ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 It becomes distinctly visible around fj=2(1+za. with the ratio between flux from counter and forward Jet peaking at 6 at 1 GHz at 3800 days for the simulation settings (at z2 1).," It becomes distinctly visible around $t_{cj} = 2 ( 1+z) t_{NR}$, with the ratio between flux from counter and forward jet peaking at 6 at 1 GHz at 3800 days for the simulation settings (at $z = 1$ )."3 We first present the main results for both small and large observer angles. looking both at the light curves and the corresponding temporal slopes.," We first present the main results for both small and large observer angles, looking both at the light curves and the corresponding temporal slopes."4 An overview of light curves is shown in Fig. l..," An overview of light curves is shown in Fig. \ref{collective_figure},"5 where we have plotted multi-frequency light curves spanning from 10° to 10! Hz., where we have plotted multi-frequency light curves spanning from $10^9$ to $10^{17}$ Hz.6 The temporal slopes for the lowest frequency 10? Hz and the highest frequency 1017 Hz are separately plotted in Figs., The temporal slopes for the lowest frequency $10^9$ Hz and the highest frequency $10^{17}$ Hz are separately plotted in Figs.7 2 and 3.., \ref{slopes_low_figure} and \ref{slopes_high_figure}.8 For the on-axis results we estimate the jet break. a combination of lateral spreading and jet edges becoming visible. to occur around 3.5 days (the 7 days mentioned in ZMO09 is for z= I).," For the on-axis results we estimate the jet break, a combination of lateral spreading and jet edges becoming visible, to occur around 3.5 days (the 7 days mentioned in ZM09 is for $z =91$ )."10 Direct comparisons at the same frequency of different observer angles are shown in figures 6 and I1.. for 8.46 GHz.," Direct comparisons at the same frequency of different observer angles are shown in figures \ref{model2_figure} and \ref{supernovae_figure}, for 8.46 GHz."11 Ás the observer angle increases. the jet break splits into two for observers still inside the jet.," As the observer angle increases, the jet break splits into two for observers still inside the jet."12 Once the observer is positioned at the jet edge only one break remains that is significantly postponed., Once the observer is positioned at the jet edge only one break remains that is significantly postponed.13 This effect is similar across all frequencies., This effect is similar across all frequencies.14" The steepest drop in slope is the one associated with the edge of the jet furthest from the observer and can therefore be estimated to occur around where Ej: 1s the isotropic equivalent energy in units of 1077erg. 2, is density of the medium in units of em"". J is the jet half opening angle. and 0,5, is the observer angle relative to the Jet axis."," The steepest drop in slope is the one associated with the edge of the jet furthest from the observer and can therefore be estimated to occur around where $E_{iso,53}$ is the isotropic equivalent energy in units of $10^{53}\,\erg$, $n_1$ is density of the medium in units of $\cm^{-3}$, $\theta_0$ is the jet half opening angle, and $\theta_{obs}$ is the observer angle relative to the jet axis."15 Jet breaks can be used to estimate the opening angles of GRB jets., Jet breaks can be used to estimate the opening angles of GRB jets.16 It is usually assumed in GRB afterglow modeling that the observer is on the jet axis., It is usually assumed in GRB afterglow modeling that the observer is on the jet axis.17 However. if the observer is near the edge of the Jet. the jet opening can be overestimated by a factor of up to 2. and the beaming-corrected total energy can be overestimated by a factor of up to 4.," However, if the observer is near the edge of the jet, the jet opening can be overestimated by a factor of up to 2, and the beaming-corrected total energy can be overestimated by a factor of up to 4."18" For a typical observer at 0,5,στ205/3. the beaming-corrected energy can be overestimated by a factor of ~3."," For a typical observer at $\theta_{obs} \approx 2\theta_0/3 $, the beaming-corrected energy can be overestimated by a factor of $\sim193$."20 The observational implications of this effeet will be further discussed in Section 6.., The observational implications of this effect will be further discussed in Section \ref{discussion_section}.21 At high observer angles. the rise of the light curve is postponed until the pomt where relativistic beaming has weakened sufficiently for the observer to be in the light cone of the radiating fluid.," At high observer angles, the rise of the light curve is postponed until the point where relativistic beaming has weakened sufficiently for the observer to be in the light cone of the radiating fluid."22 Due to limb-brightening the drop in temporal slope following a jet break initially overshoots its asymptotic value., Due to limb-brightening the drop in temporal slope following a jet break initially overshoots its asymptotic value.23 After that 1t starts to change again due to the onset of the transition into the nonrelativistic regime and the rise of flux from the counterjet. before it finally settles into its asymptotic value for the nonrelativistic regime.," After that it starts to change again due to the onset of the transition into the nonrelativistic regime and the rise of flux from the counterjet, before it finally settles into its asymptotic value for the nonrelativistic regime."24 In order to put the simulation results in context and to differentiate between the break due to lateral spreading and the break due to the edges becoming visible we will compare the simulation results against the BM solution for a hard edged jet without lateral spreading in the next subsection., In order to put the simulation results in context and to differentiate between the break due to lateral spreading and the break due to the edges becoming visible we will compare the simulation results against the BM solution for a hard edged jet without lateral spreading in the next subsection.25 In Fig., In Fig.26 4 we show a comparison between on-axis spectra at | day in observer time. calculated from the simulation and from an analytical description using the BM solution plus synchrotron emission (2)..," \ref{exactspectrum_figure} we show a comparison between on-axis spectra at 1 day in observer time, calculated from the simulation and from an analytical description using the BM solution plus synchrotron emission \citep{vanEerten2009}."27 The observed time is well before the jet break and before significant lateral spreading or slowing down of the Jet hàs occurred., The observed time is well before the jet break and before significant lateral spreading or slowing down of the jet has occurred.28 With the dynamies for both the simulation and the BM solution. still being nearly equal. the figure therefore mainly shows the difference between the two approaches to synchrotron radiation.," With the dynamics for both the simulation and the BM solution still being nearly equal, the figure therefore mainly shows the difference between the two approaches to synchrotron radiation."29 The differences below the cooling break »4. are marginal and car be attributed to the absolute scaling of the emitted power., The differences below the cooling break $\nu_c$ are marginal and can be attributed to the absolute scaling of the emitted power.30 The difference beyond 5 is significantly larger., The difference beyond $\nu_c$ is significantly larger.31 The reasor for this is that the simulation follows the approach to electror cooling from ?.. where the cooling time is globally estimated by setting it equal to the duration of the explosion. whereas build upon ? and calculate the local cooling time for each fluid element. which is given by the time passed since the fluid," The reason for this is that the simulation follows the approach to electron cooling from \citet{Sari1998}, , where the cooling time is globally estimated by setting it equal to the duration of the explosion, whereas \citet{vanEerten2009} build upon \citet{Granot2002}32 and calculate the local cooling time for each fluid element, which is given by the time passed since the fluid"3313/15 sub-millimetre galaxies with reliable modelling results (i.e. excluding 8850.2 and 8850.6 which have ry.« 2kkpe) possess Seérrsic values peaked at nm1. and confined to the range Lo«n2.5.,"13/15 sub-millimetre galaxies with reliable modelling results (i.e. excluding 850.2 and 850.6 which have $r_{1/2} < 2$ kpc) possess Sérrsic values peaked at $n=1$, and confined to the range $1<n<2.5$."34 The Sérrsie indices of the 11/13 reliably-modelled radio galaxies (.e. excluding 11204057 and 1602-174: see below) are in the range 2.5«n5.55 and peaked around n=4. corresponding to a de Vaucouleurs luminosity profile.," The Sérrsic indices of the 11/13 reliably-modelled radio galaxies (i.e. excluding 1120+057 and 1602-174; see below) are in the range $2.5<n<5.75$ and peaked around $n=4$, corresponding to a de Vaucouleurs luminosity profile."35 The distribution of half-light radii is shown in Fig. 2.., The distribution of half-light radii is shown in Fig. \ref{histhalf}. .36 Sub-millimetre galaxy seale-lengths are clearly peaked around rye.~ 8kkpe. while the radio galaxies are spread over a larger range. and are systematically larger (with an average rye.= Skkpce).," Sub-millimetre galaxy scale-lengths are clearly peaked around $r_{1/2}\sim3$ kpc, while the radio galaxies are spread over a larger range, and are systematically larger (with an average $r_{1/2}=8$ kpc)."37 These results are discussed further in Section 7., These results are discussed further in Section 7.38 As explained in Section 2. all the +—2 radio galaxy. targets were initially identified with known radio positions in the literature (Laing. Riley Longair 1983. Best et al.," As explained in Section 2, all the $z \simeq 2$ radio galaxy targets were initially identified with known radio positions in the literature (Laing, Riley Longair 1983, Best et al."39 1999)., 1999).40 In the light of our deep A-band imaging. we have revised one of these radio-galaxy identifications.," In the light of our deep $K$ -band imaging, we have revised one of these radio-galaxy identifications."41 This is the case of 14. where Best et al. (," This is the case of $-$ 14, where Best et al. ("421999) selected a discy object to the east of the radio position as seen in their /?-band imaging.,1999) selected a discy object to the east of the radio position as seen in their $R$ -band imaging.43 Our deep A -band data reveals a multi-component merging system closer to the radio centroid., Our deep $K$ -band data reveals a multi-component merging system closer to the radio centroid.44 The larger component of this merger (which also displayed a redder Rfy colour) was adopted as the true galaxy counterpart. and it is this object which is shown and modelled in Fig.," The larger component of this merger (which also displayed a redder $R-K$ colour) was adopted as the true galaxy counterpart, and it is this object which is shown and modelled in Fig."45 Al., A1.46 In the case of 1120] OS. the highest-redshift radio galaxy in the 3CR catalogue. we find a partially-obscured. point-like nucleus which is elearly shown in the two-dimensional modelling residual (see Fig. ΑΟ).," In the case of $+$ 05, the highest-redshift radio galaxy in the 3CR catalogue, we find a partially-obscured point-like nucleus which is clearly shown in the two-dimensional modelling residual (see Fig. \ref{ukirtmodel1}) )."47 A nuclear component is also clearly present in 17., A nuclear component is also clearly present in $-$ 17.48 In this case. the //-band image from Best et al. (," In this case, the $R$ -band image from Best et al. ("491999) shows a distinctly different morphology (with no sign of activity in the nucleus) to that revealed in our A -band data. which is dominated by a very compact source suggestive of obscured AGN emission.,"1999) shows a distinctly different morphology (with no sign of activity in the nucleus) to that revealed in our $K$ -band data, which is dominated by a very compact source suggestive of obscured AGN emission."50 As we do not believe our data are of sufficient quality to reliably separate a significant nuclear contribution from the host. and still derive robust galaxy scalelengths and Sérrsic indices. | 05 and 17 have been excluded from further discussion of the statistical distribution of galaxy morphological parameters for the radio-galaxy sample.," As we do not believe our data are of sufficient quality to reliably separate a significant nuclear contribution from the host, and still derive robust galaxy scalelengths and Sérrsic indices, $+$ 05 and $-$ 17 have been excluded from further discussion of the statistical distribution of galaxy morphological parameters for the radio-galaxy sample."51 Due in part to their early redshift determinations by Chapman et al. (, Due in part to their early redshift determinations by Chapman et al. (522003: 2005). two of the ELAIS ΝΟ 8-mJy sources. 8850.2 and 8850.4. have previously been imaged in some detail at sub-millimetre. optical and near-infrared wavelengths (Smail et al.,"2003; 2005), two of the ELAIS N2 8-mJy sources, 850.2 and 850.4, have previously been imaged in some detail at sub-millimetre, optical and near-infrared wavelengths (Smail et al."53 2003: Tacconiet al., 2003; Tacconiet al.54 2006: Tacconi et al., 2006; Tacconi et al.55 2008)., 2008).56 In particular. Taeconi et al. (," In particular, Tacconi et al. ("572008) report that. as viewed via high-resolution,"2008) report that, as viewed via high-resolution"58would expect to see an additional emission component with a similar ~40bansο velocity olfset on the blue side of the line.,would expect to see an additional emission component with a similar $\sim 40\kms$ velocity offset on the blue side of the line.59 Because we observed the [NelI] emission in only one order. ihe GM Aur spectrum has much higher noise on the blue side of the line (see 82). and it is impossible to determine whether a corresponding blueshifted component is present.," Because we observed the [NeII] emission in only one order, the GM Aur spectrum has much higher noise on the blue side of the line (see 2), and it is impossible to determine whether a corresponding blueshifted component is present."60 A more complete study of the [Nell] emission from GAL Aur is needed to distinguish between these possibilities., A more complete study of the [NeII] emission from GM Aur is needed to distinguish between these possibilities.61 The enussion feature centered near the stellar velocity has an equivalent width of 2A. and the feature ~40kms.1 recdward of the stellar velocity has an equivalent. width of 8z2A.," The emission feature centered near the stellar velocity has an equivalent width of $18\pm 2$ , and the feature $\sim 40 \kms$ redward of the stellar velocity has an equivalent width of $8\pm 2$."62. In comparison. the equivalent width of the spectrally unresolved. [Nell] feature detected in an 600Spitzer IRS spectrum of GM. Aur (Najita et al.," In comparison, the equivalent width of the spectrally unresolved [NeII] feature detected in an $R$ =600 IRS spectrum of GM Aur (Najita et al.,"63 in preparation) is approximatelyTOA.. almost three times the combined equivalent width of the two [Nell] enussion features detected at high spectral resolution.," in preparation) is approximately, almost three times the combined equivalent width of the two [NeII] emission features detected at high spectral resolution."64 As discussed above. variability in the Nell} line or the mic-infrared continuum. alternatively spatially extended. [Nel] emission. might account for the difference in the equivalent widths.," As discussed above, variability in the [NeII] line or the mid-infrared continuum, alternatively spatially extended [NeII] emission, might account for the difference in the equivalent widths."65 We are also insensitive lo very broad. [Nell] emission. particulary given the limited signal-to-noise ratio in the continuum.," We are also insensitive to very broad [NeII] emission, particulary given the limited signal-to-noise ratio in the continuum."66 A line above the marked continuum in Figure 2 and 300kms2+1 wide. which is within aSpilzer resolution element. would have an equivalent width of13À.. similar to the equivalent width reported for the [Nel] line.," A line above the marked continuum in Figure 2 and $300\kms$ wide, which is within a resolution element, would have an equivalent width of, similar to the equivalent width reported for the [NeII] line."67 Such a broad component would be difficult to detect with our data., Such a broad component would be difficult to detect with our data.68 Another possibility is spectrally unresolved. emission [from other lines., Another possibility is spectrally unresolved emission from other lines.69 In theSpilzer spectrum of GAL Aur. the emission feature detected at the wavelength of [Nell] is broader (han an unresolved line.," In the spectrum of GM Aur, the emission feature detected at the wavelength of [NeII] is broader than an unresolved line."70 Perhaps (he feature includes a contribution from lines other than (Nell)., Perhaps the feature includes a contribution from lines other than [NeII].71 Mid-infrared molecular features such as H30. HCN. or Collo would contribute very neeligiblv to our TEXES observations. because any such emission features. if present in theSpilzer spectrum of GAL Aur. are much weaker than in AA Tan.," Mid-infrared molecular features such as $_2$ O, HCN, or $_2$ $_2$ would contribute very negligibly to our TEXES observations, because any such emission features, if present in the spectrum of GM Aur, are much weaker than in AA Tau."72 We therefore interpret the emission features detected with TEXES as [Nell] for the purpose of this paper., We therefore interpret the emission features detected with TEXES as [NeII] for the purpose of this paper.73 Thus. as in the case of TW Iva (Llerezeg οἱ 22007). the [Nel] line profiles of AA Tau and GM Aur are consistent with emission centered near the stellar velocity.," Thus, as in the case of TW Hya (Herczeg et 2007), the [NeII] line profiles of AA Tau and GM Aur are consistent with emission centered near the stellar velocity."74 Ia comparison with the intrinsic (deconvolved) line width of 21kms| (FWIIM) obtained by Herczeg et ((2007) for TW Iva. the width of the [NeII] emission from AA Tau is significantly broader (~TOkms !).," In comparison with the intrinsic (deconvolved) line width of $21\kms$ (FWHM) obtained by Herczeg et (2007) for TW Hya, the width of the [NeII] emission from AA Tau is significantly broader $\sim 70 \kms$ )."75 While the [NeII] emission from GAL Aur has a velocity component centered on the stellar velocity that is more similar in width (oLI4kms !) to the [Nell] emission from TW Ilva. the [NelI] emission may also include a redshifted emission component that extends to =50kms! of the stellar velocity.," While the [NeII] emission from GM Aur has a velocity component centered on the stellar velocity that is more similar in width $\sim 14\kms$ ) to the [NeII] emission from TW Hya, the [NeII] emission may also include a redshifted emission component that extends to $\gtrsim 50\kms$ of the stellar velocity."76latter is al LOO kev. we expect the ejecta from the exploding star to be bathed in a radiation field with a peak at <25 kev. which is closer to the optimum enerev for photoionizing the eas in the ejecta.,"latter is at 100 kev, we expect the ejecta from the exploding star to be bathed in a radiation field with a peak at $\lta 25$ kev, which is closer to the optimum energy for photoionizing the gas in the ejecta."77 In order to have significant back-scattering of photons. 7 should be close to unity.," In order to have significant back-scattering of photons, $\tau$ should be close to unity."78" Taking n-= 100%=LOY em. r,=5X104 em. this requires 2,~7XLO""em.7. which is substantially larger than the number density expected for a tvpical WIR star wind."," Taking $\eta_\pm=10$, $r_0=10^{15}$ cm, $r_1=5\times10^{14}$ cm, this requires $n_0 \sim 7\times10^7 ~{\rm79cm^{-3}}$, which is substantially larger than the number density expected for a typical WR star wind."80 The pre-supernova star must have had an unusually heavy mass-loss rate within the last few vears of its life just before the explosion., The pre-supernova star must have had an unusually heavy mass-loss rate within the last few years of its life just before the explosion.81 Assuming 7Z1. the fraction of the backward scattered energy. intercepted by the exploding star. assuming the ejecta are expanding wnilormly with a velocity isGU.," Assuming $\tau\ \gta\ 1$, the fraction of the backward scattered energy intercepted by the exploding star, assuming the ejecta are expanding uniformly with a velocity is."82.. The intercepted Πας is a factor of two larger when we include the dipole nature of Thomson scattering., The intercepted flux is a factor of two larger when we include the dipole nature of Thomson scattering.83 Thus the total οποιον incident on the star is 3κ107 eres., Thus the total energy incident on the star is $3\times10^{48}$ ergs.84 This [alls short of the required amount in GRD 011211. which is 5065)xLONEys=5LOMey)Eqs eres.," This falls short of the required amount in GRB 011211, which is $50\zeta_{50}\times10^{48}E_{48}85=5\times10^{49}\zeta_{50}E_{48}$ ergs."86 If the supernova explosion is non-spherical. as evidenced by recent polarization observations. wilh the equatorial region expanding at about (ice (he speed of the polar region. then about of the back scattered τις will be intercepted by the ejecta and the total energv incident on the expanding stellar surface is ~2xLO” eres.," If the supernova explosion is non-spherical, as evidenced by recent polarization observations, with the equatorial region expanding at about twice the speed of the polar region, then about of the back scattered flux will be intercepted by the ejecta and the total energy incident on the expanding stellar surface is $\sim 2\times 10^{49}$ ergs."87 Instead. of an asymmetric supernova. we could also consider a rapidly expanding cocoon. possibly associated with the GRB jet.," Instead of an asymmetric supernova, we could also consider a rapidly expanding cocoon, possibly associated with the GRB jet."88 This will work equally well provided the density is sufficiently high (eq 6) aud (he transverse velocity is DZ0.3c., This will work equally well provided the density is sufficiently high (eq 6) and the transverse velocity is $\gta0.3c$.89 The deceleration radius for the relativistic GRB ejecta. for the wind clensity deduced above. is sienilicantly smaller than the radius r4 of the pair sereen.," The deceleration radius for the relativistic GRB ejecta, for the wind density deduced above, is significantly smaller than the radius $r_1$ of the pair screen."90 Thus a substantial fraction of the energv of the relativisically expanding GRD fireball will be converted to x-ray raciiation before the expanding material hits the pair screen. aud (his energy. will also be scattered by the pair screen and intercepted by (he supernova ejecta.," Thus a substantial fraction of the energy of the relativistically expanding GRB fireball will be converted to x-ray radiation before the expanding material hits the pair screen, and this energy will also be scattered by the pair screen and intercepted by the supernova ejecta."91 The early alterglow spectral peak is (wpically at an energy smaller than the GRB peak. and the peak shifts to lower energies with time as the Lorentz factor of the shock decreases.," The early afterglow spectral peak is typically at an energy smaller than the GRB peak, and the peak shifts to lower energies with time as the Lorentz factor of the shock decreases."92 In the case of the hieh density surrounding medium considered here. (he two emissions could have similar peak enerev al early limes. but (he alterglow emission will subsequently shift to lower frequencies.," In the case of the high density surrounding medium considered here, the two emissions could have similar peak energy at early times, but the afterglow emission will subsequently shift to lower frequencies."93 When we include the scattered alterelow flix. we find that the expanding supernova ejecta could receive a total of ~5x10 eres in 120 keV band.," When we include the scattered afterglow flux, we find that the expanding supernova ejecta could receive a total of $\sim945\times10^{49}$ ergs in 1–20 keV band."95 The afterglow radiation will be more efficient. compared to the GRB photons. in ionizing Si ancl other atoms which have ionization energles of a few keV. Such a continuum. x-ray [lux can be efficiently. processed," The afterglow radiation will be more efficient, compared to the GRB photons, in ionizing Si and other atoms which have ionization energies of a few keV. Such a continuum x-ray flux can be efficiently processed"96and the trio provides 0.03. 0.33 minor improvement over the case without BAO.,"and the trio provides 0.08, 0.33 – minor improvement over the case without BAO."97 Thus. the accuracy attainable with the BAO method is important to know rigorously.," Thus, the accuracy attainable with the BAO method is important to know rigorously."98 We have seen from the above results that SN data are a kev element lor the clark energy constraints iimproving estimation of wo by a [actor of 2-4 alone. and a [factor 3-4 added to BAO).," We have seen from the above results that SN data are a key element for the dark energy constraints improving estimation of $w_0$ by a factor of 2-4 alone, and a factor 3-4 added to BAO)."99 But given the complementarity. if BAO can provide measurements then the SN data set mav not need {ο be as stringent.," But given the complementarity, if BAO can provide measurements then the SN data set may not need to be as stringent."100 Reducing the survey depth to. sav. 2=0.8 but somehow keeping the SN systematics at the same low level as for the space based SNAP survey. degrades the BAO+CAIB+SN constraints only to 0.06. 0.25.," Reducing the survey depth to, say, $z=0.8$ but somehow keeping the SN systematics at the same low level as for the space based SNAP survey, degrades the BAO+CMB+SN constraints only to 0.06, 0.25."101 However if the BAO precision slips to this becomes 0.09. 0.42.," However if the BAO precision slips to this becomes 0.09, 0.42."102 Careful study is required., Careful study is required.103 We will also see later that the SN depth is an important element in several other respects., We will also see later that the SN depth is an important element in several other respects.104 Note that just because BAO effectively involves a distance ratio of. sav. d(z=3) to d(z=1039). this does not mean that BAO can simply separate out the conditions of the universe between z=3 and 2=1089.," Note that just because BAO effectively involves a distance ratio of, say, $d(z=3)$ to $d(z=1089)$, this does not mean that BAO can simply separate out the conditions of the universe between $z=3$ and $z=1089$."105" That is. one does not isolate the effects of ""evervthing but” dark energy or the effects of unexpected early dark energy."," That is, one does not isolate the effects of “everything but” dark energy or the effects of unexpected early dark energy."106 Both distances entering the ratio are still integral quantities. and while the conditions at 2>3 are involved. they are not given separately.," Both distances entering the ratio are still integral quantities, and while the conditions at $z>3$ are involved, they are not given separately."107 Still. BAO does olfer the possibility of putting some constraints on 2>3 dark energy. (though one expects the mass growth factor to be more sensitive to this property).," Still, BAO does offer the possibility of putting some constraints on $z>3$ dark energy (though one expects the mass growth factor to be more sensitive to this property)."108 None of the probes considered above have dependence on mass growth. and so are incapable of comparing the expansion history (the growth history to test the theoretical framework (see. e.g.. Linder (2005a))).," None of the probes considered above have dependence on mass growth, and so are incapable of comparing the expansion history the growth history to test the theoretical framework (see, e.g., \citet{groexp}) )."109 Whether the dark energy arises [from a new phlivsical component. aa high energy plivsics scalar field. or a modification of the Cheory of gravity is à crucial question.," Whether the dark energy arises from a new physical component, a high energy physics scalar field, or a modification of the theory of gravity is a crucial question."110 Answering (his is a kev requirement lor understanding the physics of acceleration., Answering this is a key requirement for understanding the physics of acceleration.111 Thus. just as a purely SN experiment would not be sufficiently revelatory about dark energy. a purely BAO experiment is not acceptable.," Thus, just as a purely SN experiment would not be sufficiently revelatory about dark energy, a purely BAO experiment is not acceptable."112 We therefore consider measurement ol the weak lensing shear power spectrum. as estimated for the SNAP satellite. as another probe of dark enerey to be taken in complementaritv.," We therefore consider measurement of the weak lensing shear power spectrum, as estimated for the SNAP satellite, as another probe of dark energy to be taken in complementarity."113 Note that this. like BAO but ON. is here treated with purely statistical errors.," Note that this, like BAO but SN, is here treated with purely statistical errors."114 Fieure 3. shows that WL adds appreciable information enabling Gehter dark energy constraints., Figure \ref{fig.bocs} shows that WL adds appreciable information enabling tighter dark energy constraints.115 Recall. however. (hat we also want each probe. or at least expansion history and growth history separately. (o stand on their own to allow for crosschecks ancl test. of the theoretical Lramework nunodilicalions of Einstein gravitv).," Recall, however, that we also want each probe, or at least expansion history and growth history separately, to stand on their own to allow for crosschecks and test of the theoretical framework modifications of Einstein gravity)."116 With (is kept firmly in, With this kept firmly in117is satisfied.,is satisfied.118" If it is not, the expansion takes place too fast for an wave to cross the jet and an mode instability cannot grow."," If it is not, the expansion takes place too fast for an wave to cross the jet and an mode instability cannot grow."119" While the critical value of ι is arguable, we note that causal contact across the jet by Alfvénn waves is only possible if.>π."," While the critical value of $\iota$ is arguable, we note that causal contact across the jet by Alfvénn waves is only possible if $\iota \ge \pi$."120 The situation in our simulations is illustrated in Figs., The situation in our simulations is illustrated in Figs.121 6 and 7..," \ref{fig:growthcondition}122 and \ref{fig:acrosstime}."123 Instabilities can grow only slowly on magnetic surfaces with large 9., Instabilities can grow only slowly on magnetic surfaces with large $\vartheta$.124" Depending on the ι needed for efficient growth, they may even be stalled due to the jet's expansion."," Depending on the $\iota$ needed for efficient growth, they may even be stalled due to the jet's expansion."125" In any case, instabilities grow most rapidly if they start at small r."," In any case, instabilities grow most rapidly if they start at small $r$."126" In regions where the jet is accelerating (dv,/dr> 0) or decollimating (d3/dr>0 along a field line), the effective crossing time is underestimated by Eq."," In regions where the jet is accelerating $\de v_r / \de r > 0$ ) or decollimating $\de127\vartheta / \de r > 0$ along a field line), the effective crossing time is underestimated by Eq."128(23).. The jet is then stabler than condition suggests., The jet is then stabler than condition suggests.129" We observe non-axisymmetric, kink-like distortions in the magnetic field and other quantities in both 3D simulations."," We observe non-axisymmetric, kink-like distortions in the magnetic field and other quantities in both 3D simulations."130" They emerge near the radius, propagate with the flow and grow in amplitude along the way."," They emerge near the radius, propagate with the flow and grow in amplitude along the way."131 It is convenient to look at the current density j=£VxB for a quantitative analysis., It is convenient to look at the current density $\vec{j}=\frac{c}{4\pi}\Nabla \times \vec{B}$ for a quantitative analysis.132" The radial component j, is related to B, and is as such characteristic for the distortions in the magnetic field.", The radial component $j_r$ is related to $B_\varphi$ and is as such characteristic for the distortions in the magnetic field.133" In the unperturbed case, it is concentrated about the central axis and along the outer boundary of the cavity illustrated in Fig. 4,,"," In the unperturbed case, it is concentrated about the central axis and along the outer boundary of the cavity illustrated in Fig. \ref{fig:rhot},"134 with respectively opposite orientation., with respectively opposite orientation.135" In our simulations, B, is directed in negative y-direction and the axial current, accordingly, in negative r-direction."," In our simulations, $B_\varphi$ is directed in negative $\varphi$ -direction and the axial current, accordingly, in negative $r$ -direction."136" We denote this backward current with j;, so that j,=J;+jy."," We denote this backward current with $j_r^-$, so that $j_r =137j_r^+ + j_r^-$."138" In the rigid rotation case (R3), the distortions attained large amplitudes of several degrees."," In the rigid rotation case (R3), the distortions attained large amplitudes of several degrees."139" Looking at B, in the r=const plane, we find that the whole jet is affected by the kink."," Looking at $B_\varphi$ in the $r=\const$ plane, we find that the whole jet is affected by the kink."140" The number of visible radial nodes is 2-4, corresponding to wavelengths on the order of 150, i.e. several times larger than the magnetic pitch."," The number of visible radial nodes is 2–4, corresponding to wavelengths on the order of $150$, i.e. several times larger than the magnetic pitch."141" Owing to the distortions in the magnetic field, the axial current was perturbed as shown in Fig."," Owing to the distortions in the magnetic field, the axial current was perturbed as shown in Fig."142 8 on the right-hand image., \ref{fig:jrvolren} on the right-hand image.143" j; helically twines around the central axis in reminiscence of ""ideal"" kink instabilities with an azimuthal mode number m=1.", $j_r^-$ helically twines around the central axis in reminiscence of “ideal” kink instabilities with an azimuthal mode number $m=1$.144" To analyze the unstable displacements, we determine the barycenter of the backward current j; in the r=const plane, denoting its location with (2j,;)."," To analyze the unstable displacements, we determine the barycenter of the backward current $j_r^-$ in the $r=\const$ plane, denoting its location with $(\vartheta_j,\varphi_j)$."145" The result, from which one can directly read off amplitudes and wavelengths, is shown in Fig. 9.."," The result, from which one can directly read off amplitudes and wavelengths, is shown in Fig. \ref{fig:jrmbarycenter}."146" The slope of the points of constant phase o; in the r- t diagram corresponds with the flow velocity v,.", The slope of the points of constant phase $\varphi_j$ in the $r$ $t$ diagram corresponds with the flow velocity $v_r$ .147" That is, the instabilities are at rest with respect to a comoving frame."," That is, the instabilities are at rest with respect to a comoving frame."148 We estimate the growth time in such a frame by introducing an observer moving with flow and measure 2; in doing so., We estimate the growth time in such a frame by introducing an observer moving with flow and measure $\vartheta_j$ in doing so.149" We find strictly increasing, exponential growth if the observer is located just behind the jet front, see upper panel in Fig. 10.."," We find strictly increasing, exponential growth if the observer is located just behind the jet front, see upper panel in Fig. \ref{fig:comovingthj}."150 The exponential growth time τε is generally on the order of the crossing times shown in Fig. 7.., The exponential growth time $\taug$ is generally on the order of the crossing times shown in Fig. \ref{fig:acrosstime}.151" For observers which are farther behind the jet front, the amplitude does not follow a simple exponential increase, see lower panel in Fig."," For observers which are farther behind the jet front, the amplitude does not follow a simple exponential increase, see lower panel in Fig."152 10 for an example., \ref{fig:comovingthj} for an example.153" Rather, it saturates and even declines in some cases."," Rather, it saturates and even declines in some cases."154 The reason for this is not clear., The reason for this is not clear.155 We cannot rule out the possibility that there is stabilizing feedback from the upper boundary., We cannot rule out the possibility that there is stabilizing feedback from the upper boundary.156" Considering that the flow is there, this seems unlikely though."," Considering that the flow is there, this seems unlikely though."157" In the Keplerian rotation case (K3), the jet also exhibits kink-like distortions, see left-hand image in Fig. 8.."," In the Keplerian rotation case (K3), the jet also exhibits kink-like distortions, see left-hand image in Fig. \ref{fig:jrvolren}."158" However, the perturbation amplitudes are much smaller, with 2; attaining peak values of about 1.4? directly behind the jet front and only about 0.5? farther behind."," However, the perturbation amplitudes are much smaller, with $\vartheta_j$ attaining peak values of about $1.4\degree$ directly behind the jet front and only about $0.5\degree$ farther behind."159" Unlike in the rigid rotation case, only inner regions of the jet are affected by the kinks, the jet border is relatively unharmed."," Unlike in the rigid rotation case, only inner regions of the jet are affected by the kinks, the jet border is relatively unharmed."160" The wavelengths are on the order of 25—50, i.e. there are more radial nodes than in the rigid rotation case."," The wavelengths are on the order of 25–50, i.e. there are more radial nodes than in the rigid rotation case."161" Even for an observer traveling just behindthe jet front, the amplitude is not strictly increasing, but saturates and tapers"," Even for an observer traveling just behindthe jet front, the amplitude is not strictly increasing, but saturates and tapers"162ddecreases with increasing luminosity (e.g..Netzeretal.2006:Meléndezetal. 2008).,"decreases with increasing luminosity \citep[e.g.,][]{netzeretal2006,melendezetal2008}."163. We find no evidence for a correlation between —L residuals and Eddington ratio., We find no evidence for a correlation between $L$ residuals and Eddington ratio.164 In fact. the intrinsic. scatter in all relations is surprisingly small.," In fact, the intrinsic scatter in all relations is surprisingly small."165 On the one hand. the X-rays are variable on short timescales. but. às we show. that does not translate into significant errors in the rrelation.," On the one hand, the X-rays are variable on short timescales, but, as we show, that does not translate into significant errors in the relation."166. On. the. other hand. the narrow emission-line luminosities do not respond at all to state changes on timescales of a year.," On the other hand, the narrow emission-line luminosities do not respond at all to state changes on timescales of a year."167 Thus. we find it surprising that even in these cases the intrinsic scatter is only at the factor of two level.," Thus, we find it surprising that even in these cases the intrinsic scatter is only at the factor of two level."168 Still. this scatter translates directly into uncertainties in the BH masses (e.g..Vestereaard&Peterson2006:McGilletal.2008).," Still, this scatter translates directly into uncertainties in the BH masses \citep[e.g.,][]{vestergaardpeterson2006,mcgilletal2008}."169. As the reverberation-mapped samples increase. it should become possible to search for evidence of secondary. parameters that might allow one to decrease the total scatter. thereby increasing the fidelity of our BH mass estimates. NAGS5-7007..," As the reverberation-mapped samples increase, it should become possible to search for evidence of secondary parameters that might allow one to decrease the total scatter, thereby increasing the fidelity of our BH mass estimates. ."170approximately ITubble-like jet fIows cited earlier. we conclude that jet acceleration is probably nol the primary effect. and that the jet-Iag sequence is (he preferred one.,"approximately Hubble-like jet flows cited earlier, we conclude that jet acceleration is probably not the primary effect, and that the jet-lag sequence is the preferred one."171 On the basis that the expansion times are reasonable approximations of (he travel times. we can reconstruct the Gime evolution of the torus-]et sequence.," On the basis that the expansion times are reasonable approximations of the travel times, we can reconstruct the time evolution of the torus-jet sequence."172 The time line for each object is shown in Fig., The time line for each object is shown in Fig.173 2., 2.174" The filled svinbols denote (he values of /, already discussed. ancl represent the average or characteristic expansion times of the tori."," The filled symbols denote the values of $t_t$ already discussed, and represent the average or characteristic expansion times of the tori."175 The horizontal lines represent the {ime interval over which the tori are ejected., The horizontal lines represent the time interval over which the tori are ejected.176 These are based on the radial extents of the tori (e.g.. (he half intensity widths or model fits to the radial extent). and assuming the ejection lakes place al the mean expansion velocity for each object listed in the Table 1.," These are based on the radial extents of the tori (e.g., the half intensity widths or model fits to the radial extent), and assuming the ejection takes place at the mean expansion velocity for each object listed in the Table 1."177 If the tori are ejected wilh a significant dispersion in velocity. the time lines overestimate the width of (he corresponding ejection interval.," If the tori are ejected with a significant dispersion in velocity, the time lines overestimate the width of the corresponding ejection interval."178 M 1-92 may be an extreme case with a velocity gradient that suggests it was ejected in a short time (Aleoleaetal.2007.seealsoAppendix.A2).., M 1-92 may be an extreme case with a velocity gradient that suggests it was ejected in a short time \citep[][see also Appendix A2]{alc07}.179 The information on the partially resolved tori (AFGL 618 and IHe3-1475) is incomplete., The information on the partially resolved tori (AFGL 618 and He3-1475) is incomplete.180 The {riangles on each line in Fig., The triangles on each line in Fig.181 2 denote the times at which the jets are ejected. and are subject to the uncertainties in timing discussed above.," 2 denote the times at which the jets are ejected, and are subject to the uncertainties in timing discussed above."182 For two objects. M 1-16 and Πο 3-1475. the timing of later jets (see appendix) is also shown. to illustrate the overall sequence.," For two objects, M 1-16 and He 3-1475, the timing of later jets (see appendix) is also shown, to illustrate the overall sequence."183 The ejection sequences for all the objects shown in Fig., The ejection sequences for all the objects shown in Fig.184 2 are qualitatively similar., 2 are qualitatively similar.185 There is a rapid build-up of the torus and then the jets are launched. ancl may reoccur.," There is a rapid build-up of the torus and then the jets are launched, and may reoccur."186 As discussed above. our best estimates suggest a finite lag time for the jets. with a median of 300 vr.," As discussed above, our best estimates suggest a finite lag time for the jets, with a median of 300 yr."187 If (his is measured with respect to the onset of the torus ejecton. it is probably somewhat longer.," If this is measured with respect to the onset of the torus ejection, it is probably somewhat longer."188 The interval between (he jets in the objects wilh a sequence of jets is comparable to the jet-lag time., The interval between the jets in the objects with a sequence of jets is comparable to the jet-lag time.189 The ejection of jets and tori are among the most important events in the transition ol stars [from the AGB to the PN phase., The ejection of jets and tori are among the most important events in the transition of stars from the AGB to the PN phase.190 Our finding that they occur close together in lime provides strong evidence (hat thev are physically related. either causally. or by some underlving process or event linking (he two.," Our finding that they occur close together in time provides strong evidence that they are physically related, either causally, or by some underlying process or event linking the two."191 Ow addiüonal finding Chat jets and tori probably occur in a particular sequence. underscores their connection.," Our additional finding that jets and tori probably occur in a particular sequence, underscores their connection."192 These results. together will the time-scale for the torus ejection and (he time scale for (he torus-jet sequence. provide basic constraints on formation scenarios.," These results, together with the time-scale for the torus ejection and the time scale for the torus-jet sequence, provide basic constraints on formation scenarios."193 Despite (heir connections. it is important to emphasize that the actual ejections of jets," Despite their connections, it is important to emphasize that the actual ejections of jets"194which is independent of galaxy mass (because it only describes the shape. not the amplitude. of the intensity profile).,"which is independent of galaxy mass (because it only describes the shape, not the amplitude, of the intensity profile)."195 Note that i;1 for kA] and nu;πολλιμ} for kun31., Note that $u_J \rightarrow 1$ for $k \lambda_{\rm mfp} \ll 1$ and $u_J \rightarrow \pi/(2 k \lambda_{\rm mfp})$ for $k \lambda_{\rm mfp} \gg 1$.196 The “single-source” term. describing correlations within randomly distributed sources” profiles. is where n(nm) is the mass function of the sources (or the halo mass function in our calculations) and psiΞnima is the mean mass density of galaxies Cand i4 is the mean mass of the ionizing sources).," The “single-source"" term, describing correlations within randomly distributed sources' profiles, is where $n(m)$ is the mass function of the sources (or the halo mass function in our calculations) and $\bar{\rho}_{\rm gal}=n_i \bar{m}_{\rm gal}$ is the mean mass density of galaxies (and $\bar{m}_{\rm gal}$ is the mean mass of the ionizing sources)."197 Note that the single-source correlation function ean also be derived from the two-point probability density (2:: see also ?))., Note that the single-source correlation function can also be derived from the two-point probability density \citealt{Zuo93}; see also \citealt{Furlanetto09-heliumcorrs}) ).198 Furthermore. the amplitude is determined by the luminosity function. but the shape is entirely determined by our imposed attenuation profile.," Furthermore, the amplitude is determined by the luminosity function, but the shape is entirely determined by our imposed attenuation profile."199" Similarly. the term describing the correlations between two sources may be written where f,(À.2) is the linear matter power spectrum."," Similarly, the term describing the correlations between two sources may be written where $P_{\rm lin}(k,z)$ is the linear matter power spectrum."200 Again. this two-point function has a shape fixed by the source profiles. but an amplitude that depends on the nature of the sources.," Again, this two-point function has a shape fixed by the source profiles, but an amplitude that depends on the nature of the sources."201 In fact. the term in square brackets is simply equal to unity: we have left it in only for comparison to the halo model. where ή.) is a function of m and so must be left inside the integral.," In fact, the term in square brackets is simply equal to unity; we have left it in only for comparison to the halo model, where $u(k)$ is a function of $m$ and so must be left inside the integral."202 Because for small 4. the two-source term traces the linear matter power[7 spectrum on these scales. before being truncated at AA~1.," Because $|u_J|^2 \rightarrow 1$ for small $k$, the two-source term traces the linear matter power spectrum on these scales, before being truncated at $k \lambda_{\rm mfp} \sim 1$."203 If we take a simple model in which all sources have a fixed mass. we find that Thus the two-source term becomes more and more important as the number density of sources. their bias. and the underlying linear. clustering increase: this is simply because all of these increase the importance of deterministic clustering relative to the correlations inherent to the flux profile itself.," If we take a simple model in which all sources have a fixed mass, we find that Thus the two-source term becomes more and more important as the number density of sources, their bias, and the underlying linear clustering increase: this is simply because all of these increase the importance of deterministic clustering relative to the correlations inherent to the flux profile itself."204 As discussed above. we account for flux attenuation. through re factor e.Fn). in eq. (1).," As discussed above, we account for flux attenuation through the factor $e^{-r/\lmfp}/(4\pi r^2)$ in eq. \ref{eq:sum}) )."205 Thus flux. attenuation is taken into account in a spatially homogeneous way through 1e free parameter Άιμην., Thus flux attenuation is taken into account in a spatially homogeneous way through the free parameter $\lmfp$.206 Although such an approach misses the )bvious correlation of absorbers (LLSs and DLAs) with sources. had several benetits over using the typical approximate radiative ransfer algorithms in cosmological hydrodynamical simulations.," Although such an approach misses the obvious correlation of absorbers (LLSs and DLAs) with sources, it had several benefits over using the typical approximate radiative transfer algorithms in cosmological hydrodynamical simulations."207 Firstly. our approach is versatile. easy to calibrate and to run cuickly for large-scale boxes.," Firstly, our approach is versatile, easy to calibrate and to run quickly for large-scale boxes."208 This allows us to easily explore re effects of varying Ag. Which is important. given the large uncertainties in this value at these redshifts (e.g. 2).," This allows us to easily explore the effects of varying $\lmfp$, which is important, given the large uncertainties in this value at these redshifts (e.g. \citealt{Faucher-Giguere08}) )."209 Secondly. our formalism allows for easy comparisons with analytic models. and provides direct insight into the features of the UVB.," Secondly, our formalism allows for easy comparisons with analytic models, and provides direct insight into the features of the UVB."210 Finally. and most importantly. large-scale cosmological hydrodynamical simulationsDLAs: thus they too must employ analytic prescriptions to populate their box with absorbers.," Finally, and most importantly, large-scale cosmological hydrodynamical simulations; thus they too must employ analytic prescriptions to populate their box with absorbers."211 We also note that the mean free paths at these redshifts is so large (=20 Mpe: ??22)) that flux received by each cell is sourced by tens of thousands of sources. likely averaging out detailed radiative transfer effects.," We also note that the mean free paths at these redshifts is so large $\gsim20$ Mpc; \citealt{Storrie-Lombardi94, MHR99, Miralda-Escude03, Faucher-Giguere08}) ) that flux received by each cell is sourced by tens of thousands of sources, likely averaging out detailed radiative transfer effects."212 We thus do not expect our results © be significantly affected by the fact that we neglect the details of radiative transfer and the clustering of absorbers., We thus do not expect our results to be significantly affected by the fact that we neglect the details of radiative transfer and the clustering of absorbers.213 Nevertheless. stochastic fluctuations in. the absorber ;xopulation. will help to increase the variance in the radiation Ποιά: if LLSs are primarily responsible for absorption. each attenuation length will contain only a single absorber on average and the absorption length will vary quite strongly.," Nevertheless, stochastic fluctuations in the absorber population will help to increase the variance in the radiation field: if LLSs are primarily responsible for absorption, each attenuation length will contain only a single absorber on average and the absorption length will vary quite strongly."214 However. in oraetice. —5054. of the absorption is typically due to lower-column density absorbers (see. e.g.. the Appendix to 2)). so this is probably not a large factor for us.," However, in practice $\ga 50\%$ of the absorption is typically due to lower-column density absorbers (see, e.g., the Appendix to \citealt{FO05}) ), so this is probably not a large factor for us."215" In Figure 2.. we plot the flux PDFs for a £=100 Mpe box with 0.5 Mpe cells at >=10. Awe,=10 Mpe. and Ai,=107 Mιν"," In Figure \ref{fig:mfp_att}, we plot the flux PDFs for a $L=100$ Mpc box with $0.5$ Mpc cells at $z=10$, $\lmfp=10$ Mpc, and $\Mmin=10^8$ $\Msun$."216 We show the effects of truncating the sum over contributing sources in eq. (L9) , We show the effects of truncating the sum over contributing sources in eq. \ref{eq:sum}) )217"at distances of DÀ, λιμιρ. and 3À, curves)."," at distances of $\lmfp$, $\lmfp$, and $\lmfp$ )."218" The distributions appear to converge at 2A, - AÀuup.", The distributions appear to converge at $\lmfp$ $\rightarrow$ $\lmfp$.219 The high end tails of the distribution are dominated by nearby ionizing sources and are fairly insensitive to the effective horizon (ie. the high-value tails are roughly constant as more distant sources are included in the UVB calculation)., The high end tails of the distribution are dominated by nearby ionizing sources and are fairly insensitive to the effective horizon (i.e. the high-value tails are roughly constant as more distant sources are included in the UVB calculation).220 When plotted in unnormalized units (.e. ο) instead of 7/253. this overlap is more pronounced and the leftmost (blue) curve shifts to even smaller values.," When plotted in unnormalized units (i.e. $J$ instead of $J/\langle J \rangle$ ), this overlap is more pronounced and the leftmost (blue) curve shifts to even smaller values."221 In contrast. the low-end tails of the PDFs correspond to locations far away from ionizing sources and so are very sensitive to the inclusion of more distant sources. which roughly translates to changing the amplitude an effective homogeneous UVB.," In contrast, the low-end tails of the PDFs correspond to locations far away from ionizing sources and so are very sensitive to the inclusion of more distant sources, which roughly translates to changing the amplitude an effective homogeneous UVB."222" If sources were homogeneously distributed. truncating the flux distribution at distances greater than μμ would underestimate the ionizing flux by a factor of (1ο"")."," If sources were homogeneously distributed, truncating the flux distribution at distances greater than $n \lmfp$ would underestimate the ionizing flux by a factor of $(1-e^{-n})$."223 The clustering of sources results in the more complicated behavior seen in Fig. 2.., The clustering of sources results in the more complicated behavior seen in Fig. \ref{fig:mfp_att}.224 The dotted curve in Fig., The dotted curve in Fig.225 2. neglects the exponential attenuation term in eg. (1))," \ref{fig:mfp_att} neglects the exponential attenuation term in eq. \ref{eq:sum}) ),"226 and instead only includes the contributions of sources at distances r«Ay., and instead only includes the contributions of sources at distances $r<\lmfp$.227 This is analogous to assuming a step-function optical depth so that 7=0 for distances r«Ay and 7=ox at distances rAlp., This is analogous to assuming a step-function optical depth so that $\tau=0$ for distances $r<\lmfp$ and $\tau=\infty$ at distances $r>\lmfp$.228 Such a prescription can simplify computation in analytic models (e.g.. 23) and numerical calculations (e.g.. 23) and seems to result in fairly accurate flux distributions. though it slightly overestimates the number of faint regions.," Such a prescription can simplify computation in analytic models (e.g., \citealt{Zuo92}) ) and numerical calculations (e.g., \citealt{Bolton06}) ) and seems to result in fairly accurate flux distributions, though it slightly overestimates the number of faint regions."229 This overestimate worsens somewhat if one integrates sources only out to LÀ; but also includes exponential attenuation (e.g. 2))., This overestimate worsens somewhat if one integrates sources only out to $\lmfp$ but also includes exponential attenuation (e.g. \citealt{Santos08}) ).230 In Figure 3.. we explore the impact of varying Aj.," In Figure \ref{fig:mfp_pdfs}, we explore the impact of varying $\lmfp$."231 Flux PDFs at 2=5 curves) and 2.=6 curves) are shown assuming Adwin=1.6«107A/. and DC=0.1., Flux PDFs at $z=5$ ) and $z=6$ ) are shown assuming $\Mmin=1.6\times10^8 \Msun$ and DC=0.1.232 Note that the evolution of structure from 2=10 in Fig., Note that the evolution of structure from $z=10$ in Fig.233 2. to 2= 5 and 6in Fig., \ref{fig:mfp_att} to $z=$ 5 and 6 in Fig.234 3 preferentially suppresses the low-end tail of the PDFs as regions containing few ionizing sources become extremely rare., \ref{fig:mfp_pdfs} preferentially suppresses the low-end tail of the PDFs as regions containing few ionizing sources become extremely rare.235 This results in narrower and more asymmetric distributions., This results in narrower and more asymmetric distributions.236 As expected. increasing the m.f.p.," As expected, increasing the m.f.p."237 also results in narrower flux distributions. as the gus cells see increasingly representative volumes of space inside their horizon.," also results in narrower flux distributions, as the gas cells see increasingly representative volumes of space inside their horizon."238 We note however that the Aut»=+0 Mpe distributions are still fairly broad., We note however that the $\lmfp=40$ Mpc distributions are still fairly broad.239 Understandably. when plotted in unnormalized units (i.e. / instead of J /¢./)). the high-value tails overlap as they are dominated by nearby halos.," Understandably, when plotted in unnormalized units (i.e. $J$ instead of $J/\langle J \rangle$ ), the high-value tails overlap as they are dominated by nearby halos."240 Perhaps surprisingly. we see very little variation of the flux PDF with redshift. over the range 2= 5 to 6.," Perhaps surprisingly, we see very little variation of the flux PDF with redshift, over the range $z=$ 5 to 6."241The 2dE instrument was designed to measure large numbers of redshifts in as short an observing time as possible.,The 2dF instrument was designed to measure large numbers of redshifts in as short an observing time as possible.242 In so doing it has made very large projects such as the 2dGIU possible., In so doing it has made very large projects such as the 2dFGRS possible.243 Llowever. in order to optimise the number of redshifts that can be measured in a given period of timo. compromises have had to be mace with respect to the spectral quality of the observations.," However, in order to optimise the number of redshifts that can be measured in a given period of time, compromises have had to be made with respect to the spectral quality of the observations."244 Therefore if one wishes to characterise the observed galaxy population in terms of their spectral properties care must be taken in order to ensure that these properties are robust to the instrumental uncertainties (see e.g. Lewis et al..," Therefore if one wishes to characterise the observed galaxy population in terms of their spectral properties care must be taken in order to ensure that these properties are robust to the instrumental uncertainties (see e.g. Lewis et al.,"245 2001. for a more detailed discussion).," 2001, for a more detailed discussion)."246" The 2dl instrument makes use of up to 400 optical fibres with a diameter of 140y;am (corresponding to 2.02.16"" on the sky. depending on plate position)."," The 2dF instrument makes use of up to 400 optical fibres with a diameter of $\mu$ m (corresponding to $2.0 - 2.16''$ on the sky, depending on plate position)."247 The quality and representativencss of the observed. spectra. can. be compromised in many wavs. the most significant of which are: The source of the chromatic dispersion. mentioned above is due to a design feature of the 2dE corrector lens which gives us our extended (2 degree) Ποιά of view.," The quality and representativeness of the observed spectra can be compromised in many ways, the most significant of which are: The source of the chromatic dispersion mentioned above is due to a design feature of the 2dF corrector lens which gives us our extended (2 degree) field of view."248 This dispersion. combined. with the random. positioning errors. results in uncertainties in calibrating the continuum of each galaxy spectrum.," This dispersion, combined with the random positioning errors, results in uncertainties in calibrating the continuum of each galaxy spectrum."249 For this reason we will not make use of the information contained in the continuum of cach galaxy in our subsequent analysis., For this reason we will not make use of the information contained in the continuum of each galaxy in our subsequent analysis.250 However. we will make use of the continuum calculated by averaging over a sullicicntly large ensemble of galaxy spectra since this will be much more robust (see Section 4.2 for further details).," However, we will make use of the continuum calculated by averaging over a sufficiently large ensemble of galaxy spectra since this will be much more robust (see Section 4.2 for further details)."251 The random errors in positioning the fibre aperture could also result. in uncertainties in measuring the, The random errors in positioning the fibre aperture could also result in uncertainties in measuring the252This radio source has been identified. by Saripalli et al. (,This radio source has been identified by Saripalli et al. (253"2005) as the core of a ""double-double Giant Badio Galaxy.",2005) as the core of a “double-double” Giant Radio Galaxy.254 Figure 4. shows the optical SuperCOSMOS blue. image overlaid with SUADSS radio contours at S43MIIz the total extent of the SUMSS source is 5.5aarcmin. corresponding— o à largest linear size of τοῦ kkpe.," Figure \ref{fig:J074618-570258_sumss} shows the optical SuperCOSMOS blue image overlaid with SUMSS radio contours at 843MHz – the total extent of the SUMSS source is arcmin, corresponding to a largest linear size of $\sim$ kpc."255 This source was classified as EI-L by Saripalli ct al. (, This source was classified as FR-I by Saripalli et al. (2562005) on the basis of the edge.darkened radio morphology in the SUMSS image.,2005) on the basis of the edge–darkened radio morphology in the SUMSS image.257 Saripalli et ((2005) also obtained a igher-resolution Εις racio image of JOTAGIS| 570258 with the ATCA (their Figure 9). which shows an inner pair of radio hotspots indicative of a core-jet morphology with he jet pointing towards the weaker (South-West) of the argerscale radio lobes.," Saripalli et (2005) also obtained a higher-resolution GHz radio image of $-$ 570258 with the ATCA (their Figure 9), which shows an inner pair of radio hotspots indicative of a core-jet morphology with the jet pointing towards the weaker (South-West) of the larger–scale radio lobes."258 The component identified. as the core by Saripalli et al. (, The component identified as the core by Saripalli et al. (2592005). which is identified with a >=0.13 galaxy. is also coincident with the Αθ source detected in our CWLBI observation.,"2005), which is identified with a $z=0.13$ galaxy, is also coincident with the AT20G source detected in our eVLBI observation."260 Suripalli et ((2005) note that the optical spectrum of this galaxy (shown in their Figure 19) has stellar absorption lines but no obvious emission lines., Saripalli et (2005) note that the optical spectrum of this galaxy (shown in their Figure 19) has stellar absorption lines but no obvious emission lines.261 They suggest that JOTAGIS 570258 may be an example of a restarting racio jet within relic lobes., They suggest that $-$ 570258 may be an example of a restarting radio jet within relic lobes.262 The 6dECGS spectrum. of this galaxy shows strong emissionlines of Ha. HH] anc HL]. although 1:37 LII] lines are not seen.," The 6dFGS spectrum of this galaxy shows strong emission–lines of $\alpha$, II] and II], although $\beta$ III] lines are not seen."263 The e-VEDI position is οκο aaresce north of the optical centroid of the galaxy., The e-VLBI position is offset arcsec north of the optical centroid of the galaxy.264 ‘This galaxy. has a WK-band absolute magnitude Mi= 22.6. making it significantly less luminous than the host galaxies of most nearby. radioloud AGN (which typically have My<24. see eg. Figure S of AMlauch Sadler 2007).," This galaxy has a K-band absolute magnitude $_{\rm K}=-22.6$ , making it significantly less luminous than the host galaxies of most nearby radio–loud AGN (which typically have $_{\rm K}<-24$, see e.g. Figure 8 of Mauch Sadler 2007)."265 ‘This. together with the relatively Hat. racio spectrum (compared to the other sources in our GPS sample) and the aaresec radiooptical position ollsct. suggests that the radio emission in 243829 may come from a background quasar rather than the galaxy. itself," This, together with the relatively flat radio spectrum (compared to the other sources in our GPS sample) and the arcsec radio–optical position offset, suggests that the radio emission in $-$ 243829 may come from a background quasar rather than the galaxy itself."266 This galaxy appears in the SUAISS ancl NVSS catalogues as a point source of άν and mmy. respectively. sugeesting a strong upturn in the radio spectrum. above GGllz.," This galaxy appears in the SUMSS and NVSS catalogues as a point source of mJy and mJy respectively, suggesting a strong upturn in the radio spectrum above GHz."267 Phe ο spectrum shows strong absorption lines and weak HE] emission. consistent with the galaxy's designation as a possible LINER.," The 6dFGS spectrum shows strong absorption lines and weak II] emission, consistent with the galaxy's designation as a possible LINER."268 This object is associated with the brighter of the two objects in the galaxy. pair 11257. 435 (galaxy A in Figure 5))., This object is associated with the brighter of the two objects in the galaxy pair $-$ 435 (galaxy A in Figure \ref{fig:J130031-441442_optical}) ).269 Galaxy D. the second. member of the pair. is aarcmin aw.," Galaxy B, the second member of the pair, is arcmin away."270 441442 (galaxy A) is listed as à shell galaxy in the catalogue of Malin and Carter (1983). who describe it as having “shells NW and SE. 2 companions”.," $-$ 441442 (galaxy A) is listed as a shell galaxy in the catalogue of Malin and Carter (1983), who describe it as having “shells NW and SE, 2 companions”."271 Such shells are generally attributed to a past merger of two easpoor ealaxies., Such shells are generally attributed to a past merger of two gas–poor galaxies.272 441442 is also identified with the UV. source FC-238 by Brosch et al. (, $-$ 441442 is also identified with the UV source FC-238 by Brosch et al. (2732000). who [ist it as aSAB(s) pec galaxy with UV magnitude of 12.58+0.61.,"2000), who list it as a SAB(s) pec galaxy with UV magnitude of $12.58\pm0.61$."274 The 6dEX€S spectrum of this galaxy (marked: as object A in Figure 6)) shows stellar absorption lines twpical of early galaxies but no obvious optical emission lines., The 6dFGS spectrum of this galaxy (marked as object A in Figure \ref{fig:J181857-550815_optical}) ) shows stellar absorption lines typical of early--type galaxies but no obvious optical emission lines.275 “This ealaxy lies between two SUMSS sources. as shown in Figure," This galaxy lies between two SUMSS sources, as shown in Figure"276to LemὉ to explain the observed [κος near the Earth.,to $1$ $^{-3}$ to explain the observed fluxes near the Earth.277 The fhience spectra of such beam densities correspond to weak to medium solar energetic electron events observed near the Earth ancl are required for realistic simulation computational times., The fluence spectra of such beam densities correspond to weak to medium solar energetic electron events observed near the Earth and are required for realistic simulation computational times.278 The initial heieht of the beam was 5x10? em corresponding to the density 2.1xLO?  (local plasma frequency ~415 MIIz)., The initial height of the beam was $5\times 10^9$ cm corresponding to the density $2.1\times 10^9$ $^{-3}$ (local plasma frequency $\sim 415$ MHz).279 The initial beam spectral indices 0=0/2 were between 2.5 and 4.5. consistent with the observational values ?..," The initial beam spectral indices $\delta=\alpha/2$ were between $2.5$ and $4.5$, consistent with the observational values \citet{Krucker_etal09}."280 Generally. it is seen from our simulations (hat as soon as the plasma wave growth time e»Lise) is less than the time scale of an electron cloud d/v for some enerev E(v). the wave-parlicle interactions start to play an important role in the electron transport.," Generally, it is seen from our simulations that as soon as the plasma wave growth time $\sim 1/\gamma (v,x)$ is less than the time scale of an electron cloud $d/v$ for some energy $E(v)$, the wave-particle interactions start to play an important role in the electron transport."281 Since (his condition is energy dependent (he electrons above certain energies are (oo dilute to generate plasma waves., Since this condition is energy dependent the electrons above certain energies are too dilute to generate plasma waves.282 The overall spectrum observed at (he Earth becomes close to a broken where electrons below the break energy generale and absorb Langmuir waves. while electrons above the break energy. are not allectecl by the wave-particle interactions.," The overall spectrum observed at the Earth becomes close to a broken power-law, where electrons below the break energy generate and absorb Langmuir waves, while electrons above the break energy are not affected by the wave-particle interactions."283 Traditionallyηδη measurements of energetic electrons (e.g.?)— provide the flux density differential in energy F(E.c.1)=f(e.v.d0)/m [electrons ? + 4] and the [nences (flux integrated over the duration of an event) [electrons ? !].," Traditionally measurements of energetic electrons \citep[e.g.][]{Lin_etal95} provide the flux density differential in energy $F(E,x,t)=f(v,x,t)/m$ [electrons $^{-2}$ $^{-1}$ $^{-1}$ ] and the fluences (flux integrated over the duration of an event) [electrons $^{-2}$ $^{-1}$ ]."284 The injected electron fluence in our model |UEPleo)oevyfede can be caleulated from. equations⋅ (3..4)). . and is presented in Figure 1..," The injected electron fluence in our model $\int _{-\infty}^{\infty}f(v,x,t)/v dx $ can be calculated from equations \ref{init_f}, \ref{init_g0}) ) and is presented in Figure \ref{fig:1}."285 The corresponding energy spectral index of the injected electron fence at (he Sun is (a+1)/2—01/2., The corresponding energy spectral index of the injected electron fluence at the Sun is $(\alpha +1)/2=\delta+1/2$.286 The resulting spectrum of solar energetic particles at the Earth is also presented in Figure 1.., The resulting spectrum of solar energetic particles at the Earth is also presented in Figure \ref{fig:1}.287 As can be seen from Figure 1.. the spectrum of energetic particles above (he break 35 keV is identical to the spectrum of injected electrons so we can deduce (hese particles have indeed propagated scatter-Iree. (1η our model).," As can be seen from Figure \ref{fig:1}, the spectrum of energetic particles above the break $\sim 35$ keV is identical to the spectrum of injected electrons so we can deduce these particles have indeed propagated scatter-free (in our model)."288 The particles below the break energy do not propagate freely but generate electron plasma waves., The particles below the break energy do not propagate freely but generate electron plasma waves.289 The beam generated plasma waves drift in velocity-space toward lower phase velocities due to the solar wind density gradient (2).., The beam generated plasma waves drift in velocity-space toward lower phase velocities due to the solar wind density gradient \citep{Kontar01a}.290 This diit. caused by the decreasing ambient plasma density. takes waves out of resonance wilh the particles which generated them and so reduces the wave energy al a given point in phase space.," This drift, caused by the decreasing ambient plasma density, takes waves out of resonance with the particles which generated them and so reduces the wave energy at a given point in phase space."291 At lower phase velocities these waves can be more easilv absorbed bv the thermal plasma via Landau damping., At lower phase velocities these waves can be more easily absorbed by the thermal plasma via Landau damping.292 Therefore. particles arriving later to (this point in phase space are unable to restore the injected spectrum because ihey cannot absorb the same amount of energy [from the waves.," Therefore, particles arriving later to this point in phase space are unable to restore the injected spectrum because they cannot absorb the same amount of energy from the waves."293 This results in a [latter energy spectrum of electrons below some energv where beam-plasma interactions are importan (Figure 1))., This results in a flatter energy spectrum of electrons below some energy where beam-plasma interactions are important (Figure \ref{fig:1}) ).294and galaxies.,and galaxies.295 Observationallv. this requires constructing a colour-colour plot of all objects with a stellar morphology. using an optical colour and. a colour that straddles the band.," Observationally, this requires constructing a colour-colour plot of all objects with a stellar morphology, using an optical colour and a colour that straddles the H-band."296 In this paper we explore regions of the quasar colour-redshift space unavailable in previous work. and test a WX method variant.," In this paper we explore regions of the quasar colour-redshift space unavailable in previous work, and test a KX method variant."297 We aim to find the boundaries of the quasar colour-redshift. parameter space that is occupied., We aim to find the boundaries of the quasar colour-redshift parameter space that is occupied.298 In doing so. we will improve the estimate of the red quasar fraction and. possibly shed light on the mechanism that creates red quasars.," In doing so, we will improve the estimate of the red quasar fraction and possibly shed light on the mechanism that creates red quasars."299 In testing a IN method variant. we intend to verily if is a viable method of selecting quasars. without bias. fromit the entire quasar colour-redshift parameter space.," In testing a KX method variant, we intend to verify if it is a viable method of selecting quasars, without bias, from the entire quasar colour-redshift parameter space."300 We intend to apply a INN method variant to our quasar sample. and then contrast it with established methods of selecting potential quasars for spectroscopic follow-up.," We intend to apply a KX method variant to our quasar sample, and then contrast it with established methods of selecting potential quasars for spectroscopic follow-up."301 To achieve these. goals we use a sub-sample of the quasars identified in the Fornax Cluster Spectroscopic Survey (PCSS) (Drinkwaterctal.2000)... a spectroscopic survey of all extended objects to ο=19.8 ancl point sources to 5;=21.5.," To achieve these goals we use a sub-sample of the quasars identified in the Fornax Cluster Spectroscopic Survey (FCSS) \citep{2000A&A...355..900D}, a spectroscopic survey of all extended objects to $b_J = 19.8$ and point sources to $b_J = 21.5$."302 The sub-sample consists of all quasars that mateh to an object in Ixs-band. imaging to a depth of Wo= I&4. obtained using the Infrared Imager and Spectrograph 2. (1182) instrument on the 3.92-m. Anelo-Australian Telescope (AAT).," The sub-sample consists of all quasars that match to an object in Ks-band imaging to a depth of K = 18.4, obtained using the Infrared Imager and Spectrograph 2 (IRIS2) instrument on the 3.92-m Anglo-Australian Telescope (AAT)."303 The Ixs-band imaging is deeper than 2ALASS allowing us to explore parts of theb;fy colour space unavailable in Glikmanetal.(2004)... which was limited το 5;ἰν 25 by the Ix — 14.5 magnitude limit of 2MLASS.," The Ks-band imaging is deeper than 2MASS allowing us to explore parts of the$b_J - K$ colour space unavailable in \citet{2004ApJ...607...60G}, which was limited to $b_J - K \geq$ 5 by the K = 14.5 magnitude limit of 2MASS."304 Furthermore. the quasar sample used: covers a larger range of redshift than was examined. in Hopkinsοἱal.(2004):Richardset (2003).. whieh were limited. to z= 2.2.," Furthermore, the quasar sample used covers a larger range of redshift than was examined in \citet{2004AJ....128.1112H,2003AJ....126.1131R}, which were limited to z $\leq$ 2.2."305> Because the FCSS used no selection. criteria. our quasar sample is bias free. ancl ideal for testing the ability of the KX method to select. quasars from a Ix. magnitude limited survey.," Because the FCSS used no selection criteria, our quasar sample is bias free, and ideal for testing the ability of the KX method to select quasars from a K magnitude limited survey."306 Xdditionallv. most of the FCSS objects have a U magnitude as well as a b; magnitude. allowing the IXX method to be cirectlv contrasted with tracitional methocs for optically selecting quasars.," Additionally, most of the FCSS objects have a U magnitude as well as a $b_J$ magnitude, allowing the KX method to be directly contrasted with traditional methods for optically selecting quasars."307 The structure of this paper is as follows., The structure of this paper is as follows.308 In Section 2 the datasets used in this paper are described., In Section \ref{data} the datasets used in this paper are described.309 Section 3 details the detection of red. quasars in the quasar sample and an analysis of the quasar sample., Section \ref{redquasars} details the detection of red quasars in the quasar sample and an analysis of the quasar sample.310 This analysis involves a comparison of the b;A colours of the sample quasars to LBQS quasars and a —determination of the ellect of our selection on the quasar sample constructed here., This analysis involves a comparison of the $b_J - K$ colours of the sample quasars to LBQS quasars and a determination of the effect of our selection on the quasar sample constructed here.311 Section 3 concludes with the caleulation of the fraction of red quasars., Section \ref{redquasars} concludes with the calculation of the fraction of red quasars.312 The effectiveness of the KX method is assessed in Section and Following this are our conclusions in Section 5.., The effectiveness of the KX method is assessed in Section \ref{testKX} and following this are our conclusions in Section \ref{conclusion}.313 The sample of quasars used. here and their. photomoetric information were obtained by combining three datasets., The sample of quasars used here and their photometric information were obtained by combining three datasets.314 Astrometry and optical photometry were obtained. from the Automatic Plate Measuring CATaloguc (APAICAT) of POSS/UIST sky survey plates (Irwin.Maddox.&MeMa-hon 1994)., Astrometry and optical photometry were obtained from the Automatic Plate Measuring CATalogue (APMCAT) of POSS/UKST sky survey plates \citep{APMCAT}. .315. IRIS2 imaging was used to obtain the Ix- photometry used here., IRIS2 imaging was used to obtain the K-band photometry used here.316 The. necessary. spectroscopic identifications were provided by the Fornax Cluster Spectroscopic Survey (ο) catalogue of(2000)., The necessary spectroscopic identifications were provided by the Fornax Cluster Spectroscopic Survey (FCSS) catalogue of.317. “Phe datasets were combined by. independently matching the astrometry of WKW-hand catalogue objects and FOSS objects to that of APMICAT catalogue objects., The datasets were combined by independently matching the astrometry of K-band catalogue objects and FCSS objects to that of APMCAT catalogue objects.318 In the rest of this section. we describe the datasets in more detail.," In the rest of this section, we describe the datasets in more detail."319 The FCSS catalogue is a blind. spectroscopic survey of Fornax objects in the APAICAT catalogue., The FCSS catalogue is a blind spectroscopic survey of Fornax objects in the APMCAT catalogue.320 Phe ECSS is an ideal source of spectroscopic identifications because the lack of target selection precludes biasing., The FCSS is an ideal source of spectroscopic identifications because the lack of target selection precludes biasing.321" In the FCSS. spectroscopy was carried out on all exteneled sources to 5,:19.8 and all point sources to by<21.5."," In the FCSS, spectroscopy was carried out on all extended sources to $b_J \leq 19.8$ and all point sources to $b_J \leq 21.5$."322 Not every source was spectroscopically observed. and the fraction of observed sources is referred to as the spectroscopic completeness.," Not every source was spectroscopically observed, and the fraction of observed sources is referred to as the spectroscopic completeness."323 The FOSS obtained a redshift ancl spectroscopic. identification or more than of the objects observed. referred o as the redshift completeness.," The FCSS obtained a redshift and spectroscopic identification for more than of the objects observed, referred to as the redshift completeness."324 In. most. cases where a spectroscopic identification could not be obtained. neither =vas a recshift because of the poor spectrum quality.," In most cases where a spectroscopic identification could not be obtained, neither was a redshift because of the poor spectrum quality."325 Because o redshift completeness was Consistently high for the entire FOSS. we have combined the redshift) completeness. with )0 spectroscopic completeness. and throughout the paper Ίο term ‘completeness’ refers. to this combination.," Because the redshift completeness was consistently high for the entire FCSS, we have combined the redshift completeness with the spectroscopic completeness, and throughout the paper the term `completeness' refers to this combination."326" The completeness of the FCSS is for by«20.5. for 20.5xb,<<21 and for 21«b;21.5 sources."," The completeness of the FCSS is for $b_J < 20.5$, for $20.5 \leq b_J < \leq 21$ and for $21 < b_J \leq 21.5$ sources."327 We account for the completeness bv appropriately weighting quasars during our analysis in later sections., We account for the completeness by appropriately weighting quasars during our analysis in later sections.328 IRIS2 was used in December 2001 to obtain IExs-band imaging using GOs exposures., IRIS2 was used in December 2001 to obtain Ks-band imaging using 60s exposures.329 Phe raw data were processed using the Observatory. Reduction and. Acquisition Control project - Data Reduction pipeline (OILAC-DIU) outlined in Eeonomouetal.(1999):Jenness&Economou(1999).," The raw data were processed using the Observatory Reduction and Acquisition Control project - Data Reduction pipeline (ORAC-DR) outlined in \citet{1999ASPC..172...11E,1999ASPC..172..171J}."330. The reduced LRIS2 imaging dataset was then analvsed with SExtractor (Bertin&Arnouts1996) to obtain a photometric catalogue of corrected: isophotal magnitudes., The reduced IRIS2 imaging dataset was then analysed with SExtractor \citep{1996A&AS..117..393B} to obtain a photometric catalogue of corrected isophotal magnitudes.331 Corrected isophotal magnitucles were used instead of PSE or small aperture magntiudes. because PSE and small aperture magnitudes minimise anv possible. extended: contribution o the llux of sources in the URIS? imaging.," Corrected isophotal magnitudes were used instead of PSF or small aperture magntiudes, because PSF and small aperture magnitudes minimise any possible extended contribution to the flux of sources in the IRIS2 imaging."332 The Exs-xxl catalogue magnitude zero-point was then calibrated. » matching point sources in the Wks-band catalogue o the 2MLASS point source catalogue.," The Ks-band catalogue magnitude zero-point was then calibrated, by matching point sources in the Ks-band catalogue to the 2MASS point source catalogue."333 Calibrating also acilitated the conversion [rom Ixs magnitudes to the Ix-band magnitudes used throughout this paper., Calibrating also facilitated the conversion from Ks magnitudes to the K-band magnitudes used throughout this paper.334 After calibration. he magnitude limit of the K-band photometry was found ο be 18.4 magnitudes.," After calibration, the magnitude limit of the K-band photometry was found to be 18.4 magnitudes."335 In the FCSS. quasars were spectroscopically identified as objects with broad. permitted lines with a measured. full width half-maximum > 1100 km «s5 (Meveretal.20010..," In the FCSS, quasars were spectroscopically identified as objects with broad permitted lines with a measured full width half-maximum $>$ 1100 km $s^{-1}$ \citep{2001MNRAS.324..343M}."336" After matching the LRIS2 imaging catalogues and the FC!5 quasar identifications to the APMCAT. object. positions using blind matching. to a radius of 107: a catalogue of all the necessary photometry was created. and. all quasars within both the LRIS2 imaging Ix magnitude limit. and the FOSS spectroscopic identifications 6, magnitude limit were identified."," After matching the IRIS2 imaging catalogues and the FCSS quasar identifications to the APMCAT object positions using blind matching, to a radius of 10""; a catalogue of all the necessary photometry was created, and all quasars within both the IRIS2 imaging K magnitude limit, and the FCSS spectroscopic identifications $b_J$ magnitude limit were identified."337 This resulted in a sample of 69 spectroscopicallv identified. quasars with U. 5; and Ix magnitudes.," This resulted in a sample of 69 spectroscopically identified quasars with U, $b_J$ and K magnitudes."338 All 69 of these quasars are APAICAT point sources: therefore. our quasar sample is limited to A:18.4 and 5;< 21.5.," All 69 of these quasars are APMCAT point sources; therefore, our quasar sample is limited to $K \leq 18.4$ and $b_J \leq 21.5$ ."339 Of these 69 quasars. 62 have an It magnitude as required by our WN method. variant.," Of these 69 quasars, 62 have an R magnitude as required by our KX method variant."340 Phe missing Ro magnitudes are caused. by the dillerent magnitude limits in the 5; and Ro bands of the APMCAT catalogue. 22.5 and 21 magnitudes respectively.," The missing R magnitudes are caused by the different magnitude limits in the $b_J$ and R bands of the APMCAT catalogue, 22.5 and 21 magnitudes respectively."341 ~ -—1 ~LO100 ~LOO ~1200 25 LL15 are ~1.2«10? objects with more than 100 maenitiude nieasuremoenuts., $\sim$ $\sim$ $\sim10-100$ $\sim400$ $\sim 1200$ $-$ $14-15$ are $\sim1.2\times10^5$ objects with more than 100 magnitude measurements.342 Details of our variable selection procedure and general properties of variables found in DASCII scans near ALLL are described in Taug et al. (, Details of our variable selection procedure and general properties of variables found in DASCH scans near M44 are described in Tang et al. (34320105).,2010b).344 These variables showed unusual ~1 mag cimininegs ou timescales from 10 to 100 vr in their lighteurves. as slow in black dots iu Figure 1.," These variables showed unusual $\sim$ 1 mag dimmings on timescales from 10 to 100 yr in their lightcurves, as shown in black dots in Figure 1."345 Όλος JO83038.5|110713 (hereafter JOSSO0: named by its equatorial coordinate iu J2000: CSC2.5.2 catalog mune N2313102213) declined for l mag iu a century., DASCH J083038.5+140713 (hereafter J0830; named by its equatorial coordinate in J2000; GSC2.3.2 catalog name N2313102243) declined for 1 mag in a century.346" It is classified as à MISC"" variable in ASAS (ASAS JOs3038|1107.3: Pojmanshki. C. 2002) since it became 0.3 mae brighter iu V eracdually frou 2003 to 2007. and then became 0.1 mae fainter from 2008 to 2009."," It is classified as a `MISC' variable in ASAS (ASAS J083038+1407.3; Pojmanski, G. 2002) since it became 0.3 mag brighter in V gradually from 2003 to 2007, and then became 0.1 mag fainter from 2008 to 2009."347 DASCII J075115.9ο4L. (hereafter JO0751: CSC2.3.2 name N2211330177: ASAS JOT5116|1611.7) showed a sharp decrease around 1930. and then slowly recovered in 10 vears.," DASCH J075445.9+164141 (hereafter J0754; GSC2.3.2 name N2211330177; ASAS J075446+1641.7) showed a sharp decrease around 1930, and then slowly recovered in 10 years."348 Another dip was shown around 1592. but uufortuuatelv we can not constrain the hehtcurve profile of the dip due to the lack of data.," Another dip was shown around 1892, but unfortunately we can not constrain the lightcurve profile of the dip due to the lack of data."349 DASCII J073606.5|211131 (hereafter JOT36: CSC2.3.2 name N2230030699: ASAS JOT3607|2111.2) showed a 1 mae dip from 1930s to 1950s., DASCH J073606.5+211411 (hereafter J0736; GSC2.3.2 name N2230030699; ASAS J073607+2114.2) showed a 1 mag dip from 1930s to 1950s.350 Both J075{ aud JOT36 are new variables found with DASCTI., Both J0754 and J0736 are new variables found with DASCH.351 The lightcwrves of color variatious back in time would coustrain variable extinction. but is difficult to derive from DASCTI.," The lightcurves of color variations back in time would constrain variable extinction, but is difficult to derive from DASCH."352 The majority of the Harvard plate collection are blue scusitive plates; and a small fraction of plates usec filters to produce red aud vellow seusitive casurements with details of waveleneth respouses unavailable.," The majority of the Harvard plate collection are blue sensitive plates, and a small fraction of plates used filters to produce red and yellow sensitive measurements with details of wavelength responses unavailable."353 Ta order to generate consistent maguitiudes. we did color-term fitting for the plates in auuular bius to derive the effective color-term C in plates (Laycock. et al.," In order to generate consistent magnitudes, we did color-term fitting for the plates in annular bins to derive the effective color-term $C$ in plates (Laycock et al."354 2010). where C of a given plate is defined by where im is the effective magnitude intheplate.D dsthe GSC? DB inagnitude aud Rois the GSC2 R ," 2010), where $C$ of a given plate is defined by where $m$ is the effective magnitude intheplate,$B$ isthe GSC2 $B$ magnitude and $R$ is the GSC2 $R$ "355aand 3.2<10°!cres.. respectively. if they are in 66752.,"and $3.2\times 10^{31}$, respectively, if they are in 6752."356 The spectral type of 11 is not known: ou the basis of its maeuitucde aud colour (V=9.99. 0.5) the star could be a late F star at a distance of ~ lppe.," The spectral type of 1 is not known; on the basis of its magnitude and colour $V=9.99$, $B-V=0.5$ ) the star could be a late F star at a distance of $\sim154$ pc."357 At this distance and for an assumed unabsorbed L.tkkeV bremesstralline spectrum. the couutrate of 119 converts to an N-ray luminosity in the 0.5-2.5kkeV baud of ~3«1075cres.. a reasonable value for a late Ε niün-sequeuce star (see tthe list of ROSAT detections of bright stars by IIünusch et 11998).," At this distance and for an assumed unabsorbed keV bremsstrahlung spectrum, the countrate of 19 converts to an X-ray luminosity in the keV band of $\sim3\times10^{28}$, a reasonable value for a late F main-sequence star (see the list of ROSAT detections of bright stars by Hünnsch et 1998)."358 The Tycho Catalogue marks this star with unresolved duplieitv. with visual magnitude varving between 9.51 aud 10.58.," The Tycho Catalogue marks this star with 'unresolved duplicity', with visual magnitude varying between 9.51 and 10.88."359 991235 has a significant parallax which puts it at ppc., 94235 has a significant parallax which puts it at pc.360 Its couutrate converts to an X-ray luminosity at that distance of about 2.107?cres.. a normal X-ray bunuinositv for a GOV star.," Its countrate converts to an X-ray luminosity at that distance of about $2\times10^{29}$, a normal X-ray luminosity for a G0V star."361" Comparison of the ROSAT image with the USNO-A2 Catalogue eives a candidate identification for 116. at a distance of 272, see roftabb.."," Comparison of the ROSAT image with the USNO-A2 Catalogue gives a candidate identification for 16, at a distance of $2\farcs2$, see \\ref{tabb}."362 No other sources outside the cluster have been icleutified Vv Us., No other sources outside the cluster have been identified by us.363 We have analysed the three separate WRI observations. and find no evidence for wviriablilitv. except for X115. which in Miuch 1992 had an X-ray flux about half of that observed in March 1995 aud April 1996.," We have analysed the three separate HRI observations, and find no evidence for variablility, except for 15, which in March 1992 had an X-ray flux about half of that observed in March 1995 and April 1996."364 The globular cluster 11 is a highly reddened cluster near the galactic center (lyz9.5. d.= s.Glpc. Froeel et 11995).," The globular cluster 1 is a highly reddened cluster near the galactic center $A_{\rm V}\simeq9.5$, $d=8.6\,$ kpc, Frogel et 1995)."365 It probably has undergone core collapse (Djorgovski 1993)., It probably has undergone core collapse (Djorgovski 1993).366 11 harbours theBurster.. a highly unusual recurrent transient.," 1 harbours the, a highly unusual recurrent transient."367 When discovered iu 1977 the source enmütted short (35 ss) bursts of N-vavs every odO ss: in some later observations. AÀug 1985. it enüttec bursts of ~ 5002s separated by ss: au it has also been observed as a steady source.," When discovered in 1977 the source emitted short $\ltap5$ s) bursts of X-rays every $\sim10$ s; in some later observations, Aug 1985, it emitted bursts of $\sim500$ s separated by s; and it has also been observed as a steady source."368 The bursts are interpreted as accretion eveuts, The bursts are interpreted as accretion events.369 Iun addition to these. thermounuclear bursts have also been detected. identifviue the accreting star as a neutron star.," In addition to these, thermonuclear bursts have also been detected, identifying the accreting star as a neutron star."370 A review of this remarkable source is given by Lewin et ((1995)., A review of this remarkable source is given by Lewin et (1995).371 A low-Iununositv N-rav source near 11 is teutatively identified as the quiescent (low-state) counterpart of the Rapid Burster (Asai et 11996)., A low-luminosity X-ray source near 1 is tentatively identified as the quiescent (low-state) counterpart of the Rapid Burster (Asai et 1996).372 No source is detected in the cluster in our ROSAT IIRI observation of the globular cluster Liller 1., No source is detected in the cluster in our ROSAT HRI observation of the globular cluster Liller 1.373" Near the cluster center. no circle with radius of 5"" coutains more than 1 photous."," Near the cluster center, no circle with radius of $\arcsec$ contains more than 4 photons."374 For an expected umuber of 10 photons. the probability of getting Lor fewer photous is less than.," For an expected number of 10 photons, the probability of getting 4 or fewer photons is less than."375 We thus take 10 as the 2-0 upper μπιτ to the number of photons. which with the effective exposure finie is converted to au upper Init of: 0.6," We thus take 10 as the $\sigma$ upper limit to the number of photons, which with the effective exposure time is converted to an upper limit of 0.6."376 Axai et ((1996) report the detection on 1993 Ane : with ASCAÀ of a source near 11., Asai et (1996) report the detection on 1993 Aug 27 with ASCA of a source near 1.377 For a powerlaw with photon index: :2. absorbed by a column δι.=MNLO--ciu57. this source has an unabsorbed flux in the 210 keV baud of 25lli«10ασ7s," For a powerlaw with photon index 2, absorbed by a column $\nh=10^{22}\cmsq$, this source has an unabsorbed flux in the 2–10 keV band of $2.5^{+1.7}_{-0.8}\times10^{-13}\,\ergcms$."378" For this spectrum our upper lanit in the ROSAT IIRI correspouds to a flux of 1.1«10Perecmὃς1, slightly lower than the ASCA detection."," For this spectrum our upper limit in the ROSAT HRI corresponds to a flux of $1.4\times10^{-13}\,\ergcms$, slightly lower than the ASCA detection."379 The ROSAT DRI detects a source with a countrate of Letsksec aabout  frou the cluster center., The ROSAT HRI detects a source with a countrate of 1 about $'$ from the cluster center.380" The statistical error iu the position of this source is about 1”: the actual error is dominated by the error iu the bore sight correction. which is abou 5""."," The statistical error in the position of this source is about $''$; the actual error is dominated by the error in the bore sight correction, which is about $''$."381 The ROSAT source is not compatible with the ceuter of 11. and also not compatible with the position of the Rapid Burster as determined with Eiusteiu (sco roftal]xs) .," The ROSAT source is not compatible with the center of 1, and also not compatible with the position of the Rapid Burster as determined with Einstein (see \\ref{tabpos}) )."382 The position of the ROSAT source coincides within the bore sight uncertainty with the OL III) star (Vijapurkar DDrilling 1993)., The position of the ROSAT source coincides within the bore sight uncertainty with the O4 III(f) star (Vijapurkar Drilling 1993).383 The star is iu the Twcho Catalogue as 7738011., The star is in the Tycho Catalogue as 1.384 Frou the observed magnitude and colours (V=10.12. 5.V—0.92.0 B=0.23. Drilling 1991) we estimate a reddening aud distance of E(BV)z aud dx 3kkpe for 3317889.," From the observed magnitude and colours $V=10.12$, $B-V=0.92$, $U-B=-0.23$, Drilling 1991) we estimate a reddening and distance of $E(B-V)\simeq1.2$ and $d\simeq3$ kpc for 317889."385" The observed ROSAT IIRI couutrate is as expected for such a star. according to the eeueral correlation between bolometric Iuminosity and N-ray luminosity of O stars: Ly~loL, IWihvudritzki et 11996)."," The observed ROSAT HRI countrate is as expected for such a star, according to the general correlation between bolometric luminosity and X-ray luminosity of O stars: $L_x\simeq10^{-7}L_b$ Kudritzki et 1996)."386 3317888 is within 1” of the Ol star: we have not been able to fiud more information on this star.), 317888 is within $''$ of the O4 star; we have not been able to find more information on this star.)387 We can interpret the ROSAT aud ASCA observatious in two wavs., We can interpret the ROSAT and ASCA observations in two ways.388 The first aud mest likely is that ASCA incleed did detect the Rapid Burster inquiescence. or auother low-Iuniuositv source in 11: aud that ROSAT observed when this source had a ower fiux level.," The first and most likely is that ASCA indeed did detect the Rapid Burster in quiescence, or another low-luminosity source in 1; and that ROSAT observed when this source had a lower flux level."389 Iu fact. variation of transicuts in their quiescent state is conuuion CCampana et 11997).," In fact, variation of transients in their quiescent state is common Campana et 1997)."390 The star detected with ROSAT in this case is not detected with ASCA. presiunalbly because its spectrun is too soft.," The star detected with ROSAT in this case is not detected with ASCA, presumably because its spectrum is too soft."391 The second interpretation is that ASC'À in fact detected the star also detected with ROSAT. aud not the quiescent counterpart of the Rapid Durster.," The second interpretation is that ASCA in fact detected the star also detected with ROSAT, and not the quiescent counterpart of the Rapid Burster."392 The position of the ROSAT source is marginally compatible with that of the ASCA source: its countrate is exactly that predicted ou the basis of the ASCA source., The position of the ROSAT source is marginally compatible with that of the ASCA source; its countrate is exactly that predicted on the basis of the ASCA source.393" AAsai has kindly communicated a new determination of the position of the N-rav. source detected by ASCA.,"," Asai has kindly communicated a new determination of the position of the X-ray source detected by ASCA,"394"where the Fourier component ὃς depends only on cosmic time f. and € and are the co-moving wavevector and radius, respectively.","where the Fourier component $\delta_\kappa$ depends only on cosmic time $t$ , and $\vec{\kappa}$ and are the co-moving wavevector and radius, respectively."395" In the linear regime, the «-th perturbative mode satisfies the equation where a dot signifies differentiation with respect to f, @=a(t) is the cosmic expansion factor we defined earlier. and v?=dp/dp is the adiabatic sound speed squared. in terms of the pressure p and energy density p (see, ¢.g., Tsagas 2002)."," In the linear regime, the $\kappa$ -th perturbative mode satisfies the equation where a dot signifies differentiation with respect to $t$, $a=a(t)$ is the cosmic expansion factor we defined earlier, and $v_s^2\equiv396dp/d\rho$ is the adiabatic sound speed squared, in terms of the pressure $p$ and energy density $\rho$ (see, e.g., Tsagas 2002)."397" The second term on the left is due to the cosmic expansion and always suppresses the erowth of 6,.", The second term on the left is due to the cosmic expansion and always suppresses the growth of $\delta_\kappa$.398 The combined term on the right reflects the conflict between gravity (4z]Gp/c7) and pressure support (—v247/«7)., The combined term on the right reflects the conflict between gravity $4\pi G\rho/c^2$ ) and pressure support $-{v_s^2\kappa^2/ a^2}$ ).399" Defining the proper wavelength of the perturbation 4|.=27a/x. one sees immediately that whether gravity or pressure support dominates depends on whether Jt is greater or smaller than the so-called Jeans length In the standard model, one solves Equation (35) by first choosing the constituents of the universe (e.g.. baryonic matter, cold dark matter. and radiation) contributing to p. adopting an equation of state to calculate p and therefore v,. and then integrating ὃς over time from an assumed set of initial conditions."," Defining the proper wavelength of the perturbation $\lambda\equiv 2\pi a/\kappa$, one sees immediately that whether gravity or pressure support dominates depends on whether $\lambda$ is greater or smaller than the so-called Jeans length In the standard model, one solves Equation (35) by first choosing the constituents of the universe (e.g., baryonic matter, cold dark matter, and radiation) contributing to $\rho$, adopting an equation of state to calculate $p$ and therefore $v_s$, and then integrating $\delta_\kappa$ over time from an assumed set of initial conditions."400" The origin of the initial seed perturbations is uncertain, one possible explanation being that they are quantum fluctuations boosted to macroscopic scales by inflation."," The origin of the initial seed perturbations is uncertain, one possible explanation being that they are quantum fluctuations boosted to macroscopic scales by inflation."401" The primordial power spectrum is usually assumed to have a power-law dependence on scale, with a scale-invariant spectral index #=|. and an unknown normalization factor A that must be determined observationally."," The primordial power spectrum is usually assumed to have a power-law dependence on scale, with a scale-invariant spectral index $n=1$, and an unknown normalization factor $A$ that must be determined observationally."402" The initial conditions for the solution to Equation (35) follow from this because at any redshift z, the power spectrum may also be written so the starting size of the fluctuation is Equation (35) is adequate for most applications, but not in situations where the pressure is à significant fraction of p."," The initial conditions for the solution to Equation (35) follow from this because at any redshift $z$, the power spectrum may also be written so the starting size of the fluctuation is Equation (35) is adequate for most applications, but not in situations where the pressure is a significant fraction of $\rho$."403" In general relativity, both p and p contribute to the “active” mass inducing curvature, as evidenced by the appearance of both p andp in Equations (4) and (5)."," In general relativity, both $\rho$ and $p$ contribute to the “active"" mass inducing curvature, as evidenced by the appearance of both $\rho$ and$p$ in Equations (4) and (5)."404" Thus, to analyze the growth of perturbations in an A),=cf universe, we must resort to the relativistic version"," Thus, to analyze the growth of perturbations in an $R_{\rm h}=ct$ universe, we must resort to the relativistic version"405could also contribute to the observed sub-Iinear dependence On CODO Miss.,could also contribute to the observed sub-linear dependence on core mass.406 The exchange or conversion of energies that occurs during an encounter takes place over a finite period of lime. so dH is important to specify whether or not the system has fully relaxed post-encounter when discussing the remaining stellar configuration.," The exchange or conversion of energies that occurs during an encounter takes place over a finite period of time, so it is important to specify whether or not the system has fully relaxed post-encounter when discussing the remaining stellar configuration."407 For one thing. Sillsetal.(2001) showed: that. although collision products may be in hyelrodynanic equilibrium. they are not. in thermal equilibrium. upon formation ancl so contract on a thermal time-scale.," For one thing, \citet{sills01} showed that, although collision products may be in hydrodynamic equilibrium, they are not in thermal equilibrium upon formation and so contract on a thermal time-scale."408 Simulations also suggest that most merger products should be rapid rotators (Sillsetal.2002. 2005).," Simulations also suggest that most merger products should be rapid rotators \citep{sills02, sills05}."409. However. at least in the case of blue stragelers. this is rarely supported bv. the observations.," However, at least in the case of blue stragglers, this is rarely supported by the observations."410 Some mechanism for angular momentum loss must. therefore be operating either during or after the merger takes place in order to spin down the remnant., Some mechanism for angular momentum loss must therefore be operating either during or after the merger takes place in order to spin down the remnant.411 The time-scale considered must also be sullicienthy short that subsequent dynamical interactions are unlikely to have occurred since these could alfect the total energy and momentum of the system., The time-scale considered must also be sufficiently short that subsequent dynamical interactions are unlikely to have occurred since these could affect the total energy and momentum of the system.412 With this last. point. in mind. N-body simulations considering. BS [formation have shown that after they are formed. 5 are often exchanged into other multiple star systems (Llurleyctal.2005).," With this last point in mind, N-body simulations considering BS formation have shown that after they are formed, BSs are often exchanged into other multiple star systems \citep{hurley05}."413.. This suggests that for multiple star svstems containing more than one Bs. the DSs could. have first been formed: separately or. in parallel. and then exchanged into their presently observed configuration.," This suggests that for multiple star systems containing more than one BS, the BSs could have first been formed separately or in parallel, and then exchanged into their presently observed configuration."414 For the case of SIOS2. this would. require at least 3 separate dynamical interactions.," For the case of S1082, this would require at least 3 separate dynamical interactions."415 Given that the derived. times between encounters are relatively long and the fact that the most likely formation scenario is usually. that for which the number of encounters is minimized. the current state of M67 suggests that the probability of 510532 having formed from a scenario involving 3 encounters is low.," Given that the derived times between encounters are relatively long and the fact that the most likely formation scenario is usually that for which the number of encounters is minimized, the current state of M67 suggests that the probability of S1082 having formed from a scenario involving 3 encounters is low."416 Conversely. the derived encounter time-scales in NGC 18S are sullicientlv short that many of the BS binaries could have experienced. a subsequent dynamical interaction after their formation.," Conversely, the derived encounter time-scales in NGC 188 are sufficiently short that many of the BS binaries could have experienced a subsequent dynamical interaction after their formation."417 BSs tend to be more massive than normal MS stars. contributing to an increase in their. eravitationally-focussecl cross section for collision.," BSs tend to be more massive than normal MS stars, contributing to an increase in their gravitationally-focussed cross section for collision."418 This suggests that the encounter time-scale for multiple star systems. containing BSs is slightly shorter than for otherwise identical svstenmis composed. only of normal MS stars., This suggests that the encounter time-scale for multiple star systems containing BSs is slightly shorter than for otherwise identical systems composed only of normal MS stars.419 This contributes to à slight increase in the probability that a BS will experience an exchange encounter after it is formed., This contributes to a slight increase in the probability that a BS will experience an exchange encounter after it is formed.420 Ónterestinglv. it could also contribute to an increase in the probability that a close binary containing two BSs will form during an encounter between two different multiple star svstenis each containing their own Bss (Mathieu&Geller(2009): lt. Mathieu. private communication).," Interestingly, it could also contribute to an increase in the probability that a close binary containing two BSs will form during an encounter between two different multiple star systems each containing their own BSs \citet{mathieu09}; R. Mathieu, private communication)."421 This is because it is the heaviest stars that will experience. the strongest eravitational focussing ancl are therefore the most likely to experience a close encounter. end up in a closely. bound configuration. or even merge.," This is because it is the heaviest stars that will experience the strongest gravitational focussing and are therefore the most likely to experience a close encounter, end up in a closely bound configuration, or even merge."422 Most exchange interactions will involve. wide binarics for which the cross section for collision is large., Most exchange interactions will involve wide binaries for which the cross section for collision is large.423 Since wide binaries are typically relatively soft and the hardest binary involved in the interaction will usually determine the orbital energy of the left-over BS binary. most exchange interactions will leave the periods of BS binaries relatively unalfectecd.," Since wide binaries are typically relatively soft and the hardest binary involved in the interaction will usually determine the orbital energy of the left-over BS binary, most exchange interactions will leave the periods of BS binaries relatively unaffected."424 This need not be the case. of course. provided one or more stars are ejected from the system with a very high escape velocity.," This need not be the case, of course, provided one or more stars are ejected from the system with a very high escape velocity."425 With these last points in mind. we have assumed hroughout our analysis that all binaries and. triples are dynamically hard.," With these last points in mind, we have assumed throughout our analysis that all binaries and triples are dynamically hard."426 This is à reasonable assumption since he hard-soft. boundary. corresponds to a period. of ~10) davs in both M67 and NGC ISS. for which the cross section or collision is sullicicntly large that we do not expect such xnaries to survive for very lone.," This is a reasonable assumption since the hard-soft boundary corresponds to a period of $\sim 10^6$ days in both M67 and NGC 188, for which the cross section for collision is sufficiently large that we do not expect such binaries to survive for very long."427 Nonetheless. considerations such as these must be properly taken into account when isolating a preferred formation scenario ancl predicting the inal clistribution of energies.," Nonetheless, considerations such as these must be properly taken into account when isolating a preferred formation scenario and predicting the final distribution of energies."428 We have presented. an analytic technique to constrain he dynamical origins of multiple star systems containing one or more DSs., We have presented an analytic technique to constrain the dynamical origins of multiple star systems containing one or more BSs.429 Our results suggest. that. in ol open clusters. most dynamical interactions resulting in mergers involve triple stars.," Our results suggest that, in old open clusters, most dynamical interactions resulting in mergers involve triple stars."430 LE most. triples are forme dynamically. this could suggest that many. stellar. mergers are the culmination of a hierarchical build-up of dsnamica interactions.," If most triples are formed dynamically, this could suggest that many stellar mergers are the culmination of a hierarchical build-up of dynamical interactions."431 Consequently. this mechanism for BS formation should be properly included in future N-bods simulations of cluster evolution.," Consequently, this mechanism for BS formation should be properly included in future N-body simulations of cluster evolution."432 A better understanding of the interplay tween the cluster dynamics and the internal evolution of triple svstems is needed in order to better understanc 10 expected. period distribution of BS binaries formed from riples., A better understanding of the interplay between the cluster dynamics and the internal evolution of triple systems is needed in order to better understand the expected period distribution of BS binaries formed from triples.433 Simulations will therefore need to track both the ormation and destruction of triples as well as their interna evolution via Ixozai eveles. stellar and binary evolution. etc.," Simulations will therefore need to track both the formation and destruction of triples as well as their internal evolution via Kozai cycles, stellar and binary evolution, etc."434 On the observational front. our results highlight the nee or a more detailed knowledge of binary and especially triple »opulations in clusters.," On the observational front, our results highlight the need for a more detailed knowledge of binary and especially triple populations in clusters."435 The gravitationallv-Ffocused. cross sections for. 111. 112. 2|2. 113. 2|3 and 313 collisions can be found. using Equation 6 [rom Leonard.(1989).," The gravitationally-focused cross sections for 1+1, 1+2, 2+2, 1+3, 2+3 and 3+3 collisions can be found using Equation 6 from \citet{leonard89}."436. Neglecting the first term and assuming that binary and. triple stars are on average tice and three times as massive as single stars. respectively. this gives for the various collisional cross sections: Values for the pericenters assumed for the various types of encounters are shown in Table Al.. where A? is the average stellar racius. αρ is the average binary semi-major axis anc," Neglecting the first term and assuming that binary and triple stars are on average twice and three times as massive as single stars, respectively, this gives for the various collisional cross sections: Values for the pericenters assumed for the various types of encounters are shown in Table \ref{table:peri}, where $R$ is the average stellar radius, $a_b$ is the average binary semi-major axis and"437. Neglecting the first term and assuming that binary and. triple stars are on average tice and three times as massive as single stars. respectively. this gives for the various collisional cross sections: Values for the pericenters assumed for the various types of encounters are shown in Table Al.. where A? is the average stellar racius. αρ is the average binary semi-major axis ancl," Neglecting the first term and assuming that binary and triple stars are on average twice and three times as massive as single stars, respectively, this gives for the various collisional cross sections: Values for the pericenters assumed for the various types of encounters are shown in Table \ref{table:peri}, where $R$ is the average stellar radius, $a_b$ is the average binary semi-major axis and"438Iu discussing the position augle. 7. of the leus trajectory. WO are LO concerned with the case of spherically απλο] expanding shells. for which the microlensing effects are independent of 5 a fixed dyfrg.,"In discussing the position angle, $\gamma$, of the lens trajectory, we are not concerned with the case of spherically symmetric expanding shells, for which the microlensing effects are independent of $\gamma$ at fixed $d_0/\rein$."439 However. this is uot hne case for a rotatiic shell. because even if the shell desity is spherical. the isovelocity zones im the rotating case are nof axially ποίαο about the sieht (except for a poe-on viewiue perspective}.," However, this is not the case for a rotating shell, because even if the shell density is spherical, the isovelocity zones in the rotating case are not axially symmetric about the line-of-sight (except for a pole-on viewing perspective)."440" Figure 7 shows microleused line profiles for four values of 5=Ww. 9”, 2TV. and 3157.ro"," Figure \ref{fig:f7} shows microlensed line profiles for four values of $\gamma = 0^\circ$, $45^\circ$, $270^\circ$, and $315^\circ$."441 The position augle Is niecasured couutercockwise frou the Y axis which is assuned coincident with the projected axis of rotation., The position angle is measured counterclockwise from the $Y$ –axis which is assumed coincident with the projected axis of rotation.442 Ilence. 5=(Vv runs parallel to the projected rotation axis in the direction vottom to top. and ~=2707 runs orthogonal to that axis from left to right.," Hence, $\gamma=0^\circ$ runs parallel to the projected rotation axis in the direction bottom to top, and $\gamma=270^\circ$ runs orthogonal to that axis from left to right."443 The simulations are for fixed values of ra/rg=1.0 and ορ=0.3., The simulations are for fixed values of $\rsh/\rein = 1.0$ and $d_0/\rein = 0.3$.444 Let us first compare the two cases of +=07 and 2707, Let us first compare the two cases of $\gamma=0^\circ$ and $270^\circ$.445" Recall that the isovelocity zones are circular rines that are seen as linear strips iu projection. thus for 5;=07 he lens trajectory runs along the strip with dur,3. corresponding to Wop.=0.3."," Recall that the isovelocity zones are circular rings that are seen as linear strips in projection, thus for $\gamma=0^\circ$, the lens trajectory runs along the strip with $d_0/\rsh = 0.3$ , corresponding to $\wobs=0.3$."446 €ousequenutlv. the peal auplification awars appears at this velocity shift in the xofile.," Consequently, the peak amplification always appears at this velocity shift in the profile."447" For =270"". the leus transits eac1 Isovelocity strip. aud the result. as iu the pxvious fieures. is that he peak amplification smoothly migrates across the line xofile with time."," For $\gamma=270^\circ$, the lens transits each isovelocity strip, and the result, as in the previous figures, is that the peak amplification smoothly migrates across the line profile with time."448 Now for lei» trajectories that are oblique relative o the rotation axis (as is the case for >15? aud 3157). the leus does not trausi all of the isoveocity stilos," Now for lens trajectories that are oblique relative to the rotation axis (as is the case for $\gamma=45^\circ$ and $315^\circ$ ), the lens does not transit all of the isovelocity strips."449 Neither does the lens position at muni mipact xuwneter lie along the isovelocity strip of zero velocity shift., Neither does the lens position at minimum impact parameter lie along the isovelocity strip of zero velocity shift.450 The coIBCGUCTICE as SCCIL iu Fig., The consequence as seen in Fig.451 7 is tha the Oai; amplification moves simoothlv across the profile mut is sienificautly ereater than unitv only for those velocity shifts where the correspouding isoveocity zones are trausitted bv the Ίος., \ref{fig:f7} is that the peak amplification moves smoothly across the profile but is significantly greater than unity only for those velocity shifts where the corresponding isovelocity zones are transitted by the lens.452 Eurtjer. we have plotte dashed the line profile correspouclue o when the location of the lens is dyraj.," Further, we have plotted as dashed the line profile corresponding to when the location of the lens is $d_0/\rsh$."453 The peaς amplification at tus tine is uot at line center., The peak amplification at this time is not at line center.454 The evolution of the peak auplificati relative to this time is different for >=0 than for 3157, The evolution of the peak amplification relative to this time is different for $\gamma=45^\circ$ than for $315^\circ$.455 We couclude that the value of 5 Way be recovered front profile evolution by virtue of where the peak auplifica occurs in the Lue profile when the leus is at the positio nuiunmuun inipact parameter combined with how the peak. aüuplificatioun evolves across the line relative to that ti, We conclude that the value of $\gamma$ may be recovered from the profile evolution by virtue of where the peak amplification occurs in the line profile when the lens is at the position of minimum impact parameter combined with how the peak amplification evolves across the line relative to that time.456 This paper has focussed on the cittects of nucrolensiug or the shapes of cussion liue pxfiles frou expanding or rotating extended spherical siclls., This paper has focussed on the effects of microlensing for the shapes of emission line profiles from expanding or rotating extended spherical shells.457 From the liue xofile simulations. it appears that wicrolensing. which is rormally use as a luicaus of constraining f1e properties of the lens. oxovides a unique and powerful probe of he stellar sotrco environnent.," From the line profile simulations, it appears that microlensing, which is normally used as a means of constraining the properties of the lens, provides a unique and powerful probe of the stellar source environment."458 We fud that mucrolensing can be used to infer the velocity field of he flow. the ratios rag/rg and dyfrg. aud the orientation of the leus rajectorv 5 in the case of rotation.," We find that microlensing can be used to infer the velocity field of the flow, the ratios $\rsh/\rein$ and $d_0/\rein$, and the orientation of the lens trajectory $\gamma$ in the case of rotation."459 Although our treatnent has been hiehv simplified. his work represents an iutial investigation iuto a broad ranec of diagnostics for cqetuustellar envelope structure roni nuücrolensius events.," Although our treatment has been highly simplified, this work represents an initial investigation into a broad range of diagnostics for circumstellar envelope structure from microlensing events."460" Tere we sunmnuuidze aveuues of ""uture research ou this topic:", Here we summarize avenues of future research on this topic:461The most aportaut source of containimatioun in a CMD experiment likePlenck will come from the residual of astroplivsical foreerounds.,The most important source of contamination in a CMB experiment like will come from the residual of astrophysical foregrounds.462 In fact. althoueh the wide fequency coverage. possibly complemented bx WALAP maps and grouud-based anc balloou-borue experiment daais particularly advantageous for a precise removal of astrophysical signals from the maps aud the accurate maponus of CAIB anisotropics. nevertheless we expect that a certain level of residual coutamination will remain into CMD maps. particularly in polarization.," In fact, although the wide frequency coverage, possibly complemented by WMAP maps and ground-based and balloon-borne experiment data, is particularly advantageous for a precise removal of astrophysical signals from the maps and the accurate mapping of CMB anisotropies, nevertheless we expect that a certain level of residual contamination will remain into CMB maps, particularly in polarization."463 Miuiv methods of componen separation. cach with its own pros and cons. have been auk are continuously elaborated for the analysis of PlanchaItiftequency maps (see Leachetal.(2008) aud reerences tiere).," Many methods of component separation, each with its own pros and cons, have been and are continuously elaborated for the analysis of multifrequency maps (see \citet{2008A&A...491..597L} and references therein)."464 Ta the present work. we are interested iu the residiuUs from astrophysical forcerounds affecting the reccovery of the CMD aneular power spectrum.," In the present work, we are interested in the residuals from astrophysical foregrounds affecting the recovery of the CMB angular power spectrum."465 It is typically eiven as a clitference between the input CAIB angular power spectrum aud the CAIB augular power spectrum estimate after the couiponenut separation laver., It is typically given as a difference between the input CMB angular power spectrum and the CMB angular power spectrum estimated after the component separation layer.466 Ii genera. if is not so mcaninetul to provide a description of foreeround residuals cliffereut a ifereut frequencies. siuce. by definiion. the comonent se]aration laver exploits exactly the iiultifrequeucy lapping of he sky.," In general, it is not so meaningful to provide a description of foreground residuals different at different frequencies, since, by definition, the component separation layer exploits exactly the multifrequency mapping of the sky."467 Thus. the estimate adopted in this wors have to Happly to the whole xcTof frequency channels.," Thus, the estimate adopted in this work have to apply to the whole set of frequency channels."468 Differcl methods show different residuals a various ranges of niultipoles., Different methods show different residuals at various ranges of multipoles.469 The imultipole depeudence. or. iu ot101) words. hesrape of this residual also depends on the cousiered nxthod.," The multipole dependence, or, in other words, the shape of this residual also depends on the considered method."470 Concerning residuals for the TZ mode. recet πιαος (Leacheal.2008) show residual shapes only slightly dependent o1 the multipole. with iuuplitudes 1 the rauge the exact value depending ou the method aad. for each method. ou t1e particular multiple baud. with typical variations of about.," Concerning residuals for the $T$ mode, recent simulations \citep{2008A&A...491..597L} show residual shapes only slightly dependent on the multipole, with amplitudes in the range the exact value depending on the method and, for each method, on the particular multiple band, with typical variations of about."471". Iu this work. we model his T spurious power as flat iu C,((6|1)."," In this work, we model this $T$ spurious power as flat in $ C_\ell \; \ell \; (\ell+1) $."472 Galactic polarized foreground. (mainly roni diffuse svuchrotrou and dust οςΙΟ) affects CAIB angular power spectrin recovery nixe sieuificautlv iu pol:wization than in tempcraure., Galactic polarized foreground (mainly from diffuse synchrotron and dust emission) affects CMB angular power spectrum recovery more significantly in polarization than in temperature.473 We expect that their residual after component separation will taxe outiallvs memory of t1e original shape of the oreground power spectrum. oein particular at large scales where they she»v much more power han the CMB.," We expect that their residual after component separation will take partially memory of the original shape of the foreground power spectrum, in particular at large scales where they show much more power than the CMB."474 Again. different methods eive diiffereut residuals. regarding both multipole depeidence and amplitude.," Again, different methods give different residuals, regarding both multipole dependence and amplitude."475 Iu this work. we mode the foreground residual for the TEL mode aud E and £2 maiodes (assuured to be equal. B = E) as the sum of two srapes. the first one (dominant at low multipoles) described by the foreround. shape propervy rescaled in amplitude. the second one constructed from the foreground shape properly rescaed in amplitude aud ¢hanged in slope.," In this work, we model the foreground residual for the $TE$ mode and $E$ and $B$ modes (assumed to be equal, $B$ = $E$ ) as the sum of two shapes, the first one (dominant at low multipoles) described by the foreground shape properly rescaled in amplitude, the second one constructed from the foreground shape properly rescaled in amplitude and changed in slope."476 Fie., Fig.477 2 displays o1 rovsfarfius conservaive models for the residuals in TE mode iud in polarization modes., \ref{foreres_TE_EE} displays our “starting” conservative models for the residuals in $TE$ mode and in polarization modes.478 We let us the freedom t«» 3nplyv rescale them with iultiplicative factors in order to address tvveal level of foregrouud residuals for which t1e inipact on our cosmological aimi is not critical (see also Sect. 15)]., We let us the freedom to simply rescale them with multiplicative factors in order to address typical level of foreground residuals for which the impact on our cosmological aim is not critical (see also Sect. \ref{subsec:param}) ).479 All the svsteinatic effects discussed above. coming fron instrunmeutal effect. «kv signal. or from their coupling. cau be cousidered in two cüffereut schemes.," All the systematic effects discussed above, coming from instrumental effect, sky signal, or from their coupling, can be considered in two different schemes."480 ithe frst. simplest case. they can be treated as sources of spurious additional uoise power. ic. they do not introduce abjas affecting the recovery of the estimation of the CND augular power spectrum but hey increase our uncertainty inits recovery.," In the first, simplest case, they can be treated as sources of spurious additional noise power, i.e. they do not introduce a bias affecting the recovery of the estimation of the CMB angular power spectrum but they increase our uncertainty in its recovery."481 Therefore. the effect can be modeled ading nu qualrature the quoted C; of the power of the residual SVScluatics to those comune from seusitivitv. resolution. aud cosuic plus sampling variance.," Therefore, the effect can be modeled adding in quadrature the quoted $ C_\ell $ of the power of the residual systematics to those coming from sensitivity, resolution, and cosmic plus sampling variance."482 This approach is equivalent toswstune that we will be able to properly model aud ναibtract a οςπου estimation for he systematic eftects so that ouly a statistical uncertainty m their subtraction will aftect the data., This approach is equivalent to assume that we will be able to properly model and subtract a correct estimation for the systematic effects so that only a statistical uncertainty in their subtraction will affect the data.483 I1 another. more critical approach. one can assunie o nüss the correct estimation ¢X the spurious effects.," In another, more critical approach, one can assume to miss the correct estimation of the spurious effects."484 Their SVScluatic effects will be then 1mch more dramatic. ic. they will iutroduce also a bias 1i the estimation of the CAIB aneular power spectimm.," Their systematic effects will be then much more dramatic, i.e. they will introduce also a bias in the estimation of the CMB angular power spectrum."485 This case can be modeled “perπαιο the €; to be compared with the exact model lmearly acine the additional spurious power as described above., This case can be modeled “perturbing” the $ C_\ell $ to be compared with the exact model linearly adding the additional spurious power as described above.486 I reeneral. we do not use in this work a precise (still not completely available) description of the considered svstematic effects. but oulv suitable representations of them.," In general, we do not use in this work a precise (still not completely available) description of the considered systematic effects, but only suitable representations of them."487 Therefore. we will use our estimations to understand if the considered classes of svsteiiatic effects may siguificautlv affect the cosmological exploitation ofPlanch data with respect to the determination of cosmological paraiueters possibly by rescaling the eximation quoted above.," Therefore, we will use our estimations to understand if the considered classes of systematic effects may significantly affect the cosmological exploitation of data with respect to the determination of cosmological parameters possibly by rescaling the estimation quoted above."488 This is done with the aini of identifvius the corresponding levels at which it is necessary to coitrol the systematic effects in order to avoid to spoil the scientific accuracy of thePlanck data., This is done with the aim of identifying the corresponding levels at which it is necessary to control the systematic effects in order to avoid to spoil the scientific accuracy of the data.489" We technically nupleimeit this rescaling with a multiplicative coustant on the residuals of systematic effects on the C, described in the previots sections.", We technically implement this rescaling with a multiplicative constant on the residuals of systematic effects on the $ C_\ell $ described in the previous sections.490 We describe in this section the theoretical basis of our simulations whe experimental errors are treated as statistical noise., We describe in this section the theoretical basis of our simulations when experimental errors are treated as statistical noise.491 This includes the iustriueutal white noise as well as the residuals frou svstematic errors and foregrounds as described iu the previous section., This includes the instrumental white noise as well as the residuals from systematic errors and foregrounds as described in the previous section.492 In other words. we asstme that the noise contribution to the observed CMD skies," In other words, we assume that the noise contribution to the observed CMB skies"493These parameters are constrained by the available observational data on each source and reasonable theoretical considerations.,These parameters are constrained by the available observational data on each source and reasonable theoretical considerations.494 In the following section. we describe the procedure used to obtain the particle distributions along the jet and the radiative output that then arises.," In the following section, we describe the procedure used to obtain the particle distributions along the jet and the radiative output that then arises."495 The existence of heavy jets magnetically driven in AGN and microquasars has been supported by several scientific works in the last few years., The existence of heavy jets magnetically driven in AGN and microquasars has been supported by several scientific works in the last few years.496 For example. conclude that mildly relativistic proton-electron jets might be formed by magnetocentrifugal launching by inner portion. of magnetized disks around rotating black holes.," For example, conclude that mildly relativistic proton-electron jets might be formed by magnetocentrifugal launching by inner portion of magnetized disks around rotating black holes."497 This leads to a triple-component jet structure: proton-electron component sourrounded by the relativistic pair-dominated sheat., This leads to a triple-component jet structure: proton-electron component sourrounded by the relativistic pair-dominated sheat.498 The final speed of this centrifugal outflow depends strongly on the disk vertical structure which is certainly unknown., The final speed of this centrifugal outflow depends strongly on the disk vertical structure which is certainly unknown.499 However. for barionie outflows to reach mildly relativistic speeds. some inital boost would be neccesary. which would be produced by heating or mechanically. by flaring activity and/or by radiation pressure.," However, for barionic outflows to reach mildly relativistic speeds, some inital boost would be neccesary, which would be produced by heating or mechanically, by flaring activity and/or by radiation pressure."500 Previous work by has proved the existence of a relativistic and baryon-loaded jet in Cygnus X-] and that the bulk of the kinetic energy is carried by cold protons. as in the case of SS 433.," Previous work by has proved the existence of a relativistic and baryon-loaded jet in Cygnus X-1 and that the bulk of the kinetic energy is carried by cold protons, as in the case of SS 433."501 For further information about magnetically launched jets see (2).. where the production. acceleration. collimation. and composition of jets are well explained.," For further information about magnetically launched jets see , where the production, acceleration, collimation, and composition of jets are well explained."502 The model developed for this work is based on the energy distribution of the different particle populations along the jet., The model developed for this work is based on the energy distribution of the different particle populations along the jet.503 These are obtained as solutions of a 1-dimensional steady-state transport equation that includes the relevant cooling terms and a convective one., These are obtained as solutions of a 1-dimensional steady-state transport equation that includes the relevant cooling terms and a convective one.504 The radiative output is obtained in the jet reference frame. where the particle distributions are isotropic. and the result is transformed back to the observer frame.," The radiative output is obtained in the jet reference frame, where the particle distributions are isotropic, and the result is transformed back to the observer frame."505 The procedure begins with the calculation of the distribution of primary electrons along the jet taking into account synchrotron and adiabatic cooling., The procedure begins with the calculation of the distribution of primary electrons along the jet taking into account synchrotron and adiabatic cooling.506 After that. the synchrotror radiation emitted by the primary electrons can be calculated.," After that, the synchrotron radiation emitted by the primary electrons can be calculated."507 To check that the electron distribution is consistent with the energy loss mechanisms operating. the synchrotron cooling rate must be much greater than the inverse Compton (IC) one due to electrons interacting. with. the. synchrotron photons (SSC).," To check that the electron distribution is consistent with the energy loss mechanisms operating, the synchrotron cooling rate must be much greater than the inverse Compton (IC) one due to electrons interacting with the synchrotron photons (SSC)."508 If this 15 the case. it means that the main cooling is due to synchrotron radiation. and neglecting the IC energy loss is a valid approximation to obtain the electron distribution.," If this is the case, it means that the main cooling is due to synchrotron radiation, and neglecting the IC energy loss is a valid approximation to obtain the electron distribution."509 If the SSC cooling can not be neglected. then the transport equation becomes more complicated and a different approach is needed ?).," If the SSC cooling can not be neglected, then the transport equation becomes more complicated and a different approach is needed ."510. Having obtained the electron distribution. the next step is to calculate the distribution of primary protons taking into account the cooling due to synchrotron emission. adiabatic expansion. pp and py interactions.," Having obtained the electron distribution, the next step is to calculate the distribution of primary protons taking into account the cooling due to synchrotron emission, adiabatic expansion, $pp$ and $p\gamma$ interactions."511 The latter two types of interactions yield the production. of secondary pions. muons. and electron-positron pairs.," The latter two types of interactions yield the production of secondary pions, muons, and electron-positron pairs."512 These three populations of particles are also described with the transport equation. ane the radiative output that they produce is also considered.," These three populations of particles are also described with the transport equation, and the radiative output that they produce is also considered."513 According to. e.g. and?.. it can be seen that in the present scenario. IC cascades are suppressed by the synchrotror cooling of secondary e7. since the magnetic field is greater than 10 G in the regions of the jet where emission takes place.," According to, e.g. and, it can be seen that in the present scenario, IC cascades are suppressed by the synchrotron cooling of secondary $e^\pm$, since the magnetic field is greater than $10$ G in the regions of the jet where emission takes place."514" Therefore. we neglect the effect of IC cascading anc calculate the synchrotron emission of the secondary electrons and positrons,"," Therefore, we neglect the effect of IC cascading and calculate the synchrotron emission of the secondary electrons and positrons."515 In this section we present all the relevant expressions usec in this model., In this section we present all the relevant expressions used in this model.516 We discuss on the injection of primary particles. the relevant cooling rates. the transport equation used. the injection of secondary particles. and the emission of photons and neutrinos.," We discuss on the injection of primary particles, the relevant cooling rates, the transport equation used, the injection of secondary particles, and the emission of photons and neutrinos."517 Q'&E'.2):- (5) -K Here. N; represents the total number of relativistic electrons (i= e) or protons (j= p). and the cut-off energy is obtained from the balance of particle gains and losses.," Q'_i(E',z) := ) = Here, $\mathcal{N}_i$ represents the total number of relativistic electrons $i=e$ ) or protons $i=p$ ), and the cut-off energy is obtained from the balance of particle gains and losses."518 These processes are described below., These processes are described below.519 The injection function can be transformed to the observer frame by taking into account that is a Lorentz invariant22)., The injection function can be transformed to the observer frame by taking into account that is a Lorentz invariant.520". From this. it follows that the particle injection in the observer frame 1s given by ΟΕ.z)= [iQue E-r, (ue- right)."," From this, it follows that the particle injection in the observer frame is given by Q_i(E,z)= E'= (E- )."521 The normalization constant A; is found in each case using the power in relativistic species Z4. integrating in the energy. solid angle. and volume ofthe acceleration zone Az]," The normalization constant $K_i$ is found in each case using the power in relativistic species $L_{\{e,p\}}$, integrating in the energy, solid angle, and volume ofthe acceleration zone$z\in[z_{\rm acc},z_{\rm acc}+\Delta z]$ ):"522how auch more (or less) probable model Lis than model 2. iu light of the data.,"how much more (or less) probable model 1 is than model 2, in light of the data."523" Traditionally. this is eauecd on Jeffrews scale where a Bayes factor of luBy»«l is labeled ‘incouclusive’ evidence for model 1 over model 2 while weak. moderate. and “strong” evidence corresponds to InBy values <2.5. «5. aud >4h, respectively."," Traditionally, this is gauged on Jeffrey's scale where a Bayes factor of $\ln B_{12}<1$ is labeled `inconclusive' evidence for model 1 over model 2 while `weak', `moderate', and `strong' evidence corresponds to $\ln B_{12}$ values $<2.5$, $<5$, and $>5$, respectively."524 We choose priors which are constaut in the logarithius of r» and p2., We choose priors which are constant in the logarithms of $r_{-2}$ and $\rho_{-2}$.525 The flat logarithmic prior is the uiufonuative prior for scaling parameters (Trotta2008) since it reflects ignorance about the maguitude of the xuwanmeter., The flat logarithmic prior is the uninformative prior for scaling parameters \citep{2008ConPh..49...71T} since it reflects ignorance about the magnitude of the parameter.526 Dowever we restrict the range of the priors. so that we end up with top-hat priors in logr» and ogD2.," However we restrict the range of the priors, so that we end up with top-hat priors in $\log r_{-2}$ and $\log \rho_{-2}$."527 As a reference point we first assume a top-hat xior relative to the best estimate of ro3og as determined in the MC analvsis. (, As a reference point we first assume a top-hat prior relative to the best estimate of $r_{2500}$ as determined in the MC analysis. (528The scale radius (9399 is defined as he radius within which the mean deusity is 2500 times he critical density of the universe.),The scale radius $r_{2500}$ is defined as the radius within which the mean density is $2500$ times the critical density of the universe.)529 The top-hat prior in erο rauges from 1.5E magnitudes below rosyy fo 4.5 vausitionabove., The top-hat prior in $\log r_{-2}$ ranges from $1.5$ magnitudes below $r_{2500}$ to 0.5 above.530 The basic idea behind this prior is that the or roll of a model should occur close to 179399. as df does in haloes in nunuerical sinmmulations. aud also to xeveut the model from behaving as a simple power-law wo pushing the transition from the mner to the outer over law far away from the range of the data.," The basic idea behind this prior is that the transition or `roll' of a model should occur close to $r_{2500}$, as it does in haloes in numerical simulations, and also to prevent the model from behaving as a simple power-law by pushing the transition from the inner to the outer power law far away from the range of the data."531 We cluphasize that this is still a conservative prior. as current sinulatious typically resolve 2.23 radial magnitudes with re» located about one order of magnitude below the virial radius (Bullocketal.2001b)..," We emphasize that this is still a conservative prior, as current simulations typically resolve 2–3 radial magnitudes with $r_{-2}$ located about one order of magnitude below the virial radius \citep{2001MNRAS.321..559B}."532 The prior iu p2 is also a top-hat in the logarithim and a range of IR a a ⋅⋅ ⋅ ↓∩−↙⇂↓∩−↓↨↘↽∶↴∙⊾⋯⊽⋟∙↖↖↽↕∐↸⊳∐∐↕↻⋯↸⊳⊓∩∖∐∐∖⋜⋯↴∖↴↑∐⋜↧↑↑∐↸∖ [m ↕∐↘↽↸∖↕∐⋯∪≺↧↕↴∖↴↖↽⋜∐∐↴∖↴↕∐∐∩↕↖↽↴∖↴↕⊔⋜↧∐⋜↧↑↑↕∐∖↴⋝≺∏⋯≼↧⋜∐⋅↕↸∖↴∖↴∪↕≯↑∐↸∖ prior.," The prior in $\rho_{-2}$ is also a top-hat in the logarithm and a range of $10^{-26}$ $10^{-21}\,$ $\,$ $^{-3}$, which in practice means that the likelihood is vanishingly small at the boundaries of the prior."533" The result of the model comparison is sinmniamrized in Table 2.. where the NEW model is compared agaiust each of the other two-parameter models,"," The result of the model comparison is summarized in Table \ref{tb:bayes2}, where the NFW model is compared against each of the other two-parameter models."534 A positive Baves factor indicates that the NEW model is preferred., A positive Bayes factor indicates that the NFW model is preferred.535 This does uot imply aux bias ou the NEW since iu two models can be compared by subtracting the Baves factors we eive for them from one another., This does not imply any bias on the NFW since any two models can be compared by subtracting the Bayes factors we give for them from one another.536 We find that. individually. the clusters vield strong coustraits only agaistun the Moore model. while. the evidences. for. or against the MM and Heruquist models are either weak or inconclusive on Joeffrevs scale.," We find that, individually, the clusters yield strong constraints only against the Moore model, while the evidences for or against the M and Hernquist models are either weak or inconclusive on Jeffrey's scale."537 If iustead we consider the cuuulative Baves factor sunuued over the full zuuple. the NEW is found to be the preferred model overall. Ίου as a universal two-parameter profile our suuple favors the NFW ος.," If instead we consider the cumulative Bayes factor summed over the full sample, the NFW is found to be the preferred model overall, i.e., as a universal two-parameter profile our sample favors the NFW model."538 The Ieruquist profile and the MM. profile are weakly and moderately disfavored. els with cumulative Baves factors of 2.l and ithepee3.6 while the Moore profile is convincinely ruled out w a factor of 51.," The Hernquist profile and the M profile are weakly and moderately disfavored, respectively, with cumulative Bayes factors of 2.4 and 3.6 while the Moore profile is convincingly ruled out with a factor of 51."539 The weak coustraint on the Ueruquist profile is not surprising as data extending out to the virial radius would Likely be needed to properly distinguish this model frou the NFW., The weak constraint on the Hernquist profile is not surprising as data extending out to the virial radius would likely be needed to properly distinguish this model from the NFW.540 Tn Table 3 we present the effects of varving the priors., In Table \ref{tb:priors} we present the effects of varying the priors.541 The evidence against the MM profile increases to the evel of strong when we Πατ the rage of the prior iu logr» to the smaller interval (70.75.0.25).the while he Baves factor is reduced slightly ou larecr ranec (3.3).," The evidence against the M profile increases to the level of strong when we limit the range of the prior in $\log r_{-2}$ to the smaller interval $(-0.75,0.25)$, while the Bayes factor is reduced slightly on the larger range $(-3,3)$."542 The evidence also becomes stroug if we choose op-hat priors in (r».p2) instead of the logarithiuic xiors.," The evidence also becomes strong if we choose top-hat priors in $(r_{-2},\rho_{-2})$ instead of the logarithmic priors."543 Finally. the MM. model is disfavored slelthy nore if we apply a ‘soft’ Gaussiau prior iu logr.2.," Finally, the M model is disfavored slightly more if we apply a `soft' Gaussian prior in $\log r_{-2}$."544 The Daves factor for the Ποιοι model is robust under he same variations. while the Moore profile is very strouglv ruled out in all cases.," The Bayes factor for the Hernquist model is robust under the same variations, while the Moore profile is very strongly ruled out in all cases."545 We conclude that our wo-paraineter model selection results are stable against variation amonest reasonable choices of priors. which ues that the data are of sufficicut quality to make robust conclusions.," We conclude that our two-parameter model selection results are stable against variation amongst reasonable choices of priors, which means that the data are of sufficient quality to make robust conclusions."546 A amore interesting issue to consider than the priors is that the preference for the NEW profile over the Teruquist aud MM. profiles is somewhat susceptible Qjackkuite’ resampling: if we recompute the cumulative Daves factor eleven times systematically leaving a single cluster out each time. there are a few cases where he streneth of the evidence is reduced. to meouclusive mt also cases where it is iucreased to strong (agaist he DEAAD.," A more interesting issue to consider than the priors is that the preference for the NFW profile over the Hernquist and M profiles is somewhat susceptible to `jackknife' resampling: if we recompute the cumulative Bayes factor eleven times systematically leaving a single cluster out each time, there are a few cases where the strength of the evidence is reduced to inconclusive but also cases where it is increased to strong (against the M)."547 This is largely due to the fact that our data sample is somewhat inhomogencous in terms of he relative statistical uncertainty on the mass profile., This is largely due to the fact that our data sample is somewhat inhomogeneous in terms of the relative statistical uncertainty on the mass profile.548 For example. a comparison of the error bars of ALNW9 with those of ALT95 or Sévrsic 159-3 (see Figure 1)) mnuuediatelv shows that the former is much less constraining than the latter two.," For example, a comparison of the error bars of MKW9 with those of A1795 or Sérrsic 159-3 (see Figure \ref{fi:mass}) ) immediately shows that the former is much less constraining than the latter two."549 This means that our siuuple is à mixture of strongly and weakly coustrainiug clusters and this is reflected in Figure 2. where the contributious from individual clusters clearly varies., This means that our sample is a mixture of strongly and weakly constraining clusters and this is reflected in Figure \ref{fi:chart} where the contributions from individual clusters clearly varies.550" There appears to be a trend that the clusters A262 NOC533. and A196. which are the lowest redshift aud some of the least massive iu our sample. stand out bv preferring the MM, aud the Moore profile."," There appears to be a trend that the clusters A262, NGC533, and A496, which are the lowest redshift and some of the least massive in our sample, stand out by preferring the M and the Moore profile."551 However. such trends are just as likely spurious selection effects caused by the relatively simall sample but could be investigated with a larger sample.," However, such trends are just as likely spurious selection effects caused by the relatively small sample but could be investigated with a larger sample."552 The D&AMAL profile can easilv be preferred bw clusters that also prefer the Moore profile since. by extending the transition region. the D&MM profile can push the iuner asvinptotic power law well inside the radial range of the data.," The M profile can easily be preferred by clusters that also prefer the Moore profile since, by extending the transition region, the M profile can push the inner asymptotic power law well inside the radial range of the data."553 Finally we compare with a standard goodnessoffit test: the miunuun 47 values for the models support our more detailed analysis: for a total of 53 degrees of freedom we get nàüunmimn s of S1 for the NFW.," Finally we compare with a standard goodness–of–fit test: the minimum $\chi^2$ values for the models support our more detailed analysis: for a total of 53 degrees of freedom we get minimum $\chi^2$ 's of 81 for the NFW, 93"554from a sinele initial UIE οταν photou could be sienificautly larger than the muuberof J-decav clectrous.,from a single initial UHE $\gamma$ -ray photon could be significantly larger than the numberof $\beta$ -decay electrons.555 Therefore iu case of comparable powers in the neutron aud sanuus-ray coniponeuts of the neutral beam. as expected for FR2 radio quasars (Atovan&Dermer2003). the totalniimber of leptons with 10' needed for the second electrou population iu the knots would be deteriuued bv the 5-rav component of the ΤΠ: neutral beam.," Therefore in case of comparable powers in the neutron and gamma-ray components of the neutral beam, as expected for FR2 radio quasars \citep{ad03}, the total of leptons with $\gamma \gg 10^7$ needed for the second electron population in the knots would be determined by the $\gamma$ -ray component of the UHE neutral beam."556" Tu the statiouary-frame maguctic field By,= Lye upstream of the shock (corresponding to comovingEM] D5,,Qf~D«Bay3oT1 LOpG) thexο electrons cool to cucreics uring time Af=Af),kyr since their production in the jet fiuid aud until they are overtaken by the radius relativistic shock."," In the stationary-frame magnetic field $B_{up.\perp} \gtrsim 1 \, \rm557\mu$ G upstream of the shock (corresponding to comoving $B^{\prime}_{up.\perp} \sim558\Gamma \times B_{up.\perp} \gtrsim 10\,\rm \mu G$ ) these electrons cool to energies during time $\Delta t = \Delta t_{kyr} \,\rm kyr$ since their production in the jet fluid and until they are overtaken by the trailing relativistic shock."559 Note that our model does not require an extremely ordered maguctic field along the jet. although stretching of tle pre-existing interealactic magnetic field alone the jet isa very plausible outcome of the decaving neutral can and appearance of the beam of charged UIE secoudazics driving the extended jet.," Note that our model does not require an extremely ordered magnetic field along the jet, although stretching of the pre-existing intergalactic magnetic field along the jet is a very plausible outcome of the decaying neutral beam and appearance of the beam of charged UHE secondaries driving the extended jet."560 Because the ine of injection for different electrons would be different. a broad spectrun of ultrarclativistic ele pairs up to their enerev at production. will be overtaken.," Because the time of injection for different electrons would be different, a broad spectrum of ultrarelativistic $e^+$ $e^{-}$ pairs up to their energy at production, will be overtaken."561 The cnhauced maguetic field downstream of the shock results in rapid radiative losses. a “lighting up” these electrons aud the appearance of an X-ray knot.," The enhanced magnetic field downstream of the shock results in rapid radiative losses, a “lighting up” these electrons and the appearance of an X-ray knot."562 Iu case of 2»44i29107. the cooling svuchrotron PAectrumn with ay~0.5 is produced.," In case of $\gamma_{2.\rm min} \gg 10^8$, the cooling synchrotron spectrum with $\alpha_{X} \simeq 0.5$ is produced."563" A small tribution of electrous from the pai-photon cascade on the CAIBR. as discussed above. could effectively result in 22444,ZLO."," A small contribution of electrons from the pair-photon cascade on the CMBR, as discussed above, could effectively result in $\gamma_{\rm 2.min}564\lesssim 10^8$."565" It may also be the result of higher £,, aud louger cooling tine At. which in principle could reach =10? vrs at LOOEkpe distances."," It may also be the result of higher $B_{up.\perp}$ and longer cooling time $\Delta t$, which in principle could reach $\gtrsim 10^5\,$ yrs at $>100\,\rm kpc$ distances."566 In that case steeper svuclrotrou spectra at keV energies will be produced. as iu Fie.," In that case steeper synchrotron spectra at keV energies will be produced, as in Fig."567 2., 2.568 The external Compton model for exteuded N-rav jets faces difficulties with laree energy requirements. aud in explaining the different spatial profiles at radio. optical. aud N-ray frequencies.," The external Compton model for extended X-ray jets faces difficulties with large energy requirements, and in explaining the different spatial profiles at radio, optical, and X-ray frequencies."569 Tt also cannot be invoked to explain knots and hot spots where the N-rav spectral iudices are sieuificautlv steeper than the radio spectral iudices. in which case a svuchrotron model is favored.," It also cannot be invoked to explain knots and hot spots where the X-ray spectral indices are significantly steeper than the radio spectral indices, in which case a synchrotron model is favored."570 The large cherey requirements in the EC model can be reduced to acceptable values only bx assuniueDoppler factors 6z10.," The large energy requirements in the EC model can be reduced to acceptable values only by assumingDoppler factors $\delta \geq57110$."572 Iu these cases. the jet would have to be directed towards us at very sinall angles of oulv 0<67.," In these cases, the jet would have to be directed towards us at very small angles of only $\theta \leq 6^\circ $."573" Although we cannot exclude that the nunber of X-ray jets with such stall angles could still be significant. the probability for one of the 2 jets of any quasar to be directed within such an angle is ouly Py=(1.cos0)/2x<8.7«10H0/G""y."," Although we cannot exclude that the number of X-ray jets with such small angles could still be significant, the probability for one of the 2 jets of any quasar to be directed within such an angle is only $P_\theta = (1-\cos574\theta)/2\pi \leq 8.7\times 10^{-4} (\theta/6^\circ)^2$."575 Allowing for X-ray jets with 0X207 will increase the probability to detect several such sources by several orders of magnitude., Allowing for X-ray jets with $\theta \lesssim 20^\circ$ will increase the probability to detect several such sources by several orders of magnitude.576 A common model for N-rav knots would then have to be able to deal with suticicutly laree 0 aud to allow debeamed jets with à<Dz10., A common model for X-ray knots would then have to be able to deal with sufficiently large $\theta$ and to allow debeamed jets with $\delta \ll \Gamma \simeq 10$.577 The cenerev demands for such jets become unrealistic iu the EC model., The energy demands for such jets become unrealistic in the EC model.578 The laree cucrey requirements are siguificantly relaxed for svuchrotrou models., The large energy requirements are significantly relaxed for synchrotron models.579 Svuchrotron X-ravs are produced by very high euergv clectrous with short cooling times. which nuüunuizes the injection power of clectrous needed to explain the N-rav flux.," Synchrotron X-rays are produced by very high energy electrons with short cooling times, which minimizes the injection power of electrons needed to explain the X-ray flux."580 For a wo-colmpouent svuchrotron model. unlike for the EC model. the magnetic feld is not limited bv the ratio of A-rav to radio fluxes and a eiven inclination anele (obtained. for example. by fixing the maxima possible Dopler factor).," For a two-component synchrotron model, unlike for the EC model, the magnetic field is not limited by the ratio of X-ray to radio fluxes and a given inclination angle (obtained, for example, by fixing the maximum possible Dopler factor)."581 This uinmuzes the total energv acciunulated iu the form of radio cutting electrons and maguctic fields iu the knot needed to explain the observed radio flux., This minimizes the total energy accumulated in the form of radio emitting electrons and magnetic fields in the knot needed to explain the observed radio flux.582 The comoving equipartition fields i FR2 knots are typically at the level ~DO 1004. which are higher than D-—10- Wwyee deduced from EC models.," The comoving equipartition fields in FR2 knots are typically at the level $\sim 50$ $100\,\rm \mu G$, which are higher than $B \sim 10$ $20 \,\rm \mu G$ deduced from EC models."583 The svuchrotron interpretation of A-ravs also allows one to have sienificautly debeamed jets aud still romain within i1 acceptable range for the energy budget. as iu the knots of 3C 273 (Fie.," The synchrotron interpretation of X-rays also allows one to have significantly debeamed jets and still remain within an acceptable range for the energy budget, as in the knots of 3C 273 (Fig."584 1)., 1).585 The relative advantage of svuchrotron models for debemned jets with 6<<DE is due esseutiallv to the more narrow beamline diaerain for the EC radiation than for the svuchrotron radiation iu the stationary frame (Dermer 1995).., The relative advantage of synchrotron models for debeamed jets with $\delta << \Gamma$ is due essentially to the more narrow beaming diagram for the EC radiation than for the synchrotron radiation in the stationary frame \citep{d95}. .586 This is the case when the photons are detected at an anele 0x L/T., This is the case when the photons are detected at an angle $\theta \gg 1/\Gamma$ .587 In the comoving frame such photons are produced in Compton ‘tail-ow collisions with beamed (nu the comoving frame) external photons, In the comoving frame such photons are produced in Compton `tail-on' collisions with beamed (in the comoving frame) external photons588Incidentally. it may be of some interest (ο compute the tidal parameter of Ser A* itself to see if its action could be detected from its influence on the motion of the solar svstem’s planets.,"Incidentally, it may be of some interest to compute the tidal parameter of Sgr $^{\ast}$ itself to see if its action could be detected from its influence on the motion of the solar system's planets."589 By assuming for it (Reid&Brunthaler2004) My=4x10M. and ry=8.5 kpe. we have which is 9 orders of magnitude siialler (han (he present-day level of accuracy in measuring A.," By assuming for it \citep{Rei04} $M_{\rm X}=4\times 10^6 M_{\odot}$ and $r_{\rm X}=8.5$ kpc, we have = which is 9 orders of magnitude smaller than the present-day level of accuracy in measuring $\mathcal{K}$."590 Let us. now. abandon the direction of GC. ancl. consequently. the MOND scenario. aud look at A as a [unction of the ecliptic longitude and latitude of X without assuming; any a-priori limitations on them.," Let us, now, abandon the direction of GC, and, consequently, the MOND scenario, and look at $\mathcal{K}$ as a function of the ecliptic longitude and latitude of X without assuming any a-priori limitations on them."591 Let us. first. use the Pitjeva result of(1).," Let us, first, use the Pitjeva result of."592. It turns out that the maximum value of A. and. consequently. the minimum value for rx. occurs for ie. perpendicularly to the ecliptic: The minimum for A. corresponding to the maximum for rx. occurs for ie. basically in the ecliptic: The heliocentric distances for X.are as follows," It turns out that the maximum value of $\mathcal{K}$ , and, consequently, the minimum value for $r_{\rm X}$, occurs for i.e. perpendicularly to the ecliptic; In this case, the distances of X, for different values of its postulated mass, are The minimum for $\mathcal{K}$, corresponding to the maximum for $r_{\rm X}$, occurs for i.e. basically in the ecliptic; The heliocentric distances for Xare as follows"593class CO).,class C0).594 The three active reeious with the low soft N-rav flaw levels appear to be quiescent. judeine from the GOES fux profile. or mav be subject to micro-flaring at a low level.," The three active regions with the low soft X-ray flux levels appear to be quiescent, judging from the GOES flux profile, or may be subject to micro-flaring at a low level."595 There is a clear correlation between the soft N-rav level of the active region (when it was on disk) and the overa Lunisaliguinent angle (Fig., There is a clear correlation between the soft X-ray level of the active region (when it was on disk) and the overall misalignment angle (Fig.596 11). as well as with the nuisalieumenut angle àyp attributed to the nou-potentialtv. varving from àyp~--%57 for the lowest €(OES A-class levels toe yp~--9° for an active region with a GOES C-class flare.," 11), as well as with the misalignment angle $\alpha_{NP}$ attributed to the non-potentiality, varying from $\alpha_{NP} \approx 5^\circ$ for the lowest GOES A-class levels to $\alpha_{NP} \approx 9^\circ$ for an active region with a GOES C-class flare."597 A higher soft X-ray flux οςnerallv meaus a üeher heating rate with stronger nhupulsive heaing or flaring., A higher soft X-ray flux generally means a higher heating rate with stronger impulsive heating or flaring.598 A hieier degree of nou-poteutialitv. on the other haud. indicates the presence of a higher level o: electric currents (which are non-potertial).," A higher degree of non-potentiality, on the other hand, indicates the presence of a higher level of electric currents (which are non-potential)."599 Therefore. the observed correlation suggests a physical relationship between the eectric currents m an active region aud he amount of heating input.," Therefore, the observed correlation suggests a physical relationship between the electric currents in an active region and the amount of heating input."600" This 1s not surprisiis. since evidence for current-carrving eniYeiug fux was denonstratec previously for Ho aud soft N-rav structires that are no»teutial (οιοι, Leka et al."," This is not surprising, since evidence for current-carrying emerging flux was demonstrated previously for $\alpha$ and soft X-ray structures that are non-potential (e.g., Leka et al."601 1996: Jiao e al., 1996; Jiao et al.602 1997: Schinieder et al., 1997; Schmieder et al.603 1996)., 1996).604 Ou nieasurenmient of the degree «X 10n-potenutialitv with the magnetic field άμαοτιnent averaged over the entire active regkn. Is a VOYV COσιe technique. but à more detailed investigation of the misaligniieut iu separate parts of he active regio- hat are quiesceut or flaring will be pursued im Paper II.," Our measurement of the degree of non-potentiality with the magnetic field misalignment averaged over the entire active region, is a very coarse technique, but a more detailed investigation of the misalignment in separate parts of the active region that are quiescent or flaring will be pursued in Paper II."605 The agreement between theoretical magnetic field models of active regious iu the solar corona with the true 3-D magnetic field as delimeated from the stereoscopic triaugulation of coronal loops in EUV waveleusthlis has never been quantified uutil the recent advent of the STEREO iiissiou., The agreement between theoretical magnetic field models of active regions in the solar corona with the true 3-D magnetic field as delineated from the stereoscopic triangulation of coronal loops in EUV wavelengths has never been quantified until the recent advent of the STEREO mission.606" To evervbodvs surprise. the average nuüsaliennnient between the theoretical aud observed maguetie field was quite substautial. in the amount of à,,;,2207LO for both potential aud noulinear force-free field models (DeRosa ct al."," To everybody's surprise, the average misalignment between the theoretical and observed magnetic field was quite substantial, in the amount of $\alpha_{mis} \approx 20^\circ-40^\circ$ for both potential and nonlinear force-free field models (DeRosa et al."607 2009: Sandman et al., 2009; Sandman et al.608 2009)., 2009).609 In this study we investigate the various contributions of this large misaligunent for four different active regions observed with STEREO aud arrive at the following conclusions:, In this study we investigate the various contributions of this large misalignment for four different active regions observed with STEREO and arrive at the following conclusions:610by observations (see. e.g.. Schmidt.Webster&Lewis1998:Daietal.2003:Vakulik2006:Fedorova 2008)).,"by observations (see, e.g., \citealt{Schmidt_98, Dai_03,611Vakulik_06, Fedorova_09}) )."612 Since the Einstein Cross is a very suitable object for microlensing studies. its images have been continuously monitored by clillerent eroups for more than a dozen of vears.," Since the Einstein Cross is a very suitable object for microlensing studies, its images have been continuously monitored by different groups for more than a dozen of years."613 In this svstem. significant microlensing-induced brightness peaks on light curves of the quasar images were detected (sec. ee. Wozniaketal.2000:Alcaldect2002:Moreau 2005)).," In this system, significant microlensing-induced brightness peaks on light curves of the quasar images were detected (see, e.g., \citealt{wozniak_00, alcald_02, Moreau_05}) )."614 We now apply formula (23)) to the fitting of the light curves near LLAL., We now apply formula \ref{eq18}) ) to the fitting of the light curves near HAE.615 For a moving source. 3;—V5(6fe). where (is the ime. fer is the time of the crossing of the caustic by the source centre. V; is the projection of the source velocity on the axis yy.," For a moving source, $Y_{i} = V_i \left( {t - t_C } \right)$, where $t$ is the time, $t_C $ is the time of the crossing of the caustic by the source centre, $V_i $ is the projection of the source velocity on the axis $y_i $."616 We suppose that 152V4. Le. the source crosses the caustic elfectively ancl does not move along it.," We suppose that $V_2 >617> V_1 $, i.e. the source crosses the caustic effectively and does not move along it."618 Our numerical simulations rave shown that the terms depending upon the coordinate s contribute only for small angles between the source trajectory and the tangent to the caustic., Our numerical simulations have shown that the terms depending upon the coordinate $s$ contribute only for small angles between the source trajectory and the tangent to the caustic.619 Therefore. we do not take them into account. and. correspondingly. the parameter € is not involved into consideration.," Therefore, we do not take them into account, and, correspondingly, the parameter $Q$ is not involved into consideration."620 Introducing the parameter 7=L/[V5|. we obtain h—Ελ) (the sign 17 corresponds to he source motion along the positive direction of the yo axis).," Introducing the parameter $T = L621\mathord{\left/ {\vphantom {L {\left| {V_2 } \right|}}} \right.622\kern-\nulldelimiterspace} {\left| {V_2 } \right|}$, we obtain $h = \pm623{\left( {t - t_C } \right)} \mathord{\left/ {\vphantom {{\left( {t624- t_C } \right)} T}} \right. \kern-\nulldelimiterspace} T$ (the sign “+” corresponds to the source motion along the positive direction of the $y_2 $ axis)."625 We consider the known ΗΛΙΟ in the light curve of image C of CLS (223710305 using the OGLE data recorded during 999 (Wozniaketal.2000)., We consider the known HAE in the light curve of image C of GLS Q2237+0305 using the OGLE data recorded during 1999 \citep{wozniak_00}.626. Let fy be the flux from image € when the microlensing is absent., Let $F_0 $ be the flux from image C when the microlensing is absent.627 Under the supposition that he proper brightness variations of the quasar in GLS can be neglected and taking expression (23)) for the amplification into account. we obtain the formula for fitting the Dux from the microlensed Gaussian source. which contains the parameters and fe and Yo which appear nonlinearly.," Under the supposition that the proper brightness variations of the quasar in GLS can be neglected and taking expression \ref{eq18}) ) for the amplification into account, we obtain the formula for fitting the flux from the microlensed Gaussian source, which contains the parameters and $t_C \mbox{ }$ and $T$ which appear nonlinearly."628 Phe quantity Av in the expression for tis a part of the amplification due to noncritical images., The quantity $K_0 $ in the expression for $A$ is a part of the amplification due to noncritical images.629 “Phe parameters οἱ and D. are evidently. positive. 2 is negative. and C can have values of both signs.," The parameters $A$ and $B$ are evidently positive, $D$ is negative, and $C$ can have values of both signs."630 As discussed above. the possibility to use the linear caustic approximation or formula (23)) is determined by the ratios of corrections cocllicicnts to the coellicient D of thezeroth approximation: C/D—LP.Dí/D-L&sj2. ," As discussed above, the possibility to use the linear caustic approximation or formula \ref{eq18}) ) is determined by the ratios of corrections coefficients to the coefficient $B$ of thezeroth approximation: $C \mathord{\left/ {\vphantom {C {B =631LP,}}} \right. \kern-\nulldelimiterspace} {B = LP,} \quad D632\mathord{\left/ {\vphantom {D {B = { - L\kappa } \mathord{\left/633{\vphantom {{ - L\kappa } 2}} \right. \kern-\nulldelimiterspace}6342}}} \right. \kern-\nulldelimiterspace} {B = { - L\kappa }635\mathord{\left/ {\vphantom {{ - L\kappa } 2}} \right.636\kern-\nulldelimiterspace} 2}$."637To fit the light curve. we used the minimization of the weighted sum of squares: where Ly is the result. of the i-th measurement. and Wy=1/67 is its weight that is expressed through the corresponding dispersion estimate a; (Woziiaketal.2000).," To fit the light curve, we used the minimization of the weighted sum of squares: where $F_i$ is the result of the $i$ -th measurement, and $W_i = 1 \mathord{\left/ {\vphantom {1 {\sigma638_i^2 }}} \right. \kern-\nulldelimiterspace} {\sigma _i^2 }$ is its weight that is expressed through the corresponding dispersion estimate $\sigma _i $ \citep{wozniak_00}."639. The fitting quality is often characterized hy the parameter \7—Sup. ν being the number of degrees of freedom.," The fitting quality is often characterized by the parameter $\chi ^2 = {S_{\min } } \mathord{\left/ {\vphantom640{{S_{\min } } \nu }} \right. \kern-\nulldelimiterspace} \nu $, $\nu $ being the number of degrees of freedom."641 The value of this parameter in the optimal case should tend to 1., The value of this parameter in the optimal case should tend to 1.642" As FM we have considered the following mocels: We also analysed the model that takes both correction terms CO,(h)|2s(f) into account."," As $F^{M}$, we have considered the following models: We also analysed the model that takes both correction terms $C\Phi _1 \left( h \right)+D\Phi _2643\left( h \right)$ into account."644 Llowever. we found that it does not allow us to obtain the cocllicicnts that are statistically significant simultaneously.," However, we found that it does not allow us to obtain the coefficients that are statistically significant simultaneously."645 For comparison. we also considered the model with a correction term linear in /: such a correction can be caused by the own variability of the quasar. or by the influence of noncritical images (cf Yonehara 2001)):," For comparison, we also considered the model with a correction term linear in $h$; such a correction can be caused by the own variability of the quasar, or by the influence of noncritical images (cf. \citealt {yonehara_01}) ):"646 The results of best-fitting with cilferent models are presented in Table 1.., The results of best-fitting with different models are presented in Table \ref{tabl}.647 It contains the estimates of model parameters and their central 95-per-cent confidence intervals that have been found by the Monte-Carlo simulations under supposition of the normal distribution of errors., It contains the estimates of model parameters and their central 95-per-cent confidence intervals that have been found by the Monte-Carlo simulations under supposition of the normal distribution of errors.648 In all the models. the correction terms are statistically significant.," In all the models, the correction terms are statistically significant."649 Phe probability that the correction coelIieient is occasionally nonzero is certainly less than LO? in every case., The probability that the correction coefficient is occasionally nonzero is certainly less than $10^{ - 3}$ in every case.650 On the other hand. all theee mocoels can compete with one another on an equal footing (and probably with another effects such as those due to a complicated source structure).," On the other hand, all three models can compete with one another on an equal footing (and probably with another effects such as those due to a complicated source structure)."651 Note that the flux variation of the model light curve is roughly equal to 0.15 mv. and the standard deviation of data is a=0.006 my.," Note that the flux variation of the model light curve is roughly equal to 0.18 mJy, and the standard deviation of data is $\sigma \approx 0.006$ mJy."652 Thus. the assumption of the 5-per-cent tolerance in a vicinity of the light curve maximum. which has been used in criteria (27). is rather realistic.," Thus, the assumption of the 5-per-cent tolerance in a vicinity of the light curve maximum, which has been used in criteria \ref{LCA}) ), is rather realistic."653 In the ease of the ft-model. we find €/D=LPz 0.076.," In the case of the $F^1$ -model, we find $C/B=LP\approx0.076$ ."654" ""he comparison with the first inequality in (27)) indicates the agreement with the statistical significance of the first correction term.", The comparison with the first inequality in \ref{LCA}) ) indicates the agreement with the statistical significance of the first correction term.655leptonic models for the gamma-ray production.,leptonic models for the gamma-ray production.656 In particular. the extension. indication for an offset of the source from the globular cluster core and a power-law spectrum are not evident for such a scenario.," In particular, the extension, indication for an offset of the source from the globular cluster core and a power-law spectrum are not self-evident for such a scenario."657 The intensityof leptonic inverse-Compton (IC) radiation scales linearly with the energy density of the target photon field., The intensityof leptonic inverse-Compton (IC) radiation scales linearly with the energy density of the target photon field.658 For Terzan 5 the energy density of the stellar photon field drops from about 1000 eV/cm? in the core region to 40 eV/em™ at the half-mass radius (Venteretal..2009) to about a few eV/cm at the extension of the VHE source., For Terzan 5 the energy density of the stellar photon field drops from about 1000 $^{-3}$ in the core region to 40 $^{-3}$ at the half-mass radius \citep{venter2009} to about a few $^{-3}$ at the extension of the VHE source.659 Consequently a very centrally peaked source centered on the GC would be expected. which does not seem to be supported by the H.E.S.S. observations.," Consequently a very centrally peaked source centered on the GC would be expected, which does not seem to be supported by the H.E.S.S. observations."660 IC. emission in the VHE range should be accompanied by synchrotron emission in the X-ray band., IC emission in the VHE range should be accompanied by synchrotron emission in the X-ray band.661 Diffuse X-ray emission centered on Terzan 5 of possible synchrotron origin has indeed been discovered (Egeretal..2010) but the potential offset of the VHE gamma-ray emission from the peaks of the X-ray emission and radiation field challenges a leptonic scenario., Diffuse X-ray emission centered on Terzan 5 of possible synchrotron origin has indeed been discovered \citep{eger2010} but the potential offset of the VHE gamma-ray emission from the peaks of the X-ray emission and radiation field challenges a leptonic scenario.662 Furthermore. since the optical to near-infrared starlight photon field should be up-scattered by the very-high energy electrons. Klein-Nishina (KN) suppression of the IC process should be significant at multiple TeV energies causing a steepening in the VHE gamma-ray spectrum.," Furthermore, since the optical to near-infrared starlight photon field should be up-scattered by the very-high energy electrons, Klein-Nishina (KN) suppression of the IC process should be significant at multiple TeV energies causing a steepening in the VHE gamma-ray spectrum."663 For a target stellar photon field with mean temperature of 4500 K (Venteretal..2009) and electron energies of 10 TeV the KN suppression factor is already about 0.025 (Coppi&Blandford.1990).. so the VHE gamma-ray spectrum should steepen well before this energy.," For a target stellar photon field with mean temperature of 4500 K \citep{venter2009} and electron energies of 10 TeV the KN suppression factor is already about 0.025 \citep{coppi1990}, so the VHE gamma-ray spectrum should steepen well before this energy."664 In comparison. the observed spectrum may follow a straight power law. but this result is influenced by limited statistics.," In comparison, the observed spectrum may follow a straight power law, but this result is influenced by limited statistics."665 To account for the aforementioned arguments. as an alternative to an IC scenario. hadronic gamma-ray production ts explored in this paper as the origin of the VHE source.," To account for the aforementioned arguments, as an alternative to an IC scenario, hadronic gamma-ray production is explored in this paper as the origin of the VHE source."666 GRBs are generally believed. to be caused by a pair of ultrarelativistic jets that are ejected from the central engine., GRBs are generally believed to be caused by a pair of ultrarelativistic jets that are ejected from the central engine.667 Relativistic shock waves accelerate all particles from the incoming plasma to relativistic energies (Blandford&Me-Kee. 1976).. thus a substantial fraction of the initial energy of the relativistic blast wave is transferred into cosmic rays (seeAtoyanetal..2006.forthecaseofaGRB remnant)..," Relativistic shock waves accelerate all particles from the incoming plasma to relativistic energies \citep{blandford76}, thus a substantial fraction of the initial energy of the relativistic blast wave is transferred into cosmic rays \citep[see][for the case of a GRB remnant]{atoyan06}."668 Therefore. for such a scenario. the energy in cosmic rays is a measure for the kinetic energy of the relativistic outflow.," Therefore, for such a scenario, the energy in cosmic rays is a measure for the kinetic energy of the relativistic outflow."669 From the luminosity of the VHE gamma-ray source the energy in hadronic cosmic rays can be estimated if the density of target material 1s assumed., From the luminosity of the VHE gamma-ray source the energy in hadronic cosmic rays can be estimated if the density of target material is assumed.670 At the location of Terzan 5 the density of target material should be on the order of 5= em? (Clapsonetal..2011)., At the location of Terzan 5 the density of target material should be on the order of $n \approx 0.1$ $^{-3}$ \citep{clapson2011}.671. Additionally. to constrain the total energy in hadronic cosmic rays for the entire relevant cosmic ray energy range above about | GeV a spectral index for the region below the range that can be probed with H.E.S.S. has to be assumed.," Additionally, to constrain the total energy in hadronic cosmic rays for the entire relevant cosmic ray energy range above about 1 GeV a spectral index for the region below the range that can be probed with H.E.S.S. has to be assumed."672 If a cosmic ray spectral index of 2.0 Is adopted below 5 TeV. the cosmic ray energy that produces gamma rays at the energy threshold of 440 GeV of the H.E.S.S. measurements. the total energy in hadronic cosmic rays would be Ecyg=10(1/0.1em7)7! eres (Abramowskietal..201L)..," If a cosmic ray spectral index of 2.0 is adopted below 5 TeV, the cosmic ray energy that produces gamma rays at the energy threshold of 440 GeV of the H.E.S.S. measurements, the total energy in hadronic cosmic rays would be $E_\mathrm{CR} \approx 10^{51} (n/0.1 \mathrm{cm}^{-3})^{-1}$ ergs \citep{hesspaper}."673 Particles accelerated by a relativistic shock wave will not feature a single power-law spectrum but should have a break towards low energies where the break energy Ey is given by the bulk Lorenz factor I of the relativistic shock (Blandford&McKee.1976:Katz.1994) according to Ey~mpcE/2 with my the mass of the particle and c the speed of light.," Particles accelerated by a relativistic shock wave will not feature a single power-law spectrum but should have a break towards low energies where the break energy $E_\mathrm{br}$ is given by the bulk Lorenz factor $\Gamma$ of the relativistic shock \citep{blandford76,katz94} according to $E_\mathrm{br} \sim m_\mathrm{p} c^2 \Gamma^2 /2$ with $m_\mathrm{p}$ the mass of the particle and $c$ the speed of light."674 Ifa proton energy of 5 TeV. which produces gamma rays at the H.E.S.S. threshold. is adopted as the break energy. then the Lorenz factor at the time when most particles are accelerated would be x 100.," If a proton energy of 5 TeV, which produces gamma rays at the H.E.S.S. threshold, is adopted as the break energy, then the Lorenz factor at the time when most particles are accelerated would be $\lesssim$ 100."675 Lower break energies would result in lower Lorenz factors., Lower break energies would result in lower Lorenz factors.676" A spectral break towards lower particle energies would reduce the Ee, needed to explain the VHE source depending on the break energy by up to a factor of 2 (Atoyanetal..2006).", A spectral break towards lower particle energies would reduce the $E_\mathrm{CR}$ needed to explain the VHE source depending on the break energy by up to a factor of 2 \citep{atoyan06}.677. Since ultrarelativistic blast waves are expected to transfer a substantial part of their kinetic energy into cosmic rays the energetics of short GRBs could be roughly adequate for the observed VHE source if a ratio of prompt electromagnetic energy release to kinetic energy of 0.1 - 0.01 (Nakar.2007) is assumed., Since ultrarelativistic blast waves are expected to transfer a substantial part of their kinetic energy into cosmic rays the energetics of short GRBs could be roughly adequate for the observed VHE source if a ratio of prompt electromagnetic energy release to kinetic energy of 0.1 - 0.01 \citep{nakar07} is assumed.678 Extending VHE observations to lower energies with the planned CTA array (CTAConsortium.2010) could probe for a break in the gamma-ray spectrum of this source to test this scenario., Extending VHE observations to lower energies with the planned CTA array \citep{cta2010} could probe for a break in the gamma-ray spectrum of this source to test this scenario.679 After the acceleration. cosmic rays will diffuse away from the location of the GRB and will therefore form extended. center-filled gamma-ray sources (Atoyanetal..2006).," After the acceleration, cosmic rays will diffuse away from the location of the GRB and will therefore form extended, center-filled gamma-ray sources \citep{atoyan06}."680. The age of a GRB remnant would in such à case be given by the diffusive propagation time of cosmic rays to the extension of the source., The age of a GRB remnant would in such a case be given by the diffusive propagation time of cosmic rays to the extension of the source.681 For the VHE source in Terzan 5 an age of the remnant of 105(D/1075 ems7!)*! years would be found (Abramowskietal..201 D.. where D is the uncertain diffusion coefficient here compared to the value estimated for 5 TeV protons in the galactic disk of 1075 ems7! (Atoyanetal..2006).," For the VHE source in Terzan 5 an age of the remnant of $10^3 (D/ 10^{28}$ $^2$ $^{-1})^{-1}$ years would be found \citep{hesspaper}, where $D$ is the uncertain diffusion coefficient here compared to the value estimated for 5 TeV protons in the galactic disk of $10^{28}$ $^2$ $^{-1}$ \citep{atoyan06}."682. The age obtained for the potential GRB remnant at Terzan 5 can be compared to the rate of compact binary mergers in the Galaxy and to the rate of short GRBs in the local Universe., The age obtained for the potential GRB remnant at Terzan 5 can be compared to the rate of compact binary mergers in the Galaxy and to the rate of short GRBs in the local Universe.683 From field NSNS binaries a galactic merger rate to one event per (0.5 - 7)x107 years is found (Kalogeraetal..2004.., From field NSNS binaries a galactic merger rate to one event per (0.5 - $\times 10^4$ years is found \citep{kalogera04}.684. For merger induced bursts which are formed in globular clusters a local rate of 20 - 90 events per Gpc yr! (Salvateraetal.2008) or «4 Gpc yr! (Guetta&Stella.2009) ας been estimated., For merger induced bursts which are formed in globular clusters a local rate of 20 - 90 events per $^{-3}$ $^{-1}$ \citep{salvaterra08} or $\sim$ 4 $^{-3}$ $^{-1}$ \citep{guetta09} has been estimated.685" With à density of Milky way-type galaxies in the local Universe of 0.01 galaxies per Mpc? (Coleet this results in a rate of short bursts per galaxy of about one event per (0.1 - 0.5)x10* Cf,|ον years or 2.5x107 Cf,|ον years.", With a density of Milky way-type galaxies in the local Universe of 0.01 galaxies per $^{-3}$ \citep{cole01} this results in a rate of short bursts per galaxy of about one event per (0.1 - $\times 10^4$ $(f_\mathrm{b}^{-1}/100)^{-1}$ years or $\times 10^4$ $(f_\mathrm{b}^{-1}/100)^{-1}$ years.686 Here fj is the beaming factor of short bursts. uncertain in the range of | « ho « 100 (Nakar. 2007)..," Here $f_\mathrm{b}$ is the beaming factor of short bursts, uncertain in the range of 1 $\ll$ $f_\mathrm{b}^{-1}$ $<$ 100 \citep{nakar07}. ."687 It appears that the age of the potential GRB remnant would be roughly comparable to the rate of short, It appears that the age of the potential GRB remnant would be roughly comparable to the rate of short688 Tt has long been known that carly-type galaxies teud to be the reddest galaxies. and that the more luminous the ealaxy. the redder its color (c.g. Sandage Viswanathan 1978a.b: Bower. Lucey Ellis 1992a.b).,"] It has long been known that early-type galaxies tend to be the reddest galaxies, and that the more luminous the galaxy, the redder its color (e.g. Sandage Viswanathan 1978a,b; Bower, Lucey Ellis 1992a,b)."689 The tightuess of the correlation between color aud maguitude has been used to coustrain models of low carly-type ealaxies formed., The tightness of the correlation between color and magnitude has been used to constrain models of how early-type galaxies formed.690 However. a luminous ealaxy may appear red either because its stars are older. or because. although its stars are younger. they are more metal rich.," However, a luminous galaxy may appear red either because its stars are older, or because, although its stars are younger, they are more metal rich."691 This has complicated the coustraints one can place ou galaxy formation models: should the models produce luminous metal-rich ealaxies. or huninous old galaxies?," This has complicated the constraints one can place on galaxy formation models: should the models produce luminous metal-rich galaxies, or luminous old galaxies?"692 To illustrate. Appendix ?? shows the color-magnitude relation associated with the recent stellar population svuthesis models of Bruzual Charlot (2003).," To illustrate, Appendix \ref{bc2003} shows the color-magnitude relation associated with the recent stellar population synthesis models of Bruzual Charlot (2003)."693 The colors aud of Iuninosities galaxies are expected to evolve wore slowly than thoseolderyounger oues., The colors and luminosities of older galaxies are expected to evolve more slowly than those of younger ones.694 Therefore. if age is changing alone the color-maenitudeof sequence (e.g. if the more hninous galaxies are older). one would expect the differential evolution of the older aud younger sopulations along the sequence to manifest as a clauge in the slope of the color-magnitude relation with redshift.," Therefore, if age is changing along the color-magnitude sequence (e.g. if the more luminous galaxies are older), one would expect the differential evolution of the older and younger populations along the sequence to manifest as a change in the slope of the color-magnitude relation with redshift."695 Recent measurements have shown that the relation was already in place at redshifts of order unity. aud that its slope appears to be unchanged frou its value locally (e.g. Kodama ct al.," Recent measurements have shown that the relation was already in place at redshifts of order unity, and that its slope appears to be unchanged from its value locally (e.g. Kodama et al."696 1998: Blakeslee et al., 1998; Blakeslee et al.697 2003)., 2003).698 If the high redshift population does indeed represent the local low redshift population iu its vouth. then the fact that the slope has evolved little argues against a large age-spread along the relation.," If the high redshift population does indeed represent the local low redshift population in its youth, then the fact that the slope has evolved little argues against a large age-spread along the relation."699 In this case. the coloranagnuitude relation is caused primarily by a correlation between wctallicity and huninosity (IlXodainaa ct al.," In this case, the color-magnitude relation is caused primarily by a correlation between metallicity and luminosity (Kodama et al."700 1998). (, 1998). (701This arguineut beconies weaker if the redshift at which the population formed the lulls of its stars 15 large.),This argument becomes weaker if the redshift at which the population formed the bulk of its stars is large.)702 Iu this fraanework. the scatter around the color-imaguitude relation is usually attributed to the effects of age.," In this framework, the scatter around the color-magnitude relation is usually attributed to the effects of age."703 It ix not eutirely obvious. however. that this ean be correct.," It is not entirely obvious, however, that this can be correct."704 This is because differential evolution must make the scatter around the mean relation larger at higher lookback times., This is because differential evolution must make the scatter around the mean relation larger at higher lookback times.705 Therefore. the fact that the color-magnitude relation is well defined at redshifts of order unity can be translated iuto a constraint on the mix of ages prescut at redshift zero.," Therefore, the fact that the color-magnitude relation is well defined at redshifts of order unity can be translated into a constraint on the mix of ages present at redshift zero."706 For this reason. it would be interesting to quantify how the scatter around the mean relation evolves. (," For this reason, it would be interesting to quantify how the scatter around the mean relation evolves. ("707Blakeslee et al.,Blakeslee et al.708 2003 fd little evolution in the slope aud scatter of the relation. using cluster earlv-tvpes out to redshifts of order ήν)∙⇁ ↕," 2003 find little evolution in the slope and scatter of the relation, using cluster early-types out to redshifts of order unity.)"709↕⊴∖↖⊽↸∖↕↕↨⋤↕↕⊲⋝∖↖⊽↕↕↾⋯↾↕↕↕↕↕↕↕↕↓⊲⋝⊴↕↾⋅↖⊽⋮↕↕⊴⊲⋝↸↾⊲⋝↕⋅↕⋅↸∖⋮↕↾↸∖⊴∖↖⊽↕↾↕↕⋅⋅ ⋅ velocity dispersion (Poveda 1961: Faber Jackson 1976). so it is natural to ask if velocity dispersion is also tightly coupled to metallicity.," It is well known that luminosity also correlates with velocity dispersion (Poveda 1961; Faber Jackson 1976), so it is natural to ask if velocity dispersion is also tightly coupled to metallicity."710 The tiehtuess of the correlation between Me» aud o (e.c. Bernardi ct al., The tightness of the correlation between $_2$ and $\sigma$ (e.g. Bernardi et al.711 1998: Colless et al., 1998; Colless et al.712" 1999). is thought to be a consequence of variations iu age and immetallicitv which couspire to keep the observed correlation tight (οι, I&untsehner et al."," 1999), is thought to be a consequence of variations in age and metallicity which conspire to keep the observed correlation tight (e.g. Kuntschner et al."713 2001)., 2001).714 In this, In this7152 processors. and candidates were inspected with JIteaper (?7).. a graphical tool for selecting candidates based: upon user-definable parameters.,"72 processors, and candidates were inspected with JReaper \citep{kel+09}, a graphical tool for selecting candidates based upon user-definable parameters."716 “Vhis first. pass vielded only one new discovery. 6132 (2). cüiscussed in Section 4.1.," This first pass yielded only one new discovery, $-$ 6132 \citep{obrien08}, discussed in Section 4.1."717 One of the possible reasons why the first pass through the data found only. one pulsar may have been the lack of dispersion. delay. making it dillicult to distinguish astrophysical signals from. REL at this high. frequency. (as cliscussecl in Section 2?)).," One of the possible reasons why the first pass through the data found only one pulsar may have been the lack of dispersion delay, making it difficult to distinguish astrophysical signals from RFI at this high frequency (as discussed in Section \ref{sec:high_f}) )."718 This resulted in an overwhelming number of spurious candidates. making the task of finding &ood candidates which should be reobserved. very. cdillicult.," This resulted in an overwhelming number of spurious candidates, making the task of finding good candidates which should be reobserved very difficult."719 Therefore. it was decided that a second. pass through the data would be useful. after introducing some techniques to remove. or reduce the effects of. these REL signals.," Therefore, it was decided that a second pass through the data would be useful, after introducing some techniques to remove, or reduce the effects of, these RFI signals."720 In reprocessingre the data. much of the pipeline was very similar to that used originally.," In reprocessing the data, much of the pipeline was very similar to that used originally."721 Llowever. the processing was carried out on ‘Lycra’. a 108-node cluster. with cach node consisting of dual quad-core processors with 46D of memory.," However, the processing was carried out on `Hydra', a 108-node cluster, with each node consisting of dual quad-core processors with 4GB of memory."722" In order to take advantage of this processing power. a threaded. tree algorithm written by one of us (Bailes) was used. which performed. dedispersion many times faster than was possible with ""DCore and the original dedispersion Code."," In order to take advantage of this processing power, a threaded tree algorithm written by one of us (Bailes) was used, which performed dedispersion many times faster than was possible with `DCore' and the original dedispersion code."723 When preparing the data for processing. we decided not to use the time-clomain clipping algorithm. that was previously emploved by this and other surveys. since the discovery that this algorithm: introduced: periodic signals to the data.," When preparing the data for processing, we decided not to use the time-domain clipping algorithm that was previously employed by this and other surveys, since the discovery that this algorithm introduced periodic signals to the data."724 “Phese signals were apparent even at high DM. polluting the search output.," These signals were apparent even at high DM, polluting the search output."725 By removing this step. the effects of REL at low DAL were increased. however the sensitivity to these artificial signals was removed.," By removing this step, the effects of RFI at low DM were increased, however the sensitivity to these artificial signals was removed."726 Steps were taken to reduce our sensitivity to REL in other wavs. outlined in the following sections.," Steps were taken to reduce our sensitivity to RFI in other ways, outlined in the following sections."727 Instead. of making changes to the processing pipeline. alterations were made in the post-processing stage. as outlined. in Section ??..," Instead of making changes to the processing pipeline, alterations were made in the post-processing stage, as outlined in Section \ref{sec:filters}."728 For example. the cata were not searched. in acceleration space to look for pulsars in short-period binary systems.," For example, the data were not searched in acceleration space to look for pulsars in short-period binary systems."729 Ehe additional computation required by such a search is large. while this technique would. also produce enormous numbers of candidates. something that we were attempting to avoid with this reprocessing.," The additional computation required by such a search is large, while this technique would also produce enormous numbers of candidates, something that we were attempting to avoid with this reprocessing."730 Interstellar dispersion. described. by equation (3)).. is often a good wav to distinguish between extra-terrest sources and terrestrial sources (that is. REL). since one wouldrial ordinarily expect that any. periodic sources of REL would not follow the dispersion. law. and that they would. peak in strength. at a DM of 0 em*pe.," Interstellar dispersion, described by equation \ref{dispersion}) ), is often a good way to distinguish between extra-terrestrial sources and terrestrial sources (that is, RFI), since one would ordinarily expect that any periodic sources of RFI would not follow the dispersion law, and that they would peak in strength at a DM of 0 $\mathrm{cm}^{-3}\,\mathrm{pc}$."731 At high. frequencies. rowever. where the effects of dispersion are small. à signal with zero dispersion will reduce in S/N very. slowly as trial DM increases - the simulated pulse in Fig.," At high frequencies, however, where the effects of dispersion are small, a signal with zero dispersion will reduce in S/N very slowly as trial DM increases - the simulated pulse in Fig."732 5. falls in S/N by ess then one percent when the dillerence between the true DM and the trial DM is 50 em?pe.," \ref{snr_vs_dm_f} falls in S/N by less then one percent when the difference between the true DM and the trial DM is 50 $\mathrm{cm}^{-3}\,\mathrm{pc}$."733 ὃν comparison. at an observing frequeney of 14 Giz (in. for example. the PMPS). he same simulated. pulse falls bv ten percent in S/N when he true and. trial DMs differ by only 4 em.pe.," By comparison, at an observing frequency of 1.4 GHz (in, for example, the PMPS), the same simulated pulse falls by ten percent in S/N when the true and trial DMs differ by only 4 $\mathrm{cm}^{-3}\,\mathrm{pc}$."734 Due to heir short. periods. this elect should not reduce sensitivity o milliscconcl pulsars (MSPs). for whom the dependance of S/N with DM is very strong.," Due to their short periods, this effect should not reduce sensitivity to millisecond pulsars (MSPs), for whom the dependance of S/N with DM is very strong."735 The effect. of the small amount of dispersion delay at ugh frequencies is that the variation of S/N with trial DM value is low compared to observations at lower frequencies., The effect of the small amount of dispersion delay at high frequencies is that the variation of S/N with trial DM value is low compared to observations at lower frequencies.736 ]t is normal to use a plot of the variation of S (with. DM o help identify good candidates. but for this survey these dots were of little value. except for the highest DM sources (sce Section. 727)).," It is normal to use a plot of the variation of S/N with DM to help identify good candidates, but for this survey these plots were of little value, except for the highest DM sources (see Section \ref{sec:plane}) )."737 In. lower DM cases. one has to judge," In lower DM cases, one has to judge"738oei general. comparison of data in GOS and C99 shows iat the two evolutionary scenarios have a rather simular dependence of luminosities on the chemical composition. ms with the quoted systematic difference at any given netallicity. “,"in general, comparison of data in G98 and C99 shows that the two evolutionary scenarios have a rather similar dependence of luminosities on the chemical composition, thus with the quoted systematic difference at any given metallicity. """739"Sic stantibus τουσ, the already quoted evidence at GOS evolutionary scenario appears able to nicely fit tie. Ihpparcos mean magnitude of chnipius IIc nrninue stars. Προς that C99 mast xedicet too Iuninous ejauts. runnins agaiust the Ilüpparcos evidence.","Sic stantibus rebus"", the already quoted evidence that G98 evolutionary scenario appears able to nicely fit the Hipparcos mean magnitude of clumping He burning stars, implies that C99 must predict too luminous giants, running against the Hipparcos evidence."740 This is been confirmed by independent simiion of the chua» population based on €99 evolutionary tracks. as ransferred dito the CAL diagram w adopting ποσο] atinosplheres by Castelli et al.(1997a.b).," This has been confirmed by independent simulation of the clump population based on C99 evolutionary tracks, as transferred into the CM diagram by adopting model atmospheres by Castelli et al.(1997a,b)."741 Data iu Fig.l eives the adcitional evidence that reasolable variatious in the assmned original Ie content cannot decrease the C'99 precicted Iluninositv by the required amount., Data in Fig.1 gives the additional evidence that reasonable variations in the assumed original He content cannot decrease the C99 predicted luminosity by the required amount.742 Therefore one coucludes that C98 evoluOAV scenario works better., Therefore one concludes that G98 evolutionary scenario works better.743 However. for the sake of the discussion one las to rotice that there is -at least im principle - a wav to recoucile C99 prediction with Wipparcos oservations.," However, for the sake of the discussion one has to notice that there is -at least in principle - a way to reconcile C99 prediction with Hipparcos observations."744 Fig., Fig.745 lin this paper shows that a substantial amount of mass OSS could lower the C99 predictions bv the required amount of about AlogL-—0.1., 4 in this paper shows that a substantial amount of mass loss could lower the C99 predictions by the required amount of about $\Delta$ $\sim$ 0.1.746 As an example. oue would require a nass loss bv about 0.9 AL. or a 2.0 AL... and * abot 0.6 AD. for a 1.5 M. model.," As an example, one would require a mass loss by about 0.9 $_{\odot}$ for a 2.0 $_{\odot}$, and by about 0.6 $_{\odot}$ for a 1.5 $_{\odot}$ model."747 This. however. appear a too large requireiieut vis-a-vis current estimates Or dnass loss.," This, however, appear a too large requirement vis-a-vis current estimates for mass loss."748 Talking also iuto accom the muacertaiuties on evolutionary parameters of the field population in the solar neighborhood. we regard the previous discussion rot as a proof. but at least as a suggestion that the nost updated models. as C99 are. when dealing with the srogeny of clegeucrated RC tend to give too luminous Te mining models.," Taking also into account the uncertainties on evolutionary parameters of the field population in the solar neighborhood, we regard the previous discussion not as a proof, but at least as a suggestion that the most updated models, as C99 are, when dealing with the progeny of degenerated RG tend to give too luminous He burning models."749 It appears of obvious relevance to address the problem of the discrepancies between the models by C8 aud C99. trvine to understand them in terms of different descriptions of the input physics.," It appears of obvious relevance to address the problem of the discrepancies between the models by G98 and C99, trying to understand them in terms of different descriptions of the input physics."750 We leave out differences nn the actual treatineut of the input physics interpolation in and between opacity tables). which we think are of smaller influence and müght coutribute to a minor part of the variations in the clump huuinosities as shown in Fie.," We leave out differences in the actual treatment of the input physics interpolation in and between opacity tables), which we think are of smaller influence and might contribute to a minor part of the variations in the clump luminosities as shown in Fig."751 2., 2.752 Since the most iuportant quantity determuniie the core elimi burning luminosity is the core mass at the helium dash. we will concentrate on this parameter.," Since the most important quantity determining the core helium burning luminosity is the core mass at the helium flash, we will concentrate on this parameter."753 Fig., Fig.754 5 shows that the 1 M. CS models have core LASSCS lower bv zm0.03AL. compared to €99 at the time of helinu ignition at the RGB tip.," \ref{f:mccomp} shows that the 1 $_{\odot}$ G98 models have core masses lower by $\approx 0.03\,M_\odot$ compared to C99 at the time of helium ignition at the RGB tip."755 Fie., Fig.756 5 is iuade for solar composition but we checked that even for other imoetallicities and helium abundances the differences i the Ile core mass are verv sail., \ref{f:mccomp} is made for solar composition but we checked that even for other metallicities and helium abundances the differences in the He core mass are very similar.757" We have identified the followine differences in the input plysics used in the two evolutionary programs (""Padua for CS aud ΕΠΑΝ for C99 models) nuder consideration (other aspects such as reaction rates. electron screcuing. mixiue-eusth formali. ete."," We have identified the following differences in the input physics used in the two evolutionary programs (“Padua” for G98 and “FRANEC” for C99 models) under consideration (other aspects such as reaction rates, electron screening, mixing-length formalism, etc.,"758 are to ercat extent ideutical): The influence of some of these differences could be investigated quite casily because the two codes to sole extent allow the selection of several sources of iuput physics., are to great extent identical): The influence of some of these differences could be investigated quite easily because the two codes to some extent allow the selection of several sources of input physics.759 The tests were done for differentcases of initial chemical composition and mass., The tests were done for differentcases of initial chemical composition and mass.760" For the composition Y=0.27. Z=0.02. and an initial mass of L2A/.. we find that AL, decreases from 0.182 to 0.176. (-0.006) ALL. if we switch"," For the composition $Y=0.27$, $Z=0.02$ and an initial mass of $1.2\,M_\odot$ we find that $M_c$ decreases from 0.482 to 0.476 (-0.006) $M_\odot$ , if we switch"761"Besides the CO emissions. Reach aid Rho (2001) obtained spectra of the H» S(9) aid S3) lines for Ws. WEE aud 3C391 within the LI”x20"" aperture of the Short Wavelengih Spect'OImmeter (SWS) on /SO.","Besides the CO emissions, Reach and Rho (2001) obtained spectra of the $_2$ S(9) and S(3) lines for W28, W44 and 3C391 within the $14''\times20''$ aperture of the Short Wavelength Spectrometer (SWS) on $\it{ISO}$."762 The central positious of all these {50 observatious are markecl by the CLOSSES ou Figures d — 6., The central positions of all these $\it{ISO}$ observations are marked by the crosses on Figures 1 – 6.763 For W28. WII and 3€C391 the LWS and SWS observations share tle same beam ceuters and are consistent with tie. (0.0) positious of the IRS maps.," For W28, W44 and 3C391 the LWS and SWS observations share the same beam centers and are consistent with the $(0,0)$ positions of the IRS maps."764 The meastred. Η» S(9)/5(3) ratios are another valuable diagnostic[n] tool and are used in our fits to constrain {je parameters of the gas., The measured $_2$ S(9)/S(3) ratios are another valuable diagnostic tool and are used in our fits to constrain the best-fit parameters of the gas.765 The LWS meastred CO line fluxes along with the 1 6 errors aud tle SWS S(9)/5(3) ratios are all listed in Table 1., The LWS measured CO line fluxes along with the 1 $\sigma$ errors and the SWS S(9)/S(3) ratios are all listed in Table 1.766 The Ho emission spectrum is amoug the most important claguostics needed to coustraiu couditious in shocked molecular gas as well as to distieuish between different shock moces., The $_{2}$ emission spectrum is among the most important diagnostics needed to constrain conditions in shocked molecular gas as well as to distinguish between different shock models.767 Over the last several decades. it has been widely observe iat the rotational diagrams of H» often exhibit positive curvatures.," Over the last several decades, it has been widely observed that the rotational diagrams of $_{2}$ often exhibit positive curvatures."768 This kind o curvature cau not be accounted lor by extinction e[Tects ouly. which affect the H» 5(3) line much more strongly than the other rotational lites. aid may imply the existeuce of a mixture of gas temperatures.," This kind of curvature can not be accounted for by extinction effects only, which affect the $_{2}$ S(3) line much more strongly than the other rotational lines, and may imply the existence of a mixture of gas temperatures."769 NOG aud NOT investigated the H» excitation cliagrais for the six sources we are studying here. iu which the molecular hydrogen emissiOl) Was uodeled with a combination of gas at two temperatures.," N06 and N07 investigated the $_{2}$ excitation diagrams for the six sources we are studying here, in which the molecular hydrogen emission was modeled with a combination of gas at two temperatures."770 In this paper. we adopt a power-law emperature distribution similar to tha described by NYOs. with the colunnu density of gas at eimperature between To aud. T + dT assumed to be propotional to T5.," In this paper, we adopt a power-law temperature distribution similar to that described by NY08, with the column density of gas at temperature between $T$ and $T$ + $dT$ assumed to be proportional to $T^{-b}$."771" Instead of the lower eniperature limit Z,,/5, = 300 lx adopted by NYOS. we extend it to 100 Ix here because wari. eas at. LOO — 300 Ix. cau contribute siguificantly to those low-lying H» emissions accessible to IRS. especially for v = 0— 0 5(0) and S(1)."," Instead of the lower temperature limit $T_{min}$ = 300 K adopted by NY08, we extend it to 100 K here because warm gas at 100 – 300 K can contribute significantly to those low-lying $_{2}$ emissions accessible to IRS, especially for v = 0 – 0 S(0) and S(1)."772 This power-law clistribtiou is consistent with the prediction [rom the bow-shapecl C-shock model developed by $1uith. Braud Λoorhouse (1991) (NYO8).," This power-law distribution is consistent with the prediction from the bow-shaped C-shock model developed by Smith, Brand Moorhouse (1991) (NY08)."773 Ucmith. Brand Moorhouse found that bow shocks can procice gas at a wide range of excitation temperatures aid thus provide a way of explaining the H» liue ratios observed [or many. sources. while planar shock models failto reproduce the observed raticS.," Smith, Brand Moorhouse found that bow shocks can produce gas at a wide range of excitation temperatures and thus provide a way of explaining the $_{2}$ line ratios observed for many sources, while planar shock models failto reproduce the observed ratios."774 Another interesting characteristic of tte H» rotational diagrams lies in the zigzag pattern. corresponcdiug to uou-equilibrium Ho ortho-to-para ratios.," Another interesting characteristic of the $_{2}$ rotational diagrams lies in the zigzag pattern, corresponding to non-equilibrium $_{2}$ ortho-to-para ratios."775 This pheuoumenon is especially notabT for the five sources W228. WIL 90201. HH? and HHS! (N06: NOT).," This phenomenon is especially notable for the five sources W28, W44, 3C391, HH7 and HH54 (N06; N07)."776" With a closer look. it is quickly apparent that the zigzag teuds to ""diminish for hieli-Iviug levels."," With a closer look, it is quickly apparent that the zigzag tends to “diminish” for high–lying levels."777 Given the fact that low- aud hieh-excitation lines are produced by different temperature components. NOG argued that the Change in the degree of zigzag is caused by tlie strong temperature depencence of tlie para-to-ortho conversion efficieucy.," Given the fact that low- and high-excitation lines are produced by different temperature components, N06 argued that the change in the degree of zigzag is caused by the strong temperature dependence of the para-to-ortho conversion efficiency."778 With this process «lomiuated by collisions with atomic hydrogen[n] iu C-type shocks Clininerimanuu 1998: Wileeubus et al.," With this process dominated by collisions with atomic hydrogen in C-type shocks (Timmermann 1998; Wilgenbus et al.,"779 2000). the current OPR is given by equation (1) iu Neufeld et al. (," 2000), the current OPR is given by equation (1) in Neufeld et al. ("7802009: hereafter ΑΟ). as a [unction of initial ratio OPI. atomic hydrogen density,"2009; hereafter N09), as a function of initial ratio $_{0}$ , atomic hydrogen density"781"distribution function for a given radius, a Boltzmann distribution can be assumed (cf. 1993),, The function F(v,r) is normalised such that, The velocity of each particle can then be obtained using the probability distribution of equation (10)).","distribution function for a given radius, a Maxwell-Boltzmann distribution can be assumed \citep[cf.][]{Hernquist93}, The function $F(v,r)$ is normalised such that, The velocity of each particle can then be obtained using the probability distribution of equation \ref{MB}) )."782" Having obtained the density and velocity profiles of the halo, the only thing left is to assign a direction to each velocity."," Having obtained the density and velocity profiles of the halo, the only thing left is to assign a direction to each velocity."783 This is done by simply requiring that the directional velocity vectors produce a smooth distribution on the surface of a unit sphere., This is done by simply requiring that the directional velocity vectors produce a smooth distribution on the surface of a unit sphere.784" To test the stability of this setup, an isolated halo with Mj,=101Mo, Nvir=10° and c=5 was left to evolve over 8 Gyr using GADGET--2 (Springel2005)."," To test the stability of this setup, an isolated halo with $M_{\rm vir}=10^{14} \rm M_{\odot}$, $N_{\rm vir}=10^6$ and $c=5$ was left to evolve over 8 Gyr using -2 \citep{Springel05}."785. The spline gravitational softening was set to «=3kpc corresponding roughly to the radius of the 100th particle (seePower 2003)., The spline gravitational softening was set to $\epsilon=3 \rm kpc$ corresponding roughly to the radius of the 100th particle \citep[see][]{Power03}.786. Fig., Fig.787" 1 shows that the halo retains the overall shape of an NFW profile, except at the centre where the profile has flattened similar to that observed by Kazantzidis,Magor-rian&Moore (2004)."," \ref{dens} shows that the halo retains the overall shape of an NFW profile, except at the centre where the profile has flattened similar to that observed by \citet*{Kazantzidis04}."788. This flattening of the density profile is caused by approximating the distribution function with a Maxwell-Boltzmann., This flattening of the density profile is caused by approximating the distribution function with a Maxwell-Boltzmann.789" As demonstrated in Kazantzidis (2004),, this will lead to an over estimate of any stripping that occurs."," As demonstrated in \citet{Kazantzidis04}, this will lead to an over estimate of any stripping that occurs."790" Despite this, it will have no effect on the ability of halo finders to recover the haloes."," Despite this, it will have no effect on the ability of halo finders to recover the haloes."791 This was confirmed by using the method outlined in Readetal.(2006) to generate haloes with Plummer(1911) and density profiles based on their 6D distribution functions., This was confirmed by using the method outlined in \citet{Read06} to generate haloes with \citet{Plummer11} and density profiles based on their 6D distribution functions.792" When the same tests were carried out on these haloes, the same patterns between the halo finders was found as for the NFW with the Maxwell-Boltzmann approximation."," When the same tests were carried out on these haloes, the same patterns between the halo finders was found as for the NFW with the Maxwell-Boltzmann approximation."793 The first method of modelling the infall of a subhalo we adopted was to consider how well different halo finders recovered the subhalo at a given radius., The first method of modelling the infall of a subhalo we adopted was to consider how well different halo finders recovered the subhalo at a given radius.794 This was achieved by placing the same sized subhalo at different radii within the main halo and attempting to recover it with each halo finder., This was achieved by placing the same sized subhalo at different radii within the main halo and attempting to recover it with each halo finder.795" A halo was generated with My;=10'4Mo, Ny=106 and c=5 and a subhalo with My,=10?Mo, Nu,=104 and c=12."," A halo was generated with $M_{\rm vir}=10^{14} \rm M_{\odot}$, $N_{\rm vir}=10^6$ and $c=5$ and a subhalo with $M_{\rm vir}=10^{12} \rm M_{\odot}$, $N_{\rm vir}=10^4$ and $c=12$."796" The concentration of the subhalo was set to be higher than the halo in order to reflect the conditions found in cosmological simulations (seeBullocketal.2001;Eke,Navarro&Steinmetz 2001).."," The concentration of the subhalo was set to be higher than the halo in order to reflect the conditions found in cosmological simulations \citep[see][]{Bullock01, Eke01}. ."797" The subhalo was then placed at different distances away from the centre of the halo and given a velocity, where Mnaio is the mass of the halo and Τεορ is the separation of the centres of the halo and subhalo, towards the centre of the halo."," The subhalo was then placed at different distances away from the centre of the halo and given a velocity, where $M_{\rm halo}$ is the mass of the halo and $r_{\rm sep}$ is the separation of the centres of the halo and subhalo, towards the centre of the halo."798" This velocity corresponds to the conversion of potential energy to kinetic, for two point masses, as the subhalo falls in from infinity."," This velocity corresponds to the conversion of potential energy to kinetic, for two point masses, as the subhalo falls in from infinity."799" When the subhalo was placed at the centre of the halo, rsep=0.0 so v—oo."," When the subhalo was placed at the centre of the halo, $r_{\rm sep}=0.0$ so $v\rightarrow\infty$."800" To overcome this, the subhalo was given a velocity of the previous closest separation when it was at the centre of the halo."," To overcome this, the subhalo was given a velocity of the previous closest separation when it was at the centre of the halo."801 This set-up was produced 100 times for each separation using different random number seeds., This set-up was produced 100 times for each separation using different random number seeds.802 Consistent realisations were found each time., Consistent realisations were found each time.803 Fig., Fig.804 2 shows the fraction of particles recovered by each halo finder at different separations., \ref{subpos} shows the fraction of particles recovered by each halo finder at different separations.805 Neither halo finder can recover the subhalo when it is near the centre of the halo., Neither halo finder can recover the subhalo when it is near the centre of the halo.806 This corresponds to the densest region of the halo and leads to any overdensity from the subhalo being hidden., This corresponds to the densest region of the halo and leads to any overdensity from the subhalo being hidden.807 As the separation is increased has a steep rise in the fraction of particles it recovers until it is finding the complete subhalo from ~0.5ryir outwards., As the separation is increased has a steep rise in the fraction of particles it recovers until it is finding the complete subhalo from $\sim0.5r_{\rm vir}$ outwards.808 does not have such a drastic change and continues to underestimate the size of subhalo all the way out to ~1.5ryi., does not have such a drastic change and continues to underestimate the size of subhalo all the way out to $\sim1.5r_{\rm vir}$.809 We can gain some insight into the strong radial dependence in recovered particle number in by considering the following simple argument., We can gain some insight into the strong radial dependence in recovered particle number in by considering the following simple argument.810 identifies subhaloes as overdensities; it identifies when a subhalo's local density equals its host halo's local density., identifies subhaloes as overdensities; it identifies when a subhalo's local density equals its host halo's local density.811" This equates to, where 6¢,,,,, and 6.,,, are the characteristic densities of the halo and subhalo respectively (equation 5)), and Ts. are the scale radii of the halo and subhalo respectively,r;,,,, Τρορ is the separationof the centres of the halo and subhalo and r is the radius of the subhalo at which the densities are equal."," This equates to, where $\delta_{c_{\rm halo}}$ and $\delta_{c_{\rm sub}}$ are the characteristic densities of the halo and subhalo respectively (equation \ref{deltac}) ), $r_{s_{\rm halo}}$ and $r_{s_{\rm sub}}$ are the scale radii of the halo and subhalo respectively, $r_{\rm sep}$ is the separationof the centres of the halo and subhalo and $r$ is the radius of the subhalo at which the densities are equal."812" The number of particles within r cannot exceed Ny, ", The number of particles within $r$ cannot exceed $N_{\rm vir}$ 813by HEAQO1 (Alushotzky 1982) at a (unabsorbecl) lux level of about 10+4 cre em7 until 1994. when it was observed by ASCA (Weaver ct al.,"by HEAO–1 (Mushotzky 1982) at a (unabsorbed) flux level of about $\times$ $^{-11}$ erg $^{-2}$ $^{-1}$, until 1994, when it was observed by ASCA (Weaver et al."814 1996) at a flux level more than one order of magnitude fainter., 1996) at a flux level more than one order of magnitude fainter.815 Phen the source underwent a rapid recovery: in 1997 it was observed. by JopposXX. at a flux level somewhat higher than in. 1994. while in 1998 it Lully recovered its LOTS brightness (Culli et al.," Then the source underwent a rapid recovery: in 1997 it was observed by BeppoSAX at a flux level somewhat higher than in 1994, while in 1998 it fully recovered its 1978 brightness (Gilli et al."816 2000: see Fig. 5))., 2000; see Fig. \ref{polittico}) ).817 In this case the comparison between the Compton-thin and the ASCA almost rellection-dominated: states clearly rules out the possibility that the reflector is the inner wall of the ¢ysorber., In this case the comparison between the Compton-thin and the ASCA almost reflection-dominated states clearly rules out the possibility that the reflector is the inner wall of the absorber.818 The 4-10 to 2-4 keV [lux ratio during the ASCA observation is 0.35+0.02 (corresponding to - 5). which is largely inconsistent with the theoretical value expected from a rellection dominated spectrum by a column density ~10772 emi7 (0.53).," The 4-10 to 2-4 keV flux ratio during the ASCA observation is $0.35819\pm 0.02$ (corresponding to $\Gamma \simeq 1.15$ ), which is largely inconsistent with the theoretical value expected from a reflection dominated spectrum by a column density $\sim 10^{22}$ $^{-2}$ (0.53)."820 Leis worth noting that in both Deppos;XX observations the power law spectral index was vpical for AGN (Eo 1.7). again indicating that the [Lux recovery is likely to be associated with the re-emergence of he AGN nuclear emission.," It is worth noting that in both BeppoSAX observations the power law spectral index was typical for AGN $\Gamma \simeq 1.7$ ), again indicating that the flux recovery is likely to be associated with the re-emergence of the AGN nuclear emission."821 In summary. for this source there is no doubt that the absorbing and rellecting regions do not jàve the same column density and likely belong to cilferent gaseots structures.," In summary, for this source there is no doubt that the absorbing and reflecting regions do not have the same column density and likely belong to different gaseous structures."822 We have presented. evidence of the switchingolf of the nucleus in a [ew Sevfert 2 galaxies based on their changed looks (from Comptonthin to reflectiondominated Or viceversa) when observed. a few vears apart., We have presented evidence of the switching–off of the nucleus in a few Seyfert 2 galaxies based on their changed looks (from Compton–thin to reflection–dominated or viceversa) when observed a few years apart.823 The evidence cannot be considered conclusive vet. and. further investigations. both on the same objects and in search of new objects with à similar behaviour. are needed.," The evidence cannot be considered conclusive yet, and further investigations, both on the same objects and in search of new objects with a similar behaviour, are needed."824 La the meantime. let us. briellv discuss a few interesting consequences of the proposed scenario.," In the meantime, let us briefly discuss a few interesting consequences of the proposed scenario."825 This is a question that involves. of course. both Sevfert Ls and Sevfert 2s.," This is a question that involves, of course, both Seyfert 1s and Seyfert 2s."826 Ht is basically impossible to estimate the fraction of these transitions in obscured AGN. due to the lack of a complete and. unbiased. sample of homosgeneously defined Sevlert 2 galaxies with sullicient X-ray temporal and spectroscopic coverage.," It is basically impossible to estimate the fraction of these transitions in obscured AGN, due to the lack of a complete and unbiased sample of homogeneously defined Seyfert 2 galaxies with sufficient X-ray temporal and spectroscopic coverage."827 A NATALNewton prograni is ongoing to address this question on the complete sample of Comptonthick AGN defined in Risaliti et al. (, A XMM–Newton program is ongoing to address this question on the complete sample of Compton–thick AGN defined in Risaliti et al. (8281999).,1999).829 The existence of a population of Sevlert 1 galaxies with significant NXray absorption (Maiolino et al., The existence of a population of Seyfert 1 galaxies with significant X–ray absorption (Maiolino et al.830 2001: Fiore et al., 2001; Fiore et al.831 2001: Della Ceca. ct al., 2001; Della Ceca et al.832 2001). has been recently recognized., 2001) has been recently recognized.833 For most of these sources evidence for absorption comes from the flatness of the Nray spectrum as derived from a hardness ratio analysis. rather than from a clirect measurement of the column density. because they are oftentoo faint to allow for a proper spectral analysis.," For most of these sources evidence for absorption comes from the flatness of the X–ray spectrum as derived from a hardness ratio analysis, rather than from a direct measurement of the column density, because they are oftentoo faint to allow for a proper spectral analysis."834 As the X and optical observations are usually not simultaneous. itis possible that this mismatch is. as least for a fraction of these sources. due to a temporary switchingoll of the nuclear radiation.," As the X--ray and optical observations are usually not simultaneous, it is possible that this mismatch is, as least for a fraction of these sources, due to a temporary switching–off of the nuclear radiation."835 Other explanations are still possible (c.g. ionization of the X-ray. absorbing medium. low gas-to-dust ratio in the GN nuclear environment. dust. sublimation)," Other explanations are still possible (e.g. ionization of the X-ray absorbing medium, low gas-to-dust ratio in the AGN nuclear environment, dust sublimation)."836 Llowever. if the explanation is indeed in terms of variability. with the sources caught in dillerent. states by the X-ray anc optical observations. one would expect to find also sources whieh were switchedolf when observed in the optical and switchedon when observed in. Xrays. namely Xrav. unobscured. αλ with a type 2 optical spectrum.," However, if the explanation is indeed in terms of variability, with the sources caught in different states by the X-ray and optical observations, one would expect to find also sources which were switched–off when observed in the optical and switched–on when observed in X–rays, namely X–ray unobscured AGN with a type 2 optical spectrum."837 Objects of this kind. have indeed: been recently discovered in sparse samples of nearby Sevlert galaxies. as reported by Pappa et al. (," Objects of this kind have indeed been recently discovered in sparse samples of nearby Seyfert galaxies, as reported by Pappa et al. ("8382001) ancl Pancssa et al. (,2001) and Panessa et al. (8392002).,2002).840 Another possible implication concerns the mocdeling of the Xrav Background (ARB)., Another possible implication concerns the modeling of the X–ray Background (XRB).841 Popular synthesis models of the ARB (e.g Comastri et al., Popular synthesis models of the XRB (e.g Comastri et al.842 1995) require a significant fraction of moderately Compton.thick sources. in which the nuclear radiation can be directly observed at energies of tens of keV. Η many of the rellection.dominated sources will be proven to be simply switched:olf AGN. there may be in. principle the need. for a revision of the NRB synthesis models.," 1995) require a significant fraction of moderately Compton–thick sources, in which the nuclear radiation can be directly observed at energies of tens of keV. If many of the reflection–dominated sources will be proven to be simply switched–off AGN, there may be in principle the need for a revision of the XRB synthesis models."843 As. however. the covering factor of the rellecting matter is by all evidence pretty large (e.g. Matt ct al.," As, however, the covering factor of the reflecting matter is by all evidence pretty large (e.g. Matt et al."844 2000). it is unlikely that the possible lack of intermediate. thick sources will result to be a serious problem.," 2000), it is unlikely that the possible lack of intermediate Compton--thick sources will result to be a serious problem."845 Ao question that instead directly follows from the observations of Sevfert 2s which change look. is that of the xesence of more than one cold cireumnuclear regions.," A question that instead directly follows from the observations of Seyfert 2s which change look, is that of the presence of more than one cold circumnuclear regions."846 For at least two out of four sources in our sample. at east two fone thin the other thick) circumnuclear regions are definitely required. (," For at least two out of four sources in our sample, at least two (one thin the other thick) circumnuclear regions are definitely required. ("847LL they actually correspond. to wo physically anc ecometrically distinct regions or simply o inhomogencities in one and the same absorber. it is cillicult to say with certainty.,"If they actually correspond to two physically and geometrically distinct regions or simply to inhomogeneities in one and the same absorber, it is difficult to say with certainty."848 Llowever. there is evidence hat the Comptonthin absorbers are usually located: at much larger distances than the Comptonthick ones. see xlow).," However, there is evidence that the Compton–thin absorbers are usually located at much larger distances than the Compton–thick ones, see below)."849 For the other two. this is possible as well. but the imitec bandwidth of the observations when the sources were rellection.dominated does not permit to rule out hin reflection.," For the other two, this is possible as well, but the limited bandwidth of the observations when the sources were reflection–dominated does not permit to rule out Compton--thin reflection."850 It is worth noting that in another C'omptonhin AGN. NGC 5506. the presence of a Comptonthick rellector can be derived from direct spectral analvsis (Matt et al.," It is worth noting that in another Compton--thin AGN, NGC 5506, the presence of a Compton–thick reflector can be derived from direct spectral analysis (Matt et al."851 2001)., 2001).852 Moreover. other Compton-thick AGN in which he soft X-ray. spectrum is further absorbed by. Compton-hin matter with Ng~107 cni are known.," Moreover, other Compton-thick AGN in which the soft X-ray spectrum is further absorbed by Compton-thin matter with $N_H \sim 10^{21-22}$ $^{-2}$ , are known."853 The Comptonthin absorber may. be associated with the host, The Compton–thin absorber may be associated with the host854 One,The computation of functional determinants for various background field configurations has recently found renewed interest.855-loop corrections," In particular, the elegant Gel'fand-Yaglom \cite{Gelfand:1960,vanVleck:1928,Cameron:1945,Dashen:1974} approach, denoted sometimes as “the Coleman method” (as presented in \cite{Coleman85}) ), has been considered by various authors \cite{Baacke:2003uw,Kirsten:2003py,856Kirsten:2004qv,Burnier:2005he,857Dunne:2005rt,Dunne:2006ct,Dunne:2007mt}, following earlier work on vacuum decay and bubble nucleation \cite{Kiselev:1975eq,Kiselev:1985er,Selivanov:1988jx,858Baacke:1993ne,Baacke:1995bw,Surig:1997ne}."859 tothe instanton transi," Another method for computing the functional determinant, based on the integration of the Euclidean Green's function, has been used in Refs."860tion in the Abelian Higgs model: ," \cite{Baacke:1994bk} and \cite{Baacke:1993aj,Baacke:1994ix} for computing the fluctuation determinants for the instanton in the Abelian Higgs model in $1+1$ dimensions and for the sphaleron in the SU(2) Higgs model in 3 dimensions, respectively."861Gel'fand-Yaglom and , When one tries to naively apply the Gel'fand-Yaglom method to these cases of topological solutions in gauge theories one encounters a specific difficulty: the topological soliton modifies the centrifugal barriers and as a consequence the contribution of the s-wave sector is infinite.862Green's function methods Jürgen , The problem is avoided when using the Green's function method if the summation over partial waves is carried out before the integration of the Green's function.863Baacke! Fachbe, For the Gel'fand-Yaglom method a modified approach is required; it is the aim of this work to elucidate the problem and its solution.864reic," At the same time we consider the relation between the methods, analytically and numerically."865"h Physik, "," We use the Abelian Higgs model here mainly as a typical example of a model with a topological soliton, the problem is present for the sphaleron transition in the electroweak SU(2) Higgs model as well."866Technische Universit," The Abelian Higgs model in $(1+1)$ has found considerable attention since on the one hand it shares certain features with the electroweak theory, and on the other hand it is simple enough to serve as a theoretical and numerical laboratory."867at Dortinund D 44221 Dortinun," In the context of the baryon number violation the high temperature sphaleron transition in this model has been studied \cite{Grigoriev:1989je,Tang:1997cy} for which exact classical solutions and an exact expression of the sphaleron determinant \cite{Bochkarev:1987wg,Bochkarev:1989vu} are known, thus providing a complete one-loop semiclassical transition rate which can be studied numerically on the lattice, e.g. by measuring the fluctuations of the Chern-Simons number."868"d, Germany l"," Another prominent feature of the model is the existence of instanton solutions \cite{Nielsen:1973cs,deVega:1976mi} which give rise again to fluctuations in the topological charge of the vacuum and thereby to baryon number violation."869eanaihΑΕ ος," In the dilute gas approximation for the instantons transition rate, or equivalently the density"870additional forms of particle acceleration. ancl even. exotic possibilities.,additional forms of particle acceleration and even exotic possibilities.871 ''rving to narrow down future observational clirections. it is important to search for possible timing/cirectional correlations of the arrival direction. of cosmic ray with AGN flares.," Trying to narrow down future observational directions, it is important to search for possible timing/directional correlations of the arrival direction of cosmic ray with AGN flares."872 Such exercise currently lacks the dedicated sky monitoring that could potentially identify the majority of AGN flares in real time., Such exercise currently lacks the dedicated sky monitoring that could potentially identify the majority of AGN flares in real time.873 Lt would. also require the rapid release of VILECR. cetections (including position) in real time., It would also require the rapid release of UHECR detections (including position) in real time.874 The existing Leet of MeV-TeV telescopes inchucdingAGILE. ILIZS.S.. ALACHIC. αμα VERITAS could. help trace strong Wares in the gamma-ray banc.," The existing fleet of MeV-TeV telescopes including, H.E.S.S., MAGIC, and VERITAS could help trace strong flares in the gamma-ray band."875— LBowever.— eroundbreaking progress into the gamma-ray variability domain might have to wait for the next generation. of VILE experiments.," However, groundbreaking progress into the gamma-ray variability domain might have to wait for the next generation of VHE experiments."876 In the theoretical front. it is critical to improve existing models of cosmic ray propagation.," In the theoretical front, it is critical to improve existing models of cosmic ray propagation."877" La particular. based. on current cross-correlation studies. the initial expectation that cosmic ray trajectories at energies 107"" eV should. be fairly. rigid. does not appear to be so obvious."," In particular, based on current cross-correlation studies, the initial expectation that cosmic ray trajectories at energies $> 10^{19}$ eV should be fairly rigid does not appear to be so obvious."878 We thank all the members of Cirupo de Altas. Encretaas (GALE) at the Universidad. Complutense ce Madrid: for stimulating conversations during our dailv morning collec., We thank all the members of Grupo de Altas Energíaas (GAE) at the Universidad Complutense de Madrid for stimulating conversations during our daily morning coffee.879 We also thank the anonymous referee for useful suggestions., We also thank the anonymous referee for useful suggestions.880 N.M. also acknowledges support from the Spanish Ministry of Science and Innovation. through a Ramonn v Cajal fellowship., N.M. also acknowledges support from the Spanish Ministry of Science and Innovation through a Ramónn y Cajal fellowship.881to realize (hat the amplitudes shown in Figures 5-7 are not exponentially erowing as in the usual unforced dvuamo solutions. but instead represent aniplitudes of forced oscillatory solutions.,"to realize that the amplitudes shown in Figures 5-7 are not exponentially growing as in the usual unforced dynamo solutions, but instead represent amplitudes of forced oscillatory solutions."882 Strictly speaking. these are not self excited dvnamos. because of the top boundary foreing. but thev are dvnamos nontheless.," Strictly speaking, these are not self excited dynamos, because of the top boundary forcing, but they are dynamos nontheless."883" For these parameter values. equations (43) and (44) predict resonance will occur near o,=0.801.—0.225 [or Pip=0.03 and 0.535.—0.003 lor 2,=0.003."," For these parameter values, equations (43) and (44) predict resonance will occur near $\alpha_L=0.807,-0.225$ for $P_{\eta L}=0.03$ and $0.585,-0.003$ for $P_{\eta L}=0.003$."884 We see strong upward spikes in LBL. the amplitucle (absolute value) of the toroidal field in the lower laver (gold curve) al about these values of αι.," We see strong upward spikes in $ABL$, the amplitude (absolute value) of the toroidal field in the lower layer (gold curve) at about these values of $\alpha_L$ ."885 The lower laver poloidal potential AL (red curve) also peaks there., The lower layer poloidal potential $AAL$ (red curve) also peaks there.886" 5maller peaks al (he same ay, are present in the toroidal fields in the middle ancl upper laver (AAS. dark blue curvezADU. dark green curve) while (he poloidal potentials GLLV. light blue curve: LAU. light ereen curve) of these lavers respond to the resonance hardly at all."," Smaller peaks at the same $\alpha_L$ are present in the toroidal fields in the middle and upper layer $ABM$, dark blue $ABU$, dark green curve) while the poloidal potentials $AAM$, light blue curve; $AAU$, light green curve) of these layers respond to the resonance hardly at all."887" Finally. (here isa downward spike in (he poloidal potential of the lower laver al a,—0."," Finally, there isa downward spike in the poloidal potential of the lower layer at $\alpha_L=0$."888" The poloidal potential of the upper laver is much lareer than that of the middle laver because the former is determined directly by Che forcing at the top. while in the middle laver only a small o4, is present."," The poloidal potential of the upper layer is much larger than that of the middle layer because the former is determined directly by the forcing at the top, while in the middle layer only a small $\alpha_M$ is present."889 Several features of Figures 5 and 6 are notable., Several features of Figures 5 and 6 are notable.890" We see in Figure 5 that for all values of a, (here is a large response in the lower laver. compared to the other lavers. to the forcing applied at the top. even though (he magnetic diffusivity in the lower laver is the same as (hat ol the middle laver."," We see in Figure 5 that for all values of $\alpha_L$ there is a large response in the lower layer, compared to the other layers, to the forcing applied at the top, even though the magnetic diffusivity in the lower layer is the same as that of the middle layer."891 This is because the meridional flow and the a of the middle laver are not close to the values needed for resonance in that laver., This is because the meridional flow and the $\alpha$ of the middle layer are not close to the values needed for resonance in that layer.892 But at the same time. the middle and upper lavers do show successively lower but still significant peaks in toroidal fields near the same values of αι.," But at the same time, the middle and upper layers do show successively lower but still significant peaks in toroidal fields near the same values of $\alpha_L$."893 This is caused by maenetic diffusion upward across (he interfaces between lavers., This is caused by magnetic diffusion upward across the interfaces between layers.894 The main changes seen in Figure 6 compared (to Figure 5 are that with diffusivity ol the lower laver reduced by a [actor of ten. the resonance becomes much narrower ancl sharper.," The main changes seen in Figure 6 compared to Figure 5 are that with diffusivity of the lower layer reduced by a factor of ten, the resonance becomes much narrower and sharper."895" In other words. with lower cdiffusivity the range of a, over which there is substantial amplification of the effect of (he forcing at the top is narrower."," In other words, with lower diffusivity the range of $\alpha_L$ over which there is substantial amplification of the effect of the forcing at the top is narrower."896" Bul where resonance does occur. the middle and upper lavers respond more strongly to the resonance for non-zero a,."," But where resonance does occur, the middle and upper layers respond more strongly to the resonance for non-zero $\alpha_L$."897 This is not true for the resonance near a;=0. because such a low value leads to less production of poloidal field in the lower laver (compare the red curves in Figures 5 and 6 in the neighborhood of the resonance for negative αρ). from which the lower laver toroidal lield must be produced by the differential rotation there.," This is not true for the resonance near $\alpha_L=0$, because such a low value leads to less production of poloidal field in the lower layer (compare the red curves in Figures 5 and 6 in the neighborhood of the resonance for negative $\alpha_L$ ), from which the lower layer toroidal field must be produced by the differential rotation there."898 Figures 5 and 6 ave for a rather precisely chosen lower laver meridional [low speed., Figures 5 and 6 are for a rather precisely chosen lower layer meridional flow speed.899 What happens to the resonance if we move away from that speed?, What happens to the resonance if we move away from that speed?900" We have examined (his (question by computing amplitudes of toroidal aud poloidal fields as functions of a,for other speeds. namely ve;=—15.—14.—13.212. 211."," We have examined this question by computing amplitudes of toroidal and poloidal fields as functions of $\alpha_L$for other speeds, namely $v_U=-15,-14,-13,901-12,-11$ ."902 We find the same resonances as seen in Figures 5, We find the same resonances as seen in Figures 5903"It is evident that the criterion for the formation of Pop IL5 stus. Ej=By~10Ἴονο, is fulfilled in halos that cool via atomic hydrogen lines. but not in those that cool via II».","It is evident that the criterion for the formation of Pop II.5 stars, $E_b \ga E_0 \sim 10^{53}$ erg, is fulfilled in halos that cool via atomic hydrogen lines, but not in those that cool via $_{2}$."904 Within the framework presented in this paper. Pop II stars can clearly form in epoch 3. ab which point we assume that most of the IGM is enriched to a level in excess of Zug.," Within the framework presented in this paper, Pop II stars can clearly form in epoch 3, at which point we assume that most of the IGM is enriched to a level in excess of $Z_{\rm crit}$."905 It is likely. however. (hat Pop II star formation already ensues during epoch 2.," It is likely, however, that Pop II star formation already ensues during epoch 2."906 The metal enrichment due (ο VMSs is so efficient that the host svstem is expected to reach the critical metallicity well belore the general IGM does., The metal enrichment due to VMSs is so efficient that the host system is expected to reach the critical metallicity well before the general IGM does.907" In fact. one can estimate that already. VMS could enrich the 10*M. of gas in the typical star-forming halo in epoch 2 to the eritical level: where we have assumed for simplicity (hat none of the metals have escaped the halo. corresponding to the limiting case of fii,=0 (see 2.3)."," In fact, one can estimate that already VMS could enrich the $\sim 10^7\,\msun$ of gas in the typical star-forming halo in epoch 2 to the critical level: where we have assumed for simplicity that none of the metals have escaped the halo, corresponding to the limiting case of $f_{\rm mix}=0$ (see 2.3)."908 During epoch 2. therefore. we expect all three stellar populations (o occur almost simultaneously in a given star forming svstem.," During epoch 2, therefore, we expect all three stellar populations to occur almost simultaneously in a given star forming system."909 In Table 1. we summarize (he association of the various stellar populations with the distinct epochs of star formation.," In Table 1, we summarize the association of the various stellar populations with the distinct epochs of star formation."910 We now tentatively suggest how these stellar populations might relate to the dilferent ‘lasses of SNe as proposed by Qian&Wasserburg(2002)., We now tentatively suggest how these stellar populations might relate to the different classes of SNe as proposed by \citet{QiaWas02}.911. These authors (henceforth QW) account for the observed. abundance patterns in low-metallicity Galactic halo stars within 1ο [raanework of three distinct classes of SNe., These authors (henceforth QW) account for the observed abundance patterns in low-metallicity Galactic halo stars within the framework of three distinct classes of SNe.912 At the beginning of the nucleosvnthetic chain. a generation of very massive stars explodes to enrich (he primordial material mostly with Fe. but producing no elements bevond the iron peak.," At the beginning of the nucleosynthetic chain, a generation of very massive stars explodes to enrich the primordial material mostly with Fe, but producing no elements beyond the iron peak."913 It seems natural to identilv the QW VAIS SNe with the Pop HI PISNe discussed here., It seems natural to identify the QW VMS SNe with the Pop III PISNe discussed here.914 According to QW. at some later stage in (he chemical enrichment history. more normal. (vpe II. SNe begin to contribute nucleosynthetic products.," According to QW, at some later stage in the chemical enrichment history, more normal, type II, SNe begin to contribute nucleosynthetic products."915 More specilically. QW. distinguish between a class of high-frequency ancl type IE SNe. named SN UC) and SN ICL). respectively.," More specifically, QW distinguish between a class of high-frequency and low-frequency type II SNe, named SN ) and SN ), respectively."916 The7/ events produce mainlv (he heavy r-process elements bul no Fe. whereas the events contribute mainly the light process elements as well as Fe.," The events produce mainly the heavy -process elements but no Fe, whereas the events contribute mainly the light -process elements as well as Fe."917 These two classes of SN II are postulated. on purelv phenomenological grounds. and it is presently not known what kind of progenitor stars could physically give rise to them.," These two classes of SN II are postulated on purely phenomenological grounds, and it is presently not known what kind of progenitor stars could physically give rise to them."918 There are. however. some indications (hat the// evenis correspond to the explosion of comparatively low-mass stars that are only barely able to reach the SN stage (see QW and references therein).," There are, however, some indications that the events correspond to the explosion of comparatively low-mass stars that are only barely able to reach the SN stage (see QW and references therein)."919 Given that Pop 11.9 stars are more massive (han Pop II stars by ~one order of magnitude. we speculate that Population 11.5 might predominantly give rise to SNe LCL). whereas Population II could lead to both the," Given that Pop II.5 stars are more massive than Pop II stars by $\sim$ one order of magnitude, we speculate that Population II.5 might predominantly give rise to SNe ), whereas Population II could lead to both the"920 Given that Pop 11.9 stars are more massive (han Pop II stars by ~one order of magnitude. we speculate that Population 11.5 might predominantly give rise to SNe LCL). whereas Population II could lead to both the ," Given that Pop II.5 stars are more massive than Pop II stars by $\sim$ one order of magnitude, we speculate that Population II.5 might predominantly give rise to SNe ), whereas Population II could lead to both the"921 Given that Pop 11.9 stars are more massive (han Pop II stars by ~one order of magnitude. we speculate that Population 11.5 might predominantly give rise to SNe LCL). whereas Population II could lead to both the {," Given that Pop II.5 stars are more massive than Pop II stars by $\sim$ one order of magnitude, we speculate that Population II.5 might predominantly give rise to SNe ), whereas Population II could lead to both the"922 Given that Pop 11.9 stars are more massive (han Pop II stars by ~one order of magnitude. we speculate that Population 11.5 might predominantly give rise to SNe LCL). whereas Population II could lead to both the {/," Given that Pop II.5 stars are more massive than Pop II stars by $\sim$ one order of magnitude, we speculate that Population II.5 might predominantly give rise to SNe ), whereas Population II could lead to both the"923shows that small amplitude variations can be detected more often on long time scale than on short time scale.,shows that small amplitude variations can be detected more often on long time scale than on short time scale.924 On the other end we note that. considering only sources for which variability has been detected. on time scale less than 30 hours the amplitude of the variation. are mainly lower than 30 per cent while on longer time scale. the amplitude are mainly greater than 30 per cent.," On the other end we note that, considering only sources for which variability has been detected, on time scale less than 30 hours the amplitude of the variation are mainly lower than 30 per cent while on longer time scale the amplitude are mainly greater than 30 per cent."925 Unfortunallv. using only the ROSAT data we are not able to determine the very nature of the detected variability and to understand if the different intensity detected on time scale shorter and longer than 30 hours is due to cdillerent ohvsical and/or geometrical properties.," Unfortunally, using only the ROSAT data we are not able to determine the very nature of the detected variability and to understand if the different intensity detected on time scale shorter and longer than 30 hours is due to different physical and/or geometrical properties."926 As shown by Haardt. Maraschi and. Ghisellini. (1997). he only wav to determine the real nature of an observed X- variability is an accurate analysis of the (us variability as à function of the spectral variability in the 0 keV xuxd together with simultaneous observation in the 2.0 keV band.," As shown by Haardt, Maraschi and Ghisellini (1997), the only way to determine the real nature of an observed X-ray variability is an accurate analysis of the flux variability as a function of the spectral variability in the $-$ 10 keV band together with simultaneous observation in the $-$ 2.0 keV band."927 However. it is interesting to note that a time scale of 30 1ours corresponds to an upper limit to the size of the source (R<edt) of ~ 1017 em.," However, it is interesting to note that a time scale of 30 hours corresponds to an upper limit to the size of the source $\leq$ $\delta$ t) of $\sim$ $\times 10^{15}$ cm."928 In the most accepted picture of he physical structure of AGN (sec. for example. Urry and 'adovani 1905). this region is between the accretion disk around the central black hole (~1300 em for a central black hole of 107 M.) and the region of the broad line clouds (2.201019 em).," In the most accepted picture of the physical structure of AGN (see, for example, Urry and Padovani 1995), this region is between the accretion disk around the central black hole $\sim1-30\times 10^{14}$ cm for a central black hole of $^8$ $_{\odot}$ ) and the region of the broad line clouds $\sim2-20\times 10^{16}$ cm)."929 Therefore. while the variability on time scale shorten than 30 hours is surely associated with a variation in the accretion disk. on longer time scale it can arise [rom larger regions where other factors (£c. scattered radiation. absorbing clouds) can contribute to the observed variability.," Therefore, while the variability on time scale shorten than 30 hours is surely associated with a variation in the accretion disk, on longer time scale it can arise from larger regions where other factors $i.e.$ scattered radiation, absorbing clouds) can contribute to the observed variability."930 bor one source 1257) the observed variability is not due to a Hux variation but. instead. to a variation in the column density along the line of sight.," For one source $-$ 1257) the observed variability is not due to a flux variation but, instead, to a variation in the column density along the line of sight."931 Since this variability has been observed on a time scale of ~ 3.9 days. it is probably associate to the broad line clouds.," Since this variability has been observed on a time scale of $\sim$ 3.9 days, it is probably associated to the broad line clouds."932 Spectral variability was cletected in only two sources., Spectral variability was detected in only two sources.933 AMS1158.6 0323 shows an widening of the spectrum with increasing intensity while 3712 shows a softening of the spectrum wit1 increasing intensity., $-$ 0323 shows an hardening of the spectrum with increasing intensity while $-$ 3712 shows a softening of the spectrum with increasing intensity.934 Finally AIS1215.9|3005. (AINN766). which was excluded from our analysis because already. stucied in detail by Alolenedi zux Alaccacaro (1994) but is part of the selected. sample. shows a cdillerent behavior between the soft. (0.1-0.9. keV). anc hard (0.9-2.0 keV) part of the spectrum.," Finally MS1215.9+3005 (MKN766), which was excluded from our analysis because already studied in detail by Molendi and Maccacaro (1994) but is part of the selected sample, shows a different behavior between the soft (0.1-0.9 keV) and hard (0.9-2.0 keV) part of the spectrum."935 The soft. par harden as the source brightens while the hard part does no change significantly., The soft part harden as the source brightens while the hard part does not change significantly.936 μονο results confirm that the overal picture of the flux. and. spectral variability is still. rather confused., These results confirm that the overall picture of the flux and spectral variability is still rather confused.937 An improvement of our knowledge in this fiel should come from the data of the recently launchecl NTE and SAN X-ray. satellite and [rom the forthcoming ANAL and NMM missions. characterized by the possibility of long. uninterrupted observations over a broader energy. band.," An improvement of our knowledge in this field should come from the data of the recently launched XTE and SAX X-ray satellite and from the forthcoming AXAF and XMM missions, characterized by the possibility of long, uninterrupted observations over a broader energy band."938 We thank the referee for useful. comments and. criticisms., We thank the referee for useful comments and criticisms.939 This work has received. partial financial support from the ]talian Space Ageney (ASL contract 95-RS-72 1G1PALE/2)., This work has received partial financial support from the Italian Space Agency (ASI contract 95-RS-72 161FAE/2).940 This research has made use of. the NASA/IPAC Extragalactic Database (NIED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Acronautics ancl 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 Aeronautics and Space Administration."941"ionization implied by the observed low-ionization Me and Fe absorption lines with the inferred values of ης and L (2 10""ergs s7!).",ionization implied by the observed low-ionization Mg and Fe absorption lines with the inferred values of $n_e$ and $L$ (= $10^{46} {\rm ergs~s^{-1}}$ ).942 One can reduce this distance estimate by attenuating the incident continuum by an intermediate gas “shield.”, One can reduce this distance estimate by attenuating the incident continuum by an intermediate gas “shield.”943 In this model. however. ions at different ionization states (such as the Fe Il and Mg I components seen in FBQS 1044) are expected to occupy different regions in space. with lower values of U corresponding to larger distances from the center (e.g..Voit.Weymann.&Korista1993).," In this model, however, ions at different ionization states (such as the Fe II and Mg I components seen in FBQS 1044) are expected to occupy different regions in space, with lower values of $U$ corresponding to larger distances from the center \citep[e.g.,][]{VWK93}."944. This stratification. will likely lead to disparate. velocities for the different ions: for example. models of self-similar MHD winds and of radiatively-driven constant-U’ outflows predict that the terminal velocity. v4. varies as DM where sa is the radius at which the gas is injected into the outflow (e.g..Blandford&Payne1982:Arav.Lt.Begelman1994).," This stratification will likely lead to disparate velocities for the different ions: for example, models of self-similar MHD winds and of radiatively-driven $U$ outflows predict that the terminal velocity, $v_\infty$, varies as $r_{\rm945inject}^{-1/2}$, where $r_{\rm inject}$ is the radius at which the gas is injected into the outflow \citep*[e.g.,][]{BP82,A94}."946 Models that rely solely on shielding and distance to separate the different ionization components therefore cannot explain dKOI's observations. in which different ionization states are found to have similar velocities.," Models that rely solely on shielding and distance to separate the different ionization components therefore cannot explain dK01's observations, in which different ionization states are found to have similar velocities."947 We propose to explain the observations of FBQS 1044 by generalizing the single-phase shielded-gas model. attributing the different ionization states to different density components in à multiphase outflow.," We propose to explain the observations of FBQS 1044 by generalizing the single-phase shielded-gas model, attributing the different ionization states to different density components in a multiphase outflow."948 These components coexist at the same distance from the center and thus have different ionization parameters but essentially the same velocities., These components coexist at the same distance from the center and thus have different ionization parameters but essentially the same velocities.949 In particular. if the high- and low-ionization lines arise. respectively. in a continuous wind and in dense clouds that are embedded in the outflow. then all the absorption components produced in a given region of the wind will exhibit similar kinematic signatures.," In particular, if the high- and low-ionization lines arise, respectively, in a continuous wind and in dense clouds that are embedded in the outflow, then all the absorption components produced in a given region of the wind will exhibit similar kinematic signatures."950 In our model. the continuous gas component extends from near the black hole's event horizon out to the distance where the observed Fe II absorption and electron density can be reproduced.," In our model, the continuous gas component extends from near the black hole's event horizon out to the distance where the observed Fe II absorption and electron density can be reproduced."951" The inner part of this component (interior to the BALR) is identified as the ""shield.""", The inner part of this component (interior to the BALR) is identified as the “shield.”952 This region could be associated with an MHD-driven (Kónigl&Kartje1994). a Thomson scattering-driven (e.g...Blandford 2001).. or a “failed” line-driven (e.g...Murrayetal.1995;Proga.&Kallman2000) disk wind. or with a disk corona (e.g.Emmeringetal. 1992).," This region could be associated with an MHD-driven \citep{KK94}, a Thomson scattering-driven \citep[e.g.,][]{B01}, , or a “failed” line-driven \citep[e.g.,][]{M95,P00} disk wind, or with a disk corona \citep[e.g.,][]{EBS92}."953. The outer region of the continuous gas component Is outflowing and accounts for the Fe II and Mg II absorption. but is still too highly ionized to contain Mg I absorbing gas.," The outer region of the continuous gas component is outflowing and accounts for the Fe II and Mg II absorption, but is still too highly ionized to contain Mg I absorbing gas."954 Within this outflow are embedded higher-density clouds that account for the lower-ionization Mg I absorption: their high density yields a lower U in the clouds. allowing Mg 1 to exist.," Within this outflow are embedded higher-density clouds that account for the lower-ionization Mg I absorption: their high density yields a lower U in the clouds, allowing Mg I to exist."955 Such a two-component outflow may arise naturally in the context of a centrifugally driven disk wind. which could uplift clouds from the disk surface by its ram pressure and confine them by its internal magnetic pressure (e.g..Emmer-2001 ).," Such a two-component outflow may arise naturally in the context of a centrifugally driven disk wind, which could uplift clouds from the disk surface by its ram pressure and confine them by its internal magnetic pressure \citep[e.g.,][]{EBS92,KKE99,EKK01}."956. Alternatively. the clouds may represent transient density enhancements that are produced by turbulence (e.g..BottorffFerland2001) or by shocks in a radiatively driven wind (e.g..Aravetal. 1994).," Alternatively, the clouds may represent transient density enhancements that are produced by turbulence \citep[e.g.,][]{BF01} or by shocks in a radiatively driven wind \citep[e.g.,][]{A94}."957". For illustration. we adopt here the “clouds uplifted and confined by an MHD wind"" picture."," For illustration, we adopt here the “clouds uplifted and confined by an MHD wind” picture."958 Our model consists of two segments that represent two distinct gas phases., Our model consists of two segments that represent two distinct gas phases.959 The first segment. which corresponds to the continuous phase. extends from ry=10.GM/c27.4«108em (following dKOl. we take the central black-hole mass to be M25<IOM ..) out to just past the hydrogen recombination front. which corresponds to the Fe HII. > Fe II transition.," The first segment, which corresponds to the continuous phase, extends from $r_{\rm in}=10~GM/c^{2}=7.4 \times 10^{13} \ {\rm cm}$ (following dK01, we take the central black-hole mass to be $M=5 \times96010^{8} M_{\sun}$ ) out to just past the hydrogen recombination front, which corresponds to the Fe III $\rightarrow$ Fe II transition."961 The second segment. which models the confined dense clouds. is a constant-density zone located just beyond the continuous gas component (since the cloud temperature is nearly uniform. this provides a good representation of magnetically confined constant-pressure clouds).," The second segment, which models the confined dense clouds, is a constant-density zone located just beyond the continuous gas component (since the cloud temperature is nearly uniform, this provides a good representation of magnetically confined constant-pressure clouds)."962 In reality. the continuous outflow in the line-absorption region can be expected to engulf the clouds. but this simplified model should capture the basic physical effects of a two-phase medium. (," In reality, the continuous outflow in the line-absorption region can be expected to engulf the clouds, but this simplified model should capture the basic physical effects of a two-phase medium. ("963We verified that our results are independent of the cloud radial distribution. within. the Fe II/Mg I absorption region.),We verified that our results are independent of the cloud radial distribution within the Fe II/Mg I absorption region.)964 We obtain the ionization. structure of the different gas phases using the photoionization code Cloudy (Ferland2000).. adopting the same source parameters as in dKOL and assuming (as they do in most of their models) à Mathews&Ferlanc (1987) spectrum.," We obtain the ionization structure of the different gas phases using the photoionization code Cloudy \citep{F00}, adopting the same source parameters as in dK01 and assuming (as they do in most of their models) a \citeauthor{MF87} (1987) spectrum."965 We take the scaling of the hydrogen number density with spherical radius to be n(r)x77!. as in the AG disk-wind models considered by Kónigl&Kartje (1994).," We take the scaling of the hydrogen number density with spherical radius to be $n(r) \propto966r^{-1}$, as in the AGN disk-wind models considered by \citeauthor{KK94} (1994)."967 In these self-similar MHD outflows. the magnetic field Bying also scales as 77!. which results in magnetically confined clouds having a constant lonization parameter.," In these self-similar MHD outflows, the magnetic field $B_{\rm wind}$ also scales as $r^{-1}$, which results in magnetically confined clouds having a constant ionization parameter."968" We first calculate the photoionization of the continuous component. stopping the computation when 7n, drops to 4«10? em? (the value inferred from the observations).We then calculate how the radiation emerging through the continuous segment affects clouds located at that distance."," We first calculate the photoionization of the continuous component, stopping the computation when $n_{e}$ drops to $4 \times 10^{3}$ $^{-3}$ (the value inferred from the observations).We then calculate how the radiation emerging through the continuous segment affects clouds located at that distance."969" The two parameters we adjust in our model are με, the wind hydrogen number density at 75,. and ης. the hydrogen number density of the clouds."," The two parameters we adjust in our model are $n_{w,i}$, the wind hydrogen number density at $r_{\rm in}$, and $n_c$ , the hydrogen number density of the clouds."970" We explore a range of models to find the values of n,; and n. that best reproduce the observations."," We explore a range of models to find the values of $n_{w,i}$ and $n_c$ that best reproduce the observations."971" Our best-fit value for the wind density is 4,z107cm."," Our best-fit value for the wind density is $n_{w,i} \approx 10^{8.75}\972{\rm cm}^{-3}$."973" This yields the observed 7, in the region (at 7z4pc) where the Fe II column density in the wind attains the observed value of3«10P em™. which is significant since the 7, measurement comes from the Fe II absorption lines."," This yields the observed $n_e$ in the region (at $r974\approx 4\ {\rm pc}$ ) where the Fe II column density in the wind attains the observed value of $ 3 \times 10^{15}$ $^{-2}$, which is significant since the $n_{e}$ measurement comes from the Fe II absorption lines."975 However. we do have to cut off the outflow very close to the end of the hydrogen recombination. front so as not to exceed the observed Fe II column (see Fig.," However, we do have to cut off the outflow very close to the end of the hydrogen recombination front so as not to exceed the observed Fe II column (see Fig."976 1)., 1).977 Although the abrupt end of the absorbing column could be an artifact caused by our simplified treatment. the occurrence of a strong reduction in the absorption at this location may have an actual physical basis.," Although the abrupt end of the absorbing column could be an artifact caused by our simplified treatment, the occurrence of a strong reduction in the absorption at this location may have an actual physical basis."978" It may be a consequence of the decrease in the ionization fraction in this region. which reduces the efficiency with which the disk can drive an MHD outflow. and it may also reflect a transition from a gaseous to a ""clumpy disk (seeShlosman&Begelman or from differential to solid-body disk rotation Korista.&Shlosman2000) on that scale."," It may be a consequence of the decrease in the ionization fraction in this region, which reduces the efficiency with which the disk can drive an MHD outflow, and it may also reflect a transition from a gaseous to a “clumpy” disk \citep[see][]{SB87} or from differential to solid-body disk rotation \citep[see][]{BKS00} on that scale."979 We also note from Figure | that the Mg II front occurs — 2.5 times closer to the central source than the Fe II front. (, We also note from Figure 1 that the Mg II front occurs $\sim$ 2.5 times closer to the central source than the Fe II front. (980This ts due to the formation of a He Π » He II front in the wind that absorbs photons with E > 54.4 eV. allowing Mg HI. with an ionization energy of 80.1 eV. to recombine into Mg IL),"This is due to the formation of a He III $\rightarrow$ He II front in the wind that absorbs photons with E $>$ 54.4 eV, allowing Mg III, with an ionization energy of 80.1 eV, to recombine into Mg II.)"981 Since v4xl'inica in our chosen disk-wind model (see $1)). the predicted smaller initial radius of the Mg II front is consistent with the higher Mg II velocities observed in FBQS 1044.," Since $v_\infty \propto r^{-1/2}_{\rm inject}$ in our chosen disk-wind model (see \ref{intro}) ), the predicted smaller initial radius of the Mg II front is consistent with the higher Mg II velocities observed in FBQS 1044."982" Besides determining the measured values of the Fe II column and of n,. the continuous wind componentin our model also exerts a strong influence on the cloud absorption properties through its effect on the transmitted continuum spectrum."," Besides determining the measured values of the Fe II column and of $n_e$ , the continuous wind componentin our model also exerts a strong influence on the cloud absorption properties through its effect on the transmitted continuum spectrum."983 Wefind that. in order for the clouds to account for the," Wefind that, in order for the clouds to account for the"984 (Willianis&Cieza2011)— (Shakura&Suuvaev1973).. (Lvuden-Pringle1971). (Lubow&Ida," \citep{williams11} \citep{shakura73}. \citep{lyndenbell74}, \citep{lubow10}."9852010). (Chiang&Youcin2010) (VOIkctal.1980:Oriel&Cuzzi2007) (AIRE:Tawley1998) review.secArmitage2011).. and acerction rates (Hartinaun 1998). which nuplv that protoplauetary disks around low-mass stars evolve and are dispersed ou Aber time scales.," \citep{chiang10} \citep{volk80,ormel07} \cite[MRI;][]{balbus98} \citep[for a review, see][]{armitage11}, and accretion rates \citep{hartmann98}, which imply that protoplanetary disks around low-mass stars evolve and are dispersed on Myr time scales."986 This observation pius cown the aueular monentun transport cfiicicnucy if the evolution results from turbulence: the efficiency. is conventionally expressed in terms of a Shakura&Sunvaev(1973) ocm107., This observation pins down the angular momentum transport efficiency if the evolution results from turbulence; the efficiency is conventionally expressed in terms of a \cite{shakura73} $\alpha \approx 10^{-2}$.987" Cenerically, this level of stress within a Hid disk implies characteristic velocity. perturbations eoneuxOle, whereοςisthesoundspeed.c.g.Balbus&Hawley 1998).. but this estimateis so crude as o be useful mainly for motivating further observations."," Generically, this level of stress within a fluid disk implies characteristic velocity perturbations $v \sim \alpha^{1/2} c_s 988\sim 0.1 c_s$ \citep[where $c_s$ is the sound speed, e.g.][]{balbus98}, but this estimateis so crude as to be useful mainly for motivating further observations."989 Neither if. nor other constraints on o from detailed uodeling of individual svstemis (Iueso&Cuillot2005) xovide auv information ou the nature of turbulence or on any dependence of its properties ou height above the uid-planuc.," Neither it, nor other constraints on $\alpha$ from detailed modeling of individual systems \citep{hueso05} provide any information on the nature of turbulence or on any dependence of its properties on height above the mid-plane."990 Direct deteziination of the streneth of protoplauctary disk turbulence is possible bv detecting the turbuleut xoadenime of molecular lues observed in the infrared (Corr.Tokunaga&Najita2001). or sub-nuua (IIushesetal 2011)., Direct determination of the strength of protoplanetary disk turbulence is possible by detecting the turbulent broadening of molecular lines observed in the infrared \citep{carr04} or sub-mm \citep{hughes11}.991 Subsouic turbulent broadening is a challenging quantity to mieasure. as protoplanctary disks are conrprised of sipersouically orbiting eas: thus. precise measurements are needed to separate the small turbulent component from the dominant bulk rotation.," Subsonic turbulent broadening is a challenging quantity to measure, as protoplanetary disks are comprised of supersonically orbiting gas; thus, precise measurements are needed to separate the small turbulent component from the dominant bulk rotation."992 Furthermore. iu the inner disk. observed diues frou the disk max be contaminated bv outflow components (Bastotal. 20111...," Furthermore, in the inner disk, observed lines from the disk may be contaminated by outflow components \citep{bast11}. ."993 Nonetheless. current observationsoftheouterregions of disks already attain precisious conrparable to the level (ο~0.16;) where a signal cau," Nonetheless, current observationsoftheouterregions of disks already attain precisions comparable to the level $v \sim 0.1 c_s$) where a signal can"994Double barred galaxies are barred spiral galaxies that contain an additional small bar nested witün the main€ bar.,Double barred galaxies are barred spiral galaxies that contain an additional small bar nested within the main bar.995 First observed by «e Vaucouleurs (1975). they may constitute ~ of barred salaxies. as Buplied: by photometric surveys (Erwin Sparke E2002. Laine: ct al.," First observed by de Vaucouleurs (1975), they may constitute $\sim$ of barred galaxies, as implied by photometric surveys (Erwin Sparke 2002, Laine et al."996 2002)., 2002).997 Ilowever. cross-correlaion of ⋅⋀∖↕⋜↧↸⊳↕↸∖↿↸∖↖↖⇁↴∖↴↘↽↕∙∖↽⊀≚↑∐⋜⋯⋜↧↴∖∷∖↴⋯∏⋜↧⋖⊇∩∩≺∖∙∐↸∖↥⋅↸∖⋜↧⇈↸∖↥⋅⋀∖↕⋎∩≺∖⋟ sugeests a lower perceitage (Molseev 2010). which is consistent with a sInematic survey of dio»ible. barred candidates using iutegral feld soectroscopyv (Moilseev et al.," However, cross-correlation of these surveys suggests a lower percentage (Moiseev 2010), which is consistent with a kinematic survey of double barred candidates using integral field spectroscopy (Moiseev et al."998 2001)., 2004).999 The freqenev at which double bars are observed 1xdicates tiat they are either recurrent or lived phenolena., The frequency at which double bars are observed indicates that they are either recurrent or long-lived phenomena.1000 Since inner bars occur often in carly-type [m]galaxies with litte or no eas to drive evolution. they are lost ikelv long-lived.," Since inner bars occur often in early-type galaxies with little or no gas to drive evolution, they are most likely long-lived."1001 This is consiseut with the fact that 1mer bars are detected iu both optical aud IR observatious. iudicatiis that they are stellar structures.," This is consistent with the fact that inner bars are detected in both optical and IR observations, indicating that they are stellar structures."1002 Observations of the apparent raudonm orieutations of tle two bars suggest that the bars are rotating independently (Buta Crocker 1993: Eriedli Martinet. 1993)., Observations of the apparent random orientations of the two bars suggest that the bars are rotating independently (Buta Crocker 1993; Friedli Martinet 1993).1003 This was later confined for the ealaxv NGC 2950. whose inner and outer bar do not rotate at the same pattern speed (Corsini et al.," This was later confirmed for the galaxy NGC 2950, whose inner and outer bar do not rotate at the same pattern speed (Corsini et al."1004 2003)., 2003).1005 It is difücult to understand how two iudepoeudeutlv rotating nested bars can be maintained bw regular motions of stars to create a loue-lived stable svstem., It is difficult to understand how two independently rotating nested bars can be maintained by regular motions of stars to create a long-lived stable system.1006 Iu particular. tje resonances of oue bar will interfere with t1ο orbita πιyport of the other. which is likely to produce ciiotfic motkus and thus coustrain possible parameters of stable seconsistent double bars.," In particular, the resonances of one bar will interfere with the orbital support of the other, which is likely to produce chaotic motions and thus constrain possible parameters of stable self-consistent double bars."1007 However. when studyius he orbital response to an assumed potential of two 1ideudeutlv/ rotating bars Maciejewski Smarke (2JOO. hereafter MS00) found stable orbits that Cui support cach bar in its rotation.," However, when studying the orbital response to an assumed potential of two independently rotating bars Maciejewski Sparke (2000, hereafter MS00) found stable orbits that can support each bar in its rotation."1008 Maciejewski Athauassoula (2007. hereafter NLAOT) showed that double bars are sustained bv families of stable double frequency. orbits. ie. orbits that oscillate only with the driving. frequenciesH+ ofn the two bars.," Maciejewski Athanassoula (2007, hereafter MA07) showed that double bars are sustained by families of stable double frequency orbits, i.e. orbits that oscillate only with the driving frequencies of the two bars."1009" SupportB for"" the two barsus ;is Dprovidedvided bvJl trajectoriesctories trapped aroundarouic thexe nu frequencyv‘Cy orbits", Support for the two bars is provided by trajectories trapped around these double frequency orbits.1010"""ts.VA double↕↸∖↴∖↸∖↴∖↿∐↖↸∖∙↖↴∖ | . studied the trappiie of trajectories around regular ordts in 23 models of cleble bars. bv varving he λαταιOCLs characterising botji bars."," Maciejewski Athanassoula (2008, hereafter MA08) studied the trapping of trajectories around regular orbits in 23 models of double bars, by varying the parameters characterising both bars."1011 They varicc the cheths. masses aud eccentricities of the bars. but they foiuid that out of the parameters of the inner bar. its pattern speed affeced the trapping most.," They varied the lengths, masses and eccentricities of the bars, but they found that out of the parameters of the inner bar, its pattern speed affected the trapping most."1012 In this peyer we 1ivestieate how the appearance of double frequency οἱ]dts supportlue the inner bar changes with its patterji speed., In this paper we investigate how the appearance of double frequency orbits supporting the inner bar changes with its pattern speed.1013 Tus we perform the orbital sructure studies. following he method developed by Cotopotos Papavaunopotlos (1980). Athaissonula et al. (," Thus we perform the orbital structure studies, following the method developed by Contopoulos Papayannopoulos (1980), Athanassoula et al. ("10141983). Teuyon Saunders (1985) aud others.,"1983), Teuben Sanders (1985) and others."1015 These studies do not aim to construct selt-cousistent models. but rathcr explore changes in he svsteni that occur when is lain paramecrs Vary.," These studies do not aim to construct self-consistent models, but rather explore changes in the system that occur when its main parameters vary."1016 We study orbits in Mocels OL 05 from ALAOs. where he patter1 speed of the inner bar was varied between SO aand 1204.," We study orbits in Models 01 – 05 from MA08, where the pattern speed of the inner bar was varied between 80 and 120."1017 We also construct new m0els PE aud 5E here. which exteud this range cown to TU aand up to 10f.," We also construct new models 02E and 05E here, which extend this range down to 70 and up to 140."1018 Thus all iuoels considered iu tUs paper are ideutical excet for he )attern spccc of the inner bar., Thus all models considered in this paper are identical except for the pattern speed of the inner bar.1019 They are the sale as Model 2 from MS00. where thο send-najor axis of he outer bar is 6 koc aud the senmi-niajor axis ο| the inwer uds 1.2 kpc.," They are the same as Model 2 from MS00, where the semi-major axis of the outer bar is 6 kpc and the semi-major axis of the inner bar is 1.2 kpc."1020 The axial ratios «of the outer aud imuer uu are 2.5 aud 2.0. respectively.," The axial ratios of the outer and inner bar are 2.5 and 2.0, respectively."1021 The mass of the inier uu is of the mass of the outer bir., The mass of the inner bar is of the mass of the outer bar.1022 The patern speed of the outer bar js 36, The pattern speed of the outer bar is 361023the integrated It-profile.,the integrated -profile.1024" It can iudicate that we observe the sui of two ""narrow [l-profiles displaced at about 1050 kan + each from other.", It can indicate that we observe the sum of two “narrow” -profiles displaced at about 40–50 km $^{-1}$ each from other.1025 Ouly 21 c line mapping of velocity field and/or very high quality Tea velocity data can help to make a final interpretation of this svsten., Only 21 cm line mapping of velocity field and/or very high quality $\alpha$ velocity data can help to make a final interpretation of this system.1026 The search in the NED resulted. in the bright conrpanion galaxy NGC 332 (= Arp 206 = VV O11) at the aueular distauce 67° with D — ποτ aud the radial velocity 616 lau +. very close to that of VV T1T.," The search in the NED resulted in the bright companion galaxy NGC 3432 (= Arp 206 = VV 011) at the angular distance $^{\prime}$ with B = $11\fm67$ and the radial velocity 616 km $^{-1}$, very close to that of VV 747."1027 This galaxy. classified as SB(sji (LINER Iu). has Mp = [NU," This galaxy, classified as SB(s)m (LINER ), has $_{B}$ = $-18\fm3$."1028 At the projected distance z 190 kpe the tidal action of this galaxy to VV 717 may also be strong enough to trigeer SF in this tiuv dw., At the projected distance $\approx$ 190 kpc the tidal action of this galaxy to VV 747 may also be strong enough to trigger SF in this tiny dwarf.1029 Oue of the important questions concerning the nature of the “nest” and “chains” of V'V-sealaxies ds their evolution status., One of the important questions concerning the nature of the “nest” and “chains” of VV-galaxies is their evolution status.1030 Current study as well as several previous publications demoustrate that many of the Iow-Iuuinosity VV-ealaxics are relatively nearby regular galaxies with several bright knots of enhanced SE., Current study as well as several previous publications demonstrate that many of the low-luminosity VV-galaxies are relatively nearby irregular galaxies with several bright knots of enhanced SF.1031 Their position in two-colour diagram indicates a presence of SF burst in many of, Their position in two-colour diagram indicates a presence of SF burst in many of1032"results for the 83CRAR sub-sample are combined with existing literature results on 3€C-class galaxies to search lor any evidence for dynamical evolution amongst the most powerful radio galaxies within the redshift interval 0.0<τςOLS,",results for the 3CRR sub-sample are combined with existing literature results on 3C-class galaxies to search for any evidence for dynamical evolution amongst the most powerful radio galaxies within the redshift interval $0.0<z<0.8$.1033 In common with the results regarding the ZP5 host-galaxy luminosities. an inspection of Table 4 reveals an apparent correlation between mean scaleleneth and racio luminosity within the 3CRR. 6CI and TORS sub-samples.," In common with the results regarding the ZP5 host-galaxy luminosities, an inspection of Table \ref{tab4} reveals an apparent correlation between mean scalelength and radio luminosity within the 3CRR, 6CE and 7CRS sub-samples."1034" his is entirely as expected. ogiven the correlation between host-galaxy ancl radio luminosity discussed. above. ancl the well known correlation between host. luminosity and scalelengthamong earlv-tvpe galaxies (c.g. r,xLUlost09x05, Dernardi et al."," This is entirely as expected given the correlation between host-galaxy and radio luminosity discussed above, and the well known correlation between host luminosity and scalelengthamong early-type galaxies (e.g. $r_{e} \propto L_{host}^{0.63\pm0.03}$; Bernardi et al."1035 2003) ]5arlv-tvpe galaxies are known to exist on a two-dimensional manifold (fundamental. plane) the threc-dimensional parameter space defined by effective scalelength. the mean surface brightness within the ellective scalelength. and. the central stellar-velocity dispersion (eg.," 2003) Early-type galaxies are known to exist on a two-dimensional manifold (fundamental plane) in the three-dimensional parameter space defined by effective scalelength, the mean surface brightness within the effective scalelength and the central stellar-velocity dispersion (eg."1036 Dressler. Lvnden-Bell Burstein 1987: Djorgovski Davis LOST).," Dressler, Lynden-Bell Burstein 1987; Djorgovski Davis 1987)."1037" At present we are engagced in obtaining stellar-velocity— dispersion nieasurements for the ZP5 sample to investigate !1011’ locaion on the fumzmoenta plane. and to estimate the masses of their centra black holes via t10 My,6 correlajon (Willott et ab."," At present we are engaged in obtaining stellar-velocity dispersion measurements for the ZP5 sample to investigate their location on the fundamental plane, and to estimate the masses of their central black holes via the $M_{bh}-\sigma$ correlation (Willott et al.,"1038 in. prep)., in prep).1039" However. armed. with just the scalcloneth anc| surface brighness parameters for each host ealaxy. it is posible o examine the piotometric projection of the ful fundamental plane. the so-called. IXormendy. or fh,re reation (Ixormoendv O77)."," However, armed with just the scalelength and surface brightness parameters for each host galaxy, it is possible to examine the photometric projection of the full fundamental plane, the so-called Kormendy or $\mu_{e}-r_{e}$ relation (Kormendy 1977)."1040 Phe Ixormendsy relation or the ZP5 sample is shown in he top panel o {Fie 5., The Kormendy relation for the ZP5 sample is shown in the top panel of Fig \ref{fig5}.1041 Intis panel the <yr:S values of the 215 objecs have been Ix-corrected and corrected for (1|5)! surfacc-brightness cimming. out have not been corrected Lor osslve evolution.," In this panel the $<\mu>_{e}$ values of the ZP5 objects have been K-corrected and corrected for $(1+z)^4$ surface-brightness dimming, but have not been corrected for passive evolution."1042 Using 116 iterative 47 EYPENY routine. which takes account of errors in both parameters (Press et al.," Using the iterative $\chi^{2}$ FITEXY routine, which takes account of errors in both parameters (Press et al."1043 1992). the best-fitting form of the Ixormencdyv relation for he non-evolutionary corrected ZI5 sample is: In the micelle panel of Fig 5 je same ZP5 data are repeated. along with the τὸ Dow-redshift radio galaxies from the fundamental plane study of Betoni οἱ al. (," 1992), the best-fitting form of the Kormendy relation for the non-evolutionary corrected ZP5 sample is: In the middle panel of Fig \ref{fig5} the same ZP5 data are repeated, along with the 73 low-redshift radio galaxies from the fundamental plane study of Bettoni et al. ("10442001).,2001).1045 The best-fitting relation to Bettoni ct al., The best-fitting relation to Bettoni et al.1046 sample is: Given that the Jettoni οἱ al., sample is: Given that the Bettoni et al.1047 sample is virtually at redshift) zero. he vertical offset between the. IXormendvy relation of the Jettoni οἱ al.," sample is virtually at redshift zero, the vertical offset between the Kormendy relation of the Bettoni et al."1048 sample and hat of the ZP5 sample is a direct. indication o “the amount of luminosity evolution between z=0 and z=0.5., sample and that of the ZP5 sample is a direct indication of the amount of luminosity evolution between $z=0$ and $z=0.5$.1049 If he two samples are fitted with a Ixormendy relation of ixecl slope 3.52 (intermediate ο their two indexendent fits) then the best-fitting intercepts are 16.30(-E0.07) and 16.77 EO.05). for the ZP5 and sotteoni et al.," If the two samples are fitted with a Kormendy relation of fixed slope 3.52 (intermediate to their two independent fits) then the best-fitting intercepts are $16.30(\pm 0.07)$ and $16.77(\pm 0.05)$ , for the ZP5 and Bettoni et al."1050 samples respectively., samples respectively.1051 This directly implies O47dFE0.09 maenituc of &R band. Iuminosity, This directly implies $0.47\pm0.09$ magnitudes of $R-$ band luminosity1052In the current concordance model. galaxies are the result of continuous mergers of dark matter halos driving baryonic matter assembly.,"In the current concordance model, galaxies are the result of continuous mergers of dark matter halos driving baryonic matter assembly."1053 In the last decades. simulations on halo occupation models have been able to quite accurately plot the formation of dark matter clusters.," In the last decades, simulations on halo occupation models have been able to quite accurately plot the formation of dark matter clusters."1054 However. big uncertainties still remain at the time of translating dark matter haloes to what ean actually be detected with our telescopes.," However, big uncertainties still remain at the time of translating dark matter haloes to what can actually be detected with our telescopes."1055 To this respect. he luminosity function (LF) of galaxies. i.e. the number density of galaxies per unit flux. is an extremely powerful tool to study he galaxy population and its evolution with cosmic time.," To this respect, the luminosity function (LF) of galaxies, i.e. the number density of galaxies per unit flux, is an extremely powerful tool to study the galaxy population and its evolution with cosmic time."1056 Speciticaly. the analysis of the LF at different rest-frame wavelengths can give us information on different aspects of our present view of the Universe.," Specifically, the analysis of the LF at different rest-frame wavelengths can give us information on different aspects of our present view of the Universe."1057 The UV-optical LF allows for the study of the content and the evolution of the star formation rates with cosmic time., The UV-optical LF allows for the study of the content and the evolution of the star formation rates with cosmic time.1058 On the other hand the near infra-red (NIR) LF. being less sensitive to the absorption by dust and dominated by the light of older stars. is a better estimator of the overall stellar mass assembly of galaxies and of its rate of growth with time. revealing itself as a good test-bench for halo models.," On the other hand the near infra-red (NIR) LF, being less sensitive to the absorption by dust and dominated by the light of older stars, is a better estimator of the overall stellar mass assembly of galaxies and of its rate of growth with time, revealing itself as a good test-bench for halo models."1059 The local NIR LF is still not yet well determined., The local NIR LF is still not yet well determined.1060 Although a number of measurements have been derived so far. there seems to be uncertainties especially for the faint end slope a.," Although a number of measurements have been derived so far, there seems to be uncertainties especially for the faint end slope $\alpha$."1061 Estimates of theslope a range from zz0.5 (Belletal.2003:: Ekeetal. 2005). toax139 (onesetal. 2006). with a median value around -| (Mobasher.Sharples.&Ellis1993: Glazebrooketal. 1995:: Cowieetal. 1996: Gardneretal.1997 and Szokolyetal.1998: Kochaneketal. 2001:: Coleetal.2001. andHilletal. 20103).," Estimates of theslope $\alpha$ range from $\approx -0.8$ \citealt{bell2003}; \citealt{eke2005}) ), to $\alpha \approx -1.2$ \citealt{jones2006}) ), with a median value around -1 \citealt{mobasher93}; \citealt{glazebrook1995}; \citealt{cowie96}; \citealt{gardner97} and \citealt{szokoly98}; \citealt{kochanek2001}; \citealt{cole2001} and\citealt{hill2010}) )."1062 At even larger redshift. the LF determinations (most of which are done in the rest-frame A's band) still suffer from significant uncertainties (Saraccoeal. 2006).," At even larger redshift, the LF determinations (most of which are done in the rest-frame $K_S$ band) still suffer from significant uncertainties \citealt{saracco2006}) )."1063 The faint-end slope seems to be always compatible with a=——1 (Droryetal.2003: etal. 2003:: Dahlenet:i]. 2005: Saraccoetal. 2006:: Cirasuoloetal. 20103) although these measurements suffer from the large uncertainties given by the limitsin the depth of the photometric catalogues availableso far., The faint-end slope seems to be always compatible with $\alpha=-1$ \citealt{drory2003}; \citealt{pozzetti2003}; \citealt{dahlen2005}; \citealt{saracco2006}; \citealt{cirasuolo2010}) ) although these measurements suffer from the large uncertainties given by the limitsin the depth of the photometric catalogues availableso far.1064 There seems to be a general consensus however that the NIR LF does not significantly evolve to.=1 with respect to the local LF € Cowieetal. 1996: Pozzettietal. 2003:: Droryetal. 2003:: Feulneretal. 2003:: Dahlenetal. 2005»)., There seems to be a general consensus however that the NIR LF does not significantly evolve to $z \approx 1$ with respect to the local LF ( \citealt{cowie96}; ; \citealt{pozzetti2003}; ; \citealt{drory2003}; ; \citealt{feulner2003}; ; \citealt{dahlen2005}) ).1065 A brightening of the characteristic magnitude is instead found around 2z1.2.1.5 together with a decrease of the normalization. decrease that is seen up to 2=3 (Saraccoetal. 2006:: 3010)).," A brightening of the characteristic magnitude is instead found around $z \approx 1.2-1.5$ together with a decrease of the normalization, decrease that is seen up to $z=3$ \citealt{saracco2006}; ; \citealt{cirasuolo2010}) )."1066 , 1067"In the late 70's many authors (Krimskii|1977;|Axford,Leer&Skardon||Blandford1978;1978) introduced the theory of particle acceleration at strong collisionless shocks due to first order Fermi mechanism.","In the late 70's many authors \citep{krimskii,als77,b078,bell78} introduced the theory of particle acceleration at strong collisionless shocks due to first order Fermi mechanism."1068" However, quantitative"," However, quantitative"1069and the maximum bolometric luminosity or the nickel mass in the ejecta of the underlying SNe derived by Li(2006). as shown in Figs.,"and the maximum bolometric luminosity or the nickel mass in the ejecta of the underlying SNe derived by \citet{li06}, as shown in Figs."1070" 3 and 4. (where the central value of ££, 18 0.12 keV estimated by the Amati relation).", \ref{mag_epeak} and \ref{n56_epeak} (where the central value of $E_\p$ is 0.12 keV estimated by the Amati relation).1071 All known nearby GRBs/XREs with SNe have strong radio emissions. including CiliDs 980425. 030829. 031203. 060218. and NRE IHadio emissions have also been detected. for. NRE 080109/8N. 2008D. although not as bright as the other GRB-SNe (Socerbereetal.2008).," All known nearby GRBs/XRFs with SNe have strong radio emissions, including GRBs 980425, 030329, 031203, 060218, and XRF Radio emissions have also been detected for XRF 080109/SN 2008D, although not as bright as the other GRB-SNe \citep{sod08}."1072. The peakradio luminosities at 6 cm (Leen) of the six GRBs/XREs are plotted in Fig. 5.," The peakradio luminosities at 6 cm $L_{\nu,6{\rm cm}}$ ) of the six GRBs/XRFs are plotted in Fig. \ref{grb_radio},"1073 versus their average uminosityv of the prompt emission in the X-ray ancl gamama-rav band (Lx +)., versus their average luminosity of the prompt emission in the X-ray and gamma-ray band $L_{\x-\gamma}$ ).1074 Phe data suggest a correlation between he radio luminosity ancl the X-rav/gamma-ray. Luminosity. be. brighter GRBs/XREs tend to have a larger raclio uniinosityv.," The data suggest a correlation between the radio luminosity and the X-ray/gamma-ray luminosity, i.e., brighter GRBs/XRFs tend to have a larger radio luminosity."1075 Type le SN 19941 and SN 2002ap were also detected in radio band. although. no GRBs/XREs have been found ο be associated with them.," Type Ic SN 1994I and SN 2002ap were also detected in radio band, although no GRBs/XRFs have been found to be associated with them."1076 With the relation between the »ealk spectral energy of GRBs and the maximum bolometric uminositv of the underlving SNe (or the mass of generated in the SN ejecta). the peak spectral energy of the »otential NRIs associated: with SN. 19941 and SN. 2002ap was derived to be 0.07 keV (or 0.12 keV) and 0.016 keV. (or 19 keV). respectively (Li2006).," With the relation between the peak spectral energy of GRBs and the maximum bolometric luminosity of the underlying SNe (or the mass of generated in the SN ejecta), the peak spectral energy of the potential XRFs associated with SN 1994I and SN 2002ap was derived to be $0.07$ keV (or $0.12$ keV) and $0.016$ keV (or $0.19$ keV), respectively \citep{li06}."1077. Using the Amati relation. he peak spectral energv can be converted to the isotropic-equivalent energy in the 1-120000. keV band.," Using the Amati relation, the peak spectral energy can be converted to the isotropic-equivalent energy in the 1-10000 keV band."1078 Assuming a duration of 600 s (the same duration of NRE 080109). for hese potential faint. bursts. the average Luminosity of the »ompt emission. in the N-rav/gamma-ray band can be calculated.," Assuming a duration of 600 s (the same duration of XRF 080109) for these potential faint bursts, the average luminosity of the prompt emission in the X-ray/gamma-ray band can be calculated."1079 The peak radio luminosities of SN. 19941. and SN 2002ap and the derived: average luminosities of their x»ential bursts in the N-rav/gamama-ray. band are shown Fig., The peak radio luminosities of SN 1994I and SN 2002ap and the derived average luminosities of their potential bursts in the X-ray/gamma-ray band are shown Fig.1080 5. bv open circles., \ref{grb_radio} by open circles.1081 Lt appears that they follow. the rend of the Lig Lx~ relation suggested by the nearby CRBs/XREs.," It appears that they follow the trend of the $L_{\nu,6{\rm cm}}$ $L_{\x-\gamma}$ relation suggested by the nearby GRBs/XRFs."1082 In the standard: collapsar model of long-cluration GRBs (AMlackacven Woosley 1900 Macbadyen.. Woosley lleger 2001). it is assumed that after the core-collapse of the progenitor star à torus is formed. surrounding a rapidlv rotating black hole.," In the standard collapsar model of long-duration GRBs (MacFadyen Woosley 1999; MacFadyen, Woosley Heger 2001), it is assumed that after the core-collapse of the progenitor star a torus is formed surrounding a rapidly rotating black hole."1083 X bipolar relativistic fireball outllow powered either hy the aceretion energy of the torus or the spin energv of the black hole is generated. and collimated into two oppositelv-directed. jets moving along the spin axis of the hole.," A bipolar relativistic fireball outflow powered either by the accretion energy of the torus or the spin energy of the black hole is generated, and collimated into two oppositely-directed jets moving along the spin axis of the hole."1084 The fireball is presumably. highly nonhomogeneous ancl composed. of a number of outward moving shells., The fireball is presumably highly nonhomogeneous and composed of a number of outward moving shells.1085 Ehe collision between the shells produces the prompt ezmnia-ray emission. and the collision between the shells and the surrounding medium produces the afterglow emission (theso-calledinternal/external-shockmodel.Piran 2004)..," The collision between the shells produces the prompt gamma-ray emission, and the collision between the shells and the surrounding medium produces the afterglow emission \citep[the so-called internal/external-shock model,][]{pir04}. ."1086 In this mocel. collimation of the outflow is essential for avoiding barvon loading and maintaining a large Lorentz factor (2« 100).," In this model, collimation of the outflow is essential for avoiding baryon loading and maintaining a large Lorentz factor $> 100$ )."1087variation of the growth rate with the spin of the black hole (Pig.,variation of the growth rate with the spin of the black hole (Fig.1088 7 (d)), \ref{relecc} (d)).1089 The warp. being à nl mode. has a variation with radius that strongly depends on the Lense-Thirring precession frequency. and therefore. that. strongly depends on à.," The warp, being a $n=1$ mode, has a variation with radius that strongly depends on the Lense-Thirring precession frequency, and therefore, that strongly depends on $a$."1090 On the other hand. the variation of the eccentricity amplitude with radius. given by equation (37)). is less dependent on the spin of the black hole.," On the other hand, the variation of the eccentricity amplitude with radius, given by equation \ref{eqe}) ), is less dependent on the spin of the black hole."1091 Pherefore. he variation of @ only causes variations of a factor of. maximum. 2 in the growth rate obtained for the interaction within the eccentric disc.," Therefore, the variation of $a$ only causes variations of a factor of, at maximum, $2$ in the growth rate obtained for the interaction within the eccentric disc."1092 A very important. dillerence is the act that. in this interaction. a reasonable erowth rate can x obtained in the case where e=0.," A very important difference is the fact that, in this interaction, a reasonable growth rate can be obtained in the case where $a=0$."1093 Therefore. in slowly rotating black holes. HE(ODPOs might be detected if the disc is eccentric. and if this excitation mechanism is responsible or the increase in the amplitude of oscillations.," Therefore, in slowly rotating black holes, HFQPOs might be detected if the disc is eccentric, and if this excitation mechanism is responsible for the increase in the amplitude of oscillations."1094 In this paper we have described an excitation. mechanism for trapped inertial modes. based on a non-linear coupling mechanism between these waves and global deformations (warping or cecentricity) in aceretion cliscs.," In this paper we have described an excitation mechanism for trapped inertial modes, based on a non-linear coupling mechanism between these waves and global deformations (warping or eccentricity) in accretion discs."1095 We have seen that the interaction of a trapped. r mode with an intermediate mode and a deformation in the cise results in growth of the trapped mode. if there is some process capable of making the intermediate mode clissipate in the disc.," We have seen that the interaction of a trapped r mode with an intermediate mode and a deformation in the disc results in growth of the trapped mode, if there is some process capable of making the intermediate mode dissipate in the disc."1096 Dissipation is required so that this mode can remove rotational kinetic energv [from the disc. which becomes available for the r mode to grow.," Dissipation is required so that this mode can remove rotational kinetic energy from the disc, which becomes available for the r mode to grow."1097 Depending on the values of the sound speed. spin of the black hole and amplitude of the deformation at the inner radius. reasonable growth rates can be obtained for a warp or eccentricity of modest aniplitucle.," Depending on the values of the sound speed, spin of the black hole and amplitude of the deformation at the inner radius, reasonable growth rates can be obtained for a warp or eccentricity of modest amplitude."1098 In a warped disc. where the growth rate varies significantly with the spin of the compact object. growth rates as large as w/10. where w is the oscillation frequency. can be obtained.," In a warped disc, where the growth rate varies significantly with the spin of the compact object, growth rates as large as $\omega/10$ , where $\omega$ is the oscillation frequency, can be obtained."1099 a=Ü. no oscillations are excited in these dises.," If $a=0$, no oscillations are excited in these discs."1100 However. it may still possible to excite trapped moces in discs around non-rotating black holes if they are eccentric.," However, it may still possible to excite trapped modes in discs around non-rotating black holes if they are eccentric."1101 The coupling process described. here works as an excitation mechanism for trapped. inertial waves. under a wide range of conditions. provided elobal deformations reach the inner disc region with non-negligible amplitude.," The coupling process described here works as an excitation mechanism for trapped inertial waves, under a wide range of conditions, provided global deformations reach the inner disc region with non-negligible amplitude."1102 “Phe propagation of elobal modes. in à more realistic disc mocel. is the subject of a forthcoming paper (Ferreira.&Ovilvic 3005).," The propagation of global modes, in a more realistic disc model, is the subject of a forthcoming paper \citep{ferreiraogilvie2008}."1103 In this paper we considered the excitation of trapped waves due to a non-linear coupling mechanism with global deformations. in a simple dise model.," In this paper we considered the excitation of trapped waves due to a non-linear coupling mechanism with global deformations, in a simple disc model."1104 While this cllect is responsible for the growth of these modes. it has to compete with others that contribute to the damping of these waves.," While this effect is responsible for the growth of these modes, it has to compete with others that contribute to the damping of these waves."1105 For example. since the conditions at the marginally stable orbit are unknown. it is possible for a ‘leakage’ of the trapped mode (similar to the one considered in the potential barrier analogv) through mu. to exist.," For example, since the conditions at the marginally stable orbit are unknown, it is possible for a `leakage' of the trapped mode (similar to the one considered in the potential barrier analogy) through $r_\textrm{ms}$ to exist."1106 This cllect ds. to be considered. in the future., This effect is to be considered in the future.1107 Also. and more importantly. viscous dissipation in the disc can cause damping of these nmides.," Also, and more importantly, viscous dissipation in the disc can cause damping of these modes."1108 A simple estimate gives a damping rate of aO., A simple estimate gives a damping rate of $\alpha\Omega$.1109 For small enough values of a and large enough. warp or eccentricity. net growth can occur.," For small enough values of $\alpha$ and large enough warp or eccentricity, net growth can occur."1110 Another point to be discussed is the applicability. of our results to observed. disces., Another point to be discussed is the applicability of our results to observed discs.1111 We consider a very simple. isothermal disc model ancl wave perturbations for which ?=1.," We consider a very simple, isothermal disc model and wave perturbations for which $\gamma=1$."1112 In a more realistic disc. the vertical structure of he waves is changed. while they propagate racially.," In a more realistic disc, the vertical structure of the waves is changed while they propagate radially."1113 The wave energv concentrates either. near the surface of the disc (Lubow&Ogilvie1998). or towards the disc. mid-plane (Ixorvcansky&Pringle1995)..iare which could potentially uncer the propagation of intere modes away from the Lindblad: resonance where they are excited.," The wave energy concentrates either near the surface of the disc \citep{lubowogilvie1998} or towards the disc mid-plane \citep{korycanskypringle1995}, which could potentially hinder the propagation of intermediate modes away from the Lindblad resonance where they are excited."1114 However. the orocess of wave channelling. mentioned by Lubow&Ogilvie(1998) is only relevant at a clistance from the resonance of ο (ry being the radius of the Lindblad. resonance). where the radial wavelength becomes. comparable to the scmithickness of the disc.," However, the process of `wave channelling' mentioned by \cite{lubowogilvie1998} is only relevant at a distance from the resonance of $\sim r_\textrm{L}/m$ $r_\textrm{L}$ being the radius of the Lindblad resonance), where the radial wavelength becomes comparable to the semithickness of the disc."1115 Since the intermediate modes have m= this effect. is not important in the region where wave coupling occurs.," Since the intermediate modes have $m=1$, this effect is not important in the region where wave coupling occurs."1116 Phe same is expected. for cases in which the energv concentrates towards the disc mid-plane., The same is expected for cases in which the energy concentrates towards the disc mid-plane.1117 The global deformation modes do not undergo significant wave channelling because their wavelengths are always long compared to ff., The global deformation modes do not undergo significant wave channelling because their wavelengths are always long compared to $H$.1118 Therefore. we belicve that our results. obtained in a simple dise model. are still qualitatively valid in more realistic clises.," Therefore, we believe that our results, obtained in a simple disc model, are still qualitatively valid in more realistic discs."1119 We thank John Papaloizou for some helpful suggestions. in particular for pointing out the possibility of a relation between the coupling mechanism. described. here and. the parametric instability.," We thank John Papaloizou for some helpful suggestions, in particular for pointing out the possibility of a relation between the coupling mechanism described here and the parametric instability."1120 We alsothank an anonymous referee for useful comments., We alsothank an anonymous referee for useful comments.1121 The work of BPE was supported by ECT (Portugal) through grant no., The work of BTF was supported by FCT (Portugal) through grant no.1122 SERIL/BD/22251/2005., SFRH/BD/22251/2005.1123at LO aad Greaves&Tolland(2000) at 850 pan.,"at 10 and \cite{gh00}1124 at 850 ."1125. Foster&Fischer(1996) also utilized IRAS observations to obtain upper limits on the infrared ciission from their sample of pulsars., \cite{ff96} also utilized IRAS observations to obtain upper limits on the infrared emission from their sample of pulsars.1126 As Figure 1. shows. the upper Μις set bv IRAS are typically well above the limits set by our ISO observations.," As Figure \ref{fig:b1257+12} shows, the upper limits set by IRAS are typically well above the limits set by our ISO observations."1127 Moreover. there is unfortunately little overlap between these three samples of pulsars (those whose observations are reported here. Foster&Fischer 1996.. aud Ctreaves&Tolland 2000)).," Moreover, there is unfortunately little overlap between these three samples of pulsars (those whose observations are reported here, \citealt*{ff96}, and \citealt*{gh00}) )."1128 Most of the pulsars that have been observed )otween 10 aud 850 thave beeu observed at oulv one or two waveleuglis., Most of the pulsars that have been observed between 10 and 850 have been observed at only one or two wavelengths.1129 Foster&Fischer(1996). deveoped a model for he infrared οσο from a cdist disk around a uillisecond. pulsar., \cite{ff96} developed a model for the infrared emission from a dust disk around a millisecond pulsar.1130 Their iiodoel assumes that t disk consists of particles of a uniform radius reated bv a fraction fig of the pulsus spin-down Lhuuinositv Loy., Their model assumes that the disk consists of particles of a uniform radius $a$ heated by a fraction $f_{\mathrm{sd}}$ of the pulsar's spin-down luminosity ${}_{\mathrm{sd}}$.1131 The total mass of the disk is ay., The total mass of the disk is $m_d$.1132 While the model is simplistican actual dust disk presumably consists of particles with a range of sizes. the heating miechauisni ids left unspecified. non-equilibrium effects such as stochastic heating are ignored. and the impact of anv stellar companious (see Table 1)) ou the disk are ignoredwe bolieve that this simplicity is justified given the uncertainties of the heating uechanism and of the euxirons of a nüllisecond nlsur.," While the model is simplistic—an actual dust disk presumably consists of particles with a range of sizes, the heating mechanism is left unspecified, non-equilibrium effects such as stochastic heating are ignored, and the impact of any stellar companions (see Table \ref{tab:log}) ) on the disk are ignored—we believe that this simplicity is justified given the uncertainties of the heating mechanism and of the environs of a millisecond pulsar."1133 Tn this model. for fra~ typical dust enrperatures are predicted to ef 5lo hol or disks haviug mn~1 OAT) and e~14nu aand heated by a pusar wit ÜiLa~1 Lb.," In this model, for $f_{\mathrm{sd}} \sim 1$, typical dust temperatures are predicted to be $T \approx 10$ –50 K for disks having $m_d \sim 100$ ${}_\oplus$ and $a \sim 1$ and heated by a pulsar with ${}_{\mathrm{sd}} \sim 1$ ${}_\odot$."1134 These tenrperatures are similar to the lower eniperature range use| by Kocl-Mikuuoudet(2002) and cousierably lower than those assuied (m150 WN) bv Philips&Chaxdler (1991).. who estimateL disk temperatures bv scaling from observatiois of T Tami stars.," These temperatures are similar to the lower temperature range used by \cite{k-mhppns02} and considerably lower than those assumed $\approx1135150$ K) by \cite{pc94}, , who estimated disk temperatures by scaling from observations of T Tauri stars."1136 The wver temperatures result from our assuniption of a weaker coupling between the pulsars Πο ΠΕΠΩ aud he disk. Phillips&C, The lower temperatures result from our assumption of a weaker coupling between the pulsar's spin-down luminosity and the disk.1137"haxdler(199D). considered dis]- eniperature to bea uajor uncerttüntyv in converting from measure fiux densities to inferred disk masses,", \cite{pc94} considered disk temperature to be a major uncertainty in converting from measured flux densities to inferred disk masses.1138 Accordingly. our asstuuption ofa weaker coupling mcaus that larger disk masses can be tolerated without violating the observational constraints.," Accordingly, our assumption of a weaker coupling means that larger disk masses can be tolerated without violating the observational constraints."1139 Given the paucity of data. it is not possible. iu general. to coustrain allthree parametersof this model with the existing observations.," Given the paucity of data, it is not possible, in general, to constrain allthree parametersof this model with the existing observations."1140 We therefore, We therefore1141refcont.,.1142". In order to run full grid of models for a range of temperatures and avibrational states for each molecule over a wide wavelength range, it was necessary to utilize a list of transitions that was both relatively complete and manageable in size."," In order to run a full grid of models for a range of temperatures and vibrational states for each molecule over a wide wavelength range, it was necessary to utilize a list of transitions that was both relatively complete and manageable in size."1143" We primarily used data from the HITRAN2008 database for the full grid of models; however, we then compared our results to models computed with more complete line lists - data from the CH,@Titan line database for methane (?) and data from the HITEMP2010 database (7) for water and OH."," We primarily used data from the HITRAN2008 database for the full grid of models; however, we then compared our results to models computed with more complete line lists - data from the $_4$ Titan line database for methane \citep{ch4titan2010p?} and data from the HITEMP2010 database \citep{Rothman2010p2139} for water and OH."1144" Differences between the low-resolution models based on HITRAN and the more complete models were virtually non-existent at lower temperatures, and while the flux for some increased up to for the highest temperatures, these differences are insignificant due to the already-poor fit between higher-temperature models and the S10 results as illustrated in Figure 3 and the fact that our upper limits are significantly smaller than the expected signal."," Differences between the low-resolution models based on HITRAN and the more complete models were virtually non-existent at lower temperatures, and while the flux for some increased up to for the highest temperatures, these differences are insignificant due to the already-poor fit between higher-temperature models and the S10 results as illustrated in Figure \ref{models} and the fact that our upper limits are significantly smaller than the expected signal."1145" In Figure 4,, we plot the scaled models based on the more complete data sets over our spectrum, which covers"," In Figure \ref{data}, we plot the scaled models based on the more complete data sets over our spectrum, which covers"1146For the sake of simplicity we will assume that our model galaxies do not have radial gradient in a-enhancement.,For the sake of simplicity we will assume that our model galaxies do not have radial gradient in $\alpha$ -enhancement.1147" As shown by Pipino, D’Ercole Matteucci (2008), in fact, even though most ellipticals form outside-in, the expected strong and positive [«a/Fe >] gradient can be affected by the metal rich gaseous flows inside the galaxy acting togheter with the SFR."," As shown by Pipino, D'Ercole Matteucci (2008), in fact, even though most ellipticals form outside-in, the expected strong and positive $<\alpha /Fe>$ ] gradient can be affected by the metal rich gaseous flows inside the galaxy acting togheter with the SFR."1148 We recall that also osservations suggest that the observed gradient slope in the [<Mg/Fe >] has a null mean value (e.g. Mehlert et al., We recall that also osservations suggest that the observed gradient slope in the $<Mg/Fe>$ ] has a null mean value (e.g. Mehlert et al.1149 2003)., 2003).1150 Therefore we will refer to a one zone model in which the metallicity and the o enhancement do not vary with radius., Therefore we will refer to a one zone model in which the metallicity and the $\alpha$ enhancement do not vary with radius.1151" In general, we will expect that mergers cannot account for the steep metallicity gradient observed in the majority of ellipticals (e.g. Carollo et al."," In general, we will expect that mergers cannot account for the steep metallicity gradient observed in the majority of ellipticals (e.g. Carollo et al."1152" 1993), and we postpone to a forthcoming paper the analysis of the gradients survival to several dry-mergers."," 1993), and we postpone to a forthcoming paper the analysis of the gradients survival to several dry-mergers."1153" Under these assumptions, we predict the properties of the Composite Stellar Populations of the merger remnant in a straightforward manner."," Under these assumptions, we predict the properties of the Composite Stellar Populations of the merger remnant in a straightforward manner."1154" In fact, the stellar metallicity distribution function for the end product of a dry-merger is simply Yfinai summed over all progenitors and can be written as: where M.prog is the stellar mass of the single progenitors."," In fact, the stellar metallicity distribution function for the end product of a dry-merger is simply $\Upsilon_{\rm final}$ summed over all progenitors and can be written as: where $M_{*,prog}$ is the stellar mass of the single progenitors."1155 Similar equations hold for other distributions as functions of either [Mg/Fe] or [Fe/H]., Similar equations hold for other distributions as functions of either [Mg/Fe] or [Fe/H].1156" We stress again that this is possible because we are studying dry merger remnants, i.e. systems where no further SF is allowed to occur."," We stress again that this is possible because we are studying dry merger remnants, i.e. systems where no further SF is allowed to occur."1157" Let us first assume the extreme case in which our massive elliptical has been made by merging of several progenitors of the kind only, as expected from galaxy formation models which assume a short SF process at high redshift, but let the galaxy assembly happen much later (e.g. De Lucia et al."," Let us first assume the extreme case in which our massive elliptical has been made by merging of several progenitors of the kind only, as expected from galaxy formation models which assume a short SF process at high redshift, but let the galaxy assembly happen much later (e.g. De Lucia et al."1158" 2006, Kobayashi et al."," 2006, Kobayashi et al."1159 2007)., 2007).1160" In order to have the right final mass, we need 400 of such small builiding blocks."," In order to have the right final mass, we need 400 of such small builiding blocks."1161" Since progenitor A has been built in order to yield the final correct @ enhancement, our massive spheroid will have a Mg enhancement of 0.28 dex and will match fairly well the average observational value for galaxies of the same mass."," Since progenitor A has been built in order to yield the final correct $\alpha$ enhancement, our massive spheroid will have a Mg enhancement of 0.28 dex and will match fairly well the average observational value for galaxies of the same mass."1162 It is rather intuitive from eq., It is rather intuitive from eq.1163" 1 that the final stellar metallicity distribution will still look like Fig. 1,,"," \ref{eq1} that the final stellar metallicity distribution will still look like Fig. \ref{prog_A},"1164" therefore its final metallicity in terms of [Fe/H] will remain very low, thus not matching either the MMR or the CMR."," therefore its final metallicity in terms of [Fe/H] will remain very low, thus not matching either the MMR or the CMR."1165 The predicted value of the SFR per unit mass is 0.02/Gyr for the progenitor of kindA., The predicted value of the SFR per unit mass is 0.02/Gyr for the progenitor of kind.1166". Again, it is rather intuitive that the final spheroid will have the same value, at variance with the results from Thomas et al. ("," Again, it is rather intuitive that the final spheroid will have the same value, at variance with the results from Thomas et al. ("1167"2005), which require this factor to be at least 2-3/Gyr, namely a factor of a hundred higher.","2005), which require this factor to be at least 2-3/Gyr, namely a factor of a hundred higher."1168" Such a high SFR is needed also to reproduce the observated SFR in Lyman Break (5—940h?Mgyr!, Shapley et al."," Such a high SFR is needed also to reproduce the observated SFR in Lyman Break $\sim 5-940 \, \rm h^{-2}M_{\odot}yr^{-1}$, Shapley et al."1169 2001) ad SCUBA (e.g. Swinbank et al., 2001) ad SCUBA (e.g. Swinbank et al.1170 2004) galaxies., 2004) galaxies.1171" On the other hand, a quasi-monolithic model can have naturally the required SFR per unit mass."," On the other hand, a quasi-monolithic model can have naturally the required SFR per unit mass."1172 In fact the prediction PM04 (Fig. 4)), In fact the prediction PM04 (Fig. \ref{sfr}) )1173 is in good agreement for what concerns with those inferred by Thomas et al. (, is in good agreement for what concerns with those inferred by Thomas et al. (1174"2005, see their Fig.","2005, see their Fig."1175" 10), the only difference being the sharp truncation due to the galactic wind."," 10), the only difference being the sharp truncation due to the galactic wind."1176" It should be noticed that many models based on the hierarchical clustering, which claim to have incorporated downsizing (e.g. De Lucia et al 2006, Kobayashi et al."," It should be noticed that many models based on the hierarchical clustering, which claim to have incorporated downsizing (e.g. De Lucia et al 2006, Kobayashi et al."1177" 2007) have average SFR per unit mass lower at least by a factor of 3-5 than what is required from chemical evolution studies and line-strenght indices analysis to reproduce the [Mg/Fe] in massive ellipticals; according to our calculations, with such a low SFR per unit mass is possible to reproduce only a very modest a- enhancement (if any)."," 2007) have average SFR per unit mass lower at least by a factor of 3-5 than what is required from chemical evolution studies and line-strenght indices analysis to reproduce the [Mg/Fe] in massive ellipticals; according to our calculations, with such a low SFR per unit mass is possible to reproduce only a very modest $\alpha$ -enhancement (if any)."1178" In fact, such a value for the SFR per unit mass ( 1/Gyr) will only suffice to explain the [«Mg/Fe »]  0.1 dex of the less massive spheroids."," In fact, such a value for the SFR per unit mass $\sim 1/Gyr$ ) will only suffice to explain the $<Mg/Fe>$ ] $\sim$ 0.1 dex of the less massive spheroids."1179" We tried to overcome the problem of having a too low SFR by introducing another ad hoc building block, namely the progenitorA+,, which has a SFR per unit mass of the order of unity."," We tried to overcome the problem of having a too low SFR by introducing another ad hoc building block, namely the progenitor, which has a SFR per unit mass of the order of unity."1180" In this case, however, the lack of agreement with the MMR is much more evident, and also the predicted [«Mg/Fe »] is too high."," In this case, however, the lack of agreement with the MMR is much more evident, and also the predicted $<Mg/Fe>$ ] is too high."1181" We notice in passing that if we allow for a subsequent gas-rich merger triggering a substantial episode of SE, we may be able to reproduce the MFMR, but we fail in obtaining other properties, such as the CMRs or the"," We notice in passing that if we allow for a subsequent gas-rich merger triggering a substantial episode of SF, we may be able to reproduce the MFMR, but we fail in obtaining other properties, such as the CMRs or the"1182It has been suggested (Gebhardt.Rich.&Ilo2002).. Chat globular clusters may contain central black holes with masses lving along the extension of the correlation between black hole mass and bulge velocity dispersion as seen [or galaxies (Ferrarese&MerrittGebhardtetal. 2000).,"It has been suggested \citep{G1}, that globular clusters may contain central black holes with masses lying along the extension of the correlation between black hole mass and bulge velocity dispersion as seen for galaxies \citep{fm00,geb00}."1183. ILowever it has also been suggested that the observational evidence can be otherwise explained (Batneare(etal.2003a.b:Dull2003).," However it has also been suggested that the observational evidence can be otherwise explained \citep{b1,b2,d3}."1184. These difficulties of interpretation are compounded by the small number of observable stars in the cores of elobular clusters., These difficulties of interpretation are compounded by the small number of observable stars in the cores of globular clusters.1185 In contrast to a galactic center. current observations approach the limit when the uncertainty. of ai aggregate measurement. such as a velocity dispersion. cannot be reduced by further observations.," In contrast to a galactic center, current observations approach the limit when the uncertainty of an aggregate measurement, such as a velocity dispersion, cannot be reduced by further observations."1186 Once every star has been observed. there is nothing more to be done. (," Once every star has been observed, there is nothing more to be done. ("1187See Drukier et al.,See Drukier et al.1188 2003 for a general discussion of issues relating to the observation and interpretation of velocity dispersions in globular clusters.), 2003 for a general discussion of issues relating to the observation and interpretation of velocity dispersions in globular clusters.)1189 This is particularly the case for central black holes. since there is only a relatively small region over which the black hole provides the dominant contribution to the gravitational potential.," This is particularly the case for central black holes, since there is only a relatively small region over which the black hole provides the dominant contribution to the gravitational potential."1190 Alost current observational work relating to the possible presence of central black holes in globular clusters has been done using racial velocity. measurements to determine the central value and radial gradient of the velocity dispersion., Most current observational work relating to the possible presence of central black holes in globular clusters has been done using radial velocity measurements to determine the central value and radial gradient of the velocity dispersion.1191 In this Lef/er we explore an, In this Letter we explore an1192indicated by the long-dashed white lines.,indicated by the long-dashed white lines.1193 The remaining calculations are now all calculated using the center of the ellipse as the image center., The remaining calculations are now all calculated using the center of the ellipse as the image center.1194" The calculated PA for the data is 55?, while the planet's PA is —25?."," The calculated PA for the data is $55\degr$, while the planet's PA is $-25\degr$."1195" The angle between minor axis and planet PA is small, so aligning the planet with the inclination vector of the model disks is a reasonable assumption."," The angle between minor axis and planet PA is small, so aligning the planet with the inclination vector of the model disks is a reasonable assumption."1196" The major and minor axes of the best fitting ellipses for the observed and simulated images are tabulated in Table 1,, assuming that 1”=144AU."," The major and minor axes of the best fitting ellipses for the observed and simulated images are tabulated in Table \ref{ellipsetable}, , assuming that $1\arcsec = 144$."1197. The offset listed for the model images is the distance between the star’s position and the center of the ellipse., The offset listed for the model images is the distance between the star's position and the center of the ellipse.1198" The best-fit ellipses for the model images are slightly more eccentric than that for the data, indicating that either the inclination of 25° is too high, or that the scattering properties are incompletely modeled."," The best-fit ellipses for the model images are slightly more eccentric than that for the data, indicating that either the inclination of $25\degr$ is too high, or that the scattering properties are incompletely modeled."1199" For example, a small amount of forward scattering or slight flattening of the flared disk structure could both create a less eccentric best fit ellipse."," For example, a small amount of forward scattering or slight flattening of the flared disk structure could both create a less eccentric best fit ellipse."1200" However, we are interested in studying the perturbative effect of a planet on the overall disk structure, not creating an exact match to all the disk properties."," However, we are interested in studying the perturbative effect of a planet on the overall disk structure, not creating an exact match to all the disk properties."

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