale of 100 Mpc is between the two scales $100h^{-1}$, $200h^{-1}$ Mpc diameters, equivalent to $71$, $143$ Mpc for spherical filtering used by \citealt{Miller2004} to find LQGs.)"274 The 34 quasars connected at this 100 Mpe linkage scale are listed in Table 1.., The 34 quasars connected at this 100 Mpc linkage scale are listed in Table \ref{lqg_U1.28_table}.275 Their mean redshift is 1.28. identical to that of the original 18 members of the LQG.," Their mean redshift is 1.28, identical to that of the original 18 members of the LQG."276 They cover the redshift range 1.1865.»1.4232. whereas the original 15 cover the range 1.207.*1.386.," They cover the redshift range $1.1865277\rightarrow 1.4232$, whereas the original 18 cover the range $1.207278\rightarrow 1.386$."279 The centroids of this unit o£ 34 and of the original I8 are separated by only ~0.927., The centroids of this unit of 34 and of the original 18 are separated by only $\sim 0.92^\circ$.280 Phe identification as the LOG of this unit of 34. occurring at the correct redshift. within 0.927. and also (see the next section) with essentially the same western. northern and southern boundaries. therefore seenis certain.," The identification as the LQG of this unit of 34, occurring at the correct redshift, within $0.92^\circ$, and also (see the next section) with essentially the same western, northern and southern boundaries, therefore seems certain."281 For convenience in what follows. this LOC: unit. of 34 quasars will be designated U1.28 from its mean redshift. and similarly for two other units of interest that are discussed below.," For convenience in what follows, this LQG unit of 34 quasars will be designated U1.28 from its mean redshift, and similarly for two other units of interest that are discussed below."282 The Clowes Campusano LQG has been detected by three independent methods. (Clowes&Canmpusano1991:New-manetal.1998:Newman1999:Willigeret 2002).," The Clowes Campusano LQG has been detected by three independent methods \citep{Clowes1991, Newman1998, Newman1999, Williger2002}."283. The detection in the DRTQS8O database as U1.28 adds a fourth., The detection in the DR7QSO database as U1.28 adds a fourth.284 The location on the sky of the 34 members of Ul.28 corresponds well to that of the original LQG: the western. northern and southern boundaries sccm to be essentially the same. apart from two compact clumps to the north and south-west. (Fig. 1)).," The location on the sky of the 34 members of U1.28 corresponds well to that of the original LQG: the western, northern and southern boundaries seem to be essentially the same, apart from two compact clumps to the north and south-west, (Fig. \ref{skydist_U1.28}) ),"285 while the eastern boundary is extended by ~27., while the eastern boundary is extended by $\sim 2^\circ$.286 Note that for the original LS only the western boundary did not encounter the limits of the survey. but the extension seen with UT.28 is predominantly castwarels. with no major extensions either northwards or southwarels.," Note that for the original 18 only the western boundary did not encounter the limits of the survey, but the extension seen with U1.28 is predominantly eastwards, with no major extensions either northwards or southwards."287 The coincidence of these sets of LS and 34 seems particularly striking given that only six quasars are in common (of ten possible for ¢< 19.1)., The coincidence of these sets of 18 and 34 seems particularly striking given that only six quasars are in common (of ten possible for $i \le 19.1$ ).288 The intensity map of Fig., The intensity map of Fig.289 1. is many times (~ 6) larger than the area covered by U1.28 itself, \ref{skydist_U1.28} is many times $\sim 6$ ) larger than the area covered by U1.28 itself.290 In the upper histogram of Fig., In the upper histogram of Fig.291 ὸ we show the redshift distribution [or quasars in a smaller rectangular area of ~47 deg7 CAAT. actually 46.3 deg?) that contains both U1.28 and the original members of the LOG.," \ref{zdist_A47} we show the redshift distribution for quasars in a smaller rectangular area of $\sim 47$ $^{-2}$ (A47, actually 46.3 $^2$ ) that contains both U1.28 and the original members of the LQG."292 Phe limits of this arca are shown ον the grey rectangle in Fig. L.., The limits of this area are shown by the grey rectangle in Fig. \ref{skydist_U1.28}.293 In the lower histogram we show the redshift distribution of the control area (3725 for comparison., In the lower histogram we show the redshift distribution of the control area A3725 for comparison.294 Both of the histograms are derived. from the DRTOQSO catalogue restricted. to 7x:19.1. and for clarity hey have been further restricted to zx2.4.," Both of the histograms are derived from the DR7QSO catalogue restricted to $i \le 19.1$, and for clarity they have been further restricted to $z \le 2.4$."295 The histogram for X47 (upper) shows a prominent peak or 1.20«zx1.35. which corresponds to U1.28.," The histogram for A47 (upper) shows a prominent peak for $1.20 < z \le 1.35$, which corresponds to U1.28."296 Note also he peaks for 1.10«zx1.15 and 1.50<zx1.60. which will be discussed further below.," Note also the peaks for $1.10 < z \le 1.15$ and $1.50 < z \le 1.60$, which will be discussed further below."297 Fig., Fig.298 3 shows the recshilt distribution within the unit U1.28 of 34 100Mpec-linked. quasars that. corresponds. to the Clowes Campusano LOG., \ref{zdist_U1.28} shows the redshift distribution within the unit U1.28 of 34 100Mpc-linked quasars that corresponds to the Clowes Campusano LQG.299 Although there are no particularly compelling features in the distribution. there is possibly some concentration of redshifts to the lower half of the range.," Although there are no particularly compelling features in the distribution, there is possibly some concentration of redshifts to the lower half of the range."300 While investigating the appearance of the Clowes Campusano LOG in the SDSS data two further (candidate) LOCs became apparent in the same general direction. on the sv., While investigating the appearance of the Clowes Campusano LQG in the SDSS data two further (candidate) LQGs became apparent in the same general direction on the sky.301 We were considering only units with a minimum membership of 20 at the LOO Mpe linkage scale., We were considering only units with a minimum membership of 20 at the 100 Mpc linkage scale.302 These additional candidate LOGs are. designated: as Ula and U1.54. from their mean redshifts.," These additional candidate LQGs are designated as U1.11 and U1.54, from their mean redshifts."303 Ul.11 has 38 members. 2=1.11. and angular separation (of RA. Dec centroids) of 1.077 from {19δ.," U1.11 has 38 members, $\bar{z} = 1.11$, and angular separation (of RA, Dec centroids) of $^\circ$ from U1.28."304 Ul.54 has 21 members. 2=154. and angular separation of 1.62 from U1.28.," U1.54 has 21 members, $\bar{z} = 1.54$, and angular separation of $^\circ$ from U1.28."305 We present. below a method. for assessing the statistical significance ancl overdensity of groups found by linkage of points., We present below a method for assessing the statistical significance and overdensity of groups found by linkage of points.306 We find that UI.28 and 1] are significant. but U1.54 is not.," We find that U1.28 and U1.11 are significant, but U1.54 is not."307 However. we note that U1.54 corresponds to a known LOG (of marginal significance) at z=1.53 (or. as published. median >=1.51) that was discovered by Newmanetal.(1998). and Newman(1099). in an independent UV- survey (Chile-Ulx Quasar Survey).," However, we note that U1.54 corresponds to a known LQG (of marginal significance) at $\bar{z} = 1.53$ (or, as published, median $z = 1.51$ ) that was discovered by \citet{Newman1998} and \citet{Newman1999} in an independent UV-excess survey (Chile-UK Quasar Survey)."308 Thirteen members were found in the original discovery. of which LO are present in this re-discovery.," Thirteen members were found in the original discovery, of which 10 are present in this re-discovery."309 The peaks in the upper redshift histogram of Fig., The peaks in the upper redshift histogram of Fig.310 2. for the intervals 1.10«τς1.15 and 1.50«z.60.( which were mentioned brielly in theearlier discussion of that figure. correspond to U1.11 and U1.54.," \ref{zdist_A47} for the intervals $1.10 < z \le 1.15$ and $1.50 < z \le 1.60$, which were mentioned briefly in theearlier discussion of that figure, correspond to U1.11 and U1.54."311 UL.I1. however. is a new discovery. notable for both its appearance in the same cosmological neighbourhood as U1.28 and for its similarly large number of members.," U1.11, however, is a new discovery, notable for both its appearance in the same cosmological neighbourhood as U1.28 and for its similarly large number of members."312 The 38 quasars of Ul.11 are listed in Table 2.. , The 38 quasars of U1.11 are listed in Table \ref{lqg_U1.11_table}. .313The distribution of redshifts lor Ul.I11 is shown in Fig. 4.., The distribution of redshifts for U1.11 is shown in Fig. \ref{zdist_U1.11}.314 Again. there are no particularlv compelling features in the distribution. but in this case there is possibly some concentration of redshifts to the upper half of the range.," Again, there are no particularly compelling features in the distribution, but in this case there is possibly some concentration of redshifts to the upper half of the range."315 Figure 5. shows three projections (Dec-IUX. M-z. 2) of the spatial distributions of Ul.11 and U1.285.," Figure \ref{units_project} shows three projections (Dec-RA, $z$, $z$ ) of the spatial distributions of U1.11 and U1.28."316 In the entire DRTOSO catalogue aarea [XO380) we find a total of 15 LOG candidates of such high membership GN.m 34)., In the entire DR7QSO catalogue area A9380) we find a total of 15 LQG candidates of such high membership $N \ge 34$ ).317 Of these. UL28S and ULll are the closest. with a separation of centroids of ~410 Alpe.," Of these, U1.28 and U1.11 are the closest, with a separation of centroids of $\sim 410$ Mpc."318 From the density of such candidates. the probability of a pair within this separation occurring by chance somewhere within the coverage of the whole catalogue (and 1.0<2x LS) is 0.5. ancl so this pair is consistent.," From the density of such candidates, the probability of a pair within this separation occurring by chance somewhere within the coverage of the whole catalogue (and $1.0 \le z \le 1.8$ ) is $\sim 0.5$, and so this pair is consistent."319 Note. however. that U1.28 and ULL do appear to be quite distinct: a small increase. in the linkage scale does not lead to their merger as a single unit.," Note, however, that U1.28 and U1.11 do appear to be quite distinct: a small increase in the linkage scale does not lead to their merger as a single unit."320 Phe volume occupied by U1.28 and 1.11 together thus appears rather distinctive for quasars on a Large scale and would presumably correspond to some notable features in the cosmic web if the distribution of galaxies was accessible toobservation., The volume occupied by U1.28 and U1.11 together thus appears rather distinctive for quasars on a large scale and would presumably correspond to some notable features in the cosmic web if the distribution of galaxies was accessible toobservation.321 As mentioned above. and as is apparent [rom Figure 5.. U1.28 and Ε.Τ] are also quite closely aligned with the line of sight.," As mentioned above, and as is apparent from Figure \ref{units_project}, , U1.28 and U.11 are also quite closely aligned with the line of sight."322Selection biases against BALQSOs has been proposed by previous studies. where a continuum anisotropy causes (he selection biases (e.g.. Goodrich 1997: Ixrolik Voit 1995).,"Selection biases against BALQSOs has been proposed by previous studies, where a continuum anisotropy causes the selection biases (e.g., Goodrich 1997; Krolik Voit 1998)."323 In our simulations we show that Che selection biases can be explained wilh obscuration [rom dust extinction and absorption troughs in BALQSOs., In our simulations we show that the selection biases can be explained with obscuration from dust extinction and absorption troughs in BALQSOs.324 Essentially. an anisotropy is also produced alter (he optical obseuration which. combined with the steep quasar Iuminosity function. will produce lower BALQSO fractions in those bands more sensitive to obseuration.," Essentially, an anisotropy is also produced after the optical obscuration which, combined with the steep quasar luminosity function, will produce lower BALQSO fractions in those bands more sensitive to obscuration."325 An intrinsic continuum anisotropy is also possible: however. it needs (o be fine (ined as a function of wavelength: that behaves similarly to the effect of dust extinction. especially in the longer wavelength bands.," An intrinsic continuum anisotropy is also possible; however, it needs to be fine tuned as a function of wavelength that behaves similarly to the effect of dust extinction, especially in the longer wavelength bands."326 Different continuun emission between BALQSO and non-BALQSOs is also expected if the BALQSOs are either at special evolution stages of quasar evolution. or ihe near infrared emission of BALQSOs are enhanced by the reprocessed emission from the absorption lines.," Different continuum emission between BALQSO and non-BALQSOs is also expected if the BALQSOs are either at special evolution stages of quasar evolution, or the near infrared emission of BALQSOs are enhanced by the reprocessed emission from the absorption lines."327 This fact is also connected to the idea that BALQSOs are in the transition stage between Infrared. Luminous Galaxies and quasar phases (Lipari et al., This fact is also connected to the idea that BALQSOs are in the transition stage between Infrared Luminous Galaxies and quasar phases pari et al.328 2005)., 2005).329 To test whether the continuum emission in (he BALQSOs and non-DALGOSOSs are similar. we need to compare the absorption corrected spectra for BALQSOs with non-BALQSOs. which involves senilicant complexity in the analvsis of the optical spectra.," To test whether the continuum emission in the BALQSOs and non-BALQSOs are similar, we need to compare the absorption corrected spectra for BALQSOs with non-BALQSOs, which involves significant complexity in the analysis of the optical spectra."330 As the observed near infrared band is little affected by the BAL features. it would be ideal to make the comparison there.," As the observed near infrared band is little affected by the BAL features, it would be ideal to make the comparison there."331 llowever. a near infrared. spectroscopic survev is needed (o better measure (he power-law slope aud IN-correction of the quasars before we draw a solid conclusion.," However, a near infrared spectroscopic survey is needed to better measure the power-law slope and K-correction of the quasars before we draw a solid conclusion."332 Our sample size is limited bv the 2\LASS survey. limits., Our sample size is limited by the 2MASS survey limits.333 Future infrared survevs (e.g.. UINIDSS with survey limits of A.=18.3 mag) will significantly increase (he sample size. and enable us to extend this study of BALQSO fractions to less luminous quasars.," Future infrared surveys (e.g., UKIDSS with survey limits of $K = 18.3$ mag) will significantly increase the sample size, and enable us to extend this study of BALQSO fractions to less luminous quasars."334 Our analvsis indicates that the near infrared BALQSO Iraction more accurately reflects the true fraction of BALQSOs., Our analysis indicates that the near infrared BALQSO fraction more accurately reflects the true fraction of BALQSOs.335 This is important when using the [raction of BALQSOs to constrain quasar geometric and evolutionary models., This is important when using the fraction of BALQSOs to constrain quasar geometric and evolutionary models.336 In this paper. we found a BALQSO fraction of e40% in the 2\LASS bands under the T06 criterion.," In this paper, we found a BALQSO fraction of $\sim40$ in the 2MASS bands under the T06 criterion."337 This indicates a correction of [actor 1.5 is needed for the optical fractions. consistent will the modeling of Hewett Foltz (2003).," This indicates a correction of factor $\sim1.5$ is needed for the optical fractions, consistent with the modeling of Hewett Foltz (2003)."338 We note that the fraction of BALQSOs is also dependent on the spectral definition ol BALQSOs., We note that the fraction of BALQSOs is also dependent on the spectral definition of BALQSOs.339 T06 also analvzed the fraction of BALQSOs under the original delinition of Wevinann et al. (, T06 also analyzed the fraction of BALQSOs under the original definition of Weymann et al. (3401991) and found à BALQSO fraction of1054... different [rom the under ihe T06 οποιος.,"1991) and found a BALQSO fraction of, different from the under the T06 criterion."341 We analvzed the fraction of BALQSOs in 2422ASS under the Wevmann et al. (, We analyzed the fraction of BALQSOs in 2MASS under the Weymann et al. (342"1991) definition and obtained fractions of 23d:3463t and 20+42% in the A, complete and 2MASS sample using the balnicitv indices provided by TOG.",1991) definition and obtained fractions of $23\pm3$ and $20\pm2$ in the $K_s$ complete and 2MASS sample using the balnicity indices provided by T06.343 We obtained a correction factor of ~2 for the optical fraction under (he Wevinann οἱ ddefinition., We obtained a correction factor of $\sim 2$ for the optical fraction under the Weymann et definition.344 This result is nol surprising since the Wevimann et ddelinition for BALQSOs is more strict. ancl we expect more severe optical obscuration and a larger correction factor for the optical fraction.," This result is not surprising since the Weymann et definition for BALQSOs is more strict, and we expect more severe optical obscuration and a larger correction factor for the optical fraction."345 This, This346and empty space form infinite connected networks.,and empty space form infinite connected networks.347" If we continue to increase the density of spheres. we reach a second critical point at p,2124/((4/3)17]. at which the vacuum stops to form an infinite network: now of space is covered by spheres. and for n>Πρ. only isolated. vacuum bubbles remain."," If we continue to increase the density of spheres, we reach a second critical point at $\bar n_c \simeq 1.24/[(4\pi/3)r^3]$, at which the vacuum stops to form an infinite network: now of space is covered by spheres, and for $n>\bar n_c$, only isolated vacuum bubbles remain."348 Let us then consider hadrons of intrinsic size Vj=(4x/3)r7./ with rj20.8 fm.," Let us then consider hadrons of intrinsic size $V_h=(4\pi/3)r_h^3$, with $r_h \simeq 0.8$ fm."349 In space. the formation of a connected large-scale cluster first. occurs at. the densitv| n.— 0.16*.," In three-dimensional space, the formation of a connected large-scale cluster first occurs at the density n_c= 0.16."350(18) This point specilies (he onset of hadronicmatter. in contrast to agas of hadrons. aud il indeed correctly reproduces the density of normal nuclear matter.," This point specifies the onset of hadronic, in contrast to a of hadrons, and it indeed correctly reproduces the density of normal nuclear matter."351 However. at this density the vacuum as connected medium also still exists (see refpercotransaa).," However, at this density the vacuum as connected medium also still exists (see \\ref{percotrans}a a)."352 To prevent inlinite connecting vacuum clusters. a much higher hadron density is needed. as we saw above.," To prevent infinite connecting vacuum clusters, a much higher hadron density is needed, as we saw above."353" Measured in hadronic size units. the vacuum disappears for oisE 0.56*. schemalically illustrated in relpercotransbb. If we assume that at this point. the medium is of an ideal gas of all known hadrons ancl hadronic resonances. (hen we can calculate the temperature of the eas al the density n: n4,(1.)=n, implies T.~170 MeV. which agrees quite well with the value of the deconfinement temperature found in lattice QCD for ji=0."," Measured in hadronic size units, the vacuum disappears for _c= 0.56, schematically illustrated in \\ref{percotrans}b b. If we assume that at this point, the medium is of an ideal gas of all known hadrons and hadronic resonances, then we can calculate the temperature of the gas at the density $\bar{n}_c$: $n_{\rm res}(T_c) = \bar{n}_c$ implies $T_c \simeq 354170$ MeV, which agrees quite well with the value of the deconfinement temperature found in lattice QCD for $\mu=0$."355 We can thus use percolation to deline the states of hadronic matter., We can thus use percolation to define the states of hadronic matter.356" At low density. we have a hadron gas. which at the percolation point », turis into connected hadronic matter."," At low density, we have a hadron gas, which at the percolation point $n_c$ turns into connected hadronic matter."357" When (his becomes so dense that only isolated vacuum bubbles survive. at n,. il (urns into a euark-gluon plasma."," When this becomes so dense that only isolated vacuum bubbles survive, at $\bar{n}_c$, it turns into a quark-gluon plasma."358 This approach provides the correct values both for the density of standard nuclear matter and for (he deconfinement (ransilion temperature., This approach provides the correct values both for the density of standard nuclear matter and for the deconfinement transition temperature.359"we write F(T)= and the energy expectation value may be written -—kgTf(T)as We find that a well-behaving function fitting perfectly into our simulation data, allows analytical integration of Eq.","we write $F(T) = -k_\text{B}T f(T)$ and the energy expectation value may be written as We find that a well-behaving function fitting perfectly into our simulation data, allows analytical integration of Eq."360" for f(T) or InZ(T), Using the boundary condition for the molecular partition function with a nondegenerate ground state, Z(0=1 or MZ(0)=0, we get D= in our model."," for $f(T)$ or $\ln361Z(T)$, Using the boundary condition for the molecular partition function with a nondegenerate ground state, $Z(0) = 1$ or $\ln Z(0) = 0$, we get $D=a/b$ in our model."362" However, inclusion of the contributions a/bfrom the ground state spin degeneracy factor and the zero-point rotations would give Z(0)=€>1, which would lead to D=a/b+In€, and thus, shift the function InZ by a constant, only."," However, inclusion of the contributions from the ground state spin degeneracy factor and the zero-point rotations would give $Z(0)=\xi>1$, which would lead to $D=a/b+\ln\xi$, and thus, shift the function $\ln Z$ by a constant, only."363" The weighted least squares fit of the above energy function, Eq. (7),"," The weighted least squares fit of the above energy function, Eq. ,"364", to our data for temperatures up to about 3900 K, see Table 1,, gives the parameters In the fit, in addition to the (28EM)~? weights, we force the first derivative of the energy with respect to the temperature to be monotonically increasing up to 3900 K. The fit extrapolates the 0 K energy to about 0.000549 above that of the i.e. it gives an excellent Egmatch within the statistical para-Hj,error estimate."," to our data for temperatures up to about $3900$ K, see Table \ref{Table1}, , gives the parameters In the fit, in addition to the $(2\text{SEM})^{-2}$ weights, we force the first derivative of the energy with respect to the temperature to be monotonically increasing up to $3900$ K. The fit extrapolates the $0$ K energy to about $0.000549E_\text{H}$ above that of the $_3^+$ , i.e. it gives an excellent match within the statistical error estimate."365 In Fig., In Fig.366 3 the function InZ(T) from Eq., \ref{Fig3} the function $\ln Z(T)$ from Eq.367 is shown in the range 0«T'4000 K — the behaviour of the model at higher T' is illustrated by the dashed line., is shown in the range $0 < T < 4000$ K — the behaviour of the model at higher $T$ is illustrated by the dashed line.368 Above 4000 K the three curves for different densities are obtained from those shown in Fig., Above $4000$ K the three curves for different densities are obtained from those shown in Fig.369 1 by numerical integration of Eq., \ref{Fig1} by numerical integration of Eq.370" as where Τι=500 K. NealeandTennyson(1995) have presented the partition function InZ(T) based on a semi-empirical potential energy surface, see Fig. 3.."," as where $T_1 = 500$ K. \cite{Neale95ApJ} have presented the partition function $\ln Z(T)$ based on a semi-empirical potential energy surface, see Fig. \ref{Fig3}."371 The overall shape is similar to the one of ours., The overall shape is similar to the one of ours.372" However, the energy (E) evaluated from their fit tends to be systematically lower than ours, although roughly within our 2 SEM error limits."," However, the energy $\ka{E}$ evaluated from their fit tends to be systematically lower than ours, although roughly within our 2 SEM error limits."373" Thus, the deviations are not visible in Fig. 1.."," Thus, the deviations are not visible in Fig. \ref{Fig1}."374" For the partition function the main difference is in their zero reference, which also leads to In£=—oo."," For the partition function the main difference is in their zero reference, which also leads to $\ln\xi = -\infty$."375 This difference in zero reference goes back to that of energetics: our (E) in Eq., This difference in zero reference goes back to that of energetics: our $\ka{E}$ in Eq.376 at T—0 fits perfectly the zero Kelvin energy of as mentioned earlier.," at $T = 0$ fits perfectly the zero Kelvin energy of $_3^+$ , as mentioned earlier."377" The zero Kelvin energy of the para-H;Neale,andTennyson(1995) behind their partition function is that of the spin forbidden J—0 state, ie. Z(0)—0."," The zero Kelvin energy of the \cite{Neale95ApJ} behind their partition function is that of the spin forbidden $J=0$ state, i.e. $Z(0)=0$."378" This in fact, leads to the divergence of InZ(T) at T—0."," This in fact, leads to the divergence of $\ln Z(T)$ at $T = 0$."379 Our low temperature partition function Eq., Our low temperature partition function Eq.380 is close to complete., is close to complete.381 With the PIMC approach weimplicitlyinclude all of the quantumstates in the system with correct weight without any approximations., With the PIMC approach weimplicitlyinclude all of the quantumstates in the system with correct weight without any approximations.382 This partition function isthe best one for the modeling of, This partition function isthe best one for the modeling of383our fitting formula works quite well.,our fitting formula works quite well.384 We caution that the concentration dependence here is based. on our CiX-series simulations only and so should. be confirmed with similar resolution simulations of other objects., We caution that the concentration dependence here is based on our GA-series simulations only and so should be confirmed with similar resolution simulations of other objects.385 We emphasize that this formula applies to subhalo populations defined. above a given lower mass limit. not to populations defined above circular velocity or luminosity limits.," We emphasize that this formula applies to subhalo populations defined above a given lower mass limit, not to populations defined above circular velocity or luminosity limits."386 Our subhalo number density profiles agree well with, Our subhalo number density profiles agree well with387inclination of the normal to the orbital plane with respect to the line-of-sight. and (he brakets report the lo errors on the last significantS dieit.,"inclination of the normal to the orbital plane with respect to the line-of-sight, and the brakets report the $1\sigma$ errors on the last significant digit."388"S The mass ratio ο1]=PSR,ραίσονOM can be derived by combining eq. (1))", The mass ratio $q=M_{\rm PSR}/M_{\rm COM}$ can be derived by combining eq. \ref{eq:mfpsr}) )389 with eq. (2)).," with eq. \ref{eq:mfcom}) ),"390" and results q=7.49+0.64. solving separatelv for the masses of the (wo stars would require a determination of the orbital inclination: the relation between pag and 7? [or differenti. values of eos, is displaved in Figure 2.. for a reasonable choice of the neutron star mass (1—2.5M.. Shapiro Teukolsky 1983)."," and results $q=7.49\pm3910.64.$ Solving separately for the masses of the two stars would require a determination of the orbital inclination: the relation between $M_{\rm392PSR}$ and $i$ for different values of $M_{\rm COM}$ is displayed in Figure \ref{MvsI}, for a reasonable choice of the neutron star mass $1-2.5~{\rm M_\odot}$, Shapiro Teukolsky 1983)."393 The measured mass ratio (will its uncertainty) selects a narrow strip of allowed parameters in Figure 2.., The measured mass ratio (with its uncertainty) selects a narrow strip of allowed parameters in Figure \ref{MvsI}. .394 In particular. Mpag21.1M. and ον>0.16M. (lo limits).," In particular, $M_{\rm PSR}>1.1~{\rm395M_\odot}$ and $M_{\rm COM}>0.16~{\rm M_\odot}$ $1\sigma$ limits)."396 Moreover. Meo£0.30AL. and the orbital inclination is 2607. Tighter constraints can be obtained in the hypothesis that the companion is a IHe-WD: in this case. the range of masses determined by Ferraro et al. (," Moreover, $M_{\rm COM}\lapp 0.30~{\rm M_\odot}$ and the orbital inclination is $\gapp 60^\circ.$ Tighter constraints can be obtained in the hypothesis that the companion is a He-WD: in this case, the range of masses determined by Ferraro et al. ("3972003a) implies that the svstem is almost edge-on GZ 70°) and the pulsar mass is in (he range 1.2—1.5M... It is worthwhile to note that the latter mass interval brackets (he values of all neutron star masses accurately measured so fav (Lorimer 2005). but one case (Nice et al.,"2003a) implies that the system is almost edge-on $i\gapp 70^\circ$ ) and the pulsar mass is in the range $1.2-1.5~{\rm M_\odot}.$ It is worthwhile to note that the latter mass interval brackets the values of all neutron star masses accurately measured so far (Lorimer 2005), but one case (Nice et al."398 2005)., 2005).399 The photometric observations were performed in service mode at thesnd 81-telescope of the ESO-VLT during (wo nights in 2003. March and May (ESO Program ID 071.D-0232). and six nights in 2004. August (ESO Program ID 073.D-0067A).," The photometric observations were performed in service mode at the 8m-telescope of the ESO-VLT during two nights in 2003, March and May (ESO Program ID 071.D-0232), and six nights in 2004, August (ESO Program ID 073.D-0067A)."400 All the images were acquired using D-band filter in high-resolution mode with the FORSI camera., All the images were acquired using B-band filter in high-resolution mode with the FORS1 camera.401" In (his configuration the instrumental pixels scale is 0.1"" ! and the Field of View of the 2048x pixels Tektronix-CCD is 2.4x3.4.", In this configuration the instrumental pixels scale is $0.1\arcsec$ $^{-1}$ and the Field of View of the $2048\times2048$ pixels Tektronix-CCD is $3\arcmin.4\times3\arcmin.4$.402 The data comprise twenty-one 600s ancl five 3608 exposures. centered roughlv less then 1 far from the nominal position (D'Amico et al.," The data comprise twenty-one 600s and five 360s exposures, centered roughly less then $1\arcmin$ far from the nominal position (D'Amico et al."403 2002)., 2002).404 The observations on 2004 were planned in order (o evenly distribute along the orbit of the binary svstem., The observations on 2004 were planned in order to evenly distribute along the orbit of the binary system.405 From all the original Irznmies we have extracted a subimage of 500x pixels. roughly centered on the nominal position of PSR. J1911—5953AÀ. The scientific images have been reduced using ROMAFOT. a package specifically developed to achieve accurate photometry in crowded [fields (Buonanno et al.," From all the original frames we have extracted a subimage of $500\times 500$ pixels, roughly centered on the nominal position of PSR $-$ 5958A. The scientific images have been reduced using ROMAFOT, a package specifically developed to achieve accurate photometry in crowded fields (Buonanno et al."406 1933): it enables the visual inspection of the quality οἱ point-spread function (PSF) procedure., 1983); it enables the visual inspection of the quality of point-spread function (PSF) procedure.407" PSF best-fittàng has been performed. for all the images separately, and (he mask with the star position obtained from the best-quality image was adapted to each image."," PSF best-fitting has been performed for all the images separately, and the mask with the star position obtained from the best-quality image was adapted to each image."408 The instrumental magnitudes have been reported (ο a 'onmon photometric svstem. then we have obtained a catalog with the coordinates aud the instrumental magnitudes for all the stars common to all the images.," The instrumental magnitudes have been reported to a common photometric system, then we have obtained a catalog with the coordinates and the instrumental magnitudes for all the stars common to all the images."409 We haveperformed the photometric calibration using (wo different and indipendent methods., We haveperformed the photometric calibration using two different and indipendent methods.410 First. magnitudes have," First, magnitudes have"411We have studied spectral and pulse profile variability of dduring its 2008 outburst.,We have studied spectral and pulse profile variability of during its 2008 outburst.412 We found that the large drop in the pulse amplitude and the associated change of the pulse profile on September 27 (seefig.|inHartmanetal.2009) was accompanied by a simultaneous spectral transition in the accretion disc. which was most evidently seen in the ddata.," We found that the large drop in the pulse amplitude and the associated change of the pulse profile on September 27 \citep[see fig. 1 in][]{HPC09} was accompanied by a simultaneous spectral transition in the accretion disc, which was most evidently seen in the data."413" Our interpretation. of this transition is that the magnetospheric radius 7, changes because of opening of the field lines that connect the NS magnetic field to the accretion disc.", Our interpretation of this transition is that the magnetospheric radius $\Rm$ changes because of opening of the field lines that connect the NS magnetic field to the accretion disc.414 We speculated that the physical origin of the field line opening is related to the change of magnetic diffusivity jjj or viscosity 4A., We speculated that the physical origin of the field line opening is related to the change of magnetic diffusivity $\eta_{\rm t}$ or viscosity $\nu_{\rm t}$.415 Through this interpretation we could explain why the apparent inner dise radius — which we associate with the magnetospheric radius Ruy~Raise — decreases from 50 to 30 km in the spectral modelling. why the accretion dise temperature increases from 0.3 to 0.4 keV and why the dise contribution to the bolometric flux increases from 30 to 40 per cent.," Through this interpretation we could explain why the apparent inner disc radius – which we associate with the magnetospheric radius $\Rm \sim \Rdisc$ – decreases from 50 to 30 km in the spectral modelling, why the accretion disc temperature increases from 0.3 to 0.4 keV and why the disc contribution to the bolometric flux increases from 30 to 40 per cent."416 We also saw a decrease in the apparent radius of the hotspot in the spectral analysis and this is also consistent with our interpretation., We also saw a decrease in the apparent radius of the hotspot in the spectral analysis and this is also consistent with our interpretation.417" The field lines that connect the dise at /,, are the ones that connect closest to the magnetie pole of the NS.", The field lines that connect the disc at $\Rm$ are the ones that connect closest to the magnetic pole of the NS.418 As we assumed that the hotspot shape is a ring around the magnetic pole. the opening of the field lines should change the location of the inner hotspot edge pix.," As we assumed that the hotspot shape is a ring around the magnetic pole, the opening of the field lines should change the location of the inner hotspot edge $\rhoin$ ."419 Therefore. as the outer hotspot edge pu should not change in the transition — because for a dipole magnetic field its mostly determined by the mass accretion rate that remained constant — we can associate the decrease in the hotspot radius to a change in the value of pi.," Therefore, as the outer hotspot edge $\rhout$ should not change in the transition – because for a dipole magnetic field its mostly determined by the mass accretion rate that remained constant – we can associate the decrease in the hotspot radius to a change in the value of $\rhoin$."420 Our pulse profile modelling showed that this is exactly what is required to produce the observed transition., Our pulse profile modelling showed that this is exactly what is required to produce the observed transition.421 Furthermore. our results from the pulse protile modelling for the other unknown parameters. such as & and ἐς were also consistent with previous estimates.," Furthermore, our results from the pulse profile modelling for the other unknown parameters, such as $\theta$ and $i$, were also consistent with previous estimates."422 We did not try to place constrains on the neutron star mass and radius based on these data. but the identification that varying hotspot size can lead to pulse profile changes has profound implications for determination of these most important parameters.," We did not try to place constrains on the neutron star mass and radius based on these data, but the identification that varying hotspot size can lead to pulse profile changes has profound implications for determination of these most important parameters."423 However. in order to place tight constraints. we should not only concentrate on modelling these two specific pulse profiles. but instead make use of all the outbursts of11808.," However, in order to place tight constraints, we should not only concentrate on modelling these two specific pulse profiles, but instead make use of all the outbursts of."4244—3658.. A detailed re-analysis of these data will the main attention of our future work., A detailed re-analysis of these data will the main attention of our future work.425 To summarize. for the first time we have found evidence that a sudden pulse profile transition in wwas most likely caused by a change in the way that the NS magnetic field is coupled to the accretion disc.," To summarize, for the first time we have found evidence that a sudden pulse profile transition in was most likely caused by a change in the way that the NS magnetic field is coupled to the accretion disc."426 This mechanism can be one of the causes for pulse profile variability (and. the associated timing noise) in other AMPs as well., This mechanism can be one of the causes for pulse profile variability (and the associated timing noise) in other AMPs as well.427" We constrained the dise truncation radius at Z=21j km and estimated the magnetospheric radius to be about fu,30—50 km.", We constrained the disc truncation radius at $\Rt = 21_{-3}^{+5}$ km and estimated the magnetospheric radius to be about $\Rm \sim 30$ –50 km.428" This would allow in principle to estimate the torques acting on the NS. but the spectroscopic determination of /7,, suffers from several systematic uncertainties that currently prevent such an attempt."," This would allow in principle to estimate the torques acting on the NS, but the spectroscopic determination of $\Rm$ suffers from several systematic uncertainties that currently prevent such an attempt."429" This. however. could be improved if radial profiles of ω. D. and L,, in the magnetospheric region (2,<r«Ih) were accurately known."," This, however, could be improved if radial profiles of $\omega$, $\Bz$ and $\Bphi$ in the magnetospheric region $\Rt < r < \Rm$ ) were accurately known."430 This work was supported by the Finnish Graduate School in Astronomy and Space Physics (EK). EU FP6 Transfer. of Knowledge Project “Astrophysics of Neutron Stars” MTKD-CT-2006-04272? CAT). Viiiisiillii foundation (MA). and the Academy of Finland grant 127512 (P).," This work was supported by the Finnish Graduate School in Astronomy and Space Physics (JJEK), EU FP6 Transfer of Knowledge Project “Astrophysics of Neutron Stars"" MTKD-CT-2006-042722 (AI), Väiisällä foundation (MA), and the Academy of Finland grant 127512 (JP)."431 AP acknowledges partial support from the Netherlands Organization for Scientitic Research (NWO) Veni Fellowship and from à ESF/COMPSTAR visit grant., AP acknowledges partial support from the Netherlands Organization for Scientific Research (NWO) Veni Fellowship and from a ESF/COMPSTAR visit grant.432 We thank the referee for helpful comments., We thank the referee for helpful comments.433 This research made use of the NASA Astrophysics Data System and of the data obtained from the High Energy Astrophysics Science Archive (HEASARC). which is a service of the Astrophysics Science Divisionat NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory.," This research made use of the NASA Astrophysics Data System and of the data obtained from the High Energy Astrophysics Science Archive (HEASARC), which is a service of the Astrophysics Science Divisionat NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory."434interior reads If the planet is a polytrope and the internal energy is entirely thermal then the sum of internal and gravitational energies can be written as —kGM?/R where k is a constant typical somewhat smaller than unity (Chandrasekhar,interior reads If the planet is a polytrope and the internal energy is entirely thermal then the sum of internal and gravitational energies can be written as $- k GM^2/R$ where $k$ is a constant typically somewhat smaller than unity \citep{1957QB461.C45......}.435 In the case of highly degenerate bodies (e.g. 1957).Jupiter itself) the zero temperature part of the internal energy changes in such a way as to exactly cancel the change in gravitational energy as radius changes (Hubbard1984) and the LHS above becomes only the time derivative of thermal energy to a good approximation. (, In the case of highly degenerate bodies (e.g. Jupiter itself) the zero temperature part of the internal energy changes in such a way as to exactly cancel the change in gravitational energy as radius changes \citep{1984plin.book.....H} and the LHS above becomes only the time derivative of thermal energy to a good approximation. (436"This invalidates the claim, often made but erroneous, that the luminosity of degenerate planets is derived from contraction).","This invalidates the claim, often made but erroneous, that the luminosity of degenerate planets is derived from contraction)."437 The bodies of interest to us have non-ideal thermodynamics and are not in the degenerate limit so no simple result holds., The bodies of interest to us have non-ideal thermodynamics and are not in the degenerate limit so no simple result holds.438" However, direct calculation shows that it is still approximately true to replace the LHS above with something like d/dt(—kGM?/R) with k of order unity, even though it is not correct to think of the energy as being derived solely from changes in gravitational energy."," However, direct calculation shows that it is still approximately true to replace the LHS above with something like $d/dt(-kGM^2/R)$ with $k$ of order unity, even though it is not correct to think of the energy as being derived solely from changes in gravitational energy."439 All of this discussion ignores possible effects arising from redistribution of the heavy elements., All of this discussion ignores possible effects arising from redistribution of the heavy elements.440" 'The transition from stable to unstable solutions can only be understood through detailed models, because it depends on the details of opacity and conductivity structure, but the essential physics lies in the comparison of Ohmic heating at depth with the total radiative heat loss from the convective interior evaluated at the radiative/convective boundary."," The transition from stable to unstable solutions can only be understood through detailed models, because it depends on the details of opacity and conductivity structure, but the essential physics lies in the comparison of Ohmic heating at depth with the total radiative heat loss from the convective interior evaluated at the radiative/convective boundary."441" This heat loss scales as the adiabatic temparature gradient, which depends in turn on g, the gravitational acceleration."," This heat loss scales as the adiabatic temparature gradient, which depends in turn on $g$, the gravitational acceleration."442" This is approxcimately linear in mass because radius does not vary much, so Ohmic heating overwhelms heat loss from the interior once the mass is sufficiently small."," This is approxcimately linear in mass because radius does not vary much, so Ohmic heating overwhelms heat loss from the interior once the mass is sufficiently small."443" In the limit where the Ohmic heating dominates the evolution of the deep interior, we expect that the characteristic timescale of inflation Ting;=R/(dR/dt) is (to order of magnitude) the ratio of GM?/R to Ohmic heating, or As can be seen in Figure 5, after a sufficient amount of time, unstable solutions enter a phase of runaway growth, with the instability driven by the fact that the cumulative heating rate is proportional to the surface area of the planet."," In the limit where the Ohmic heating dominates the evolution of the deep interior, we expect that the characteristic timescale of inflation $\tau_{infl} \equiv R/(dR/dt)$ is (to order of magnitude) the ratio of $GM^2/R$ to Ohmic heating, or As can be seen in Figure 5, after a sufficient amount of time, unstable solutions enter a phase of runaway growth, with the instability driven by the fact that the cumulative heating rate is proportional to the surface area of the planet."444 This inevitably leads to Roche-lobe overflow and evaporation of the planet etal. 2008).., This inevitably leads to Roche-lobe overflow and evaporation of the planet \citep{2008ApJ...685..521L}.445" The timescale over which the planet(Laine can remain intact while on an unstable path is a function of the planetary mass and high-mass planets can, in principle, remain intact and grow slowly over many Gyr, while low-mass giant planets evaporate on a ~ 1Gyr timescale."," The timescale over which the planet can remain intact while on an unstable path is a function of the planetary mass and high-mass planets can, in principle, remain intact and grow slowly over many Gyr, while low-mass giant planets evaporate on a $\sim 1$ Gyr timescale."446 It is noteworthy that the timescale will also likely be affected by the slowdown of winds equation 16) and thus a possible 1/Rmodification of the (seeefficiency (which we kept constant) with a growing radius., It is noteworthy that the timescale will also likely be affected by the $1/R$ slowdown of winds (see equation 16) and thus a possible modification of the efficiency (which we kept constant) with a growing radius.447" Still, it is very likely that evaporation is unavoidable in certain circumstances."," Still, it is very likely that evaporation is unavoidable in certain circumstances."448" Low-mass planets can be stabilized against evaporation, if they possess sufficiently massive metallicity cores (Bodenheimeretal.2003;Ibgui 2010).."," Low-mass planets can be stabilized against evaporation, if they possess sufficiently massive high-metallicity cores \citep{2003ApJ...592..555B, 2010ApJ...713..751I}."449 However the critical core mass is far from being trivially small., However the critical core mass is far from being trivially small.450" In fact, a simulation of an 0.5Mju; planet with a p= 3g/cc, 20M@, core at T,;;=1800K reveals that it is only able to retain its envelope for ~1 Gyr before overflowing the Roche-lobe."," In fact, a simulation of an $0.5M_{Jup}$ planet with a $\rho = 3$ g/cc, $20 M_{\oplus}$, core at $T_{eff}=1800K$ reveals that it is only able to retain its envelope for $\sim 1$ Gyr before overflowing the Roche-lobe."451" Given that hot low-mass planets tend to reside in compact multiple systems (Terquem&Papaloizou2007),, while hot Jupiters usually lack close-by companions (LoCurtoetal. the discussion of evaporation is suggestive of the 2010),,possibility that a significant fraction of hot, sub-giant planets, without companions, may have been born as giant planets and have since lost their gaseous"," Given that hot low-mass planets tend to reside in compact multiple systems \citep{2007ApJ...654.1110T}, while hot Jupiters usually lack close-by companions \citep{2010A&A...512A..48L}, the discussion of evaporation is suggestive of the possibility that a significant fraction of hot, sub-giant planets, without companions, may have been born as giant planets and have since lost their gaseous"452"epochs, at least at z=5.","epochs, at least at $z=5$ ."453 ? suggested possible ways around this problem: an early reionization to suppress gas condensation; a very strong feedback from stars or central black holes to reduce overall star formation; or a small-scale cutoff in the primordial fluctuation power spectrum., \cite{2009ApJ...692L...1J} suggested possible ways around this problem: an early reionization to suppress gas condensation; a very strong feedback from stars or central black holes to reduce overall star formation; or a small-scale cutoff in the primordial fluctuation power spectrum.454" However, ? was able to form a more extended disk galaxy at z=0 using the AMR code RAMSES."," However, \cite{2011MNRAS.410.1391A} was able to form a more extended disk galaxy at $z=0$ using the AMR code RAMSES."455" They performed a parameter study with the star formation efficiency per free-fall time varying between eg=0.01 and 0.05, and found that decreasing eg led to a less concentrated stellar distribution, despite smaller stellar mass and weaker feedback."," They performed a parameter study with the star formation efficiency per free-fall time varying between $\epsilon_\mathrm{ff} = 0.01$ and 0.05, and found that decreasing $\epsilon_\mathrm{ff}$ led to a less concentrated stellar distribution, despite smaller stellar mass and weaker feedback."456 We use an even smaller star formation efficiency (eg= but find steeper stellar profiles., We use an even smaller star formation efficiency $\epsilon_\mathrm{ff} = 0.007$ ) but find steeper stellar profiles.457 This discrepancy 0.007)is probably due to a combination of two effects., This discrepancy is probably due to a combination of two effects.458" First, the ? simulation has lower spatial resolution pc vs. 90 pc in our run A at z— 2) and forms stars (340based on the gas density rather the density, and at much lower density than in our case."," First, the \cite{2011MNRAS.410.1391A} simulation has lower spatial resolution (340 pc vs. 90 pc in our run A at $z=2$ ) and forms stars based on the gas density rather the density, and at much lower density than in our case."459 Molecular hydrogen naturally forms only at high gas density and therefore in our simulations star formation takes place in systematically more concentrated regions (see also Figure 1))., Molecular hydrogen naturally forms only at high gas density and therefore in our simulations star formation takes place in systematically more concentrated regions (see also Figure \ref{fig:disc}) ).460" For any given feedback model, the feedback is less efficient in our simulations."," For any given feedback model, the feedback is less efficient in our simulations."461" Second, ? analyze the stellar disk at z=0, as opposed to z2 in our case."," Second, \cite{2011MNRAS.410.1391A} analyze the stellar disk at $z=0$, as opposed to $z \approx 2$ in our case."462 The high-redshift disks are expected to grow gradually in size and may become less concentrated by the present epoch., The high-redshift disks are expected to grow gradually in size and may become less concentrated by the present epoch.463 We have presented a study of the impact of baryon physics on the matter distribution in galaxy formation simulations., We have presented a study of the impact of baryon physics on the matter distribution in galaxy formation simulations.464 An important new feature of our simulations is the modeling of the physics of molecular hydrogen and the star formation prescription based on the local density and not on the gas density., An important new feature of our simulations is the modeling of the physics of molecular hydrogen and the star formation prescription based on the local density and not on the gas density.465" We investigated the properties of the most massive halos with Magog,>10!!Mg to redshift zzz2, using three simulations of the same cosmological volume that differ by the included gas physics and stellar feedback."," We investigated the properties of the most massive halos with $M_\mathrm{200b} \geq 10^{11}\, \Mo$ to redshift $z \approx 2$, using three simulations of the same cosmological volume that differ by the included gas physics and stellar feedback."466" 'The main conclusions of this work are: MZ, OYG, NYG, and AVK are supported in part by NSF grant AST-0708087."," The main conclusions of this work are: MZ, OYG, NYG, and AVK are supported in part by NSF grant AST-0708087."467" The simulations and analysis in this work have been performed on the Joint Fermilab-KICP Supercomputing Cluster (supported by grants from Fermilab, Kavli Institute for Cosmological Physics, and the University of Chicago) and the Legato and Flux clusters at the University of Michigan."," The simulations and analysis in this work have been performed on the Joint Fermilab-KICP Supercomputing Cluster (supported by grants from Fermilab, Kavli Institute for Cosmological Physics, and the University of Chicago) and the Legato and Flux clusters at the University of Michigan."468" This research has made use of NASA’s Astrophysics Data System (ADS), the arXiv.org preprint server, the visualization tool VisIt, the computer algebra system Maxima, and the Python plotting library Matplotlib."," This research has made use of NASA's Astrophysics Data System (ADS), the arXiv.org preprint server, the visualization tool VisIt, the computer algebra system Maxima, and the Python plotting library Matplotlib."469" In order to determine the properties of simulated galaxies, we have built aprofiling routine that takes the"," In order to determine the properties of simulated galaxies, we have built aprofiling routine that takes the"470assess the Luminosity and the viscosity parameter in the BL of VW Ivi.,assess the luminosity and the viscosity parameter in the BL of VW Hyi.471 We sugeest that the second component observed in the EUM spectrum of VW Lyi. commonly. identified as the accretion belt. is really the outer edge of thespread boundary. laver and therefore its contribution in the FUV [lux has to be taken into account when computing the boundary layer luminosity.," We suggest that the second component observed in the FUV spectrum of VW Hyi, commonly identified as the accretion belt, is really the outer edge of the boundary layer and therefore its contribution in the FUV flux has to be taken into account when computing the boundary layer luminosity."472 This belt accounts for of the FUY Hux. and consequenthy the boundary laver Luminosity that is observed is actually: where we have substituted Lypay=0L (Belloni et al.," This belt accounts for of the FUV flux, and consequently the boundary layer luminosity that is observed is actually: where we have substituted $L_{X-ray}=0.1 L_{opt}$ (Belloni et al."473 1991) and Ley=Lo (Pringle et al., 1991) and $L_{UV}=L_{opt}$ (Pringle et al.474 1987)., 1987).475 Ancl since one-half of the boundary laver is occulted by the star. the total emission [from the boundary [aver is twice the amount observed. such that one has: since it is assumed that Lu;=Loa.," And since one-half of the boundary layer is occulted by the star, the total emission from the boundary layer is twice the amount observed, such that one has: since it is assumed that $L_{disc}=L_{opt}$."476 1ο summarize. rom an expected Οτο. the boundary laver. racliates kGLz. one third of which is emitted in the N-rayv and wo third emitted in the PUY (as predicted by Pandel et al.," To summarize, from an expected $0.77L_{disc}$, the boundary layer radiates $0.6 L_{disc}$, one third of which is emitted in the X-ray and two third emitted in the FUV (as predicted by Pandel et al."477 2003)., 2003).478 The remaining energy is most probably advyected into he outer laver of the star (implving Low.=0.17 Las). as expected for advection dominated. optically thin boundary avers solutions (Naravan Pophani 1993. Popham 1999).," The remaining energy is most probably advected into the outer layer of the star (implying $L_{adv}=0.17L_{disc}$ ), as expected for advection dominated optically thin boundary layers solutions (Narayan Popham 1993, Popham 1999)."479 Llowever. no quantitative results have been presented for the optically thin branch of solutions ofthe boundary Iaver.," However, no quantitative results have been presented for the optically thin branch of solutions of the boundary layer."480 The only quantitative results for advection dominated boundary lavers are for the optically thick branch. (Popham 1997. Codon 1997) which predict à ratio μοι©OL02 in rough agreement with what we find here Lf0.085zz 0.1.," The only quantitative results for advection dominated boundary layers are for the optically thick branch (Popham 1997, Godon 1997) which predict a ratio $L_{adv}/L_{acc} \approx 0.1-0.2$ in rough agreement with what we find here $L_{adv}/L_{acc} \approx 0.085 \approx 0.1$ ."481 X-ray observations of VW. Livi in outburst (van der Woere Lleise 1987) have revealed the presence of a 145 DNO. which has been associated with the rotation period of the Ixeplerian flow in the very inner disc.," X-ray observations of VW Hyi in outburst (van der Woerd Heise 1987) have revealed the presence of a 14s DNO, which has been associated with the rotation period of the Keplerian flow in the very inner disc."482 On the other hand. Panelel et al. (," On the other hand, Pandel et al. ("4832003) found that the time it takes for the matter to transit through the boundary layer is about 1005. which is equivalent to the time it takes to spin down the matter [rom Ixeplerian speed to a stellar rotational velocity.,"2003) found that the time it takes for the matter to transit through the boundary layer is about 100s, which is equivalent to the time it takes to spin down the matter from Keplerian speed to a stellar rotational velocity."484"- We use here these two basic time scales to assess the viscosity parameter in the boundary [aver of VW νι,", We use here these two basic time scales to assess the viscosity parameter in the boundary layer of VW Hyi.485" From simple hyvdrodynamical considerations. the spindown (or spinup) time Τον of arotating [low is the ecometric mean of the rotation time τω and the viscous cüllusion time 7. (Gill 1982): or equivalently: Using the value 7,,;7Ids (van der Woerd Leise LOST) and τον&100s (Pandel et al."," From simple hydrodynamical considerations, the spindown (or spinup) time $\tau_{spin}$ of arotating flow is the geometric mean of the rotation time $\tau_{rot}$ and the viscous diffusion time $\tau_{\nu}$ (Gill 1982): or equivalently: Using the value $\tau_{rot} \approx 14$ s (van der Woerd Heise 1987) and $\tau_{spin} \approx 100$ s (Pandel et al."486 2003). leads to τν26618. An estimate of the viscosity coellicient 7 in the boundary laver region can then be assessed. using a basic scaling argument.," 2003), leads to $\tau_{\nu} \approx 667$ s. An estimate of the viscosity coefficient $\nu$ in the boundary layer region can then be assessed using a basic scaling argument."487 The straight viscous diffusion in a Low would spread the boundary. effects in a time / outward. to a distance ὃ given by ὃ=Yel (Gill 1982)., The straight viscous diffusion in a flow would spread the boundary effects in a time $t$ outward to a distance $\delta$ given by $\delta = \sqrt{\nu t}$ (Gill 1982).488 Therefore the viscous diffusion time 7. is given by the simple:: where NJ is the size of the boundary. laver., Therefore the viscous diffusion time $\tau_{\nu}$ is given by the simple: where $\Delta R$ is the size of the boundary layer.489" Inverting the relation. one obtains: where we have assumed AR&410.4/2, (Popham 1999. Pandel et al."," Inverting the relation, one obtains: where we have assumed $\Delta R \approx H \approx 0.4 R_{wd}$ (Popham 1999, Pandel et al."490 2003) and. Rogzz]S«100m., 2003) and $R_{wd} \approx 8 \times 10^{8}$ cm.491 This value is in agreement. within one order of magnitude with the value expected. for the dise viscosity., This value is in agreement within one order of magnitude with the value expected for the disc viscosity.492 For a thiner boundary laver region. of AR=OLR. the viscosity. parameter. is smaller by an order of magnitude »zLOMenrs +.," For a thiner boundary layer region of $\Delta R \approx 0.1 R_{wd}$, the viscosity parameter is smaller by an order of magnitude $\nu \approx 10^{13}$ $^2$ $^{-1}$."493 For a temperature of 107Ix in the BL. the sound speed is close to c. l0°em ! and one has We find that in the DL region the viscosity parameter o ds rather small.," For a temperature of $10^8$ K in the BL, the sound speed is close to $c_s \approx 10^8$ cm $^{-1}$ and one has We find that in the BL region the viscosity parameter $\alpha$ is rather small."494" For comparison. in the inner disc. at re2/2,,47 Wem. where T« 10.000K. one has Hrz001. 1O’em t+ andy2acdza αυ."," For comparison, in the inner disc, at $r\approx 2R_{wd} \approx 1.6 \times 10^9$ cm, where $T < 10,000$ K, one has $H/r \approx 0.01$, $c_s \approx 10^6$ cm $^{-1}$ and $\nu = \alpha c_s H \approx495\alpha \times 10^{13}$ $^2$ $^{-1}$."496 1n this letter. we claim that the BL in VW. Livi radiates 2/3 of its emission in the UV (as the component previously identified as the aceretion belt) anc 1/3 in the X-ray. summing up to 0.6 of the cise DIuminosity.," In this letter, we claim that the BL in VW Hyi radiates 2/3 of its emission in the UV (as the component previously identified as the accretion belt) and 1/3 in the X-ray, summing up to 0.6 of the disc luminosity."497 “Phe remaining BL energy. (0.17 Las) is apparently acdvectecl into the star., The remaining BL energy $0.17 L_{disc}$ ) is apparently advected into the star.498 We suggest that the BL in most quicscent DN is probably raciating a large fraction of the emission in the UV., We suggest that the BL in most quiescent DN is probably radiating a large fraction of the emission in the UV.499 We also estimated that the alpha viscosity. parameter in the BL region of VW Livi is as small as az 0.004., We also estimated that the alpha viscosity parameter in the BL region of VW Hyi is as small as $\alpha \approx 0.004$ .500 The present findings are important. since the origin aud nature of the viscosity in the boundary laver are not known and might be verv cillerent from. that in. the Ixeplerian disc.," The present findings are important, since the origin and nature of the viscosity in the boundary layer are not known and might be very different from that in the Keplerian disc."501 The Balbus-Llawley instability. (Balbus, The Balbus-Hawley instability (Balbus502The object in the centre of 664 (?) is known to be a laarcsec diameter background spiral galaxy (???)..,"The object in the centre of 64 \citep{bp94} is known to be a arcsec diameter background spiral galaxy \citep{k00, sp02, sharina01}."503 We have determined the radial velocity of the background galaxy to be cz—57540 and have fitted its stellar population in order to properly model its contamination in the 664 spectrum., We have determined the radial velocity of the background galaxy to be ${\rm cz}=57540$ and have fitted its stellar population in order to properly model its contamination in the 64 spectrum.504 See the details of the analysis in Appendix A.., See the details of the analysis in Appendix \ref{sect:bg}.505 We have extracted the region of the galaxy in a diameter of 110aarcsec excluding the 15aarcsec central region contaminated by the background galaxy (Fig.10))., We have extracted the region of the galaxy in a diameter of arcsec excluding the arcsec central region contaminated by the background galaxy \ref{fig:k64prof}) ).506 We also split the extraction in inner and outer regions (as it is shown in Fig.10)) to search for radial changes in the galaxy's stellar population., We also split the extraction in inner and outer regions (as it is shown in \ref{fig:k64prof}) ) to search for radial changes in the galaxy's stellar population.507 As for 661 (Sect.3.3)) we corrected the zero point of the velocity using the UVES sky spectrum., As for 61 \ref{subs:k61}) ) we corrected the zero point of the velocity using the UVES sky spectrum.508 The fit against one SSP shows an age of 4+2GGyr and metallicity of —1.5+ 0.1ddex., The fit against one SSP shows an age of $4\pm2$ Gyr and metallicity of $-1.5\pm0.1$ dex.509 For the radial velocity we find —15+13 in agreement with —18+14 from previous measurements of ?.., For the radial velocity we find $-15\pm13$ in agreement with $-18\pm14$ from previous measurements of \citet{sp02}.510 For multi-population analysis we tried to decompose the spectrum in two components: young (<2.5GGyr) and old fixed at GGyr., For multi-population analysis we tried to decompose the spectrum in two components: young $<2.5$ Gyr) and old fixed at Gyr.511 This choice for the old population gives smaller residuals than using the age of 13 Gyr inferred from the CMD analysis., This choice for the old population gives smaller residuals than using the age of 13 Gyr inferred from the CMD analysis.512 We found the young component to have an age of ~1.6 +1GGyr which is consistent with the CMD studies., We found the young component to have an age of $\sim1.6\pm1$ Gyr which is consistent with the CMD studies.513" However, the mass fraction in the young component is pperccents, which is significantly higher than indicated from the CMD analysis ccents)."," However, the mass fraction in the young component is cents, which is significantly higher than indicated from the CMD analysis cents)."514 To determine the values and the errors of the metallicity we performed 1000 Monte-Carlo simulations., To determine the values and the errors of the metallicity we performed 1000 Monte-Carlo simulations.515 The metallicity of the old component is [Fe/H]=—1.6+ 0.4ddex., The metallicity of the old component is ${\rm [Fe/H]}=-1.6\pm0.4$ dex.516 The young stars have almost the same metallicity [Fe/H]=—1.5+ 0.4ddex., The young stars have almost the same metallicity ${\rm [Fe/H]}=-1.5\pm0.4$ dex.517 Therefore the galaxy shows no metallicity evolution., Therefore the galaxy shows no metallicity evolution.518 This result is consistent with the CMD analysis., This result is consistent with the CMD analysis.519" Encouraged from the good results and the higher S/N (~ 8) comparable to 661, we tried to find population gradients along the galaxy."," Encouraged from the good results and the higher S/N $\sim\,8$ ) comparable to 61, we tried to find population gradients along the galaxy."520 To be consistent with the CMD studies we compared the inner aarcsec part and the rest of the galaxy., To be consistent with the CMD studies we compared the inner arcsec part and the rest of the galaxy.521 We could not find any difference in the two extractions., We could not find any difference in the two extractions.522 The ages and metallicities are the same within the error bars like the general extraction., The ages and metallicities are the same within the error bars like the general extraction.523modulation of RAV Dra got dramatically Another wellestucdied example is XZ €vg.,modulation of RW Dra got dramatically Another well-studied example is XZ Cyg.524 LaCluyzéal.(2004) report that the Blazhko period. of XZ νο has changed on a time scale of decades. ancl that these changes are anticorrelateck with observed changes of the pulsation period.," \citet{LaClu04} report that the Blazhko period of XZ Cyg has changed on a time scale of decades, and that these changes are anticorrelated with observed changes of the pulsation period."525" While in the first half of the 20th century (Blazhko1922).. the star was known to a Blazhko period of 57.4 d. it increased to 58.5 T in the⋅ 1960s. while∢ theH pulsation period.H underwent076 , steep decline in several steps."," While in the first half of the 20th century \citep{bla22}, the star was known to have a Blazhko period of 57.4 d, it increased to 58.5 d in the 1960s, while the pulsation period underwent a steep decline in several steps."526" “Phere was an interval − the Blazhko mocdulation disappeared⋠ for⋅ a⋠ while. L∙ additional modulation. period.. of⋅ 41.6 d0.72 was reported [ occur at the times when the period. of the main 0.68 was low. and the presence of an overlying g modulation period"" of. almostmM LO vears wasE: also OQ only Blazhko star for which it was possible to − detect the two modulation frequencies 056 cause the complex multiperiodic — | is CZ Lac (Sódor |2009:Sódoretal.modulation2010)."," There was an interval where the Blazhko modulation disappeared for a while, an additional modulation period of 41.6 d was reported to occur at the times when the period of the main modulation was low, and the presence of an overlying long modulation period of almost 10 years was also The only Blazhko star for which it was possible to unambiguously detect the two modulation frequencies that cause the complex multiperiodic modulation behavior is CZ Lac \citep{sodor09, sodor10}."527.L——31 two periods have similar aniplituces. so that there is 4560 no dominant one. and a strong beating is the result.," The two periods have similar amplitudes, so that there is no dominant one, and a strong beating is the result."528 Phe periodic decrease in the modulation therefore resembles the cessation © “the Blazhko etllect in RR Lyrac. ane the authors sugges that the cause of the 4-vear evele of RR Lyrae might be the same as in CZ Lac. which would also explain why various dillerent Blazhko periods in the range [rom 38.8 d to 40.8 d have been Another one of the few stars which have observations available over a sulliciently long time span to investigate the long-term changes of the modulation properties is RV UAla.," The periodic decrease in the modulation therefore resembles the cessation of the Blazhko effect in RR Lyrae, and the authors suggest that the cause of the 4-year cycle of RR Lyrae might be the same as in CZ Lac, which would also explain why various different Blazhko periods in the range from 38.8 d to 40.8 d have been Another one of the few stars which have observations available over a sufficiently long time span to investigate the long-term changes of the modulation properties is RV UMa."529 lt was known to show a regular large-amplituce moclulation. but based on 90 veas of observation," It was known to show a regular large-amplitude modulation, but based on 90 years of observation"530perform a preliminary membership analvsis using proper motion components from UCAC3 (Zacharias et 22010).,perform a preliminary membership analysis using proper motion components from UCAC3 (Zacharias et 2010).531 This effort was not successful. and our conclusion is that this catalog is not useful to study clusters al large distances [rom the Sun (3 kpe in the case of Trunpler 20).," This effort was not successful, and our conclusion is that this catalog is not useful to study clusters at large distances from the Sun (3 kpc in the case of Trumpler 20)."532 We therefore used the standard procedure of selecting more probable cluster members on the basis of their distance from the cluster In Fig., We therefore used the standard procedure of selecting more probable cluster members on the basis of their distance from the cluster In Fig.533 9 we show a zoom of the red clump region in the V. (D-V)C'M Dof Trumpler 20.consideringo ," 9 we show a zoom of the red clump region in the $V$ $(B-V)$ CMD of Trumpler 20, considering only stars within 5 arcmin from the cluster center."534θαμαδι)," The red clump of Trumpler 20 indeed shows a structure which closely resembles that of NGC 7789, which we know has a similar age (Girardi et al 2000b, Fig 4a)."535=13.7. as derived above.," In this figure we have also plotted a model (evolutionary track) from Girardi Salaris (2001), adopting $E(B-V)=0.35$ and $(V-M_V)=13.7$, as derived above."536 The fit is reasonable. and provides a further confirmation of the age. reddening aud distance we obtained in previous As discussed by Girardi et al. (," The fit is reasonable, and provides a further confirmation of the age, reddening and distance we obtained in previous As discussed by Girardi et al. ("5372000b). this morphology of the clamp may be resulting either [rom star-to-star variations in the mass-loss rates during the RGB phase or by other ellects. such as stellar rotation or convective core overshooting. which can cause a significant spread in the core mass at Ie-ignition for stars of similar mass.,"2000b), this morphology of the clump may be resulting either from star-to-star variations in the mass-loss rates during the RGB phase or by other effects, such as stellar rotation or convective core overshooting, which can cause a significant spread in the core mass at He-ignition for stars of similar mass."538 Apart from NGCZI 7789 and Trunpler 20. a similar morphology has been found in NGC 2204 and NGC 2660 (Girardi el al.," Apart from NGC 7789 and Trumpler 20, a similar morphology has been found in NGC 2204 and NGC 2660 (Girardi et al."539 2000b)., 2000b).540 The close similarity between the CMDs of Trumpler 20 and NGC! 7789 also applies to the population of bright blue stars., The close similarity between the CMDs of Trumpler 20 and NGC 7789 also applies to the population of bright blue stars.541 These stars can be either field stars located between the cluster and the observer. or blue stragglers (3humacda Lapasset 2007).," These stars can be either field stars located between the cluster and the observer, or blue stragglers (Ahumada Lapasset 2007)."542" These latter should preferentially lie within the cluster area,", These latter should preferentially lie within the cluster area.543 According to a recent study by Carraro et ((2003). in the case of NGC ZI7789 it turns out that most bright stars in (is part of its CMD are interlopers. and only a minor percentage are DSs.," According to a recent study by Carraro et (2008), in the case of NGC 7789 it turns out that most bright stars in this part of its CMD are interlopers, and only a minor percentage are BSs."544moment of time.,moment of time.545 After the predicted 2005 outburst was observed. a new solution was calculated using 6 outbursts. allowing the determination of 5 parameters (Valtoneu 2007).," After the predicted 2005 outburst was observed, a new solution was calculated using 6 outbursts, allowing the determination of 5 parameters (Valtonen 2007)."546 The new additional paramcter is the thickness of the accretion disk (scale height ~150 AU). while the precession rate was updated to 31.57.39.17.," The new additional parameter is the thickness of the accretion disk (scale height $\sim150$ AU), while the precession rate was updated to $37.5^\circ - 39.1^\circ$."547 The tiuiug of the 2007 outburst together with some new historical data allowed a solution using 9 outbursts. and solving for S parameters (Valtonen et al.," The timing of the 2007 outburst together with some new historical data allowed a solution using 9 outbursts, and solving for 8 parameters (Valtonen et al."548 2010)., 2010).549 These 9 outbursts all follow the basic light curve shape of Figure 3. with a rapid rise to the παπια and then a slower decay to pre-outhurst level.," These 9 outbursts all follow the basic light curve shape of Figure 3, with a rapid rise to the maximum and then a slower decay to pre-outburst level."550 The time scales of the outbursts follow the depeideuce ou the impact distance established by Leliο aud Valtonen (1996)., The time scales of the outbursts follow the dependence on the impact distance established by Lehto and Valtonen (1996).551 They form a verv well «efiued sequence., They form a very well defined sequence.552 There are no cases when au outburst iu this sequence was expected but was not observed., There are no cases when an outburst in this sequence was expected but was not observed.553 All nüssing iuenibers are at times when there were no observations., All missing members are at times when there were no observations.554 Neither are there any extra unexplaimed members of this sequence., Neither are there any extra unexplained members of this sequence.555 The new parameters are the spin of the primary black hole. with X40.28+0.08. the inass of the secondary 1.1430LSIOSAL. uid 4 which is clesribecdk below.," The new parameters are the spin of the primary black hole, with $\chi_1 = 0.28 \pm 0.08$, the mass of the secondary $1.4 \pm 0.1 \times 10^{8}\, M_{\odot}$, and $q$ which is desribed below."556" Parallel το the nlerease dn the nuniber of outbursts in the sohtion. the nuuber of post-Newtoniau (PN) terius was increase Lin calculating the acceleration between the binary"" conuponents."," Parallel to the increase in the number of outbursts in the solution, the number of post-Newtonian (PN) terms was increased in calculating the acceleration between the binary components."557 Valtouen et al. (, Valtonen et al. (55820]0) include he donünaut order general relativistic and classical spin-orbit coupling. which is recmired in order to relate the diueusionless quadpole parameter gq. of the primary to its Kerr peunueter.,"2010) include the dominant order general relativistic and classical spin-orbit coupling, which is required in order to relate the dimensionless quadrupole parameter $q_2$ of the primary to its Kerr parameter."559 They write and let 4 be noiie the 8 parameters of the solution., They write and let $q$ be among the 8 parameters of the solution.560 Its value was determined as q—140.3., Its value was determined as $q=1 \pm 0.3$.561 Valtoneu et al. (, Valtonen et al. (562"2010) noted tha the timune of the next outburst in 2015 S»ld help O improve the accuracy of the X estinate to about πο, ",2010) noted that the timing of the next outburst in 2015 should help to improve the accuracy of the $\chi$ estimate to about $\pm 5 \%$.563This couclusio oug with he fact flat the Lass of the prnuarv ds cetermuned wili the accuracy of x1( prompted 1s to explore the wavs of testing he no-hair theorems at ie 410% level in o nieasurne q more accurately., This conclusion along with the fact that the mass of the primary is determined with the accuracy of $\pm 1 \%$ prompted us to explore the ways of testing the no-hair theorem at the $\pm 10 \%$ level in by measuring $q$ more accurately.564 Thi the literativs there exits a nuniber of proposas to test the |dack hole 1Q-hair theorems. plausidle in the nex decade with the help of electromagnetic aud gravitational wave 6servations.," In the literature, there exits a number of proposals to test the black hole no-hair theorems, plausible in the next decade with the help of electromagnetic and gravitational wave observations."565 The scenarios include radio timine 6 eccentric nilisecouc binary pulsars having au extreme [err lack Lede as a companion (Wex and Iopeisin 1999) ail observing several stars orbiting the massive galactie center black hole at iudliursec «instances with intrarecdl telescopes capable of doiug astro11οry at ~LOp arecseconcds evel (Wil20SL., The scenarios include radio timing of eccentric millisecond binary pulsars having an extreme Kerr black hole as a companion (Wex and Kopeikin 1999) and observing several stars orbiting the massive galactic center black hole at milliarsec distances with infrared telescopes capable of doing astrometry at $\sim 10 \mu$ arcseconds level \citep{Will2008}.566 Γιrther. LISA oloervations | gravitational waves. fia extreme nass ratio iuspirals (C:aupedalsis&Babals2006) and quasirormal ringdown phases :issoclatedl wilh massive lack hoe nerecrs (Bertietal.2006) will also rv fo vaKkate black hole jo-liar theorems.," Further, LISA observations of gravitational waves from extreme mass ratio inspirals \citep{gb_06} and quasi-normal ringdown phases associated with massive black hole mergers \citep{eb_06} will also try to validate black hole no-hair theorems."567" It las also Όσοι argued that the mniaenme of accretion flow arol11( Ser A*. if its Kerr pariter is iot CLOSC to O1ο, Inav allow the testing of the ir theor(qus in the near future (Joiumsen&Psaltis2 )."," It has also been argued that the imaging of accretion flow around Sgr A*, if its Kerr parameter is not close to one, may allow the testing of the no-hair theorems in the near future \citep{JP10}."568. The test relies on the arguneut ji a bright οπήο rine characterizing he How jac will be elliptical and asvnunetric if 1ο theoreus are violated., The test relies on the argument that a bright emission ring characterizing the flow image will be elliptical and asymmetric if the theorems are violated.569 Johannsen aud Psatis (2011) further explore the possibility of detecting nodes of quasiperiodic variability in accretion disks as test cases for the uo-hair theorenis., Johannsen and Psaltis (2011) further explore the possibility of detecting modes of quasiperiodic variability in accretion disks as test cases for the no-hair theorems.570or suggested (seeDeustetal.1996.2001.detections).. so the extrasolar cometary system around IRC+10216 is not the first to be discovered.,"or suggested \citep[see][for discussions of plausible but unconfirmed571detections]{beu96,BKL01}, so the extrasolar cometary system around IRC+10216 is not the first to be discovered."572 But it is the first extrasolar cometary svstem that can be at least partially chemically characterized., But it is the first extrasolar cometary system that can be at least partially chemically characterized.573 Belore we can understand (he chemical composition of the extrasolar cometary system around IRC+10216. however. we should examine the chemistry of Solar Svstem comets.," Before we can understand the chemical composition of the extrasolar cometary system around IRC+10216, however, we should examine the chemistry of Solar System comets."574 Formaldehyde. specifically. presents some complications.," Formaldehyde, specifically, presents some complications."575 Formaltcdehvee was first. observed in a comet by Sagdeevetal.(1986)., Formaldehyde was first observed in a comet by \citet{sag86}.576.. HILowever. if was not until several vears later that Meieretal.(1993) discovered (hat formaldehyde is not usually a parent molecule: that is. lormaldehyde is not usually emitted in significant quantities directly from comet nuclei.," However, it was not until several years later that \citet{mei93}577 discovered that formaldehyde is not usually a parent molecule; that is, formaldehyde is not usually emitted in significant quantities directly from comet nuclei."578 Instead. it is now thought (hat formaldehyde is produced in most comet comae by the photodissociation of a parent molecule or molecules. probably polvoxvinetlvlenes (Meierelal.1993:Cottinοἱ2001. 2004).," Instead, it is now thought that formaldehyde is produced in most comet comae by the photodissociation of a parent molecule or molecules, probably polyoxymethylenes \citep{mei93,cot01,cot04}."579. Recent observations indicate that formaldehyde is a parent molecule in some Solar Svstem comets (Michael A. DiSanti. personal communication): however. most comets appear to have substantial extended sources of formaldehyde (indicating that it is primarily a daughter product).," Recent observations indicate that formaldehyde is a parent molecule in some Solar System comets (Michael A. DiSanti, personal communication); however, most comets appear to have substantial extended sources of formaldehyde (indicating that it is primarily a daughter product)."580 The abundance of formaldehyde in comets. as determined [rom line strengths. depends ou whether the molecule is assumed to have a spatial distribution which corresponds to a parent or a daughter product.," The abundance of formaldehyde in comets, as determined from line strengths, depends on whether the molecule is assumed to have a spatial distribution which corresponds to a parent or a daughter product."581 Assuming a daughter distribution. as now seems likely for the majority of cases. formaldelivde. abundancees. in comels are generally found to be a few tenths (ο a few percent. relative to water 1996).," Assuming a daughter distribution, as now seems likely for the majority of cases, formaldehyde abundances in comets are generally found to be a few tenths to a few percent, relative to water \citep{boc96}."582. An extended distribution of H3CO around IRC+10216 could indicate that formaldehyde is produced. by the photoclissociation of a parent molecule vaporized [rom comelarv nuclei., An extended distribution of $_2$ CO around IRC+10216 could indicate that formaldehyde is produced by the photodissociation of a parent molecule vaporized from cometary nuclei.583 We will need to construct a photodissociation model to determine the expected spatial distribution of formaldehyde around IRC+10216 for the cases of both parent and daughter production. and carefully compare our models (o our observations.," We will need to construct a photodissociation model to determine the expected spatial distribution of formaldehyde around IRC+10216 for the cases of both parent and daughter production, and carefully compare our models to our observations."584 Methanol. bv contrast. is a parent molecule in Solar System comets. so our methanol observations should be easier to interpret.," Methanol, by contrast, is a parent molecule in Solar System comets, so our methanol observations should be easier to interpret."585 We explain our observational search for formaldehyde aid methanol below in 82., We explain our observational search for formaldehyde and methanol below in 2.586 In. 83 we discuss our interpretations of the data., In 3 we discuss our interpretations of the data.587 A summary of our conclusions is given in 84., A summary of our conclusions is given in 4.588 The main observations discussed in this paper were carried out using the IILAM 30m radio telescope in late August. and early September of 2002., The main observations discussed in this paper were carried out using the IRAM $30$ m radio telescope in late August and early September of 2002.589" For our initial observations. we used the C150 and D150 receivers to observe the 24»—ly, and 244,—149. transitions of formaldehyde. with rest frequencies of 140839.5020 and 150493.3340 MIIZ. respectively."," For our initial observations, we used the C150 and D150 receivers to observe the $2_{12}-1_{11}\>$ and $2_{11}-1_{10}\>$ transitions of formaldehyde, with rest frequencies of $140839.5020$ and $150498.3340\,$ MHz, respectively."590 We, We591we attempt to constrain the kinds of substructure models that will reproduce the observed parity dependence.,we attempt to constrain the kinds of substructure models that will reproduce the observed parity dependence.592 We show that the distribution of substructure necessary is inconsistent both with the results of ? and with the anomalous flux ratios being solely due to observed luminous satellite galaxies., We show that the distribution of substructure necessary is inconsistent both with the results of \citet{mao_etal04} and with the anomalous flux ratios being solely due to observed luminous satellite galaxies.593 The paper is organized as follows., The paper is organized as follows.594 Section 2. describes the lens modeling. while Section 3. discusses the observational sample and reproduces the previously observed parity dependence.," Section \ref{sec:lens_model} describes the lens modeling, while Section \ref{sec:observations} discusses the observational sample and reproduces the previously observed parity dependence."595 Section 4. describes the substructure models used and how mock observations are created., Section \ref{sec:mock} describes the substructure models used and how mock observations are created.596 Section 5 presents the results of testing several substructure models and compares them to the observational sample., Section \ref{sec:results} presents the results of testing several substructure models and compares them to the observational sample.597 Discussion and conclusions are presented in Sections 6 and 7.., Discussion and conclusions are presented in Sections \ref{sec:discussion} and \ref{sec:conclusions}.598 We model the positions of lensed images using an automated lens fitting code with à singular isothermal ellipsoid (SIE) mass distribution and an external shear component., We model the positions of lensed images using an automated lens fitting code with a singular isothermal ellipsoid (SIE) mass distribution and an external shear component.599 The 9 nodel parameters are 1.), The 9 model parameters are 1.)600 the Einstein radius 5: 2.), the Einstein radius $b$; 2.)601 the projected axis ratio q: 3.), the projected axis ratio $q$; 3.)602" the orientation of the halo ellipticity 4,: 4.)", the orientation of the halo ellipticity $\theta_{q}$; 4.)603 the external shear y which describes the effect of structure near the lens halo (e.g.. a nearby group of galaxies): 5.)," the external shear $\gamma$ which describes the effect of structure near the lens halo (e.g., a nearby group of galaxies); 5.)"604 the orientation of the shear 6): 6.), the orientation of the shear $\theta_{\gamma}$; 6.)605 7.), 7.)606 the source position. Aource and Yu: and 8.)," the source position, $x_{\rm source}$ and $y_{\rm source}$; and 8.)"607 9.), 9.)608 the center of lens. xa; and vago.," the center of lens, $x_{\rm center}$ and $y_{\rm center}$ ."609 The SIE has a projected surface density where £ is the elliptical coordinate satisfying &=x77/q7 and where x and y are the Cartesian coordinates and q is the axis ratio., The SIE has a projected surface density where $\xi$ is the elliptical coordinate satisfying $\xi^2 = x^2+ y^2/q^2$ and where $x$ and $y$ are the Cartesian coordinates and $q$ is the axis ratio.610" In the limit of circular symmetry. 5. the Einstein radius. is related to the 1-d velocity dispersion c by where c is the speed of light in à vacuum. and Di, and Do. are the angular diameter distances from the lens to the source and from the observer to the source. respectively."," In the limit of circular symmetry, $b$ , the Einstein radius, is related to the 1-d velocity dispersion $\sigma$ by where $c$ is the speed of light in a vacuum, and $D_{\rm ls}$ and $D_{\rm os}$ are the angular diameter distances from the lens to the source and from the observer to the source, respectively."611 We restrict ourselves to lensed systems with four observed images., We restrict ourselves to lensed systems with four observed images.612 The observed constraints consist of 8 coordinates of the Images and a constraint from the observed center of the lens potential (presumably the position of the lensing galaxy). Neer Ad ορ. for a total of 10 constraints.," The observed constraints consist of 8 coordinates of the images and a constraint from the observed center of the lens potential (presumably the position of the lensing galaxy), $x_{\rm center}$ and $y_{\rm center}$, for a total of 10 constraints."613 Fluxes are not included as constraints., Fluxes are not included as constraints.614 The lens modeling algorithm requires several steps and is based upon the publicly available lens modeling code (?).., The lens modeling algorithm requires several steps and is based upon the publicly available lens modeling code \citep{keeton01b}.615" We employ a downhill simplex minimization routine. and we first find best-fit parameters first in the source plane. which is faster than fitting in the image We start by finding appropriate values for the lens halo parameters — 6. q. and 4, — then fixing the lens halo parameters and finding appropriate values for the external shear y and 6,."," We employ a downhill simplex minimization routine, and we first find best-fit parameters first in the source plane, which is faster than fitting in the image We start by finding appropriate values for the lens halo parameters – $b$, $q$, and $\theta_{q}$ – then fixing the lens halo parameters and finding appropriate values for the external shear $\gamma$ and $\theta_{\gamma}$."616 We do several iterations of fits for all the parameters in the source plane., We do several iterations of fits for all the parameters in the source plane.617" At each iteration, we slightly perturb the image positions."," At each iteration, we slightly perturb the image positions."618 Perturbing the image positions gives us several sets of data with formally identical observational constraints and may help to avoid ending in local minima., Perturbing the image positions gives us several sets of data with formally identical observational constraints and may help to avoid ending in local minima.619 Finally. we do several iterations of fitting all the parameters in the image plane.," Finally, we do several iterations of fitting all the parameters in the image plane."620 Additional details are found in Appendix AppendixA:., Additional details are found in Appendix \ref{sec:appendix}.621. We use a set of observed lens systems both to test the observed parity dependence and as the basis for mock observations., We use a set of observed lens systems both to test the observed parity dependence and as the basis for mock observations.622 ? use 7 four-image lens systems with anomalous flux ratios: their sample also represents a fair fraction of all 4-image systems with galaxy lenses observed in the radio., \citet{dalal_kochanek02} use 7 four-image lens systems with anomalous flux ratios; their sample also represents a fair fraction of all 4-image systems with galaxy lenses observed in the radio.623 ? use those 7 systems with the exception of PG1115+080 and add two more systems in order to test the parity dependence of anomalous flux ratio systems., \citet{kochanek_dalal04} use those 7 systems with the exception of PG1115+080 and add two more systems in order to test the parity dependence of anomalous flux ratio systems.624 In this paper. we use 5 of the 7 lens systems used in 2.. excluding PGII15+080 which does not have observed radio fluxes and B1608+656 which 1s a double lens system.," In this paper, we use 5 of the 7 lens systems used in \citet{dalal_kochanek02}, excluding PG1115+080 which does not have observed radio fluxes and B1608+656 which is a double lens system."625 The systems used are MGO4144-0534 (22).. BO712+472 (?).. B1422423102?).. B19334+503 (2). and B2045+265 (2).," The systems used are MG0414+0534 \citep{katz_etal97,ros_etal00}, B0712+472 \citep{jackson_etal98}, \citep{patnaik_etal99,patnaik_etal92}, B1933+503 \citep{sykes_etal98}, and B2045+265 \citep{mckean_etal07}."626 Using our automated lens modeling code. we try to reproduce the results of ?..," Using our automated lens modeling code, we try to reproduce the results of \citet{kochanek_dalal04}."627 As discussed previously. we fit the positions of the images and the lensinggalaxy (10 constraints) with a SIElens plus external shear.," As discussed previously, we fit the positions of the images and the lensinggalaxy (10 constraints) with a SIElens plus external shear."628 The fluxes (and magnifications) of the images are not used as constraints., The fluxes (and magnifications) of the images are not used as constraints.629 The estimated flux perturbation for each image is defined by, The estimated flux perturbation for each image is defined by630according to the inferred reddening ratio Ευ.p/Egy= 0.73.,according to the inferred reddening ratio $E_{U-B}/E_{B-V} = 0.73$ .631 Note that the adopted field reddening lines are unchanging for Εν.;/Epg.y and exhibit only small variations for Egr/Epv., Note that the adopted field reddening lines are unchanging for $E_{V-I}/E_{B-V}$ and exhibit only small variations for $E_{R-I}/E_{B-V}$.632" Initial tests with two-color diagrams using intrinsic BV(RI)c colors for dwarfs from Caldwelletal.(1993) revealed small anomalies in the inferred ΕΕ.y reddenings derived from the two diagrams, as well as an overabundance of unreddened and negatively-reddened stars relative to the intrinsic relation, not explainable as luminosity effects (Caldwelletal.1993)."," Initial tests with two-color diagrams using intrinsic $_C$ colors for dwarfs from \citet{ca93} revealed small anomalies in the inferred $E_{B-V}$ reddenings derived from the two diagrams, as well as an overabundance of unreddened and negatively-reddened stars relative to the intrinsic relation, not explainable as luminosity effects \citep{ca93}."633". Such non-physical results suggested the need for slight corrections to the intrinsic colors used with the present data sets, which are normalized to the Kron-Cousins system."," Such non-physical results suggested the need for slight corrections to the intrinsic colors used with the present data sets, which are normalized to the Kron-Cousins system."634 Small adjustments to the intrinsic relations for late B-type and A-type dwarfs to make them bluer were therefore tried using alternative intrinsic colors from Johnson(1966) adjusted to the Cape system (Fernie1983)., Small adjustments to the intrinsic relations for late B-type and A-type dwarfs to make them bluer were therefore tried using alternative intrinsic colors from \citet{jo66} adjusted to the Cape system \citep{fe83}.635" That produced greater consistency in the derived reddenings and better agreement for unreddened stars, and was adopted throughout the remainder of the study."," That produced greater consistency in the derived reddenings and better agreement for unreddened stars, and was adopted throughout the remainder of the study."636" Theintrinsic colors corresponding to such changes are presented in 'Table 1 for reference purposes, where they are compared with the Caldwelletal.(1993,SAAO) colors for dwarfs, which were adopted for all other stars."," Theintrinsic colors corresponding to such changes are presented in Table \ref{tab1} for reference purposes, where they are compared with the \citet[][SAAO]{ca93} colors for dwarfs, which were adopted for all other stars."637" Given that the analysis was restricted to stars that dereddened uniquely to the AF-dwarf relation, the modification affects the resulting space reddenings, but only to a minor extent."," Given that the analysis was restricted to stars that dereddened uniquely to the AF-dwarf relation, the modification affects the resulting space reddenings, but only to a minor extent."638 Likely B-type stars in the field of each Cepheid were only used when analyzing 2MASS colors for the stars., Likely B-type stars in the field of each Cepheid were only used when analyzing 2MASS colors for the stars.639" Reddening lines run nearly parallel to the intrinsic relations for B-dwarfs and KM-dwarfs, particularly in V-Ic versusB-V diagrams, which is why the analysis was restricted to stars indicated to be likely AF-dwarfs, which are reasonably plentiful in each field."," Reddening lines run nearly parallel to the intrinsic relations for B-dwarfs and KM-dwarfs, particularly in $_C$ versus diagrams, which is why the analysis was restricted to stars indicated to be likely AF-dwarfs, which are reasonably plentiful in each field."640" The slope of the intrinsic relation for AF-dwarfs relative to the effects of interstellar reddening in the BV(RI)c system results in sufficient separation, particularly in (R—-D)c relative toB-V, to produce unique photometric dereddening solutions for each star, and the use of two separate color-color diagrams provides independent estimates for the intrinsic color of each star, although greater precision is obtained with solutions from the (R-I)c versusB-V diagram alone, because the angle between the intrinsic relation and typical reddening lines is larger."," The slope of the intrinsic relation for AF-dwarfs relative to the effects of interstellar reddening in the $_C$ system results in sufficient separation, particularly in $_C$ relative to, to produce unique photometric dereddening solutions for each star, and the use of two separate color-color diagrams provides independent estimates for the intrinsic color of each star, although greater precision is obtained with solutions from the $_C$ versus diagram alone, because the angle between the intrinsic relation and typical reddening lines is larger."641" Infrared JHK, observations exist for most stars (Cutri from the Two Micron All Sky Survey (2MASS,Skrut-skieetal. 2006),, and confirm the adopted reddenings from BV(RI)c data, although the scatter in 2MASS JHK, colors tends to be rather significant, larger than in color-color diagrams (Turner1976a)."," Infrared $_{\rm s}$ observations exist for most stars \citep{cu03} from the Two Micron All Sky Survey \citep[2MASS,][]{sk06}, and confirm the adopted reddenings from $_C$ data, although the scatter in 2MASS $_{\rm s}$ colors tends to be rather significant, larger than in color-color diagrams \citep{tu76a}."642". 'Typical companions and progenitors of Cepheids are B-type stars (Turner1984), which are rare enough that their occurrence in the field of a Cepheid raises the possibility of a physical association."," Typical companions and progenitors of Cepheids are B-type stars \citep{tu84}, which are rare enough that their occurrence in the field of a Cepheid raises the possibility of a physical association."643" AF-type stars, on the other hand, are à more common constituent of Galactic star fields (McCuskey1965),, so the possibility of their physical association with a nearby Cepheid is reduced, but not necessarily to zero."," AF-type stars, on the other hand, are a more common constituent of Galactic star fields \citep{mc65}, so the possibility of their physical association with a nearby Cepheid is reduced, but not necessarily to zero."644" In many of our program fields some of the stars identified as likely AF-type may be associated with the Cepheid of interest, but that was not explored here since there are no catalogued star clusters in the fields, although the regions around UY Mon, BE Pup, YZ CMa, and VY Sgr appear to contain faint anonymous clusters, and BD Pup and FO Cas are located in bright groups of surrounding stars."," In many of our program fields some of the stars identified as likely AF-type may be associated with the Cepheid of interest, but that was not explored here since there are no catalogued star clusters in the fields, although the regions around UY Mon, BE Pup, YZ CMa, and VY Sgr appear to contain faint anonymous clusters, and BD Pup and FO Cas are located in bright groups of surrounding stars."645 The additional scatter in Fig., The additional scatter in Fig.646 2 illustrates some of the problems associated with dereddening stars in BV(RI)c color-color diagrams., \ref{fig2} illustrates some of the problems associated with dereddening stars in $_C$ color-color diagrams.647" Such scatter for a small proportion of stars is a common characteristic of color- diagrams, including those in UBV and those used for 2MASS photometry, and is readily explained in most cases by observational error, typically one or more of"," Such scatter for a small proportion of stars is a common characteristic of color-color diagrams, including those in and those used for 2MASS photometry, and is readily explained in most cases by observational error, typically one or more of"6481983:: Fellietal. 1984)) — an evolutionary state with high mass loss which follows an earlier accretion phase.,; \citealp{fms+84}) ) – an evolutionary state with high mass loss which follows an earlier accretion phase.649 The rate at which S106 IRS 4 ts losing mass is atypically high for a star of this bolometric lummosity., The rate at which S106 IRS 4 is losing mass is atypically high for a star of this bolometric luminosity.650 At MW1.6x10°Mc yyr!. corresponding to M/L=[1.6-8] x107ML! yr! (Fellietal. 19849). this is 1-2 orders of magnitude higher than most normal early type stars and comparable to the values measured in Wolf-Rayet stars.," At $\dot{M}\sim 1.6 \times65110^{-6}\,M_{\sun}$ $^{-1}$, corresponding to $\dot{M}/L \simeq652[1.6$ $8] \times 10^{-11} M_\odot\, L_\odot^{-1}$ $^{-1}$ \citealp{fms+84}) ), this is 1–2 orders of magnitude higher than most normal early type stars and comparable to the values measured in Wolf-Rayet stars."653 At the same time the terminal wind velocity of v4200 kms ∣ Is lower than typical values measured for equally luminous stars. for which v. 1000-1500 km s! (Panagia&Macchetto 1982)).," At the same time the terminal wind velocity of $v_{\infty} \sim 200$ km $^{-1}$ is lower than typical values measured for equally luminous stars, for which $v_{\infty} \sim6541000$ $1500$ km $^{-1}$ \citealp{pm82}) )."655 Radio observations suggests that this wind may be mainly equatorial (Hoareetal. 1994))., Radio observations suggests that this wind may be mainly equatorial \citealp{hdm+94}) ).656" Schneideretal.(2002) attribute the dynamies of the molecular gas in the $106 region to the impact of the ionized wind ofS106 IRS 4. driving a shock into an inhomogeneous molecular cloud,"," \cite{ssk+02} attribute the dynamics of the molecular gas in the S106 region to the impact of the ionized wind of S106 IRS 4, driving a shock into an inhomogeneous molecular cloud."657 The oobservation provides the first detection of S106 IRS 4 in X-rays., The observation provides the first detection of S106 IRS 4 in X-rays.658 We estimated for this source an X-ray luminosity of 2xIOere aassuming a plasma temperature KT.=2.16 keV. as for all the other sources in our sample.," We estimated for this source an X-ray luminosity of $2659\times 10^{30}$ assuming a plasma temperature $kT = 2.16$ keV, as for all the other sources in our sample."660 This luminosity corresponds to Lx/Ly[0.5—1]x102. which is about one order of magnitude lower than typically observed for older massive stars (Sciortinoetal. 1990)). although there is a large scatter (+1 dex) on the Lx/Ly4 relation for massive stars (e.g. Moffatetal. 2002).," This luminosity corresponds to $L_{\rm X}/L_{\rm bol} \sim [0.5-1] \times 10^{-8}$, which is about one order of magnitude lower than typically observed for older massive stars \citealp{svh+90}) ), although there is a large scatter $\pm6611$ dex) on the $L_{\rm X}/L_{\rm bol}$ relation for massive stars (e.g. \citealp{mcs+02}) )."662 The assumed X-ray plasma temperature for S106 IRS 4 is however likely too high for an early type star., The assumed X-ray plasma temperature for S106 IRS 4 is however likely too high for an early type star.663 Chlebowskietal.(1989) have shown that typical plasma temperatures for wind related emission in O stars are around kT=0.5 keV. significantly lower than the value we have assumed.," \cite{chs89}664 have shown that typical plasma temperatures for wind related emission in O stars are around $kT = 0.5$ keV, significantly lower than the value we have assumed."665 Given the high absorption toward the source. the choice of plasma temperature ts rather critical for determining the X-ray luminosity.," Given the high absorption toward the source, the choice of plasma temperature is rather critical for determining the X-ray luminosity."666" Assuming AT=0.5 keV one derives for S106 IRS 4 an intrinsic X-ray luminosity of Ly=4.810""!s|.. corresponding to a range Ly/Lpo [1.223]x1077. at the lower end of the typical values for O stars (Sciortino 1990))."," Assuming $kT = 0.5$ keV one derives for S106 IRS 4 an intrinsic X-ray luminosity of $L_{\rm X} =4.8\times66710^{31}$, corresponding to a range $L_{\rm X}/L_{\rm bol} \sim668[1.2$ $3] \times 10^{-7}$, at the lower end of the typical values for O stars \citealp{svh+90}) )."669" On the basis of the correlations determined by Sciortinoetal.(1990) in their study of X-ray emission from O-stars an X-ray luminosity of 4.8x10?! us a factor of 15 below the value typical for stars with comparable mass loss. but it i5 similar to the X-ray luminosities found in relation to the star wind momentum flux (£j,Mv,22x10 gems Ko"," On the basis of the correlations determined by \cite{svh+90} in their study of X-ray emission from O-stars an X-ray luminosity of $4.8\times 10^{31}$ is a factor of 15 below the value typical for stars with comparable mass loss, but it is similar to the X-ray luminosities found in relation to the star wind momentum flux $F_{\rm m} = \dot{M} v_{\infty} = 2\times67010^{27}~{\rm g~cm~s^{-2}}$ )."671"hnoetal.(2002) have recently reported the detection of X-ray emission from four high-mass YSOs in Mon R2. deriving typical best fit plasma temperatures. absorption column densities and X-ray luminosities of ~2 keV, ~ὃ- 10x1077 em and 10910?ergs7!.. that is X-ray luminosities similar to the one derived here for S106 IRS 4."," \cite{kkh02} have recently reported the detection of X-ray emission from four high-mass YSOs in Mon R2, deriving typical best fit plasma temperatures, absorption column densities and X-ray luminosities of $\sim 2$ keV, $\sim 5$ $10\times 10^{22}$ $^{-2}$ and $10^{30}$ $10^{31}$, that is X-ray luminosities similar to the one derived here for S106 IRS 4."672 The X-ray flux from the Mon R2 high mass YSOs appears to be highly variable with flare-like behavior: because of this and the high plasma temperatures Kohnoetal.(2002) suggest that the X-ray activity of these massive YSOs may be magnetically driven. in a similar way to that seen in low mass PMS stars.," The X-ray flux from the Mon R2 high mass YSOs appears to be highly variable with flare-like behavior; because of this and the high plasma temperatures \cite{kkh02} suggest that the X-ray activity of these massive YSOs may be magnetically driven, in a similar way to that seen in low mass PMS stars."673 Unfortunately. for 106 IRS 4 no plasma temperature can be determined. which means that we cannot compare it with the values derived for the Mon R2 sources and that we have to base the estimate of its X-ray luminosity on an assumed plasma temperature.," Unfortunately, for S106 IRS 4 no plasma temperature can be determined, which means that we cannot compare it with the values derived for the Mon R2 sources and that we have to base the estimate of its X-ray luminosity on an assumed plasma temperature."674 Nevertheless. assuming a plasma temperature typical for older massive stars. the X-ray luminosity of S106 IRS 4 is consistent to the values predicted for older stars on the basis of their wind momentum flux. which is the dominating factor in determining the X-ray luminosity of a massive star (as established by Sciortinoetal.1990 — Fig.," Nevertheless, assuming a plasma temperature typical for older massive stars, the X-ray luminosity of S106 IRS 4 is consistent to the values predicted for older stars on the basis of their wind momentum flux, which is the dominating factor in determining the X-ray luminosity of a massive star (as established by \citealp{svh+90} – Fig."675 σα)., 16a).676 This suggests that the activity in SIOG IRS 4 maybe wind-driven. with no need to invoke the presence of magnetically confined plasma.," This suggests that the activity in S106 IRS 4 maybe wind-driven, with no need to invoke the presence of magnetically confined plasma."677 In S106 IRS 4. we would thus be witnessing the onset of X-ray emission from the wind. at a stage in which the protostar is still deeply embedded in the circumstellar material.," In S106 IRS 4, we would thus be witnessing the onset of X-ray emission from the wind, at a stage in which the protostar is still deeply embedded in the circumstellar material."678 Among the 7 sources for which we were able to study the X-ray spectra. sources 32. 39 and 60 are intermediate mass stars. with estimated masses of 2.4. 2.7 and 2.9Mos. respectively.," Among the 7 sources for which we were able to study the X-ray spectra, sources 32, 39 and 60 are intermediate mass stars, with estimated masses of 2.4, 2.7 and $2.9\,M_{\sun}$, respectively."679 Were they main sequence they would correspond to À stars. which are. at most. weak X-ray sources (Ly€3x10°?sv. see e.g. Favata&Micela 2003)).," Were they main sequence they would correspond to A stars, which are, at most, weak X-ray sources $L_{\rm X} \la 3\times 10^{27}$, see e.g. \citealp{fm03}) )."680 Given their young age however they could be Herbig Ae/Be stars. which have significant X-ray activity. or even their precursors. since according to theoretical models a two million year old star of 223 Moe will have spectral type K-G. The luminosities (Lx= 2-9x10 s7')) and plasma temperatures (AT~2 keV) of sources 32. 39 and 60 are similar to those typically found for Herbig Ae/Be stars (Preibisch&Zinnecker 1996:; Hamaguchietal. 2002)).," Given their young age however they could be Herbig Ae/Be stars, which have significant X-ray activity, or even their precursors, since according to theoretical models a two million year old star of 2–3 $M_{\sun}$ will have spectral type K–G. The luminosities $L_{\rm X} = 2$ $9 \times 10^{30}$ ) and plasma temperatures $kT \sim 2$ keV) of sources 32, 39 and 60 are similar to those typically found for Herbig Ae/Be stars \citealp{pz96}; \citealp{hky+02}) )."681 While these values are not inconsistent with the X-ray emission being from unseen low-mass counterparts. evidence is gathering that the origin of the emission are the Herbig Ae/Be stars themselves (Preibisch&Zinnecker 1996:: Hamaguchietal. 20031: Giardinoetal. 2004)).," While these values are not inconsistent with the X-ray emission being from unseen low-mass counterparts, evidence is gathering that the origin of the emission are the Herbig Ae/Be stars themselves \citealp{pz96}; \citealp{hky+02}; \citealp{gfm+04}) )."682 Recently Beutheretal.(2002) have reported X-ray emission from four intermediate mass YSOs in the massive star forming region IRAS 1941042336 which have comparable X-ray luminosity (Lx= 10-107 )) and high plasma temperature (AT2 keV).," Recently \cite{bkp+02} have reported X-ray emission from four intermediate mass YSOs in the massive star forming region IRAS 19410+2336 which have comparable X-ray luminosity $L_{\rm X} =68310^{31}$ $10^{32}$ ) and high plasma temperature $kT \ga 2$ keV)."684 The XX-ray observation. combined with the 2MASS data. has allowed the S106 and $106 south clusters to be studied in more detail confirming them as sites of recent star formation. with age comparable to that of the ONC.," The X-ray observation, combined with the 2MASS data, has allowed the S106 and S106 south clusters to be studied in more detail confirming them as sites of recent star formation, with age comparable to that of the ONC."685 In addition. the X- observation has allowed the low-mass YSO population of S106 to be identified. opening the way for the IR study of the individual stars.," In addition, the X-ray observation has allowed the low-mass YSO population of S106 to be identified, opening the way for the IR study of the individual stars."686 The X-ray characteristics of this population appear to be similar to the ones of the (much better characterized) ONC., The X-ray characteristics of this population appear to be similar to the ones of the (much better characterized) ONC.687that reported by Ransom (2003).,that reported by Ransom (2008).688 Owing to the limited amount of telescope time. many clusters Chat host only a single pulsar have not been searched (o the same sensilivily level as (hose of the specifically selected targets. such as 47 Tuc.," Owing to the limited amount of telescope time, many clusters that host only a single pulsar have not been searched to the same sensitivity level as those of the specifically selected targets, such as 47 Tuc."689 Therefore. the selection ellect biases the observed numbers of MSPs in different clusters.," Therefore, the selection effect biases the observed numbers of MSPs in different clusters."690 In order to alleviate this problem. we suggest that the use of the CLEs of the investigated clusters.," In order to alleviate this problem, we suggest that the use of the CLFs of the investigated clusters."691 With the best-fits of the CLFs (see 822). we are able to estimate the number of MSP in these GC's above a given Iuminosity. Uireshold and (aus obtain an unbiased sample.," With the best-fits of the CLFs (see 2), we are able to estimate the number of MSP in these GCs above a given luminosity threshold and thus obtain an unbiased sample."692 Specifically. we (take (he best-fit values of Ny in these GC's (o estimate the numbers of the MSPs in these clusters with their pseudo-Iuminosities above >1 mJy kpc? and examine whether it is related. to dillerent physical quantities of the clusters.," Specifically, we take the best-fit values of $N_{0}$ in these GCs to estimate the numbers of the MSPs in these clusters with their pseudo-luminosities above $>1$ mJy $^{2}$ and examine whether it is related to different physical quantities of the clusters."693 In (his analvsis. the possible correlation between Vy with (wo-body encounter rate P. metallicity |Fe/I]. cluster niass Mc. velocity dispersion σι and escape velocity Cescape at the cluster center are explored.," In this analysis, the possible correlation between $N_{0}$ with two-body encounter rate $\Gamma_{\rm c}$ , metallicity [Fe/H], cluster mass $M_{\rm GC}$ , velocity dispersion $\sigma_{0}$ and escape velocity $v_{\rm escape}$ at the cluster center are explored."694 All these quantities are speculated to have influence on the binary formation and hence the MSP population in a cluster., All these quantities are speculated to have influence on the binary formation and hence the MSP population in a cluster.695 While the (wo-bocly encounter rate D. is related to (he binary population resulting from dynamical interactions. the metallicity [Fe/IH] of a cluster can have a profound influence on the evolution of LAINBs (see Ivanova 2006 ancl the discussion in 844).," While the two-body encounter rate $\Gamma_{\rm c}$ is related to the binary population resulting from dynamical interactions, the metallicity [Fe/H] of a cluster can have a profound influence on the evolution of LMXBs (see Ivanova 2006 and the discussion in 4)."696 On the other hand. if stellar encounters were not (he major channel of the binary formation. one would expect the binary population to be correlated with the cluster mass Mc.," On the other hand, if stellar encounters were not the major channel of the binary formation, one would expect the binary population to be correlated with the cluster mass $M_{\rm GC}$."697" Assuming a constant ratio. Mee can be estimated [rom the absolute visual magnitude M: MoexLO014,"," Assuming a constant mass-to-light ratio, $M_{\rm GC}$ can be estimated from the absolute visual magnitude $M_{V}$: $M_{\rm GC}\propto 10^{-0.4M_{V}}$."698 We have also tested the correlation with ση and (i5 Which may possibly be related to the retention of the neutron stars in a cluster., We have also tested the correlation with $\sigma_{0}$ and $v_{\rm escape}$ which may possibly be related to the retention of the neutron stars in a cluster.699 Without a priori knowledge of the distributions of the tested quantities. a nonparanmetric correlation analvsis is adopted.," Without a priori knowledge of the distributions of the tested quantities, a nonparametric correlation analysis is adopted."700 The computed Spearman rank correlation coellicients between Ny and the various quantities are tabulated in Table 4.., The computed Spearman rank correlation coefficients between $N_{0}$ and the various quantities are tabulated in Table \ref{correl}.701" Among all the tested quantities. the strongest correlation is found between V,, and D."," Among all the tested quantities, the strongest correlation is found between $N_{0}$ and $\Gamma_{\rm c}$ ."702 The corresponding Spearman correlation is 0.78 with a chance correlation probability of 0.0125., The corresponding Spearman correlation is 0.78 with a chance correlation probability of 0.0125.703 The plot of NyΤι is displaved in Fig., The plot of $N_{0}-\Gamma_{\rm c}$ is displayed in Fig.704" 3aa. The correlation between Vy and [Fe/H] with a Spearman correlation=0.72 has also been found to be significant with a chance correlation probability—0.0298. which is plotted in Figure 3bb. By taking the errors of Ay as the weight in the linear regression analvsis. the logarithnic slopes of the VyΕς and ;N,— |[Fe/H] relations are found to be 0.6940.11 and 0.72zc0.11 respectively."," \ref{n_gamma_metal}a a. The correlation between $N_{0}$ and [Fe/H] with a Spearman correlation=0.72 has also been found to be significant with a chance correlation probability=0.0298, which is plotted in Figure \ref{n_gamma_metal}b b. By taking the errors of $N_{0}$ as the weight in the linear regression analysis, the logarithmic slopes of the $N_{0}-\Gamma_{\rm c}$ and $N_{0}-$ [Fe/H] relations are found to be $0.69\pm0.11$ and $0.72\pm0.11$ respectively."705 For the other tested quantities. (here are marginal correlations of No versis. Cescape and oy al a confidence level =80%. though it is not sullicientlysignifica to secure the relations.," For the other tested quantities, there are marginal correlations of $N_{0}$ versus $v_{\rm escape}$ and $\sigma_{0}$ at a confidence level $\gtrsim89\%$, though it is not sufficientlysignificant to secure the relations."706 It is not surprising to note that the rank correlation coefficients are the same forthese (woquantities. as Gnedin et al. (," It is not surprising to note that the rank correlation coefficients are the same forthese twoquantities, as Gnedin et al. ("7072002) have found that the ratio of (op lo oy has a narrow range between ~3— 5.,2002) have found that the ratio of $v_{\rm escape}$ to $\sigma_{0}$ has a narrow range between $\sim3-5$ .708 Among all the testedquantities. the weakest," Among all the testedquantities, the weakest"709insets).,).710" In Baade's Window, our MDF at [Fe/H]>—0.5 is similar to that of Zoccali et ((2008; from spectroscopy of giants) but has more stars at lower metallicities."," In Baade's Window, our MDF at $> -0.5$ is similar to that of Zoccali et (2008; from spectroscopy of giants) but has more stars at lower metallicities."711" The inner fields (Stanek’s Window and SWEEPS) exhibit a distinctly bimodal distribution of color in the V vs. C—I CMDs (Figure 1), while the outer fields (Baade’s Window and OGLE29) exhibit a bimodal distribution in the [m] vs. [t] plane (Figure 2), which is reflected in the inferred MDFs."," The inner fields (Stanek's Window and SWEEPS) exhibit a distinctly bimodal distribution of color in the $V$ vs. $C-I$ CMDs (Figure 1), while the outer fields (Baade's Window and OGLE29) exhibit a bimodal distribution in the $m$ ] vs. $t$ ] plane (Figure 2), which is reflected in the inferred MDFs."712" This is due to the nonlinear relationship between the indices, traditional CMD colors, and chemical composition."," This is due to the nonlinear relationship between the indices, traditional CMD colors, and chemical composition."713" If the position in the [m] vs. [t] plane is taken as an indication of metallicity, the stars at [Fe/H]>0 overwhelmingly lie in the red ridge of the V vs. C-I CMDs, while the stars at prominent[Fe/H]«-1 tend to lie in the weaker blue ridge of these CMDs."," If the position in the $m$ ] vs. $t$ ] plane is taken as an indication of metallicity, the stars at $>0$ overwhelmingly lie in the prominent red ridge of the $V$ vs. $C-I$ CMDs, while the stars at $<-1$ tend to lie in the weaker blue ridge of these CMDs."714" Brown et ((2008) discussed the advantages of the [m] vs. [t] diagram regarding depth effects, but made no mention of binaries."," Brown et (2008) discussed the advantages of the $m$ ] vs. $t$ ] diagram regarding depth effects, but made no mention of binaries."715" In a CMD, depth blurs the photometric distribution along the ordinate, blurring the inferred MDF when comparing to isochrones, but a color-color diagram is insensitive to depth."," In a CMD, depth blurs the photometric distribution along the ordinate, blurring the inferred MDF when comparing to isochrones, but a color-color diagram is insensitive to depth."716" In a CMD, binaries are brighter and redder than the single-star sequence; comparison of binaries to isochrones can thus overestimate their metallicities."," In a CMD, binaries are brighter and redder than the single-star sequence; comparison of binaries to isochrones can thus overestimate their metallicities."717" In our color-color diagram, a companion of either equal or much lower mass will not shift the position of the primary, but a companion that is only somewhat fainter and cooler will artificially shift the implied metallicity lower (i.e., opposite to the CMD effect)."," In our color-color diagram, a companion of either equal or much lower mass will not shift the position of the primary, but a companion that is only somewhat fainter and cooler will artificially shift the implied metallicity lower (i.e., opposite to the CMD effect)."718 This is because the secondary has a larger impact on [t] than [m]., This is because the secondary has a larger impact on $t$ ] than $m$ ].719 The metallicities of any binaries in our field can be underestimated by up to ~0.3 dex., The metallicities of any binaries in our field can be underestimated by up to $\sim$ 0.3 dex.720" From strictly statistical perspective, a Kolmogorov-Smirnov a(KS) test indicates that no pair of these fields has populations drawn from the same distribution; the chance is for the populations in the SWEEPS field and Baade's Window, and «196 for any other pair."," From a strictly statistical perspective, a Kolmogorov-Smirnov (KS) test indicates that no pair of these fields has populations drawn from the same distribution; the chance is for the populations in the SWEEPS field and Baade's Window, and $\ll$ for any other pair."721" The MDFs in the two innermost fields (Stanek's Window and SWEEPS) are similar in appearance, although the metallicity appears to be shifted to slightly lower [Fe/H] in the SWEEPS field."," The MDFs in the two innermost fields (Stanek's Window and SWEEPS) are similar in appearance, although the metallicity appears to be shifted to slightly lower [Fe/H] in the SWEEPS field."722" Progressing outward, Baade's Window and the OGLE29 field each exhibit more stars shifting to lower metallicities, with the MDFs appearing more bimodal than that in the interior fields, due to a stronger presence of relatively metal-poor stars."," Progressing outward, Baade's Window and the OGLE29 field each exhibit more stars shifting to lower metallicities, with the MDFs appearing more bimodal than that in the interior fields, due to a stronger presence of relatively metal-poor stars."723" Taking the relationship between indices and [Fe/H] at face value, the fraction of stars with super-solar metallicities"," Taking the relationship between indices and [Fe/H] at face value, the fraction of stars with super-solar metallicities"724sinilulv. we have another eielt-parameter mocdel for the spectral evolution defined by where (/4.D4) and (/4.D3) are the first and third break points. respectively. between linear seements in the log-Inear plot. ancl oy. 05. 043. aud ὃν are the sequential four slopes.,"Similarly, we have another eight-parameter model for the spectral evolution defined by where $t_1$ $\Gamma_1$ ) and $t_3$ $\Gamma_3$ ) are the first and third break points, respectively, between linear segments in the log-linear plot, and $\delta_1$, $\delta_2$, $\delta_3$, and $\delta_4$ are the sequential four slopes."725" Given these eight [ree parameters. the position ol the second break point is also fixed according to Equation (8)) and can be determined by The best-fitling results (bottom panel in Figure 3.. thick line) ave /4,=12.4d0.1 s. I4,21.4520.01. /4=421.829.2 s. D=1.99d 0.01. 04=O17z 0.01. 05=0.79|—rr dy=—0.4T40.05. and à;=04c0.01 GR?~ 0.93993)."," Given these eight free parameters, the position of the second break point is also fixed according to Equation \ref{eq:phontofit2}) ) and can be determined by The best-fitting results (bottom panel in Figure \ref{fig:restframelc2}, , thick line) are $t_1=13.4\pm0.7$ s, $\Gamma_1=1.45\pm0.01$, $t_3=421.8\pm29.2$ s, $\Gamma_3=1.99\pm0.01$ $\delta_1=0.17\pm0.01$ , $\delta_2=0.79\pm0.01$, $\delta_3=-0.47\pm0.05$, and $\delta_4=0.04\pm0.01$ $\bar{R}^2\sim0.93993$ )."726 Given the best-fitting parameters. we have {ο~131.0 8 and D»~2.23 according to Equations (9)) and (10)).," Given the best-fitting parameters, we have $t_2\sim131.0$ s and $\Gamma_2\sim 2.23$ according to Equations \ref{eq:spet2}) ) and \ref{eq:spegamma2}) )."727 The goodness of fit has been improved for both the lisht curve and the spectral evolution. though the spectral evolution süll appears to be a Little more deviant (han is presumed bv the fitting model.," The goodness of fit has been improved for both the light curve and the spectral evolution, though the spectral evolution still appears to be a little more deviant than is presumed by the fitting model."728 The general agreement of the three break times of the light curve and (hose of the spectral evolution. in spite of the fact that the (wo fittings are made separately. justifies the existence of the extra breaks we have just assumed.," The general agreement of the three break times of the light curve and those of the spectral evolution, in spite of the fact that the two fittings are made separately, justifies the existence of the extra breaks we have just assumed."729" Therefore. the [our-segment fitting model (with eight Iree parameters) is a more realistic interpretation for the underlying"" elobal feature. which. hereby. is composed of an early plateau (x /"") with a mild softening (AP~0.5 on average). a following steep decline (x/. 7°) with a [further severe softening (AT~1.0 on average). a newly emereing shallow decline (x/. ""°) with a slight spectral hardening (AT<0.5 on average). and a following single power-law decline (x/. F4) without spectral variation (D 2) until (he detection limit is reached."," Therefore, the four-segment fitting model (with eight free parameters) is a more realistic interpretation for the underlying global feature, which, hereby, is composed of an early plateau $\propto t^{0}$ ) with a mild softening $\Delta \Gamma \sim 0.5$ on average), a following steep decline $\propto t^{-2.6}$ ) with a further severe softening $\Delta \Gamma \sim 1.0$ on average), a newly emerging shallow decline $\propto t^{-0.9}$ ) with a slight spectral hardening $\Delta \Gamma < 0.5$ on average), and a following single power-law decline $\propto t^{-1.4}$ ) without spectral variation $\Gamma\sim 2$ ) until the detection limit is reached."730 However. as indicated by Figure 3.. (he fow-segment model is not overwhelmingly better than the (wo-segment model. since the steep decline and the shallow decline of most bursts are interlacing with each other and cannot be well defined in both the light curves and spectral evolution.," However, as indicated by Figure \ref{fig:restframelc2}, the four-segment model is not overwhelmingly better than the two-segment model, since the steep decline and the shallow decline of most bursts are interlacing with each other and cannot be well defined in both the light curves and spectral evolution."731For some bursts (e.g...GIRDO050319D). the existence of the shallow decline and the steep decline is debatable.,"For some bursts (e.g.,GRB080319B), the existence of the shallow decline and the steep decline is debatable."732straight line fit to the region between Που the low resolution data set.,straight line fit to the region between for the low resolution data set.733 The most prominent feature in Figs., The most prominent feature in Figs.734 9 and LO is the clip at phase 0.5.," \ref{kfac_long} and \ref{kfac_short}735 is the dip at phase 0.5."736 Phe obvious interpretation for this is that it is an eclipse of the secondary star by. the accretion disc., The obvious interpretation for this is that it is an eclipse of the secondary star by the accretion disc.737 This is a rather remarkable result. since the accretion clises of cquiescent cdiwvarf novae are normally thought to be optically thin.," This is a rather remarkable result, since the accretion discs of quiescent dwarf novae are normally thought to be optically thin."738 However. we are viewing the disc in IP Peg at an unusual angle (nearly edee on). and whilst it may. be that the clises are optically thin when viewed from the pole. the lareeὃν column lengthe to the secondary star at phase 0.5 may be enough to obseure it.," However, we are viewing the disc in IP Peg at an unusual angle (nearly edge on), and whilst it may be that the discs are optically thin when viewed from the pole, the large column length to the secondary star at phase 0.5 may be enough to obscure it."739 Alternatively. it may be that there are some optically thick regions in the disc. which cause the eclipse we see.," Alternatively, it may be that there are some optically thick regions in the disc, which cause the eclipse we see."740 At other phases the lighteurves are broadly. consistent with the clouble-humped ellipsoidal modulation we might expect., At other phases the lightcurves are broadly consistent with the double-humped ellipsoidal modulation we might expect.741 To see just how close they are to this expectation. and prove that the suggestion of an eclipse is at. least plausible. we modelled the cata using the code described in loannou ct al (1999).," To see just how close they are to this expectation, and prove that the suggestion of an eclipse is at least plausible, we modelled the data using the code described in Ioannou et al (1999)."742 Phe model is a stanclard ellipsoidal model with Roche geometry. but importantly for this work. includes the mutual eclipses between the dise and secondary star.," The model is a standard ellipsoidal model with Roche geometry, but importantly for this work, includes the mutual eclipses between the disc and secondary star."743 Here the disc is assumed to be a cold (ice. dark) obscurer., Here the disc is assumed to be a cold (i.e. dark) obscurer.744 We used the parameters derived in Section 7. in addition to a limb darkening cocllicient of 0.4. a gravity darkening exponent of 0.08 and a secondary star (pole) temperature of 3375Ilx.. We performed a grid. search in opening angle and radius to find the best fit to the data.," We used the parameters derived in Section \ref{masses} in addition to a limb darkening coefficient of 0.4, a gravity darkening exponent of 0.08 and a secondary star (pole) temperature of 3375K. We performed a grid search in opening angle and radius to find the best fit to the data."745 In Figs., In Figs.746 9 and LO we plot the best fitting models., \ref{kfac_long} and \ref{kfac_short} we plot the best fitting models.747 This shows that the model can account for the broad. outline of the lishteurves. but there are problems in. detail.," This shows that the model can account for the broad outline of the lightcurves, but there are problems in detail."748 This is rellected by the fact that the best 42 obtained was 6.1 (for the cata of Fig 10)). and that all the datasets requirecl a disc radius equal to the Roche-lobe radius of the primary (the maximum we allowed).," This is reflected by the fact that the best $\chi_{\nu}^2$ obtained was 6.1 (for the data of Fig \ref{kfac_short}) ), and that all the datasets required a disc radius equal to the Roche-lobe radius of the primary (the maximum we allowed)."749 For the lower resolution data of Fig., For the lower resolution data of Fig.750 9 the best fit opening angle was 8°. 4 for the higher resolution.," \ref{kfac_long} the best fit opening angle was $^{\circ}$, $^{\circ}$ for the higher resolution."751 For Fig., For Fig.752 10. the opening angle was , \ref{kfac_short} the opening angle was $^{\circ}$.753Phe models throw into sharp relief how the [lux at ó= is less than that at ὁ=0.25., The models throw into sharp relief how the flux at $\phi=0.75$ is less than that at $\phi=0.25$.754 Furthermore. Fig.," Furthermore, Fig."755 9 shows how this asvnunetry can vary from night to night., \ref{kfac_long} shows how this asymmetry can vary from night to night.756 Similar night-to-night variability was seen in the Z Cha TiO flux deficits by Wade Horne (1988)., Similar night-to-night variability was seen in the Z Cha TiO flux deficits by Wade Horne (1988).757 The asymmetry. and its variability. could be explained by strong irradiation from 10 bright spot. depleting the TiO on the side of the red star facing the bright spot. ie. the side seen at ó=0.75.," The asymmetry, and its variability, could be explained by strong irradiation from the bright spot depleting the TiO on the side of the red star facing the bright spot, i.e. the side seen at $\phi=0.75$."758 Llowever. this would produce a marked. eccentricity in the radial velocity curves deduced from the TiO regions of the spectrum.," However, this would produce a marked eccentricity in the radial velocity curves deduced from the TiO regions of the spectrum."759 As shown in Section 6.. no significant eccentricity is found from any of the LP Peg absorption features.," As shown in Section \ref{circularity}, no significant eccentricity is found from any of the IP Peg absorption features."760 The models suggest that the problem is with the data around phase 0.25., The models suggest that the problem is with the data around phase 0.25.761 Εις means obscuration of the secondary star by the disc is unlikely. given the star's position well clear of the disc at this phase.," This means obscuration of the secondary star by the disc is unlikely, given the star's position well clear of the disc at this phase."762 Thus we suspect the problem [ies with our simple contamination model (a straight line fit)., Thus we suspect the problem lies with our simple contamination model (a straight line fit).763" The spectral variations of the disc with time are probably LDiore ccmpl""Xl", The spectral variations of the disc with time are probably more complex.764 The main conclusions from this work are as follows. (, The main conclusions from this work are as follows. (7651) There is some form of variability which means that racial velocity studies of the infraredNal doublet in LP oo can sometimes return an apparently elliptical orbit.,1) There is some form of variability which means that radial velocity studies of the infrared doublet in IP Peg can sometimes return an apparently elliptical orbit.766 We suspect this is contamination from disc emission. (, We suspect this is contamination from disc emission. (7672) We strongly recommend the use of TiO rather than for future racial velocity studies.,2) We strongly recommend the use of TiO rather than for future radial velocity studies.768 Not only does it avoid he contamination. problem described above. but it gives a actor two eain in signal-to-noise. (," Not only does it avoid the contamination problem described above, but it gives a factor two gain in signal-to-noise. ("769"3) Our TiO study suggests the radial velocity semi-amplitude for the secondary star should. be revised: to Áo=331.9+ 5skm and as à result. the primary and secondary star niasses become AM,=1.05LLL(5:M. and Ab=00:33yeI ΝΕ. respectively.. (","3) Our TiO study suggests the radial velocity semi-amplitude for the secondary star should be revised to $K_{2}=331.3\pm 5.8$ km $^{-1}$, and as a result the primary and secondary star masses become $M_{1}=1.05^{+0.14}_{-0.07}$ $_{\odot}$ and $M_{2}=0.33^{+0.14}_{-0.05}$ $_{\odot}$ respectively. ("7704) Despite this downwards revision of the secondary μαar mass. it is still over-massive for its observed spectral vpe. but now agrees with the current semi-enipirical and Yeoretical mass-ractius-pertocd relationships. (,"4) Despite this downwards revision of the secondary star mass, it is still over-massive for its observed spectral type, but now agrees with the current semi-empirical and theoretical mass-radius-period relationships. ("7715) The aceretion disc eclipses the secondary. star in uiescence. implving that. when viewed at high inclination. -- is optically thick.,"5) The accretion disc eclipses the secondary star in quiescence, implying that, when viewed at high inclination, it is optically thick."772 The INT and. JAP is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias., The INT and JKT is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias.773 Data reduction was carried out on the Ixecle Starlink node using the software., Data reduction was carried out on the Keele Starlink node using the software.774 Data on the outburst state of LP Peg was ecnerously provided. by the AAWSO International Database and we gratefully acknowledge with thanks all the variable star observers worldwide who participate in this program., Data on the outburst state of IP Peg was generously provided by the AAVSO International Database and we gratefully acknowledge with thanks all the variable star observers worldwide who participate in this program.775 We also thank Sandi C'atalánn. Janet Wood and Rob Jeffries for useful discussions.," We also thank Sandi Catalánn, Janet Wood and Rob Jeffries for useful discussions."776where AT is the active period of quasar. my is the uuuber density of star cluster at 1 pe in the range of about 10 /pe? (Blandford 1991). oy is the dispersion velocity of star in the cluster. and Cy~6.,"where $\Delta T$ is the active period of quasar, $\nu_0$ is the number density of star cluster at 1 pc in the range of about $10^7$ $^3$ (Blandford 1991), $\sigma_0$ is the dispersion velocity of star in the cluster, and $C_d\approx 6$."777 Iuteeratiug over the disk. there are ~107 iain sequence stars captured by disk in the active phase of quasar or the captured rate is~LOCyr+.," Integrating over the disk, there are $\sim 10^5$ main sequence stars captured by disk in the active phase of quasar or the captured rate is $\sim 10^{-3} yr^{-1}$."778 The captured stars will coorotate with the medi in the disk (Sver et al 1991). and accrete gas from the disk with Bondi rate uutil a gap appears in disk with condition that the stars Roche radius exceeds the disk scale-heieht  (Liu Papaloizou. 1996).," The captured stars will coorotate with the medium in the disk (Syer et al 1991), and accrete gas from the disk with Bondi rate until a gap appears in disk with condition that the star's Roche radius exceeds the disk scale-height $h$ (Lin Papaloizou, 1996)."779 The timescale of Boudi accretion is and the πιαται accreted mass of the captured star is lanited by ⊺∐↕↴∖↴↸⊳∪⋯∐↑↕∪∐↕↴∖↴⋜↧↕↴∖↴∪↸⊳∪↕↕∐⊳↕≼∐∖≼↧↖↖⇁↕↑∐↑∐⋜↧↑↑∐↸∖↕≧∪∐≼∐ ↥⋅⋜↧≼∐∏↴∖↴≺∣⋮⊔∶∊≓∣∣⊔↙⋅⋅∖−⋟⋟≼↧∪↸∖↴∖↴∐∪↑↸∖⊼∩∖↸∖≼↧↑∐↸∖↕∪↸⊳⋜↧↕↕∐∖↕∶↴⋁∐↑ h., The timescale of Bondi accretion is and the maxium accreted mass of the captured star is limited by This condition is also coincided with that the Bondi radius $r_{\rm B}=Gm_*/c_{\rm s}^2$ ) does not exceed the local height $h$.780 With the typical parameters of the quasars aud a = l. the maxima acereted mass of the captured stars is iu the range of 10 ~ 20 AL. (but the maxima mass of the captured stars could be πιο higher than 20 M. if a is much less than unity).," With the typical parameters of the quasars and $\alpha$ = 1, the maximum accreted mass of the captured stars is in the range of 10 $\sim$ 20 $M_{\odot}$ (but the maximum mass of the captured stars could be much higher than 20 $M_{\odot}$ if $\alpha$ is much less than unity)."781 The star in this mass range will evolve off their main sequence quickly auc likely. become ueutron stars plus small fraction of black holes (see e.g. Shapiro Teukolsky 1983)., The star in this mass range will evolve off their main sequence quickly and likely become neutron stars plus small fraction of black holes (see e.g. Shapiro Teukolsky 1983).782 For more massive stars (1127 20 M.) they could become neutron stars or black holes (Tinumes. Woosley Weaver 1996).," For more massive stars (m $\ge$ 20 $M_{\odot}$ ) they could become neutron stars or black holes (Timmes, Woosley Weaver 1996)."783" The simple foriuula of the evolution time scale for the main sequence star is (Mours vau den Ieuvel 1989) where the iudex a, aud e» are tabulated in their table 3.", The simple formula of the evolution time scale for the main sequence star is (Meurs van den Heuvel 1989) where the index $a_1$ and $a_2$ are tabulated in their table 3.784" For interested cases. we have a,=9.3. a2=2 for BSxoanjM.<12. and ay= 8.2.2Ξ1 for star larecr than L2A/..."," For interested cases, we have $a_1=9.3$, $a_2=-2$ for $3.8\le m/M_{\odot}\le 12$, and $a_1=8.2$, $a_2=-1$ for star larger than $12M_{\odot}$."785 Substituting parameters for lower mass case iuto Eq.9. we obtain: The higher mass case will evolve faster than that eiveu in Eq.(10).," Substituting parameters for lower mass case into Eq.9, we obtain: The higher mass case will evolve faster than that given in Eq.(10)."786 It has been estimated that the maim sequence stars start to be captured by the disk at the disk radius l pe CArtviuowicz. Lin Wampler 1993) but the exact value of this radius is not crucial in our model.," It has been estimated that the main sequence stars start to be captured by the disk at the disk radius $\sim$ 1 pc (Artymowicz, Lin Wampler 1993) but the exact value of this radius is not crucial in our model."787" The more iuportant radius A, is before which the captured stars finish the evolution of supernova stage.", The more important radius $R_c$ is before which the captured stars finish the evolution of supernova stage.788 This radius must be larger than that of the tidal radius Rp = (A)r otherwise the captured stars will disrupted by the ceutral massive black hole.," This radius must be larger than that of the tidal radius $R_{\rm t}$ = $\left(\frac{M_{\rm BH}}{m_*}\right)^{1/3}r_*$, otherwise the captured stars will disrupted by the central massive black hole."789 This radius can be estimated by equating the radial inward driftingo time scale Eq.(5) aud the evolutiou time scale Eq.(11) aud is giveu by It appears that this radius is always larger than that of RS for typical quasar parameters., This radius can be estimated by equating the radial inward drifting time scale Eq.(5) and the evolution time scale Eq.(11) and is given by It appears that this radius is always larger than that of $R_t$ for typical quasar parameters.790" Iu the carly stage. almost all of the captured stars can evolve to neutron stars/black holes with mass i, which will be ejected from the disk after superuova explosion."," In the early stage, almost all of the captured stars can evolve to neutron stars/black holes with mass $\mns$ which will be ejected from the disk after supernova explosion."791 But these neutron stars/black holes can only shoot up to a scale height where ος~ 300 kun/s is the neutron star kick velocity produced by supernova explosion., But these neutron stars/black holes can only shoot up to a scale height where $v_{\infty}\sim$ 300 km/s is the neutron star kick velocity produced by supernova explosion.792 Taking the typical paralcters. ὃς 101 cn.," Taking the typical parameters, $h_{\rm ns}\sim$ $10^{16}$ cm."793 The compact stars will be oscillating up aud down crossing the disk., The compact stars will be oscillating up and down crossing the disk.794 Artvinowicz. Liu Winpler (1993) also note the possibility of retrapping of compact stars bv disk. but the following case is more interesting.," Artymowicz, Lin Wampler (1993) also note the possibility of retrapping of compact stars by disk, but the following case is more interesting."795 Before evolving to compact star. the captured star will go through the red giant phase with radius (Rees) and mass Age;," Before evolving to compact star, the captured star will go through the red giant phase with radius $\rrg$ ) and mass $\mrg$."796 During the close encounter with a neutron star. the red eiat star would undergo substantial tidal deformation at the cost of a part of the relative kinetic energv of the orbit.," During the close encounter with a neutron star, the red giant star would undergo substantial tidal deformation at the cost of a part of the relative kinetic energy of the orbit."797 Such a tidal process can eventually dissipate the total positive euergv of the initial unbound orbit via oscillatious aud heating. aud a (NS/DII. RC) binary system will be created.," Such a tidal process can eventually dissipate the total positive energy of the initial unbound orbit via oscillations and heating, and a (NS/BH, RG) binary system will be created."798 One aight arene that the velocity dispersion of NS/BIT is much larger than the escape velocity of RG at its surface (about τοπικ)., One might argue that the velocity dispersion of NS/BH is much larger than the escape velocity of RG at its surface (about 70km/s).799" However, it is interesting to note the following situation."," However, it is interesting to note the following situation."800 The surface deusity of RO “peroMp:Ree:~QU fen? isch larecr than that of disk ~10? g/cem? at Ope., The surface density of RG $\Sigma_{\rm RG}\sim M_{\rm RG}/R_{\rm RG}^2\sim 10^7$ $^2$ is much larger than that of disk $\sim 10^3$ $^2$ at 0.1pc.801 This leads to an effiieut dissipation of NS/BIT kinetic energy in the process of encountering RCs envelope., This leads to an efficient dissipation of NS/BH kinetic energy in the process of encountering RG's envelope.802 The probability of NS/BIT encountering the dense envelope of RC can be casily estimated where Spe: is the total surface area of all RC. aud Sak is the area of disk capturing main sequence star.," The probability of NS/BH encountering the dense envelope of RG can be easily estimated where $S_{\rm RG}$ is the total surface area of all RG, and $S_{\rm disk}$ is the area of disk capturing main sequence star."803 The drag force acting on NS/DII by the dense envelope of RG reads CArtviuowicz ct al 1993) After N times of encountering the disk. the kinetic enerev of NS/BIT will be reduced significantly so that NS/BIT can be captured by RC through tidal process. and the capture time scale of NS/BIT bv the RG envelope is about," The drag force acting on NS/BH by the dense envelope of RG reads (Artymowicz et al 1993) After $N$ times of encountering the disk, the kinetic energy of NS/BH will be reduced significantly so that NS/BH can be captured by RG through tidal process, and the capture time scale of NS/BH by the RG envelope is about"804spectrum of(6 objects).,spectrum (6 objects).805 We indicate in the last column of Table l which these additional criteria were applied. for each object. 7, We indicate in the last column of Table 1 which of these additional criteria were applied for each object. “806"187. 7OD and “PI” mean “Interacting System? ""Other Data and. 7Perturbed. Ixinematies"" respectively.","IS”, “OD” and “PK” mean ""Interacting System"", “Other Data” and “Perturbed Kinematics” respectively."807 A in that column means that no additional criteria were applied. apart from the three mentioned above. which were common to all objects.," A “–” in that column means that no additional criteria were applied, apart from the three mentioned above, which were common to all objects."808 The selection. criteria applied. by other authors in their programmes are unknown., The selection criteria applied by other authors in their programmes are unknown.809 Therefore. our sample is likely to be allected by dilferent biases and the results obtained with our work cannot be extrapolated to the general population of optically selected tvpe 2 quasars.," Therefore, our sample is likely to be affected by different biases and the results obtained with our work cannot be extrapolated to the general population of optically selected type 2 quasars."810 The observing progranume consisted of obtaining for each object a continuum|emission line image followed by long slit spectroscopy., The observing programme consisted of obtaining for each object a continuum+emission line image followed by long slit spectroscopy.811 Besides the interest of their scientific content. the goal of obtaining these images was to identify extended ionized nebulae and/or other interesting &ascous features such as tidal tails. compact knots. ete which helped to decide how to place the spectroscopic slit.," Besides the interest of their scientific content, the goal of obtaining these images was to identify extended ionized nebulae and/or other interesting gaseous features such as tidal tails, compact knots, etc which helped to decide how to place the spectroscopic slit."812" Unfortunately, due to technical problems at. the observatory such deep. continuum|emission. line images could. only be obtained during the 2008 run (Le. for 4 objects) and shallow continuumimages are available for the 2009 run(9 informationonlyobjects)."," Unfortunately, due to technical problems at the observatory such deep continuum+emission line images could only be obtained during the 2008 run (i.e. for 4 objects) and only shallow continuum images are available for the 2009 run (9 objects)."813about As à consequence. we did not have prior the possible existence of extended diffuse emission line structures ancl their morphology for most objects observed during this run.," As a consequence, we did not have prior information about the possible existence of extended diffuse emission line structures and their morphology for most objects observed during this run."814 The continuum images were not deep enough in general either to. look for interesting features such as tidal tails. bridges. ete.," The continuum images were not deep enough in general either to look for interesting features such as tidal tails, bridges, etc."815 So. the spectroscopic slit had to be placed blindly or through continuum sources near the quasar in the image. with the goal of checking their z.," So, the spectroscopic slit had to be placed blindly or through continuum sources near the quasar in the image, with the goal of checking their $z$."816 All spectra were obtained with the 60010|19 grism and the G@G435 order sorting filter., All spectra were obtained with the 600RI+19 grism and the GG435+81 order sorting filter.817 Phe useful spectral range was c95030-8XReEM50 iin the 200 run and 75300-8600 iin the 2009( run. so that in all cases atleast the LL? and OLL]AA4959.50t)7 lines were within the observed. spectral range.," The useful spectral range was $\sim$ 5030-8250 in the 2008 run and $\sim$ 5300-8600 in the 2009 run, so that in all cases atleast the $\beta$ and $\lambda\lambda$ 4959,5007 lines were within the observed spectral range."818 The imaging and spectroscopic data reduction orocess is described in. inet al. (2010)), The imaging and spectroscopic data reduction process is described in n et al. \citeyear{vil10}) ).819" The pixel scales are 0.25"" 1 and 0.83 qain the spatial. and spectral directions. respectively.", The pixel scales are $\arcsec$ $^{-1}$ and 0.83 $^{-1}$ in the spatial and spectral directions respectively.820. The spectral resolution. as measured from the sky emission ines. was 7.20.2 aand 5.40.2 or the 2008 ancl 2009 runs respectively.," The spectral resolution, as measured from the sky emission lines, was $\pm$ 0.2 and $\pm$ 0.2 for the 2008 and 2009 runs respectively."821" The slit width was 1.3"" in 2008 and. 1.0"" in 2009.", The slit width was $\arcsec$ in 2008 and $\arcsec$ in 2009.822 The log of the observations is shown in Table 1., The log of the observations is shown in Table 1.823 The seeing size was measured for each object using several stars in the image., The seeing size was measured for each object using several stars in the image.824" Comparison of several spectrophotomoetric standard stars taken with a 5"" slit during the run gave a Dux calibration accuracy of over the entire spectral range.", Comparison of several spectrophotometric standard stars taken with a $\arcsec$ slit during the run gave a flux calibration accuracy of over the entire spectral range.825 Using the spectra of several standard stars. geometric distortion was found to be <2 pixels (0.57) across the entire spectral range in all cases. with different values for cillerent stars.," Using the spectra of several standard stars, geometric distortion was found to be $<$ 2 pixels $\arcsec$ ) across the entire spectral range in all cases, with different values for different stars."826 In order to correct. for this effect. for cach quasar. observations ofa bright star with a similar telescope position would be required.," In order to correct for this effect for each quasar, observations of a bright star with a similar telescope position would be required."827 Since these are not available and. given the small magnitude of the distortion. we decided. not to apply any correction (the quasar continuum cannot be used [or this purpose. because the continuum spatial centroid at cdilferent wavelengths can change lor various reasons such as reddening).," Since these are not available and given the small magnitude of the distortion, we decided not to apply any correction (the quasar continuum cannot be used for this purpose, because the continuum spatial centroid at different wavelengths can change for various reasons such as reddening)."828We were careful when extracting the spectra from clilferent apertures for a given object to make sure that such distortion did not have any negativo impact on the analysis., We were careful when extracting the spectra from different apertures for a given object to make sure that such distortion did not have any negative impact on the analysis.829 To perform the spectroscopic analysis. the line profiles were fitted with Gaussian. functions (one or more. depending on the quality of the fit).," To perform the spectroscopic analysis, the line profiles were fitted with Gaussian functions (one or more, depending on the quality of the fit)."830 The FWLAL values were corrected for instrumental broadening in. quadrature WLAI=7.2+0.2 or 5440.2 ddepending on the observing run)., The FWHM values were corrected for instrumental broadening in quadrature $\pm$ 0.2 or $\pm$ 0.2 depending on the observing run).831" Slit cllects could be present specially during the 2¢v run. since polnt sources cid not fill the slit (seeing EWILM=0.654£0.05"" vs; 1.37 slit)."," Slit effects could be present specially during the 2008 run, since point sources did not fill the slit (seeing $\pm$ $\arcsec$ vs. $\arcsec$ slit)."832 We do not expect1 this to allect m conclusions 1presented in this paper., We do not expect this to affect the conclusions presented in this paper.833 The results of the imaging and spectroscopic analysis are presented in this section., The results of the imaging and spectroscopic analysis are presented in this section.834 Several considerations must be taken into account., Several considerations must be taken into account.835 One of the studies we perform. here is the characterization of the gas ionization properties with the goal of exploring the nature of the excitation mechanism at different spatial locations for cach quasar (stellar vs. GN photoionization. i.c. ionization bv the continuum emitted by the quasar).," One of the studies we perform here is the characterization of the gas ionization properties with the goal of exploring the nature of the excitation mechanism at different spatial locations for each quasar (stellar vs. AGN photoionization, i.e., ionization by the continuum emitted by the quasar)."836 The diagnostic diagram. OLLIA5007 /LE2 vs. OLL|A312 7/1147 is used for this purpose., The diagnostic diagram $\lambda$ $\beta$ vs. $\lambda$ $\beta$ is used for this purpose.837 We chose this diagram. because it involves the strongest. Lines detected in the spectra of most spatial locations under consideration and because they provide useful information about the presence of both ACIN and/or stellar photoionization., We chose this diagram because it involves the strongest lines detected in the spectra of most spatial locations under consideration and because they provide useful information about the presence of both AGN and/or stellar photoionization.838 Diagnostic diagrams will be shown only. for objects with OL] within the observed spectral range and with detected: extended: emission. line structures., Diagnostic diagrams will be shown only for objects with [OII] within the observed spectral range and with detected extended emission line structures.839 The data will be compared. with predictions from the standard. photoionization model sequence (Robinson ct al. 19873) , The data will be compared with predictions from the standard photoionization model sequence (Robinson et al. \citeyear{rob87}) )840often applied to low ancl high redshift type 2 active ealaxies (see inet al. 2008..," often applied to low and high redshift type 2 active galaxies (see n et al. \citeyear{vil08},"841 2010. for à discussion about its application to tvpe 2 quasars)., \citeyear{vil10} for a discussion about its application to type 2 quasars).842 The models assume solar metallicity. eas density. 100 and. power-law index a -—-1.5.," The models assume solar metallicity, gas density $n$ =100 $^{-3}$ and power-law index $\alpha$ =-1.5."843 lteddening is ignored., Reddening is ignored.844 Phe ionization parameter. (C varies along the (models with log(()2 -3. -2 and -l are marked in cach diagram).," The ionization parameter $U$ varies along the (models with $U$ )= -3, -2 and -1 are marked in each diagram)."845 Phe assumption of this n value is supported. by measurements of EEL]. densities associated with tvpe 1 man in the range d tons to several hundred em.) (eg. Fu Stockton 2008))., The assumption of this $n$ value is supported by measurements of EELR densities associated with type 1 quasars in the range $\sim$ several tens to several hundred $^{-3}$ (e.g. Fu Stockton \citeyear{fu08}) ).846" The existence of densities as high as 10""  in theNarrow Line Region (NLR) are not discarded. but the large strength of the OL]JA3 line. which has a critical density of M32 10° . suggests that the line Duxes have à very high contribution of much lower density gas."," The existence of densities as high as $^6$ $^{-3}$ in the Narrow Line Region (NLR) are not discarded, but the large strength of the $\lambda$3727 line, which has a critical density of $\sim$ $\times$ $^3$ $^{-3}$ , suggests that the line fluxes have a very high contribution of much lower density gas."847 In addition. varving the eas density between. several eni.| and. «3000 em.? is equivalent to varving the the ionization parameter C. which is accounted for in the models.," In addition, varying the gas density between several $^{-3}$ and $<$ 3000 $^{-3}$ is equivalent to varying the the ionization parameter $U$ , which is accounted for in the models."848Wallenquist (L975) studied non-uniform extinction in open clusters using star counts [rom the Palomar Sky Survey.,Wallenquist (1975) studied non-uniform extinction in open clusters using star counts from the Palomar Sky Survey.849 The underlying assumption in this type of investigation is that the observed deficieney of stars is mainly due to the presence of absorbing matter between the observer and. the cluster., The underlying assumption in this type of investigation is that the observed deficiency of stars is mainly due to the presence of absorbing matter between the observer and the cluster.850 Sagar (1987) studied. interstellar extinction. in. 15 open clusters using UBY photoolectric photometric observations of proper motion cluster members. and. found that. ten of rem. show non-uniform extinction across the cluster region.," Sagar (1987) studied interstellar extinction in 15 open clusters using UBV photoelectric photometric observations of proper motion cluster members, and found that ten of them show non-uniform extinction across the cluster region."851" Reddish (1967) has shown that redcdening increases with stellar luminosity in all clusters ancl associations with ages <107 vears. but only in some objects with ages between LO’ and 2«10"" vears. and such relations are not observed in the clusters older than 2«10"" vears."," Reddish (1967) has shown that reddening increases with stellar luminosity in all clusters and associations with ages $\leq10^{5}$ years, but only in some objects with ages between $10^{5}$ and $2\times10{^6}$ years, and such relations are not observed in the clusters older than $2\times10{^6}$ years."852 Bohannan (1975) re-examüned the voung clusters. data of. Hecddish (1967) and after identifving foreground stars and. applying correct intrinsic colour indices for bright supergiants found no correlation of reddening with luminosity., Bohannan (1975) re-examined the young clusters data of Reddish (1967) and after identifying foreground stars and applying correct intrinsic colour indices for bright supergiants found no correlation of reddening with luminosity.853 Sagar (LOST) observed that in some voung clusters the variation of colour excess ECD1) correlated with Luminosity. in the sense hat brighter cluster members were more highly. reddened.," Sagar (1987) observed that in some young clusters the variation of colour excess $E(B-V)$ correlated with luminosity, in the sense that brighter cluster members were more highly reddened."854 Most of the above analyses were based on UDV clata aken primarily with either photographie plates or single-channel photometers., Most of the above analyses were based on UBV data taken primarily with either photographic plates or single-channel photometers.855 Current optical ancl infrared imaging echnology allows us to derive more accurate photometry. as he elleets of nebular surface brightness which are generally esent in voung clusters can be properly removed.," Current optical and infrared imaging technology allows us to derive more accurate photometry, as the effects of nebular surface brightness which are generally present in young clusters can be properly removed."856 RecentA such observations have become available in the literature.," Recently, such observations have become available in the literature."857 We have therefore used. them to study the non-uniform extinction as well as its nature in 14 voung open clusters., We have therefore used them to study the non-uniform extinction as well as its nature in 14 young open clusters.858 Section 2 describes the selection of the sample., Section 2 describes the selection of the sample.859 In Section 3 the details of the reddening determinations are given. while the results derived from the present analysis and their discussions are given in the remaining part of the paper.," In Section 3 the details of the reddening determinations are given, while the results derived from the present analysis and their discussions are given in the remaining part of the paper."860 This section provides information about the criteria adopted for selection of clusters and their members along with information about observational clata., This section provides information about the criteria adopted for selection of clusters and their members along with information about observational data.861 The observations used in this study are taken from the compilation database on star clusters by Mermilliod (1995) at web site//obswww., The observations used in this study are taken from the compilation database on star clusters by Mermilliod (1995) at web site.862unige.ch/webda/. We have selected those 1H voung (age « 20 Myr) open clusters which have JLUs data for at least 10 cluster members., We have selected those 14 young (age $<$ 20 Myr) open clusters which have JHK data for at least 10 cluster members.863 The general information about them are listed in Table 1., The general information about them are listed in Table 1.864 The distances of the sample clusters range from 0.8 to 3.9 kpe., The distances of the sample clusters range from 0.8 to 3.9 kpc.865 They ave distributed non-uniformly along the galactic plane with longitude ranging from about 15 to 290 deg., They are distributed non-uniformly along the galactic plane with longitude ranging from about 15 to 290 deg.866 The cluster size ranges from  1 to 10 pc with an average radius of  4.5 pe. while the galacto-centric distance ranges [rom  6 to 12 kpe.," The cluster size ranges from $\sim$ 1 to 10 pc with an average radius of $\sim$ 4.5 pc, while the galacto-centric distance ranges from $\sim$ 6 to 12 kpc."867 Eight clusters of the sample have UBVJILUN cata while remaining six have UBYRIL cata., Eight clusters of the sample have UBVJHK data while remaining six have UBVRIJHK data.868 In those cases in which the RL photometry was reported in the Ixron-C'ousin system. the colours ave converted to Johnson's VIU svstem using the relations given by Bessell (1979).," In those cases in which the RI photometry was reported in the Kron-Cousin system, the colours are converted to Johnson's VRI system using the relations given by Bessell (1979)."869 We have used homogeneous and accurate cata if they are available from more than one sources., We have used homogeneous and accurate data if they are available from more than one sources.870 The observations used in this present. analysis are mostly. based. on modern optical ancl infrared. imaging except for NGC 1502. Tr 15 and Tr 37.," The observations used in this present analysis are mostly based on modern optical and infrared imaging except for NGC 1502, Tr 15 and Tr 37."871 Fhey have accuracies generally better than 0.02 mag in V. ND). H0) and D) and 0.03 mag in (UB).," They have accuracies generally better than 0.02 mag in V, $-$ V), $-$ R) and $-$ I) and 0.03 mag in $-$ B)."872 The accuracy o£ 111 data are generally ~ 0.07 mag., The accuracy of JHK data are generally $\sim$ 0.07 mag.873 The spectroscopic data wherever available are also taken., The spectroscopic data wherever available are also taken.874 Phe accuracy of MIS. classification is generally better than two subclasses in spectral type and a class in luminosity., The accuracy of MK classification is generally better than two subclasses in spectral type and a class in luminosity.875 Selection of cluster menibers is important for the study. of interstellar extinction across the cluster region., Selection of cluster members is important for the study of interstellar extinction across the cluster region.876 Among the most Commonly used methods. the one based on kinematical data (proper motion and radial velocity) is considered. the most reliable.," Among the most commonly used methods, the one based on kinematical data (proper motion and radial velocity) is considered the most reliable."877 As reliable proper motion data are available for δ of the 14 clusters uncer study. we use them to select. cluster members.," As reliable proper motion data are available for 8 of the 14 clusters under study, we use them to select cluster members."878 Phe histograms of the membership probability (P) of all the investigated stars in clusters NGC S60. NGC δε Tr 14. Pr 16 and Tr 37 are shown in Fig.," The histograms of the membership probability (P) of all the investigated stars in clusters NGC 869, NGC 884, Tr 14, Tr 16 and Tr 37 are shown in Fig."879 1., 1.880 For NGC 2244. NGC 2264 and NGC 6611 such clagrams are available in the sources listed in Table 1.," For NGC 2244, NGC 2264 and NGC 6611 such diagrams are available in the sources listed in Table 1."881 “Phe histograms of D distribution indicate that in a cluster. stars are generally," The histograms of P distribution indicate that in a cluster, stars are generally"882If the companion is of low mass (brown dwarf or planet). it enters the AGB star and spirals in toward the core. where il is eravitationallv shredded to form a disk that max blow jets through (the envelope (Soker1996:Reves-Ituiz&López2006).,"If the companion is of low mass (brown dwarf or planet), it enters the AGB star and spirals in toward the core, where it is gravitationally shredded to form a disk that may blow jets through the envelope \citep{sok96,rey98,nor06}."883. A very low mass secondary has insullicient energy to eject much of the AGB envelope during the spiral-in process. so it does not naturally lead to Che formation of a massive torus.," A very low mass secondary has insufficient energy to eject much of the AGB envelope during the spiral-in process, so it does not naturally lead to the formation of a massive torus."884 llowever. (he primary may go on to later eject the envelope. possibly with an equatorial enhancement.," However, the primary may go on to later eject the envelope, possibly with an equatorial enhancement."885 In (this scenario. (here is no particular co-ordination of jets and torus. and il vields a sequence of jets followed by a torus. which is opposite to that observed in all the objects discussed here.," In this scenario, there is no particular co-ordination of jets and torus, and it yields a sequence of jets followed by a torus, which is opposite to that observed in all the objects discussed here."886 This scenario can be rejected., This scenario can be rejected.887 Ina variant of this scenario (Nordhaus&Blackman2006).. the mass of the secondary max be enough to ejeet part of the AGB envelope in a torus before the companion is shredded to Form a disk.," In a variant of this scenario \citep{nor06}, the mass of the secondary may be enough to eject part of the AGB envelope in a torus before the companion is shredded to form a disk."888 This leads to a torus-jet sequence. as observed.," This leads to a torus-jet sequence, as observed."889 The (ime sequence is likely to be short because the spiral-in and break-up times are rapid. but a viscous jet-lag of the form given by equation (2) may be relevant. if (he viscosity. parameter is low enough to compensate for a small disk radius.," The time sequence is likely to be short because the spiral-in and break-up times are rapid, but a viscous jet-lag of the form given by equation (2) may be relevant, if the viscosity parameter is low enough to compensate for a small disk radius."890 An allernalive scenario with an accretion disk around the primary occurs when the secondary is a main sequence star of mass Z0.1 M...," An alternative scenario with an accretion disk around the primary occurs when the secondary is a main sequence star of mass $\ga8910.1$ $_{\odot}$."892 In this case. the envelope of the AGB star is ejected in the common envelope phase as a torus: the spiral-in process of the secondary comes to halt. but it may subsequently undergo Roche lobe overflow to lorm a disk around the primary (Soker&Livio1994).," In this case, the envelope of the AGB star is ejected in the common envelope phase as a torus; the spiral-in process of the secondary comes to halt, but it may subsequently undergo Roche lobe overflow to form a disk around the primary \citep{sok94}."893. This produces a clear torus-]et sequence as observed., This produces a clear torus-jet sequence as observed.894 However. there are two problems with this scenario.," However, there are two problems with this scenario."895" First. the timescale between (he torus ejection and (he disk-jet formation is governed by the thermal response lime of the secondary, which is 107 10! vr (Soker&Livio1994)."," First, the timescale between the torus ejection and the disk-jet formation is governed by the thermal response time of the secondary, which is $^3$ $^4$ yr \citep{sok94}."896. This is somewhat too long compared with the (vpical jet-lag sequence that we find from the observations., This is somewhat too long compared with the typical jet-lag sequence that we find from the observations.897 The second. problem is that the jets in this scenario are produced after the common envelope phase., The second problem is that the jets in this scenario are produced after the common envelope phase.898 It. seenis unlikely (hat the coolest objects (hat we consider (which have already. lormed jets) are post common-envelope: this mav also apply (o all the objects in the sample given the ages of (heir jets ancl (heir likely evolution (mes across the II-R. diagram., It seems unlikely that the coolest objects that we consider (which have already formed jets) are post common-envelope; this may also apply to all the objects in the sample given the ages of their jets and their likely evolution times across the H-R diagram.899 Except for the ejection plus break-up case noted above. (hese primary disk scenarios are not well matched to the observations.," Except for the ejection plus break-up case noted above, these primary disk scenarios are not well matched to the observations."900 It is interesting to note that. Mitchelletal.(2006) have recently reported on the kinematies of the PN Abell 63. which has a close binary central star and must have gone through a common envelope phase.," It is interesting to note that \cite{mit06} have recently reported on the kinematics of the PN Abell 63, which has a close binary central star and must have gone through a common envelope phase."901 Mitchellοἱal.(2000) fined that the lobes (jets) in Abell 63 are older than the nebular rim which forms the inner edge of a evlindrical torus.," \cite{mit06}902 find that the lobes (jets) in Abell 63 are older than the nebular rim which forms the inner edge of a cylindrical torus."903 Thev conclude that this is consistent with jets formed after a common envelope (Iron a disk around the primary core) but before formation of the main nebula., They conclude that this is consistent with jets formed after a common envelope (from a disk around the primary core) but before formation of the main nebula.904 As remarked above. the," As remarked above, the"905racial distance dr (H3; for specilic parcel of gas is replaced by the general radial coordinate r) I am interested in regions [ar [rom the star rZ9Ry. such that (1−fs)~1. and I will omit this term.,"radial distance $d r$ $R_M$ for specific parcel of gas is replaced by the general radial coordinate $r$ ) I am interested in regions far from the star $r \gg R_0$, such that $\left( 1- \frac {R_0}{R_m} \right)^{-(1+k_v)/2} \simeq 1$, and I will omit this term."906" This gives that dM,/drxr|? and the average (over the shell) densitv p.(r)x5j2", This gives that ${d M_e}/{dr} \propto r^{-1/2}$ and the average (over the shell) density $\rho_e (r) \propto r^{-5/2}$.907 The mass of the wind in the same spherical shell is The ratio of the bound mass to the wind (escaping) mass in each spherical shell is equal io the density ratio We can summarize (his section as follows., The mass of the wind in the same spherical shell is The ratio of the bound mass to the wind (escaping) mass in each spherical shell is equal to the density ratio We can summarize this section as follows.908 The fundamental assumption of the model is (hat mass is ejected at velocitiesbelow (he escape speed from a radius JylewxHR; and that no other forces act on the gas beside gravity alter ejection.," The fundamental assumption of the model is that mass is ejected at velocitiesbelow the escape speed from a radius $R_0 \simeq {\rm few} \times R_\ast$, and that no other forces act on the gas beside gravity after ejection."909" The main result of the phenomenological model is the finding that an extended circumstellar zone with an average (over a shell) density profile of p,(r)2(0/2).>? is formed.", The main result of the phenomenological model is the finding that an extended circumstellar zone with an average (over a shell) density profile of $\rho_e(r) \simeq (r/R_0)^{-5/2}$ is formed.910 The gas in this extended zone is rising and falling. but most of the time it is at a verv slow motion.," The gas in this extended zone is rising and falling, but most of the time it is at a very slow motion."911 I term this zone the effervescence zone., I term this zone the effervescence zone.912 The ratio of the bound gas mass per racial distance to that of the wind is given by equation (13))., The ratio of the bound gas mass per radial distance to that of the wind is given by equation \ref{eta1}) ).913 In general the second equality is not accurate because close to Ry the term (1−RivRy) is not negligible., In general the second equality is not accurate because close to $R_0$ the term $\left( 1- \frac {R_0}{R_m} \right)^{-(1+k_v)/2}$ is not negligible.914" H is accurate only for |,=—1: this implies that more bound mass is ejected al high velocities.", It is accurate only for $k_v = -1$; this implies that more bound mass is ejected at high velocities.915" Nonetheless. I take the result of Har)egtltgyir/Ry).τι or p,c(r/Ry)72°. to be a general result of the elfervescent model."," Nonetheless, I take the result of $\eta(r) \simeq \eta(R_0) ( {r}/{R_0}) ^{-1/2}$, or $\rho_e \simeq (r/R_0)^{-2.5}$, to be a general result of the effervescent model."916" Under the assumptions of the phenomenological model the density of the bound material in the effervescent zone decreases as ~r. 7, ", Under the assumptions of the phenomenological model the density of the bound material in the effervescent zone decreases as $\sim r^{-2.5}$ .917The effervescent zone will extend (o a distance, The effervescent zone will extend to a distance918hole and ~2.5x10.*Iz—510?Ilz for a M=LOSAL. black hole.,hole and $\sim 2.5 \times 10^{-7}\hz - 5 \times 10^{-5}\hz$ for a $M=10^8\msun$ black hole.919 Low frequency. QPOs. which generally occur in GBIIs at ~1 EHz. would therefore be at best only marginally detectable in our data.," Low frequency QPOs, which generally occur in GBHs at $\sim 1$ Hz, would therefore be at best only marginally detectable in our data."920 High frequency QPOs. which are sometimes seen al e200 300 Iz. might in principle have appeared. bul we see no evilence for any.," High frequency QPOs, which are sometimes seen at $\sim 200$ $300$ Hz, might in principle have appeared, but we see no evidence for any."921 On the other hand. they appear in real black hole svstems only in association with the transition to the steep power law state.," On the other hand, they appear in real black hole systems only in association with the transition to the steep power law state."922 Although our simulation code very accurately conserves energy. the cooling [unetion we emplov is no more than a tov-model.," Although our simulation code very accurately conserves energy, the cooling function we employ is no more than a toy-model."923 A more complete description of radiative cooling will be necessary to understad spectral state (ransitions. and that might be a prerequisite for understanding high frequency QPOs as well.," A more complete description of radiative cooling will be necessary to understand spectral state transitions, and that might be a prerequisite for understanding high frequency QPOs as well."924 Our optically thin limit Gi= 0.001) phenomenologically resembles the hard state of Galactic black hole binaries in the sense that our definition of “coronal” eliminates any opticallv-thick thermal disk in the inner part of the accretion flow.," Our optically thin limit $\dot m = 0.001$ ) phenomenologically resembles the hard state of Galactic black hole binaries in the sense that our definition of “coronal"" eliminates any optically-thick thermal disk in the inner part of the accretion flow."925 Intriguinelv. the slope that we consistently find (a~ —2) is crudely consistent with the mean slope of the power spectrum measured in νο X-1 in the range 1500 Iz: steepening Irom ~—1.7 fom—2.4 ?..," Intriguingly, the power-law slope that we consistently find $\alpha \simeq -2$ ) is crudely consistent with the mean slope of the power spectrum measured in Cyg X-1 in the range 1–500 Hz: steepening from $\simeq -1.7$ to $\simeq -2.4$ \cite{Rev00}."926 For higher accretion rates. our corona is restricted to the outer lavers of the flow. more in keeping with what is often imagined for AGN.," For higher accretion rates, our corona is restricted to the outer layers of the flow, more in keeping with what is often imagined for AGN."927 A power-law slope ~—2 is also very roughly consistent with. observations of these objects., A power-law slope $\simeq -2$ is also very roughly consistent with observations of these objects.928 For example. ? shows that the slope of the power spectrum in IC: 4329A steepens from 7—1 to ~—2 across the frequency range 10.7 10! Hz.," For example, \cite{Mark09} shows that the slope of the power spectrum in IC 4329A steepens from $\simeq -1$ to $\simeq -2$ across the frequency range $10^{-8}$ $10^{-4}$ Hz."929 Similarly. ? find that the power spectrum of Mrk 766 steepens [rom ~—1.5 to c—3 [rom ~3x10? Hz to eI07 Lz.," Similarly, \cite{Mark07} find that the power spectrum of Mrk 766 steepens from $\simeq -1.5$ to $\simeq -3$ from $\simeq 3 \times 10^{-5}$ Hz to $\simeq 10^{-3}$ Hz."930 In this latter case. Markowilz et al.," In this latter case, Markowitz et al."931 estimate that the central black hole mass may be only ~105. LOTAL.. which would place our simulated frequency range roughly coincident will (he observed banc.," estimate that the central black hole mass may be only $\sim 10^6$ $10^7 M_{\odot}$, which would place our simulated frequency range roughly coincident with the observed band."932 As already mentioned. the decrease in radial coherence length with increasing freeuenevy steepens (he power spectrum of the aggregate light curve relative to (he power spectrum of the local emissivity.," As already mentioned, the decrease in radial coherence length with increasing frequency steepens the power spectrum of the aggregate light curve relative to the power spectrum of the local emissivity."933 In our verv approximate treatment. we described (he result in terms ol a new. steeper power-law.," In our very approximate treatment, we described the result in terms of a new, steeper power-law."934 A more careful and complete treatment might improve upon this description., A more careful and complete treatment might improve upon this description.935 In particular. the factor that controls the radial coherence length is whether the fluctuation Lrequency is larger or smaller than Che local inflow rate.," In particular, the factor that controls the radial coherence length is whether the fluctuation frequency is larger or smaller than the local inflow rate."936 It is the oulwarel decrease of the inflow rate that leads to higher power al lower Irequencies by stretching the range of radial coherence., It is the outward decrease of the inflow rate that leads to higher power at lower frequencies by stretching the range of radial coherence.937 However. at sufficiently low frequencies. greater radial coherence does not add appreciably to the power spectrum because material al larger radius does nol contribute much to the Iuminositv.," However, at sufficiently low frequencies, greater radial coherence does not add appreciably to the power spectrum because material at larger radius does not contribute much to the luminosity."938 At frequencies lower than the inflow rate at the radius within which most of the lisht is emitted. the slope of the composite flix power spectrum should therefore match the slope of the emissivitv power spectrum.," At frequencies lower than the inflow rate at the radius within which most of the light is emitted, the slope of the composite flux power spectrum should therefore match the slope of the emissivity power spectrum."939 One mieht then expect a smooth roll-off from the slope of the emissivity power spectrum at these very low Irequencies, One might then expect a smooth roll-off from the slope of the emissivity power spectrum at these very low frequencies940wyticaf/(1+2).,$w_0+w_a z/(1+z)$.941 Fig., Fig.942" S shows the mareinalizedS O,,-O;nm Á and i-i, ( contours.", \ref{fig8} shows the marginalized $\Omega_m$ $\Omega_k$ and $w_0$ $w_a$ contours.943 From Figs., From Figs.944S 7 and 8.. we see that the difference in the results between the analvtical marginalization ancl the {lux averaging is small.," \ref{fig7} and \ref{fig8}, we see that the difference in the results between the analytical marginalization and the flux averaging is small."945 The ACDAM model is consistent with the observation at the lolevel., The $\Lambda$ CDM model is consistent with the observation at the $1\sigma$level.946 Fie., Fig.947" 9 shows the marginalized probabilities for Q,,. Qe. i04 ancl i; for the DE moclel wydansz/(12)."," \ref{fig9} shows the marginalized probabilities for $\Omega_m$ , $\Omega_k$, $w_0$ and $w_a$ for the DE model $w_0+w_a z/(1+z)^2$."948 Fig., Fig.949" 10. shows the marginalized ,,-O, and i-i, contours.", \ref{fig10} shows the marginalized $\Omega_m$ $\Omega_k$ and $w_0$ $w_a$ contours.950 From Figs., From Figs.951 9 and 10.. we see that the parameters are a little better constrained with the analvtical marginalization.," \ref{fig9} and \ref{fig10}, we see that the parameters are a little better constrained with the analytical marginalization."952 The ACD model is consistent with the observation at the lo level., The $\Lambda$ CDM model is consistent with the observation at the $1\sigma$ level.953 We stummarize (he results in Tables 1 and 2., We summarize the results in Tables 1 and 2.954 We do not see much improvement on the constraints on the DE parameters aud the cosmic curvature byusing the fhix averaging method., We do not see much improvement on the constraints on the DE parameters and the cosmic curvature byusing the flux averaging method.955" For the DE model i+,z/(1—z). the gold data gives better constraints than the ESSENCE data on the DE parameters ij and i,. but both data give good constraints on the cosmic curvature."," For the DE model $w_0+w_a z/(1+z)$, the gold data gives better constraints than the ESSENCE data on the DE parameters $w_0$ and $w_a$, but both data give good constraints on the cosmic curvature."956" For the DE model i+02/0.2). the ESSENCE data gives much better constraint on thecosmic curvature than the gold data. although the constraints on the DE parameters eei ancl i0, are almost the same for both data."," For the DE model $w_0+w_a z/(1+z)^2$, the ESSENCE data gives much better constraint on thecosmic curvature than the gold data, although the constraints on the DE parameters $w_0$ and $w_a$ are almost the same for both data."957" For the 182 gold data. the DE model iei+(60,2/(12) gives much better constraints on the cosmic curvature Q;."," For the 182 gold data, the DE model $w_0+w_a z/(1+z)$ gives much better constraints on the cosmic curvature $\Omega_k$ ."958" For the ESSENCE data. the two DE models give almost the same constraint on O,, and 9,."," For the ESSENCE data, the two DE models give almost the same constraint on $\Omega_m$ and $\Omega_k$."959" For the DE model io40,2/(1+2). the mean value of wy determined from the observation tends (o be wy>—1. while the mean value of ey is less (han —1 for the DE model wo4(60,2/(127>z)7."," For the DE model $w_0+w_a z/(1+z)$, the mean value of $w_0$ determined from the observation tends to be $w_0\geq -1$, while the mean value of $w_0$ is less than $-1$ for the DE model $w_0+w_a z/(1+z)^2$."960 From Tables 1and 2. we see that the constraints on ο are almost the same for the two different DE models (5)) and (7)).," From Tables 1and 2, we see that the constraints on $\Omega_k$ are almost the same for the two different DE models \ref{lind}) ) and \ref{wzeq}) )."961 In other words. the results we obtained on O; do not depend on the chosen models much.," In other words, the results we obtained on $\Omega_k$ do not depend on the chosen models much."962 Recently. the authors in Clarksonetal.(2007). found that (he assumption of a flat universe induces critically large errors in reconstructing the dark energy. equation of state at 20.9 even if the true cosmic curvature is very small. ο~0.01 or less.," Recently, the authors in \cite{clarkson} found that the assumption of a flat universe induces critically large errors in reconstructing the dark energy equation of state at $z\ga 0.9$ even if the true cosmic curvature is very small, $\Omega_k\sim 0.01$ or less."963 Thev obtained the result by fitting the data derived [rom a DE model with ος40 with a flat model. so the result may not be conclusive.," They obtained the result by fitting the data derived from a DE model with $\Omega_k\neq 0$ with a flat model, so the result may not be conclusive."964" To see how the value of Q, allect (he constraints on the property of DE. we perform the AICAIC analvsis on the DE models (5)) and (7)) with Q,= 0."," To see how the value of $\Omega_k$ affect the constraints on the property of DE, we perform the MCMC analysis on the DE models \ref{lind}) ) and \ref{wzeq}) ) with $\Omega_k=0$ ."965 The results are reported in Tables 3 and 4., The results are reported in Tables 3 and 4.966" Although the uncertainties of ο change the values of wy and i;. the ranges of ey and we, are almost the same lor small O,."," Although the uncertainties of $\Omega_k$ change the values of $w_0$ and $w_a$, the ranges of $w_0$ and $w_a$ are almost the same for small $\Omega_k$."967" In conclusion. we first confini previous results that the shift parameter 7? alone does not give good constraint on δε. we must combine2 and /, to constrain λε, "," In conclusion, we first confirm previous results that the shift parameter $R$ alone does not give good constraint on $\Omega_k$ , we must combine$R$ and $l_a$ to constrain $\Omega_k$ ."968"By using A. /, and their covariance matrix. weget almost the same results as those obtained by using the original WMAP3 data."," By using $R$ , $l_a$ and their covariance matrix, weget almost the same results as those obtained by using the original WMAP3 data."969 Without ealeulating the power spectrum.the fitting process is much faster and efficient.," Without calculating the power spectrum,the fitting process is much faster and efficient."970 The cosmic curvature is found to be ο)< 0.03.," The cosmic curvature is found to be $|\Omega_k| \la9710.03$ ."972Fie.,Fig.973 2 for an iron abundance of 5. solar., \ref{fig:mcspectraFe5} for an iron abundance of $5\times$ solar.974 LE Compton down-scattering is ‘turned olf” so that. photoclectric absorption remains the only source of opacity. this particular cdillieulty does not arise. as Fig.," If Compton down-scattering is `turned off' so that photoelectric absorption remains the only source of opacity, this particular difficulty does not arise, as Fig."975 3. shows., \ref{fig:photoelspectra} shows.976 We cliseuss here the model fits to both the NRB spectrum and the source counts (logNolog S) in the several bancs. for various values of the evolutionary parameters toute Soa and p. and dillerent Ny distributions.," We discuss here the model fits to both the XRB spectrum and the source counts $\log N-\log S$ ) in the several bands, for various values of the evolutionary parameters $z_{cut}$, $z_{max}$ and $p$, and different $N_{\rm{H}}$ distributions."977" We parameterise the latter with the following recdshift-dependence for 2: p=3 forOcixü05 j—go for 0.5<2<LO d=33 for LO<2<2.0 d=3, for 2.02<3.0 $=35 for 3.0zxtae We take Ngauus=107 as Ligs"," We parameterise the latter with the following redshift-dependence for $\beta$ $\beta=\beta_{1}$ for $0 \leq z < 0.5$ $\beta=\beta_{2}$ for $0.5 \leq z < 1.0$ $\beta=\beta_{3}$ for $1.0 \leq z < 2.0$ $\beta=\beta_{4}$ for $2.0 \leq z < 3.0$ $\beta=\beta_{5}$ for $3.0 \leq z < z_{max}$ We take $N_{\rm{H},max}=10^{25}$, as Figs."978 1 and 2 show that there is essentially no direct. Hux (and hence ittle contribution to the NRB) from more heavily obscured sources (but Fig., \ref{fig:mcspectraFe1} and \ref{fig:mcspectraFe5} show that there is essentially no direct flux (and hence little contribution to the XRB) from more heavily obscured sources (but Fig.979 3. shows that this is not so when Compton down-scattering is neglected)., \ref{fig:photoelspectra} shows that this is not so when Compton down-scattering is neglected).980 Acceptable fits o the observed NRB spectrum: as. parameterisecl above by Gruber et al. (, Acceptable fits to the observed XRB spectrum as parameterised above by Gruber et al. (9811992) were defined as satisfving he criteria given by Celotti et al. (,1992) were defined as satisfying the criteria given by Celotti et al. (9821995).,1995).983 As stated therein. he model spectrum is first re-normalized to the observed ARB at by between ~0.7 ancl 1.5. to take into account uncertainty in the normalization of the tvpe 1. NLE. as set by the assumed. value of Ny. and the level type 2 contamination in the Piecinotti οἱ al. (," As stated therein, the model spectrum is first re-normalized to the observed XRB at by between $\sim 0.7$ and 1.5, to take into account uncertainty in the normalization of the type 1 XLF, as set by the assumed value of $N_{\rm{H},\star}$ and the level type 2 contamination in the Piccinotti et al. ("9841982) NLE.,1982) XLF.985" With solar iron abundance and 3)5=8. acceptable models can be found for zen, 21.21.4. p 2.52.9 and να 23.54.0 (ie."," With solar iron abundance and $\beta_{1-5}=8$, acceptable models can be found for $_{cut} \simeq$ 1.2–1.4, $p \simeq$ 2.5–2.9 and $_{max} \simeq$ 3.5--4.0 (ie."986 within the 68 per cent confidence limits derived. by Jones et al., within the 68 per cent confidence limits derived by Jones et al.987 1997)., 1997).988 There is no freedom. for the inclusion of larger numbers of type 2 sources at high redshift., There is no freedom for the inclusion of larger numbers of type 2 sources at high redshift.989 The predicted local emissivities in the band lie at or, The predicted local emissivities in the band lie at or990As always in astronomv. the determination of distances is a crucial ancl difficult problem.,"	As always in astronomy, the determination of distances is a crucial and difficult problem."991 Until recently. the distance scale of GRBs was unknown by over 12 orders-of-magnitude.," Until recently, the distance scale of GRBs was unknown by over 12 orders-of-magnitude."992 In 1997. the discovery. of optical and radio counterparts (Costaοἱal.LOOT:vanParadijset1997:Frailetal.1997). proved that at least the long-duration bursters were al cosmological distances wilh redshifts of z1.," In 1997, the discovery of optical and radio counterparts \citep{cos97,van97,fra97} proved that at least the long-duration bursters were at cosmological distances with redshifts of $z \sim 1$."993 The measurement of GRB redshifts requires deep optical spectra. and to date only 24 redshifts are known for bursts with unknown selection effects.," The measurement of GRB redshifts requires deep optical spectra, and to date only 24 redshifts are known for bursts with unknown selection effects."994 If GRB distance indicators can be found that use only gamma-ray data. (hen we can measure (he demographics and cosmologv of large and. well-understood samples of bursts.," 	If GRB distance indicators can be found that use only gamma-ray data, then we can measure the demographics and cosmology of large and well-understood samples of bursts."995function depends ou the local iudex of the power spectra? aud is smaller for negative indices.,function depends on the local index of the power spectrum \cite{galclus} and is smaller for negative indices.996 Iu order to appv the results eiven above to clustering of galaxies. we nist Incorporate effects of the mass function of galaxies.," In order to apply the results given above to clustering of galaxies, we must incorporate effects of the mass function of galaxies."997 The apitie of halo correlation func1ο starts increasing earlier for low mass halos., The amplitude of halo correlation function starts increasing earlier for low mass halos.998 As thπο are nanny more low nass halos than high mass ones. the epoch at which the auplitude of eaaxy correlation function starts increasing will «epexd on the uass of the sialest galaxies that can be seen at Ligh redshitts," As there are many more low mass halos than high mass ones, the epoch at which the amplitude of galaxy correlation function starts increasing will depend on the mass of the smallest galaxies that can be seen at high redshifts."999"21 uudlations hat conibine seni-analvtie models of galaxy formation with eraviaticnal chisterine cal )o used to compute ealaxy correlation function aud for the uodels where his has been do1ο, the galaxy. correlation function follows tlic saue] yattern as he iio correlaion b Dwespective of tre detailed evoliiiol. We Call concude. that a lüeh redshifts. galaxies cluster muuch more stroely than the uudlying mass cüstribution."," Simulations that combine semi-analytic models of galaxy formation with gravitational clustering can be used to compute galaxy correlation function and for the models where this has been done, the galaxy correlation function follows the same pattern as the halo correlation \cite{tcdm} Irrespective of the detailed evolution, we can conclude, that at high redshifts, galaxies cluster much more strongly than the underlying mass distribution."1000 Thus. the observe clustering of eaaxies at high reds ufts” 1s LO a strong coustraint for most nucxdels of structive formation? Some other duplications of strong clustering at high reclslüfts are: (1) The evolution of galaxy chstoring is not a good indicaor of cosmological paraneters. (," Thus, the observed clustering of galaxies at high redshifts \cite{wallobs} is not a strong constraint for most models of structure \cite{walls} Some other implications of strong clustering at high redshifts are: (1) The evolution of galaxy clustering is not a good indicator of cosmological parameters. ("1001"2) The shape o the galaxy correlation function is ciffereu frou t16 shape of the mass correlation ""nuctiou.",2) The shape of the galaxy correlation function is different from the shape of the mass correlation function.1002 Therefore galaxy correlatioji function is not a very good indicator o the iuitial power spectun. (, Therefore galaxy correlation function is not a very good indicator of the initial power spectrum. (10033) Sources res])onisie for reheating aud reionisaion of the ICAL will have a very uouuΠο ΠΕtion.,3) Sources responsible for reheating and reionisation of the IGM will have a very non-uniform distribution.1004 This will leac to a patch strποιο at earVY Cpoci., This will lead to a patchy structure at early epochs.1005 The scale of pateJuess. which may be le canbe used to constrain ealaxy Kkoxuation sce1urlos. (," The scale of patchiness, which may be \cite{tomo} can be used to constrain galaxy formation scenarios. ("1006"1) Formatio1 of niaiv donishus sources 1l a Slul regioji will iicrease the teniperature: Xt16 TOAD and inhibit collapsc of low nass halos in these ""Therefore. t10 Lass function of galaxies rear anl AWAY roni these ionising centres will be differeit. (","4) Formation of many ionising sources in a small region will increase the temperature of the IGM and inhibit collapse of low mass halos in these \cite{supress} Therefore, the mass function of galaxies near and away from these ionising centres will be different. ("10075) Tf quasars fonu preferentially ii high mass halos then they shouk show strongor clustering han eaaxies. (,5) If quasars form preferentially in high mass halos then they should show stronger clustering than galaxies. (1008Recent estimates of quasar correlation function show that it is stronger than the galaxy correlation function?’)) A conrparison of the two. aud their evolution. cau be a useful indicator of the xevaleuce of ACN activity in galaxies.,"Recent estimates of quasar correlation function show that it is stronger than the galaxy correlation \cite{qsocorr1}$ $^{\!,\,}$ \cite{qsocorr2}) ) A comparison of the two, and their evolution, can be a useful indicator of the prevalence of AGN activity in galaxies."1009 Tackuowledge the support of PPARC fellowship at the Institute of Astronomy., I acknowledge the support of PPARC fellowship at the Institute of Astronomy.1010 T thank the organisers of the for their, I thank the organisers of the for their1011"In. turbulent MHD systems where the ratio of fluid viscosity and magnetic diffusivity (the magnetic Prandtl number. Pri,2 77/1) is very large. there exists a broad range of subviscous scales available to magnetic fluctuations. but not to hydrodynamic ones.","In turbulent MHD systems where the ratio of fluid viscosity and magnetic diffusivity (the magnetic Prandtl number, $\Pr=\nu/\eta$ ) is very large, there exists a broad range of subviscous scales available to magnetic fluctuations, but not to hydrodynamic ones."1012" This MHD regime is encountered. for example. in such astrophysical environments as the interstellar medium and protogalactic plasmas. where Pri, can be as large as 10'7 to 107 (Kulsrud1999).."," This MHD regime is encountered, for example, in such astrophysical environments as the interstellar medium and protogalactic plasmas, where $\Pr$ can be as large as $10^{14}$ to $10^{22}$ \citep{Kulsrud_review}."1013 Since the ratio of the resistive and viscous cut-off wave numbers ts ΚιΚω—pil. this gives rise to subviscous scale ranges 7 to 1] decades wide.," Since the ratio of the resistive and viscous cut-off wave numbers is $k_\eta/k_\nu\sim\Pr^{1/2}$, this gives rise to subviscous scale ranges 7 to 11 decades wide."1014 Since the fluid is highly conducting. the magnetic-field lines are (nearly) perfectly frozen into the fluid flow.," Since the fluid is highly conducting, the magnetic-field lines are (nearly) perfectly frozen into the fluid flow."1015 The fluid motions. even though restricted to the scales above the viscous cutoff. can excite magnetic fluctuations at much smaller scales via stretching and folding of the field lines.," The fluid motions, even though restricted to the scales above the viscous cutoff, can excite magnetic fluctuations at much smaller scales via stretching and folding of the field lines."1016 This possibility was first indicated by Batchelor(1950)., This possibility was first indicated by \citet{Batchelor}.1017. The weak-field (kinematic) limit has been an attractive object of analytical study since the seminal work of Kazantsev(1967)., The weak-field (kinematic) limit has been an attractive object of analytical study since the seminal work of \citet{Kazantsev}.1018. The spectral theory of the kinematic dynamo driven by a random velocity field predicts exponential growth of the magnetic energy and its accumulation at the resistive scales (seeKazantsev1967:ences therein)..," The spectral theory of the kinematic dynamo driven by a random velocity field predicts exponential growth of the magnetic energy and its accumulation at the resistive scales \citep[see][and 1019references therein]{Kazantsev,KA,Gruzinov_Cowley_Sudan,SBK_review}."1020. More recently. it was realized that small-scale magnetic fields generated by this “streteh-and-fold” dynamo possess a distinctive. spatial 1)): the smallness of the field scale is due to rapid transverse spatial oscillation of the field direction. while the field lines remain largely unbent up to the scale of the flow (Ott1998;forthreferredtoas SCMM02)..," More recently, it was realized that small-scale magnetic fields generated by this “stretch-and-fold” dynamo possess a distinctive spatial ): the smallness of the field scale is due to rapid transverse spatial oscillation of the field direction, while the field lines remain largely unbent up to the scale of the flow \citep[][--- this last paper is henceforth referred to 1021as SCMM02]{Ott_review,Kinney_etal,SCMM_folding}."1022 With the dramatic increase in the reach of the numerical experiment. the nonlinear regime became increasingly amenable to detailed study.," With the dramatic increase in the reach of the numerical experiment, the nonlinear regime became increasingly amenable to detailed study."1023 The pioneering work of Meneguzzi.Frisch.&Pouquet(1981) was in recent years followed by a number of numerical investigations (Cattaneo.Hughes.&Kimbreviated MCMO02)..," The pioneering work of \citet{Meneguzzi_Frisch_Pouquet} was in recent years followed by a number of numerical investigations \citep[][the latter paper henceforth abbreviated MCM02]{Cattaneo_Hughes_Kim,Brandenburg_etal,Zienicke_Politano_Pouquet,Kinney_etal,Cho_Vishniac,Brandenburg,Chou,Brummell_Cattaneo_Tobias,MCM_dynamo}."1024" However. the physical difference between the Pr,=| and Pr,=>| regimes is not always realized."," However, the physical difference between the $\Pr=1$ and $\Pr\gg1$ regimes is not always realized."1025 Another defining physical feature of the MHD regime we are considering is the absence of an externally imposed uniform magnetic field., Another defining physical feature of the MHD regime we are considering is the absence of an externally imposed uniform magnetic field.1026 The difference is essential., The difference is essential.1027 First. a fixed uniform field implies a nonzero net flux through the system.," First, a fixed uniform field implies a nonzero net flux through the system."1028 Second. in the presence of a strong such field. magnetic-field lines cannot be bent. so the physies of the subviscous-scale magnetic fluctuations is more akin to that of the scalar turbulence (cf.Cho.Lazarian.&Vishniae 2002).," Second, in the presence of a strong such field, magnetic-field lines cannot be bent, so the physics of the subviscous-scale magnetic fluctuations is more akin to that of the scalar turbulence \citep[cf.][]{Cho_Lazarian_Vishniac}."1029. In the astrophysical context. the main question has been of the impact small-scale magnetic. fluctuations have on the feasibility of generating the large-scale galactic magnetic field by means of turbulent dynamo.," In the astrophysical context, the main question has been of the impact small-scale magnetic fluctuations have on the feasibility of generating the large-scale galactic magnetic field by means of turbulent dynamo."1030 In particular. one wonders how the accumulated small-scale magnetic energy affects the applicability of the mean-field à O-dynamo theory. which. in one form or another. has been at the center of all attempts," In particular, one wonders how the accumulated small-scale magnetic energy affects the applicability of the mean-field $\alpha\Omega$ -dynamo theory, which, in one form or another, has been at the center of all attempts"1031inaege so that the coutimmun subtracted Pan image (fiux calibrated) did not show negative values.,image so that the continuum subtracted $\alpha$ image (flux calibrated) did not show negative values.1032 This method eenecrallv produces satisfactoryp results. except iu. those cases where the differential extinction between 1.60444 and 1.87 pu is significant (typically edgc-on galaxies aud the nuclei of some galaxies).," This method generally produces satisfactory results, except in those cases where the differential extinction between $1.60\,\mu$ m and $1.87\,\mu$ m is significant (typically edge-on galaxies and the nuclei of some galaxies)."1033 As we shall see in the next section. the region photometry software takes into account the local backerouud. so the coutinman subtraction is not a donünaut source of error. although errors associated with the background subtraction depend on the huninosity of the region.," As we shall see in the next section, the region photometry software takes into account the local background, so the continuum subtraction is not a dominant source of error, although errors associated with the background subtraction depend on the luminosity of the region."1034 Throughout the paper we have converted the Paa huuinosity into the more conuuonlv used Πα huuinositsy. assuniiue case D recombination ue— N.," Throughout the paper we have converted the $\alpha$ luminosity into the more commonly used $\alpha$ luminosity, assuming case B recombination $\frac{{\rm1035H}\alpha}{{\rm Pa}\alpha} = 8.7$ )."1036Woalso stress that the effects of reddening in the central reeious will be attenuatedwith the of usePao luminosities with respect to We bhuninosities ο~0.2 AMTa}: Rieke Lebofsv 1985).," We also stress that the effects of reddening in the central regions will be attenuated with the use of $\alpha$ luminosities with respect to $\alpha$ luminosities $A({\rm1037Pa}\alpha) \simeq 0.2\,A({\rm H}\alpha$ ); Rieke Lebofsky 1985)."1038 The region catalogs were produced using the softwareREGION. kindly provided by Dr. C. IL Teller (see Plouss et al.," The region catalogs were produced using the software, kindly provided by Dr. C. H. Heller (see Pleuss et al."1039 2000. and references therein for a detailed description).," 2000, and references therein for a detailed description)."1040 1s a senir-autonmated method to locate aud compute statistics of roeious in an image. based ou conutourius. aud taking into account the local background.," is a semi-automated method to locate and compute statistics of regions in an image, based on contouring, and taking into account the local background."1041 The lower huit for the size of au region is set to 9 contiguous pixels. which corresponds to linear sizes of between 2 and G0ppc.," The lower limit for the size of an region is set to 9 contiguous pixels, which corresponds to linear sizes of between 2 and pc."1042 Each pixel τις lave au intensity above the local background of at least three times the rius noise of that local backgrouud (see Baud 1992 and Kkuapen et al., Each pixel must have an intensity above the local background of at least three times the rms noise of that local background (see Rand 1992 and Knapen et al.1043 1993 for more details ou the criteria emiploved)., 1993 for more details on the criteria employed).1044 After identifving the regions. the program measures their position. size (area) and huninositv bv subtracting the closest local backeround froii the observed fux.," After identifying the regions, the program measures their position, size (area) and luminosity by subtracting the closest local background from the observed flux."1045 For tliose ealaxies with detected regions. in Table 2 we list the uunuber of reeious identified. the Πα huninosity of the brightest. faintest. and medianLin. as well as the diameter of the largest and median region.," For those galaxies with detected regions, in Table 2 we list the number of regions identified, the $\alpha$ luminosity of the brightest, faintest, and median, as well as the diameter of the largest and median region."1046 A total of LO galaxies were excluded. from most of the region analyses for various reasons. as detailed in the footuote to Table 2 There are two iicthods to define the exteut of au region: percentage-of-peak photometry (PPP) auc fixed-threshold photometry (FTP).," A total of 10 galaxies were excluded from most of the region analyses for various reasons, as detailed in the footnote to Table 2 There are two methods to define the extent of an region: percentage-of-peak photometry (PPP) and fixed-threshold photometry (FTP)."1047 The former defines the area to be assigned to an region Within an isophote whose brightuess is a fixed percentage of the intensity peak. aud avoids problems of S/N at the boundary of the region.," The former defines the area to be assigned to an region within an isophote whose brightness is a fixed percentage of the intensity peak, and avoids problems of S/N at the boundary of the region."1048 The latter uses a Iuuitiug surface brieltuess method to define an region (see Kiugsburgh MeCall 1998 for a detailed comparison of the two method)., The latter uses a limiting surface brightness method to define an region (see Kingsburgh McCall 1998 for a detailed comparison of the two methods).1049 We used the FTP method. but we still needed to impose the condition of a minimum size (in pixels) for identifvine au reeion.," We used the FTP method, but we still needed to impose the condition of a minimum size (in pixels) for identifying an region."1050 Thus for ealaxies at different distances this corresponds to differiug physical sizes., Thus for galaxies at different distances this corresponds to differing physical sizes.1051 This effect can be clearly ποσα in the median diameters (iun pc) of the detected regious found for cach galaxy. (Table 2)., This effect can be clearly seen in the median diameters (in pc) of the detected regions found for each galaxy (Table 2).1052 Iu order to show the effect of distance on the derived properties. the galaxies in Table 2 are sorted by increasing distance.," In order to show the effect of distance on the derived properties, the galaxies in Table 2 are sorted by increasing distance."1053 Ono of the most important issues when analyzing the xoperties of the region LF is the role of observational xuanieters. especially spatial resolution.," One of the most important issues when analyzing the properties of the region LF is the role of observational parameters, especially spatial resolution."1054" Until wow, most region LFs were based upon ground-hased Io imaging with spatial resolutions rauging frou 0.5 to a few arcsec. or from ppc Gn M31: Walterbos Braun 1992) to a few mudred pe (SET: Baud 1992: Kuapen ct al."," Until now, most region LFs were based upon ground-based $\alpha$ imaging with spatial resolutions ranging from 0.8 to a few arcsec, or from pc (in M31; Walterbos Braun 1992) to a few hundred pc (KEH; Rand 1992; Knapen et al."1055 1993: Banfi et al., 1993; Banfi et al.1056 1993: Rozas et al., 1993; Rozas et al.1057 1996a. Kuapen 1998). depending upou the distance of the galaxy.," 1996a, Knapen 1998), depending upon the distance of the galaxy."1058 Rand (1992) discussed he effects of blending on the properties of the region LF., Rand (1992) discussed the effects of blending on the properties of the region LF.1059 Such blending. e.g. in the case where a smaller region is spatially coincident with a larger one and is rot cataloged. is expected to occur more frequently as he spatial resolution decreases.," Such blending, e.g., in the case where a smaller region is spatially coincident with a larger one and is not cataloged, is expected to occur more frequently as the spatial resolution decreases."1060 Raud (1992) concluded roni his mocdoeliug of this problem that blending does not siguificautly affect the luceatred slope of the region LF as determined from his erouud-based iiaeeIu of M51., Rand (1992) concluded from his modeling of this problem that blending does not significantly affect the measured slope of the region LF as determined from his ground-based image of M51.1061 More recently. Pleuss et al. (," More recently, Pleuss et al. ("10622000) specifically studied the impact ofdiffercut spatial resolution on. among other parameters. the diameter distribution aud LF of regions.,"2000) specifically studied the impact of different spatial resolution on, among other parameters, the diameter distribution and LF of regions."1063 They usedZ£5T archive Πα nuages of selected areas of the spiral galaxw MIOL. and degraded these to a typical ground-based resolution of 0:5 arcsec C(FWIIAL).," They used archive $\alpha$ images of selected areas of the spiral galaxy M101, and degraded these to a typical ground-based resolution of 0.8 arcsec (FWHM)."1064" The linear scales sanypled by their high and low resolution inages were 3.6 and 77.6 pe/pixcl. respectively,"," The linear scales sampled by their high and low resolution images were 3.6 and 77.6 pc/pixel, respectively."1065" Although the integral diameter distributions of the regions are significautly different at ligh aud low resolution (as expected. see Isnapen 1998). the LF slopes are only slightly different. being shallower iu the low resolution case,"," Although the integral diameter distributions of the regions are significantly different at high and low resolution (as expected, see Knapen 1998), the LF slopes are only slightly different, being shallower in the low resolution case."1066 A sinl effect is fouud by Scoville et al. (, A similar effect is found by Scoville et al. (10672001) who compared theirZZ5T (both. WEPC2 aud NICMOS) region LF with that of Rand (1992) for M51. with the high-resolution LF significantly steeper than the low-resolution one.,"2001) who compared their (both WFPC2 and NICMOS) region LF with that of Rand (1992) for M51, with the high-resolution LF significantly steeper than the low-resolution one."1068 Not only are the fitted slopes quite differeut but the methods used to arrive at them. so the comparison is less direct than in the work by Pleuss et al.," Not only are the fitted slopes quite different but the methods used to arrive at them, so the comparison is less direct than in the work by Pleuss et al."1069 aud Baud., and Rand.1070 It iust be kept in mind that the use of higher spatial resolution Huaging also introduces some problems., It must be kept in mind that the use of higher spatial resolution imaging also introduces some problems.1071 For instance. regions may be over-resolved. aud individual components or stars witlin what ought to be considered one single region my he cataloged as separate. and by implication smaller and less Iuminous. oues.," For instance, regions may be over-resolved, and individual components or stars within what ought to be considered one single region may be cataloged as separate, and by implication smaller and less luminous, ones."1072 Tt is outside the scope ofthe current paper to diseuss In detail the problems of resolution on the statistical results on ensenibles of regions in spiral galaxies., It is outside the scope of the current paper to discuss in detail the problems of resolution on the statistical results on ensembles of regions in spiral galaxies.1073 However. we do briefly stunmarize a few basic considerations which give some idea of plivsical scales.," However, we do briefly summarize a few basic considerations which give some idea of physical scales."1074 Firsth. consider the ideal case of a Stronuugren sphere. where the radius of au region eani be approximated in terms of the number of ionizing photons and a number of factors which depeud ou the electron. temperature and density (see c.g.. Strónunugren 1939: Osterbrock 1989).," Firstly, consider the ideal case of a Strömmgren sphere, where the radius of an region can be approximated in terms of the number of ionizing photons and a number of factors which depend on the electron temperature and density (see e.g., Strömmgren 1939; Osterbrock 1989)."1075 One finds that the radius of the Strouuneren spliere of à main sequence 05 star is ppc. whereas that of a BO.S star would be ppc (COsterbrock 1989).," One finds that the radius of the Strömmgren sphere of a main sequence O5 star is pc, whereas that of a B0.5 star would be pc (Osterbrock 1989)."1076 Iu sites of stroug SP. nieve stars tend to be clustered in OB associations. so the expected sizes of the regions ionized by these associations would be of the order of a few hundred. pe.," In sites of strong SF, massive stars tend to be clustered in OB associations, so the expected sizes of the regions ionized by these associations would be of the order of a few hundred pc."1077" Secondly, Walterbos Brauu (1992) estimate au upper limit for the Wa luninosity of"," Secondly, Walterbos Braun (1992) estimate an upper limit for the $\alpha$ luminosity of"1078There are marked. differences in the observed. properties of the field. and. cluster galaxy populations.,There are marked differences in the observed properties of the field and cluster galaxy populations.1079 Perhaps the best known cifference is the larger fraction of galaxies that are ellipticals or SOs (and the correspondingly lower spiral fraction) in clusters relative to the field (e.g. Dressler 1980: Coto et 22003).," Perhaps the best known difference is the larger fraction of galaxies that are ellipticals or $0$ s (and the correspondingly lower spiral fraction) in clusters relative to the field (e.g., Dressler 1980; Goto et 2003)."1080 Not only are the morphologies of cluster ealaxies cillerent from those of field galaxies. but so too are a variety of their other observed. properties. including colours (ο... Balogh et 22004: Loge et 22004). star forming properties (e.g. Pogeianti et al.," Not only are the morphologies of cluster galaxies different from those of field galaxies, but so too are a variety of their other observed properties, including colours (e.g., Balogh et 2004; Hogg et 2004), star forming properties (e.g., Poggianti et al."1081 1999: Balogh ct 22000: Gomez et 22003). and the distribution and total mass of their gaseous component (c.e.. Cavatte et 11994: Solanes et 2001).," 1999; Balogh et 2000; Gomez et 2003), and the distribution and total mass of their gaseous component (e.g., Cayatte et 1994; Solanes et 2001)."1082 These. observed: dillerences. indicate that. the dense environments. of groups and. clusters are. somehow stroneglv mocdifving the properties of galaxies as they fall in., These observed differences indicate that the dense environments of groups and clusters are somehow strongly modifying the properties of galaxies as they fall in.1083 Uncovering the physical mechanisms that give rise to the observed variation in galaxy properties has been an active topic of research over the past two or three decades (e.g. Dressler 1984: Sarazin 1988).," Uncovering the physical mechanisms that give rise to the observed variation in galaxy properties has been an active topic of research over the past two or three decades (e.g., Dressler 1984; Sarazin 1988)."1084 One of the most commonly mentioned processes is ram pressure stripping (Gunn Cott 1972)., One of the most commonly mentioned processes is ram pressure stripping (Gunn Gott 1972).1085 Here the gascous component (which can be composed of both cold atomic/molecular gas ancl a, Here the gaseous component (which can be composed of both cold atomic/molecular gas and a1086"The AKARI is a Japanese infrared satellite (Murakamietal., 2007),, which has continuous filter coverage in the mid IR wavelengths (N2,N3,N4,S7,S9W,S11,£15,L18W and 1:24).","The AKARI is a Japanese infrared satellite \citep{2007PASJ...59S.369M}, which has continuous filter coverage in the mid IR wavelengths $N2,N3,N4,S7,S9W,S11,L15,L18W$ and $L24$ )."1087" The AKARI has observed a massive galaxy cluster, RXJ1716.4+6708, in N3,S'7 and £15 (Koyamaetal., 2008).. RXJ1716."," The AKARI has observed a massive galaxy cluster, $+$ 6708, in $N3, S7$ and $L15$ \citep{2008MNRAS.391.1758K}. ."1088"44-6708 is at z=0.81 and has σ= 15227733km s!, Lx,=13.86+1.04x1074 erg s+, kT=6.86 keV. Mass estimate from weak lensing and X-ray are 3.7+1.3x101Mg and 4.35--0.83x10'4Mo, respectively (seeKoyamaetal.,2007,for references)."," $+$ 6708 is at z=0.81 and has $\sigma=1522^{+215}_{-150}$ km $^{-1}$, $L_{X_{bol}}=13.86\pm1.04\times 10^{44}$ erg $^{-1}$ , $kT=6.8^{+1.0}_{-0.6}$ keV. Mass estimate from weak lensing and X-ray are $\pm1.3 \times 10^{14}M_{\odot}$ and $\pm0.83\times 10^{14}M_{\odot}$, respectively \citep[see][for references]{2007MNRAS.382.1719K}."1089". An important advantage of the AKARI observation is 15 filter, which corresponds to the restframe 8um at z=0.81."," An important advantage of the AKARI observation is $L15$ filter, which corresponds to the restframe $\mu$ m at z=0.81."1090" With 15 (3) pointings, £15 reaches 66.5 (96.5)uJy in deep (shallow) regions at 5c."," With 15 (3) pointings, $L15$ reaches 66.5 $\mu$ Jy in deep (shallow) regions at $\sigma$."1091" Here flux is measured in 11"" aperture, and coverted to total flux using AKARI’s IRC correction table(2009."," Here flux is measured in 11” aperture, and coverted to total flux using AKARI's IRC correction table."1092"5.1)!.. Cluster studies with the Spitzer are often performed in 24μπι and thus needed a large extrapolation to estimate either Lg,,,, or total infrared luminosity (Lrrg, 1000um)."," Cluster studies with the Spitzer are often performed in $\mu$ m and thus needed a large extrapolation to estimate either $L_{8\mu m}$ or total infrared luminosity $L_{TIR},8-1000\mu m$ )."1093" Note that wedo not claim the Lg, is a better indicator of the total IR luminosity than other indicators (Brandletal.,2006;Calzetti2007;Rieke2009),, but it is important that the AKARI can meausure redshifted 8um flux directly in one of the filters."," Note that wedo not claim the $L_{8\mu m}$ is a better indicator of the total IR luminosity than other indicators \citep{2006ApJ...653.1129B,2007ApJ...666..870C,2009ApJ...692..556R}, but it is important that the AKARI can meausure redshifted $8\mu m$ flux directly in one of the filters."1094" Thanks to the AKARI’s wide field of view x10’), the total area coverage around the cluster is 200 arcmin’, which cover larger area than previous cluster studies with the Spitzer, allowing us to study IR sources in the outskirts, where important galaxy evolution takes place (e.g.,Gotoetal., 2003).."," Thanks to the AKARI's wide field of view $\times$ 10'), the total area coverage around the cluster is 200 $^2$, which cover larger area than previous cluster studies with the Spitzer, allowing us to study IR sources in the outskirts, where important galaxy evolution takes place \citep[e.g.,][]{2003MNRAS.346..601G}."1095" Previously, Koyamaetal.(2008) reported a high fraction of L15 sources in the intermediate density region in the cluster, suggesting a presence of environmental effect in the intermediate density environment."," Previously, \citet{2008MNRAS.391.1758K} reported a high fraction of $L15$ sources in the intermediate density region in the cluster, suggesting a presence of environmental effect in the intermediate density environment."1096 This same region was imagedwith Suprime-Cam in VRi’z’ and has a good photometric redshift estimate (Koyama 2007).. , This same region was imagedwith Suprime-Cam in $VRi'z'$ and has a good photometric redshift estimate \citep{2007MNRAS.382.1719K}. .1097Used in this work are 54 L15-detected galaxies which are well identified with opticalsources with 0.83., Used in this work are 54 $L15$ -detected galaxies which are well identified with opticalsources with $0.76\leq z_{photo}\leq 0.83$ .1098(VCC 1490) mis-identified by SDSS as a point source (unlike point sources. for sullicientIv. extended: objects no signal is lost [rom the fibre due to seeing).,"(VCC 1490) mis-identified by SDSS as a point source (unlike point sources, for sufficiently extended objects no signal is lost from the fibre due to seeing)."1099 NGC 1316 exposure set 3 hac uniformly low S/N because the exposure was curtailed by cloud., NGC 1316 exposure set 3 had uniformly low S/N because the exposure was curtailed by cloud.1100 We obtained: redshifts for some σος with optimal S/N by using their Call triplet features.," We obtained redshifts for some CSSs with sub-optimal S/N by using their $\,$ II triplet features."1101 Raw spectral images were reduced in a standard. manner with and spliced to. produce. spectra which are continuous over the range 5000.A., Raw spectral images were reduced in a standard manner with and spliced to produce spectra which are continuous over the range $8900 \; \mbox{\AA}$.1102 Initial reclshilt measurement was done in automatic mode using cross-correlation with. stanclarel star. emission-line. galaxy and QSO templates.," Initial redshift measurement was done in automatic mode using cross-correlation with standard star, emission-line galaxy and QSO templates."1103 We then individually inspected. cach spectrum. and: corrected the redshift by identifving prominent absorption or emission lines., We then individually inspected each spectrum and corrected the redshift by identifying prominent absorption or emission lines.1104 For QSOs we identified broad: emission. features V. S&IV. CIV. CLLL AleLh Eh. OIL) using a series of template spectra at increasing redshift.," For QSOs we identified broad emission features $\,$ V, $\,$ IV, $\,$ IV, $\,$ III, $\,$ II, $\beta$, $\,$ III) using a series of template spectra at increasing redshift."1105 At low S/N where absorption features are clillicult to detect. our successful redshift results are dominated by background galaxies with strong. casily identifiable emission features.," At low S/N where absorption features are difficult to detect, our successful redshift results are dominated by background galaxies with strong, easily identifiable emission features."1106 Due to variable observing conditions and the magnitude range of cach multi-fibre exposure set. we achieved: a wide range of S/N in our target spectra.," Due to variable observing conditions and the magnitude range of each multi-fibre exposure set, we achieved a wide range of S/N in our target spectra."1107 Fig., Fig.1108 4— compares the smoothed (3 ) spectra of four successfully recishifted CSSS ab various S/N levels., \ref{fig:targspectra} compares the smoothed $\times 3$ ) spectra of four successfully redshifted CSSs at various S/N levels.1109 In. general. our CSS spectra have insullicient S/N to make a detailed comparison of the spectral features between cluster environments.," In general, our CSS spectra have insufficient S/N to make a detailed comparison of the spectral features between cluster environments."1110" The redshift, measurement completeness of our observations varies between the four observed. fields: (see Fig. 5))", The redshift measurement completeness of our observations varies between the four observed fields (see Fig. \ref{fig:aaovirgofornax_3}) ).1111 Both cluster core ficlds hae already been extensively. surveved. (2227). leaving relatively Low bright point source targets with unmeasured redshifts. whereas the two intracluster fields contained many bright point source targets with no measured redshift.," Both cluster core fields had already been extensively surveyed \citep{Drinkwater..2000a, Mieske..2004I, Jones..2006} leaving relatively few bright point source targets with unmeasured redshifts, whereas the two intracluster fields contained many bright point source targets with no measured redshift."1112 Weather significantly limited our observing programs and. reduced the intended redshift completeness., Weather significantly limited our observing programs and reduced the intended redshift completeness.1113" ‘Vo identify, cluster members we define cluster recession", To identify cluster members we define cluster recession1114 Dwarf novae (DNe) are close interacting binaries in which a Roche-lobe filling main sequence-like dwarl transfers matter wilh angular momentum through a disk onto a white dwarf (WD)., Dwarf novae (DNe) are close interacting binaries in which a Roche-lobe filling main sequence-like dwarf transfers matter with angular momentum through a disk onto a white dwarf (WD).1115 The rapid disk accretion during outburst. due to a thermal instability (hat causes cvelie changes of (he accretion rate. releases gravitational potential energy identified as the DN outburst.," The rapid disk accretion during outburst, due to a thermal instability that causes cyclic changes of the accretion rate, releases gravitational potential energy identified as the DN outburst."1116 The high accretion rate (~107 to LO? AL. /vr) outburst phase (which lasts a few days to weeks) is preceded and followed by a low accretion rate (~LOTAL. /vr) quiescence stage.," The high accretion rate $\sim 10^{-8}$ to $10^{-9}$ $_{\odot}$ /yr) outburst phase (which lasts a few days to weeks) is preceded and followed by a low accretion rate $\sim 10^{-11}1117M_{\odot}$ /yr) quiescence stage."1118 This DN behavior is punctuated every. lew thousand vears or more by episodes of explosively unstable thermonuclear burning. the classical nova explosion (Warner 1995 and references (herein).," This DN behavior is punctuated every few thousand years or more by episodes of explosively unstable thermonuclear burning, the classical nova explosion (Warner 1995 and references therein)."1119 Perhaps the least uiderstood topic in CV/DN research. (along with what drives the wind outflow in outburst) is the state and structure of the boundary laver and accretion disk during quiescence and the phvsies of how long term accretion of ass. angular momentum and enerev affects the WD.," Perhaps the least understood topic in CV/DN research (along with what drives the wind outflow in outburst) is the state and structure of the boundary layer and accretion disk during quiescence and the physics of how long term accretion of mass, angular momentum and energy affects the WD."1120 Our studies with archivalJOE. andHST STIS have found that ~50% of the DNe in quiescence are dominated (i.e.. > of UV flux) by the accretion disk: ~25% are dominated bv the WD and —25'4 have nearly equal contribution of WD and accretion disk each) (Urban&Sion2006) A number of studies (Sion1991:Aranjo-Betancoretal.2005:Urban&SionTownsley&Bildsten2003) have shown that CV WDs above the gap are tvpically on-average e»10. 000Ix hotter than CV. WDs below the period gap (almost cerlainiv a consequence of hieher (time-averaged accretion rates of svstems above (he gap but possibly with svstem total age also being a factor).," Our studies with archival, and STIS have found that $\sim$ of the DNe in quiescence are dominated (i.e., $>$ of UV flux) by the accretion disk; $\sim$ are dominated by the WD and $\sim$ have nearly equal contribution of WD and accretion disk each) \citep{urb06}1121 A number of studies \citep{sio91,ara05,urb06, tow03} have shown that CV WDs above the gap are typically on-average $\sim 10,000$ K hotter than CV WDs below the period gap (almost certainly a consequence of higher time-averaged accretion rates of systems above the gap but possibly with system total age also being a factor)."1122 It is also (rue that [ar fewer svstems with reliably known WD properties are known above (he period gap compared wilh below the eap. thus impeding detailed comparisons between the two groups.," It is also true that far fewer systems with reliably known WD properties are known above the period gap compared with below the gap, thus impeding detailed comparisons between the two groups."1123 For example. among CVs below the gap. there are now roughly 20 svstems with reliable WD temperatures compared with only 8 such systems above the eap.," For example, among CVs below the gap, there are now roughly 20 systems with reliable WD temperatures compared with only 8 such systems above the gap."1124 The primary reason lor this disparity is that in long period CVs. mass transfer rates are higher and their disks brighter.," The primary reason for this disparity is that in long period CVs, mass transfer rates are higher and their disks brighter."1125 Hence. it is diffieult to disentangle the white dwarl flux," Hence, it is difficult to disentangle the white dwarf flux"1126The LE. of the rregions in the dise of ALLOO was constructed. using bins of 0.1 and 0.2 in the log of the luminosity. in order to check possible elfects of the bin size on the LE shape.,"The LF of the regions in the disc of M100 was constructed using bins of 0.1 and 0.2 in the log of the luminosity, in order to check possible effects of the bin size on the LF shape."1127 Phese cllects were found to be very small. and not allecting the fit of the slope to the LE. the main parameter deduced from the LES.," These effects were found to be very small, and not affecting the fit of the slope to the LF, the main parameter deduced from the LFs."1128 L thus decided to follow the precedent set in the literature. and show only LEs with 0.2 bin.," I thus decided to follow the precedent set in the literature, and show only LFs with 0.2 bin."1129 Fig., Fig.1130 2 shows the LE for the disc of the galaxy. but excluding the rregions in the CNl1t (see below)," \ref{disclf} shows the LF for the disc of the galaxy, but excluding the regions in the CNR (see below)."1131 The detection. limit. of individual rregions of logL~36.6 + is clearly visible in the LE as à drop on the low luminosity side., The detection limit of individual regions of $\log L\sim36.6$ $^{-1}$ is clearly visible in the LF as a drop on the low luminosity side.1132 This detection limit is slightly lower than that in Ixnapen et al. (, This detection limit is slightly lower than that in Knapen et al. (11331993a) ancl similar o those reported in Itozas et al. (,1993a) and similar to those reported in Rozas et al. (113419962).,1996a).1135 Ehe peak in the LE occurs around logL=37.1eergss. !. again comparable ο our previous studies.," The peak in the LF occurs around $\log L=37.1$ $^{-1}$, again comparable to our previous studies."1136 These similarities are of course a result. of the equal observing techniques used in all cases. »iit do show the consistently high quality of the data.," These similarities are of course a result of the equal observing techniques used in all cases, but do show the consistently high quality of the data."1137" L fitted a function of type INCL)=AL""dL to the L side of the LE. and determined a slope of the LE above ogL=3r 9eergss+ of a=2.47d0.04."," I fitted a function of type $N(L)=A\,L^a\,dL$ to the $L$ side of the LF, and determined a slope of the LF above $\log1138L=37.9$ $^{-1}$ of $a=-2.17\pm0.04$."1139 This slope is well within the usual range of LE slopes found for galaxies of similar morphological tvpe (e.g. Wennicutt et al., This slope is well within the usual range of LF slopes found for galaxies of similar morphological type (e.g. Kennicutt et al.1140 1989: I|xnapen et al., 1989; Knapen et al.1141 1993a: Rozas et al., 1993a; Rozas et al.1142 1996a), 1996a).1143 Note that LE slopes for MIOO in the literature range from 1.4 (Arsenault et al. (, Note that LF slopes for M100 in the literature range from $-1.4$ (Arsenault et al. (11441990). via. 2.1 (Banfi et al.,"1990), via $-2.1$ (Banfi et al."1145 1993) to 2.7 (Copa, 1993) to $-2.7$ (Cepa1146solution does not describe the December 1993 fare.,solution does not describe the December 1993 flare.1147 If the relativistic plasmoids are magnetically initiated then it follows (hat the plasmoids should be magnetically dominated at early times., If the relativistic plasmoids are magnetically initiated then it follows that the plasmoids should be magnetically dominated at early times.1148 A scenario in which a plasmoid starts out magnetic (then converts to pair plasma then back (o equipartition seems very contrived ancl has no known physical basis., A scenario in which a plasmoid starts out magnetic then converts to pair plasma then back to equipartition seems very contrived and has no known physical basis.1149 The only causal scenario for plasmoid evolution is one in which an energelic plasmoicd is created by magnetic forces., The only causal scenario for plasmoid evolution is one in which an energetic plasmoid is created by magnetic forces.1150 The magnetically dominated object clissipates its energy into violent shocks. nonlinear MIID waves and high power reconnection evenis. thereby converüng magnetic energv into a relativisticallv hot pair plasma.," The magnetically dominated object dissipates its energy into violent shocks, nonlinear MHD waves and high power reconnection events, thereby converting magnetic energy into a relativistically hot pair plasma."1151 Thusly motivated. one can explore (he magnetically dominated (ime evolution (rack rough solution space in detail," Thusly motivated, one can explore the magnetically dominated time evolution track through solution space in detail."1152 Figure 15 is a plot of the radius of C2 versus time for je magnetic solutions (hat conserve enerev and approach the mininnun energy solution on December 14 as indicated in Figure 14., Figure 15 is a plot of the radius of C2 versus time for the magnetic solutions that conserve energy and approach the minimum energy solution on December 14 as indicated in Figure 14.1153 The solutions follow a (track of uniform expansion very loselv., The solutions follow a track of uniform expansion very closely.1154 The time offset was adjusted in such a wav that all the solutions reach approximately zero radius at time zero., The time offset was adjusted in such a way that all the solutions reach approximately zero radius at time zero.1155 All values of Γρ vield virtually the same offset. indicating that 1e plasmoid was 1.6 davs old on December 6.," All values of $E_{min}$ yield virtually the same offset, indicating that the plasmoid was 1.6 days old on December 6."1156" For £,,;,—1. 5. 10. 20. 30. the least squares fit to (he expansion rate. d2/dl. is 0.0085c. 0.0082ce. 0.0078e. 0.0069c and 0.0064c. respectively."," For $E_{min}$ =1, 5, 10, 20, 30, the least squares fit to the expansion rate, $dR/dt$, is 0.0085c, 0.0082c, 0.0078c, 0.0069c and 0.0064c, respectively."1157" One can perform an analvsis similar to Chat which was done lor Figure 11 for the protonic plasmoids using equation (16) to restrict the allowable range of £2,,5", One can perform an analysis similar to that which was done for Figure 11 for the protonic plasmoids using equation (16) to restrict the allowable range of $E_{min}$.1158" Figure 14 is used to illustrate this and also plot the power. Q(Im)=Qj,(injected). required by the central engine lo enereize and eject the lepontic plasmoids at relativistic velocities. where (he conversion from £ is givenby equation (14)."," Figure 14 is used to illustrate this and also plot the power, $Q(\mathrm{lm})\equiv Q_{\mathrm{lm}}(\mathrm{injected})$, required by the central engine to energize and eject the lepontic plasmoids at relativistic velocities, where the conversion from $E$ is givenby equation (14)."1159 The plots of Q(Im) are color coded so that each model is the same color at all three epochs., The plots of $Q(\mathrm{lm})$ are color coded so that each model is the same color at all three epochs.1160 Recall that the restriction discussed in Section 4 arises because large values of D require small values of E(1.4GIIz) to create a svnchrotron peak near 1.4 Gllz., Recall that the restriction discussed in Section 4 arises because large values of $B$ require small values of $E(\mathrm{1.4 GHz})$ to create a synchrotron peak near 1.4 GHz.1161 The spectral fits indicate that the 1.4 GIIz flux is large and only appears suppressed because of svnclirotron-sell absorption (i.e. the background power law spectrum should extend lower than 1.4 Gllz).," The spectral fits indicate that the 1.4 GHz flux is large and only appears suppressed because of synchrotron-self absorption (i,e, the background power law spectrum should extend lower than 1.4 GHz)."1162" The restriction equates to Z(1.4Gllz)>£,,;,.", The restriction equates to $E(\mathrm{1.4 GHz})>E_{min}$.1163" As for Figure 11. the color coded short vertical lines and arrows indicate the radius of the model such (hat D is sulficiently large that equation (16) implies. E(1.4GlIz)=£,,;,."," As for Figure 14, the color coded short vertical lines and arrows indicate the radius of the model such that $B$ is sufficiently large that equation (16) implies, $E(\mathrm{1.4 GHz})=E_{min}$."1164 The arrow points to the left. the region of smaller D. where E(1.4GlIz)>ο and the solutions are allowed.," The arrow points to the left, the region of smaller $B$, where $E(\mathrm{1.4 GHz})> E_{min}$ and the solutions are allowed."1165 To the right of the vertical partition. 2 is larger. therelore E(1.4G1Iz)<£5 anc the solutions are forbidden.," To the right of the vertical partition, $B$ is larger, therefore $E(\mathrm{1.4 GHz})< E_{min}$ and the solutions are forbidden."1166 These partitions were added to the December ο. 1993. plots.," These partitions were added to the December 6, 1993 plots."1167" In the the evolutionary (rack in which magnetic energy is converted to mechanical energy. the magnetic field is largest at this epoch and therefore more likely to provide the lightest constraint on £2,,,."," In the the evolutionary track in which magnetic energy is converted to mechanical energy, the magnetic field is largest at this epoch and therefore more likely to provide the tightest constraint on $E_{min}$ ."1168 In summary. (he solution space is restricted by (τος constraints.," In summary, the solution space is restricted by three constraints,"1169"that its velocity vector lies in the plane that contains n, and v and is defined by r-(n,xv/|v|)=0.",that its velocity vector lies in the plane that contains $\vecbf{n}_s$ and $\vecbf{v}$ and is defined by $\vecbf{r}\cdot(\vecbf{n}_s\times \vecbf{v}/|v|)=0$.1170" The intersection of this plane and the plane of the sky (given by z—0 for our choice of coordinates) yields the past transverse orbit of the post-shock gas, vo. ("," The intersection of this plane and the plane of the sky (given by $z=0$ for our choice of coordinates) yields the past transverse orbit of the post-shock gas, $v_\rmn{2,t}$. ("1171"5) Solving Equation (9)) for the unknown shock obliquity ¢ enables us to derive the current radial position of the galaxy (relative to the cluster center) according to rg]=Rs— with v=v,V1+tan?0. (",5) Solving Equation \ref{eq:v2t}) ) for the unknown shock obliquity $\phi$ enables us to derive the current radial position of the galaxy (relative to the cluster center) according to $r_\rmn{gal}=R_s - v \tau_s \cos\phi$ with $v=v_r\sqrt{1+\tan^2\theta}$. (1172"6) We compare the galaxy’s velocity, v, to the escape velocity, vesc(Tgal)=V2GM(< rga)/rga.","6) We compare the galaxy's velocity, $v$, to the escape velocity, $v_\rmn{esc}(r_\rmn{gal})=\sqrt{2G1173 M(<r_\rmn{gal})/r_\rmn{gal}}$ ."1174" For the large radial velocity of v,=2170kms! it is not trivial to meet the criterion, US Vege, stating that, the galaxy is gravitationally bound; hence we prefer small values of R, and 0<32° (while still evading the electron cooling bound on 0 as derived in Equation (4)))."," For the large radial velocity of $v_r=2170\,\rmn{km~s}^{-1}$, it is not trivial to meet the criterion, $v\lesssim1175v_\rmn{esc}$ , stating that the galaxy is gravitationally bound; hence we prefer small values of $R_s$ and $\theta \lesssim 32^\circ$ (while still evading the electron cooling bound on $\theta$ as derived in Equation \ref{eq:theta}) ))."1176" The head-tail morphology of the jet also argues for a large ram pressure that it can only experience inside Roo9 and hence for small values of R,.", The head-tail morphology of the jet also argues for a large ram pressure that it can only experience inside $\sim R_{200}$ and hence for small values of $R_s$.1177 We finally check whether the model violates any constraints on the shock obliquity ¢ as will be derived in Section 5.2.., We finally check whether the model violates any constraints on the shock obliquity $\phi$ as will be derived in Section \ref{sec:stability}.1178" If this does not yield a consistent model we vary the shock radius R,, the inclination of the galaxy’s orbit 0, and the position of the galaxy’s shock crossing, O, and start the next iteration until we arrive at a consistent and physically plausible model."," If this does not yield a consistent model we vary the shock radius $R_s$, the inclination of the galaxy's orbit $\theta$, and the position of the galaxy's shock crossing, $\mathcal{O}$, and start the next iteration until we arrive at a self-consistent and physically plausible model."1179" Our final model that fits best these constraints is shown in Figure 3 and has the parameters C,— 3.4, Rs=Roo 1.9Mpc, 6=32°, ὁ=9°, x=23°."," Our final model that fits best these constraints is shown in Figure \ref{fig3}1180 and has the parameters $C_s=3.4$ , $R_s=R_{200}=1.9\,$ Mpc, $\theta=32^\circ$, $\phi=9^\circ$, $\chi=23^\circ$."1181" We find the time since shock crossing of NGC 1265 to be 1.8x108yr, the Cartesian vector of the shock normal n=(0.2,0.34,0.92), and the velocity vector for NGC 1265 of v=—v(0,sin0,cos (note that we define the Cartesian coordinate system6) in Figure 3))."," We find the time since shock crossing of NGC 1265 to be $1.8\times10^8\,\rmn{yr}$, the Cartesian vector of the shock normal $\vecbf{n}=(0.2,0.34,0.92)$, and the velocity vector for NGC 1265 of $\vecbf{v}=-v\,(0,\sin\theta,\cos\theta)$ (note that we define the Cartesian coordinate system in Figure \ref{fig3}) )."1182" The galaxy’s velocity has a radial and transverse component of v,=2170kms! and Uy= s, respectively, which yields a total velocity of the galaxy, v=2550kms!."," The galaxy's velocity has a radial and transverse component of $v_r=2170\,\rmn{km~s}^{-1}$ and $v_t=1360\,\rmn{km~s}^{-1}$ , respectively, which yields a total velocity of the galaxy, $v=2550\,\rmn{km~s}^{-1}$."1183" This is only slightly larger than the escape velocity, =2350kms+, where we used Τραι= 1.45Mpc, vesc(rgai)M(<rga)XturbM200=9x neglect a logarithmic correction factor of the mass 10'4Mo,and assume a turbulent pressure support of Xturb=0.2 (???).. "," This is only slightly larger than the escape velocity, $v_\rmn{esc}(r_\rmn{gal}) = 2350\,\rmn{km~s}^{-1}$, where we used $r_\rmn{gal}=1.45\,$ Mpc, $M(<r_\rmn{gal})\simeq X_\rmn{turb}1184M_{200}=9\times10^{14}M_\odot$ , neglect a logarithmic correction factor of the mass and assume a turbulent pressure support of $X_\rmn{turb}=0.2$ \citep{2008Sci...320..909R, 2009ApJ...705.1129L, 2010ApJ...725...91B}."1185"Note that if one relaxes the escape velocity constraint and assumes that tidal processes are able to dissipate more energy to bind the galaxy during first passage, we find consistent solutions at larger shock radii that nevertheless lie close-by in the parameter space (θ,Φ,χ,6Ο)."," Note that if one relaxes the escape velocity constraint and assumes that tidal processes are able to dissipate more energy to bind the galaxy during first passage, we find consistent solutions at larger shock radii that nevertheless lie close-by in the parameter space $(\theta,\phi,\chi,\mathcal{O})$."1186 The choice of the virial radius as the site of the accretion shock might seem to be too small compared to the typical locations inferred from cosmological simulations (???)..," The choice of the virial radius as the site of the accretion shock might seem to be too small compared to the typical locations inferred from cosmological simulations \citep{2000ApJ...542..608M, 2007ApJ...669..729K, 2008MNRAS.385.1211P}."1187" However, the location of the accretion shock (in particular along a filament) is not stationary but dynamically determined."," However, the location of the accretion shock (in particular along a filament) is not stationary but dynamically determined."1188" Depending on the ram pressure of the accreting material and the post-shock pressure, its position will re-adjust dynamically to account for the conservation laws."," Depending on the ram pressure of the accreting material and the post-shock pressure, its position will re-adjust dynamically to account for the conservation laws."1189 We have shown that the velocity of NGC 1265 is quite large which implies a large ram pressure and hence should yield a shock position that liescloser toward the cluster center compared to the shock position where dilute IGM accretes from voids with a considerable smaller density and ram pressure., We have shown that the velocity of NGC 1265 is quite large which implies a large ram pressure and hence should yield a shock position that liescloser toward the cluster center compared to the shock position where dilute IGM accretes from voids with a considerable smaller density and ram pressure.1190 We note that there have been attempts to constrain the 3D velocity of NGC 1265 based on, We note that there have been attempts to constrain the 3D velocity of NGC 1265 based on1191"on December 27th, 2004 in the energy range from 80 keV to 8 MeV (?)..","on December 27th, 2004 in the energy range from 80 keV to 8 MeV \citep{mere05}."1192 SGR 1806-20 is known to have a rotational period of 7.56 s and the methodology adopted here should be able to recover this periodicity., SGR 1806-20 is known to have a rotational period of 7.56 s and the methodology adopted here should be able to recover this periodicity.1193 We removed the very bright initial pulse and focused on the emission from ~50 s to 175 s (see Fig[3))., We removed the very bright initial pulse and focused on the emission from $\approx 50$ s to 175 s (see \ref{fig:sgr}) ).1194" We unambiguously recover the main pulsation period (P~7.56 s) together with the first, second, third and fifth harmonic."," We unambiguously recover the main pulsation period $P\approx 7.56$ s) together with the first, second, third and fifth harmonic."1195 We conclude that the here applied methodology is appropriate and reliable for the further analysis., We conclude that the here applied methodology is appropriate and reliable for the further analysis.1196" For the purpose of its analysis we use CSPEC and CTIME data of detectors Nal 3, Nal 4 and Nal 5 with a time-resolution of 1.024 s (4.096 s pre-trigger) and 0.064 s (0.256 s pre-trigger), respectively."," For the purpose of its analysis we use CSPEC and CTIME data of detectors NaI 3, NaI 4 and NaI 5 with a time-resolution of 1.024 s (4.096 s pre-trigger) and 0.064 s (0.256 s pre-trigger), respectively."1197 In the energy range from 50 keV to 1 MeV this solar flare lasted for about 500 s. The light curve (Fig) consists of several peaks and a compellingly looking quasi-periodic behavior lasting to ~500 s. After de-trending the raw light curve with a simple moving average (50 s) the QPP pattern becomes more visible (see inset of FigH))., In the energy range from 50 keV to 1 MeV this solar flare lasted for about 500 s. The light curve \ref{fig:110224312_sfl}) ) consists of several peaks and a compellingly looking quasi-periodic behavior lasting to $\approx 500$ s. After de-trending the raw light curve with a simple moving average (50 s) the QPP pattern becomes more visible (see inset of \ref{fig:110224312_sfl}) ).1198 Applying a standard periodogram analysis (??) on the light curve several peaks are above the 3σ confidence limit as can be seen in the middle panel of Fig/4}.," Applying a standard periodogram analysis \citep{lomb76, scargle82} on the light curve several peaks are above the $3\sigma$ confidence limit as can be seen in the middle panel of \ref{fig:110224312_sfl}."1199" However, applying the previously introduced method (?) on the original light curve, thus taking into account the red-noise properties of the source we did not find any significant QPP during the solar flare life-time, as is pointed out in the lower panel of Fig]."," However, applying the previously introduced method \citep{vaughan05} on the original light curve, thus taking into account the red-noise properties of the source we did not find any significant QPP during the solar flare life-time, as is pointed out in the lower panel of \ref{fig:110224312_sfl}."1200 We performed this analysis making use of the CTIME data with a time resolution of 64 ms., We performed this analysis making use of the CTIME data with a time resolution of 64 ms.

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