ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" Recall, that a function A:(0.5c)—IE is called whenever 1t saüsfies the Cauchy equation, that is AGe4gy)=ACr)+ Ay) nig>0."," Recall, that a function $A:(0,\infty)\to\R$ is called whenever it satisfies the Cauchy equation, that is $A(x+y)=A(x)+A(y)$ , $x,y>0$."3" Similarly, à function £:(0.56)—IE is termed funcuon provided that {αμ=Lor)+Lay). i.y>0."," Similarly, a function $L:(0,\infty)\to\R$ is termed function provided that $L(xy)=L(x)+L(y)$, $x,y>0$."4" Semi-constant, additive and logarithmic type funcuons will play the crucial role in our approach to the Olkin-Baker equation, when no regularity conditions are imposed onthe unknown functions."," Semi-constant, additive and logarithmic type functions will play the crucial role in our approach to the Olkin-Baker equation, when no regularity conditions are imposed onthe unknown functions."5even at zο6 bv ~20—30%.,even at $z\gtrsim 6$ by $\sim 20-30$.6. This is because the gas density becomes higher and temperature becomes lower (see ligure 5ec) by responding to the enhanced cooling rate by metals., This is because the gas density becomes higher and temperature becomes lower (see Figure \ref{fig:Evolv4}c c) by responding to the enhanced cooling rate by metals.7 In summary. we consider that our study serves to demonstrate the importance of metal enrichment and metal cooling in galaxy formation. bevond our original motivation o perform a simple numerical study.," In summary, we consider that our study serves to demonstrate the importance of metal enrichment and metal cooling in galaxy formation, beyond our original motivation to perform a simple numerical study."8 Our study highlights he role of metals at Γουντς and high-z to enhance the star ormation in the Universe. and demonstrates that the metals increase the SE ellicienev in the star-forming ISM. as well as enabling more IGM to acercte onto galaxies and fuel star ormation.," Our study highlights the role of metals at $z$ and $z$ to enhance the star formation in the Universe, and demonstrates that the metals increase the SF efficiency in the star-forming ISM, as well as enabling more IGM to accrete onto galaxies and fuel star formation."9 We expect that metal cooling would. also alter some of the galaxy properties such as the mass-metallicity relationship (e.g..Tremontietal.2004). and specific SER (c.g..Noeskeetal.2007).," We expect that metal cooling would also alter some of the galaxy properties such as the mass-metallicity relationship \citep[e.g.,][]{Tremonti.etal:04} and specific SFR \citep[e.g.,][]{Noeske.etal:07}."10. We plan to investigate these issues in the future. as well as alternative models for star formation and feedback.," We plan to investigate these issues in the future, as well as alternative models for star formation and feedback."11 We thank V. Springel for allowing us to use the updated version of. code for our study. and for useful comments on the manuscript.," We thank V. Springel for allowing us to use the updated version of code for our study, and for useful comments on the manuscript."12 KN is grateful. for. the hospitality. of Institute for the Physics anc Mathematics of the Universe. University of Tokvo. where part. of this work was done.," KN is grateful for the hospitality of Institute for the Physics and Mathematics of the Universe, University of Tokyo, where part of this work was done."13 We are also grateful to the anonymous referee for constructive comments which improved. this paper., We are also grateful to the anonymous referee for constructive comments which improved this paper.14" ""his research was supported. in part by the National Acronautics anc Space Achministration under Crant{Cooperative Agreement No.", This research was supported in part by the National Aeronautics and Space Administration under Grant/Cooperative Agreement No.15 NNNOSAIZ57. issued by the Nevada NASA ος program. by. the National Science Foundation through TeraCirid resources provided by the San Diego Supercomputer Center (SDSC). and by the President's Infrastructure Award at UNLV.," NNX08AE57A issued by the Nevada NASA EPSCoR program, by the National Science Foundation through TeraGrid resources provided by the San Diego Supercomputer Center (SDSC), and by the President's Infrastructure Award at UNLV."16 The simulations were performed at the UNLY Cosmology Computing Cluster and the Datastar at SDSC., The simulations were performed at the UNLV Cosmology Computing Cluster and the Datastar at SDSC.17Observations of distant tvpe la supernovae (SNIa) indicate that the universe is undergoing a phase of accelerated expansion (Perlmutter ct al.,Observations of distant type Ia supernovae (SNIa) indicate that the universe is undergoing a phase of accelerated expansion (Perlmutter et al.18 L999. Itiess 1905].," 1999, Riess 1998)."19 This. combined with the αι geometry favored by the cosmic microwave backeround (CAIB) measurements (Miller et al.," This, combined with the flat geometry favored by the cosmic microwave background (CMB) measurements (Miller et al."20 1999. de Bernardis ct al.," 1999, de Bernardis et al."21 2002. Llalverson οἱ al.," 2002, Halverson et al."22 2002. Sievers et al.," 2002, Sievers et al."23 2002. Lee et al.," 2002, Lee et al."24 2001) and the evidence for a low matter-censity with Qy~0.3 (Peacock 2001. Percival et al.," 2001) and the evidence for a low matter-density with $\Omega_0 \sim 0.3$ (Peacock 2001, Percival et al."25 2001). suggests that the bulk of the total energy. density of the universe is in the form of some exotic clark energy with a negative equation of state.," 2001), suggests that the bulk of the total energy density of the universe is in the form of some exotic dark energy with a negative equation of state."26 One of the primary objectives of cosmology today is to uncover the origin and nature of this dark energy., One of the primary objectives of cosmology today is to uncover the origin and nature of this dark energy.27 A possible candidate for the dark. energy is a cosmological constant A. with an equation of state w=p/p (where p is the pressure ancl p is the energy density of the dark energy) strictly equal το 1.," A possible candidate for the dark energy is a cosmological constant $\Lambda$, with an equation of state $w = p / \rho$ (where $p$ is the pressure and $\rho$ is the energy density of the dark energy) strictly equal to $-1$."28 Another possibility. and one that may find favor from a particle-physics point of view. is a dynamical scalar field. termed. quintessence. €.," Another possibility, and one that may find favor from a particle-physics point of view, is a dynamical scalar field, termed quintessence, $Q$."29 Unlike the cosmological constant. the Q-component is both time-dependent and spatially inhomogencous with an equation of state wo1 that is likely to be redshift) dependent.," Unlike the cosmological constant, the $Q$ -component is both time-dependent and spatially inhomogeneous with an equation of state $w > -1$ that is likely to be redshift dependent."30 Determining the value of w and how it changes with time are key to constraining the nature of the dark energy., Determining the value of $w$ and how it changes with time are key to constraining the nature of the dark energy.31spectrum of density fluctuations. (A).,"spectrum of density fluctuations, $P(k)$."32 This latter quantity provides a very convenient means of describing structure in the Universe for a number of reasons., This latter quantity provides a very convenient means of describing structure in the Universe for a number of reasons.33 Firstly its primordial form is produced by models of inflation. which prescribe the initial pattern of density [uctuations 9p/p.," Firstly its primordial form is produced by models of inflation, which prescribe the initial pattern of density fluctuations $\delta\rho/\rho$."34 Furthermore. in linear theory for t1e growth of perturbations. Huctuations described by cülfercnt wavenumboers & evolve independently. enabling the mode power spectrum to be easily scaled with redshift.," Furthermore, in linear theory for the growth of perturbations, fluctuations described by different wavenumbers $k$ evolve independently, enabling the model power spectrum to be easily scaled with redshift."35 Phe physies of linear perturbations are hence more naturally clescribec Lin Fourier space., The physics of linear perturbations are hence more naturally described in Fourier space.36 In contrast. t1e angular correlation function is more easily related. to tje spatial correlation function £(r). the Fourier transform of Pik).," In contrast, the angular correlation function is more easily related to the spatial correlation function $\xi(r)$, the Fourier transform of $P(k)$."37 Correlation functions more naturally serve tocescribe the real-space profile of collapsing structures evolving out of the linear regime., Correlation functions more naturally serve to describe the real-space profile of collapsing structures evolving out of the linear regime.38 We emphasize that although the two functions C and w(8) arefheorelically equivalent — linke| by a Legendre transform — this is not true in anobservational sense., We emphasize that although the two functions $C_\ell$ and $w(\theta)$ are equivalent – linked by a Legendre transform – this is not true in an sense.39 For example. (0) can only be successfully measured for angles up to a few degrees. but C'; depends on w(8) ataff angles.," For example, $w(\theta)$ can only be successfully measured for angles up to a few degrees, but $C_\ell$ depends on $w(\theta)$ at angles."40 We derive the angular power spectrum using two independent methods., We derive the angular power spectrum using two independent methods.41 Firstly. we apply a direct. spherical harmonic estimator following Peebles (1973)., Firstly we apply a direct spherical harmonic estimator following Peebles (1973).42 Secondly. we use maximum: likelihood estimation. commonly emploved for deriving the angular power spectra of the CALB temperature and polarization maps.," Secondly, we use maximum likelihood estimation, commonly employed for deriving the angular power spectra of the CMB temperature and polarization maps."43 ποσο two methods are described in Section 3.., These two methods are described in Section \ref{secmeth}.44 We find that these two approaches vielcl very similar results (Section 4)). which is unsurprising given the wide sky coverage of the NVSS.," We find that these two approaches yield very similar results (Section \ref{secres}) ), which is unsurprising given the wide sky coverage of the NVSS."45 In Section 5 we interpret the NVSS angular power spectrum in terms of the underlving spatial power spectrum of mass fluctuations and the racial distribution of radio sources., In Section \ref{secpk} we interpret the NVSS angular power spectrum in terms of the underlying spatial power spectrum of mass fluctuations and the radial distribution of radio sources.46 Finally in Section 6 we employ these models to derive the linear bias factor of NVSS radio ealaxies by marginalizing over the other mocel parameters., Finally in Section \ref{secbias} we employ these models to derive the linear bias factor of NVSS radio galaxies by marginalizing over the other model parameters.47 Vhe L4 Gllz NRAO VLA Sky Survey (NVSS: Condon et al., The 1.4 GHz NRAO VLA Sky Survey (NVSS; Condon et al.48 1998) was performed at the Very Large Array over the period 1993 to 1996 and covers the sky north of declination —40, 1998) was performed at the Very Large Array over the period 1993 to 1996 and covers the sky north of declination $-40^\circ$.49" The source catalogue contains 2L.8«10"" entries and is 99 per cent complete at integrated. Lux density S,τον=3.5 mv."," The source catalogue contains $\approx 1.8 \times 10^6$ entries and is 99 per cent complete at integrated flux density $S_{\rm 1.4 \, GHz} = 3.5$ mJy."50 The full width at half-maximum of the svnthesizec beam is 45 aresec: the majority of radio sources are thus unresolved., The full width at half-maximum of the synthesized beam is 45 arcsec; the majority of radio sources are thus unresolved.51 The relatively broad NVSS beam vields excellen surface brightness sensitivity and photometric completeness., The relatively broad NVSS beam yields excellent surface brightness sensitivity and photometric completeness.52 [fore analvzing the survey for large-scale structure we imposed various angular masks., Before analyzing the survey for large-scale structure we imposed various angular masks.53 Fiestlv we exclude catalogue entries within 5° of the Galactic plane. many of which are Galactic in origin (mostly. supernova remnants and LIE regions).," Firstly we excluded catalogue entries within $5^\circ$ of the Galactic plane, many of which are Galactic in origin (mostly supernova remnants and HII regions)."54 The contribution of foreground. Galactic sources at latitudes [b]25! is negligible., The contribution of foreground Galactic sources at latitudes $|b| > 5^\circ$ is negligible.55 We also. place, We also placed56We have already. established which rauk two vector buudles can arise as R'a.Ox for a four-fold with trivial canonical bundle X fibred over I? by abelian surfaces;,We have already established which rank two vector bundles can arise as $R^1\pi_*\O_X$ for a four-fold with trivial canonical bundle $X$ fibred over $\P^2$ by abelian surfaces.57 Recall that Παπ.ον ust be one of the following: If X is the compactified relative Jacobian of a family of curves with mild degenerations. then the generic singular fibre of X>E? will be the compactified Jacobian of a curve with a single node.," Recall that $R^1\pi_*\O_X$ must be one of the following: If $X$ is the compactified relative Jacobian of a family of curves with mild degenerations, then the generic singular fibre of $X\rightarrow\P^2$ will be the compactified Jacobian of a curve with a single node."58 In this case. both of the conditionsiu Lenuua 13. will be satisfied. μηνπο οπ.Ον)=3.," In this case, both of the conditionsin Lemma \ref{first_chern} will be satisfied, implying $c_1(R^1\pi_*\O_X)=-3$."59 This Q.s(.2) is impossible: we are left with the three other possibilities., Thus $\O_{\P^2}(-2)\oplus\O_{\P^2}(-2)$ is impossible; we are left with the three other possibilities.60 Returning to the construction of the family of curves. WT ust be isomorphic to Rf.Oy. up to tensoring with a line bundle.," Returning to the construction of the family of curves, $W$ must be isomorphic to $R^1f_*\O_Y$ up to tensoring with a line bundle."61" We can normalize the first Cheri class of W by assunniug this liue bundle is trivial. νου, we set The isomorplisin of Lema 20. then vields and hence the branch divisor is the zero locus of a generic section of on IC)."," We can normalize the first Chern class of $W$ by assuming this line bundle is trivial, i.e., we set The isomorphism of Lemma \ref{normalize} then yields and hence the branch divisor is the zero locus of a generic section of on $\P(W)$ ."62" Now We consider the three possibilities for W2REf.O,y.=Riz. Ox.", Now We consider the three possibilities for $W\cong R^1f_*\O_Y\cong R^1\pi_*\O_X$ .63"yields come from the theoretical predictions of the Geneva group, which include only the pre-supernovae phase.","yields come from the theoretical predictions of the Geneva group, which include only the pre-supernovae phase."64" Our models can reproduce these ratios well, and also predict some stars in the locus of HE 0107—5240, whereas HE 1327—2326 is not reproduced."," Our models can reproduce these ratios well, and also predict some stars in the locus of HE $-$ 5240, whereas HE $-$ 2326 is not reproduced."65" Moreover, our models cannot account for the CEMP-no stars."," Moreover, our models cannot account for the CEMP-no stars."66" For nitrogen, there is a marginal disagreement in the intermediate metallicity range, pointing to an extra source of nitrogen not accounted for in our models."," For nitrogen, there is a marginal disagreement in the intermediate metallicity range, pointing to an extra source of nitrogen not accounted for in our models."67 As discussed in Chiappini et al. (, As discussed in Chiappini et al. (68"2006, 2008) and Pipino et al. (","2006, 2008) and Pipino et al. ("69"2009), this is most probably because current chemical evolution models do not include the contribution of super AGB stars.","2009), this is most probably because current chemical evolution models do not include the contribution of super AGB stars."70" Super AGB stars could contribute with important quantities of nitrogen, and their contribution would be visible just before the appearance of the intermediate-mass stars (Chiappini et al."," Super AGB stars could contribute with important quantities of nitrogen, and their contribution would be visible just before the appearance of the intermediate-mass stars (Chiappini et al."71 in prep.)., in prep.).72" Finally, although our models cannot explain the [N/Fe] ratio of HE 1327-2326, we are able to reach the very low enrichment in Fe observed in this star and to predict almost the correct ratios of [C/Fe] and [O/Fe] in models A and B, in the chemical inhomogeneous framework."," Finally, although our models cannot explain the [N/Fe] ratio of HE $-$ 2326, we are able to reach the very low enrichment in Fe observed in this star and to predict almost the correct ratios of [C/Fe] and [O/Fe] in models A and B, in the chemical inhomogeneous framework."73" Moreover, we reproduce the ratio of the three elements [C/Fe], [N/Fe], and [O/Fe] for the other star with an [Fe/H] €—5, namely, HE 0107-5240."," Moreover, we reproduce the ratio of the three elements [C/Fe], [N/Fe], and [O/Fe] for the other star with an [Fe/H] $\lesssim -5$, namely, HE $-$ 5240."74 We also reproduce HE 0557—4840 discovered and analyzed by Norris et al (2007) for which we only have the [C/Fe] ratio., We also reproduce HE $-$ 4840 discovered and analyzed by Norris et al (2007) for which we only have the [C/Fe] ratio.75" In this paper we have shown the results of an inhomogeneous chemical evolution model for the mean trend and scatter of C/O and N/O in the Galactic halo, taking the contribution of rotator stars into account."," In this paper we have shown the results of an inhomogeneous chemical evolution model for the mean trend and scatter of C/O and N/O in the Galactic halo, taking the contribution of fast-rotator stars into account."76 The observational studies of chemical enrichment in very metal-poor stars of the halo have found a large scatter (larger than the uncertainties in the derived abundances) for the measured C/O and N/O. A large scatter was also found for neutron capture elements in the same stars., The observational studies of chemical enrichment in very metal-poor stars of the halo have found a large scatter (larger than the uncertainties in the derived abundances) for the measured C/O and N/O. A large scatter was also found for neutron capture elements in the same stars.77" These findings contrast with the results for a-elements, which instead presented striking homogeneous [a/Fe] ratios."," These findings contrast with the results for $\alpha$ -elements, which instead presented striking homogeneous $\alpha$ /Fe] ratios."78" In Cescutti (2008), the spread in the chemical abundance ratios of neutron capture elements has been explained with a different mass range for the production of these elements (from 12 to 30 Μο). compared to the whole range of massive stars for the a-"," In Cescutti (2008), the spread in the chemical abundance ratios of neutron capture elements has been explained with a different mass range for the production of these elements (from 12 to 30 $_{\odot}$ ), compared to the whole range of massive stars for the $\alpha$ -elements."79" In this work the nucleosynthesis differences for the elements C, N, and O come from the rotation of massive stars, which strongly affects the ratio of the production among these elements at low metallicity (see Hirschi et al."," In this work the nucleosynthesis differences for the elements C, N, and O come from the rotation of massive stars, which strongly affects the ratio of the production among these elements at low metallicity (see Hirschi et al."80 2007)., 2007).81" Moreover, we consider two possible contributions to the enrichment of the ISM by massive stars at very low metallicity, the usual enrichment through supernovae ejecta, and the enrichment only through their stellar winds."," Moreover, we consider two possible contributions to the enrichment of the ISM by massive stars at very low metallicity, the usual enrichment through supernovae ejecta, and the enrichment only through their stellar winds."82 We find that the assumption that the most massive fast rotators only contribute to the ISM enrichment via stellar winds leads to chemical evolution models that are able to account for both the large scatter in the N/O and C/O and the simultaneous lack of scatter in a-elements observed in very metal-poor normal halo stars., We find that the assumption that the most massive fast rotators only contribute to the ISM enrichment via stellar winds leads to chemical evolution models that are able to account for both the large scatter in the N/O and C/O and the simultaneous lack of scatter in $\alpha$ -elements observed in very metal-poor normal halo stars.83" In fact, the stellar yields of the latter elements do not show any strong dependency on the stellar mass, contrary to what happens for N, C, and n-capture elements."," In fact, the stellar yields of the latter elements do not show any strong dependency on the stellar mass, contrary to what happens for N, C, and n-capture elements."84" In this context, we also explored whether the scatter in N and C created by the strong yields dependence on the stellar mass, when including the fast rotators, would also account for the existence of the so-called carbon-enhanced stars (in particular the CEMP-no ones)."," In this context, we also explored whether the scatter in N and C created by the strong yields dependence on the stellar mass, when including the fast rotators, would also account for the existence of the so-called carbon-enhanced stars (in particular the CEMP-no ones)."85" We find that, even when considering that the more massive fast rotators enrich the early ISM mainly via stellar winds strongly enhanced in CNO, it is impossible to explain the abundances observed in CEMP-no stars."," We find that, even when considering that the more massive fast rotators enrich the early ISM mainly via stellar winds strongly enhanced in CNO, it is impossible to explain the abundances observed in CEMP-no stars."86" However, we point out that the latter model marginally agrees with the abundance ratios of the only CEMP-r star for which the CNO abundances have been measured, and of the two of the three UMP stars known to date, HE 0107—5240 and HE 0557—4840."," However, we point out that the latter model marginally agrees with the abundance ratios of the only CEMP-r star for which the CNO abundances have been measured, and of the two of the three UMP stars known to date, HE $-$ 5240 and HE $-$ 4840."87 These results suggest that very metal-poor massive stars would collapse directly into black holes as predicted by Heger et al. (, These results suggest that very metal-poor massive stars would collapse directly into black holes as predicted by Heger et al. (882003).,2003).89" The discrepancy with respect to the CEMP-no stars, and in particular, HE 1327—2326, suggest that these objects are born from the gas expelled during the wind phase of fast rotators, without much mixing with the surrounding ISM."," The discrepancy with respect to the CEMP-no stars, and in particular, HE $-$ 2326, suggest that these objects are born from the gas expelled during the wind phase of fast rotators, without much mixing with the surrounding ISM."90" A way to test this hypothesis is to look for the abundances of ""Li, ?C/P?C, and helium in CEMP-no stars."," A way to test this hypothesis is to look for the abundances of $^{7}$ Li, $^{12}$ $^{13}$ C, and helium in CEMP-no stars."91" In fact, the wind material is"," In fact, the wind material is"92"Way, the LMC, and the SMC.","Way, the LMC, and the SMC."93" The Milky Way gas metallicity is represented by the Orion Nebula (12+log(O/H)= 8.58), which has a similar metallicity to local B-type stars (Peimbert1987;Gies&Lambert1992;KilianMathis 2000)."," The Milky Way gas metallicity is represented by the Orion Nebula $12+\log (\mathrm{O/H})=8.58$ ), which has a similar metallicity to local B-type stars \citep{peimbert87,gies92,kilian92,mathis00}."94". For the LMC and the SMC, we adopt the oxygen abundance from Dufour(1984) (12+log(O/H)=8.43 and 8.02, respectively)."," For the LMC and the SMC, we adopt the oxygen abundance from \citet{dufour84} $12+\log (\mathrm{O/H})=8.43$ and 8.02, respectively)."95 We confirm that metal-poor galaxies tend to have high dust temperatures., We confirm that metal-poor galaxies tend to have high dust temperatures.96 We should keep in mind that the story of star formation properties in terms of metallicity is not so simple as we discussed above., We should keep in mind that the story of star formation properties in terms of metallicity is not so simple as we discussed above.97 Engelbrachtetal.(2008) show that the dust temperature shows the peak around 12+log(O/H)~8., \citet{engelbracht08} show that the dust temperature shows the peak around $12+\log (\mathrm{O/H})\sim 8$.98" Due to our small sample in such a low metallicity range, we cannot confirm it, but their results imply that the size and density of star-forming region is not a monotonic function of metallicity."," Due to our small sample in such a low metallicity range, we cannot confirm it, but their results imply that the size and density of star-forming region is not a monotonic function of metallicity."99" There are also pieces of evidence that there are two categories of BCDs: ""active"" and “passive”.", There are also pieces of evidence that there are two categories of BCDs: “active” and “passive”.100" The former hosts compact and intense star formation activities, while the latter has diffuse star formation properties (Hunt,Giovanardi,&Helou2002;HirashitaHunt2004)."," The former hosts compact and intense star formation activities, while the latter has diffuse star formation properties \citep{hunt02,hirashita04}."101". Even with a similar metallicity, such a dichotomy exists, indicating that the star formation properties are not determined simply by the metallicity."," Even with a similar metallicity, such a dichotomy exists, indicating that the star formation properties are not determined simply by the metallicity."102 Active BCDs tend to be luminous in FIR because of large dust optical depth (Hirashita&Hunt2004)., Active BCDs tend to be luminous in FIR because of large dust optical depth \citep{hirashita04}.103". Thus, it would be possible that the current sample is biased to the ""active"" class."," Thus, it would be possible that the current sample is biased to the “active” class."104 The presence of BCDs hosting cold dust in Virgo Cluster (Popescuetal.2002) also implies that such a bias could be present., The presence of BCDs hosting cold dust in Virgo Cluster \citep{popescu02} also implies that such a bias could be present.105 This kind of bias should be examined in the future with more sensitive facilities., This kind of bias should be examined in the future with more sensitive facilities.106" Finally, it is worth questioning which of dust-to-gas ratio and metallicity is more fundamental in regulating dust temperature."," Finally, it is worth questioning which of dust-to-gas ratio and metallicity is more fundamental in regulating dust temperature."107 Larger absolute values of correlation coefficient found in Fig., Larger absolute values of correlation coefficient found in Fig.108 than those in Fig., \ref{fig:dg_clr} than those in Fig.109 6 imply that dust-to-gas ratio rather than metallicity is more strongly connected with dust temperature., \ref{fig:metal_clr} imply that dust-to-gas ratio rather than metallicity is more strongly connected with dust temperature.110" Thus,"," Thus,"111are selected. solely because. of their. large. [lux densities in the submillimetre waveband. are. candidates for further investigation as potential lenses: however. an optimized selection could be made if submillimetre/far-infrared colours were determining for these galaxies ina £45survey (Blain 19972).,"are selected solely because of their large flux densities in the submillimetre waveband, are candidates for further investigation as potential lenses; however, an optimized selection could be made if submillimetre/far-infrared colours were determining for these galaxies in a survey (Blain 1997a)."112 The sub-aresecond angular resolution and. excellen sensitivity of an MLX will allow the rapid. resolution and identification of any sources containing structures tha resemble ares or multiple images in the£485 and.Surveyor catalogues., The sub-arcsecond angular resolution and excellent sensitivity of an MIA will allow the rapid resolution and identification of any sources containing structures that resemble arcs or multiple images in the and catalogues.113 Most. catalogued sources are expectet to be distant active or vigorous star-forming galaxies. anc so are unlikely to be extended. or to contain significan substructure that could. be misinterpreted: as a signature of lensing.," Most catalogued sources are expected to be distant active or vigorous star-forming galaxies, and so are unlikely to be extended or to contain significant substructure that could be misinterpreted as a signature of lensing."114 The far-infrared luminosity of merging luminous starburst) galaxies at small redshifts is dominated: hy the emission. from a single compact core region. which is typically only several hundred parsees across (Solomon ct al.," The far-infrared luminosity of merging luminous starburst galaxies at small redshifts is dominated by the emission from a single compact core region, which is typically only several hundred parsecs across (Solomon et al."115 1997)., 1997).116 Llence. the detection of ares or multiple images in an ALLA follow-up observation would provide a strong indication that a lensecl galaxy had been found.," Hence, the detection of arcs or multiple images in an MIA follow-up observation would provide a strong indication that a lensed galaxy had been found."117 Based on the size of theLIRST andSurveyor catalogues and the estimated fractions of lensed. galaxies shown in 44. à catalogue containing several hundreds of galaxy. lenses across a large area of skv could be compiled.," Based on the size of the and catalogues and the estimated fractions of lensed galaxies shown in 4, a catalogue containing several hundreds of galaxy–galaxy lenses across a large area of sky could be compiled."118 The selection method. ensures that the Dux. densities of the candidates at a wavelength of jim. will be at cast mim.v. corresponding to a bolometric luminosity of order 107 LL..," The selection method ensures that the flux densities of the candidates at a wavelength of $\mu$ m will be at least mJy, corresponding to a bolometric luminosity of order $^{13}$ $_\odot$."119 Llenec. follow-up observations of these very uminous sources in other wavebands should. be relatively easy.," Hence, follow-up observations of these very luminous sources in other wavebands should be relatively easy."120 The candidates are expected to have properties similar o tha of the archetypal lensed ultraluminous galaxy£/2.15 EL10214|4724 (Rowan-Robinson et al., The candidates are expected to have properties similar to that of the archetypal lensed ultraluminous galaxy F10214+4724 (Rowan-Robinson et al.121 199). which has a L-rand magnitude of about 22.," 1991), which has a B-band magnitude of about 22."122 Lensed strucures were clearN detected. in near-infrared images of FP10214 using a 4mm-class telescope in a 90-minute integration (Close et al., Lensed structures were clearly detected in near-infrared images of F10214 using a m-class telescope in a 90-minute integration (Close et al.123 1995)., 1995).124 The Hux densities of the candidate sources are expected to be sulliciently large for many of them to appear in the48.15 faint source catalogue:ὃν however. they will constitute only a very small proportion of the total number of sources.," The flux densities of the candidate sources are expected to be sufficiently large for many of them to appear in the faint source catalogue; however, they will constitute only a very small proportion of the total number of sources."125 The accurate. counts of lensecl and ünlensed: galaxics derived. from this programme of observations could. be compared with model predictions. such as those shown in 33 and 4. in order to investigate the form of the work model and the growth of cosmic structure.," The accurate counts of lensed and unlensed galaxies derived from this programme of observations could be compared with model predictions, such as those shown in 3 and 4, in order to investigate the form of the world model and the growth of cosmic structure."126 As. discussec by Blain (1997a.c) his programme would require a large. but not impractical. amount of observing time: severa months of dedicated observations with an MEX in order to identify lensecl structures. and many nights of spectroscopic observations using large telescopes in the near-infrared anc optical wavebands in order to determine the redshifts of the detected sources and lensing galaxies.," As discussed by Blain (1997a,c), this programme would require a large, but not impractical, amount of observing time; several months of dedicated observations with an MIA in order to identify lensed structures, and many nights of spectroscopic observations using large telescopes in the near-infrared and optical wavebands in order to determine the redshifts of the detected sources and lensing galaxies."127 The cllects of lensing by à. cluster on. the population of background. galaxies can be considered in terms of a magnification bias. which mocilies the counts of lensec images às compared with background: galaxies. (Borgees et al.," The effects of lensing by a cluster on the population of background galaxies can be considered in terms of a magnification bias, which modifies the counts of lensed images as compared with background galaxies (Borgeest et al."128 1991: Broadhurst. Tavlor Peacock 1995).," 1991; Broadhurst, Taylor Peacock 1995)."129 The bias ds introduced because. both the lux densities anc mean separations of the images of background. galaxies are increased by a lens. and its magnitude is determined. by the steepness. of the slope of the counts of backgroun galaxies.," The bias is introduced because both the flux densities and mean separations of the images of background galaxies are increased by a lens, and its magnitude is determined by the steepness of the slope of the counts of background galaxies."130 In general these counts are expected to be steeper in the submillimetre waveband as compared with the optica waveband (Blain 1997b). and so the bias is expected to be relatively large in the submillimetre waveband.," In general these counts are expected to be steeper in the submillimetre waveband as compared with the optical waveband (Blain 1997b), and so the bias is expected to be relatively large in the submillimetre waveband."131 The angular size of the region within which the bias is expected to be significant depends on the relative size of the observer.lens and lenssource clistance., The angular size of the region within which the bias is expected to be significant depends on the relative size of the observer–lens and lens–source distance.132 The orms of both the counts of background. galaxies. (Lie., The forms of both the counts of background galaxies (Fig.133 L Blain 1997b) and these distances are expected to depen on the form of the work model. and. so detailed. observations of the properties of lensecl images in clusters could. be used. to constrain the values of cosmological parameters.," 3; Blain 1997b) and these distances are expected to depend on the form of the world model, and so detailed observations of the properties of lensed images in clusters could be used to constrain the values of cosmological parameters."134 The predicted surface density and magnification bias of lensed images in a rich cluster are compared in Fig., The predicted surface density and magnification bias of lensed images in a rich cluster are compared in Fig.135 5 as a function of Lux density and position in the cluster for four world models selected from the list in Table 1., 5 as a function of flux density and position in the cluster for four world models selected from the list in Table 1.136 Phe expecte number of detectable images within each radius are also shown., The expected number of detectable images within each radius are also shown.137 The details of the calculations are described in Blain (1997h)., The details of the calculations are described in Blain (1997b).138 Phe form of the magnification bias is predicte to diller. considerably between world. models. particularly ab [lux densities of about mmy. and. racüi of abou aarcsec. for which the bias factor is expected to exceec," The form of the magnification bias is predicted to differ considerably between world models, particularly at flux densities of about mJy and radii of about arcsec, for which the bias factor is expected to exceed"13917024637.,.140 Our identification is at 4 aresec to the north of the radio position., Our identification is at 4 arcsec to the north of the radio position.14118414568.. Our identification is at 3 aresec to the south of the radio position., Our identification is at 3 arcsec to the south of the radio position.14218544605.. Our tentative identification is 3.6 aresec to the south-west of the radio position., Our tentative identification is 3.6 arcsec to the south-west of the radio position.143 We give in Table 4 and 5 the radio and IR position. angles along with the differences between them for the USS anc GPS sub-samples of radio galaxies., We give in Table 4 and 5 the radio and IR position angles along with the differences between them for the USS and GPS sub-samples of radio galaxies.144 In case of USS sources we used the VLA radio maps provided us from Rengelink (private communication) in order to measure the radio positior angles., In case of USS sources we used the VLA radio maps provided us from Rengelink (private communication) in order to measure the radio position angles.145 After selecting the objects with definite identification. we have not found evidence for an IR alignment effect: 3 objects. although resolved. show an IR round morphology: [ objects are too faint in the IR to say if they are elongated: for 3un objects we have measured radio to IR position angle differences clearly not biased toward zero.," After selecting the objects with definite identification, we have not found evidence for an IR alignment effect: 3 objects, although resolved, show an IR round morphology; 4 objects are too faint in the IR to say if they are elongated; for 5 objects we have measured radio to IR position angle differences clearly not biased toward zero."146 These results. although obtained on a small number of objects. suggest that the IR alignment in our sample of USS sources is not as strong as detected in the optical on powerful distant radio sources (e.g. MeCarthy 1993)).," These results, although obtained on a small number of objects, suggest that the IR alignment in our sample of USS sources is not as strong as detected in the optical on powerful distant radio sources (e.g. McCarthy \cite{mccarthy}) )."147 Furthermore. we are unable to confirm on our sample the claim for a precise IR-radio alignment obtained by Dunlop and Peacock (1993)) for 3CR sources at :.~ |.," Furthermore, we are unable to confirm on our sample the claim for a precise IR-radio alignment obtained by Dunlop and Peacock \cite{dunlop}) ) for 3CR sources at $z \sim$ 1."148 We suggest that the lack of alignment in our sample may be connected with its lower radio power., We suggest that the lack of alignment in our sample may be connected with its lower radio power.149 It seems in fact plausible that the alignment effect. if it 15 a manifestation of the nuclear activity on the optical/IR morphology. would decrease with radio power which ts a measure of nuclear activity.," It seems in fact plausible that the alignment effect, if it is a manifestation of the nuclear activity on the optical/IR morphology, would decrease with radio power which is a measure of nuclear activity."150 In the case of GPS sources we have defined the radio position angles using the analysis of multifrequency VLBI observations carried out by Snellen (PhD thesis) for our sample of faint objects., In the case of GPS sources we have defined the radio position angles using the analysis of multifrequency VLBI observations carried out by Snellen (PhD thesis) for our sample of faint objects.151 In all cases. we chose the lowest frequency maps to enhance the importance of the extended parts.," In all cases, we chose the lowest frequency maps to enhance the importance of the extended parts."152 The IR position angles of GPS galaxies are in general not aligned with the radio axis (see Table 5)., The IR position angles of GPS galaxies are in general not aligned with the radio axis (see Table 5).153 The only exception (1942+721) could well happen by chance., The only exception (1942+721) could well happen by chance.154 Furthermore. 3 objects show an IR round morphology and 1 object is too faint in the IR to measure any orientation.," Furthermore, 3 objects show an IR round morphology and 1 object is too faint in the IR to measure any orientation."155 The lack of optical-radio alignment in GPS sources has also been noticed by Snellen et al. (1996))., The lack of optical-radio alignment in GPS sources has also been noticed by Snellen et al. \cite{snellen}) ).156 One of the main objectives of the WENSS survey was to increase the small number of known gravitational lenses by mapping flat-spectrum radio sources. in order to provide for the first time a sample large enough to do reasonable statistics.," One of the main objectives of the WENSS survey was to increase the small number of known gravitational lenses by mapping flat-spectrum radio sources, in order to provide for the first time a sample large enough to do reasonable statistics."157 In addition. optical/IR follow-up studies of confirmed lens systems allow the determination of the redshifts of the lensed objects and provide information about the lensing galaxy type.," In addition, optical/IR follow-up studies of confirmed lens systems allow the determination of the redshifts of the lensed objects and provide information about the lensing galaxy type."158 In our run of 1995 August. we performed IR imaging of the object 1600--434. a lensed quasar at redshift 1.6. which consists of two images. separated by 1.4 aresec. both in the radio and in the optical (Jackson et al. 1995)).," In our run of 1995 August, we performed IR imaging of the object 1600+434, a lensed quasar at redshift 1.6, which consists of two images, separated by 1.4 arcsec, both in the radio and in the optical (Jackson et al. \cite{jackson}) )."159 The lens has been detected in the A- and J-bands but not resolved. although the seeing was good. probably because our pixel was 0.55 aresec and undersampled the point spread function (PSF).," The lens has been detected in the $K$ - and $J$ -bands but not resolved, although the seeing was good, probably because our pixel was 0.55 arcsec and undersampled the point spread function (PSF)."160 In order to estimate the IR magnitudes and colours of the lensing galaxy. we have tried to carefully subtract the two quasar images using the astrometry of these two point sources from Jackson et al. (1995))," In order to estimate the IR magnitudes and colours of the lensing galaxy, we have tried to carefully subtract the two quasar images using the astrometry of these two point sources from Jackson et al. \cite{jackson}) )"161 and the astrometry of the lensing galaxy obtained from HST images (Jackson. private communication).," and the astrometry of the lensing galaxy obtained from HST images (Jackson, private communication)."162 We computed the pixel positions of the two quasar components assuming that the position of the lensing galaxy coincided with the light peak of the image., We computed the pixel positions of the two quasar components assuming that the position of the lensing galaxy coincided with the light peak of the image.163 The quasars subtractior procedure was carried out constructing two empirical two-dimensional PSFs., The quasars subtraction procedure was carried out constructing two empirical two-dimensional PSFs.164 To this aim. after selecting some isolated stars in the field. we calculated the FWHM for all these objects and used its mean value to construct a gaussian PSF.," To this aim, after selecting some isolated stars in the field, we calculated the FWHM for all these objects and used its mean value to construct a gaussian PSF."165 The intensity of the PSF to be subtracted for the North Western image of the quasar has been obtained with a trial and error procedure which best eliminates, The intensity of the PSF to be subtracted for the North Western image of the quasar has been obtained with a trial and error procedure which best eliminates166sPhe halo model of. galaxy clustering. (see .Cooray and Sheth. 2002 for. a review). takes as one of »its usual assumptions. that 1e clustering of a dark matter halo is dictated solely by its mass.,The halo model of galaxy clustering (see Cooray and Sheth 2002 for a review) takes as one of its usual assumptions that the clustering of a dark matter halo is dictated solely by its mass.167 Observationally. when looking: at a cluster or group it. is easiest to count galaxies (see e.g. Hao 2010. Yang 2005. for recent cluster ancl eroup catalogues). which are usually associated with the population of dark matter subhalos.," Observationally when looking at a cluster or group it is easiest to count galaxies (see e.g., Hao 2010, Yang 2005, for recent cluster and group catalogues), which are usually associated with the population of dark matter subhalos."168 The role that the number of subhalos plays in the clustering: of. halos and also how that number is. allected⋅ environment has. the potential to. be linked directly. with. onaa Lf., The role that the number of subhalos plays in the clustering of halos and also how that number is affected by environment has the potential to be linked directly with observations.169 halo⋅ mass and number of subhalos⋅ alfect ⋅(2007) independently ..then this is .a challenge to a main .ab of. the halo model., If halo mass and number of subhalos affect clustering independently then this is a challenge to a main assumption of the halo model.170 In this paper. we examine .more the role of the number of subhalos in a halo on clustering in two cillerent ways. first by studing the environments (nearby overdensity) of halos and second by computing the correlation function.," In this paper we examine the role of the number of subhalos in a halo on clustering in two different ways, first by studing the environments (nearby overdensity) of halos and second by computing the correlation function."171 Gao. Springe and. White (2005) showed that the clustering strength of dark matter halos cepends not only on mass but also on formation time.," Gao, Springel and White (2005) showed that the clustering strength of dark matter halos depends not only on mass but also on formation time."172 This result used. a high. resolution. large volume simulation. (the Millennium. Simulation of Springel 2005) and was the first of a set of⋅ results showing. that halo mass is. only the first. order driver. of halo clustering., This result used a high resolution large volume simulation (the Millennium Simulation of Springel 2005) and was the first of a set of results showing that halo mass is only the first order driver of halo clustering.173: Subsequent. studies. confirmed⋅ the result (c.g. Zhu 2006. LLarker 2006) and showed that other dependencies exist. apart from halo mass. such as concentration (c.g.. Wechsler 2006. hereafter WO06). and halo spin and shape (Bett 2007).," Subsequent studies confirmed the result (e.g., Zhu 2006, Harker 2006) and showed that other dependencies exist apart from halo mass, such as concentration (e.g., Wechsler 2006, hereafter W06), and halo spin and shape (Bett 2007)."174 WOG also found dependence on number of subhalos.⋅ anc Cao and.⇁⊀ White by: Chereafter⋅ CWOT7)⊲⇁− on⋅ the substructure fraction. both. observations. fixed mass⊀ in that⊀ halos with more⋠⊲ substructure are clustering clustered.," W06 also found a dependence on number of subhalos, and Gao and White (2007) (hereafter GW07) on the substructure fraction, both at fixed mass in that halos with more substructure are more clustered."175. Lt. is these∙⊀ relationships that⊀. we will be: assumption inVEN qemore detail in .this paper., It is these relationships that we will be investigating in more detail in this paper.176investigating The clustering of halos can be probed. in a dilferent. related. fashion by measuring properties. of the local environment.," The clustering of halos can be probed in a different, related fashion by measuring properties of the local environment."177 Again in this case to first order the dependence of halo properties on environment was shown to be limited to mass by Lemson Ixaufmann. (1999)., Again in this case to first order the dependence of halo properties on environment was shown to be limited to mass by Lemson Kaufmann (1999).178 Xdvances in simulation size and resolution enabled this (wpe of analysis to be extended to measure smaller. cllects and. cülferent, Advances in simulation size and resolution enabled this type of analysis to be extended to measure smaller effects and different179"formed by the different values of initial N and initial ry;, is referred to as the parameter space in the later part of the paper.",formed by the different values of initial N and initial $r_{\rm vir}$ is referred to as the parameter space in the later part of the paper.180 For all the simulations listed here our aim has been to investigate the effect of primordial mass-segregation on te. of young clusters with different initial conditions (NV and ryir)., For all the simulations listed here our aim has been to investigate the effect of primordial mass-segregation on $t_{\rm cc}$ of young clusters with different initial conditions $N$ and $r_{\rm vir}$ ).181" We have calculated t.. based on the central relaxation time ένο defined as where cc, n, (m), are the three-dimensional dispersion, number density, and average stellar mass respectively at the cluster center (?,eq. 3.37).."," We have calculated $t_{\rm cc}$ based on the central relaxation time $t_{\rm rc}$ defined as where $\sigma_c$, n, $ \left<m\right>_{c}$ are the three-dimensional dispersion, number density, and average stellar mass respectively at the cluster center \citep[eq. 3.37]{Spi1987}."182" As a typical reference model similar to Paper I, all the simulations in Table 6 are initiated with Plummer models and Salpeter IMF (withinMmin=0.2Mo and Mmax= 120Mo)."," As a typical reference model similar to Paper I, all the simulations in Table \ref{t3} are initiated with Plummer models and Salpeter IMF (within$\rm M_{\rm min}=0.2\, \rm M_{\rm \odot}$ and $\rm M_{\rm max}=120\, \rm M_{\rm \odot}$ )."183 Another reason for using Plummer sphere is that the ? formalism starts with an isolated Plummer sphere., Another reason for using Plummer sphere is that the \citet{Subr08} formalism starts with an isolated Plummer sphere.184 ? were the first to study the core collapse and collisional runaway for unsegregated clusters using à MC simulation code including stellar collisions., \citet{freitag06} were the first to study the core collapse and collisional runaway for unsegregated clusters using a MC simulation code including stellar collisions.185" Similar to ? we did not take into account stellar evolution in the simulations since all the simulations were limited to the first 3Myr, before the most massive stars lose mass in supernovae explosions."," Similar to \citet{freitag06} we did not take into account stellar evolution in the simulations since all the simulations were limited to the first $3\, \rm Myr$, before the most massive stars lose mass in supernovae explosions."186 If a cluster had a core collapse time more than 3Myr we implicitly took stellar evolution into account by ending the simulation at 3Myr.," If a cluster had a core collapse time more than $3\, \rm Myr$ we implicitly took stellar evolution into account by ending the simulation at $3\, \rm Myr$."187" Since our code now includes stellar collisions, we first checked whether we are able to reproduce their results."," Since our code now includes stellar collisions, we first checked whether we are able to reproduce their results."188" They found that for all models with ένο«20Myr, runaway formation of a VMS occured."," They found that for all models with $t_{\rm rc}< 20\, \rm Myr$, runaway formation of a VMS occured."189" Figure 5 is à parameter survey similar to 7,theirFig.1, showing for each simulation whether a runaway occurred (filled circles) or not (open circles), for all our unsegregated models varying ry, and the number of stars in the cluster."," Figure \ref{fig:parameterspace-unseg} is a parameter survey similar to \citet[][their Fig. 1]{freitag06}, showing for each simulation whether a runaway occurred (filled circles) or not (open circles), for all our unsegregated models varying $r_{\rm vir}$ and the number of stars in the cluster."190" The solid straight line corresponds to tee=0.15t,,3Myr, not including collisions."," The solid straight line corresponds to $t_{\rm cc}=0.15t_{rc}=3\,\rm Myr$, not including collisions."191" Simulations of clusters with initial conditionslying below the straight line will have t..«3Myr, whereas t.->3Myr for simulations with initial conditions above the line."," Simulations of clusters with initial conditionslying below the straight line will have $t_{\rm cc} < 3\, \rm Myr$, whereas $t_{\rm cc} > 3\, \rm Myr$ for simulations with initial conditions above the line."192 It can be clearly seen in Figure ὅ that the initial conditions leading to a runaway fall indeed below this line., It can be clearly seen in Figure \ref{fig:parameterspace-unseg} that the initial conditions leading to a runaway fall indeed below this line.193 Thus we have successfully reproduced the results of ? with our code and have reconfirmed the validity of the simple criterion for runaway collisions to occur in young dense star clusters., Thus we have successfully reproduced the results of \citet{freitag06} with our code and have reconfirmed the validity of the simple criterion for runaway collisions to occur in young dense star clusters.194 We then repeated the same set of simulations for primordially mass-segregated clusters using the recipe from ? with S>0., We then repeated the same set of simulations for primordially mass-segregated clusters using the recipe from \citet{Subr08} with $S > 0$.195 Figure 6 shows our results for mass-segregation parameter S=0.30., Figure \ref{fig:parameterspace-seg} shows our results for mass-segregation parameter $S=0.30$.196" We see that, with primordial mass segregation, the initial cluster r,4 can be chosen several times larger compared to unsegregated clusters and still lead to a runaway."," We see that, with primordial mass segregation, the initial cluster $r_{\rm vir}$ can be chosen several times larger compared to unsegregated clusters and still lead to a runaway."197" Thus, simulations of primordially mass-segregated clusters increase the parameter space (range of ryir in pc) for runaway collisions to happen when compared to simulations of primordially unsegregated clusters."," Thus, simulations of primordially mass-segregated clusters increase the parameter space (range of $r_{\rm vir}$ in pc) for runaway collisions to happen when compared to simulations of primordially unsegregated clusters."198" 'To further illustrate the effect primordial mass segregation has on the mass growth of the most massive star we compared results of a primordially mass-segregated vs an unsegregated cluster, with otherwise identical initial conditions."," To further illustrate the effect primordial mass segregation has on the mass growth of the most massive star we compared results of a primordially mass-segregated vs an unsegregated cluster, with otherwise identical initial conditions."199" Figure 7 shows the growth curve of the most massive star in an unsegregated cluster and in a primordially mass-segregated cluster (S= 0.3), with N=5x10? stars and ri,=0.64pc."," Figure \ref{fig:Mergertree2} shows the growth curve of the most massive star in an unsegregated cluster and in a primordially mass-segregated cluster $S=0.3$ ), with $N=5\times 10^{5}$ stars and $r_{\rm vir}=0.64\, \rm pc$."200" The unsegregated cluster does not have a runaway or a very steep mass growth before it reaches core collapse, and only a 200Mg star is formed within 3Myr."," The unsegregated cluster does not have a runaway or a very steep mass growth before it reaches core collapse, and only a $200\, \rm M_{\odot}$ star is formed within $3\, \rm Myr$."201" For the primordially mass-segregated cluster, we clearly see à very steep mass growth leading to a formation of a 900Mo star within 3Myr and hence a runaway."," For the primordially mass-segregated cluster, we clearly see a very steep mass growth leading to a formation of a $900\, \rm M_{\odot}$ star within $3\,\rm Myr$ and hence a runaway."202" A general result, in agreement with ?,, is that only one VMS forms in the cluster and there is no sign of multiple runaways."," A general result, in agreement with \citet{freitag06}, is that only one VMS forms in the cluster and there is no sign of multiple runaways."203 Note that this result might be different for clusters with significant fractions of primordial binaries (?).., Note that this result might be different for clusters with significant fractions of primordial binaries \citep{GU06}.204" As in this example, we also note inall our simulations that the time of the runaway coincides with the time of core-collapse, which decreases from te.6Myr for the unsegregated cluster, and to te-2Myr for the primordially mass- cluster."," As in this example, we also note inall our simulations that the time of the runaway coincides with the time of core-collapse, which decreases from $t_{cc}\sim 6\,\rm Myr$ for the unsegregated cluster, and to $t_{\rm cc}\sim2\,\rm Myr$ for the primordially mass-segregated cluster."205" To show how strongly the core collapse time decreases for other values of S we plot in Figure 8 the core collapse time for clusters with different initial ry, against S."," To show how strongly the core collapse time decreases for other values of $S$ we plot in Figure \ref{fig:corecollapse} the core collapse time for clusters with different initial $r_{\rm vir}$ , against $S$ ."206 We clearly see a trend of decreasing t.. with increasing S., We clearly see a trend of decreasing $t_{\rm cc}$ with increasing $S$ .207 The decrease in, The decrease in208We present new. deep. photometry. which has allowed us to put the fundamental parameters of Trumpler 20 on a firmer base.,"We present new, deep, photometry, which has allowed us to put the fundamental parameters of Trumpler 20 on a firmer base."209 We study (he clusters CMD in detail. and investigate the nature of the conspicuous sequence of bright blue stars in the upper CMD.," We study the cluster's CMD in detail, and investigate the nature of the conspicuous sequence of bright blue stars in the upper CMD."210 This latter feature is common in clusters located at low Galactic latitudes. aud in Chis particular case ils presence has led in (he past to a misinterpretation of the cluster CAD (AleSwain Gies 2005): here. moreover. we address the question: are (hese stars blue stragglers (BS) that belong to the cluster or. more conservativelv. are (μον simply field stars?," This latter feature is common in clusters located at low Galactic latitudes, and in this particular case its presence has led in the past to a misinterpretation of the cluster CMD (McSwain Gies 2005); here, moreover, we address the question: are these stars blue stragglers (BS) that belong to the cluster or, more conservatively, are they simply field stars?"211 We also cdiseuss the most prominent feature of the cluster CMD. namely its clump of Ile-burning stars. aud use it as a distance aud age estimator.," We also discuss the most prominent feature of the cluster CMD, namely its clump of He-burning stars, and use it as a distance and age estimator."212 The clump is possibly the most obvious indication (hat past classifications and basic parameters of Trumpler 20 (particularly its age) may be in This paper is organized as follows., The clump is possibly the most obvious indication that past classifications and basic parameters of Trumpler 20 (particularly its age) may be in This paper is organized as follows.213 In Sect., In Sect.214 2 we summarize previous information available for Trumpler 20., 2 we summarize previous information available for Trumpler 20.215 In Sect., In Sect.216 3 we present our observational material and describe our reduction procedure., 3 we present our observational material and describe our reduction procedure.217 The cluster color-magnitude diagram is described in Sect., The cluster color-magnitude diagram is described in Sect.218 4. while in sects.," 4, while in Sects."219 5 to T we estimale its basic parameters., 5 to 7 we estimate its basic parameters.220 Sect., Sect.221 8 is devoted to a discussion on the clusters chunp. and Sect.," 8 is devoted to a discussion on the cluster's clump, and Sect."222 9 addresses the suspected DS population of Trumpler 20., 9 addresses the suspected BS population of Trumpler 20.223 The elobal conclusions of the paper. together with suggestions for Dhuture research directions. are given in Section 10.," The global conclusions of the paper, together with suggestions for future research directions, are given in Section 10."224" ""Trumnpler 20 was first noticed by Trimpler (1930). who denoted it as 220."," Trumpler 20 was first noticed by Trumpler (1930), who denoted it as 20."225 IIe classified the cluster as a III 2r object. namely a," He classified the cluster as a III 2r object, namely a"226"wwere frequency folded and 3° order baselines were removed. while for the ddata a4!"" order baseline was used.","were frequency folded and $^{\rm rd}$ order baselines were removed, while for the data a $^{\rm th}$ order baseline was used."227" A 2""! order baseline was subtracted from the CO data.", A $^{\rm nd}$ order baseline was subtracted from the position-switched CO data.228 aand wwere mapped with hall-beam spacing. while CO πμ wwere mapped with full-beam spacing.," and were mapped with half-beam spacing, while CO and were mapped with full-beam spacing."229 The extent of the region mapped varies depencine on the spatial extent of the sources emission., The extent of the region mapped varies depending on the spatial extent of the source's emission.230 We also performed subamillimeter observations in April and December 2000 and in April 2001 with the 10 m Lleinvich Hertz (IIT)., We also performed submillimeter observations in April and December 2000 and in April 2001 with the 10 m Heinrich Hertz (HHT).231 COIL... and observations were conducted using the facility 230 GIIz SIS receiver. while aand oobservalions were conducted using the facility dual polarization 345 Gllz 915 receiver.," CO, and observations were conducted using the facility 230 GHz SIS receiver, while and observations were conducted using the facility dual polarization 345 GHz SIS receiver."232 several backends were used simultaneously. including a 1. GlIz wide (1 MIIz resolution) acousto-optical spectrometer (AOS). and three fillerbanks with | MIIz. 250 kIIz. and 62.5 kllz resolutions.," Several backends were used simultaneously, including a 1 GHz wide $\sim 1$ MHz resolution) acousto-optical spectrometer (AOS), and three filterbanks with 1 MHz, 250 kHz, and 62.5 kHz resolutions."233 The results presented in (his paper were processed using the 250 kllz filterbank., The results presented in this paper were processed using the 250 kHz filterbank.234 All observations were position-switched. ancl second order baselines were removed.," All observations were position-switched, and second order baselines were removed."235 oobservations were made of the star forming core at the IAS source position. while aad CO observations were mace using (he on-the-fly (OTF) mapping technique.," observations were made of the star forming core at the IRAS source position, while and CO observations were made using the on-the-fly (OTF) mapping technique."236" Observations of 120""x60"" regions in OTF mode were combined into maps of various spatial extents depending on the source.", Observations of $120\sec \times 60\sec$ regions in OTF mode were combined into maps of various spatial extents depending on the source.237 We observed. B335 in May of 1996 at the Caltech Submillimeter (CSO). 3), We observed B335 in May of 1996 at the Caltech Submillimeter (CSO). )238 mapping was perlormed using the OTF mapping technique., mapping was performed using the OTF mapping technique.239 The OTF, The OTF240review).,.241. In contrast to the typical rregions of the MCs. which are extended structures with sizes of several are minutes corresponding to physical scales of more than ppe and powered by a large number of exciting stars. HEBs are relatively dense and small regions of ~ to in diameter in the optical. corresponding to ~ 11.5 to ppc and exeited by à much smaller number of massive stars.," In contrast to the typical regions of the MCs, which are extended structures with sizes of several arc minutes corresponding to physical scales of more than pc and powered by a large number of exciting stars, HEBs are relatively dense and small regions of $\sim$ to in diameter in the optical, corresponding to $\sim$ 1.5 to pc and excited by a much smaller number of massive stars."242 Their excitation. derived from the rratio. is generally larger than that of ordinary MC rregions.," Their excitation, derived from the ratio, is generally larger than that of ordinary MC regions."243 For a fixed metallicity. the rratio increases with the effective temperature of the exciting star. as well as with the gas density in. homogeneous photoionization models.," For a fixed metallicity, the ratio increases with the effective temperature of the exciting star, as well as with the gas density in homogeneous photoionization models."244 These compact rregions are also heavily affected by local dust compared to other ionized features of the complex in which they are hosted (Heydari-Malayertetal...1988;Israel&Koornneef.1991).," These compact regions are also heavily affected by local dust compared to other ionized features of the complex in which they are hosted \citep[][]{MHM88,Israel91}."245. This is also the case for N66AÀ. which is marked by a prominent absorption lane of local dust erossing the whole nebula.," This is also the case for N66A, which is marked by a prominent absorption lane of local dust crossing the whole nebula."246 The two other known examples of HEBs in the SMC are N88À and N81. which were also observed with (Heydari-Malayerial..1999a.b. 2002).," The two other known examples of HEBs in the SMC are N88A and N81, which were also observed with \citep[][]{MHM99a,MHM99b,MHM02}."247. HEBs are usually located adjacent to ordinary giant rregions or seen lying across them., HEBs are usually located adjacent to ordinary giant regions or seen lying across them.248 This implies that they form as a consequence of triggering by a previous generation of massive stars in the complex., This implies that they form as a consequence of triggering by a previous generation of massive stars in the complex.249 Simple reasoning suggests that HEBs and their small exciting clusters are formed from the material remaining after a preceding massive-star formation event., Simple reasoning suggests that HEBs and their small exciting clusters are formed from the material remaining after a preceding massive-star formation event.250 More specifically. the apparent association of ΝΟ6Α with the compressed tonized front and the absorption lane. both centered on the 3346 cluster. suggests that N66A is a secondary. younger generation of stars.," More specifically, the apparent association of N66A with the compressed ionized front and the absorption lane, both centered on the 346 cluster, suggests that N66A is a secondary, younger generation of stars."251 This implies that the exciting star(s) of N66A have formed according to the sequential star-formation model (Elmegreen&Lada.1977:Whitworthetal. 1994).," This implies that the exciting star(s) of N66A have formed according to the sequential star-formation model \citep[][]{Elmegreen77,Whitworth94}."252 However. since low-mass PMS candidates have also been reported in this region. other induced star formation scenarios. such as shock waves 1npacting molecular cores (Vanhala&Cameron.1998) and/or implosion of molecular cores," However, since low-mass PMS candidates have also been reported in this region, other induced star formation scenarios, such as shock waves impacting molecular cores \citep[][]{Vanhala98} and/or radiation-driven implosion of molecular cores"253computed synthetic lline profiles. which have been compared to an observed high resolution spectrum of 6 Cet.,"computed synthetic line profiles, which have been compared to an observed high resolution spectrum of $\beta$ Cet."254 We have found that the temperature plateau (as proposed by ?)) of the chromosphere model is too high to reproduce the line cores., We have found that the temperature plateau (as proposed by \citealt{Eriksson83}) ) of the chromosphere model is too high to reproduce the line cores.255 On the basis of these first interferometric results on the spatial structure of the chromosphere of K giant stars. it now seems possible to construct reliable chromospheric models by combining spectroscopic and interferometric observations.," On the basis of these first interferometric results on the spatial structure of the chromosphere of K giant stars, it now seems possible to construct reliable chromospheric models by combining spectroscopic and interferometric observations."256to have used the IIubble period as a starting point ancl simply adjusted (he period for a best fit.,to have used the Hubble period as a starting point and simply adjusted the period for a best fit.257 Thev give a period 31.3844 for M31-VI. stating that it gives a good fit of the earlier IIubble data as well their own.," They give a period $31.384 d$ for M31-V1, stating that it gives a good fit of the earlier Hubble data as well their own."258 We show a phase curve of the Daade Swope data phased with our (likely incorrect period) and that obtained by Swope in Figure 8.., We show a phase curve of the Baade Swope data phased with our (likely incorrect period) and that obtained by Swope in Figure \ref{bsphase}.259 Both periods produce acceptable phase curves. although the period from Baacde&Swope(1965) appears slightly better.," Both periods produce acceptable phase curves, although the period from \citet{BS1965} appears slightly better."260 We therefore accept the Daade&Swope(1965) period ancl reject our own., We therefore accept the \citet{BS1965} period and reject our own.261 We used (he 31.3844 period to generate a test ephemeris with which we attempted to fit all measured historic and modern data together. which we discuss below.," We used the $31.384 d$ period to generate a test ephemeris with which we attempted to fit all measured historic and modern data together, which we discuss below."262 As a final test. we generated an ephemeris for the entire data set from 1908 to 2010 using the 1950-1951. data as a central reference point.," As a final test, we generated an ephemeris for the entire data set from 1908 to 2010 using the 1950-1951 data as a central reference point."263 We used the period of 31.384 [rom Daade&Swope(1965).. along with a well-measured time of maxinum of JD 2433898.0 io generate predicted times of maxinmumn from 1908 to 2011.," We used the period of $31.384 d$ from \citet{BS1965}, along with a well-measured time of maximum of JD 2433898.0 to generate predicted times of maximum from 1908 to 2011."264 In Figure 9 we show these data overlaid onto the Ae light curve., In Figure \ref{tomfit} we show these data overlaid onto the $R_{C}$ light curve.265 This ephemeris produces a reasonably good [it to the modern data. fitting the maxima to within about in phase.," This ephemeris produces a reasonably good fit to the modern data, fitting the maxima to within about in phase."266 Clearly an ephemeris derived from Baacle&Swope(1965) can fit the modern data acceptably well. suggesting that there has been no measurable change in period during the entire course of observations.," Clearly an ephemeris derived from \citet{BS1965} can fit the modern data acceptably well, suggesting that there has been no measurable change in period during the entire course of observations."267 llowever. (his cannot be guaranteed to be true. primarily because (he (του epochs of data are very widely separated. and it is possible that dillerent periods could fit the data simply by adjusting both the period ancl the evele number E to produce better fits.," However, this cannot be guaranteed to be true, primarily because the three epochs of data are very widely separated, and it is possible that different periods could fit the data simply by adjusting both the period and the cycle number $E$ to produce better fits."268 Such a test will be conducted in a future paper planned once another season of data is collected., Such a test will be conducted in a future paper planned once another season of data is collected.269 The primary reason that variables are observed over long; periods of time or in epochs is to look for changes in variations that provide astrophivsical insight. into their evolution., The primary reason that variables are observed over long periods of time or in widely-spaced epochs is to look for changes in variations that provide astrophysical insight into their evolution.270" Some Cepheild variables are known to change over time (Szabados1953:""Turner.Abdel-Latif.&Berdnikoy 2006).. and these changes can vield information about (heir position on the II-R. diagram. evolutionary state. and other physical properties."," Some Cepheid variables are known to change over time \citep{Szabados1983,TAB2006}, and these changes can yield information about their position on the H-R diagram, evolutionary state, and other physical properties."271 The ]Iubble(1929) and Baacle&Swope(1965) data sets are a possible starting point for stucdvine period changes in the M31 Cepheids.," The \citet{Hubble1929} and \citet{BS1965}272 data sets are a possible starting point for studying period changes in the M31 Cepheids."273 The observations bv AAVSO observers represent a first altempt at detecüng such changes serendipitously., The observations by AAVSO observers represent a first attempt at detecting such changes serendipitously.274 The single season of data which we have obtained provides a preliminary constraint on period change in M31-V1. and we expect that additional seasons of data during the current epoch will provide more conclusive constraints.," The single season of data which we have obtained provides a preliminary constraint on period change in M31-V1, and we expect that additional seasons of data during the current epoch will provide more conclusive constraints."275 In principle. a similar modern study could be attempted onaay Cepheid common to the ]Iubble and Baade Swope samples. with the only possible limitation being the available telescope time and (he ability of telescopes of siiall aperture (to reach (hese faint magnitudes.," In principle, a similar modern study could be attempted on Cepheid common to the Hubble and Baade Swope samples, with the only possible limitation being the available telescope time and the ability of telescopes of small aperture to reach these faint magnitudes."276Figure 4.,Figure 4.277" Projections to the (x1,y1) and (σι,x2) planes of points in phase space space generated by the chaotic trajectory observed at intervals At—4 (on the left) and randomly according the probability distribution (on the right)."," Projections to the $(x_1,y_1)$ and $(x_1,x_2)$ planes of points in phase space space generated by the chaotic trajectory observed at intervals $\Delta t =4$ (on the left) and randomly according the probability distribution (on the right)."278 20pt Table 2., 20pt Table 2.279 The entries in the column labeled ‘dynamics’ were obtained by numerical simulation of the dynamical system., The entries in the column labeled `dynamics' were obtained by numerical simulation of the dynamical system.280" With the exception of the last two rows, the time duration was 20000, with data sampled at intervals At=2, starting from the initial conditions 0.11, 0.09)."," With the exception of the last two rows, the time duration was $20000$, with data sampled at intervals $\Delta t=2$, starting from the initial conditions $(x_1,y_1,x_2,y_2)=(0.1,0.2,0.11,0.09)$ ."281 The last two rows were obtained by sampling at intervals At=4 over a duration 400000., The last two rows were obtained by sampling at intervals $\Delta t=4$ over a duration $400000$.282" The column labeled ‘Monte Carlo’ was obtained by hit and miss Monte Carlo computation using the proposed exact distribution with 100000 accepted data points, for all but the last two rows."," The column labeled `Monte Carlo' was obtained by hit and miss Monte Carlo computation using the proposed exact distribution with 100000 accepted data points, for all but the last two rows."283 The last two rows were obtained with 400000 accepted data points., The last two rows were obtained with 400000 accepted data points.284" 15pt In the previous section we considered invariant distributions which were polynomial, with real zeroes forming a compact manifold."," 15pt In the previous section we considered invariant distributions which were polynomial, with real zeroes forming a compact manifold."285 The inverse method may be readily generalized to more complicated analytic structures., The inverse method may be readily generalized to more complicated analytic structures.286" For example, consider distributions of the form,"," For example, consider distributions of the form,"287usually offers an underestimate when compared with Teent (Petersonetal.1998).,usually offers an underestimate when compared with $\tau_{cent}$ \citep{Peterson}.288". The centroid width is calculated as Where c; and τι are the DCF coefficients and lags, Teent is the centroid lag."," The centroid width is calculated as Where $c_{i}$ and $\tau_{i}$ are the DCF coefficients and lags, $\tau_{cent}$ is the centroid lag."289" As the DCF coefficients are only defined for a given lag, we interpolate to find the peak correlation coefficient maz at the centroid lag."," As the DCF coefficients are only defined for a given lag, we interpolate to find the peak correlation coefficient $_{max}$ at the centroid lag."290 Figure 2 show the DCFs for the X-ray-8.4 GHz and X-ray-4.8 GHz bands respectively., Figure \ref{CCF_both} show the DCFs for the X-ray-8.4 GHz and X-ray-4.8 GHz bands respectively.291 We find a lag of Teent =24+12 days at DCFmaz=0.56 for X-ray-8.4 GHz and Teent =40+13 days at nax=0.7 for X-ray-4.8 GHz., We find a lag of $\tau_{cent}=$ $\pm$ 12 days at $_{max}$ =0.56 for X-ray-8.4 GHz and $\tau_{cent}=$ $\pm$ 13 days at $_{max}$ =0.7 for X-ray-4.8 GHz.292 The time lags taken from figure 2 are summarised in table 1.., The time lags taken from figure \ref{CCF_both} are summarised in table \ref{lag_table}.293 The errors in the lag are calculated using the flux randomisation/random subset selection (FR/RSS) method of Petersonetal.(1998)., The errors in the lag are calculated using the flux randomisation/random subset selection (FR/RSS) method of \cite{Peterson}.294". For 10* samples, we randomly reduce the number of data points in our original X-ray and radio light curves by and then re-calculate the DCF."," For $10^{4}$ samples, we randomly reduce the number of data points in our original X-ray and radio light curves by and then re-calculate the DCF."295 We take the centroid lag from each of the 10* simulations and use the rms spread in the distribution of centroid lags to obtain the quoted errors., We take the centroid lag from each of the $^{4}$ simulations and use the rms spread in the distribution of centroid lags to obtain the quoted errors.296" Note that since the radio light curves are strongly correlated with one another, the statistical errors on the lags are not independent between the two bands, so that the difference in lag between the two radio bands with respect to X-rays is likely to be real (this is also highlighted by the radio-radio correlation, see below)."," Note that since the radio light curves are strongly correlated with one another, the statistical errors on the lags are not independent between the two bands, so that the difference in lag between the two radio bands with respect to X-rays is likely to be real (this is also highlighted by the radio-radio correlation, see below)."297 'To ascertain a confidence level in the DCF calculation we used the method of Timmer&Koenig(1995) to generate Monte-Carlo simulations of un-correlated red-noise light curves., To ascertain a confidence level in the DCF calculation we used the method of \cite{Timmer} to generate Monte-Carlo simulations of un-correlated red-noise light curves.298" We assumed a broken power-law-shape power spectrum with low-frequency slope -1, high-frequency slope of -2.3 and break frequency v=0.012 d~', based on the best-fitting model to fit the X-ray power spectrum (Summons, private communication)."," We assumed a broken power-law-shape power spectrum with low-frequency slope -1, high-frequency slope of -2.3 and break frequency $\nu=0.012$ $^{-1}$ , based on the best-fitting model to fit the X-ray power spectrum (Summons, private communication)."299 We used this model to generate 104 random X-ray light curves and cross-correlated them with the real radio light curves in both bands., We used this model to generate $10^{4}$ random X-ray light curves and cross-correlated them with the real radio light curves in both bands.300" We then used these correlations to estimate the distribution of cross-correlation values at lag to obtain a local confidence level, corresponding to the CCF value which exceeds P per-cent of the simulated CCF values at that lag."," We then used these correlations to estimate the distribution of cross-correlation values at lag to obtain a local confidence level, corresponding to the CCF value which exceeds $P$ per-cent of the simulated CCF values at that lag."301 From the simulations we plot on figure 2 the 9596 and 9996 local confidence levels: we therefore assign a local confidence of >9596 for both of the peaks with the 4.8 GHz peak reaching close to 99%., From the simulations we plot on figure 2 the $95\%$ and $99\%$ local confidence levels: we therefore assign a local confidence of $>95\%$ for both of the peaks with the 4.8 GHz peak reaching close to $\%$.302" It is important to note however, that without a priori expectation of what the lag should be, it is more statistically rigorous to estimate the significance of the correlation using the ‘global significance’, which is the fraction of simulated random light curves which show CCFs at better than the observed confidence level forany given lag."," It is important to note however, that without a priori expectation of what the lag should be, it is more statistically rigorous to estimate the significance of the correlation using the `global significance', which is the fraction of simulated random light curves which show CCFs at better than the observed confidence level for given lag."303" For example, to estimate the global significance of a peak which appears at the 99% local confidence level, we search the 10* simulated CCFs for any peak values (at any lag) which exceed the 99% local confidence level for that lag."," For example, to estimate the global significance of a peak which appears at the $\%$ local confidence level, we search the $10^{4}$ simulated CCFs for any peak values (at any lag) which exceed the $\%$ local confidence level for that lag."304 The fraction of CCFs which do not show such a peak defines the global significance level for the correlation observed at the given local confidence level., The fraction of CCFs which do not show such a peak defines the global significance level for the correlation observed at the given local confidence level.305" In this way, we account for the fact that we are effectively searching over a broad range in lags, and so are sampling from a larger population of potential ‘false positives’ than we would expect from searching for correlations at a single lag."," In this way, we account for the fact that we are effectively searching over a broad range in lags, and so are sampling from a larger population of potential `false positives' than we would expect from searching for correlations at a single lag."306" We find for the entire range of computed lags (-300 to +300 days) the global confidence levels at 4.8 GHz are (at local significance) and (at local significance); at 8.4 GHz, (at local significance) and (at local significance)."," We find for the entire range of computed lags (-300 to +300 days) the global confidence levels at 4.8 GHz are (at local significance) and (at local significance); at 8.4 GHz, (at local significance) and (at local significance)."307" If we restrict the range of lags to positive only (> 0 days) we find at4.8 GHz, (at local significance) and (at local significance); at 8.4 GHz, (at local significance) and (at local significance)."," If we restrict the range of lags to positive only $>$ 0 days) we find at4.8 GHz, (at local significance) and (at local significance); at 8.4 GHz, (at local significance) and (at local significance)."308There is now strong evidence that the long *5-rav bursts (LORBs) are closely associated with voung star forming regions (Woosley&Bloom2006)..,There is now strong evidence that the long $\gamma$ -ray bursts (LGRBs) are closely associated with young star forming regions \citep{woosley2006a}.309 Recent high. spatial resolution imaging of nearby LORBs has shown that. while they are closely associated with clusters of Woll-Ravet stars and of O stars. they tend also to be displaced: somewhat from the centres of the clusters (Llamimeretal.2006).," Recent high spatial resolution imaging of nearby LGRBs has shown that, while they are closely associated with clusters of Wolf-Rayet stars and of O stars, they tend also to be displaced somewhat from the centres of the clusters \citep{hammer2006}."310. This gives further insights into their population characteristics., This gives further insights into their population characteristics.311 The birth rate of LORBs is estimated to be LOὉovr ‘per galaxy like our own when allowance is made for the uncertainties in the beaming angle of the +-ravs.," The birth rate of LGRBs is estimated to be $10^{-6} - 10^{-5}\,\rm312yr^{-1}$ per galaxy like our own when allowance is made for the uncertainties in the beaming angle of the $\gamma$ -rays."313 ‘This is 100010000 times lower than the birth rate of tvpe LE supernovae (Eryeretal.2007).," This is $1\,000 - 10\,000$ times lower than the birth rate of type II supernovae \citep{fryer2007}."314.. The LOGBBDs in which optical afterglows have been detected tend in general to be about a LOO times more luminous than tvpe LL SNe and this has led to the suggestion that they form a new class of supernovae or hypernovac (Paczviski1998:Woosley1993).," The LGRBs in which optical afterglows have been detected tend in general to be about a $100$ times more luminous than type II SNe and this has led to the suggestion that they form a new class of supernovae or hypernovae \citep {paczynski1998, woosley1993}."315. The association with voung star clusters also places them in a class distinct from tvpe Ia SNe which are thermonuclear explosions of degenerate white dwarfs., The association with young star clusters also places them in a class distinct from type Ia SNe which are thermonuclear explosions of degenerate white dwarfs.316 At the same time. here have been unambiguous identifications of few LORBs with type Lbfe supernovae which are characteriseda by ivdrogen- or hvdrogen- ancl beliume-clelicient ejecta.," At the same time, there have been unambiguous identifications of a few LGRBs with type Ib/c supernovae which are characterised by hydrogen- or hydrogen- and helium-deficient ejecta."317 Type Ib/c supernovae are expected at the ends of the ives of massive stars that have lost much. of their. mass during Woll-Ravet evolution so the evidence suggests that he LOGRBs are linked in some wav to the final stages of he evolution of very massive stellar cores as they collapse o black holes or neutron stars., Type Ib/c supernovae are expected at the ends of the lives of massive stars that have lost much of their mass during Wolf-Rayet evolution so the evidence suggests that the LGRBs are linked in some way to the final stages of the evolution of very massive stellar cores as they collapse to black holes or neutron stars.318 The total energy. of about 107 ere. released. is not much greater than that released in core collapse supernovae.," The total energy, of about $10^{51}\,$ erg, released is not much greater than that released in core collapse supernovae."319 However it cilfers in. that he energy is released. in 5-ravs in the form. of collimated jets., However it differs in that the energy is released in $\gamma$ -rays in the form of collimated jets.320 These properties have led to the suggestion that the LORBs form a subset of core collapse supernovac which are distinguished bv the magnetic fields present in the core hat collapses to a black hole or a neutron star., These properties have led to the suggestion that the LGRBs form a subset of core collapse supernovae which are distinguished by the magnetic fields present in the core that collapses to a black hole or a neutron star.321 These icles collimate the jet., These fields collimate the jet.322 In a popular model. the 5-ray. jet is believed. to be launched by the magnetohyvdrodynamic (MIID) extraction of the spin energy of a disrupted torus or," In a popular model, the $\gamma$ -ray jet is believed to be launched by the magnetohydrodynamic (MHD) extraction of the spin energy of a disrupted torus or"323for the case shown iu Fig.,for the case shown in Fig.324 ? aud e.230 aud Eras=2038107 for the case shown in Fig. 5.., \ref{partly_quench} and $\egmn=230$ and $\egmx=2.3\times 10^{5}$ for the case shown in Fig. \ref{all_quench}.325 Iu the case of Fig., In the case of Fig.326 v we have €.Xμμ«10! and. as can be seen from the figure. the power- breaks above ἕ-μήν because of quenching — incdeecl. we fud that the value of ezog Is i reality lower by a factor of 2 than the oue given iu eq. (50)).," \ref{partly_quench} we have $\egmn<\egmneff=1.7\times 10^4$ and, as can be seen from the figure, the power-law breaks above $\egmneff$ because of quenching – indeed, we find that the value of $\egmneff$ is in reality lower by a factor of 2 than the one given in eq. \ref{gmineff}) ),"327 because in the nuuercal caleulatious shownhere we use the full expressions for the svuchrotron ciuissivity aud the cross-section for ++ aud not the à function approxinations nuplied im the derivation of the above relation., because in the numerical calculations shownhere we use the full expressions for the synchrotron emissivity and the cross-section for $\ggabs$ and not the $\delta-$ function approximations implied in the derivation of the above relation.328 It is interesting to note that as the + rav hDuuinositv Dpnereases aud thus he quenching becomes more effective. the break between the unabsorbed and absorbed part of the law becomes more abrupt.," It is interesting to note that as the $\gamma-$ ray luminosity increases and thus the quenching becomes more effective, the break between the unabsorbed and absorbed part of the power-law becomes more abrupt."329 Tn the case of Fig. δν," In the case of Fig. \ref{all_quench},"330" on the other hand. the choice of the parameters were such as to make €-yinct comparable to 62,44."," on the other hand, the choice of the parameters were such as to make $\egmneff$ comparable to $\egmn$."331 Thus. according to the qualitative analvsis presented above. quenching should affect the whole + rav distribution.," Thus, according to the qualitative analysis presented above, quenching should affect the whole $\gamma-$ ray distribution."332 Indeed. as can be deduced from the figure. as the Iuninositv increases. absorption is Moving progressively to lower 5 rav energies. until it affects the whole distribution.," Indeed, as can be deduced from the figure, as the luminosity increases, absorption is moving progressively to lower $\gamma-$ ray energies, until it affects the whole distribution."333" We also investigated the relation between the slope of the injected (05,4). aud the ‘quenched (que) 2-2aY spectrum.", We also investigated the relation between the slope of the injected $\alpha_{\rm inj}$ ) and the `quenched' $\alpha_{\rm que}$ ) $\gamma$ -ray spectrum.334 For that reason. we ran the code for differcut Od. Choosing each time suitable values of the source paralucters to enable quenching.," For that reason, we ran the code for different $\alpha_{\rm inj}$, choosing each time suitable values of the source parameters to enable quenching."335" Figure 9 shows the result of the ruus (solid lino) aud the slope ayy|1 (dashed liuc) for comparisou reasons,", Figure \ref{ainj} shows the result of the runs (solid line) and the slope $\alpha_{\rm inj}+1$ (dashed line) for comparison reasons.336 We fud that equXad , We find that $\alpha_{\rm que} \propto \alpha_{\rm inj}^{1.34}$.337Thus. quenching becomes more pronounced as the mjected Spectrum ects stecper.," Thus, quenching becomes more pronounced as the injected spectrum gets steeper."338 The above has a straightforward application to the so-called one-zoue homogeneous models. which are customarily used to fit the MW spectra of Active Galactic Nuclei (AGN) (??)..," The above has a straightforward application to the so-called one-zone homogeneous models, which are customarily used to fit the MW spectra of Active Galactic Nuclei (AGN) \citep{boettcher09, aleksic11}. ."339 According to these models. the," According to these models, the"340HH 158. the jet from DG Tauri was first reported by Mundt Fried (1983). who presented an He image showing a well defined HH knot at ~8” to the SW of the star connected to DG Tau itself by a faint bridge.,"HH 158, the jet from DG Tauri was first reported by Mundt Fried (1983), who presented an $\alpha$ image showing a well defined HH knot at $\sim 8''$ to the SW of the star connected to DG Tau itself by a faint bridge."341 High resolution spectroscopy of this jet was presented by Mundt et al. (, High resolution spectroscopy of this jet was presented by Mundt et al. (3421983) and Solf Bóhhm (1993).,1983) and Solf Böhhm (1993).343 In the latter paper. the jet emission was traced to within ~072 from DG Tau.," In the latter paper, the jet emission was traced to within $\sim 0\rlap.{''}2$ from DG Tau."344 DG Tau is located in the sky approximately in between the L1495 region and the star HP Tau., DG Tau is located in the sky approximately in between the L1495 region and the star HP Tau.345 There are accurate distance determinations from very long baseline interferometry geometric parallax to both the L1495 region (131.5 pe: Torres et al., There are accurate distance determinations from very long baseline interferometry geometric parallax to both the L1495 region (131.5 pc; Torres et al.346 2007: 2009) and HP Tau (161 pe: Torres 2009)., 2007; 2009) and HP Tau (161 pc; Torres 2009).347 Here we adopt for DG Tau a distance of 150 pc. intermediate to those of L1495 and HP Tau.," Here we adopt for DG Tau a distance of 150 pc, intermediate to those of L1495 and HP Tau."348 The proper motions of the knots observed up to distances of ~10” were derived by Eislófffel Mundt (1998). using several frames obtained over a -7 yr time span. giving velocities of ~150 km s! (assuming a distance of 150 pe).," The proper motions of the knots observed up to distances of $\sim 10''$ were derived by Eislöfffel Mundt (1998), using several frames obtained over a $\sim 7$ yr time span, giving velocities of $\sim 150$ km $^{-1}$ (assuming a distance of 150 pc)."349 Comparing adaptive optics images obtained with a ~2 yr time base. Dougados et al. (," Comparing adaptive optics images obtained with a $\sim 2$ yr time base, Dougados et al. ("3502000) obtained proper motion velocities of ~200 km s! for the knots within ~6” from the source.,2000) obtained proper motion velocities of $\sim 200$ km $^{-1}$ for the knots within $\sim 6''$ from the source.351 These velocities imply a dynamical timescale of ~40 yr for HH 158 at that epoch., These velocities imply a dynamical timescale of $\sim 40$ yr for HH 158 at that epoch.352 MeGroarty Ray (2004) suggested that two groups of HH knots (HH 702 to the SW and HH 830 to the NE) at angular distances of ~11 from DG Tau might be associated with the same outflow., McGroarty Ray (2004) suggested that two groups of HH knots (HH 702 to the SW and HH 830 to the NE) at angular distances of $\sim 11'$ from DG Tau might be associated with the same outflow.353 However. MeGroarty et al. (," However, McGroarty et al. ("3542007) showed that proper motion measurements only support the possibility. of HH 702 being associated with the outflow from DG Tau (the HH $830 knots have proper motions which are not aligned with the outflow axis).,2007) showed that proper motion measurements only support the possibility of HH 702 being associated with the outflow from DG Tau (the HH 830 knots have proper motions which are not aligned with the outflow axis).355 The HH 702 knots have proper motions of ~240 km s! resulting in a dynamical timescale of -2000 yr.," The HH 702 knots have proper motions of $\sim 240$ km $^{-1}$, resulting in a dynamical timescale of $\sim 2000$ yr."356 Spectroscopic data with 2D angular resolution (but with lower spectral resolution) of the region around DG Tau were presented by Lavalley et al. (, Spectroscopic data with 2D angular resolution (but with lower spectral resolution) of the region around DG Tau were presented by Lavalley et al. (3571997. 2000).,"1997, 2000)."358 These observations show that some of the ejections from DG Tau have a remarkable. bow shock-like morphology. and also show in a clear way the presence of a faint counterjet to the NE (marginally seen in some of the previous observations).," These observations show that some of the ejections from DG Tau have a remarkable, bow shock-like morphology, and also show in a clear way the presence of a faint counterjet to the NE (marginally seen in some of the previous observations)."359 Interestingly. the only optical spectrophotometric study of HH 158 with an extended wavelength coverage appears to be the one of Cohen Fuller (1985).," Interestingly, the only optical spectrophotometric study of HH 158 with an extended wavelength coverage appears to be the one of Cohen Fuller (1985)."360 The spectrum described by these authors covers from -4000 to -70004. and shows (reddening corrected) ratios of [O III] 5007/HB=0.28. [ο I] 6300/H« 20.30. [N II] 6548+83/Ha=0.64 and [S UH] 6716-31/H« 20.69.," The spectrum described by these authors covers from $\sim$ 4000 to $\sim$, and shows (reddening corrected) ratios of [O III] $\beta$ =0.28, [O I] $\alpha$ =0.30, [N II] $\alpha$ =0.64 and [S II] $\alpha$ =0.69."361 These observed [ο III/H8 and [S IH]/H« ratios identify HH 158 as a high excitation HH object (see Raga et al., These observed [O $\beta$ and [S $\alpha$ ratios identify HH 158 as a high excitation HH object (see Raga et al.362 1996)., 1996).363 More recent work has focussed on the low excitation lines., More recent work has focussed on the low excitation lines.364 The paper of Solf Bóhhm (1993. mentioned above) and the more recent papers of Bacciotti et al. (," The paper of Solf Böhhm (1993, mentioned above) and the more recent papers of Bacciotti et al. ("3652000) and Coffey et al. (,2000) and Coffey et al. (3662007. 2008. who present red and near UV STIS spectra). and Pyo et al. (,"2007, 2008, who present red and near UV STIS spectra), and Pyo et al. ("3672003. who study the |Fe II] 1.644 jm emission) do ot cover the blue region of the spectrum.,"2003, who study the [Fe II] 1.644 $\mu$ m emission) do not cover the blue region of the spectrum."368 Because of this. the O III] 5007 emission reported by Cohen Fuller (1985) has not been re-observed.," Because of this, the [O III] 5007 emission reported by Cohen Fuller (1985) has not been re-observed."369 Herezeg et al. (, Herczeg et al. (3702006) obtained ΕΙΝ spectra of DG Tauri. reporting the detection of fluorescent H» lines. and the non-detection of lines like CIV 1549. which would be expected in the spectrum of a high excitation HH object.,"2006) obtained FUV spectra of DG Tauri, reporting the detection of fluorescent $_2$ lines, and the non-detection of lines like CIV 1549, which would be expected in the spectrum of a high excitation HH object."371 This non- possibly indicates that the high exeitation emission region detected by Cohen Fuller (1985) might be absent two, This non-detection possibly indicates that the high excitation emission region detected by Cohen Fuller (1985) might be absent two372"To estimate the halo mass of the z~0.6 clumpy galaxies, we assumed that rotation velocity is a good tracer of the circular velocity of their halos, from which the halo mass can be estimated, following the formalism of Moetal.(1998).","To estimate the halo mass of the $\sim$ 0.6 clumpy galaxies, we assumed that rotation velocity is a good tracer of the circular velocity of their halos, from which the halo mass can be estimated, following the formalism of \cite{mo98}."373. Similar results were obtained from halo abundance matching models (Conroy&Wechsler2009;Mosteretal. 2009):: we indeed found that z~0.6 clumpy galaxies also reside in 10?M; haloes.," Similar results were obtained from halo abundance matching models \citep{conroy09,moster09}: we indeed found that $\sim$ 0.6 clumpy galaxies also reside in $\sim$ $^{12}$ $_\odot$ haloes."374" Therefore, clumpy galaxies at z~2 and z~0.6 inhabit halos of similar mass?."," Therefore, clumpy galaxies at $\sim$ 2 and $\sim$ 0.6 inhabit halos of similar ."375". However, according to numerical simulations (Keresetal.2005),, and theoretical expectations (Dekeletal.2009),, while cold flows are expected to penetrate such halos at z~2, they are expected to be strongly attenuated in haloes of similar mass at z«1."," However, according to numerical simulations \citep{keres05}, and theoretical expectations \citep{dekel09}, while cold flows are expected to penetrate such halos at $\sim$ 2, they are expected to be strongly attenuated in haloes of similar mass at $\leq$ 1."376" The dominant mode of accretion in such z~0.6, —10'?M, haloes is rather expected to be hot gas accretion, since these haloes are too massive to allow spherical cold gas accretion to be significant."," The dominant mode of accretion in such $\sim$ 0.6, $\sim$ $^{12}$ $_\odot$ haloes is rather expected to be hot gas accretion, since these haloes are too massive to allow spherical cold gas accretion to be significant."377 The cosmological simulations of Kere$etal.(2009) indeed suggest that the average total accretion rate of gas onto the central galaxies inhabiting 10?M halos dropped down by a factor ~3 between z~2 and z~0.6 (see their Fig., The cosmological simulations of \cite{keres09} indeed suggest that the average total accretion rate of gas onto the central galaxies inhabiting $\sim$ $^{12}$ $_\odot$ halos dropped down by a factor $\sim$ 3 between $\sim$ 2 and $\sim$ 0.6 (see their Fig.378" 7), while the fraction of gas accreted cold versus hot decreased by a factor ~1.5 over this redshift range (their Fig."," 7), while the fraction of gas accreted cold versus hot decreased by a factor $\sim$1.5 over this redshift range (their Fig."379 8)., 8).380" As a consequence, according to these simulations, the cold gas accretion rate typically dropped down from ~7.5M,/yr to ~1.5M./yr (see also Brooksetal.2009))."," As a consequence, according to these simulations, the cold gas accretion rate typically dropped down from $\sim$ $_\odot$ /yr to $\sim$ $_\odot$ /yr (see also \citealt{brooks09}) )."381" Moreover, the simulations of Kere$etal.(2009) suggest that mergers dominate the mass growth of galaxies at z«1, which is in line with spatially-resolved kinematics of z~0.6 galaxies (see Introduction)."," Moreover, the simulations of \cite{keres09} suggest that mergers dominate the mass growth of galaxies at $<$ 1, which is in line with spatially-resolved kinematics of $\sim$ 0.6 galaxies (see Introduction)."382" Finally, the average velocity dispersion is found to be roughly the same between rotating disks, perturbed rotators, and galaxies showing a complex kinematics at z~0.6 (Puechetal.2007;Epinatetal.2010),, as well as in the clumpy galaxies (see Tab. 1)):"," Finally, the average velocity dispersion is found to be roughly the same between rotating disks, perturbed rotators, and galaxies showing a complex kinematics at $\sim$ 0.6 \citep{puech07,epinat09b}, as well as in the clumpy galaxies (see Tab. \ref{comp}) ):"383" if cold flows were feeding z~0.6 clumpy galaxies, then one would expect to detect an increase of the velocity dispersion in these systems, which is not observed."," if cold flows were feeding $\sim$ 0.6 clumpy galaxies, then one would expect to detect an increase of the velocity dispersion in these systems, which is not observed."384" In summary, theoretical expectations are found to be drastically different, when comparing z~2 and z~0.6 massive haloes."," In summary, theoretical expectations are found to be drastically different, when comparing $\sim$ 2 and $\sim$ 0.6 massive haloes."385" While cold streams are expected to feed z~2 clumpy galaxies in fresh gas and trigger the formation of clumps, this is unlikely to be the dominant mechanism at z~0.6."," While cold streams are expected to feed $\sim$ 2 clumpy galaxies in fresh gas and trigger the formation of clumps, this is unlikely to be the dominant mechanism at $\sim$ 0.6."386" Numerical simulations have suggested that interactions could be also an efficient trigger for instabilities in gaseous disks, resulting in the formation of clumps (diMatteoetal.2008)."," Numerical simulations have suggested that interactions could be also an efficient trigger for instabilities in gaseous disks, resulting in the formation of clumps \citep{dimatteo08}."387. Simulations revealed that such a trigger is efficient only if the fragmenting disk in the progenitor is already marginally stable before the interaction., Simulations revealed that such a trigger is efficient only if the fragmenting disk in the progenitor is already marginally stable before the interaction.388" The interaction does not necessary result in a merger, but even in this case, it is the distant interaction that triggers the instability, and not the eventual subsequent merger (diMatteoetal.2008)."," The interaction does not necessary result in a merger, but even in this case, it is the distant interaction that triggers the instability, and not the eventual subsequent merger \citep{dimatteo08}."389". Another possibility is that distant clumpy galaxies with complex kinematics could also be compact groups observed while they are merging (Amrametal.2004,2007)."," Another possibility is that distant clumpy galaxies with complex kinematics could also be compact groups observed while they are merging \citep{amram04,amram07}."390". Finally, disk rebuilding, i.e., the latest phase of a gas-rich merger where the gas expelled during the process falls back to reform a disk, could also be a good driver for clump formation, especially in galaxies that do not show any obvious of morphological or kinematic peculiarities (although the depth of images might not be large enough, see Sect."," Finally, disk rebuilding, i.e., the latest phase of a gas-rich merger where the gas expelled during the process falls back to reform a disk, could also be a good driver for clump formation, especially in galaxies that do not show any obvious of morphological or kinematic peculiarities (although the depth of images might not be large enough, see Sect."391 3.1)., 3.1).392" Note that in principle, disk rebuilding does not necessarily require merging."," Note that in principle, disk rebuilding does not necessarily require merging."393" Indeed, the disk rebuilding phase involves mainly infalling gas, which can comes from gas accretion from the intergalactic medium (e.g., through cold streams, see below), or from the gas expelled during the merger itself."," Indeed, the disk rebuilding phase involves mainly infalling gas, which can comes from gas accretion from the intergalactic medium (e.g., through cold streams, see below), or from the gas expelled during the merger itself."394" However, given the low accretion rate at z<1, disk rebuilding is probably systematically associated with merging at these redshifts."," However, given the low accretion rate at $<$ 1, disk rebuilding is probably systematically associated with merging at these redshifts."395" It is interesting to look for local counterparts of clumpy galaxies, because of the much higher spatial resolution and sensitivity of observations."," It is interesting to look for local counterparts of clumpy galaxies, because of the much higher spatial resolution and sensitivity of observations."396" As part of a morphological study of Markarian galaxies (Markarian1977),, Casini&Heidmann(1976) identified “a new class of object, with UV emission, irregular clumpy structure, large dimension, high luminosities and large internal motions” compared to normal irregular galaxies, which they called “clumpy irregular’ (see also Casini&Heidmann 1976))."," As part of a morphological study of Markarian galaxies \citep{markarian77}, \cite{casini76} identified “a new class of object, with UV emission, irregular clumpy structure, large dimension, high luminosities and large internal motions” compared to normal irregular galaxies, which they called “clumpy irregular” (see also \citealt{casini76b}) )."397" They suggested that these galaxies might be “in a turbulent or fragmented state, with large cells where the rate of star formation is high""."," They suggested that these galaxies might be “in a turbulent or fragmented state, with large cells where the rate of star formation is high”."398" Their description matches astonishing well the definition of clumpy galaxies at high redshift (e.g., Elmegreenetal. 2007))."," Their description matches astonishing well the definition of clumpy galaxies at high redshift (e.g., \citealt{elmegreen07}) )."399 A few other clump irregulars (cI) were later identified by Maeharaetal. (1988)., A few other clump irregulars (cI) were later identified by \cite{maehara88}.400". It is likely that other unidentified cI exist, but they are clearly very rare locally, even among interacting and peculiar galaxies (Casini&Heidmann 1976):: the number of known cl so far is 11, among which only 7 arenot known members of clusters (Mrk 325, 7, 8, 432, 297, VV 523, and NGC 6120)."," It is likely that other unidentified cI exist, but they are clearly very rare locally, even among interacting and peculiar galaxies \citep{casini76}: : the number of known cI so far is 11, among which only 7 arenot known members of clusters (Mrk 325, 7, 8, 432, 297, VV 523, and NGC 6120)."401 Here we consider, Here we consider402moclulation as detected in the Hghteurvoe.,modulation as detected in the lightcurve.403 We note that 7 believed. the mmin modulation was not strictly. periodi, We note that \scite{v426ophginga} believed the min modulation was not strictly periodic.404 Significant power at a period of 30.92:0.3 mmin was detected in the SISO. GIS2 and CIS3 power spectra of LS Peg([SCC refLe:lspeeperiods )).," Significant power at a period of $\pm$ min was detected in the SIS0, GIS2 and GIS3 power spectra of LS Peg (see \\ref{fig:lspegperiods}) )."405 The power spectra appear to be relatively free from red noise., The power spectra appear to be relatively free from red noise.406 Fitting the folded SISO ighteurve with a sine function vielded: an amplitude. of 325 per cent., Fitting the folded SIS0 lightcurve with a sine function yielded an amplitude of $\pm$ 5 per cent.407 The folded: SLSO lighteurve anc best-fit sine function are oesented in rellig: pertocls.., The folded SIS0 lightcurve and best-fit sine function are presented in \\ref{fig:periods}.408 The folded SISL lighteurve is consistent with his amplitu, The folded SIS1 lightcurve is consistent with this amplitude.409c 7 report a detection of a period at 29.61.85 mmin in he circular polarisation of LS Peg., \scite{lspegip} report a detection of a period at $\pm$ min in the circular polarisation of LS Peg.410ὃν The coincidence of these detected: periods Leads Us believe that the modulation detected in th lighteurve is truly periodic and that the modulation. in X-ravs and circular polarisation have a common physical origin.," The coincidence of these detected periods leads us to believe that the modulation detected in the lightcurve is truly periodic, and that the modulation in X-rays and circular polarisation have a common physical origin."411 In refsecuüps we argue that the X-ray spectrum of LS Peg is much more like that of an intermediate polar than a non-magnetic cataclysmic variable., In \\ref{sec:ips} we argue that the X-ray spectrum of LS Peg is much more like that of an intermediate polar than a non-magnetic cataclysmic variable.412 The detection of periodic modulation also supports the reclassification of LS Pee as an intermediate polar., The detection of periodic modulation also supports the reclassification of LS Peg as an intermediate polar.413 Significant power was detected in the SISO power spectrum of EL UMa at a -. of 12.360.09 mmn {see ., Significant power was detected in the SIS0 power spectrum of EI UMa at a period of $\pm$ min (see \\ref{fig:eiumaperiods}) ).414 -Fitting à sine function to the folded SLSO lighteurve we an amplituce of Scl per cent., Fitting a sine function to the folded SIS0 lightcurve we found an amplitude of $\pm$ 1 per cent.415 The folded. SESO liehteurve and best-fit sine. function are presented in reffig: periods.., The folded SIS0 lightcurve and best-fit sine function are presented in \\ref{fig:periods}.416 This period. was seen only in the SISO lighteurve and not in the other hree instruments., This period was seen only in the SIS0 lightcurve and not in the other three instruments.417 This is probably because the SISO count rate is a factor 1.3 higher than the other instruments., This is probably because the SIS0 count rate is a factor 1.3–3.3 higher than the other instruments.418 The folded. lighteurves. of all three are consistent with our fit to the folded SISO lehCurve., The folded lightcurves of all three are consistent with our fit to the folded SIS0 lightcurve.419 ‘This is the first detection of a non-orbital period [rom this svstem., This is the first detection of a non-orbital period from this system.420 In refsecuüps we argue that our fits to the spectra of IEEE USa require it to be classified. with V426 Oph and LS Peg. as an intermediate polar.," In \\ref{sec:ips}421 we argue that our fits to the spectra of EI UMa require it to be classified, with V426 Oph and LS Peg, as an intermediate polar."422 ‘The discovery. of this period provides supporting evidence for this interpretation., The discovery of this period provides supporting evidence for this interpretation.423 The lighteurve of V603 Aql is of high quality and is of particular interest because evidence of periodic modulations have been found in a previous X-ray observation (?).., The lightcurve of V603 Aql is of high quality and is of particular interest because evidence of periodic modulations have been found in a previous X-ray observation \cite{Udalski89}.424 V603 Aql is also notable for exhibiting both positive ancl negative superhumps in its optical lightcurves (?).., V603 Aql is also notable for exhibiting both positive and negative superhumps in its optical lightcurves \cite{Patterson97}.425 ? claim the detection of a mmin period in the llighteurve of νου Aql., \scite{Udalski89} claim the detection of a min period in the lightcurve of V603 Aql.426 ? analyse the same clata and agree that there may be a periodie modulation at mmin, \scite{powerspeceinstein} analyse the same data and agree that there may be a periodic modulation at min427association to the canonical low-hard state (Vacdawaleetal.2001a).,association to the canonical low-hard state \citep{vad01a}.428. For this source. Rau&Creiner(2003) fud uo correlation between the radio emission aud both soft rav endssion and wide-band (1 - 200 keV) flaws. but fiud an auti-correlation between hard N-ray (20 - 200 keV) flux and the radio ciission.," For this source, \citet{rau03} find no correlation between the radio emission and both soft X-ray emission and wide-band (1 - 200 keV) flux, but find an anti-correlation between hard X-ray (20 - 200 keV) flux and the radio emission."429 They also find that the slope of the hard power law spectra correlates positively with the radio flux in this X state., They also find that the slope of the hard power law spectrum correlates positively with the radio flux in this $\chi$ state.430 Thus. differcut types of radio aud X-rav correlations have been reported for these sources and a clear aud cousisteut picture of radio aud X-rav flux correlation in the low-hard state for these black hole candidates is vet to emorge.," Thus, different types of radio and X-ray correlations have been reported for these sources and a clear and consistent picture of radio and X-ray flux correlation in the low-hard state for these black hole candidates is yet to emerge."431" Recently, we have carried out a systematic analysis of correlation between radio. soft. aud hare N-vav fluxes as well as a study of changes m wide band X-ray spectral behavior with radio flux in the steady quiescent X-ray state for (νο N-3 (Choudluryetal.2002.heuceforthPa-per 1).. a suspected black hole caudidate with strong radio enission from a jet (AGoduszewsldetal2001:Martial. 2001)."," Recently, we have carried out a systematic analysis of correlation between radio, soft, and hard X-ray fluxes as well as a study of changes in wide band X-ray spectral behavior with radio flux in the steady quiescent X-ray state for Cyg X-3 \citep[henceforth Paper~1]{cho02a}, a suspected black hole candidate with strong radio emission from a jet \citep{mio01, mart01}."432. The X-rax cussion of Cre N-3 quite distinctively shows low aud hieh states (Rajeevetal.—1991:Nalka-nuractal. 1993). which correspond to hard ancl soft states (Choudlhurv&Rao2002).. distinguished by the shape of the N-rav spectra characterized. chiefly but not totally. by the presence (or absence) of nulticoloured disk blackbody compoucut aud the power-law iudex (albeit with the individual model componcuts more complicated than the canonical N-ray states of classical black hole candidates characterized. chiefly. by Cre XN-1. sec. for eg. Tanaka&Lewin 19953).," The X-ray emission of Cyg X-3 quite distinctively shows low and high states \citep{raj94,nak93}, which correspond to hard and soft states \citep{cho02b}, distinguished by the shape of the X-ray spectra characterized, chiefly but not totally, by the presence (or absence) of multicoloured disk blackbody component and the power-law index (albeit with the individual model components more complicated than the canonical X-ray states of classical black hole candidates characterized, chiefly, by Cyg X-1, see, for eg. \citealt{tan95}) )."433 In Paper1. we reported a stroug and significant correlation between the radio aud the soft A-orav endsson (2 12 keV. TE-ASA| in the hard state of Cye A-3. while the hard N-rayv (20 100 keV. CGRO-BATSE) auti-correlates with both he soft. N-ray aud the radio. the last auti-correlation was first reported by AIcColoughetal.(1999).," In \citetalias{cho02a} we reported a strong and significant correlation between the radio and the soft X-ray emission (2 – 12 keV, -ASM] in the hard state of Cyg X-3, while the hard X-ray (20 – 100 keV, -BATSE) anti-correlates with both the soft X-ray and the radio, the last anti-correlation was first reported by \citet{mcc99}."434. Tho wke-band N-rayv spectral analysis of the poiuted. observatious in this hard state of the source at different radio flux levels show a definite pivoting of the spectrum around 12 keV. correlated to the radio cussion (seeFigure3audTable2ofPa-per L).., The wide-band X-ray spectral analysis of the pointed observations in this hard state of the source at different radio flux levels show a definite pivoting of the spectrum around 12 keV correlated to the radio emission \citepalias[see Figure 3 and Table 2 of][]{cho02a}.435 As the interrelatiouship between radio and X-ray flux reported in Paper1) has significant inplicatious for connectivity between accretion disk aud radio jet. we lave explored other black hole candidates. for which similar radio aud X-ray data are available. for radio aud δαν flux. correlation analysis.," As the interrelationship between radio and X-ray flux reported in \citetalias{cho02a} has significant implications for connectivity between accretion disk and radio jet, we have explored other black hole candidates, for which similar radio and X-ray data are available, for radio and X-ray flux correlation analysis."436 Tere we present results of our analysis for the two persistent X-rav binaries. wicroquasars and black hole candidates. νο X-1 aud CRS 1915|105 for which quasi-siunultaueous radio and N-ray data are available from GBI. RXTE-ASML and CCRO-DATSE.," Here we present results of our analysis for the two persistent X-ray binaries, microquasars and black hole candidates, Cyg X-1 and GRS 1915+105 for which quasi-simultaneous radio and X-ray data are available from GBI, -ASM, and -BATSE."437 We select data during seriods when there are no radio fares and the source is bright both in radio aud hard N-ravs., We select data during periods when there are no radio flares and the source is bright both in radio and hard X-rays.438 We exiuniue radio XN-rav correlatious im such hard states aud show hat these correlations are simular to those found in the ow-haurd states of well studied sources hike CON 339-1., We examine radio X-ray correlations in such hard states and show that these correlations are similar to those found in the low-hard states of well studied sources like GX 339-4.439 We complement our analysis of this state bv giviug a qualitative self cousisteut picture of the steady. N-ray non-daring states of these sources. alone with Cre N-3 aud CX 339-1. using the Two Component Advective Flow (TCAF) uodel of Chakrabarti(1996).," We complement our analysis of this state by giving a qualitative self consistent picture of the steady X-ray non-flaring states of these sources, along with Cyg X-3 and GX 339-4, using the Two Component Advective Flow (TCAF) model of \citet{cha96}."440. Feuder& I&uulkers(2001) have compiled an extensive list of N-rav binaries. both neutron stars and black hole candidates. for which simultaneous N-rayv and radio observations lave Όσο. made.," \citet{kul01} have compiled an extensive list of X-ray binaries, both neutron stars and black hole candidates, for which simultaneous X-ray and radio observations have been made."441 The Green Bauls Interferometer. West Virginia. operated by NRAO. provides data for a nuniber of X-ray sources that were mouitored during its several vears of operation.," The Green Bank Interferometer, West Virginia, operated by NRAO, provides data for a number of X-ray sources that were monitored during its several years of operation."442 Collatiug these sources with those mouitored by RYTE-ASAL aud CORO-BATSE we found two N-rav binaries (black. hole candidates) viz., Collating these sources with those monitored by -ASM and -BATSE we found two X-ray binaries (black hole candidates) viz.443 (νο N-1 aud GRS 1915|105. alongwith Cre X-3. which are persistent in radio. soft aud hard X-rav bands aud for which (quasi) smnmltaneous data frou the three observatories are available.," Cyg X-1 and GRS 1915+105, alongwith Cyg X-3, which are persistent in radio, soft and hard X-ray bands and for which (quasi) simultaneous data from the three observatories are available."444 Figure d. and Figure 2. give the daily averaged light curves of GRS 1915|105 aud Cre X-1. respectively. in the soft N-rav. (ASM. panel). hard X-ray (BATSE. panel) aud the radio (2.2 GIIz. GBI. panel) diving the period when all the three iustrunients were simultaneously monitoring the sources.," Figure \ref{fig1} and Figure \ref{fig2} give the daily averaged light curves of GRS 1915+105 and Cyg X-1, respectively, in the soft X-ray (ASM, ), hard X-ray (BATSE, ) and the radio (2.2 GHz, GBI, ) during the period when all the three instruments were simultaneously monitoring the sources."445 Analogous to our approach for testing the correlation amoung the radio. soft and hard X-ray enussou from (νο N-3 (Paper1). we je used the Spearman Rawk Correlation (SRC) test and adapted the method of partial rauk correlation to est the influence of the third parameter (Mackliu1982).," Analogous to our approach for testing the correlation among the radio, soft and hard X-ray emission from Cyg X-3 \citepalias{cho02a}, we have used the Spearman Rank Correlation (SRC) test and adapted the method of partial rank correlation to test the influence of the third parameter \citep{mac82}."446. The SRC coefficient gives the strength of the correlation vetween two variables aud the corresponding D-parametcr eives the coutidence level. in terms of standard deviation. hat the derived correlation is independent of the iuflueuce of the third parameter.," The SRC coefficient gives the strength of the correlation between two variables and the corresponding D-parameter gives the confidence level, in terms of standard deviation, that the derived correlation is independent of the influence of the third parameter."447 Here we also give the results of he correlation analvsis for data averaged over differeut nue intervals viz..," Here we also give the results of the correlation analysis for data averaged over different time intervals viz.,"448 1. 5 aud 10 days as well as correlation οπου X-rav hpnarduess ratio (ratio of observed BATSE COL rate to that of ASM cotut rate) aud radio (ASAL COL rate is taken as the third parameter) for the duration nwuch the respective sources were in a relatively long erui steady quiescent hard sate.," 1, 5 and 10 days as well as correlation between X-ray hardness ratio (ratio of observed BATSE count rate to that of ASM count rate) and radio (ASM count rate is taken as the third parameter) for the duration in which the respective sources were in a relatively long term steady quiescent hard state."449 Table 1 gives the conr]ete result of the Spearima1 Rauk Correlation (SRO) est for the correlation amoung 1) the radio. soft N-rav and iud N-vav. and 2) the harduess ratio in N-rav and racio (GBI) for GRS 1915|105 aud Cve X-1 along with Cve X-3. during the steady quiesceut hard state of X-ray cussion. or fluxes in different bands averaged over 1. 5 aud 10 davs.," Table \ref{tab1}450 gives the complete result of the Spearman Rank Correlation (SRC) test for the correlation among 1) the radio, soft X-ray and hard X-ray, and 2) the hardness ratio in X-ray and radio (GBI) for GRS 1915+105 and Cyg X-1 along with Cyg X-3, during the steady quiescent hard state of X-ray emission, for fluxes in different bands averaged over 1, 5 and 10 days."451 As in Paper1. for (νο X-3. a detailed wide baud spectral analysis of CRS 1915|105 has been done using he pointed mode observations byRATE Proportional Counter Arrav (PCA) aud High Euergv X-ray Timine Expernucut (IIENTE) iustrunmieuts available inANTE archive diving the period of radio mouitoring of this source by CBI," As in \citetalias{cho02a} for Cyg X-3, a detailed wide band spectral analysis of GRS 1915+105 has been done using the pointed mode observations by Proportional Counter Array (PCA) and High Energy X-ray Timing Experiment (HEXTE) instruments available in archive during the period of radio monitoring of this source by GBI."452 For this purpose. two sets of ταν data in the X (hard) state of the source and corresponding to two extreme values of the radio flux. within the of precincts of this state. have been used for detailed spectral analysis following the method described in Paper| ," For this purpose, two sets of X-ray data in the $\chi$ (hard) state of the source and corresponding to two extreme values of the radio flux, within the of precincts of this state, have been used for detailed spectral analysis following the method described in \citetalias{cho02a}. ."453These represeutative observations. correspondius to the extreme behavior of the sources within the precincts of the respective low aud hard states; are marked as inverted arrows in Figure db aud some features of these observations are given iu Table 2..," These representative observations, corresponding to the extreme behavior of the sources within the precincts of the respective low and hard states, are marked as inverted arrows in Figure \ref{fig1}454 and some features of these observations are given in Table \ref{tab2}. ."455 Two unfolded spectrafor CIS 1915|105 are overlaid on bottom panel of Figure 3. with top panel showing similar spectra for two extreme values of radio flux in the similar state for (νο N-23 for comparison purpose (frouPaper 1).., Two unfolded spectrafor GRS 1915+105 are overlaid on bottom panel of Figure \ref{fig3} with top panel showing similar spectra for two extreme values of radio flux in the similar state for Cyg X-3 for comparison purpose \citepalias[from][]{cho02a}. .456derivation of the position of the lensed source on the Colour-Magnitude Diagram.,derivation of the position of the lensed source on the Colour-Magnitude Diagram.457" The colour and magnitude of the blend (source and lens, plus any additional blending light), marked on Fig."," The colour and magnitude of the blend (source and lens, plus any additional blending light), marked on Fig."458 2 places it about 0.4 mag to the right of the red giant branch of the LMC., \ref{fig:cmd} places it about 0.4 mag to the right of the red giant branch of the LMC.459" If this was the position of the source, it would suggest it does not belong to the LMC and is either in the foreground (in the Milky Way halo) or in the background behind the LMC."," If this was the position of the source, it would suggest it does not belong to the LMC and is either in the foreground (in the Milky Way halo) or in the background behind the LMC."460 'This candidate was already flagged by the EROS group (Tisserandetal.2007) as anomalous., This candidate was already flagged by the EROS group \citep{TisserandEROSLMC} as anomalous.461 Their data also indicate a slight reddening during the brightening of the event., Their data also indicate a slight reddening during the brightening of the event.462" This could hint towards some kind of nova eruption, however the light curve in its rising part is too smooth for a typical outburst-like object."," This could hint towards some kind of nova eruption, however the light curve in its rising part is too smooth for a typical outburst-like object."463 Taking all this into account we can not firmly conclude on the nature of this event., Taking all this into account we can not firmly conclude on the nature of this event.464" For completeness, we checked the previously known microlensing event candidates if their OGLE-III counterparts were exhibiting additional variation| atypical for microlensing events."," For completeness, we checked the previously known microlensing event candidates if their OGLE-III counterparts were exhibiting additional variation atypical for microlensing events."465" It was not necessary for the OGLE-II events as their light curves collected during the OGLE-III were already investigated in Paper I, where it was confirmed they had constant baselines in years 2001-2009."," It was not necessary for the OGLE-II events as their light curves collected during the OGLE-III were already investigated in Paper I, where it was confirmed they had constant baselines in years 2001-2009."466 MACHO group (Alcocketal.2000) have reported 17 candidate events and all of them were located within the OGLE-III fields., MACHO group \citep{AlcockMACHOLMC} have reported 17 candidate events and all of them were located within the OGLE-III fields.467" We confirm the constant baseline behaviour during the OGLE-III phase in most of them, except MACHO-LMC-7 and MACHO-LMC-23."," We confirm the constant baseline behaviour during the OGLE-III phase in most of them, except MACHO-LMC-7 and MACHO-LMC-23."468 The secondary peak in event MACHO-LMC-23 we see in our data occurred at JDz2452250 and was already reported by(2007)., The secondary peak in event MACHO-LMC-23 we see in our data occurred at $\approx2\;452\;250$ and was already reported by.469". This object was on our list of objects which were subject to cuts applied above, but its light curve was clearly asymmetrical and it was removed in the cut 8 with its blended model not converging and with large negative blending parameter."," This object was on our list of objects which were subject to cuts applied above, but its light curve was clearly asymmetrical and it was removed in the cut 8 with its blended model not converging and with large negative blending parameter."470 Event MACHO-LMC-7 originally passed through improved selection criteria for MACHO events and was included in the optical depth determination of Bennett(2005)., Event MACHO-LMC-7 originally passed through improved selection criteria for MACHO events and was included in the optical depth determination of \citet{BennettMACHOLMC}.471" The OGLE-III light curve of this object reveals three small amplitude bumps separated by 2 years, all resembling microlensing curve with time-scales between 20 and 40 days and amplitudes around 0.5 mag."," The OGLE-III light curve of this object reveals three small amplitude bumps separated by $\sim$ 2 years, all resembling microlensing curve with time-scales between 20 and 40 days and amplitudes around 0.5 mag."472 It clearly indicates this is not a genuine microlensing event but some sort of repeating outbursting variable star., It clearly indicates this is not a genuine microlensing event but some sort of repeating outbursting variable star.473 It contributed about 10 per cent to the optical depth derived in Bennett therefore their value should be now decreased to about Tpwc70.9x1077.," It contributed about 10 per cent to the optical depth derived in \citet{BennettMACHOLMC}, therefore their value should be now decreased to about $\tau_{\rm{LMC}}\approx 0.9 \times 10^{-7}$."474 Among the events reported by EROS group (Tisserandetal.2007) we successfully cross-matched with the data only two candidates: EROS-LMC-1 and EROS-LMC-11., Among the events reported by EROS group \citep{TisserandEROSLMC} we successfully cross-matched with the OGLE-III data only two candidates: EROS-LMC-1 and EROS-LMC-11.475" The latter showed constant baseline over the course of the third phase of the OGLE project, however the former exhibited a nice symmetric microlensing-like bump at JDz2453410 and, as mentioned above, actually passed through our search pipeline."," The latter showed constant baseline over the course of the third phase of the OGLE project, however the former exhibited a nice symmetric microlensing-like bump at $\approx2\;453\;410$ and, as mentioned above, actually passed through our search pipeline."476 EROS has already informed about the second peak they detected in that event occurring after nearly 5 years after the first one., EROS has already informed about the second peak they detected in that event occurring after nearly 5 years after the first one.477" The bump we detected happened after another 7 years, showing the underlying contaminant population of mysterious bumpers towards the LMC can exhibit a microlensing-like repeating episodes of brightening with random periodicity."," The bump we detected happened after another 7 years, showing the underlying contaminant population of mysterious bumpers towards the LMC can exhibit a microlensing-like repeating episodes of brightening with random periodicity."478 The only possibility of ruling them out is to rely on as long time-baseline of observations as possible., The only possibility of ruling them out is to rely on as long time-baseline of observations as possible.479 The Earth's atmosphere blurs stellar images., The Earth's atmosphere blurs stellar images.480" Astronomical images taken with medium- and large-sized telescopes are almost never diffraction limited, unless active and/or adaptive optics is used."," Astronomical images taken with medium- and large-sized telescopes are almost never diffraction limited, unless active and/or adaptive optics is used."481 The Earth's atmosphere prevents us from seeing much sharper and clearer images than we would otherwise see in its absence., The Earth's atmosphere prevents us from seeing much sharper and clearer images than we would otherwise see in its absence.482" Our atmosphere affects crowded stellar fields the most, such as the Magellanic Clouds, as many stars merge together into composite objects (“blends”) that often can be no longer resolved by PSF fitting."," Our atmosphere affects crowded stellar fields the most, such as the Magellanic Clouds, as many stars merge together into composite objects (“blends”) that often can be no longer resolved by PSF fitting."483" Since the gravitational microlensing is equally likely to happen on any star in a blend, no matter if it is bright or faint, we would like to know how many stars contribute to one composite object, because in general the number of observed objects is not equal, and usually less, than the real number of monitored stars."," Since the gravitational microlensing is equally likely to happen on any star in a blend, no matter if it is bright or faint, we would like to know how many stars contribute to one composite object, because in general the number of observed objects is not equal, and usually less, than the real number of monitored stars."484" This is of particular importance for the optical depth estimator, since at least three of its ingredients are directly affected by blending."," This is of particular importance for the optical depth estimator, since at least three of its ingredients are directly affected by blending."485 The most obvious dependent quantity is the number of monitored stars., The most obvious dependent quantity is the number of monitored stars.486 Without correction for blending our estimate of the optical depth would be overestimated., Without correction for blending our estimate of the optical depth would be overestimated.487 Another directly dependent quantity from the optical depth estimator is the detection efficiency of microlensing events., Another directly dependent quantity from the optical depth estimator is the detection efficiency of microlensing events.488 Detecting a microlensing event on a bright source blended with fainter stars would yield almost 100 per cent detection efficiency., Detecting a microlensing event on a bright source blended with fainter stars would yield almost 100 per cent detection efficiency.489" On the other hand, in case where a faint microlensed star is"," On the other hand, in case where a faint microlensed star is"490of the eas change by less than a factor of ten over mr orders of mnaguitudeUo in deusitv.,of the gas change by less than a factor of ten over four orders of magnitude in density.491" The upperyl euvelope in the upper panel is therefore dominated x the density⋅ depeudenuce: €,xf;5 aud scatter iu⋅ eniperature intoduces: only a small scatter at the ο ο. p.", The upper envelope in the upper panel is therefore dominated by the density dependence: $\epsilon_x \propto \rho_g^2$ and scatter in temperature intoduces only a small scatter at the maximum emissivity at a given $\rho_g$.492 Note that although a large fraction of WII eas is at relatively low overdensities (ορ(Py;S 100). he N-vay cussion is dominated by gas at higher overdeusities.," Note that although a large fraction of WH gas is at relatively low overdensities $\rho_g/\langle\rho_g\rangle\lesssim 100$ ), the X-ray emission is dominated by gas at higher overdensities."493 Note also that at overdeusities of PolPah~LO most of the gas has temperatures in the range T—Lor109 K. The correlation of enissivitv and temperature with density prescuted in Figure 3) are in good agreement with results of previous studies (2%.seetheirFie.6audFig.2.respectively).," Note also that at overdensities of $\rho_g/\langle\rho_g\rangle\sim 10$ most of the gas has temperatures in the range $T\sim 10^5-10^6$ K. The correlation of emissivity and temperature with density presented in Figure \ref{fig:dte} are in good agreement with results of previous studies \citep[][see their Fig.~6 and Fig.~2,494respectively]{dave_etal01,croft_etal01}."495 The use of observational constraints iuplies that the computational box axis in our simulations are mapped with the same superealactie coordinates as the observed universe., The use of observational constraints implies that the computational box axis in our simulations are mapped with the same supergalactic coordinates as the observed universe.496 Because observational constraints small scales were not too tight. there was a room for fine-tuning the position of the origin of coordinates (1.c.. position of the Local Group in the simulations).," Because observational constraints small scales were not too tight, there was a room for fine-tuning the position of the origin of coordinates (i.e., position of the Local Group in the simulations)."497 We choose the origi o be the location of a pair of galaxy size halos in the hieh-resolutiou dissipationless simulation described in Paper E (see Fig., We choose the origin to be the location of a pair of galaxy size halos in the high-resolution dissipationless simulation described in Paper I (see Fig.498 6 in that paper)., 6 in that paper).499 For lis choice of origiu. the simulated Virgo cluster las supergalactie coordinates of (SON.SCY.SCZ)L2.13.7.0.7h!Mpe and is located 13.7LitMipe rou the Local Croup.," For this choice of origin, the simulated Virgo cluster has supergalactic coordinates of $(SGX, SGY, SGZ)=-1.2,13.7,0.7\Mpch$ and is located $13.74\Mpch$ from the Local Group."500 Iuowledege ofthe supergalactic coordinates allows us to coustruct skv maps inreal celestial coordinates., Knowledge of the supergalactic coordinates allows us to construct sky maps in real celestial coordinates.501 Iu the following we preseut a series of skv maps showing projections of various quantities in a reeion of the sky around the worth galactic pole., In the following we present a series of sky maps showing projections of various quantities in a region of the sky around the north galactic pole.502 The maps are shown as polar views in the ealactic coordinates. with the North Galactic Pole (NCP:- b= 90°) TMin the center.," The maps are shown as polar views in the galactic coordinates, with the North Galactic Pole (NGP; $b=90^{\circ}$ ) in the center."503 We- plot oulv a region. of. b2na2307., We plot only a region of $b>30^{\circ}$.504" We- do not consider. ∪↑∐↸∖↥⋅↥⋅↸∖∩⊾↕∪∐↴∖↴∪↕⋟↴∖↴↽↖⇁↴⋝↸∖≼⋈∏↕↴∖↴↸∖↕⋯∪↴∖↴↑∪≯↑∐∖© M nearby structures iu the1 1high-resohitionel: region. (=30hIMpc around. the Virgo cluster) of the simulations are conceutrated around the NGP (the Virgo cluster is located within 15"" of the NGP) 2) the sky at low galactic latitudes is more difficult to observe due to galactic obscuration.", We do not consider other regions of sky because 1) most of the nearby structures in the high-resolution region $\approx 30\mpch$ around the Virgo cluster) of the simulations are concentrated around the NGP (the Virgo cluster is located within $15^{\circ}$ of the NGP) 2) the sky at low galactic latitudes is more difficult to observe due to galactic obscuration.505 All maps iuclude only. cells in the high-resolution region of the simulation:- the resolution outside this reeion was considerably. worse (cell size. of ai1.254. tMpe) and our predictious would be considerablv less accurate., All maps include only cells in the high-resolution region of the simulation; the resolution outside this region was considerably worse (cell size of $1.25\mpch$ ) and our predictions would be considerably less accurate.506 All quantities represent averages over a uunuber of raucom lines of sight passing through each imap pixel., All quantities represent averages over a number of random lines of sight passing through each map pixel.507 The integration along lines of sight was doue from 25.'Mpe to 25h'Mpe., The integration along lines of sight was done from $2\hmpc$ to $25\hmpc$.508 We tls exclude the regions in the imuucdiate vicinity of the LG which are uot modelled accurately in our siuulations., We thus exclude the regions in the immediate vicinity of the LG which are not modelled accurately in our simulations.509hospitalitv.,hospitality.510 The authors are grateful to Shane Davis and to Niaovue Guan [or providing unpublished data from their simulations., The authors are grateful to Shane Davis and to Xiaoyue Guan for providing unpublished data from their simulations.511point source mask Ap2 (which we extend by 2 degrees along the rim of the cut) used by the WALAP team (and available at the Lambda website) have been applied to avoid. possible sources of contamination.,point source mask $Kp2$ (which we extend by 2 degrees along the rim of the cut) used by the WMAP team (and available at the Lambda website) have been applied to avoid possible sources of contamination.512 Note that the unobserved. region of the PSC. catalogue is alreacly contained within this mask., Note that the unobserved region of the $z$ catalogue is already contained within this mask.513 The maps are all in the Llealpix pixelisation (Ciórskictal.1998). with ↓⋅∢⋅≱∖∪⇂⋯↓∪⊔↓≻⋜⊔⋅⋜⋯↓⋖⋅↿⋖⊾↓⋅⇀∖∖⊓∣↴∶⋅≻↓−≽≼⇍∪↓⋅↓⋅∢⊾⊳∖↓≻∪⊔∠⊔⊔⋏∙≟⋯↓≻∟∖∢⋅↓≱∖∖∖⊽⊔↓⊔⋅∠∟∙≟∢⋅≱∖∪⇂⋜↧∣⋡⋯∐⋀. ;. . ., The maps are all in the Healpix pixelisation \cite{healpix} with resolution parameter $N_{side}=512$ corresponding to pixels with edges of about $7'$.514 . ⋅ −∕ The PSCz redshift catalogue lists the angular positions. redshifts ancl Duxes of 15.500 LRAS PSC galaxies selected with a flux at 60 yan larecr than 0.6 Jv.," The $z$ redshift catalogue lists the angular positions, redshifts and fluxes of $\sim 15,500$ IRAS PSC galaxies selected with a flux at 60 $\mu m $ larger than $0.6$ Jy."515 A detailed cleseription of the selection criteria. star-galaxy separation algorithm ancl the procedures adopted to exclude galactic cirrus. are given in (Saundersetal.2000). to which we refer the interested. reacer.," A detailed description of the selection criteria, star-galaxy separation algorithm and the procedures adopted to exclude galactic cirrus, are given in \cite{saunders} to which we refer the interested reader."516 For our purposes the most interesting features of the LRAS PSC: catalogue is its very large sky. coverage (~84 of the sky. overlapping very well with the part of the sky outside the Ap2 sky cut used by WALA) and depth (he median redshift is ον~ΚΡΟΟKis TD)," For our purposes the most interesting features of the IRAS $z$ catalogue is its very large sky coverage $\sim 84 \%$ of the sky, overlapping very well with the part of the sky outside the $Kp2$ sky cut used by WMAP) and depth (the median redshift is $cz \sim 8500 \kms$ )."517 dn this work we consider a subsample of galaxies within a radius of SObhtAIpe for which distances have been obtained. from redshift using the iterative procedure of (Branchinietal., In this work we consider a subsample of galaxies within a radius of $80 \hmpc$ for which distances have been obtained from redshift using the iterative procedure of \cite{branchini}.51819:OV. The Ilux-limited: nature of the catalogue causes the number of objects to decrease with distance., The flux-limited nature of the catalogue causes the number of objects to decrease with distance.519" Phe average ealaxy-galaxy separation of the sample has been computed by (Branchinietal.1999) where rds the proper distance in. bh!Mpe. c,=87b!Mpe. Yo}=2.17bhMpe aid the parameter ob guarantees continuity at r=6bh!Mpe."," The average galaxy-galaxy separation of the sample has been computed by \cite{branchini}520 where $r$ is the proper distance in $\hmpc$, $r_{\star}=87 \hmpc$, $\langle l_0 \rangle=2.17 \hmpc$ and the parameter $A$ guarantees continuity at $r=6 \hmpc$."521 To obtain a continuous density. field. from galaxy positions with constant sampling errors throughout the sample. we have divided our spherical volume into spherical shells 10h‘Alpe thick and have smoothed the ealaxy density fick using a set of Gaussian filters of increasing racius.," To obtain a continuous density field from galaxy positions with constant sampling errors throughout the sample, we have divided our spherical volume into spherical shells $10 \hmpc$ thick and have smoothed the galaxy density field using a set of Gaussian filters of increasing radius."522 The latter have been fixed hy imposing a constant angular smoothing of about 27. as required by our cross correlation analysis.," The latter have been fixed by imposing a constant angular smoothing of about $2^{\circ}$, as required by our cross correlation analysis."523 As à consequence the galaxy distribution within the spherical shells with external radii of 20. 30. 40. 50. 60. τὸ and 80. bhMpe have been interpolated on a cubic grid and smoothed with Gaussian filters of racii (ENIM) 0.7. 1.05. 1.4. 1.75 2.1. 2.45 and 2.5 hMpe.," As a consequence the galaxy distribution within the spherical shells with external radii of 20, 30, 40, 50, 60, 70 and 80 $\hmpc$ have been interpolated on a cubic grid and smoothed with Gaussian filters of radii (FWHM) 0.7, 1.05, 1.4, 1.75 2.1, 2.45 and 2.8 $ \hmpc$."524 Eq., Eq.525 2 shows that this filtering procedure guarantees at least one object per resolution element. and thus keeps the sho noise errors at an acceptable level.," \ref{eq:self} shows that this filtering procedure guarantees at least one object per resolution element, and thus keeps the shot noise errors at an acceptable level."526 In this work we also use a third dataset generated by the cosmological hvdrodynamic simulation of our local universe performed by (Dolagetal.2005)., In this work we also use a third dataset generated by the cosmological hydrodynamic simulation of our local universe performed by \cite{dolag}.527. Phe simulation is based on a previous numerical experiment performed by (Mathisetal.2002). aimed at reproducing the mass distribution within 12.000. Kins* traced by the LRAS galaxies in the 1.2Jv recshift survey 1995)..," The simulation is based on a previous numerical experiment performed by \cite{mathis} aimed at reproducing the mass distribution within 12,000 $\kms$ traced by the IRAS galaxies in the 1.2Jy redshift survey \cite{fisher}."528 Phe original galaxy distribution was smoothed with a Gaussian filter of rewlius 5btAlpe and traced. back in time at z=50 using the method of (Ixolattetal.1996)., The original galaxy distribution was smoothed with a Gaussian filter of radius $5 \hmpc$ and traced back in time at $z=50$ using the method of \cite{kolatt}.529".. This initial field was used as €russian constraint for an otherwise random realisation of a Hat Aeoa, cosmology with ,,=0.3. Hubble constant of //)=TOKins*\Ipe+ and a rms density luctuation as=0.9."," This initial field was used as Gaussian constraint for an otherwise random realisation of a flat $\Lambda_{CDM}$ cosmology with $\Omega_m=0.3$, Hubble constant of $H_0=70 \ {\rm Km\,s^{-1}Mpc^{-1}} $ and a rms density fluctuation $\sigma_8=0.9$."530 The initial density. field. specified in a box of 240bhtMpe with a high resolution region covering a sphere of SO. bh1Mpc. has been evolved forward in time using the latest version of CADGET code (Springeletal.2001) inclucling eas-phiysies with smoothed particle hvdrodynamies in the high resolution region.," The initial density field, specified in a box of $240 \hmpc$ with a high resolution region covering a sphere of 80 $\hmpc$, has been evolved forward in time using the latest version of GADGET code \cite{springel} including gas-physics with smoothed particle hydrodynamics in the high resolution region."531 As shown by the simulated: mass clistribution at 2=0 reproduces well the main characteristics of the most prominent nearby. cosmic structures. including elusters like Virgo and Coma. the Perseus-Pisces and the Great Attractor complexes.," As shown by \cite{mathis} the simulated mass distribution at $z=0$ reproduces well the main characteristics of the most prominent nearby cosmic structures, including clusters like Virgo and Coma, the Perseus-Pisces and the Great Attractor complexes."532 “Phe hyclrodynamic re-siniulation of these initial conditions has been used to study the propagation of costnic ravs through the local universe (Dolagetal.2005)., The hydrodynamic re-simulation of these initial conditions has been used to study the propagation of cosmic rays through the local universe \cite{dolag}.533. In this work. we have considered. the simulated mass anc σας disribution at z=0 within the high resolution spherical region of radius S0. h.!Mpe and applied the same procedure adoped for the PSCz datasets. with the purpose of smoothing the mass density ancl eas density and. temperature fields on an angular smoothing scale of 2°.," In this work, we have considered the simulated mass and gas distribution at $z=0$ within the high resolution spherical region of radius 80 $\hmpc$ and applied the same procedure adopted for the $z$ datasets, with the purpose of smoothing the mass density and gas density and temperature fields on an angular smoothing scale of $2^{\circ}$."534 Το minimise boundary ellects in the smoothing procedure we have assigned gas density. and emperature to dark matter density also in each resolution element bevond SO. hi.IMpe according to the gas vs. mass relations measured in the high resolution region containing the simulated. eas particles., To minimise boundary effects in the smoothing procedure we have assigned gas density and temperature to dark matter density also in each resolution element beyond 80 $\hmpc$ according to the gas vs. mass relations measured in the high resolution region containing the simulated gas particles.535 Phe end. product consist of values of the dark matter density. gas density. ancl temperature specified at the same locations as the PSC: galaxy density. feld. within t1 same set of spherical shells and smoothed with the same Gaussian filters specified in Section 2," The end product consist of values of the dark matter density, gas density and temperature specified at the same locations as the $z$ galaxy density field, within the same set of spherical shells and smoothed with the same Gaussian filters specified in Section \ref{sect:pscz}."536 In this section. we describe how we use the galaxy catalogue to derive an estimate of the eas density and temperature in the local universe.," In this section, we describe how we use the galaxy catalogue to derive an estimate of the gas density and temperature in the local universe."537 From this estimate. we make a spherical projection to make a prediction for the SZ ellect.," From this estimate, we make a spherical projection to make a prediction for the SZ effect."538 The projection is mace onto a Lealpix-pixclised sphere with resolution parameter Ny;=64 correspondinσ to pixel edges of roughly 0.9, The projection is made onto a Healpix-pixelised sphere with resolution parameter $N_{side}=64$ corresponding to pixel edges of roughly $0.9^\circ$ .539show filamentary structures (Fieure 2).,show filamentary structures (Figure 2).540 This could help explain electron spike-like eveuts observed upstream and downstream of terrestrial and interplanetary shocks (Andersonctal.1979:Tsurutani&Lin1985:Simmettetal.2005).," This could help explain electron spike-like events observed upstream and downstream of terrestrial and interplanetary shocks \citep{Anderson1979GeoRL,Tsurutani1985JGR,Simnett2005}."541. Observation by Vovager lat the termination shock and in the heliosheath also show the evidence of electrou spike-like cnhancemenuts at the shock front (Deckeretal.2005).., Observation by Voyager $1$ at the termination shock and in the heliosheath also show the evidence of electron spike-like enhancements at the shock front \citep{Decker2005Sci}.542 The upstream spatial distribution of energetie electrons shows iregular features which depend on both the regularity in the shock surface aud the global topology of magnetic field lines., The upstream spatial distribution of energetic electrons shows irregular features which depend on both the irregularity in the shock surface and the global topology of magnetic field lines.543 At first the electrons are accelerated aud reflected at the shock front. and then they travel upstream along the magnetic field lines.," At first the electrons are accelerated and reflected at the shock front, and then they travel upstream along the magnetic field lines."544 The clectrous could be taken far wpstream by field line random walk., The electrons could be taken far upstream by field line random walk.545 This result cau possibly lead to an interpretation to the complex electron foreshock event:J4. recently observed to be associated with iuterplanetaryv shocks (Baleetal.1999:Pulupa&Dale2008)..," This result can possibly lead to an interpretation to the complex electron foreshock events recently observed to be associated with interplanetary shocks \citep{Bale1999GRL,Pulupa2008ApJ}."546 Daleetal.(1999) and Pulupa&Dale(2008) proposed the complex upstream electron events are resulted from hurge-scale ireguluities in shock surface., \citet{Bale1999GRL} and \citet{Pulupa2008ApJ} proposed the complex upstream electron events are resulted from large-scale irregularities in shock surface.547 ID this paper we have demonstrated that the upstream electron flux may be controlled by both au imegular shock surface aud scale mncandering magnetic field Ines., In this paper we have demonstrated that the upstream electron flux may be controlled by both an irregular shock surface and large-scale meandering magnetic field lines.548 The authors would hike to thank Dr. D. Burecss for sharing the details of nunerical methods and Dr. J. R. Jokipii for valuable discussions., The authors would like to thank Dr. D. Burgess for sharing the details of numerical methods and Dr. J. R. Jokipii for valuable discussions.549 This work was supported in part by NSF under eraut ATAIOLI7351 and by NASA under eraut. NNNOTATTLOG., This work was supported in part by NSF under grant ATM0447354 and by NASA under grant NNX07AH19G.550where J; is (he estimated chump-centrie brightness of the RGBB for that metallicity. We is the weight of that brightness component in (he estimated distribution. ancl D is the measured exponential slope of the RG branch. 0.547.,"where $I_{i}$ is the estimated clump-centric brightness of the RGBB for that metallicity, $W_{i}$ is the weight of that brightness component in the estimated distribution, and $B$ is the measured exponential slope of the RG branch, $0.547$."551" We calculate the weighted mean ancl variance: obtaining a mean J=0.560 and o,=0.157.", We calculate the weighted mean and variance: obtaining a mean $\overline{I}=0.560$ and ${\sigma_{I}}=0.157$.552" This is reassurinely lower than the measured dispersion 75,6545;=0.203 mag. a ""requirement"" as (here will be additional variation induced by differential reddening. binary blending contamination and distance variation due to the large physical size of the bulge - contributions expected (o similarly affect the RC."," This is reassuringly lower than the measured dispersion ${\sigma}_{RGBB} = 0.203$ mag, a “requirement” as there will be additional variation induced by differential reddening, binary blending contamination and distance variation due to the large physical size of the bulge - contributions expected to similarly affect the RC."553 We brielly note the difference in (he mean compared (to our measurement could also be removed by discarding the small sample of expected RGBB (less than )) that are within 0.25 mag ol the RC as our fitting routine is not sensitive to (hose RGDD stars — the mode of our expected distribution is al 20.71 mag., We briefly note the difference in the mean compared to our measurement could also be removed by discarding the small sample of expected RGBB (less than ) that are within 0.25 mag of the RC as our fitting routine is not sensitive to those RGBB stars – the mode of our expected distribution is at $\sim$ 0.71 mag.554 A smaller brightness dispersion of the RGBB than for the RC is a surprise., A smaller brightness dispersion of the RGBB than for the RC is a surprise.555 Performing the same calculation as above for RC stars. assuming liletimes independent of metallicity and a brightness relation .Mgc /.N[Fe/IH] =0.14 mag/dec (Pietrzytiskietal.2010). implies a dispersion of o;50.06 mag.," Performing the same calculation as above for RC stars, assuming lifetimes independent of metallicity and a brightness relation ${\Delta}I_{RC}/{\Delta}$ [Fe/H] $= 0.14$ mag/dec \citep{2010AJ....140.1038P} implies a dispersion of ${\sigma}_{I} \approx 0.06$ mag."556 Galactic bulee RG stars have been measured to have similar proper motion distributions as (heir RC counterparts (Rattenburyetal.2007b).. an observational constraint (hat negates the possibility of a substantial bias-inducing metallidtv-geometrv correlation.," Galactic bulge RG stars have been measured to have similar proper motion distributions as their RC counterparts \citep{2007MNRAS.378.1165R}, an observational constraint that negates the possibility of a substantial bias-inducing age-metallicity-geometry correlation."557 There could be a bias induced in the parameters if the bulge RC has a skewed distribution as it is [it to a Gaussian. the residuals would then alfect the fit to the RGBLB.," There could be a bias induced in the parameters if the bulge RC has a skewed distribution as it is fit to a Gaussian, the residuals would then affect the fit to the RGBB."558 We do not expect (his to be the case as the brightness distribution of the RC should be made very svuunetric by. eeometrical dispersion., We do not expect this to be the case as the brightness distribution of the RC should be made very symmetric by geometrical dispersion.559 Forcing the intrinsic dispersion of the RGDD to be 0.05 mag higher than that of the RC increases 4? by 7320. demonstrating that a significantly different finetional form would need to be assumed ancl justified to obtain a larger dispersion for the RGDD.," Forcing the intrinsic dispersion of the RGBB to be 0.05 mag higher than that of the RC increases ${\chi}^2$ by $\sim$ 320, demonstrating that a significantly different functional form would need to be assumed and justified to obtain a larger dispersion for the RGBB."560 We therefore conclude that (he narrow huminosityv [unetion for the RGDD relative to the RC may be real., We therefore conclude that the narrow luminosity function for the RGBB relative to the RC may be real.561 This could be achieved if there are subpopulations in the bulge that contribute substantially to the RC population and (hus its dispersion but. verv weakly to the RGBB. such as a much more helium-rich population.," This could be achieved if there are subpopulations in the bulge that contribute substantially to the RC population and thus its dispersion but very weakly to the RGBB, such as a much more helium-rich population."562 hi (his scenario. it is the RC! dispersion is too high rather than the RGDD dispersion being too low.," In this scenario, it is the RC dispersion is too high rather than the RGBB dispersion being too low."563"case the slope of the increase of the phase difference is smaller than in the previous one, and the amplification also has lower values.","case the slope of the increase of the phase difference is smaller than in the previous one, and the amplification also has lower values."564 It means that the phase delay between the velocities at the formation height of these two lines is smaller than the delay between aand and the amplitude of the waves at the formation height of iis larger than that of waves at the layer where fforms., It means that the phase delay between the velocities at the formation height of these two lines is smaller than the delay between and and the amplitude of the waves at the formation height of is larger than that of waves at the layer where forms.565 Both the phase and amplification spectra locate the formation height of the ccore below the lline., Both the phase and amplification spectra locate the formation height of the core below the line.566 The parameters retrieved from the fit of the phase and amplification spectra to the theoretical model are listed in Table 3.., The parameters retrieved from the fit of the phase and amplification spectra to the theoretical model are listed in Table \ref{tb:parameters}.567" Comparing the ones retrieved for the line pair wwith the pairH,, the ccore formation height in the umbra is around 250 km below the line."," Comparing the ones retrieved for the line pair with the pair, the core formation height in the umbra is around 250 km below the line."568 The temperature obtained for the phase difference between aand iis smaller by 500 K; waves traveling from the formation height of ccore to that of ppass presumably through a region where the temperature is increasing., The temperature obtained for the phase difference between and is smaller by 500 K; waves traveling from the formation height of core to that of pass presumably through a region where the temperature is increasing.569" To study the properties of oscillations at photospheric heights, phase diagrams between pairs of the photospheric lines were calculated."," To study the properties of oscillations at photospheric heights, phase diagrams between pairs of the photospheric lines were calculated."570 We can assume that the llines in the wwing form at three different heights according to their line depth (Fig., We can assume that the lines in the wing form at three different heights according to their line depth (Fig.571 3) and to the width of the velocity histograms (Fig. 6))., 3) and to the width of the velocity histograms (Fig. \ref{fig:velocity_hist}) ).572" We take the lines 3965.4, 3966.0 and λ 3969.3 as representative of these heights, since 3966.6 and λ 3967.4 seem to form at a similar height as A 3966.0."," We take the lines $\lambda$ 3965.4, $\lambda$ 3966.0 and $\lambda$ 3969.3 as representative of these heights, since $\lambda$ 3966.6 and $\lambda$ 3967.4 seem to form at a similar height as $\lambda$ 3966.0."573" As an example, Fig."," As an example, Fig."574" 11 shows the phase spectra, coherence and amplification spectra obtained between between λ 3966.0 and A 3969.3."," \ref{fig:dfase_Fe2Fe5} shows the phase spectra, coherence and amplification spectra obtained between between $\lambda$ 3966.0 and $\lambda$ 3969.3."575 The phase spectrum shows that the phase difference is almost zero for all the frequencies that can be trusted according to the coherence spectra (from 0 to 10 , The phase spectrum shows that the phase difference is almost zero for all the frequencies that can be trusted according to the coherence spectra (from 0 to 10 mHz).576"We conclude that we can not retrieve the phase shift mHz).between the llines reliably, as the geometrical difference in their heights of the formation is too small."," We conclude that we can not retrieve the phase shift between the lines reliably, as the geometrical difference in their heights of the formation is too small."577" However, the amplification spectra reflects some increase of the amplitude with height."," However, the amplification spectra reflects some increase of the amplitude with height."578 We managed to fit both the phase and the amplification spectra with the wave model described in the previous section., We managed to fit both the phase and the amplification spectra with the wave model described in the previous section.579" These fits yield, indeed, a small geometrical height difference between the lines."," These fits yield, indeed, a small geometrical height difference between the lines."580 The temperature and the cooling time obtained from the fit are identical for all pairs of iron lines (Table 3))., The temperature and the cooling time obtained from the fit are identical for all pairs of iron lines (Table \ref{tb:parameters}) ).581 The phase difference spectrum between the λ 3969.3 line and the À 10827 line is shown in the top panel of Fig. 12.., The phase difference spectrum between the $\lambda$ 3969.3 line and the $\lambda$ 10827 line is shown in the top panel of Fig. \ref{fig:dfase_FeSi}.582" For frequencies below 2 mHz, the phase spectrum is very noisy and has no coherence (see middle panel), indicating"," For frequencies below 2 mHz, the phase spectrum is very noisy and has no coherence (see middle panel), indicating"583ess -- Swe vary the sample size to 255 or 50 subsamples at à given redshift.,less if we vary the sample size to 25 or 50 subsamples at a given redshift.584 Phe error on the AAP function. shown as a ereen shaded region in Fig. 5..," The error on the AAP function, shown as a green shaded region in Fig. \ref{5a},"585 was found using a similar method to find the variance in à at each redshift’ splitting the pairs in the simulations into LOO subsaniples., was found using a similar method to find the variance in $\alpha$ at each redshift splitting the pairs in the simulations into 100 subsamples.586 The errors on both ísin?7) and on the AAP function increase with increasing redshift as the number of pairs decreases., The errors on both $\langle \sin^2 \tau \rangle$ and on the AAP function increase with increasing redshift as the number of pairs decreases.587 This happens because of the fixed resolution of the simulation. which means that we resolve a progressively smaller fraction of the subhalo population with increasing redshift.," This happens because of the fixed resolution of the simulation, which means that we resolve a progressively smaller fraction of the subhalo population with increasing redshift."588 A similar drop in the number of pairs would happen in a lux limited galaxy survey., A similar drop in the number of pairs would happen in a flux limited galaxy survey.589 We have tested the stability of the method. by comparing simulations of dillerent. resolution., We have tested the stability of the method by comparing simulations of different resolution.590 The sample mean. (in+ (leq. 13).," The sample mean, $\langle \sin^2\tau \rangle$ (Eq. \ref{sin2t}) ),"591 of the distribution of subhalo pairs in redshift space in the two ΑςΝΤ simulations. higher and lower resolution. is shown in Fig.," of the distribution of subhalo pairs in redshift space in the two $\Lambda$ CDM simulations, higher and lower resolution, is shown in Fig."592 ο at cliflerent redshifts., \ref{3b} at different redshifts.593 The mean for the lower resolution simulation is shown as blue squares in Fig. 6., The mean for the lower resolution simulation is shown as blue squares in Fig. \ref{3b}.594 Phe AAD function. using the measured value for à at cach redshift is shown as a solid black line as in Fig. 5.., The AAP function using the measured value for $\alpha$ at each redshift is shown as a solid black line as in Fig. \ref{5a}.595 Phe sample mean from the higher resolution simulation is shown as purple circles with the corresponding AAP function shown as a solid light. blue line., The sample mean from the higher resolution simulation is shown as purple circles with the corresponding AAP function shown as a solid light blue line.596 In both the lower and higher resolution simulations. the measured distribution of pairs shows excellent agreement with the predictions of the AAP function assuming a ACDAL cosmology. and also agree with cach other in shape and amplitude within the error bars.," In both the lower and higher resolution simulations, the measured distribution of pairs shows excellent agreement with the predictions of the AAP function assuming a $\Lambda$ CDM cosmology, and also agree with each other in shape and amplitude within the error bars."597 The dillerence. between he AAP function for the higher resolution (blue shading) and for the lower resolution simulation (solid black line) in Fig., The difference between the AAP function for the higher resolution (blue shading) and for the lower resolution simulation (solid black line) in Fig.598 6 is also due to the difference in. resolution tween the two simulations., \ref{3b} is also due to the difference in resolution between the two simulations.599 Lowe select. only subhalos rom the higher resolution simulation that have a halo mass of Al95LOMATALS. whieh corresponds to the minimum halo mass selected by the FOR algorithm in the ower resolution simulation. we obtain the red stars with errors. bars plotted in. Fig. 6..," If we select only subhalos from the higher resolution simulation that have a halo mass of $M \ge 9 \times 10^{12} h^{-1}M_{\sun}$, which corresponds to the minimum halo mass selected by the FOF algorithm in the lower resolution simulation, we obtain the red stars with errors bars plotted in Fig. \ref{3b}."600 These points are almost coincident with the corresponding measurement from the ower resolution simulation (blue squares). agreeing to better han le.," These points are almost coincident with the corresponding measurement from the lower resolution simulation (blue squares), agreeing to better than $\sigma$."601 We also make contact with an observational galaxy sample in Fig. 6.., We also make contact with an observational galaxy sample in Fig. \ref{3b}.602 Lowe select subhalos from main halos which vave a mass of AL=1.105tALs we obtain the mean slotted as orange crosses in Fig. 6.., If we select subhalos from main halos which have a mass of $M \ge 1 \times 10^{14} h^{-1}M_{\sun}$ we obtain the mean plotted as orange crosses in Fig. \ref{3b}.603 Again these results are consistent with the means for the lower resolution simulation at cach redshift., Again these results are consistent with the means for the lower resolution simulation at each redshift.604 This mass corresponds to the minimum halo miss expected to contain two or more luminous red ealaxies (LRGs) on average (2).., This mass corresponds to the minimum halo mass expected to contain two or more luminous red galaxies (LRGs) on average \citep{2008MNRAS.386.2145A}.605 Vhis subhalo selection is relevan [or a spectroscopic redshift. survey such as the SDSS-LL BOSS survey (2). which will target. LRGs in the redshif range z« 0.7., This subhalo selection is relevant for a spectroscopic redshift survey such as the SDSS-III BOSS survey \citep{2007AAS...21113229S} which will target LRGs in the redshift range $z<0.7$ .606 Without applving any selection cuts. we finc approximately 27.000 subhalo pairs at >=0 which share a common halo of ÀJ=110thTALS. at =0.25 anc =0.5 the number of subhalo pairs are approximately 5.000 and. 11.000. respectively.," Without applying any selection cuts, we find approximately 27,000 subhalo pairs at $z=0$ which share a common halo of $M \ge 1 \times 10^{14} h^{-1}M_{\sun}$, at $z=0.25$ and $z=0.5$ the number of subhalo pairs are approximately 18,000 and 11,000 respectively."607 From the first semester of BOSS data. ? estimate that the cumulative probability hat a galaxy in their sample is hosted. by a halo of mass Al>1OthAL; is about5%.," From the first semester of BOSS data, \citet{2011ApJ...728..126W} estimate that the cumulative probability that a galaxy in their sample is hosted by a halo of mass $M \ge 1 \times 10^{14} h^{-1}M_{\sun}$ is about."608. LE we extend this xobabilitv to the full sample of LRGs expected by BOSS with space density η=310Th? /Mpc?. this corresponds o approximately 13.000 pairs of LItGs in the redshift range 2=05 0.6.," If we extend this probability to the full sample of LRGs expected by BOSS with space density $\bar{n} = 3 \times 10^{-4}h^3/$ $^3$, this corresponds to approximately 13,000 pairs of LRGs in the redshift range $z=0.5-0.6$ ."609 Phis is similar to the number of pairs we obtain from the higher resolution simulation restricting to idos with to ALz1510H451AL; atc0.5. shown bv he orange crosses in Fig. 6..," This is similar to the number of pairs we obtain from the higher resolution simulation restricting to halos with to $M \ge 1 \times 10^{14} h^{-1}M_{\sun}$ at $z=0.5$, shown by the orange crosses in Fig. \ref{3b}."610" The errors on the AAP function. as measured. by Abuinoni Buzzi. a=5.79TES,Uh are substantially larger han ours due to the uncertainty in fitting for the parameter o at 2=O with a smaller number of pairs."," The errors on the AAP function as measured by Marinoni Buzzi, $\alpha = 5.79^{+0.32}_{-0.35}$, are substantially larger than ours due to the uncertainty in fitting for the parameter $\alpha$ at $z=0$ with a smaller number of pairs."611 Our higher resolution simulation has approximately 4 times more subhalo pairs than the lower resolution simulation. alter making the selection cuts discussed in Section 4. which gives rise to error bars which are approximately smaller in 1 higher resolution run (see Fig. 6)).," Our higher resolution simulation has approximately 4 times more subhalo pairs than the lower resolution simulation, after making the selection cuts discussed in Section 4, which gives rise to error bars which are approximately smaller in the higher resolution run (see Fig. \ref{3b}) )."612 Phe sample of pairs isec by Marinoni Buzzi is approximately 25 times smaller ren the sample from our lower resolution simulation., The sample of pairs used by Marinoni Buzzi is approximately 25 times smaller then the sample from our lower resolution simulation.613 We have verified that by applying the Marinoni Buzzi selection cuts to our parent sample of subhalo pairs in 16 lower resolution simulation gives a=5.69. which is consistent with the value for à obtained by these authors.," We have verified that by applying the Marinoni Buzzi selection cuts to our parent sample of subhalo pairs in the lower resolution simulation gives $\alpha = 5.69$, which is consistent with the value for $\alpha$ obtained by these authors."614 llowever. we find that the measured mean for this simulation sample does not agree with the AAP function within the error bars (if our sample was the same size as that used by Alarinoni Buzzi our errors wouldbe significantly larger and the two would agree in this case).," However, we find that the measured mean for this simulation sample does not agree with the AAP function within the error bars (if our sample was the same size as that used by Marinoni Buzzi our errors wouldbe significantly larger and the two would agree in this case)."615 This demonstrates the need for the robust resolution independent selection criteriawe have presented here., This demonstrates the need for the robust resolution independent selection criteriawe have presented here.616 14=z20 (Bennett z6 (Fanetal.2001," $14 \lesssim z617\lesssim 20$ \citep{WMAP1,WMAP2} $z \sim 6$ \citep{Bec01,Fan02}. \citep{Fan01},"618).. z—7.," $z > 7$ \citep[e.g.,][]{Tin73,Sok03a}."619 (e.g..Yan. Ενα Maieretal.2003:Cub," \citep[e.g.,][]{Yan03,Sta03,Bun03,Dic03} $\alpha$ \citep[e.g.,][]{Rho03,Mai03,Cub03}."620y2003).. /-band 5.5zzς6.5) <>7 Panagia.Stiavelli.&Fall2003).," $I$ $5.5 \lesssim z \lesssim 6.5$ $z > 7$ \citep[e.g.,][]{Tho95,Tho96,Pan03}."621. Lya may boost the Ένα flux of the earliest stars (e.g..Bromm.Kudritzki.&Loeb2001:Schaerer 2003).," $\alpha$ may boost the $\alpha$ flux of the earliest stars \citep[e.g.,][]{Bro01,Sch03}."622 In addition. this emission may penetrate even a neutral [IGM with reasonable efficiency (Haiman2002;Santos2003).," In addition, this emission may penetrate even a neutral IGM with reasonable efficiency \citep{Hai02,San03}."623. Taken together. the arguments above strongly motivate the search for Lyo emission at redshifts z=>7 using narrow-band imaging in the near-infrared.," Taken together, the arguments above strongly motivate the search for $\alpha$ emission at redshifts $z \geq 7$ using narrow-band imaging in the near-infrared."624" Here. we describe a search for Lyo in a narrow Z-band ""window"" in the sky background. corresponding to z8."," Here, we describe a search for $\alpha$ in a narrow $J$ -band “window” in the sky background, corresponding to $z\sim 8$."625 We examine the star formation rates in the cosmological simulations of Springel&Hernquist(2003a)., We examine the star formation rates in the cosmological simulations of \citet{Spr03a}.626. Employing a novel treatment of smoothed particle hydrodynamics and a multiphase description of star-forming σας to incorporate feedback and stellar winds (Springel&Hern-quist2002. 2003b).. Springel&Hernquist(2003a) obtained a numerically converged prediction for the cosmic. star formation rate (SFR) as a function of redshift that agrees with the observed star formation history at low Here. we focus on the 10ΤΙcomovingMpe Q5 simulation of a WMAP-concordant cosmology with 2«324° particles.," Employing a novel treatment of smoothed particle hydrodynamics and a multiphase description of star-forming gas to incorporate feedback and stellar winds \citep{Spr02,Spr03b}, , \citet{Spr03a} obtained a numerically converged prediction for the cosmic star formation rate (SFR) as a function of redshift that agrees with the observed star formation history at low Here, we focus on the $10\ h^{-1}\ {\rm comoving\627Mpc}$ Q5 simulation of a -concordant cosmology with $2\times324^3$ particles."628 The more luminous sources in the simulations have star formation rates in the range of 107<MX1 ./yr.," The more luminous sources in the simulations have star formation rates in the range of ${\rm 10^{-2}629\leq \dot{M} \lesssim 1}$ $_{\sun}$ /yr."630 With typical dynamical masses of 105—10?M. at z—8. their intrinsic circular velocities are generally 30—50kms7!.," With typical dynamical masses of ${\rm 10^8-10^9\ M_{\sun}}$ at $z=8$, their intrinsic circular velocities are generally ${\rm 30-50\ km\ s^{-1}}$."631 The simulations predict an early rise m star formation activity at > S:atz=8. the star formation rate density is within a factor of ~2 of its peak. relatively independent of the details of the physics of star formationand feedback(HernquistSpringel2003).Theamount of Lya that we canobserve from young star- objects depends on the IMF and metallicity in early galaxies.the amount of attenuation within the galaxy itself. and the amount of scattering inthe intergalactic medium:," The simulations predict an early rise in star formation activity at $z632\geq 5$ ; at $z=8$, the star formation rate density is within a factor of $\sim$ 2 of its peak, relatively independent of the details of the physics of star formationand feedback(HernquistSpringel2003).Theamount of $\alpha$ that we canobserve from young star-forming objects depends on the IMF and metallicity in early galaxies,the amount of attenuation within the galaxy itself, and the amount of scattering inthe intergalactic medium:"633The effective size of astar ata given wavelength depends on the opacity of the stellar atmosphere at that wavelength.,The effective size of a star at a given wavelength depends on the opacity of the stellar atmosphere at that wavelength.634 Since we effectively measure the diameter of the 7=| surface of the star. the size is related to the extension of the atmospheric region where the absorption is produced.," Since we effectively measure the diameter of the $\tau = 1$ surface of the star, the size is related to the extension of the atmospheric region where the absorption is produced."635 The diameter of that surface varies with opacity. hence frequency.," The diameter of that surface varies with opacity, hence frequency."636 The atmospheres of cool giants are so extended that these size variations are observable with an interferometer., The atmospheres of cool giants are so extended that these size variations are observable with an interferometer.637 Quirrenbach et al. (1993... 2001) ," Quirrenbach et al. \cite{Quirrenbach1993}, \cite{Quirrenbach2001}) )"638studied the extended absorption regions of stellar atmospheres of cool giant stars in the TiO band at nnm with the ΜΙΚΗ interferometer., studied the extended absorption regions of stellar atmospheres of cool giant stars in the TiO band at nm with the MkIII interferometer.639 These authors measured the visibilities of a set of 47 stars using two filters. one centered in the TiO band. and the other in the continuum part of the spectrum close to the TiO band nnm).," These authors measured the visibilities of a set of 47 stars using two filters, one centered in the TiO band, and the other in the continuum part of the spectrum close to the TiO band nm)."640 They found that the sizes in the TIO band are larger than those in the continuum. and that this effect is stronger for cooler stars.," They found that the sizes in the TiO band are larger than those in the continuum, and that this effect is stronger for cooler stars."641 The sizes in the TiO absorption band are ~10% larger than in the continuum for R-7 color indices of ~1.6 (spectral types M3-M4) and as much as larger for R—I color indices of ~2.2 (spectral types M6-M7)., The sizes in the TiO absorption band are $\sim 10$ larger than in the continuum for $R-I$ color indices of $\sim1.6$ (spectral types M3–M4) and as much as larger for $R-I$ color indices of $\sim2.2$ (spectral types M6–M7).642 Similar differences between the sizes observed in the continuum and in bands containing absorption band heads of other molecules (such as H:O or CO) have been reported for AGB stars., Similar differences between the sizes observed in the continuum and in bands containing absorption band heads of other molecules (such as $_2$ O or CO) have been reported for AGB stars.643 Mennesson et al. (2002)), Mennesson et al. \cite{Mennesson2002}) )644 and Perrin et al. (2004).," and Perrin et al. \cite{Perrin2004}) ),"645 for instance. reported very large size ratios or more) for some stars.," for instance, reported very large size ratios or more) for some stars."646 Quirrenbach et al. (1993... 2001))," Quirrenbach et al. \cite{Quirrenbach1993}, \cite{Quirrenbach2001}) )"647 were successful in qualitatively reproducing their data with the latest set of cool giant models from the general-purpose stellar atmosphere codePHOENIX., were successful in qualitatively reproducing their data with the latest set of cool giant models from the general-purpose stellar atmosphere code.648 Spherical. hydrostatic. massively line-blanketed atmosphere models were constructed and used to predict the uniform-disk diameters in the TiO band and the continuum band as a function of model effective temperature. surface gravity. and mass (the stellar mass was used in the modeling. since it controls the deviation from plane-parallel atmospheres.)," Spherical, hydrostatic, massively line-blanketed atmosphere models were constructed and used to predict the uniform-disk diameters in the TiO band and the continuum band as a function of model effective temperature, surface gravity, and mass (the stellar mass was used in the modeling, since it controls the deviation from plane-parallel atmospheres.)"649 For most of the observed oxygen-rich giants. the diameter ratios of the TiO band to the continuum band agreed with the models computed for masses ~0.5M...," For most of the observed oxygen-rich giants, the diameter ratios of the TiO band to the continuum band agreed with the models computed for masses $\sim 0.5\,M_\odot$."650 Hence. model atmospheres with very low stellar masses could fit the large diameter ratios observed in many stars. although evolutionary models predict masses as high as M...," Hence, model atmospheres with very low stellar masses could fit the large diameter ratios observed in many stars, although evolutionary models predict masses as high as $M_\odot$."651 A possible explanation of this inconsistency would be the existence of a transition zone at the base of the stellar wind (theMOLsphere: e.g. Tsuji 2008.. and references therein). which could provide sufficient opacity in the TIO bands (and other molecular bands) to make AGB stars appear much larger than predicted by the hydrostatie model atmospheres such asPHOENIX.," A possible explanation of this inconsistency would be the existence of a transition zone at the base of the stellar wind (the; e.g. Tsuji \cite{Tsuji2008}, and references therein), which could provide sufficient opacity in the TiO bands (and other molecular bands) to make AGB stars appear much larger than predicted by the hydrostatic model atmospheres such as."652 According to this picture. one would expect similar size effects for the CO band heads.," According to this picture, one would expect similar size effects for the CO band heads."653" Therefore. we decided to use AMBER in the K band to measure the effective sizes of a set of four cool giant stars through the CO band heads at 2.3,m. The use of AMBER in medium-resolution mode (UAL~ 1500) provides considerably more information than could be obtained with the MkII interferometer (Quirrenbach et al. 1993))"," Therefore, we decided to use AMBER in the K band to measure the effective sizes of a set of four cool giant stars through the CO band heads at $\mu$ m. The use of AMBER in medium-resolution mode $\lambda/\Delta\lambda \sim 1500$ ) provides considerably more information than could be obtained with the MkIII interferometer (Quirrenbach et al. \cite{Quirrenbach1993}) )"654 and the [OTA interferometer (Mennesson et al. 2003:, and the IOTA interferometer (Mennesson et al. \cite{Mennesson2002};655 Perrin et al. 2004)).," Perrin et al. \cite{Perrin2004}) ),"656 in which narrow-band filters were used., in which narrow-band filters were used.657 In this paper. we report on the results obtained from the analysis of the observations of the first star of our sample: RS Cap.," In this paper, we report on the results obtained from the analysis of the observations of the first star of our sample: RS Cap."658 RS Cap 2200994) has a K-band magnitude of —0.2 (Cutri et al. 2003))., RS Cap 200994) has a K-band magnitude of $-0.2$ (Cutri et al. \cite{cutri2003}) ).659" It is a semi-regular variable (SRb) of spectral type M6/M7III and ts located at a=21h07m195.15. 0=-16*25'21.4"" (J2000.0)."," It is a semi-regular variable (SRb) of spectral type M6/M7III and is located at $\alpha = 21\textrm{h}\,07\textrm{m}\,15.4\textrm{s}$, $\delta =660-16^{\circ}\,25'\,21.4''$ (J2000.0)."661 It has a visual magnitude of 8.3 and a parallax 7=1.26+0.56 mmas (van Leeuwen 2007)). which maps into a distance between 500 and 2500 ppc.," It has a visual magnitude of 8.3 and a parallax $\pi = 1.26\pm0.86$ mas (van Leeuwen \cite{Leeuwen2007}) ), which maps into a distance between $500$ and $2500$ pc."662 However. following Scalo (1976)) or Winters et al. (2003)).," However, following Scalo \cite{Scalo1976}) ) or Winters et al. \cite{winters03}) ),"663 a bolometric absolute magnitude between —4 and —5 ts derived for RS Cap (around —4.8 in the case of Winters et al.)., a bolometric absolute magnitude between $-4$ and $-5$ is derived for RS Cap (around $-4.8$ in the case of Winters et al.).664 These estimates. in addition to the spectrum fitted between 0.1 and 2um. translate into a distance of ~300ppe (Richichi et al. 1992)).," These estimates, in addition to the spectrum fitted between 0.1 and $\mu$ m, translate into a distance of $\sim$ pc (Richichi et al. \cite{Richichi1992}) )."665 A variability amplitude of AVY~0.5 is seen in the Hippareos data (Perryman ESA 1997)). although a larger variability amplitude (in photometric magnitude) of AB~2 ," A variability amplitude of $\Delta V \sim 0.5$ is seen in the Hipparcos data (Perryman ESA \cite{Perryman1997}) ), although a larger variability amplitude (in photometric magnitude) of $\Delta B \sim 2$ "666same order of magnitude but roughly a factor four larger than the observed value of =—7.4.,same order of magnitude but roughly a factor four larger than the observed value of $\approx -7.4$.667 Given the extrapolation and Altair's latitude dependent temperature and radius. this rough agreement is remarkable. but could be a chance effect.," Given the extrapolation and Altair's latitude dependent temperature and radius, this rough agreement is remarkable, but could be a chance effect."668 While a larger amount of the hot plasma might be lost às coronal winds from open magnetic structures. a modified dynamo model seems to be physically more adequate.," While a larger amount of the hot plasma might be lost as coronal winds from open magnetic structures, a modified dynamo model seems to be physically more adequate."669 This model has to consider the particular properties of Altair. specifically its distorted structure and surface. here accounted for by the latitude dependent photospheric temperature.," This model has to consider the particular properties of Altair, specifically its distorted structure and surface, here accounted for by the latitude dependent photospheric temperature."670 We note that the similar A7 star Alderamin (α CCep) has a RASS X-ray luminosity comparable to that of Altair. indicating that the coronal properties of Altair are rather characteristic for this type of star.," We note that the similar A7 star Alderamin $\alpha$ Cep) has a RASS X-ray luminosity comparable to that of Altair, indicating that the coronal properties of Altair are rather characteristic for this type of star."671 Instead of a globally operating solar-like dynamo. we therefore additionally investigated a localized version to describe the magnetic field generation in Altair," Instead of a globally operating solar-like dynamo, we therefore additionally investigated a localized version to describe the magnetic field generation in Altair."672 ? and ? find that the activity-rotation relation holds up to 00.3. Le. the regime of early F-type stars which have effective temperatures similar to the temperatures that exist in. the equatorial region of Altair.," \cite{dob89} and \cite{ran96} find that the activity-rotation relation holds up to 0.3, i.e. the regime of early F-type stars which have effective temperatures similar to the temperatures that exist in the equatorial region of Altair."673 Repeating the above calculation for 00.3 (= 7700077200 K) leads to an expected activity level of logLx/Ly4x.—5.3., Repeating the above calculation for 0.3 $\approx$ 7200 K) leads to an expected activity level of $\log L_{\rm X}/L_{\rm bol}\approx -5.3$.674 Consequently. when generating X-rays with a similar efficiency. only a few percent of Altair’s surface would easily account for the observed X-ray emission.," Consequently, when generating X-rays with a similar efficiency, only a few percent of Altair's surface would easily account for the observed X-ray emission."675 The surface area exhibiting these photospheric temperatures Is supposably much larger. pointing to a less efficient dynamo mechanism in the localized version.," The surface area exhibiting these photospheric temperatures is supposably much larger, pointing to a less efficient dynamo mechanism in the localized version."676 In this scenario. magnetic activity occurs mainly at the cooler. lower latitudes. consistent with the X-ray emitting regions found in our analysts.," In this scenario, magnetic activity occurs mainly at the cooler, lower latitudes, consistent with the X-ray emitting regions found in our analysis."677 Likely in the most massive stars with thin outer convection zone the a—© effect is only locally operating or not the dominant dynamo mechanism at all and hence a global Rossby number is not the adequate property to describe their activity level., Likely in the most massive stars with thin outer convection zone the $\alpha - \Omega$ effect is only locally operating or not the dominant dynamo mechanism at all and hence a global Rossby number is not the adequate property to describe their activity level.678 Considering additionally the latitude dependence of radius and temperature that result from the fast rotation. differing dynamo characteristics seem inevitable.," Considering additionally the latitude dependence of radius and temperature that result from the fast rotation, differing dynamo characteristics seem inevitable."679 Comparing the X-ray results with those obtained at other wavelengths. it appears that the trend of diminished activity in the hotter A-type stars is much more pronounced in the X-ray regime when compared to chromospheric measurements (?)..," Comparing the X-ray results with those obtained at other wavelengths, it appears that the trend of diminished activity in the hotter A-type stars is much more pronounced in the X-ray regime when compared to chromospheric measurements \citep{sim97}."680 A similar trend may also be present. when comparing transition. region lines to chromospheric emission. but adequate data becomes quite sparse in this regime.," A similar trend may also be present, when comparing transition region lines to chromospheric emission, but adequate data becomes quite sparse in this regime."681 This would favor an overall diminishment of hot plasma in the outer stellar atmosphere of A-type stars in general. instead of a shift of its temperature.," This would favor an overall diminishment of hot plasma in the outer stellar atmosphere of A-type stars in general, instead of a shift of its temperature."682 On the other hand. the very low activity level of Altai might indicate a turnover in the activity-rotation relation for weakly active stars. re. around logLxy/Ly4= —6.," On the other hand, the very low activity level of Altair might indicate a turnover in the activity-rotation relation for weakly active stars, i.e. around $\log L_{\rm X}/L_{\rm bol}= -6$."683 Other inactive stars of later spectral type. e.g. Procyon (F5) with logLy/Lyo=—6.5. log 00.9/1.2 (B-V00.4. 110/20dd) and a CCen A (G2) with logLx/Li4=-7. log Roz0.3 (B-V00.7. dd) show activity levels that are likewise by up to an order of magnitude below the expected value from the above correlation.," Other inactive stars of later spectral type, e.g. Procyon (F5) with $\log L_{\rm X}/L_{\rm bol}= -6.5$, log 0.9/1.2 0.4, d) and $\alpha$ Cen A (G2) with $\log L_{\rm X}/L_{\rm bol}= -7$, log Ro=0.3 0.7, d) show activity levels that are likewise by up to an order of magnitude below the expected value from the above correlation."684 Altogether. the observed X-ray activity levels in very inactive stars exhibit a quite large spread. but are rather low when compared to expected values based on their Rossby number.," Altogether, the observed X-ray activity levels in very inactive stars exhibit a quite large spread, but are rather low when compared to expected values based on their Rossby number."685 Whether the spread or a possible turnover of the correlation between activity and rotation is related to mass or other stellar properties cannot be investigated here due to very limited statistics., Whether the spread or a possible turnover of the correlation between activity and rotation is related to mass or other stellar properties cannot be investigated here due to very limited statistics.686 However. the available data suggests that weakly active stars might be overall less active than expectec from a simple down-scaling of their more active counterparts.," However, the available data suggests that weakly active stars might be overall less active than expected from a simple down-scaling of their more active counterparts."687" An X-ray activity-rotation. study that includes many ROSAT field stars. confirms the above described correlation by using an empirical X-ray Rossby number and the activity level. albeit only stars with ,OO.Swereconsidered(?)."," An X-ray activity-rotation study that includes many ROSAT field stars, confirms the above described correlation by using an empirical X-ray Rossby number and the activity level, albeit only stars with $>$ 0.5 were considered \citep{piz03}."688 Thisstudvalsosuggestsapossiblemassdepen is acce, This study also suggests a possible mass dependence of the maximum activity level; especially towards more massive stars a decrease of the maximum activity level is indicated.689ptable for all given mass ranges (0.2MM5 «MM;1II.2MMg5) and additionally a large scatter Is present at low activity levels for the most massive sample stars.," However, within errors a saturation level of $\log L_{\rm X}/L_{\rm bol} = -3.2$ is acceptable for all given mass ranges $_{\sun}<$ $<$ $_{\sun}$ ) and additionally a large scatter is present at low activity levels for the most massive sample stars."690 Extrapolating their (almost) mass independent scaling law for the saturation limit leads to the conclusion. that Altair’s activity is actually around the X-ray saturation limit for stars of spectral type A7. although it is roughly four orders of magnitude below the corresponding value for late-type stars.," Extrapolating their (almost) mass independent scaling law for the saturation limit leads to the conclusion, that Altair's activity is actually around the X-ray saturation limit for stars of spectral type A7, although it is roughly four orders of magnitude below the corresponding value for late-type stars."691 Altair is rotating at a considerable fraction (260%) of its break-up speed. thus a significant higher X-ray activity level is ruled out for an «€ dynamo. as well as for any other dynamo mechanism. whose efficiency roughly scales linearly with rotation.," Altair is rotating at a considerable fraction $\gtrsim 60\%$ ) of its break-up speed, thus a significant higher X-ray activity level is ruled out for an $\alpha\,\Omega$ dynamo, as well as for any other dynamo mechanism, whose efficiency roughly scales linearly with rotation."692 An activity level of logLy/Lpox —3. the typical saturation value for magnetic activity in less massive stars with well-developed convection zones. is by far out of reach for Altair.," An activity level of $\log L_{\rm X}/L_{\rm bol} \approx -3$ , the typical saturation value for magnetic activity in less massive stars with well-developed convection zones, is by far out of reach for Altair."693 Therefore the X-ray observation of Altair implies that the X-ray activity saturation level for A7 stars (M= 22MM) is by about four orders of magnitude diminished. when compared to solar-like or late-type stars.," Therefore the X-ray observation of Altair implies that the X-ray activity saturation level for A7 stars $\approx$ $_{\sun}$ ) is by about four orders of magnitude diminished, when compared to solar-like or late-type stars."694 Combining our results obtained from the X-ray data of the A7 star Altair. we are able to derive a picture of the basic structure of its corona. its X-ray properties and the underlying dynamo mechanism.," Combining our results obtained from the X-ray data of the A7 star Altair, we are able to derive a picture of the basic structure of its corona, it's X-ray properties and the underlying dynamo mechanism."695 The results from the X-ray observation are compared to findings for the other outer atmospheric layers., The results from the X-ray observation are compared to findings for the other outer atmospheric layers.696 Altair is a weakly active star with a corresponding very low X-ray activity level., Altair is a weakly active star with a corresponding very low X-ray activity level.697 The observed X-ray emission is dominated by relatively cool plasma: larger flares and hot active regions are virtually absent on Altair. however moderate activity seems to contribute at a minor level.," The observed X-ray emission is dominated by relatively cool plasma; larger flares and hot active regions are virtually absent on Altair, however moderate activity seems to contribute at a minor level."698 Its X-ray brightness is fairly constant on timescales of days up to decades., Its X-ray brightness is fairly constant on timescales of days up to decades.699 Rotational modulation and emergence/decay of coronal structures mainly account for the moderate variations in X-ray brightness. which is not accompanied by significant spectral changes.," Rotational modulation and emergence/decay of coronal structures mainly account for the moderate variations in X-ray brightness, which is not accompanied by significant spectral changes."700 The spectral properties are reminiscent of those from small-scale magnetic structures or quiescent regions on the Sun and other weakly active stars., The spectral properties are reminiscent of those from small-scale magnetic structures or quiescent regions on the Sun and other weakly active stars.701 The coronal plasma ts at low density and its chemical composition shows a FIP-effect like abundance pattern with a Ne/O ratio around solar value., The coronal plasma is at low density and its chemical composition shows a FIP-effect like abundance pattern with a Ne/O ratio around solar value.702 Therefore.," Therefore,"703regions into the dilfuse interstellar medium (Ονct2007).. and results from Calzettietal.(2007) suggest wt 24 yam emission may trace the recombination line emission. from the dilfuse. gas heated by these. photons.,"regions into the diffuse interstellar medium \citep{oetal07}, and results from \citet{cetal07} suggest that 24 $\mu$ m emission may trace the recombination line emission from the diffuse gas heated by these photons."704 llence. it is possible that the infrared-brightest regions in 1e centres of some galaxies may contain a higher fraction of 24 mi emission from diffuse dust than the infrared-faint regions. so the (PALE 8. μι) δε pim ratio will increase as 1 24 yam surface brightness increases. as can be seen for GC 925 and NGC 2403 in Figure 2..," Hence, it is possible that the infrared-brightest regions in the centres of some galaxies may contain a higher fraction of 24 $\mu$ m emission from diffuse dust than the infrared-faint regions, so the (PAH 8 $\mu$ m)/24 $\mu$ m ratio will increase as the 24 $\mu$ m surface brightness increases, as can be seen for NGC 925 and NGC 2403 in Figure \ref{f_pahvs24}."705 Several mechanisms may be responsible for creating 1e dillerences in the spatial distribution of the PALL 5 and 24 jun emission., Several mechanisms may be responsible for creating the differences in the spatial distribution of the PAH 8 and 24 $\mu$ m emission.706 First. as the illuminating radiation ield increases. the 24 pam band is thought to increase more rapidly than bands that trace PALL emission (Dalectal.2001:Li&Draine 2007).," First, as the illuminating radiation field increases, the 24 $\mu$ m band is thought to increase more rapidly than bands that trace PAH emission \citep{dhcsk01, ld01, dl07}."707. Therefore. the 24 yam emission may be more strongly enhanced than the PALI] emission in regions with very high radiation fields. such as star-forming regions.," Therefore, the 24 $\mu$ m emission may be more strongly enhanced than the PAH emission in regions with very high radiation fields, such as star-forming regions."708 Second. the PALIs may be destroved in regions with strong radiation fields or in regions with large numbers of high-energy photons (c.g.Maddenetal.2006).," Second, the PAHs may be destroyed in regions with strong radiation fields or in regions with large numbers of high-energy photons \citep[e.g.][]{metal06}."709. The PALs would be absent. and the (PALL S. /m)/24 jn ratio would be Low in the centres of star-forming regions and AGN.," The PAHs would be absent, and the (PAH 8 $\mu$ m)/24 $\mu$ m ratio would be low in the centres of star-forming regions and AGN."710 Third. the ratio of the 7.7 yam PALL feature to other PALL features may. vary with changes in the charge state of the PALIs (c.g.Allamandolaetal.1999:Li&Draine2001:Draine&Li 2007).," Third, the ratio of the 7.7 $\mu$ m PAH feature to other PAH features may vary with changes in the charge state of the PAHs \citep[e.g.][]{ahs99,711ld01, dl07}."712. This could occur inLLL regions if the electron densities are high enough that recombination rates becomes significant compared to photoionisation rates. which would leac to a reduction of the ions tha ooduce the 7.7 yam emission (Weineartner&Draine2001).," This could occur in regions if the electron densities are high enough that recombination rates becomes significant compared to photoionisation rates, which would lead to a reduction of the $^+$ ions that produce the 7.7 $\mu$ m emission \citep{wd01}."713. While the enhancement. of 24 sam emission. linked. to dust. heating in star-forming regions is certainly at leas nut of the reason why the (PALL δ μπι) jn ratio varies. we argue that the variations must also be causec in part by a reduction in PALL emission in the S jun banc hrough either PALL destruction or changes in the relative strengths of PALL spectral features.," While the enhancement of 24 $\mu$ m emission linked to dust heating in star-forming regions is certainly at least part of the reason why the (PAH 8 $\mu$ m)/24 $\mu$ m ratio varies, we argue that the variations must also be caused in part by a reduction in PAH emission in the 8 $\mu$ m band through either PAH destruction or changes in the relative strengths of PAH spectral features."714 Mocels of dust emission rave sugeested that. if PALIsS are present. ancl radiating a S yan. the (PALL S. sam)/160 jn ratio would be enhance in regions with very strong radiation fields. warmer dust. and low (PALL 8 sam)/24 jm ratios (Draine&Li2007).," Models of dust emission have suggested that, if PAHs are present and radiating at 8 $\mu$ m, the (PAH 8 $\mu$ m)/160 $\mu$ m ratio would be enhanced in regions with very strong radiation fields, warmer dust, and low (PAH 8 $\mu$ m)/24 $\mu$ m ratios \citep{dl07}."715. Llowever. the (PALL S pam)/160 jim. ratio does not. peak within individual star-forming regions where local minima in the (PALL S (/m)/24 pm. ratio are found. such as the bright extranuclear regions in NGC. 2408. NGC 3184. and NGC 3938.," However, the (PAH 8 $\mu$ m)/160 $\mu$ m ratio does not peak within individual star-forming regions where local minima in the (PAH 8 $\mu$ m)/24 $\mu$ m ratio are found, such as the bright extranuclear regions in NGC 2403, NGC 3184, and NGC 3938."716 ‘This is best. demonstrated by comparisons. of the maps of (PALL8 μι)/24 pim ancl (PALL 8 pim)/160 jum ratios at matching resolutions in Figure 4.. although the acieitional discussion in Section 4. and the maps in Figure 1 also support this conclusion.," This is best demonstrated by comparisons of the maps of (PAH8 $\mu$ m)/24 $\mu$ m and (PAH 8 $\mu$ m)/160 $\mu$ m ratios at matching resolutions in Figure \ref{f_map_conv160comp}, although the additional discussion in Section \ref{s_comp_pah160} and the maps in Figure \ref{f_map} also support this conclusion."717 Furthermore. Figure 7 demonstrates that the (PALL S sam)/160 pam ratios are not alwavs higher in regions with strongly enhanced 24 sam emission.," Furthermore, Figure \ref{f_pah160vs24160}718 demonstrates that the (PAH 8 $\mu$ m)/160 $\mu$ m ratios are not always higher in regions with strongly enhanced 24 $\mu$ m emission."719 According to the models of Draine&Li(2007).. the (PALES sam){160 pam should monotonically increase with the 24 jm160 sam ratio in these regions if PALIs are present and if the PALE ionisation does not change.," According to the models of \citet{dl07}, the (PAH 8 $\mu$ m)/160 $\mu$ m should monotonically increase with the 24 $\mu$ m/160 $\mu$ m ratio in these regions if PAHs are present and if the PAH ionisation does not change."720 These results indicate that the variations in the (PALL S jim)/24 jun ratio must be in part caused. by the suppression of PALL S. sam emission., These results indicate that the variations in the (PAH 8 $\mu$ m)/24 $\mu$ m ratio must be in part caused by the suppression of PAH 8 $\mu$ m emission.721 Observations of incividual regions within the Milky Way have shown that the PALL emission may be [found wimarily in shelllike structures around. the star-forming regions (e.g.Rhoctal.2006:ChurchwelletSmith&Brooks2007). and that the strength of all PALL spectral eatures relative to 24 jim hot dust. emission. decreases within the centres of regions (c.g.Povichοἱal.2007:Lebouteilleretal.2007).," Observations of individual regions within the Milky Way have shown that the PAH emission may be found primarily in shell-like structures around the star-forming regions \citep[e.g.][]{rrlf06,722cetal06, sb07} and that the strength of all PAH spectral features relative to 24 $\mu$ m hot dust emission decreases within the centres of regions \citep[e.g.][]{pscetal07,lbbdh07}."723. HE these results are applicable to he galaxies in this paper. then the inferred. decrease. in he (PALL S. jm)/24 pim ratio within star-forming regions may also be partly caused ον PALL destruction and not just variations in the strengths of PALL spectral features.," If these results are applicable to the galaxies in this paper, then the inferred decrease in the (PAH 8 $\mu$ m)/24 $\mu$ m ratio within star-forming regions may also be partly caused by PAH destruction and not just variations in the strengths of PAH spectral features."724 Further work with mid-infrared. spectroscopic observations of star-forming regions within these galaxies. specifically studies of how the total emission in all PALL spectral feature emission varies with respect to total dust. emission. would be needed to confirm that PALL destruction is taking place.," Further work with mid-infrared spectroscopic observations of star-forming regions within these galaxies, specifically studies of how the total emission in all PAH spectral feature emission varies with respect to total dust emission, would be needed to confirm that PAH destruction is taking place."725 Although the PALL S jun emission. does not share a one-to-one correspondence with 24 jim emission or with other star formation tracers on kiloparsec scales. this does not necessarily preclude its use as a tracer of integrated star formation within nearby spiral galaxies.," Although the PAH 8 $\mu$ m emission does not share a one-to-one correspondence with 24 $\mu$ m emission or with other star formation tracers on kiloparsec scales, this does not necessarily preclude its use as a tracer of integrated star formation within nearby spiral galaxies."726 The variations between PALL S yam emission. and. other star. formation tracers could potentially be averaged out. when integrating across the optical disces of spiral galaxies., The variations between PAH 8 $\mu$ m emission and other star formation tracers could potentially be averaged out when integrating across the optical discs of spiral galaxies.727 Llowever. because a significant fraction of the PALL S sam emission still originates from the cdilfuse ISM. it would not be as reliable as other σαobal star formation tracers.," However, because a significant fraction of the PAH 8 $\mu$ m emission still originates from the diffuse ISM, it would not be as reliable as other global star formation tracers."728 Furthermore. because the ratio of PALL to FH flux and the ratio of PALL to 24 jum fux density varies with metallicity (Engelbrachtetal.2005:Dalebrachtetal. 2008).. a conversion factor relating integrated PAIL S jim emission to star formation nav also vary with elobal metallicity.," Furthermore, because the ratio of PAH to TIR flux and the ratio of PAH to 24 $\mu$ m flux density varies with metallicity \citep{eetal05, detal05, ddbetal07, cetal07, eetal08}, a conversion factor relating integrated PAH 8 $\mu$ m emission to star formation may also vary with global metallicity."729 We also note that. variations in metallicity coulel possibly. produce variations in the (PALL S sami) /24 jum ratio observed in the galaxies studied in this paper. but. these variations would not be expected to cause the dillerences in the ratio between star-forming regions and the cdilfuse ISM observed here.," We also note that variations in metallicity could possibly produce variations in the (PAH 8 $\mu$ m)/24 $\mu$ m ratio observed in the galaxies studied in this paper, but these variations would not be expected to cause the differences in the ratio between star-forming regions and the diffuse ISM observed here."730 Moreover. the gas-phase abundances of the galaxies in our sample are well above )28- S.l. where PALL 8 jam emission should be suppressed:O71 as determined. by Draineetal.(2007) anc Eneclbrachtetal. (2008).. although NGC 628. NGC 925. NGC 2403. and NGC 3031 all have characteristic abundances close to this value and might be allectecl.," Moreover, the gas-phase abundances of the galaxies in our sample are well above $\simeq$ 8-8.1, where PAH 8 $\mu$ m emission should be suppressed as determined by \citet{ddbetal07} and \citet{eetal08}, although NGC 628, NGC 925, NGC 2403, and NGC 3031 all have characteristic abundances close to this value and might be affected."731 To examine this issue further. we compared the radial eradients in the (ALIE S jim)/24 pm ratio to the racial gradients in 12|log(O/I1) measured by J. Aloustakas et al. (," To examine this issue further, we compared the radial gradients in the (PAH 8 $\mu$ m)/24 $\mu$ m ratio to the radial gradients in 12+log(O/H) measured by J. Moustakas et al. ("7322008. in preparation) using the DPilvugin&Thuan(2005) calibration for 13 of the galaxies in our sample. (,"2008, in preparation) using the \citet{pt05} calibration for 13 of the galaxies in our sample. ("733CXbundance gradients are not given by J. Moustakas et al.,Abundance gradients are not given by J. Moustakas et al.734 for NGC 3938 and NGC 4579. and so these galaxies are not included in this comparison.)," for NGC 3938 and NGC 4579, and so these galaxies are not included in this comparison.)"735 The relation between these two radial eradients can be seen in Figure 10.., The relation between these two radial gradients can be seen in Figure \ref{f_gradcomp_pah24_12logoh}.736 Lf the variations in the (PALL δ sam)δε pam ratio cdepenelec primarily on metallicity variations. then we would expect to see a correlation between the gradients in Figure 10..," If the variations in the (PAH 8 $\mu$ m)/24 $\mu$ m ratio depended primarily on metallicity variations, then we would expect to see a correlation between the gradients in Figure \ref{f_gradcomp_pah24_12logoh}. ."737 Llowever. the two eracdicnts appear uncorrelated. which indicates that the variations in the (PALLS j/im)/24 pam ratio that have been observed. here depend. primarily on cllects unrelated. to metallicity.," However, the two gradients appear uncorrelated, which indicates that the variations in the (PAH 8 $\mu$ m)/24 $\mu$ m ratio that have been observed here depend primarily on effects unrelated to metallicity."738 This conclusion for these spiral galaxies is also consistent with the results presented for the μαral galaxy MIOL by Gordonctal. (2008).. who found wt PALL equivalent: widths appeared more dependent on," This conclusion for these spiral galaxies is also consistent with the results presented for the spiral galaxy M101 by \citet{getal08}, , who found that PAH equivalent widths appeared more dependent on"739eround to further refine the TCAF model.,ground to further refine the TCAF model.740 We have presented the X-ray spectral and time variability. characteristics of GRS 19151105 when the source Was exhibiting nregular bursts., We have presented the X-ray spectral and time variability characteristics of GRS 1915+105 when the source was exhibiting irregular bursts.741 The spectral characteristics strongly sugeest the view that the source lakes a state transition ina very fast time scale (a few seconds)., The spectral characteristics strongly suggest the view that the source makes a state transition in a very fast time scale (a few seconds).742 We have found that the temporal variabilities also support this conchision., We have found that the temporal variabilities also support this conclusion.743 We conclude that the source can make spectral state transition oulv if the advective aud standard thin disk co-exist. as suggested by," We conclude that the source can make spectral state transition only if the advective and standard thin disk co-exist, as suggested by \cite{chak:95}. ."74438 0136. by the Polish Astroparticle Network 621/E-78/BWSN-0068/2008. and by the Czech Science Foundation. grant no 05/07/0052.,"38 0136, by the Polish Astroparticle Network 621/E-78/BWSN-0068/2008, and by the Czech Science Foundation, grant no 205/07/0052."745 RD acknowledges useful discussions with S. Ramanna., RD acknowledges useful discussions with S. Ramanna.746 Ferraris method is used to analytically solve a quartic equation for its roots., Ferrari's method is used to analytically solve a quartic equation for its roots.747" Given the quartic equation Le!|BatCareE=0. GL. D. €. D real or complex) its solution (i.e. the roots of the quartic) ean be found by means of the following calculations: A=—3BXu|ud 1OXP242Boo)Dμι a64128)1|loCB?BDLieQEει If ....7= then 4geDpESSE+,5./,,2-. where c. and +, are two distinct of setsplus and minuses. i.e. there are four possibilities. (σον35)—€1.νεΕν€1-6."," Given the quartic equation $Ax^4 + B x^3 + C x^2 + D x + E =0$ , $A$ , $B$, $C$, $D$ real or complex) its solution (i.e. the roots of the quartic) can be found by means of the following calculations: $\alpha = - \frac{3 B^2}{8 A^2} + \frac{C}{A}$ $\beta = \frac{B^3}{8 A^3} - \frac{BC}{2 A^2} + \frac{D}{A}$ $\gamma =- \frac{3 B^4}{256 A^4} + \frac{CB^2}{16 A^3} - \frac{BD}{4 A^2} + \frac{E}{A} $ If $\beta =0$ then $x = -\frac{B}{4A} \pm_{s} \sqrt{\frac{-\alpha \pm_{t} \sqrt{\alpha^2 - 4 \gamma}}{2}}, $ where $\pm_{s}$ and $\pm_{t}$ are two distinct sets of plus and minuses, i.e., there are four possibilities, $(\pm_{s}, \pm_{t}) = (+, +), (+,-), (-, +), (-,-)$ ."748 If 34O then continue with P-—2__a?os⊳ Q—Los3NC≊ R=«>ccVU(2|=Du (either. sign. of5 the square root will. do) U—RU? (there are three complex roots. but any one of them will do).," If $\beta \neq 0$ then continue with $P = - \frac{\alpha^2}{12} - \gamma,$ $Q = -\frac{\alpha^3}{108} + \frac{\alpha \gamma}{3} - \frac{\beta^2}{8},$ $R = -\frac{Q}{2} \pm \sqrt{\frac{Q^2}{4} + \frac{P^3}{27}}$ (either sign of the square root will do) $U = R^{1/3}$ (there are three complex roots, but any one of them will do)."749 To compute the cube-root of. a complex number. we proceed as follows:H Let 2—orp|£r».=ren where r=VULμμa7|oes and 0—lanτίm). (Here?=/ 1).," To compute the cube-root of a complex number, we proceed as follows: Let $R = x_1+ i x_2 = r e^{i \theta}$ where $r= \sqrt{x_1^2 + x_2^2}$ and $\theta = tan^{-1} (\frac{x_2}{x_1}).$ (Here $i = \sqrt{-1}$ )."750 The other possible choices are 2°* and 2?47 wherew=(1|V3)/2 is a cube root of unity., The other possible choices are $R^{1/3} \omega$ and $R^{1/3} \omega^2$ where $\omega = (-1 + \sqrt{3} i )/2 $ is a cube root of unity.751" Ift-0lty22QU le 40lkty=004 Let Έτναση Then. the four roots of the quartic are SoLi|Wi)0h22b.Td The two +, must have the same sign and the +, are two independent +."," If $U = 0$ let $y = -\frac{5 \alpha}{6} - Q^{1/3}$ If $U \neq 0$ let $y = -\frac{5 \alpha}{6} + U - \frac{P}{3 U}$ Let $W = \sqrt{\alpha + 2y}$ Then, the four roots of the quartic are $ x= -\frac{B}{4A} + \frac{\pm_{s} W \pm_{t} \sqrt{-(3 \alpha + 2 y \pm_{s} \frac{2 \beta}{W})}}{2}$ The two $\pm_{s}$ must have the same sign and the $\pm_{t}$ are two independent $\pm$."752 To get all the roots. compute .r for the four possibilities of +. and στι.," To get all the roots, compute $x$ for the four possibilities of $\pm_{s}$ and $\pm_{t}$."753 First note that the Sturm sequence (fu....fi.) is (up to signs) equal to the sequence obtained from the euclidean algorithm.," First note that the Sturm sequence $({f_0},...{f_k})$ is (up to signs) equal to the sequence obtained from the euclidean algorithm."754 Define à new sequence (gu.....qu) by gi=fiffo for’€(0...4}.," Define a new sequence $({g_0},...,{g_k})$ by ${g_i}={f_i}/{f_k}$ for $i \in \{ 0,...,k \}$."755 Note thatthe numberof sign changes in (foe).fiGe)) (resp.," Note thatthe number of sign changes in $({f_0}(x),{f_1}(x))$ $($ resp."756 Ofa6).iG)f10rd) and the number of sign changes in (gor).gíGe)) (resp.," $(f_{i-1}(x),f_i(x),f_{i+1}(x)))$ and the number of sign changes in $({g_0}(x),{g_1}(x))$ $($ resp."757 (gr16e).qiGr).qiLGe))) coincide for any ο which is not a root of f.," $({g_{i-1}}(x),{g_i}(x),{g_{i+1}}(x)))$ coincide for any $x$ which is not a root of $f$."758 Note also that the roots of gy are exactly the roots of f which are not roots of g., Note also that the roots of ${g_0}$ are exactly the roots of $f$ which are not roots of $g$.759" Observe that for /C0... Ανα, and g; are relatively prime."," Observe that for $i\in{{0,...,k}}$ ${g_{i-1}}$ and ${g_i}$ are relatively prime."760 We consider. now. how ο.g:.c) behaves when ur passes through a root e of a polynomial g;.," We consider, now, how $v(f,g;x)$ behaves when $x$ passes through a root $c$ of a polynomial ${g_i}$ ."761" If e is a root of go. then it is not a root of g,."," If $c$ is a root of ${g_0}$, then it is not a root of ${g_1}$."762" We write (ο,>0 (resp.< Ovif f'is positive ( resp.", We write $f'(c_)>0$ $resp. <0$ )if $f'$is positive $($ resp.763 negative ) immediately to the left of c., negative $)$ immediately to the left of $c$.764 Thesign of f'(c.) is defined similarly., Thesign of $f'(c_{+})$ is defined similarly.765 Now we recall the following result: if /? is a real closed field. /cX].e.bR with e«b and if the derivative  is positive (resp.," Now we recall the following result: if $R$ is a real closed field, $f\in R[X], a,b\in R$ with $a<b$ and if the derivative $f'$ is positive (resp."766 negative) on Ία. b then f is strictly increasing (resp.," negative) on $]a,b[$ , then $f$ is strictly increasing (resp."767 strictly decreasing) on. a.0]. Then. according to the signs of (ο).f//(e..) and [ο} we have the following8 cases: O.Struecm," strictly decreasing) on $[a,b].$ Then, according to the signs of $g(c), f'(c_{-})$ and $f'(c_+)$ we have the following8 cases: 0.5truecm"768Impacts pose a hazard to life on Earth. especially in the case of an event energetic enough to destroy much of the surface crust and oceans (Zahnleetal.2007).,"Impacts pose a hazard to life on Earth, especially in the case of an event energetic enough to destroy much of the surface crust and oceans \citep{zahnle}."769. The most destructive impacts are associated with comets rather than asteroids. as the former hit at high speeds when infalling from the Ixuiper Belt region (Jelfersctal.2001).. but the present-dav cometary impact rate is low. largely. because most. of the primordial bodies have been dispersed. (Morbidellietal.," The most destructive impacts are associated with comets rather than asteroids, as the former hit at high speeds when infalling from the Kuiper Belt region \citep{sandra}, but the present-day cometary impact rate is low, largely because most of the primordial bodies have been dispersed \citep{morbidelli}."770 2003).. This is thought to have occurred in the first Gyr of the Sun's life. when Jupiter anc Saturn crossed a mean motion resonance. destabilising the gas giants so that Saturn had close encounters with Uranus and Neptuno.," This is thought to have occurred in the first Gyr of the Sun's life, when Jupiter and Saturn crossed a mean motion resonance, destabilising the gas giants so that Saturn had close encounters with Uranus and Neptune."771 The expansion of their orbits perturbed the primordial Ixuiper Belt (Comesetal.2005).. producing the Late Heavy 3ombardment of the Earth at around TOO Myr. after which the comet population was greatly depleted and the impact frequeney has been much lower.," The expansion of their orbits perturbed the primordial Kuiper Belt \citep{gomes}, producing the Late Heavy Bombardment of the Earth at around 700 Myr, after which the comet population was greatly depleted and the impact frequency has been much lower."772 However. the presence of the eas giants is still significant today. as dynamical interactions can bring comets into the inner Solar System llorner&Jones(2008) have recently shown that the impact rate on the Earth would. vary significantly if the mass of Jupiter were cdilferent.," However, the presence of the gas giants is still significant today, as dynamical interactions can bring comets into the inner Solar System – \citet{horner} have recently shown that the impact rate on the Earth would vary significantly if the mass of Jupiter were different."773 Thus. in extrasolar systems we may expect that the number of comets and the architecture of the giant-planet svstem will strongly alfect the impact rate on any terrestrial planets present.," Thus, in extrasolar systems we may expect that the number of comets and the architecture of the giant-planet system will strongly affect the impact rate on any terrestrial planets present."774 Direct evidence of impacts in the inner svstems comes from detections of dust. grains at temperatures of a few hundred Welvin. representing break-up debris from parent. planetesimals.," Direct evidence of impacts in the inner systems comes from detections of dust grains at temperatures of a few hundred Kelvin, representing break-up debris from parent planetesimals."775 Such detections via à micl-infrared excess signal above the stellar photosphere are rare. but this does not imply that inner system planetesimals ancl planetary impacts are sparse. as the debris lifetime at a few AW is short (Wyatt2005).," Such detections via a mid-infrared excess signal above the stellar photosphere are rare, but this does not imply that inner system planetesimals and planetary impacts are sparse, as the debris lifetime at a few AU is short \citep{wyatt05}."776 Less clirectly. we can examine the far-infrarecdl debris signatures to assess the numbers of bodies colliding within the cool outer comet belts. and consider the influence of eas giants in. perturbing comets inwards to where they threaten terrestrial planets.," Less directly, we can examine the far-infrared debris signatures to assess the numbers of bodies colliding within the cool outer comet belts, and consider the influence of gas giants in perturbing comets inwards to where they threaten terrestrial planets."777 Llere we use the results of recent volume-Iimited surveys of Sun-like stars with Spitzer by ‘Trillingetal.(2008) and Beichmanctal.(2006) to study the dustiness of Solar-analogue systems. via the predominantly: 70 pum detections of excess above the stellar photospheres.," Here we use the results of recent volume-limited surveys of Sun-like stars with Spitzer by \citet{fgk2} and \citet{simtpf} to study the dustiness of Solar-analogue systems, via the predominantly 70 $\umu$ m detections of excess above the stellar photospheres."778 Various analytical models. as reviewed by Wyatt(2008)... predict. far-infrared clust luminosities as functions of initial size and mass of the planetesimal disc and the age of the host. star.," Various analytical models, as reviewed by \citet{wyatt08}, predict far-infrared dust luminosities as functions of initial size and mass of the planetesimal disc and the age of the host star."779 Thus the excesses detected by Spitzer can be related to the ensemble of populations of comets per star., Thus the excesses detected by Spitzer can be related to the ensemble of populations of comets per star.780 We can then place the Sun's Ixuiper Belt. for which there are measurements of the numbers ancl distribution of comets and dust. particles. in the context of similar stars.," We can then place the Sun's Kuiper Belt, for which there are measurements of the numbers and distribution of comets and dust particles, in the context of similar stars."781 For example. other systems are," For example, other systems are"782Moreover. because the exposures in the two filters are not consecutive. the detection of variability in both passbands is only a serendipitous event.,"Moreover, because the exposures in the two filters are not consecutive, the detection of variability in both passbands is only a serendipitous event."783 Similar limitations have been encountered also by Clementini et al. (2001)).," Similar limitations have been encountered also by Clementini et al. \cite{clem01}) ),"784 who for the first time. searched for RR Lyrae variables in a sample of M31 GCs using archive HST Wide Field Planetary Camera 2 (WFPC2) data.," who for the first time, searched for RR Lyrae variables in a sample of M31 GCs using archive HST Wide Field Planetary Camera 2 (WFPC2) data."785 That study. however. proved the possibility of à successful detection of likely candidates RR Lyrae also with data not optimized for this type of investigation.," That study, however, proved the possibility of a successful detection of likely candidates RR Lyrae also with data not optimized for this type of investigation."786 It is important to stress that the present analysis is not intended to obtain a complete census of the RR Lyrae population in the considered clusters but. instead. is aimed at verifying whether a significant population of RR Lyrae can be identified 1n some of them.," It is important to stress that the present analysis is not intended to obtain a complete census of the RR Lyrae population in the considered clusters but, instead, is aimed at verifying whether a significant population of RR Lyrae can be identified in some of them."787 To identify RR Lyrae candidates. we adopted the following criteria. which are ilustrated in Fig. 9: ," To identify RR Lyrae candidates, we adopted the following criteria, which are ilustrated in Fig. \ref{fig:rrly1} :"788As a result of this analysis. we found 11 (B336). 3 (BOSS). 2 (B292. B350). | (B531) and 0 (B337) candidate RR Lyrae stars in our six clusters. respectively.," As a result of this analysis, we found 11 (B336), 3 (B058), 2 (B292, B350), 1 (B531) and 0 (B337) candidate RR Lyrae stars in our six clusters, respectively."789 Their positions in the CMDs are shown in Fig. 10.., Their positions in the CMDs are shown in Fig. \ref{fig:rrly2}.790" We searched for candidate RR Lyrae variables also in comparison fields surrounding the clusters to quantify the probability that the variables detected in the cluster can be explained as merely due to the field population,", We searched for candidate RR Lyrae variables also in comparison fields surrounding the clusters to quantify the probability that the variables detected in the cluster can be explained as merely due to the field population.791 Given the observed frequency of candidate variables in the surrounding fields. the number of field RR Lyrae expected to fall on the cluster area are 0. for the clusters B336. B292. B531. B337. 1. for B350. and 2 for B058.," Given the observed frequency of candidate variables in the surrounding fields, the number of field RR Lyrae expected to fall on the cluster area are 0, for the clusters B336, B292, B531, B337, 1, for B350, and 2 for B058."792 Hence. the only cluster for which a significant excess of RR Lyrae is found with respect to the expectations 1s B336. providing further evidence supporting a very old age for this system.," Hence, the only cluster for which a significant excess of RR Lyrae is found with respect to the expectations is B336, providing further evidence supporting a very old age for this system."793 The very red colors of most of the candidates in BOSS. B350. and B531 also cast some doubt on their classification as RR Lyrae.," The very red colors of most of the candidates in B058, B350, and B531 also cast some doubt on their classification as RR Lyrae."794" Note that the lack of detection of a significant excess of candidate RR Lyrae in the other clusters cannot be taken as evidence that no such variable is present there: our data are clearly not sufficient to reach this conclusion,", Note that the lack of detection of a significant excess of candidate RR Lyrae in the other clusters cannot be taken as evidence that no such variable is present there: our data are clearly not sufficient to reach this conclusion.795 The main aim of this study was to verfy whether the intermediate age estimate obtained from integrated spectroscopy and/or photometry by several authors (Table 2)) for the M31 clusters BO58. B292. B337. and B350 was supported by the CMD obtained from the new HST-ACS observations.," The main aim of this study was to verify whether the intermediate age estimate obtained from integrated spectroscopy and/or photometry by several authors (Table \ref{tab:age}) ) for the M31 clusters B058, B292, B337, and B350 was supported by the CMD obtained from the new HST-ACS observations."796 The final answer is completely inconclusive for B058 and uncertain for B337. even if in the last case there is marginal evidence for an older age compared to the dating from integrated light.," The final answer is completely inconclusive for B058 and uncertain for B337, even if in the last case there is marginal evidence for an older age compared to the dating from integrated light."797 On the other hand. both B29? and B350 show a significant and unequivocal population of blue horizontal branch stars. indicating that they are as old as the classical Galactic GCs (ages older than 11 Gyr: see Dotter et," On the other hand, both B292 and B350 show a significant and unequivocal population of blue horizontal branch stars, indicating that they are as old as the classical Galactic GCs (ages older than 11 Gyr; see Dotter et"798DB—Ner. plot.,$\ss-N_{\rm efc}$ plot.799" An example of this is provided in Fig. 11,,"," An example of this is provided in Fig. \ref{fig:Nsharp},"800 which shows how f converges as more pulses are integrated., which shows how $\ss$ converges as more pulses are integrated.801 This simulation (which was performed in a similar way to that described above) is for the extreme jitter-dominated case., This simulation (which was performed in a similar way to that described above) is for the extreme jitter-dominated case.802 Real data would be a combination of the jitter-induced exponential convergence simulated in Fig., Real data would be a combination of the jitter-induced exponential convergence simulated in Fig.803 11 and of Gaussian white noise., \ref{fig:Nsharp} and of Gaussian white noise.804" However, because the intrinsic shape of single pulses for PSR J0437—4715 is not easily defined, we cannot compare Fig."," However, because the intrinsic shape of single pulses for PSR $-$ 4715 is not easily defined, we cannot compare Fig."805" 11 easily with the f values obtained from our data (as shown in Fig. 6)),"," \ref{fig:Nsharp} easily with the $\ss$ values obtained from our data (as shown in Fig. \ref{tsharp t2bit}) ),"806 but we do point out that 8 does not change significantly as we integrate our data., but we do point out that $\ss$ does not change significantly as we integrate our data.807" Furthermore, the variation of 8 shown in Fig."," Furthermore, the variation of $\ss$ shown in Fig."808 6 (top left panel) is far larger than the variation suggested by the simulations (Fig. 11))., \ref{tsharp t2bit} (top left panel) is far larger than the variation suggested by the simulations (Fig. \ref{fig:Nsharp}) ).809" This suggests either that the simulated level of pulse phase jitter is well below the radiometer noise present in the data, or that there are significant variations in the shape of single pulses, where our model assumes there are none."," This suggests either that the simulated level of pulse phase jitter is well below the radiometer noise present in the data, or that there are significant variations in the shape of single pulses, where our model assumes there are none."810" In summary, we have used timing measurements to derive the upper limit of f;<0.08 for pulse phase jitter in PSR J0437—4715."," In summary, we have used timing measurements to derive the upper limit of $f_{\rm J} \leq 0.08$ for pulse phase jitter in PSR $-$ 4715."811" This upper limit was subsequently used in simulations to evaluate the impact such jitter would have on the pulse shape and we found that at integration times beyond 100 pulses (~ 0.57ss) neither the S/N of the integrated profile, nor the pulse sharpness are affected significantly compared to the radiometer noise."," This upper limit was subsequently used in simulations to evaluate the impact such jitter would have on the pulse shape and we found that at integration times beyond 100 pulses $\sim 0.57$ s) neither the S/N of the integrated profile, nor the pulse sharpness are affected significantly compared to the radiometer noise."812" This lack of pulse jitter effects on the S/N and sharpness of the simulated data, implies either that the derived upper limit is overly conservative and that the underestimation of T'OA uncertainties is mostly induced by causes other than pulse phase jitter, or that our model for pulse phase jitter is overly simplistic and a more complex model is required."," This lack of pulse jitter effects on the S/N and sharpness of the simulated data, implies either that the derived upper limit is overly conservative and that the underestimation of TOA uncertainties is mostly induced by causes other than pulse phase jitter, or that our model for pulse phase jitter is overly simplistic and a more complex model is required."813 A more detailed investigation is required to distinguish between these two scenarios and to quantify the pulse phase jitter in PSR J0437—4715 more precisely., A more detailed investigation is required to distinguish between these two scenarios and to quantify the pulse phase jitter in PSR $-$ 4715 more precisely.814 Such an analysis is being prepared for a subsequent paper (?).., Such an analysis is being prepared for a subsequent paper \citep{lkl+11}.815" In this paper, we have used the brightest and most precisely timed MSP, PSR J0437—4715, to illustrate the most important phenomena known to affect the shape of pulse profiles; to estimate the impact of these phenomena and to evaluate the efficacy of mitigation schemes."," In this paper, we have used the brightest and most precisely timed MSP, PSR $-$ 4715, to illustrate the most important phenomena known to affect the shape of pulse profiles; to estimate the impact of these phenomena and to evaluate the efficacy of mitigation schemes."816" By concentrating on the brightest MSP currently known, we are able to cast some light on effects that future telescopes like FAST or the SKA will come across as a matter of course in any standard MSP."," By concentrating on the brightest MSP currently known, we are able to cast some light on effects that future telescopes like FAST or the SKA will come across as a matter of course in any standard MSP."817" We find that pulse phase jitter may be dominant in current short-term timing of PSR J0437—4715, though further analysis is required to enable quantification of this"," We find that pulse phase jitter may be dominant in current short-term timing of PSR $-$ 4715, though further analysis is required to enable quantification of this"818"l4, we can use equation (6)) to calculate the Hill radius for this section of the arm using: If the section of arm has a thickness satisfying l;/(2Humu)<1, then the section lies within its own Hill thickness.","$l_1$, we can use equation \ref{eqHill}) ) to calculate the Hill radius for this section of the arm using: If the section of arm has a thickness satisfying $l_1/(2H_{\mbox{\tiny{Hill}}}) < 1$, then the section lies within its own Hill thickness."819" In the absence of pressure forces, this means that the section is bound, as the tidal force from the central star (manifest as rotational shear) is less than the self-gravity of the section."," In the absence of pressure forces, this means that the section is bound, as the tidal force from the central star (manifest as rotational shear) is less than the self-gravity of the section."820" Once the section is bound, fragmentation occurs."," Once the section is bound, fragmentation occurs."821" Conversely, if 11/(2Huin)>1, then the section of arm is not bound and fragmentation does not occur."," Conversely, if $l_1/(2H_{\mbox{\tiny{Hill}}}) > 1$, then the section of arm is not bound and fragmentation does not occur."822 The Hill thickness tells one about the ability of shear to prevent the fragmentation of the arm and is therefore expected to be an important scale., The Hill thickness tells one about the ability of shear to prevent the fragmentation of the arm and is therefore expected to be an important scale.823" However, in comparing the radial thickness of the arm to the Hill thickness we are ignoring the role of pressure, despite strong radial pressure gradients present across the arm."," However, in comparing the radial thickness of the arm to the Hill thickness we are ignoring the role of pressure, despite strong radial pressure gradients present across the arm."824 It is therefore reasonable to expect that the critical thickness for arm fragmentation may be modified from the Hill thickness., It is therefore reasonable to expect that the critical thickness for arm fragmentation may be modified from the Hill thickness.825" There are no strong pressure gradients along the arm (the azimuthal direction) though, so it is likely that fragmentation occurs in this direction."," There are no strong pressure gradients along the arm (the azimuthal direction) though, so it is likely that fragmentation occurs in this direction."826" In this case, the Hill thickness may in fact be the critical scale."," In this case, the Hill thickness may in fact be the critical scale."827 Determining the correct scale for fragmentation requires a detailed calculation of the stability of a spiral arm accounting for differential rotation., Determining the correct scale for fragmentation requires a detailed calculation of the stability of a spiral arm accounting for differential rotation.828" In the absence of such a calculation, we posit that the correct scale to consider is indeed the Hill thickness."," In the absence of such a calculation, we posit that the correct scale to consider is indeed the Hill thickness."829" As described below, the results from our simulations are consistent with this."," As described below, the results from our simulations are consistent with this."830" The Hill criterion for fragmentation, demonstrated in Figure 6,, is thus empirically based."," The Hill criterion for fragmentation, demonstrated in Figure \ref{figArmHill}, is thus empirically based."831" An analysis of the spiral arms formed in the simulations of refsecSimulations shows that their thicknesses, and stability, are consistent with the Hill criterion for fragmentation."," An analysis of the spiral arms formed in the simulations of \\ref{secSimulations} shows that their thicknesses, and stability, are consistent with the Hill criterion for fragmentation."832" In Figure 7,, we show two examples of this analysis to illustrate this consistency."," In Figure \ref{figArmThickness}, we show two examples of this analysis to illustrate this consistency."833 Our analysis focuses on the surface density of a radial slice of the disc (with a typical angular width of 5°)., Our analysis focuses on the surface density of a radial slice of the disc (with a typical angular width of $^{\circ}$ ).834" Over this slice, a spiral arm is evident as a large over-density."," Over this slice, a spiral arm is evident as a large over-density."835" We find that arms are often asymmetric; consequently, we determine a thickness for an arm by fitting each side of the arm (with respect to the radius of highest X. Ryo), with a Gaussian of the form where X is the value of the surface density adjacent to the arm."," We find that arms are often asymmetric; consequently, we determine a thickness for an arm by fitting each side of the arm (with respect to the radius of highest $\Sigma$, $R_{\mbox{\tiny{peak}}}$ ), with a Gaussian of the form where $\Sigma_0$ is the value of the surface density adjacent to the arm."836" The thickness of the arm is taken to be byignt), and the mass of the section of arm is determined using4- a numerical evaluation of where O(R)=l;/R is the angular extent of the section of arm."," The thickness of the arm is taken to be $l_1 = 2(b_{\mbox{\tiny{left}}} + b_{\mbox{\tiny{right}}})$ , and the mass of the section of arm is determined using a numerical evaluation of where $\Theta(R)=l_1/R$ is the angular extent of the section of arm."837" Figure 7 (top) shows this analysis for an arm in Simulation A, shortly before fragmentation."," Figure \ref{figArmThickness} (top) shows this analysis for an arm in Simulation A, shortly before fragmentation."838" Consistent with the Hill criterion, the arm thickness is less than the Hill thickness and therefore fragmentation is expected to occur in this arm; indeed, this arm fragmented a short time after the time-step used for this analysis."," Consistent with the Hill criterion, the arm thickness is less than the Hill thickness and therefore fragmentation is expected to occur in this arm; indeed, this arm fragmented a short time after the time-step used for this analysis."839" In contrast, Figure 7 (bottom) shows this analysis for an arm in Simulation E, which never fragmented."," In contrast, Figure \ref{figArmThickness} (bottom) shows this analysis for an arm in Simulation E, which never fragmented."840" Consistent with the Hill criterion, the arm thickness is greater than the Hill thickness and therefore fragmentation is not expected."," Consistent with the Hill criterion, the arm thickness is greater than the Hill thickness and therefore fragmentation is not expected."841 We use these two examples here to illustrate the consistency of the fragmentation criterion with the simulations performed., We use these two examples here to illustrate the consistency of the fragmentation criterion with the simulations performed.842" More generally, we have found that lower opacity discs have arms that are consistently smaller with respect to their Hill thickness in comparison with higher opacity discs."," More generally, we have found that lower opacity discs have arms that are consistently smaller with respect to their Hill thickness in comparison with higher opacity discs."843 In each of the cases where fragmentation takes place (this occurs in the reduced, In each of the cases where fragmentation takes place (this occurs in the reduced844A spectrum [rom a shock viewed at an arbitrary angle. 0<:oz21/2. is illustrated in Figure 1.. which represents Call numerical solutious of Eqs. (3.1)). (3)). 39) ,"A spectrum from a shock viewed at an arbitrary angle, $0\leq\Theta\leq\pi/2$, is illustrated in Figure \ref{f:2}, which represents full numerical solutions of Eqs. \ref{dW/dw}) ), \ref{f}) ), \ref{w-main}) )"845for three different viewiug angles., for three different viewing angles.846 Tn caleulation of dW/di. the emittineOm electrons were assumed mouoenereetic.e for simplicity.," In calculation of $dW/d\omega$, the emitting electrons were assumed monoenergetic, for simplicity."847 An ünportant [act to note is that the jitter radiation spectrum varies with the viewing angle., An important fact to note is that the jitter radiation spectrum varies with the viewing angle.848" When filaments are (and a shock velocity is. in the GRB case) along the line of sight. the low-enerey spectrum is hard E,xpl. harder than the “svuchrotrou line of death” (E,xvl)."," When filaments are (and a shock velocity is, in the GRB case) along the line of sight, the low-energy spectrum is hard $F_\nu\propto\nu^1$, harder than the “synchrotron line of death” $F_\nu\propto\nu^{1/3}$ )."849" As the viewing augle increases. the spectrum softens. aud wheu the filaments are orthogonal to the line of sight. it becomes ἐνx»""."," As the viewing angle increases, the spectrum softens, and when the filaments are orthogonal to the line of sight, it becomes $F_\nu\propto\nu^0$."850 Another interesting feature is that at oblique angles. the spectrum does not soften simultaneously at all frequencies.," Another interesting feature is that at oblique angles, the spectrum does not soften simultaneously at all frequencies."851 Lusteacd. there appears a smooth spectral break. which position depends on ©.," Instead, there appears a smooth spectral break, which position depends on $\Theta$."852" The spectrum approaches ~»/!"" below the break and is harder above it.", The spectrum approaches $\sim\nu^0$ below the break and is harder above it.853 Unlike a GRB shock. the distribution of radiating electrons is anisotropic in most of lab experiments.," Unlike a GRB shock, the distribution of radiating electrons is anisotropic in most of lab experiments."854 In particular. to diagnose the Weibel turbulence in the Hercules experiment 2008).. it lias been suggested to launeli a probe. nearly monoenergetic electrou beam through plasina with the Weibel fields.," In particular, to diagnose the Weibel turbulence in the Hercules experiment \citep{GRB+Hercules08}, it has been suggested to launch a probe, nearly monoenergetic electron beam through plasma with the Weibel fields."855 Thus. the geometrical shape aud the electron euergy-moimeutuui distribution of the probe beam are important.," Thus, the geometrical shape and the electron energy-momentum distribution of the probe beam are important."856 Here we assume tlie electrons to be monoenergetic aud neglect the geometrical dive'gence of the beam. for simplicity (in the experiment. it is likely somewhat sinaller than the relativistic beaming cone of 1/5 anyway).," Here we assume the electrons to be monoenergetic and neglect the geometrical divergence of the beam, for simplicity (in the experiment, it is likely somewhat smaller than the relativistic beaming cone of $1/\gamma$ anyway)."857 We again start [rom the Liéuiard-Wiechart potentials aud the expression for the emitted power (3))., We again start from the Liénnard-Wiechart potentials and the expression for the emitted power \ref{dW-1}) ).858 We adopt the [n]geometry suc1 that the unit vector s is along the filaments. v is the particle's velocity and the unit vector n is toward an observed.," We adopt the geometry such that the unit vector $\bf s$ is along the filaments, $\bf v$ is the particle's velocity and the unit vector $\bf n$ is toward an observed."859" We also define the unit vector v=νο and ο,Unlike the isotropic case. we «o not neglect terius proportional to [n*wy? although they are siuall compared to those proportional to [wy2"," We also define the unit vector $\hat{\bf v}={\bf v}/v$ and $\beta$.Unlike the isotropic case, we do not neglect terms proportional to $|\bf n\cdot w_{\omega'}|^2$ although they are small compared to those proportional to $\bf |w_{\omega'}|^2$."860 Using a similar approach. we arrive at the following expression [or the euitted power per frequency. per solid augle. per electrou: One can readily see that the emitted power along the electron probe beam. Le. when n:v= 1. is proportional to tlie electron acceleration spectrum: 12.," Using a similar approach, we arrive at the following expression for the emitted power per frequency, per solid angle, per electron: One can readily see that the emitted power along the electron probe beam, i.e., when ${\bf n\cdot\hat v}=1$ , is proportional to the electron acceleration spectrum: |^2,"861 (Parmarctal.1985) (Wadeetal.1985).., \citep{Parmar:1985a} \citep{Wade:1985a}.862 Wolff(2008a) (Wolff, \citet{Wolff:2008a} \citep{Wolff:2008b}.863 Degenaareal.(2009). Wolffetal.(2008b)., \citet{Degenaar:2009a} \citet{Wolff:2008b}.864. 16«109 + δις107 (Wadeetal.1985).., $16\times10^{33}$ $^{-1}$ $8.3\times10^{33}$ $^{-1}$ \citep{Wade:1985a}.865 17.7>B16.9 (CramptonSchinidtke&Cowley1987) ~0.21unag 17.8>Voτι ounetal.1988)..," $17.7866> B > 16.9$ \citep{Crampton:1986a,Schmidtke:1987a} $\sim0.2$ $17.8 > V > 17.1$ \citep{vanParadijs:1988a}."867 R—22 (IIxunes&Jones2008:2008) EXO 07158676 is an intriguing oject for a umber of reasons.," $R\sim22$ \citep{Hynes:2008a,Torres:2008a}868 EXO 0748–676 is an intriguing object for a number of reasons."869 It is unusual among neutron star LMXDs in being a quasi-persisteut source for which we have observed the cutive period of activity and furthermore have estimates of the pre-eruption DIuumositv (Garcia&Callauau 19909).., It is unusual among neutron star LMXBs in being a quasi-persistent source for which we have observed the entire period of activity and furthermore have estimates of the pre-eruption luminosity \citep{Garcia:1999a}.870 This makes it a fascinating svsteni iu which to study the post-erupjon cooling curve aud investigate the physics| of nectrou star ΠΟΙΟΥΣ (Degenaarctal.2009).., This makes it a fascinating system in which to study the post-eruption cooling curve and investigate the physics of neutron star interiors \citep{Degenaar:2009a}.871 It also has an optimal inclination angle viclcπιο toal N-vav eclipses of the neutron star without being an accretion disk corona source. shows periodic N-rav diys. and also exhibits type I N-vayv bursts (Pariuaretal.1986:Cottwaldal 19586).," It also has an optimal inclination angle yielding total X-ray eclipses of the neutron star without being an accretion disk corona source, shows periodic X-ray dips, and also exhibits type I X-ray bursts \citep{Parmar:1986a,Gottwald:1986a}."872 The possible detection of eravitationally red-shitted absorption lines during N-ray bursts offered teuitalizing prospects for constrainius the neutron star οςuation of state (Cottametal.2002) although this «letection could not be rexoduced. m subsequent observations (Cottamctal. 2008).., The possible detection of gravitationally red-shifted absorption lines during X-ray bursts offered tantalizing prospects for constraining the neutron star equation of state \citep{Cottam:2002a} although this detection could not be reproduced in subsequent observations \citep{Cottam:2008a}.873 Independently. Ozel(2X06) arened that soft equations of state can be ruled οut based on observations of other characteristics of X-ray musts in ENO 07Ls676.," Independently, \citet{Ozel:2006a} argued that soft equations of state can be ruled out based on observations of other characteristics of X-ray bursts in EXO 0748–676."874 Since our optical observation at the end of 2008 October (IIvunes&Joues2008).. we have been following the source nightlv iu the optica.," Since our optical observation at the end of 2008 October \citep{Hynes:2008a}, we have been following the source nightly in the optical."875 We report here on the optical behavior iu quiesceuce over the following three 1uontlis., We report here on the optical behavior in quiescence over the following three months.876 Opical aud infrared photometry of UY Vol were obtained approximately uiehltlv from 2008 October 28 to 2009 February 5 using Aucicams ou the SMIARTS 1.31uu telescope., Optical and infrared photometry of UY Vol were obtained approximately nightly from 2008 October 28 to 2009 February 5 using Andicam on the SMARTS m telescope.877 Each nieht. 32 ss 2 band images were taken togetjor with 20 93 J band images.," Each night, 3 s $R$ band images were taken together with 20 s $J$ band images."878 During this period data were obtained ou 71 out of LOLnights., During this period data were obtained on 71 out of 101nights.879 We show ourconibined optical image in Fie. 1., We show ourcombined optical image in Fig. \ref{ImageFig}.880.Opicaldataweresupplied with pipeline reductions applied aud these were satisfactory., .Opticaldataweresupplied with pipeline reductions applied and these were satisfactory.881 The three images from cach might were aligned aixd combined to produce, The three images from each night were aligned and combined to produce882Sokoloski et al (2008) have presented evidence that within davs of its 2006 outburst the recurrent nova RS Ophiuchi produced a pair of highly collimated Challopening angles of a just few degrees’) and high velocity (6—5000 kms 4) jets.,Sokoloski et al (2008) have presented evidence that within days of its 2006 outburst the recurrent nova RS Ophiuchi produced a pair of highly collimated ('half–opening angles of a just few degrees') and high velocity $v \sim 5000$ km $^{-1}$ ) jets.883 Tavlor ct al. (, Taylor et al. (8841989) made similar deductions after the previous (1985) outburst.,1989) made similar deductions after the previous (1985) outburst.885 We argue here that this provides compelling evidence about the cause of the outburst in this object., We argue here that this provides compelling evidence about the cause of the outburst in this object.886 The source of the energy driving the outbursts in recurrent novae has been under cliscussion Lor some tine (c.g. Livio. Truran Webbink. 1986).," The source of the energy driving the outbursts in recurrent novae has been under discussion for some time (e.g. Livio, Truran Webbink, 1986)."887" There are two basic »ossibilities:eher the outburst is caused. by ai nuclear explosion on the surface of a white dwarf. akin to a classica nova explosion. but smaller in scale.or the outburst. is oowered by accretion energy. released. by a change in the accretion rate on to the central white ανα, akin to cdwarl nova outbursts but larger in scale. and similar in nature to he transient Xray binaries (which ciller in having a centra neutron star or black hole as the accretor)"," There are two basic possibilities: the outburst is caused by a nuclear explosion on the surface of a white dwarf, akin to a classical nova explosion, but smaller in scale, the outburst is powered by accretion energy released by a change in the accretion rate on to the central white dwarf, akin to dwarf nova outbursts but larger in scale, and similar in nature to the transient X–ray binaries (which differ in having a central neutron star or black hole as the accretor)."888 lt is. however. dillicult to see how a nuclear.powerec explosion on the surface of an accreting white dwarf coul eive rise to such wellcollimated jets.," It is, however, difficult to see how a nuclear–powered explosion on the surface of an accreting white dwarf could give rise to such well–collimated jets."889 In general one woule expect nuclear burning in the hydrogen.rich surface shell to be quasispherically svmimetric., In general one would expect nuclear burning in the hydrogen–rich surface shell to be quasi–spherically symmetric.890 The nuclear energy. viel from the hydrogenrich matter. considerably exceeds its binding energy at the surface of a white cwarl., The nuclear energy yield from the hydrogen–rich matter considerably exceeds its binding energy at the surface of a white dwarf.891 In a nuclear nova. the mass of explosively burning material is comparable to that accreted. since the last outburst.," In a nuclear--powered nova, the mass of explosively burning material is comparable to that accreted since the last outburst."892 The mass in the central regions of any disc must be much smaller than this. and is even less gravitationallv bound than the matter on the white dwarf surface.," The mass in the central regions of any disc must be much smaller than this, and is even less gravitationally bound than the matter on the white dwarf surface."893 Thus the mass in such a disc does not have enough inertia to provide strong collimation of the Dow., Thus the mass in such a disc does not have enough inertia to provide strong collimation of the flow.894 This point is underlined by the lack of any strongly collimated Hows to be seen in ejecta from classical novae (Slavin et ab.," This point is underlined by the lack of any strongly collimated flows to be seen in ejecta from classical novae (Slavin et al.,"895 1995: Gill O'Brien. 1998).," 1995; Gill O'Brien, 1998)."896 One only sees slight. asvounetrices in the shells of material expelled. by the nova explosion. presumably caused by. the presence of a close binary companion. and Iumpiness in the shells (presumably caused by instabilities in. the ejection process)," One only sees slight asymmetries in the shells of material expelled by the nova explosion, presumably caused by the presence of a close binary companion, and lumpiness in the shells (presumably caused by instabilities in the ejection process)."897 In contrast. the jets seen in RS Oph are high velocity and strongly. collimated.," In contrast, the jets seen in RS Oph are high velocity and strongly collimated."898 As such they are strongly reminiscent of jets seen in other astronomical objects such as radio galaxies. active galactic nucle: (ACN). microquasars. some binary X.ray sources and voung stellar objects.," As such they are strongly reminiscent of jets seen in other astronomical objects such as radio galaxies, active galactic nuclei (AGN), microquasars, some binary X–ray sources and young stellar objects."899 These jets all have the following in common (Pringle. 1993: Livio. 1999. 2000: Price. Pringle Ixing. 2003): the source of the jet has aceretion occurring through a disc: the jet velocities are comparable to. or slightly higher than. the escape velocity from the central accreting object: and about LO per cent of," These jets all have the following in common (Pringle, 1993; Livio, 1999, 2000; Price, Pringle King, 2003): the source of the jet has accretion occurring through a disc; the jet velocities are comparable to, or slightly higher than, the escape velocity from the central accreting object; and about 10 per cent of"900The sources in population B may have standard thin accretion disks surrounding the black holes. otherwise some black holes should be at least as huge as 10'7M...,"The sources in population B may have standard thin accretion disks surrounding the black holes, otherwise some black holes should be at least as huge as $10^{12} M_\odot$."901" If the accretion rate 17 of these sources is as small as ~0.025. slightly higher than the critical value below which the accretion flow would be in ADAF state. the black hole mass would be in 108""! MW..."," If the accretion rate $\dot m$ of these sources is as small as $\sim 0.025$, slightly higher than the critical value below which the accretion flow would be in ADAF state, the black hole mass would be in $10^{8-10}$ $M_\odot$."902 As the fact that most FSRQs have black hole mass higher than 10° M. (Laor2000:MeLure&Dunlop2001:Gu.Cao.Jiang2001).. this is compatible with the unified models of radio-loud quasars (Urry&Padovani1995).," As the fact that most FSRQs have black hole mass higher than $10^8$ $M_\odot$ \citep{laor00,md01,g01}, this is compatible with the unified models of radio-loud quasars \citep{up95}."903 There are three HBLs in our sample in population A. and all sources in population B are LBLs.," There are three HBLs in our sample in population A, and all sources in population B are LBLs."904 It may imply that the accretion flows in all HBLs are in ADAF state., It may imply that the accretion flows in all HBLs are in ADAF state.905 The fact that no broad emission line has been detected for most BL Lac objects may imply that only a small fraction of LBLs have optically thick standard thin aceretion disks surrounding the black holes with very low accretion rate close to 44., The fact that no broad emission line has been detected for most BL Lac objects may imply that only a small fraction of LBLs have optically thick standard thin accretion disks surrounding the black holes with very low accretion rate close to $\dot m_{\rm crit}$.906 We speculate that these LBLs will finally exhaust the gas near the hole and the disks will transit to ADAFs., We speculate that these LBLs will finally exhaust the gas near the hole and the disks will transit to ADAFs.907 Most other LBLs and HBLs without any broad emission line detected may be in population A. and the accretion flows have already been in ADAF state.," Most other LBLs and HBLs without any broad emission line detected may be in population A, and the accretion flows have already been in ADAF state."908 Otherwise the black holes in these sources should be very small. if the accretion flows are in standard thin disk state.," Otherwise the black holes in these sources should be very small, if the accretion flows are in standard thin disk state."909 It is most probably that the BL Lac objects studied here with one (or more) broad emission line detected are in the intermediate state of the evolutionary sequence from FSRQ to BL Lae object., It is most probably that the BL Lac objects studied here with one (or more) broad emission line detected are in the intermediate state of the evolutionary sequence from FSRQ to BL Lac object.910 The fact that no HBL ts in population B may imply that the evolutionary sequence of BL Lac objects should be >HBL., The fact that no HBL is in population B may imply that the evolutionary sequence of BL Lac objects should be $\rightarrow$ HBL.911 The results present in thisLetter support the evolutionary sequence >LBL >HBL suggested by D'Elia&Cavaliere(2000)., The results present in this support the evolutionary sequence $\rightarrow$ $\rightarrow$ HBL suggested by \citet{dc00}.912. If this ts the case. then the ratio of the BL Lac objects in population B to the remainder offers a clue to study the detailed evolutionary history of blazars. and it can also be a useful test on ADAF models.," If this is the case, then the ratio of the BL Lac objects in population B to the remainder offers a clue to study the detailed evolutionary history of blazars, and it can also be a useful test on ADAF models."913" If the evolution of blazars ts really regulated by the gas near the black hole. the reprocessing optical depth of the BLR would decrease with the depletion of the gas near the hole. and the line EW,o, of the blazar would also decrease along the evolutionary sequence."," If the evolution of blazars is really regulated by the gas near the black hole, the reprocessing optical depth of the BLR would decrease with the depletion of the gas near the hole, and the line $EW_{\rm ion}$ of the blazar would also decrease along the evolutionary sequence."914 The lower limits on the mass of the hole in evolving blazars should be modified with varying EWis4., The lower limits on the mass of the hole in evolving blazars should be modified with varying $EW_{\rm ion}$.915" In this work. we used a single EW, to derive the masses of holes in blazars and found that the holes have similar masses for these two populations of BL Lae objects."," In this work, we used a single $EW_{\rm ion}$ to derive the masses of holes in blazars and found that the holes have similar masses for these two populations of BL Lac objects."916 In this case. the lower limits on the mass of the hole in the blazars evolving at a later stage would become systematically higher than that derived in this work.," In this case, the lower limits on the mass of the hole in the blazars evolving at a later stage would become systematically higher than that derived in this work."917 The derived hole masses seem to be consistent with the evolutionary sequence »LBL >HBL., The derived hole masses seem to be consistent with the evolutionary sequence $\rightarrow$ $\rightarrow$ HBL.918 | thank the anonymous referee’s helpful comments., I thank the anonymous referee's helpful comments.919 This work is support by NSFC(No., This work is support by NSFC(No.920 10173016) and the NKBRSF (No., 10173016) and the NKBRSF (No.921 G1999075403)., G1999075403).922 This research has made use of the NASA/IPAC Extragalactic Database (NED). which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Aeronautic and Space Administration.," This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautic and Space Administration."923Contour plots of the 2-D spectra around the Ouj372.7 and Oru]500.7 emission lines are shown in 55.,Contour plots of the 2-D spectra around the ]372.7 and ]500.7 emission lines are shown in 5.924 There is a striking change in the ionisation and luminosity across the position of the continuum knot: the. side. nearest to the radio galaxy has a hieh luminosity. and a low ionisation as measured by the ratio of Or1]372.7 emission lines (0.35 20.1).," There is a striking change in the ionisation and luminosity across the position of the continuum knot: the side nearest to the radio galaxy has a high luminosity, and a low ionisation as measured by the ratio of ]372.7 emission lines $0.35 \pm 0.1$ )."925 In contrast. bevond the knot the O11372.7 ratio is muchhigher (7 10-3) and the total luminosity lower by a factor of z6.," In contrast, beyond the knot the ]372.7 ratio is muchhigher $>10\pm 3$ ) and the total luminosity lower by a factor of $\approx 6$."926 There is a velocity &eracdient of z300 km - in the line emission across the continuum knot. in the sense that the side nearest the racio ealaxy is blueshifted. and that on the far side is. within errors of zz100kms.|. at vest with respect to the starlight inc.," There is a velocity gradient of $\approx 300$ km $^{-1}$ in the line emission across the continuum knot, in the sense that the side nearest the radio galaxy is blueshifted, and that on the far side is, within errors of $\approx 100\, {\rm km\,927s^{-1}}$, at rest with respect to the starlight in `c'."928 Phere is also a faint tail of vet more highly blueshifted emission (up to zGOOkms lon the side nearest the racio galaxy. pointing towards the radio galaxy.," There is also a faint tail of yet more highly blueshifted emission (up to $\approx 600\, {\rm km\, s^{-1}}$ ) on the side nearest the radio galaxy, pointing towards the radio galaxy."929 Note that there is no sign of emission lines in 44. which used a narrow extraction about the continuum peak.," Note that there is no sign of emission lines in 4, which used a narrow extraction about the continuum peak."930 In contrast. in 55 the extended. emission-line (lux from ο ds clearly visible and is quite strong when integrated over the entire emission region (Table 1).," In contrast, in 5 the extended emission-line flux from `c' is clearly visible and is quite strong when integrated over the entire emission region (Table 1)."931 The asymmetric radio structure of οςΕΕ is interesting in the context of the models to explain the aligned. emission., The asymmetric radio structure of 3C441 is interesting in the context of the models to explain the aligned emission.932 The asymmetry in jet brightness either side of the nucleus is very pronounced. and can be interpreted. either as an asvmmetry. produced by. Doppler boosting. or in terms of 3C441 having a radio structure transitional between FRI and FRIL with one side EIUl-like and the other more ETU-like.," The asymmetry in jet brightness either side of the nucleus is very pronounced, and can be interpreted either as an asymmetry produced by Doppler boosting, or in terms of 3C441 having a radio structure transitional between FRI and FRII, with one side FRII-like and the other more FRI-like."933" Phe lack of à radio central component. commonly seen in radio galaxies with Doppler boosted one-sided jets (c.g. 3€22. Rawlings et 11994). argues stronely in favour of the latter explanation. and indeed the Haring of the jet just to the NW of the host galaxy is reminiscent of the ""Mach cisk structure seen in the MIST jet (Owen. Llarcdee Cornwell 1989)."," The lack of a radio central component, commonly seen in radio galaxies with Doppler boosted one-sided jets (e.g. 3C22, Rawlings et 1994), argues strongly in favour of the latter explanation, and indeed the flaring of the jet just to the NW of the host galaxy is reminiscent of the “Mach disk” structure seen in the M87 jet (Owen, Hardee Cornwell 1989)."934 The spectrum of ca. the host galaxy of the radio source 1s garown in 22.," The spectrum of `a', the host galaxy of the radio source is shown in 2."935 It is a typical mocerately-high ionisation =xuwrow-line radio galaxy spectrum. with strong emission lines superposed on a stellar spectrum dominated by an ol stellar population with a strong 4000 break.," It is a typical moderately-high ionisation narrow-line radio galaxy spectrum, with strong emission lines superposed on a stellar spectrum dominated by an old stellar population with a strong $\;$ break."936 Close inspection of the images shows. however. tha even in this case. where the integrated light is dominated by old stellar populations there is evidence for morphologica peculiarity.," Close inspection of the images shows, however, that even in this case, where the integrated light is dominated by old stellar populations there is evidence for morphological peculiarity."937 In. particular there is a distinct. blue alignec component to the south east of the host galaxy peak 66)., In particular there is a distinct blue aligned component to the south east of the host galaxy peak 6).938 Whether this represents a spiral arm. a merger remnan or some form of radio source-induced. aligned componen is unclear.," Whether this represents a spiral arm, a merger remnant or some form of radio source-induced aligned component is unclear."939 As its separation from the radio galaxy is only about O.5-aresec. it is hard to tell from the spectra whether it is line or continuum. dominated. but. the more. dilfuse material extending = 2-aresee to the south of the radio ealaxy is definitely. continuum. dominated.," As its separation from the radio galaxy is only about 0.5-arcsec, it is hard to tell from the spectra whether it is line or continuum dominated, but the more diffuse material extending $\approx 2$ -arcsec to the south of the radio galaxy is definitely continuum dominated."940 Although much weaker relative to the smooth underlying host galaxy in he F785LP image. the aligned component is nevertheless visible. along with some more diffuse aligned. emission on he other side of the peak. to the northwest.," Although much weaker relative to the smooth underlying host galaxy in the F785LP image, the aligned component is nevertheless visible, along with some more diffuse aligned emission on the other side of the peak, to the northwest."941 In 77. the position angle of the host galaxy (clevived [rom the second moments of the Dux cistribution) is dotted for various isophotes and apertures.," In 7, the position angle of the host galaxy (derived from the second moments of the flux distribution) is plotted for various isophotes and apertures."942 This shows two interesting aspects of the alignment., This shows two interesting aspects of the alignment.943 First. the alignment »ersists. into the A-band. suggesting the aligned. light is adrly red.," First, the alignment persists into the $K$ -band, suggesting the aligned light is fairly red."944 Second. in the457 images. there is evidence or isophotal twisting as the aperture size is increased. to include the inner aligned. components highlighted. in 66 (PA ~150 deg). and later the low surface brightness emission round the host at PA ~ 0. seen best in 11.," Second, in the images, there is evidence for isophotal twisting as the aperture size is increased to include the inner aligned components highlighted in 6 (PA $\sim 150$ deg), and later the low surface brightness emission round the host at PA $\sim9450$ , seen best in 1."946 The low-surlace brightness material to the northwest may, The low-surface brightness material to the northwest may947to distinguish between cillerent source counts models. (sce Tables 3 and 4).,to distinguish between different source counts models (see Tables 3 and 4).948 Finally. we have also studied the fit of the cüllerential number counts at 70 and 100 11 to a power law dnfds=ASU.," Finally, we have also studied the fit of the differential number counts at 70 and 100 GHz to a power law $dn/dS=A S^{-\alpha}$."949 From he cumulants previously estimated. we calculate by using ο“eqs. (," From the cumulants previously estimated, we calculate by using eqs. ("95032-34) the amplitudeοἱ and slope a of the differential r counts.,32-34) the amplitude $A$ and slope $\alpha$ of the differential number counts.951 The results at 70 Cillz for a l Jv llux limit are: à=2.19c0.43. =24.3HAS.," The results at 70 GHz for a 1 Jy flux limit are: $\alpha=2.19\pm 0.43$, $A=24.3\pm 4.3$."952 When we calculate these magnitudes from the cumulants IC and INT. computed directly from the point source only simulations. we obtain a=2.32c0.06. AP=22.1]c1.5.," When we calculate these magnitudes from the cumulants $K_3^{ps}$ and $K_4^{ps}$, computed directly from the point source only simulations, we obtain $\alpha^{ps}=2.32\pm 0.06$, $A^{ps}=22.1\pm 1.5$."953 ‘These are the average and rms deviation from ten half skies., These are the average and rms deviation from ten half skies.954" For this llux limit. the average rerelative error ofa CA) with respect to a7 (AP) is below I0 MINE(15%). ""n"," For this flux limit, the average relative error of $\alpha$ $A$ ) with respect to $\alpha^{ps}$ $A^{ps}$ ) is below $10\%$ $15\%$ )."955 The dispersion in the values obtained with the is high. though the average is consistent. with the value obtained directly. fron point sources down to a [ux limit of 0.7 Jy. as can be seen in Table 5.," The dispersion in the values obtained with the MHWF fit is high, though the average is consistent with the value obtained directly from point sources down to a flux limit of 0.7 Jy, as can be seen in Table 5."956 When we consider the 100. 611 channel. the values obtained from the MEINE fit for a flux limit of 1 Jv are: a=2.260.19. A=210642. the results from the point source simulations are: a=2.35£0.16. 47=20.003.1.," When we consider the 100 GHz channel, the values obtained from the MHWF fit for a flux limit of 1 Jy are: $\alpha=2.26\pm 0.19$, $A=21.0\pm 4.2$, the results from the point source simulations are: $\alpha^{ps}=2.35\pm 0.16$, $A^{ps}=20.0\pm 3.7$."957 The fit is better for this channel than for the 70 Gllz one. ravine a lower dispersion.," The fit is better for this channel than for the 70 GHz one, having a lower dispersion."958 For this lux limit. the average relative error of à (A) with respect to a (AP) is below 5% (6%).," For this flux limit, the average relative error of $\alpha$ $A$ ) with respect to $\alpha^{ps}$ $A^{ps}$ ) is below $5\%$ $6\%$ )."959 Ehe results are consistent down to a flux limit of V7 Jv., The results are consistent down to a flux limit of 0.7 Jy.960 The detailed. values of the parameters a and 4 can »e seen in Table 5., The detailed values of the parameters $\alpha$ and $A$ can be seen in Table 5.961 In Figure 3 we plot the differential source counts of the De Zotti model. the fit to a power law by using the MINE and the fit obtained [rom the point source only simulations. in both cases with a 1 Jv flux limit.," In Figure 3 we plot the differential source counts of the De Zotti model, the fit to a power law by using the MHWF and the fit obtained from the point source only simulations, in both cases with a 1 Jy flux limit."962 As we can see in this igure. both fits are consistent with the input counts in the range between 0.1 Jv and 1 Jy.," As we can see in this figure, both fits are consistent with the input counts in the range between 0.1 Jy and 1 Jy."963 We acknowledge partial financial support from the Spanish Ministry of Education. (MIC) under project. ESP2004067C0301., We acknowledge partial financial support from the Spanish Ministry of Education (MEC) under project ESP2004--07067--C03--01.964 We thank €. De Zotti for having kindly orovided. us with the source. number counts [orescen. by he De Zotti ct al. (, We thank G. De Zotti for having kindly provided us with the source number counts foreseen by the De Zotti et al. (9652005) cosmological evolution model at he LET frequencies.,2005) cosmological evolution model at the LFI frequencies.966 We acknowledge the use of the Planck teference Sky. prepared. by the members of the Planck Working Croup 2.," We acknowledge the use of the Planck Reference Sky, prepared by the members of the Planck Working Group 2."967 We also thank L. Tollolatti for useful discussions., We also thank L. Toffolatti for useful discussions.968 Finally. we thank the referee. Mark. Ashclown. or his useful comments and suggestions.," Finally, we thank the referee, Mark Ashdown, for his useful comments and suggestions."969"where we the observed as S and the unlensed flux as S, denotedsuch that S=µι fluxand the unlensed differential source sky density as ","where we denoted the observed flux as S and the unlensed flux as $\hat{S}$, such that $S=\mu \hat{S}$ and the unlensed differential source sky density as $d\hat{n}/d\hat{S}$."970The four panels in Figure 5 di/dS.show the lensed count predictions for SPT as the most relevant parameters are varied., The four panels in Figure \ref{f5} show the lensed count predictions for SPT as the most relevant parameters are varied.971 The cosmological uncertainty is clearly subdominant to uncertainties in the source properties and lens properties., The cosmological uncertainty is clearly subdominant to uncertainties in the source properties and lens properties.972" In particular, the overall normalization of the mass profiles (f,) and the source size can change the expected number of strong lenses by large amounts."," In particular, the overall normalization of the mass profiles $f_{\sigma}$ ) and the source size can change the expected number of strong lenses by large amounts."973 Figure 6 and 7 illustrate that there are lensing models which fit the SPT source counts quite well for both the Durham and UBC unlensed source count models., Figure \ref{f6} and \ref{f7} illustrate that there are lensing models which fit the SPT source counts quite well for both the Durham and UBC unlensed source count models.974" The lensing parameters are slightly different, with the Durham model preferring slightly larger source sizes and smaller ellipticity."," The lensing parameters are slightly different, with the Durham model preferring slightly larger source sizes and smaller ellipticity."975 The contribution of various redshift ranges to the lensed number counts can also be seen to be slightly different for the two models., The contribution of various redshift ranges to the lensed number counts can also be seen to be slightly different for the two models.976" Figure 6 shows that the Durham model finds that most of the sources lie at zZ3 over the entire SPT flux range, while Figure 7 shows that the UBC model has a significant fraction of lensed sources as low as z~2."," Figure \ref{f6} shows that the Durham model finds that most of the sources lie at $z \ga 3$ over the entire SPT flux range, while Figure \ref{f7} shows that the UBC model has a significant fraction of lensed sources as low as $z\sim 2$."977 In Figure 8 and 9 the distribution in magnification can be seen to be a strong function of flux for both models., In Figure \ref{f8} and \ref{f9} the distribution in magnification can be seen to be a strong function of flux for both models.978" At the low-flux end the cross-section is dominated by relatively low magnifications (~10), while higher fluxes are increasingly dominated by larger magnifications."," At the low-flux end the cross-section is dominated by relatively low magnifications $\sim 10$ ), while higher fluxes are increasingly dominated by larger magnifications."979" This is not surprising, given the steep unlensed luminosity function."," This is not surprising, given the steep unlensed luminosity function."980" The mean magnification at different fluxes is seen to have significant differences between the Durham and UBC models, suggesting that this could be a useful diagnostic for reconstructing the unlensed luminosity function."," The mean magnification at different fluxes is seen to have significant differences between the Durham and UBC models, suggesting that this could be a useful diagnostic for reconstructing the unlensed luminosity function."981" In Figure 8 the Durham model is largely dominated by the highest magnifications in the region of the SPT counts, while Figure 9 shows that the UBC model shows a transition from low magnification to high magnification in the flux range where SPT has reported constraints."," In Figure \ref{f8} the Durham model is largely dominated by the highest magnifications in the region of the SPT counts, while Figure \ref{f9} shows that the UBC model shows a transition from low magnification to high magnification in the flux range where SPT has reported constraints."982" This is a direct reflection of the differences in the unlensed counts: the Durham model has an abrupt fall-off at the high flux end of the unlensed counts, well below the flux range probed by SPT, while the UBC model has more unlensed high redshift bright objects."," This is a direct reflection of the differences in the unlensed counts: the Durham model has an abrupt fall-off at the high flux end of the unlensed counts, well below the flux range probed by SPT, while the UBC model has more unlensed high redshift bright objects."983(he regions centered on NGC 7618 and UGC 12491. but provide an adequate description of the diffuse emission between the galaxies.,"the regions centered on NGC 7618 and UGC 12491, but provide an adequate description of the diffuse emission between the galaxies."984 The temperature of the diffuse gas between NGC 1618 and UGC 12491 is (21., The temperature of the diffuse gas between NGC 7618 and UGC 12491 is $^{+0.50}_{-0.34}$.985 We also fit (wo temperature models to the two spectra extracted from the regions centered on NGC 7618 and UGC 12491., We also fit two temperature models to the two spectra extracted from the regions centered on NGC 7618 and UGC 12491.986" As before. both the Vy, and the elemental abundance were frozen."," As before, both the $N_H$ and the elemental abundance were frozen."987 For NGC 7618. we also froze the temperature of one component at 0.3 keV. the value determined from the ACIS-8 spectral fitting. to reduce ihe number of free parameters.," For NGC 7618, we also froze the temperature of one component at 0.8 keV, the value determined from the ACIS-S spectral fitting, to reduce the number of free parameters."988 If this parameter is allowed to freely vary. (he fit value is consistent with 0.3 keV. For UGC 12491. the temperatures of both components were allowed to freely vary.," If this parameter is allowed to freely vary, the fit value is consistent with 0.8 keV. For UGC 12491, the temperatures of both components were allowed to freely vary."989 The results of these fits are summarized in the bottom half of Table 2.., The results of these fits are summarized in the bottom half of Table \ref{spectab}.990 The two temperature model provides acceptable fits in both cases. and the temperature of the hotter component is ~2.3 keV. There are al least four possible explanations for the observed X-ray structures.," The two temperature model provides acceptable fits in both cases, and the temperature of the hotter component is $\sim$ 2.3 keV. There are at least four possible explanations for the observed X-ray structures."991 First. the complex X-ray morphology. could be Che result of a radio lobe/IGM interaction.," First, the complex X-ray morphology could be the result of a radio lobe/IGM interaction."992 NGC 17618 is a radio source., NGC 7618 is a radio source.993 It is detected in the NVSS with a flux density of 20 mJy. wilh some evidence of extension NW/SE.," It is detected in the NVSS with a flux density of 20 mJy, with some evidence of extension NW/SE."994 At higher frequencies (5 and 8 GlIz) two 15-min archival VLA observations only detect a point-like core coincident wilh the center of (he galaxy. with a flux density of 4.5 mJv al 4.9 GlIIz and 3.0 mJv at 3.4 GlIz.," At higher frequencies (5 and 8 GHz) two 15-min archival VLA observations only detect a point-like core coincident with the center of the galaxy, with a flux density of 4.5 mJy at 4.9 GHz and 3.0 mJy at 8.4 GHz."995" However. at lower frequencies. the flux density is much higher: 1.2 Jv in the 151-MlIIz 6C catalog (ales.Baldwin.& 1993).. 0.26 Jv in the 408-MIIz B3 catalog (Ficarra.(πιο,&Tomassetti1985).. ancl 1.0 Jv in the 74-MlIz VLA Low-Frequency Sky Survev (VLSS: http://Iwa.nrl.navy.mil/VLS5/)."," However, at lower frequencies, the flux density is much higher: 1.2 Jy in the 151-MHz 6C catalog \citep{hal93}, 0.26 Jy in the 408-MHz B3 catalog \citep{fic85}, and 1.0 Jy in the 74-MHz VLA Low-Frequency Sky Survey (VLSS: http://lwa.nrl.navy.mil/VLSS/)."996 The high flux densitv al low frequencies suggests that there nav be a relie radio source. the aged svnchrotron plasma from a more energetic phase of the active nucleus.," The high flux density at low frequencies suggests that there may be a relic radio source, the aged synchrotron plasma from a more energetic phase of the active nucleus."997 The X-ray morphology is very different from that seen in other examples of radio lobe/ISM interactions. however.," The X-ray morphology is very different from that seen in other examples of radio lobe/ISM interactions, however."998 There are no obvious X-ray cavities as are commonly seen in such radio lobe/ISM interactions (e.g. (AleNamarae£al2000:Jonesefaf2002:Heinz 2002))). nor is there evidence of hot. shock-heated shell that would be present if the radio lobes were expanding supersonically (νταefaf2003).," There are no obvious X-ray cavities as are commonly seen in such radio lobe/ISM interactions (e.g. \citep{mcn00,jon02,hei02}) ), nor is there evidence of hot, shock-heated shell that would be present if the radio lobes were expanding supersonically \citep{kra03}."999. It is not clear whether any of these features wotld be expected in the case of a relie radio source. however.," It is not clear whether any of these features would be expected in the case of a relic radio source, however."1000 A sensitive low-frequeney radio map would eive us a better understanding of the possible interaction between raclio-emiline plasma and (he hot eas., A sensitive low-frequency radio map would give us a better understanding of the possible interaction between radio-emitting plasma and the hot gas.1001 second. itis possible that the NGC 7618 gas is oscillating. or sloshing. in (he gravitational potential because of a recent merger/interaction with a lower mass sub-group.," Second, it is possible that the NGC 7618 gas is oscillating, or 'sloshing', in the gravitational potential because of a recent merger/interaction with a lower mass sub-group."1002 A dust lane has been detected in the optical host galaxy. perhaps indicative of a recent merger," A dust lane has been detected in the optical host galaxy, perhaps indicative of a recent merger"1003physical properties that are diagnostic of galaxy. formation.,physical properties that are diagnostic of galaxy formation.1004 Core galaxies are on average more luminous than power-law galaxies. with power-laws comitating below Aly~—21 aud cores greatly dominating at higher luminosities (Faberetal.1997).," Core galaxies are on average more luminous than power-law galaxies, with power-laws dominating below $M_V\sim-21$ and cores greatly dominating at higher luminosities \citep{f97}."1005. Co'e galaxies generally Lave boxy isophotes. while power-law galaxies are disky (Nieoetal.1991:Iwormendy&Beucer 1997).," Core galaxies generally have boxy isophotes, while power-law galaxies are disky \citep{n91, k96, f97}."1006. Core galaxies rotate slowly. while power-law gaaxies rotate more rapidly 1997): similarly. boxy galaxies include slow rotators while cisky ealaxies rotate rapidly (Beucleral.1989.19914:Ixormenu«v&Beuder 1996).," Core galaxies rotate slowly, while power-law galaxies rotate more rapidly \citep{f97}; similarly, boxy galaxies include slow rotators while disky galaxies rotate rapidly \citep{b88, b89, b94, k96}."1007. Core-boxy galaxies show miuor-axis rotation indicative of triaxiality. while co'eless-disky galaxies do not (Ixormendy&Bender1996).," Core-boxy galaxies show minor-axis rotation indicative of triaxiality, while coreless-disky galaxies do not \citep{k96}."1008. Aud core galaxies are systematically rounder than power-law galaxies (Jalleetal.1991:Ferrareseetal.1994:Rycdeu2001:Lauer: 2005).. just as bright (ONY) galaxies are systematically rouuder than faint. (disky) galaxies (Tre:iblay&Merritt.1996).," And core galaxies are systematically rounder than power-law galaxies \citep{jaffe, f94, ryden2, l05}, just as bright (boxy) galaxies are systematically rounder than faint (disky) galaxies \citep{tm}."1009. Siguiicantly. core aud power-law ealanies of identical luminosity cau still be separated by all of tLene secondary characteristics 1997).," Significantly, core and power-law galaxies of identical luminosity can still be separated by all of these secondary characteristics \citep{f97}."1010. Thus central and global properties together point oc ereces in the formation of core aud power-law ellipticals., Thus central and global properties together point to differences in the formation of core and power-law ellipticals.1011 Nortrendy&Betder(1996) propose a revision of the Hibble sequence for elliptical galaxies that recognizes this plvsical dichotomv. Isle isoshote shape asa convenient surrogate for the above physica properties.," \citet{k96} propose a revision of the Hubble sequence for elliptical galaxies that recognizes this physical dichotomy, using isophote shape as a convenient surrogate for the above physical properties."1012 lore recent work continues ο show that power-law aud core galaxies have pliysically distiuct. properties., More recent work continues to show that power-law and core galaxies have physically distinct properties.1013 Cores (Capetti&Balmaverde2005:Bal 2006).. like boxy isoyhotes (Beneeretal.1989).. correlate with radio-Iou aciive nuclei.," Cores \citep{cap, bal}, like boxy isophotes \citep{b89}, correlate with radio-loud active nuclei."1014 And cores (Pellegrini2005).. lixe )oxy isophotes (Beucleretal.1980).. correlate with strougD>oO x-ray elulssion.," And cores \citep{pell}, like boxy isophotes \citep{b89}, correlate with strong x-ray emission."1015 The properties of the power-aw versus core galaxies suggest that core systems resulted [roi the mergers of less Iumiuous powe-]aw systems., The properties of the power-law versus core galaxies suggest that core systems resulted from the mergers of less luminous power-law systems.1016 Simulatiois by Milosavljevié&Merritt(2001).. for example. showed that the mereer ol two power-law galaxies. each w‘ith à central massive black hole. would p'oduce a core galaxy.," Simulations by \citet{mnm}, for example, showed that the merger of two power-law galaxies, each with a central massive black hole, would produce a core galaxy."1017 The jimo«cal cusp distribution would thus be oue key to uncderstauciug the central structure of elliptical ealaxies over a history of nereers., The bimodal cusp distribution would thus be one key to understanding the central structure of elliptical galaxies over a history of mergers.1018 As arger samples of elliptical galaxies were observed withAST. the bimocdal slope distribution remained robist (Quillenetal.3XJOO:Rest200!|:Ravindranath2001:Lauer2005).," As larger samples of elliptical galaxies were observed with, the bimodal slope distribution remained robust \citep{quil, rest, rav, l05}."1019. While all oftlese stuies ideutilied a stuall nuunber of “inte‘uectiate” galaxies. which have limiting cusp slopes with 0.3<+! ley are Dot comainon enoug 1o fill the “valley? between the aud core Cusp-sloye distribuions.," While all of these studies identified a small number of “intermediate” galaxies, which have limiting cusp slopes with $0.3<\gamma'<0.5,$ they are not common enough to fill the “valley” between the power-law and core cusp-slope distributions."1020 This is a critical point tha has often been misunderstood in the literatwe., This is a critical point that has often been misunderstood in the literature.1021 Tle sample of e@alaxies available to Faberetal.(1997) had uo systems with 2/«Q.5. thus le cistributons of slopes was not only bimodal. but disjoiut.," The sample of galaxies available to \citet{f97} had no systems with $0.3<\gamma'<0.5,$ thus the distributions of slopes was not only bimodal, but disjoint."1022 The subsequent discovery of a sinall liuuber of 11ermediate galaxies shows that t1 distribution o “cusp slopes is truly coutiuuous. bu it has relmarect biinocdlal in its overall charact eri all ie studies cited above.," The subsequent discovery of a small number of intermediate galaxies shows that the distribution of cusp slopes is truly continuous, but it has remained bimodal in its overall character in all the studies cited above."1023 'Ehis picture has been challeneed by the recent distribution ofctsp slopes preseuted by (2006).. who «ο not find biuodality in their sample of 100 galaxies observe by theirHST Virgo Cluster Survey (VCS). altough they sti] identify a separ:e class of core galaxies. which they define as having brightuess p‘ofiles iat fall below Sérsic(1968) [o‘ios lu the ceiter.," This picture has been challenged by the recent distribution of cusp slopes presented by \citet{lf}, who do not find bimodality in their sample of 100 galaxies observed by their Virgo Cluster Survey (VCS), although they still identify a separate class of core galaxies, which they define as having brightness profiles that fall below \citet{sersic} forms in the center."1024 While the use of profiles is a new app'oach o identi[vingOm core egalaxies. the class of VCS core egalaxies," While the use of profiles is a new approach to identifying core galaxies, the class of VCS core galaxies"1025variable.,variable.1026 One could envisage a wide binary in which a Mira star transfers matter during its expansion., One could envisage a wide binary in which a Mira star transfers matter during its expansion.1027 However. im that case the outburst would be expected to last rather longer than observed.," However, in that case the outburst would be expected to last rather longer than observed."1028 Iu each of the error circles. there is one source which was brielter when the X-ray source was on. aud for which the cüfference flux is substantially bluer than that for other variables in the field.," In each of the error circles, there is one source which was brighter when the X-ray source was on, and for which the difference flux is substantially bluer than that for other variables in the field."1029 For X1. the source V1 is just outside the western edge of the error circle. while for X2. V2 is just inside the error circle.," For X1, the source V1 is just outside the western edge of the error circle, while for X2, V2 is just inside the error circle."1030 The coordinates of these variables are given in reftabpos., The coordinates of these variables are given in \\ref{tabpos}.1031.V2 may be interesting in particular. since the relative brightening for that source is the second-larecst iu the field (about in D. « in B: the largest relative ποτοιτις aud.. respectively is shown bx VU).," .V2 may be interesting in particular, since the relative brightening for that source is the second-largest in the field (about in B, $<\!4\%$ in R; the largest relative brightening – and, respectively – is shown by V0)."1032 Tt Vl or V2 were the optical counterpart of the N-rax transieut. we would expect that the source in quiesceuce had negligible coutribution to the optical flux iu the off nuage.," If V1 or V2 were the optical counterpart of the X-ray transient, we would expect that the source in quiescence had negligible contribution to the optical flux in the off image."1033 The excess flux iu the on image then would correspond to the the total flux of the source in outburst., The excess flux in the on image then would correspond to the the total flux of the source in outburst.1034 We estimate the corresponding magnitudes usine our approximate calibration., We estimate the corresponding magnitudes using our approximate calibration.1035 For Vil we fud Bz22.0. Rx 19.5. and for V2 DBz 22.7. Ro»21.1.," For V1 we find $B\simeq22.0$, $R\simeq19.3$ , and for V2 $B\simeq22.7$ , $R>21.1$."1036 Correcting for reddening. one infers 0Rjyg= liand(BRySO. respectively. again indicating that V2 is very blue.," Correcting for reddening, one infers $(B-R)_0\simeq1.1$ and $(B-R)_0\la0$, respectively, again indicating that V2 is very blue."1037 From the above. it ποσα: that V2 has all the characteristics expected for the optical counterpart.," From the above, it seems that V2 has all the characteristics expected for the optical counterpart."1038 It is clear. however. that finding a variable source inside one of the two error circles is not uulikelv. even one whose variation is relatively blue.," It is clear, however, that finding a variable source inside one of the two error circles is not unlikely, even one whose variation is relatively blue."1039 Therefore. at prescut we consider this source as no more than an interesting caucdidatoe.," Therefore, at present we consider this source as no more than an interesting candidate."1040 We have tried to recoustruct the approximate X-ray ccurve of the August 1998 outburst by combining data from various mieasureimenuts., We have tried to reconstruct the approximate X-ray curve of the August 1998 outburst by combining data from various measurements.1041 Detectious were made by the Wide Field Cameras aud the Narrow Field Iustriuueuts on board of BeppoSAX on Aue 22 aud 26. respectively: and by the NTE All Sky. Monitor in a seven-day period starting on Ane 19.," Detections were made by the Wide Field Cameras and the Narrow Field Instruments on board of BeppoSAX on Aug 22 and 26, respectively; and by the XTE All Sky Monitor in a seven-day period starting on Aug 19."1042 We revise the flux detected with the Wide Field Cameras to 35 αιτα. καστ] upwards TOlu je values eiven in Iu t Zand et ((1999). on the oasis of a better calibration.," We revise the flux detected with the Wide Field Cameras to $35\pm4$ mCrab, slightly upwards from the values given in In 't Zand et (1999), on the basis of a better calibration."1043 Upper limits were obtained with the BeppoSAX Wide Field Cameras ou Sep 1 and with the NTE All Sky Monitor iu the seven days periods recedingi auc following the detection., Upper limits were obtained with the BeppoSAX Wide Field Cameras on Sep 1 and with the XTE All Sky Monitor in the seven days periods preceding and following the detection.1044 roefxcur shows the resulting Leltcurve., \\ref{xcur} shows the resulting lightcurve.1045 Extrapolating the 5-day expoucutial decay from. he BeppoSAN detections to the time of the ROSAT IIRI observation. we predict an N-vav luminosity of LO?ores in the ROSAT baud: this is about au order of magnitude above the observed upper Huit.," Extrapolating the 5-day exponential decay from the BeppoSAX detections to the time of the ROSAT HRI observation, we predict an X-ray luminosity of $\sim 10^{35}\ergs$ in the ROSAT band; this is about an order of magnitude above the observed upper limit."1046 This may maple that the decay accelerated: or alternatively that the spectrmu softened. since low-enerev photous are much more affected by the heavy absorption towarcls 66110.," This may imply that the decay accelerated; or alternatively that the spectrum softened, since low-energy photons are much more affected by the heavy absorption towards 6440."1047 There is indeed evidence for other N-ray transicuts that the spectrum iu the low state is much softer than during outburst. flor Aql δι (Verbuut ot The Nav lightcurve shown in roefxeur dnplies hat he optical observatious were mace at an N-ravy flux evel of about LOuunCrab. corresponding to a source Iuniuositv ~ὃς10°8eresHn," There is indeed evidence for other X-ray transients that the spectrum in the low state is much softer than during outburst, for Aql X-1 (Verbunt et The X-ray lightcurve shown in \\ref{xcur}1048 implies that the optical observations were made at an X-ray flux level of about mCrab, corresponding to a source luminosity $\simeq2\times10^{36}\ergs$."1049"1, Van Paradijs AMAleChintock (1991) ejvo a senudeenipineal relation between the orbital period. N-rav Iuninositv aud absolute visual magnitude of a low-mass X-ray binary."," Van Paradijs McClintock (1994) give a semi-empirical relation between the orbital period, X-ray luminosity and absolute visual magnitude of a low-mass X-ray binary."1050 Applvine this relation to the trausieut in NGC6OGLLO with the estimate of the N-vav luminosity for the time of the optical observation. we obtain My:z10 for an assumed lhhr period.," Applying this relation to the transient in 6440 with the estimate of the X-ray luminosity for the time of the optical observation, we obtain $M_{\rm V}\simeq4.0$ for an assumed hr period."1051 At the distance and reddening of 66610 us corresponds to V-—21.7., At the distance and reddening of 6640 this corresponds to $V\simeq21.7$.1052 The intrinsic D.V 'olour of low-mass N-ray binaries is close to zero: with 1c reddening to 66LI0 we thus predict D.—22.7 or a one hour period., The intrinsic $B-V$ colour of low-mass X-ray binaries is close to zero; with the reddening to 6440 we thus predict $B\simeq22.7$ for a one hour period.1053 For a period of 5hhr hha) je predicted magnitude is about 1 maguitude brighter inter)., For a period of hr hr) the predicted magnitude is about 1 magnitude brighter (fainter).1054 We conclude that the candidate in the error ποιο of N2 is viable: the proximity of the predicted B naguitude to the observed one is fortuitous. cousidering wat thespread in the relation given by Van Paradijs ADMCCHutock is about aiaenitude. and that our estimate," We conclude that the candidate in the error circle of X2 is viable; the proximity of the predicted $B$ magnitude to the observed one is fortuitous, considering that thespread in the relation given by Van Paradijs McClintock is about a magnitude, and that our estimate"1055temperature of 5900 Ix. slishtlv higher than that of the Sun (57771X).,"temperature of 5900 K, slightly higher than that of the Sun (5777K)."1056 The flux ratio of POLITIC to the Sun is given by Bohlin. Dickinson. and Calzetti (2001) and our measured speelrophotometry was corrected accordingly.," The flux ratio of P041C to the Sun is given by Bohlin, Dickinson, and Calzetti (2001) and our measured spectrophotometry was corrected accordingly."1057 All data in Figs., All data in Figs.1058 7a ancl Tb are normalized to this corrected 0416 αν by subtracting the corrected average instrumental magnitudes of PO41C. and therefore represent a normalization to the solar πας distribution.," 7a and 7b are normalized to this corrected P041C flux by subtracting the corrected average instrumental magnitudes of P041C, and therefore represent a normalization to the solar flux distribution."1059 In Fig., In Fig.1060 Ta and Th. we show the solar analog standard stars observed on three nights in the same normalization.," 7a and 7b, we show the solar analog standard stars observed on three nights in the same normalization."1061 The data on PO4IC show a slightly blue spectrum in Figs., The data on P041C show a slightly blue spectrum in Figs.1062 Ta and Th. while the spectral energy distribution of P17T1D shows small excesses both at short and long wavelengths. both consistent. with the results by Colina and Bohlin (1997).," 7a and 7b, while the spectral energy distribution of P177D shows small excesses both at short and long wavelengths, both consistent with the results by Colina and Bohlin (1997)."1063 This good agreement in the colors of the standard stars gives us confidence that the spectrophotometric calibration of the SNIFS instrument is stable over the observing period., This good agreement in the colors of the standard stars gives us confidence that the spectrophotometric calibration of the SNIFS instrument is stable over the observing period.1064 The observed changes in (he spectrophotometry of comet Tempel 1 in the hours after impact are therefore considered real., The observed changes in the spectrophotometry of comet Tempel 1 in the hours after impact are therefore considered real.1065 The photometric errors were estimated Irom repeated observations of the comet on July 5. 2005 (UTC). ie.. alter the rapid changes in brightness induced by (the impact had. subsided.," The photometric errors were estimated from repeated observations of the comet on July 5, 2005 (UTC), i.e., after the rapid changes in brightness induced by the impact had subsided."1066 The largest error comes from changes in the image quality due to seeing changes. focus drifts. and tracking errors and affect. all wavelengths in nearly the same wav. and possibly also from intrinsic changes in brightness of the comet.," The largest error comes from changes in the image quality due to seeing changes, focus drifts, and tracking errors and affect all wavelengths in nearly the same way, and possibly also from intrinsic changes in brightness of the comet."1067 For the estimation of uncorrelated photometric errors. the photometric data were normalized to (he same magnitude average over the 625 - 825 nm range. where the signal to noise ratio was highest.," For the estimation of uncorrelated photometric errors, the photometric data were normalized to the same magnitude average over the 625 - 825 nm range, where the signal to noise ratio was highest."1068 The rms scatter of the photometric values alter (his normalization of the average flux is represented by the error bars shown in Figs., The rms scatter of the photometric values after this normalization of the average flux is represented by the error bars shown in Figs.1069 Ta and Th., 7a and 7b.1070 These error bars are characteristic of the photometric errors when the comet was at or near ils pre-inpact brightness. and also in the days alter the impact when the nucleus ancl inner coma had returned practically to pre-impact levels.," These error bars are characteristic of the photometric errors when the comet was at or near its pre-impact brightness, and also in the days after the impact when the nucleus and inner coma had returned practically to pre-impact levels."1071 While (he comet was near its maximum brightness post-impact. aud even more so for the standard stars. (he uncorrelated photometric errors were smaller than (he," While the comet was near its maximum brightness post-impact, and even more so for the standard stars, the uncorrelated photometric errors were smaller than the"1072 where CQi-geTYAVT|0VY. ος is the epicyclic frequency. =(s)/s05. and O?=00?/0:.,"Here $\omega_{A} = (\vec{k} \cdot \vec{B})/\sqrt{4 \pi \rho}$ is the Alfven frequency and where $\vec{C} = - (\beta/T) \Delta\nabla T + \delta \nabla Y$, $\Omega_{e}$ is the epicyclic frequency, $\Omega_{e}^{2} = \partial (s^{4} \Omega^{2})/ 1073s^{3} \partial s$, and $\Omega_{z}^{2} = \partial \Omega^{2}/\partial z$."1074 Eq. (, Eq. (10759) has an unstable solution if either P» or bj is negative. or In the limit of a weak field. Mn conea yield The first inequality is the criterion a convvection modified by rotation. and the second condition represents the criterion of MRI.,"9) has an unstable solution if either $b_{2}$ or $b_{0}$ is negative, or In the limit of a weak field, these conditions yield The first inequality is the criterion of convection modified by rotation, and the second condition represents the criterion of MRI."1076 The solution of Eq. (, The solution of Eq. (10779) is If cy is small compared to the other frequencies. we have The solutions » correspond to buoyant modes that cause convection: and are unstable ifm w=D|q7<0.,"9) is If $\omega_{A}$ is small compared to the other frequencies, we have The solutions $\gamma_{1,2}$ correspond to buoyant modes that cause convection and are unstable if $\omega_{c}^{2} + q^{2} <0$."1078 The solutions 75.4 deseribe the magnetorotational modes which can be unstable if the second condition (12) is satisfied.," The solutions $\gamma_{3,4}$ describe the magnetorotational modes which can be unstable if the second condition (12) is satisfied."1079 For the purpose of illustration. we plot in Fig.," For the purpose of illustration, we plot in Fig."1080 | the dependence of 2? on 4/9 for the unstable magnetorotational mode., 1 the dependence of $\gamma^2$ on $\omega_{A}/\Omega$ for the unstable magnetorotational mode.1081 Its growth rate is given by Eq.(12) with the upper sign., Its growth rate is given by Eq.(12) with the upper sign.1082 Even if stratification is negligible. the growth rate of this mode is typically low and 5.~wy ma weak magnetic field (κο- ©).," Even if stratification is negligible, the growth rate of this mode is typically low and $\gamma \sim 1083\omega_{A}$ in a weak magnetic field $\omega_{A} < \Omega$ )."1084 Stratification can substantially decrease the growth rate and this is seen very well from the figure., Stratification can substantially decrease the growth rate and this is seen very well from the figure.1085 For example. the growth rate decreases approximately by a factor of two if 22/Q?.," For example, the growth rate decreases approximately by a factor of two if $\omega_{c}^2/\Omega^2$."1086 At w2/07x1. stable stratification completely suppresses the magnetorotational instability of the considered perturbations.," At $\omega_{c}^2/ \Omega^2 \approx 1$, stable stratification completely suppresses the magnetorotational instability of the considered perturbations."1087" In the convective zone where w2|q?«0. the quantity uw?pq?o41O?(12/12) is also negative and. hence. 23,«0."," In the convective zone where $\omega_c^2 + q^2 < 0$, the quantity $\omega_c^2 + q^2 - 4 \Omega^2 (k_z^2/k^2)$ is also negative and, hence, $\gamma^2_{3,4}< 0$."1088 Therefore. the magnetorotational instability does not occur in convectively unstable regions. and these two instabilities are spatially separated if the magnetic field is weak (see also Obergaullinger et al.," Therefore, the magnetorotational instability does not occur in convectively unstable regions, and these two instabilities are spatially separated if the magnetic field is weak (see also Obergaullinger et al."1089 2009)., 2009).1090 The value of z.. is of the order of 1-10 + in collapsing cores (see Thompson et al., The value of $\omega_{c}$ is of the order of 1-10 $^{-1}$ in collapsing cores (see Thompson et al.1091 2005)., 2005).1092" Therefore. rotation has an important impact on convection only if © is of the same order of magnitude, Q~1000. rad/s (Miralles et al."," Therefore, rotation has an important impact on convection only if $\Omega$ is of the same order of magnitude, $\Omega \approx 1000$ rad/s (Miralles et al."1093 2004)., 2004).1094 This value can be reached in PNS if rotation of the progenitor was very fast (Villain et al., This value can be reached in PNS if rotation of the progenitor was very fast (Villain et al.1095 2004)., 2004).1096 On the contrary. MRI can have an important influence even if rotation is slower.," On the contrary, MRI can have an important influence even if rotation is slower."1097 The condition of MRI (second inequality (10) depends on the direction of & and can be written as follows whereNI In these expressions. we denote Is the angle between the magnetic field and the rotational axis. cosa =Befy'B?B?.," The condition of MRI (second inequality (10)) depends on the direction of $\vec{k}$ and can be written as follows where In these expressions, we denote $\alpha$ is the angle between the magnetic field and the rotational axis, $\cos \alpha = B_z / \sqrt{B_z^2 + B_s^2}$."1098| Since the dependence of F' on the direction of & 1s simple. we can obtain that £ reaches its minimum at The value of F corresponding to these 42/4? yields the following condition of instability By taking the curl of Eq. (," Since the dependence of $F$ on the direction of $\vec{k}$ is simple, we can obtain that $F$ reaches its minimum at The value of $F$ corresponding to these $k_{z}^{2}/k^{2}$ yields the following condition of instability By taking the curl of Eq. ("10991). it can be readily obtained that the conditior of hydrostatic equilibrium leads to where We consider only the magnetic field. satisfying. the condition £sQ? that is approximately equivalent to the requirement that the magnetic energy is small compared to the rotational energy.,"1), it can be readily obtained that the condition of hydrostatic equilibrium leads to where We consider only the magnetic field satisfying the condition $L \ll s 1100\Omega_s^2$ that is approximately equivalent to the requirement that the magnetic energy is small compared to the rotational energy."1101 Then. Eq. (," Then, Eq. ("110217) can be further simplified to obtain The two conditions of instability follow straightforwardly from the above expression: Conditions (20) and (21) look like the Solberg-Heiland conditions (Tassoul 2000). but with additional terms due to the,"17) can be further simplified to obtain The two conditions of instability follow straightforwardly from the above expression: Conditions (20) and (21) look like the iland conditions (Tassoul 2000), but with additional terms due to the"1103Figure The sequence of extracted. conlinmume-sublracted CN images during the night of the Deep hupact event.,"Figure The sequence of extracted, continuum-subtracted CN images during the night of the Deep Impact event."1104 The top two left frames were taken prior to impact under (wilieht conditions. so (he continuum image appears verv dark.," The top two left frames were taken prior to impact under twilight conditions, so the continuum image appears very dark."1105 In (hose (wo images. the comet nucleus was located in the upper left corner of the field of view.," In those two images, the comet nucleus was located in the upper left corner of the field of view."1106 The third image was exposed during the impact time., The third image was exposed during the impact time.1107 The weak peak found in this image is considered spurious., The weak peak found in this image is considered spurious.1108 The gaps between groups of images indicate time when no comet data were taken because of other observing tasks such as sky. fields and stanclard stars., The gaps between groups of images indicate time when no comet data were taken because of other observing tasks such as sky fields and standard stars.1109 CN emission centered on the comet nucleus begins to be visible about one half hour after impact. in the first. Lame of the second set of data.," CN emission centered on the comet nucleus begins to be visible about one half hour after impact, in the first frame of the second set of data."1110 The CN emission (hen rapidly increases in intensity. ancl expands spatially., The CN emission then rapidly increases in intensity and expands spatially.1111 About two hours after impact. the added CN emission fills the whole field of view and the average [lux levels are clearly higher (han before the impact.," About two hours after impact, the added CN emission fills the whole field of view and the average flux levels are clearly higher than before the impact."1112 This is quantitatively displaved in the lighteurves in Fie., This is quantitatively displayed in the lightcurves in Fig.1113 6., 6.1114linear relation plotted in Fig.,linear relation plotted in Fig.1115" 1 with the solid line), and has a scaling slope of zz1.5."," \ref{fig1} with the solid line), and has a scaling slope of $\approx 1.5$."1116" To understand the origin of the nonlinearity of the scaling, we need to examine how the gas is distributed over different local densities."," To understand the origin of the nonlinearity of the scaling, we need to examine how the gas is distributed over different local densities."1117" This distribution is quantified by the PDF, which is defined as the distribution of volume fraction with respect to local density (where the local density is measured in units of the mean density of the cube)."," This distribution is quantified by the PDF, which is defined as the distribution of volume fraction with respect to local density (where the local density is measured in units of the mean density of the cube)."1118" In order to have a nonlinear scaling between the surface densities of total gas and gas density peaks, the PDFs of different patches within the cube be different from each other."," In order to have a nonlinear scaling between the surface densities of total gas and gas density peaks, the PDFs of different patches within the cube be different from each other."1119 This requirement is straight forward to prove., This requirement is straight forward to prove.1120 Let the local PDF within a patch 4 of volume V; be gi(p) (1/Vi)dV/dp., Let the local PDF within a patch $i$ of volume $V_i$ be $g_i(\rho) = (1/V_i)dV/d\rho$ .1121" Then, the total dense gas mass in patch i is an integral of the PDF above some high density threshold Pden; and the total gas mass of the same patch is an integral of the PDF over all densities, while the ratio of surface densities is given by where A; is the surface area of the patch perpendicular to the line of sight."," Then, the total dense gas mass in patch $i$ is an integral of the PDF above some high density threshold $\rho_{\rm1122den}$, and the total gas mass of the same patch is an integral of the PDF over all densities, while the ratio of surface densities is given by where $A_i$ is the surface area of the patch perpendicular to the line of sight."1123" If now the PDF remains the same among different patches (all g; are identical), the right-hand side of Eq. (7))"," If now the PDF remains the same among different patches (all $g_i$ are identical), the right-hand side of Eq. \ref{seven}) )"1124" is always constant, resulting in an identically linear scaling, Xaen,gaseXgas."," is always constant, resulting in an identically linear scaling, $\Sigma_{\rm1125 den,gas} \propto \Sigma_{\rm gas}$."1126" A similar result is obtained, as long as the PDF spread is sufficiently large, if the g; have the same spread but different mean densities."," A similar result is obtained, as long as the PDF spread is sufficiently large, if the $g_i$ have the same spread but different mean densities."1127 A nonlinear scaling canonly arise if different patches exhibit different PDF spreads., A nonlinear scaling can arise if different patches exhibit different PDF spreads.1128" This feature is an inherent property of multifractals, as we show below."," This feature is an inherent property of multifractals, as we show below."1129" Figure 2 shows local PDF's for four different patches of varying mean density for multifractal A. In our multifractal geometry, the local PDFs are not identical in spread to each other, and they are not identical to the global PDF of the cube (plotted with the thin solid black line in the upper panel of Fig. 3))."," Figure \ref{fig2} shows local PDFs for four different patches of varying mean density for multifractal A. In our multifractal geometry, the local PDFs are not identical in spread to each other, and they are not identical to the global PDF of the cube (plotted with the thin solid black line in the upper panel of Fig. \ref{fig4}) )."1130" Instead, they are truncated at different densities depending on their total gas surface density."," Instead, they are truncated at different densities depending on their total gas surface density."1131" The total gas surface density is lowest for the patch represented by the solid black line, and progressively increases for the patches depicted in dashed red, long-dashed green, and dotted blue respectively."," The total gas surface density is lowest for the patch represented by the solid black line, and progressively increases for the patches depicted in dashed red, long-dashed green, and dotted blue respectively."1132" The lower the total surface density of the patch, the lower the density at which the PDF is truncated."," The lower the total surface density of the patch, the lower the density at which the PDF is truncated."1133" It is this effect which is the origin of the nonlinearity in the scaling of Naen,gas with Ugas."," It is this effect which is the origin of the nonlinearity in the scaling of $\Sigma_{\rm den,gas}$ with $\Sigma_{\rm gas}$."1134" A similar dependence of the local PDF on the mean density was pointed out by Kravtsov (2003) in the case of cosmological simulations, where the star formation law was reproduced in large scales, despite the fact that the local star formation recipe featured a timescaleconstant with density."," A similar dependence of the local PDF on the mean density was pointed out by Kravtsov (2003) in the case of cosmological simulations, where the star formation law was reproduced in large scales, despite the fact that the local star formation recipe featured a timescale with density."1135" We have demonstrated that a nonlinear scaling between very dense and total gas surface densities arises naturally in multifractal geometries, and we have traced its origin in the property of the local multifractal PDF to extend to higher local densities in regions of higher mean density."," We have demonstrated that a nonlinear scaling between very dense and total gas surface densities arises naturally in multifractal geometries, and we have traced its origin in the property of the local multifractal PDF to extend to higher local densities in regions of higher mean density."1136" However, there are still several points to be addressed before we can draw conclusions on how robust this scaling really is, and how it may relate to the star formation law."," However, there are still several points to be addressed before we can draw conclusions on how robust this scaling really is, and how it may relate to the star formation law."1137 These points are the following., These points are the following.1138"The brightest of the “unidentified” high-Calactic-latitude EGRET sources (Wartinanetal.L999). aat (£6,ο|257) has longbeen associated with the N-rav ondtting nentron-star5925.. which τομάτας its imnost plausible counterpart even though pulsations have uot been detected at any waveleneth.","The brightest of the “unidentified” high-Galactic-latitude EGRET sources \citep{har99}, at $(\ell, b)=(89^{\circ},+25^{\circ})$ has long been associated with the X-ray emitting neutron-star, which remains its most plausible counterpart even though pulsations have not been detected at any wavelength."1139 Unlike blazars. which are highly variable aud have steeper y-ray spectra. sshows no evidence for loug-terii variabilitv. and its spectrum cau be fitted by a relatively flat power kaw of photon iudex EL.7 from 70 MeV to 1 GeV. with a turn-downu above | GeV (πια:etal.2001)... sinular to known οταν pulsus.," Unlike blazars, which are highly variable and have steeper $\gamma$ -ray spectra, shows no evidence for long-term variability, and its spectrum can be fitted by a relatively flat power law of photon index $\Gamma = 1.7$ from 70 MeV to 4 GeV, with a turn-down above 4 GeV \citep{rei01}, similar to known $\gamma$ -ray pulsars."1140 lis the optically undetected N-vav source in the +-rav error onlybox. all the others being classified as uulikelv -rav chutters (Mirabaletal. 2000).," is the only optically undetected X-ray source in the $\gamma$ -ray error box, all the others being classified as unlikely $\gamma$ -ray emitters \citep{mir00}."1141. The detection of aas a weak. ultrasoft source in the AAILSky Survey (Mirabal&Talperu2001). suggested that it isa thermally cutting neutron star that is either older or more distant than the οταν pulsar Cóonmiuega (IIalperu&Ruderman1993:BignamiCaraveo 1996)..," The detection of as a weak, ultrasoft source in the All-Sky Survey \citep{mir01}1142 suggested that it is a thermally emitting neutron star that is either older or more distant than the $\gamma$ -ray pulsar Geminga \citep{hal93,big96}. ."1143 Observations using the AAdvanced CCD Buagiug Camera (ACTS) and the (LIST) further supported this interpretation (Talpern 2002)., Observations using the Advanced CCD Imaging Camera (ACIS) and the ) further supported this interpretation \citep{hal02}.1144. Two componcuts were required to fit the NA-ray spectu. a blackbody of T—235« I and a power law of photon iudex E2.240.6. cvideuee," Two components were required to fit the X-ray spectrum, a blackbody of $T \sim 3.5 \times 10^5$ K and a power law of photon index $\Gamma = 2.2 \pm 0.6$."1145iThe nou-thermal N-rav component is miportaut of magnetospheric activity that is fouud im all οταν pulsars. but not in all cooling neutron stars.," The non-thermal X-ray component is important evidence of magnetospheric activity that is found in all $\gamma$ -ray pulsars, but not in all cooling neutron stars."1146 An optical upper Πιτ of V»28.5 from the verified the star interpretation of ffrom its extreme N-ray-to-optical dux ratio. fy/f> G000..," An optical upper limit of $V > 28.5$ from the verified the neutron-star interpretation of from its extreme X-ray-to-optical flux ratio, $f_X/f_V > 6000$ ."1147 We also used the thermal ταν spectra aud optical limit to bound the distance to in the range 250«dεςs00 pew The cuerectics of aare plausible for a pulsar at d«S00 pc since its yoray huninosity (assumed isotropic) is 3.8«&10?!(d/s00pe)? eres s.L1. comparable to the spin-down power £—.—[QQ of Gemiuga (3.3<10°! cress 1).," We also used the thermal X-ray spectrum and optical limit to bound the distance to in the range $250 < d < 800$ pc.y The energetics of are plausible for a pulsar at $d < 800$ pc since its $\gamma$ -ray luminosity (assumed isotropic) is $3.8 \times 10^{34}\,(d/800\,{\rm pc})^2$ ergs $^{-1}$, comparable to the spin-down power $\dot E = -I\Omega \dot\Omega$ of Geminga $3.3 \times 10^{34}$ ergs $^{-1}$ )."1148 Efficiencies approaching are achieved by those y-ray pulsus Lavine the sinallest spiu-down power., Efficiencies approaching are achieved by those $\gamma$ -ray pulsars having the smallest spin-down power.1149 Halpernetal.(2002) also searched for radio pulsatious frou musing the Jodrell| Bank Lovell telescope at a frequency of 1. GIIz. achieving au uut of Sy.)«0.1 ταν.," \citet{hal02} also searched for radio pulsations from using the Jodrell Bank Lovell telescope at a frequency of 1.4 GHz, achieving an upper limit of $S_{1.4} < 0.1$ mJy."1150 Adopting1 an upper limit mperofαἱe<800 pe. the pulsed pseudo-Iuninositv lint of iis Ly.)=Syd?<04061 ΜΕΣ ," Adopting an upper limit of $d < 800$ pc, the pulsed pseudo-luminosity limit of is $L_{1.4} \equiv S_{1.4} d^2 < 0.064$ mJy $^2$."1151There are ouly four pulsars kuown with Ly.)0.1 wJy kpe? 2002) in addition to Ceminga (MceLbaughlliuetal.andreferences therein).., There are only four pulsars known with $L_{1.4} < 0.1$ mJy $^2$ \citep{cam02} in addition to Geminga \citep[][and references therein]{mcl99}.1152 Iu this paper. we report an even more sensitive search for radio pulsatious frou uusing the NRAO Creen Bank Telescope(GBT). as well as the first N-rav pulsation search with the Wieh Resolution Camera (IIRC-S).These Investigations approach the senusitivitv limuts of CNisting iustrunientatiou to searchfor the pulsar— in 5918..," In this paper, we report an even more sensitive search for radio pulsations from using the NRAO Green Bank Telescope (GBT), as well as the first X-ray pulsation search with the High Resolution Camera (HRC-S).These investigations approach the sensitivity limits of existing instrumentation to searchfor the pulsar in ."1153The Galactic microquasar SS 433 is famous for its continual ejection of plasma in two opposite jets at approximately one quarter the speed of light.,The Galactic microquasar SS 433 is famous for its continual ejection of plasma in two opposite jets at approximately one quarter the speed of light.1154 Precession of the jet axis gives rise to the famous moving spectral lines but the so-called stationary lines are more intense., Precession of the jet axis gives rise to the famous moving spectral lines but the so-called stationary lines are more intense.1155 The system is a binary with a period of 13.08 days (Crampton. Cowley and Hutchings 1980) and eclipses at both oppositions (e.g. Goranskii et al 1998).," The system is a binary with a period of 13.08 days (Crampton, Cowley and Hutchings 1980) and eclipses at both oppositions (e.g. Goranskii et al 1998)."1156 He II 4686 emission has been observed (Crampton and Hutchings 1981. Fabrika and Bychkova 1990). attributed to the base of the jets (Fabrika 1997).," He II 4686 emission has been observed (Crampton and Hutchings 1981, Fabrika and Bychkova 1990), attributed to the base of the jets (Fabrika 1997)."1157 C II lines orbiting with the compact object have been detected (Gies et al 2002. K. M. Blundell private communication).," C II lines orbiting with the compact object have been detected (Gies et al 2002, K. M. Blundell private communication)."1158 The orbital speed of the compact object about the binary centre of mass is now well established as 176 km s! and the mass function as 7.7 M., The orbital speed of the compact object about the binary centre of mass is now well established as 176 km $^{-1}$ and the mass function as 7.7 $M_\odot$.1159 There is no consistency among the many reports of Doppler speeds for the companion., There is no consistency among the many reports of Doppler speeds for the companion.1160 Relatively recent observations of absorption lines. attributed to the atmosphere of the companion. have vielded an orbital velocity for the companion about the binary centre of mass of 132 km s! (Cherepashchuk et al 2005). which implies a system mass of 42 M&. and 58 km s! (Hillwig Gies 2008. Kubota et al 2010). the latter value implying a system mass of 17 M...," Relatively recent observations of absorption lines, attributed to the atmosphere of the companion, have yielded an orbital velocity for the companion about the binary centre of mass of 132 km $^{-1}$ (Cherepashchuk et al 2005), which implies a system mass of 42 $M_\odot$ , and 58 km $^{-1}$ (Hillwig Gies 2008, Kubota et al 2010), the latter value implying a system mass of 17 $M_\odot$."1161 Observations in Πα interpreted 1n terms of a circumbinary disk imply à system mass of approximately 40 M.« or greater (Blundell. Bowler Schmidtobreick 2008).," Observations in $\alpha$ interpreted in terms of a circumbinary disk imply a system mass of approximately 40 $M_\odot$ or greater (Blundell, Bowler Schmidtobreick 2008)."1162 A rotating ring of glowing gas. viewed almost edge on. will produce a spectrum dominated by radiation from regions to which the line of sight is tangential.," A rotating ring of glowing gas, viewed almost edge on, will produce a spectrum dominated by radiation from regions to which the line of sight is tangential."1163 A suitable spectral line thus appears split: two horns Doppler shifted by the rotational speed of the ring., A suitable spectral line thus appears split; two horns Doppler shifted by the rotational speed of the ring.1164 Just such a split appears in various stationary features of the spectrum of the nicroquasar SS 433: Filippenko et al (1988) reported the H Paschen series to be split by approximately 290 km s! and in the blue various unblended Fe II lines split by 250-300 k ns-!., Just such a split appears in various stationary features of the spectrum of the microquasar SS 433; Filippenko et al (1988) reported the H Paschen series to be split by approximately 290 km $^{-1}$ and in the blue various unblended Fe II lines split by 250-300 km $^{-1}$.1165 Balmer Hf was split by approximately 480 km s!., Balmer $\beta$ was split by approximately 480 km $^{-1}$.1166 ΤΙhese observations covered only a few consecutive days but were interpreted as evidence for a disk structure., These observations covered only a few consecutive days but were interpreted as evidence for a disk structure.1167 The authors evicently thought radiation from the accretion disk most likely. but also considered the possibility of radiation from a circumbinary disk. fed from the L2 point in the SS 433 system.," The authors evidently thought radiation from the accretion disk most likely, but also considered the possibility of radiation from a circumbinary disk, fed from the L2 point in the SS 433 system."1168 This was taken up by Fabrika (1993) in a prescient paper., This was taken up by Fabrika (1993) in a prescient paper.1169 The same two horned structure was observed in Πα. He I. OLS446A aand the Paschen sequence through a campaign of nightly observations of SS 433 with the 3.6-m telescope on La Silla. Chile (Schmidtobreick Blundell 2006a.b).," The same two horned structure was observed in $\alpha$, He I, O I 8446 and the Paschen sequence through a campaign of nightly observations of SS 433 with the 3.6-m telescope on La Silla, Chile (Schmidtobreick Blundell 2006a,b)."1170 The relevant observations covered more than two orbits during a period when SS 433 was quiescent., The relevant observations covered more than two orbits during a period when SS 433 was quiescent.1171 The two horned signature can be followed night by night in the spectra displayed in Fig.2 of Schmidtobreick Blundell (2006b). in both Ha and He I. The least noisy signal is to be found in the brilliant Πα line and in Blundell. Bowler Schmidtobreick (2008) this stationary He line was fitted as a superposition of Gaussian profiles.," The two horned signature can be followed night by night in the spectra displayed in Fig.2 of Schmidtobreick Blundell (2006b), in both $\alpha$ and He I. The least noisy signal is to be found in the brilliant $\alpha$ line and in Blundell, Bowler Schmidtobreick (2008) this stationary $\alpha$ line was fitted as a superposition of Gaussian profiles."1172 It consists of a broac component shown to be associated with the wind from the accretion disk and two narrow components separated by about 400 km s7!., It consists of a broad component shown to be associated with the wind from the accretion disk and two narrow components separated by about 400 km $^{-1}$.1173 These narrow lines run almost railroad straight anc do not shift much in position or separation over 30 days (see Fig.1 of Blundell. Bowler Schmidtobreick 2008 and Fig.l of the present paper).," These narrow lines run almost railroad straight and do not shift much in position or separation over 30 days (see Fig.1 of Blundell, Bowler Schmidtobreick 2008 and Fig.1 of the present paper)."1174 The orbital plane of the binary system is almost edge on and this sequence of pairs of narrow lines is the classic signature of the inner rim of a eircumbinary disk. radiating strongly all the time from the regions to which the line of sight is tangent.," The orbital plane of the binary system is almost edge on and this sequence of pairs of narrow lines is the classic signature of the inner rim of a circumbinary disk, radiating strongly all the time from the regions to which the line of sight is tangent."1175 Nonetheless. the intensities vary in antiphase with a period of 13 days. the orbital period of the binary.," Nonetheless, the intensities vary in antiphase with a period of 13 days, the orbital period of the binary."1176 The interpretation was that the glowing inner rim fades and ts refreshed as the binary rotates. possibly through ejection of material through the L2 point or perhaps by ultra violet and X rays from the accretion disk.," The interpretation was that the glowing inner rim fades and is refreshed as the binary rotates, possibly through ejection of material through the L2 point or perhaps by ultra violet and X rays from the accretion disk."1177 The observations of SS 433 over an extended period (Blundell. Bowler & Schmidtobreick 2007.2008) did not reach into the blue. but published data contain in addition to the brilliant Balmer Ha line the stronger He I lines at 6678 and 7065. Which are also split. have narrow components which fluctuate with opposite phase but fade much faster than He.," The observations of SS 433 over an extended period (Blundell, Bowler $\&$ Schmidtobreick 2007,2008) did not reach into the blue, but published data contain in addition to the brilliant Balmer $\alpha$ line the stronger He I lines at 6678 and 7065, which are also split, have narrow components which fluctuate with opposite phase but fade much faster than $\alpha$."1178 Both position and separation contain marked 13 day periodicities. so that it is not immediately obvious that they share the same origin as the simple Ha structure.," Both position and separation contain marked 13 day periodicities, so that it is not immediately obvious that they share the same origin as the simple $\alpha$ structure."1179 In this paper I present those relevant data and discuss their interpretation in terms of a simple model for the stimulatedinner cireumbinary disk., In this paper I present those relevant data and discuss their interpretation in terms of a simple model for the stimulatedinner circumbinary disk.1180 In this model the data are explained by the ring of fire orbiting, In this model the data are explained by the ring of fire orbiting1181 A third region is located beyond ~3 AU., A third region is located beyond $ \sim 3$ AU.1182 Although the secular dynamics also appear similar for all values of s. the simulations show large-amplitude oscillations.," Although the secular dynamics also appear similar for all values of $s$, the simulations show large-amplitude oscillations."1183 These are not only caused by short-period terms but also from several high-order mean-motion resonances between the particles and mp., These are not only caused by short-period terms but also from several high-order mean-motion resonances between the particles and $m_B$.1184 In the plots these commensurabilities can be seen as spikes where the eccentricity is temporarily excited., In the plots these commensurabilities can be seen as spikes where the eccentricity is temporarily excited.1185 Without a detailed analysis. it is not possible to establish whether these commensurabilities will inhibit or favor aceretion.," Without a detailed analysis, it is not possible to establish whether these commensurabilities will inhibit or favor accretion."1186 Although most of our simulations have shown scattering effects and significant orbital misalignment between resonant and non-resonant orbits. we have also found cases of resonant trapping.," Although most of our simulations have shown scattering effects and significant orbital misalignment between resonant and non-resonant orbits, we have also found cases of resonant trapping."1187 This appears to be a high-probability outcome for s>5 km., This appears to be a high-probability outcome for $s \gtrsim 5$ km.1188 An example is shown in Figure 8 for a 10 km body placed in an initial circular orbit with «@=4+ AU., An example is shown in Figure \ref{fig8} for a $10$ km body placed in an initial circular orbit with $a=4$ AU.1189 After an initial decay in the semimajor axis. the body is captured in a 10/1 mean-motion resonance with the binary component.," After an initial decay in the semimajor axis, the body is captured in a $10/1$ mean-motion resonance with the binary component."1190" Both the resonant angle = 104, and the differenceius, in longitudes of pericenter librate around zero. although there seems to be a slow departure towards asymmetric librations at the end of the simulation."," Both the resonant angle = 10 _B - - 9 _B and the difference in longitudes of pericenter librate around zero, although there seems to be a slow departure towards asymmetric librations at the end of the simulation."1191 The resonant solution seems very stable. at least for timescales between 10° and 107 years.," The resonant solution seems very stable, at least for timescales between $10^6$ and $10^7$ years."1192 We have found similar outcomes in other commensurabilities. such as the 11/1 and 12/1. always for slow dissipative effects (1.9. large bodies).," We have found similar outcomes in other commensurabilities, such as the $11/1$ and $12/1$, always for slow dissipative effects (i.e. large bodies)."1193 What is curious about this result is that trapping occurs during adivergent migration: in other words. the non-conservative force increases the separation of the bodies involved.," What is curious about this result is that trapping occurs during a migration; in other words, the non-conservative force increases the separation of the bodies involved."1194 Classical works (e.g. Neishtadt 1975. Henrard 1982. Beaugé and Ferraz-Mello 1993. Nelson and Papaloizou 2002) predict that capture is only possible in cases ofconvergent migration and. thus. the behavior shown in Figure 8. should not occur.," Classical works (e.g. Neishtadt 1975, Henrard 1982, Beaugé and Ferraz-Mello 1993, Nelson and Papaloizou 2002) predict that capture is only possible in cases of migration and, thus, the behavior shown in Figure \ref{fig8} should not occur."1195 The only reference we have been able to find describing similar findings is an abstract of a presentation in the 2007 DDA meeting (Hamilton and Zhang 2007)., The only reference we have been able to find describing similar findings is an abstract of a presentation in the 2007 DDA meeting (Hamilton and Zhang 2007).1196 Although no details are available. it appears that divergent trapping is possible in high-order mean-motion resonances and with high-eccentricity perturbers.," Although no details are available, it appears that divergent trapping is possible in high-order mean-motion resonances and with high-eccentricity perturbers."1197 This may explain why the librating resonant angle includes the longitude of pericenter of the perturber instead of the planetesimal., This may explain why the librating resonant angle includes the longitude of pericenter of the perturber instead of the planetesimal.1198 However. a deeper analysis is necessary before we are able to understand this phenomena and establish its possible importance in planetary formation.," However, a deeper analysis is necessary before we are able to understand this phenomena and establish its possible importance in planetary formation."1199 The results. shown in Figure 7. for both binary configurations show almost identical results., The results shown in Figure \ref{fig7} for both binary configurations show almost identical results.1200 Although the forced eccentricity is slightly higher for 54=1.15M. for most of the semimajor axis domain. the same three regions exist in both cases. and it is plausible to assume that the collisional evolution of a planetesimal swarm should be similar.," Although the forced eccentricity is slightly higher for $m_A=1.18 M_{\odot}$ for most of the semimajor axis domain, the same three regions exist in both cases, and it is plausible to assume that the collisional evolution of a planetesimal swarm should be similar."

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