ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 From the timelines. maps were created. using the default naive mapemaker. with the default pixel sizes of (6. 10. 14) arcsec for (250. 350. jm. In map pixel 7. the signal. αι is estimated. from the N; bolometer samples {s;} lying within that pixel as while σε the uncertainty in the value of d;. is the standard error of the mean for (5;4: Prior to map-making. the residual drift present in the timelines. which is à residual from the temperature cirift correction (Cirillinctal. 2010)... was removed. by fitting a constant plus a linear slope to cach scan timeline.," From the timelines, maps were created using the default naive map-maker, with the default pixel sizes of (6, 10, 14) arcsec for (250, 350, $\mu$ m. In map pixel $i$, the signal, $d_i$, is estimated from the $N_i$ bolometer samples $\{ s_j \}$ lying within that pixel as while $\sigma_i$, the uncertainty in the value of $d_i$, is the standard error of the mean for $\{s_j\}$: Prior to map-making, the residual drift present in the timelines, which is a residual from the temperature drift correction \citep{Griffin...2010}, , was removed by fitting a constant plus a linear slope to each scan timeline."3 Another, Another4The solid lines have been computed for models with A\[=0.65. N=0.75 and Z=0.001.,"The solid lines have been computed for models with M=0.65, X=0.75 and Z=0.001."5 The dotted lines represcut models with M and Z from Jurcsik's (LE. MN. relations. the dashed lines those with AL from Jurcsik. but with Z=0.001.," The dotted lines represent models with M and Z from Jurcsik's L, M, relations, the dashed lines those with M from Jurcsik, but with Z=0.001."6 Finally. the laree open circles are models from Tueele and Ibeu (1972) for Ας and Z-—0.001 (with the old Los Alamos opacities).," Finally, the large open circles are models from Tuggle and Iben (1972) for M=0.6 and Z=0.001 (with the old Los Alamos opacities)."7 They have essentiallv the same Z as ours which are computed with the OPAL opacities (Ielesias Rogers 1996) imereged with the low temperature Alexander-Ferenson (1991) opacities., They have essentially the same $\Xi$ as ours which are computed with the OPAL opacities (Iglesias Rogers 1996) merged with the low temperature Alexander-Ferguson (1994) opacities.8 Again. because we are computing radiative models we do uot expect the location of the blue edge to be iu perfect agreement with the edge of the instability strip. but we note a very large discrepancy in the slope =.," Again, because we are computing radiative models we do not expect the location of the blue edge to be in perfect agreement with the edge of the instability strip, but we note a very large discrepancy in the slope $\Xi$."9 Figure 1 also displavs a pplot ou the right., Figure 1 also displays a – plot on the right.10 Ouly the slope of the coustant mass models is m almost acceptable agreement with the JOS data. but those calculated with the 1ος {ALL.Z] are in stroug disagreement.," Only the slope of the constant mass models is in almost acceptable agreement with the J98 data, but those calculated with the J98 $\{M, L, Z\}$ are in strong disagreement."11 Iu Figures 2 we display again a pplot which shows the effect of composition on the location of the linear blue edees., In Figures 2 we display again a – plot which shows the effect of composition on the location of the linear blue edges.12 The (radiative) models were computed with M-0.65., The (radiative) models were computed with M=0.65.13" Tere the solid lines have N=0.75. Z=0.001. the dotted lines have N=0.75. Z=0.00L aud the dashed lines have N=0.70, Z=0.001."," Here the solid lines have X=0.75, Z=0.001, the dotted lines have X=0.75, Z=0.004 and the dashed lines have X=0.70, Z=0.001."14 The location of the blue οσο displays τον Little sensitivity to either metallicity Z or helium coutent Y. within a reasonable range of values.," The location of the blue edge displays very little sensitivity to either metallicity Z or helium content Y, within a reasonable range of values."15 Adjusting the helium content or metallicity does not provide a resolution of the slope discrepancy., Adjusting the helium content or metallicity does not provide a resolution of the slope discrepancy.16 We describe further tests in stl., We describe further tests in 4.17 We couclude this section by noting that purely radiative RR Lyrae models are in severe disagreement with Jurcsiks ddata., We conclude this section by noting that purely radiative RR Lyrae models are in severe disagreement with Jurcsik's data.18 The addition of time-depeudent turbulent couvection in the models has led to some spectacular successes compared to radiative models. in particular. iu finally predicting double mode behavior both iu RR Lyrae (Feuchtinecr 1998) and in Cepheids (sollatth. Beaulieu. Buchler Yecko 1998).," The addition of time-dependent turbulent convection in the models has led to some spectacular successes compared to radiative models, in particular, in finally predicting double mode behavior both in RR Lyrae (Feuchtinger 1998) and in Cepheids (Kollátth, Beaulieu, Buchler Yecko 1998)."19 One would hope therefore that the inclusion of turbulent convection might also remove the discrepancy vofween observations aud theory described ii tle previous section., One would hope therefore that the inclusion of turbulent convection might also remove the discrepancy between observations and theory described in the previous section.20 Yet. in that respect all of our modeling efforts with urbuleut convection have proved iu vain. despite the Hexibilitv afforded by the 8 free order uuitv (0) parameters hat the turbulent convective equations coutaiu Yecko. Iollatth Buchler 1997. EKollátth 2000).," Yet, in that respect all of our modelling efforts with turbulent convection have proved in vain, despite the flexibility afforded by the 8 free order unity $\alpha$ ) parameters that the turbulent convective equations contain Yecko, Kollátth Buchler 1997, Kollátth 2000)."21 We find that turbulent convection. can shift the due edges. but cannot produce the differential effect with respect to huninositv that is required to give the right slope 5 in the pplots.," We find that turbulent convection can shift the blue edges, but cannot produce the differential effect with respect to luminosity that is required to give the right slope $\Xi$ in the plots."22 In Figure 3 we show the results for three differcut combinations of these parameters., In Figure 3 we show the results for three different combinations of these parameters.23 We uote that different codes and slightly different recipes for convection eive csscutially the same theoretical slopes., We note that different codes and slightly different recipes for convection give essentially the same theoretical slopes.24 For example. even though no linear models are computed. the nonlinear hydrodvuamical iiodoels of Dono," For example, even though no linear models are computed, the nonlinear hydrodynamical models of Bono"25We can use the ladder operator form for twist to find a simple estimator for the new distortions.,We can use the ladder operator form for twist to find a simple estimator for the new distortions.26" We consider the power that finishes in the {τι component. where f{, is the component after twist."," We consider the power that finishes in the $f_{11}$ component, where $f_{11}'$ is the component after twist."27" Since the mean untwisted fj, is expected to be zero. we have the estimator In a similar fashion. the turned {τι coefficient is given by so since the undistorted mean fi. is expected to be zero. we obtain the estimator Note the close relationship between the estimators for twist and turn. and the fact that they can indeed be written as superpositions of each other."," Since the mean untwisted $f_{11}$ is expected to be zero, we have the estimator In a similar fashion, the turned $f_{11}$ coefficient is given by so since the undistorted mean $f_{11}$ is expected to be zero, we obtain the estimator Note the close relationship between the estimators for twist and turn, and the fact that they can indeed be written as superpositions of each other."28 However. it should be noted that these will only be pure estimators for twist/turn if |-flexion is absent (or negligible).," However, it should be noted that these will only be pure estimators for twist/turn if 1-flexion is absent (or negligible)."29 This is because I-flexion also moves power into the [τι mode (see ?)) in such a fashion that our estimator (e.g. for twist) is truly The estimator is still of value to us despite this complication. as we wish to use it to see if there is a twist-like systematic in our survey: we now see that. at this shapelet order. systematic flexion can generate a twist-like effect.," This is because 1-flexion also moves power into the $f_{11}$ mode (see \citet{2007MNRAS.380..229M}) ) in such a fashion that our estimator (e.g. for twist) is truly The estimator is still of value to us despite this complication, as we wish to use it to see if there is a twist-like systematic in our survey; we now see that, at this shapelet order, systematic flexion can generate a twist-like effect."30 This simple estimator is therefore a test of combined second-order systematics. or of (real or systematic) twist on scales where flexion is negligible.," This simple estimator is therefore a test of combined second-order systematics, or of (real or systematic) twist on scales where flexion is negligible."31 Nevertheless. it should be kept in mind that a pure estimation of twist will require a more extensive joint chi-squared fit of twist and flexion to several further orders of shapelets. in order to fully remove the degeneracy.," Nevertheless, it should be kept in mind that a pure estimation of twist will require a more extensive joint chi-squared fit of twist and flexion to several further orders of shapelets, in order to fully remove the degeneracy."32 In addition. these simple estimators need correcting for the fact that twist/turn moves the centroid of the object.," In addition, these simple estimators need correcting for the fact that twist/turn moves the centroid of the object."33 ? show that the centroid is moved by the D tensor according to where we have written a form which assumes less symmetry than Goldberg Bacon: this is necessary for our generalised 10 , \citet{2005ApJ...619..741G} show that the centroid is moved by the $D$ tensor according to where we have written a form which assumes less symmetry than Goldberg Bacon; this is necessary for our generalised $D$ 34temperature which parametrizes the deerce of alieumoeut between aj aud J.,temperature which parametrizes the degree of alignment between $\ba$ and $\bJ$.35" Iu the classical approximation. the rotational cucrey of a sviunaetric oblate erai is where fy; is the largest moment of inertia. corresponding to ay. and fy—[4«Jy: for a planar svuuuetrie molecule. fo=74,A2."," In the classical approximation, the rotational energy of a symmetric oblate grain is where $I_1$ is the largest moment of inertia, corresponding to $\ba$, and $I_2=I_3<I_1$; for a planar symmetric molecule, $I_2=I_3=I_1/2$."36 For the sake of siauplieitv. we asstune that all the cutting molecules have the same moments of inertia.," For the sake of simplicity, we assume that all the emitting molecules have the same moments of inertia."37 The absorption (eqs. (3))-(1))}, The absorption (eqs. \ref{eq:absstar}) \ref{eq:absgal}) ))38 and emission (eqs. (9) (12))), and emission (eqs. \ref{eq:em1}) \ref{eq:em4}) ))39 cross sections do not depeud on J but only ou the anele ο) between aj and J., cross sections do not depend on $J$ but only on the angle $\beta$ between $\ba$ and $\bJ$.40 Therefore. we may inteerate eq. C22))," Therefore, we may integrate eq. \ref{eq:general}) )"41" with respect to J. provided Ες) is known. and the resulting probability distribution will be used to describe the degree of aligmment between a, aud J when we compute the PAIL polarized cinission in8?7.."," with respect to $J$, provided $f(J)$ is known, and the resulting probability distribution will be used to describe the degree of alignment between $\ba$ and $\bJ$ when we compute the PAH polarized emission in\ref{sec:results}."42 Iu the simple case £67)x067.) (or. in general. if f(.J) is strongly peaked at 7). the probability distribution iu eq. C272))," In the simple case $f(J)\propto\delta(J-\bar{J})$ (or, in general, if $f(J)$ is strongly peaked at $\bar{J}$ ), the probability distribution in eq. \ref{eq:general}) )"43 reduces to where eftt).=(2/\/7)—.nptexp(t-)2d£ is: the imaginary. error function.," reduces to where $\mathrm{erfi}(z)\equiv(2/\sqrt{\pi})\int_0^z\exp(t^2)\,\ud t$ is the imaginary error function."44" We have defined a dimensionless ""iuterual aliguiment™ cocficicut where a4=7{δι"," We have defined a dimensionless “internal alignment” coefficient where $T_{\rm rot}\equiv \bar{J}^2/2\,I_1 k_{_{\rm{B}}}$."45 When y>x. the molecule principal axis tends to be perfectly aligued with the iieular momentum: when >=0. ay is raucdomly oricuted Na3th respect to J.," When $\gamma\rightarrow\infty$, the molecule principal axis tends to be perfectly aligned with the angular momentum; when $\gamma=0$, $\ba$ is randomly oriented with respect to $\bJ$."46" Ax discussed at the beginning of 877.. J stavs iyproximately coustant between UV absorption aud IR (wission. aud so does Toop: however. the molecule itera aliguiment temperature Zi, iav substantially chanec if part of the absorbed photon cnerev is transterrec to rotational degrees of freedom."," As discussed at the beginning of \ref{sec:model}, $\bJ$ stays approximately constant between UV absorption and IR emission, and so does $\temp{rot}$; however, the molecule internal alignment temperature $\Tia$ may substantially change if part of the absorbed photon energy is transferred to rotational degrees of freedom."47" We account for the nucertain energv exchanee between vibrational arc rotational modes by paramctrizing the erain interna aliguiment before UV absorption aud during IR ciission respectively with συ (corresponding to Ti,= T9) am ,Xg (corresponding to Zi,= Zo).", We account for the uncertain energy exchange between vibrational and rotational modes by parametrizing the grain internal alignment before UV absorption and during IR emission respectively with $\gamma_0$ (corresponding to $\Tia\equiv T_0$ ) and $\gamma_r\leq\gamma_0$ (corresponding to $\Tia\geq T_0$ ).48" Tn principle. 7, should be different for cach IR cunuission feature. since it may be thought of as the internal alieumieut. coefücieut when most of the radiation in that band is emitted."," In principle, $\gamma_r$ should be different for each IR emission feature, since it may be thought of as the internal alignment coefficient when most of the radiation in that band is emitted."49 We now discuss another plausible choice for the paraluctrization of the aliguinent between aj aud J prior to UV absorption., We now discuss another plausible choice for the parametrization of the alignment between $\ba$ and $\bJ$ prior to UV absorption.50 If many collisions with hiyvarosgeu atoms occur iu the interval between two UV absorptions. and there are no other torques acting. the eram will be driven towards “Browuian rotation” with f(.7)x7°.," If many collisions with hydrogen atoms occur in the interval between two UV absorptions, and there are no other torques acting, the grain will be driven towards “Brownian rotation” with $f(J)\propto J^2$."51" It there is no vibrationalrotational enerev exchanec (i.o.. the PAT] acts like a rigid rotator). the internal aliguiaucut temperature Ly before UV absorption will approsximatcly equal the eas kinetic temperature T,wan"," If there is no vibrational-rotational energy exchange (i.e., the PAH acts like a rigid rotator), the internal alignment temperature $T_0$ before UV absorption will approximately equal the gas kinetic temperature $T_{\rm gas}$."52 luteeratiou of eq. (22)), Integration of eq. \ref{eq:general}) )53 with respect to J assuming £67)x7? viclds a probability distribution align2dP(())= which does uot depend on των but only ou the ecolmectrical properties of the erain via €—ιόfb).," with respect to $J$ assuming $f(J)\propto J^2$ yields a probability distribution )=, which does not depend on $T_{\rm gas}$ but only on the geometrical properties of the grain via $\epsilon\equiv I_1/(I_1-I_2)$."54 Tn the following. we paraimcetrize the cisaliguiacnt between aj and J bv using eq. (17))," In the following, we parametrize the disalignment between $\ba$ and $\bJ$ by using eq. \ref{eq:align}) )"55" both beforeUV. absorption (with. 590) aud during IB onismiou (with 2,€ay).", both beforeUV absorption (with $\gamma_0$ ) and during IR emission (with $\gamma_r\leq\gamma_0$ ).56 However. in the Appendix we preseut analytic formmlae for the expected degree of polarization if the erain aliguuneut before UV absorption can be described by eq. (224).," However, in the Appendix we present analytic formulae for the expected degree of polarization if the grain alignment before UV absorption can be described by eq. \ref{eq:align2}) ),"57 but eq. (17)), but eq. \ref{eq:align}) )58 still holds during IR eiiission., still holds during IR emission.59" Iu the dust πιο] of ?.. the 2.12sau emission features are produced primarily bv PAIT molecules or clusters containing between XN,z25 and ~1000 carbon atoms. and the 174200 couples is mainky due to ΡΑΣ with No2000."," In the dust model of \citet{draine_li07}, the $3-13\unit{\mu m}$ emission features are produced primarily by PAH molecules or clusters containing between $\NC\approx 25$ and $\sim1000$ carbon atoms, and the $\,\mu$ m complex is mainly due to PAHs with $\NC\approx 2000$."60" For purposes of estimating rotational kinetic enereies and the deusitv of vibrational states; we will take NV,.=200 as a represeutative value. with a volunc-equivalent radius οzτοÀ."," For purposes of estimating rotational kinetic energies and the density of vibrational states, we will take $\NC=200$ as a representative value, with a volume-equivalent radius $a\approx 7.5\,$."61 We suppose that all the cluitting molecules are axisviunietnÉie aud planar. with Dif-23.," We suppose that all the emitting molecules are axisymmetric and planar, with $I_1/I_2=2$."62 Following UV absorption. the aligumieut between the molecule principal axis aj and angular iuoimentuni J. aud thus the internal alieumeut temperature Tii. depends onu the efficacy of internal energv exchanec between lattice vibrational modes and rotational modes.," Following UV absorption, the alignment between the molecule principal axis $\ba$ and angular momentum $\bJ$, and thus the internal alignment temperature $\Tia$, depends on the efficacy of internal energy exchange between lattice vibrational modes and rotational modes."63 The Intramolecular Vibration-Rotation Encrey Trausfer (INRET) process (?).. due to inuperfect elasticity of the molecule when stressed by centrifugal aud Coriolis forcpa allows euerev exchange between rotation aud vibratic-ρα on a timescale ~LO2s (23. much shorter than the duration 1.10sof the IR ciission burst.," The Intramolecular Vibration-Rotation Energy Transfer (IVRET) process \citep{purcell_79}, due to imperfect elasticity of the molecule when stressed by centrifugal and Coriolis forces, allows energy exchange between rotation and vibrations on a timescale $\sim10^{-2}\unit{s}$ \citep{rouan_92}, much shorter than the duration $\sim1-10\unit{s}$of the IR emission burst."64 This means that. while the molecule is cooling after UV absorption. its internal aliguiment tempcrature Ti teuds to be equal to the imstantaneous vibrational (lattice) teniperature Ju.," This means that, while the molecule is cooling after UV absorption, its internal alignment temperature $\Tia$ tends to be equal to the instantaneous vibrational (lattice) temperature $\temp{vib}$."65" Following photon absorption. the lattice may be heated up to a temperature Ty,%3001500xIx. depending on the eram size aud the photon cucreyv."," Following photon absorption, the lattice may be heated up to a temperature $T_{\rm vib}\approx300 - 1500\unit{K}$, depending on the grain size and the photon energy."66" The erain cools ax IR energy is radiated. aud we estimate Ty,~SOOTS when most of the 3.3pam cussion takes place. Tig,z3001. for the 7.7jiu cinission. TQc200IK for the 11.3san euission. aud Tayi,zc120EK for the 17pin emission. unless the local radiation field is so intense to prevent the lattice from cooling down to sucli temperatures."," The grain cools as IR energy is radiated, and we estimate $\temp{vib}\approx 800\unit{K}$ when most of the $3.3\unit{\mu m}$ emission takes place, $\temp{vib}\approx 300\unit{K}$ for the $7.7\unit{\mu m}$ emission, $\temp{vib}\approx 200\unit{K}$ for the $11.3\unit{\mu m}$ emission, and $\temp{vib}\approx 120\unit{K}$ for the $17\unit{\mu m}$ emission, unless the local radiation field is so intense to prevent the lattice from cooling down to such temperatures."67" The internal temperature Ti, follows Tij, while the erain is cooling. with Zi,2Py, as long as the vibrational enerev levels are suffüiientlv closely spaced to allow energv transfer between vibrations and When he separation AF of vibrational levels exceeds ~ huyus. he IVRET process ceases to operate aud the rotational nodes decouple from the lattice."," The internal temperature $\temp{ia}$ follows $\temp{vib}$ while the grain is cooling, with $\Tia\approx\temp{vib}$ as long as the vibrational energy levels are sufficiently closely spaced to allow energy transfer between vibrations and When the separation $\Delta E$ of vibrational levels exceeds $\sim\hbar\,\omega_{\rm rot}$ , the IVRET process ceases to operate and the rotational modes decouple from the lattice."68 The density of states can be calculated using a model normal mode spectruuui aud the Bever-Swinechart algoritlian (7): for IN.= 200. he density of states at vibrational euergv E/hezx bi hbedNAdEsi1/0]0185o02 1.," The density of states can be calculated using a model normal mode spectrum and the Beyer-Swinehart algorithm \citep{draine_li01}: for $N_{{\msc{C}}}=200$ , the density of states at vibrational energy $E/hc69\approx 250\unit{cm^{-1}}$ is $hc\, \ud N/\ud E\approx 1/ (0.1870\unit{cm^{-1}})$ ."71 This should still, This should still72For a barred spiral galaxy. it is expected that the co-rotation radius CR would be located not far bevoud the cud of the bar.,"For a barred spiral galaxy, it is expected that the co-rotation radius CR would be located not far beyond the end of the bar."73 For 11915 this position is uncertain., For 4945 this position is uncertain.74 Accounting for unsvstematic velocity residuals of ((Sect.33.5.1). the velocity anomaly eiu be traced out to approximately #150” projected on the sky (see refFICL.IITL.BRANDTMODELcC).," Accounting for unsystematic velocity residuals of 0 – 3.5.4), the velocity anomaly can be traced out to approximately $\pm$ $''$ projected on the sky (see \\ref{FIG.HI.BRANDTMODEL}c c)."75 With an inclination to the Iimc-of-sight of 15 33.5.5) this would be equivalent to a bar extent (from the nucleus) of about kkov., With an inclination to the line-of-sight of $^{\circ}$ 3.5.5) this would be equivalent to a bar extent (from the nucleus) of about kpc.76" Since the spiral avis could be traced from the outer galaxy (~G600"" offset from the centro) to ~120” 33,1j the spiral avis might be connected with the xw. as conumionlv observed iu galaxies with snall iachation (e.g. Revnaud Downes 1997: IHüttteimicister et al"," Since the spiral arms could be traced from the outer galaxy $\sim$ $''$ offset from the centre) to $\sim$ $''$ 3.4), the spiral arms might be connected with the bar, as commonly observed in galaxies with small inclination (e.g. Reynaud Downes 1997; Hütttemeister et al."77 1999)., 1999).78 The CR mnust be located at RT kipe. the outer radius of the gaseous bar.," The CR must be located at $R$$>$ kpc, the outer radius of the gaseous bar."79" Since stellar bars are louger than their gaseous counterparts (Martinet 1995) aud since gravitational torques de-populate the co-rotation region iu a spiral galaxw (e.g. Carctaa-Burillo Cuéllin 1995: €'omnibes 1996). the drop in ILriuteusitv secu in refFIG..COMP.PVDIAGRAAL at Ro~ 150"" kkpc) and the snall rotaional velocities a this radius (see ΩΙΕΙVRAD.DYN aud 33.5.2) mar be considered as a signature of the CR (see also Freeman 1997 for ""wverage radii)."," Since stellar bars are longer than their gaseous counterparts (Martinet 1995) and since gravitational torques de-populate the co-rotation region in a spiral galaxy (e.g. a-Burillo Guéllin 1995; Combes 1996), the drop in intensity seen in \\ref{FIG.COMP.PVDIAGRAM} at $R$ $\sim$ $''$ kpc) and the small `rotational' velocities at this radius (see \\ref{FIG.VRAD.DYN} and 3.5.2) may be considered as a signature of the CR (see also Freeman 1997 for `average' radii)."80" Adopting this raclins. the pattern speed is +: the OLR Gvhich occurs where the tern speed intercepts the upper 0-2 curve in refFIG.VRAD. DYN}) Is then at a radius of skpe (aueular distance: 7650"") and the ilutra-hiuiuonic resonance is at kkpe (550). where the outermos features are seen refFIG.MAPS) )."," Adopting this radius, the pattern speed is $^{-1}$; the OLR (which occurs where the pattern speed intercepts the upper $m$ =2 curve in \\ref{FIG.VRAD.DYN}) ) is then at a radius of kpc (angular distance: $\sim$ $''$ ) and the $m$ =4 ultra-harmonic resonance is at kpc $''$ ), where the outermost features are seen \\ref{FIG.MAPS}) )."81 Our Braudt rotation curve is a good ft to the outer galaxy. but docs not allow to predict the presence of au ILR.," Our Brandt rotation curve is a good fit to the outer galaxy, but does not allow to predict the presence of an ILR."82 In the innexuost parts of the galaxy. measured angular velocities are larger than those steecsted by the Draudt curve VRAD.DY refFIC.N)). leaving open the ο that an inner Lindblad resonance exists at Ro< 3kkpc.," In the innermost parts of the galaxy, measured angular velocities are larger than those suggested by the Brandt curve \\ref{FIG.VRAD.DYN}) ), leaving open the possibility that an inner Lindblad resonance exists at $R$ $<$ kpc."83 Au attractive but speculative view is to associate the in101) molecular ring at a galactocentrie radius o La few huudred pe (Table 3)) with the ILR that might contain a nesed secondary bar (the lindow: see Sect.33.5.1} eukΠιο atomic and molecular eas to the pttative circunnunuclear torus discovered by Creenhill et aL (, An attractive but speculative view is to associate the inner molecular ring at a galactocentric radius of a few hundred pc (Table \ref{TAB.CO.NUCSIZE}) ) with the ILR that might contain a nested secondary bar (the inflow; see 3.5.4) guiding atomic and molecular gas to the putative circumnuclear torus discovered by Greenhill et al. (841997).,1997).85 Note however that the uuclear molecular rine is part of the rausitional region between solid ody ate cüffereutial rotation., Note however that the nuclear molecular ring is part of the transitional region between solid body and differential rotation.86 The ring is therefore not necessarily7 formed bva eravitational resonance., The ring is therefore not necessarily formed bya gravitational resonance.87 It could also be caused by viscots transport as e.g. outlined by Datther Biermamn (199)., It could also be caused by viscous transport as e.g. outlined by Dätther Biermann (1990).88 Adopting the Dátther Biermann mnechauisui. an age estimate applvius their last equation leads to a formation timescale of thine ~ GCGyr.," Adopting the Dätther Biermann mechanism, an age estimate applying their last equation leads to a formation timescale of $t_{\rm ring}$ $\sim$ Gyr."89 A lighvesolution study has been performed of the EGGIIz coutinmun.Tb. and eenüssion for the southern spiral galaxy 11915.," A high-resolution study has been performed of the GHz continuum, and emission for the southern spiral galaxy 4945."90 It utilizes both the Australia Telescope Compact Array (ATCA) and the Swedish-ESO-Subiuillimetre Telescope (SEST)., It utilizes both the Australia Telescope Compact Array (ATCA) and the Swedish-ESO-Submillimetre Telescope (SEST).91 The augulu resolution is ~237 (750 pe at D=6.7 MMpc) aud the spectral resolution is ~7 kins.., The angular resolution is $\sim$ $''$ (750 pc at $D$ Mpc) and the spectral resolution is $\sim$ .92. The ATCA results also vield high resolution (~3.67) nuages of the nuclear region of the eaANY., The ATCA results also yield high resolution $\sim$ $''$ ) images of the nuclear region of the galaxy.93 The main conclusions are as follows:, The main conclusions are as follows:94We can use our data to obtain the best estimate for the (me of peak in the 2010 eruption.,We can use our data to obtain the best estimate for the time of peak in the 2010 eruption.95 The discovery image was taken al JD 2455224.9385 (DGILI. and we have measured the magnitude of U Seo (with respect to the comparison star sequence in 5chaeler 2010) (o be V=7.85 with the svstematic uncertainties dominating at around 0.10 mag.," The discovery image was taken at JD 2455224.9385 (BGH), and we have measured the magnitude of U Sco (with respect to the comparison star sequence in Schaefer 2010) to be V=7.85 with the systematic uncertainties dominating at around 0.10 mag."96 The observed inilial rate of decline is 1.4 mag per dav (Schaefer et al., The observed initial rate of decline is 1.4 mag per day (Schaefer et al.97 201080)., 2010b).98 The peak magnitude of U Seo is V—1.5. primarily as based on the observed peak of the 1999 eruption (Schaefer 2010).," The peak magnitude of U Sco is V=7.5, primarily as based on the observed peak of the 1999 eruption (Schaefer 2010)."99 In an exhaustive comparison of all RN eruptions and those from U Seo in particular. Schaeler (2010) found that all RN are consistent with having the identical eruption light curve shapes. and (his is our basis for taking the peak from the 1999 U Sco eruption as being (he same for the 2010 eruption.," In an exhaustive comparison of all RN eruptions and those from U Sco in particular, Schaefer (2010) found that all RN are consistent with having the identical eruption light curve shapes, and this is our basis for taking the peak from the 1999 U Sco eruption as being the same for the 2010 eruption."100 With this. the peak of the 2010 eruption would have been 0.25 davs before discovery. which gives a peak al JD 2455224.69 with a likely uncertainty of 0.07 days.," With this, the peak of the 2010 eruption would have been 0.25 days before discovery, which gives a peak at JD 2455224.69 with a likely uncertainty of 0.07 days."101 The observational limits from the 2010 eruption show that the eruption could not have started much before the ASAS-3N image at JD 2455224.1649., The observational limits from the 2010 eruption show that the eruption could not have started much before the ASAS-3N image at JD 2455224.1649.102 From the limits on the prior eruplions. the eruption started 0.25 to 0.5 days belore the peak. which is roughly from JD 2455224.19 (o 245522444.," From the limits on the prior eruptions, the eruption started 0.25 to 0.5 days before the peak, which is roughly from JD 2455224.19 to 2455224.44."103" Thus. the Gime of the start of the expansion. as required by the ""universal decline law’ of Hachisu Nato (2006). can be expressed as JD 32+0.12."," Thus, the time of the start of the expansion, as required by the `universal decline law' of Hachisu Kato (2006), can be expressed as JD $\pm$ 0.12."104 Disappointinely. we have no observations from JD 2455224.3438 (o 2455224.9385 and thus have completely missed (he entire rise and the hour of peak.," Disappointingly, we have no observations from JD 2455224.3438 to 2455224.9385 and thus have completely missed the entire rise and the hour of peak."105 In January. U Sco is [airlv close to the Sun and hence only visible from a narrow slice of longitude al anv given lime.," In January, U Sco is fairly close to the Sun and hence only visible from a narrow slice of longitude at any given time."106 In the southern hemisphere. (he start of the rise would only have been visible from the loneitudes in the Iidian Ocean. while the peak would only have been visible from the longitudes in the South Atlantic Ocean.," In the southern hemisphere, the start of the rise would only have been visible from the longitudes in the Indian Ocean, while the peak would only have been visible from the longitudes in the South Atlantic Ocean."107 Schaeler (2005) presented a new method for predicting the date of the next eruption of a recurrent. nova based on the requirement Chat some constant amount of mass mist be accumulated by the white dwarf between eruptions., Schaefer (2005) presented a new method for predicting the date of the next eruption of a recurrent nova based on the requirement that some constant amount of mass must be accumulated by the white dwarf between eruptions.108 Accretion rates very substantially (Schaefer 2010: and see Figure 1). so the interval between eruptions (2) depends on the average accretion during that time.," Accretion rates vary substantially (Schaefer 2010; and see Figure 1), so the interval between eruptions $T$ ) depends on the average accretion during that time."109 If the accretion rate is high then the interval will be short. while if the accretion rate is low then 7 will be high.," If the accretion rate is high then the interval will be short, while if the accretion rate is low then $T$ will be high."110 For U Seo. the blue elt is dominated by the accretion disk. so the blue flux (Εμ) will be a measure of the accretion rate.," For U Sco, the blue light is dominated by the accretion disk, so the blue flux $F_B$ ) will be a measure of the accretion rate."111 In particular for U Sco. the accretion rate will be proportional to FL? (Schaeler 2005).," In particular for U Sco, the accretion rate will be proportional to $F_B^{1.5}$ (Schaefer 2005)."112 By averaging FL? over each interval T. we can derive a quantity that is proportional to the average accretion rate.," By averaging $F_B^{1.5}$ over each interval $T$, we can derive a quantity that is proportional to the average accretion rate."113 Then. (Fb°)T should be proportional to the total mass accreted," Then, $\langle F_B^{1.5} \rangle T$ should be proportional to the total mass accreted"114The thermal SZ ellect is à modification to the CMD spectrum. caused. by Compton scattering of CALB photons o» hot electrons in the intracluster medium.,The thermal SZ effect is a modification to the CMB spectrum caused by Compton scattering of CMB photons by hot electrons in the intracluster medium.115 The SZ lux measured at radio or sub-mm wavelengths can be expressed in terms of the Compton y parameter., The SZ flux measured at radio or sub-mm wavelengths can be expressed in terms of the Compton $y-$ parameter.116 For a given cosmology. the yo parameter can also be predicted rom the same X-rav data used to determine the ως measurements. being proportional to the integral along he linc-of-sight. of the product of. electron. density. and emperature. fnid.," For a given cosmology, the $y-$ parameter can also be predicted from the same X-ray data used to determine the $f_{\rm gas}$ measurements, being proportional to the integral along the line-of-sight of the product of electron density and temperature, $\int{n_{\rm e} T_{\rm e} dl}$."117 We have examined {πο additional cosmological constraining power that can be achieved. with follow-up radio/sub-mnm SZ observations of our sample of 500 clusters. assuming direct SZ llux measurements accurate o 2 or 5 per centtherein).," We have examined the additional cosmological constraining power that can be achieved with follow-up radio/sub-mm SZ observations of our sample of 500 clusters, assuming direct SZ flux measurements accurate to 2 or 5 per cent."118 The statistical uncertainties in the predicted. C'ompton y parameters will be comparable to those associated. with he Jus measurements: 5 per cent for the 500-cluster sample., The statistical uncertainties in the predicted Compton $y-$ parameters will be comparable to those associated with the $f_{\rm gas}$ measurements: $\sim 5$ per cent for the 500-cluster sample.119 We generate our predicted yo parameter cata set or the redshift distribution shown in Fig., We generate our predicted $y-$ parameter data set for the redshift distribution shown in Fig.120 1 (solid curve), 1 (solid curve).121 We have used the code to generate auto and cross temperature and polarization angular power spectra. CL. (ut and CPE. for the fiducial. Wat ACDAL cosmology cleseribecl in Table 2..," We have used the code to generate auto and cross temperature and polarization angular power spectra, $C^{\rm122 TT}_{\rm l}$, $C^{\rm TE}_{\rm l}$ and $C^{\rm EE}_{\rm l}$ , for the fiducial, flat $\Lambda$ CDM cosmology described in Table \ref{tab:fidu}."123 We follow and and assume that the temperature. 2. and polarization ££. fields are Gaussian ancl isotropic.," We follow and and assume that the temperature, $T$, and polarization $E-$ fields are Gaussian and isotropic."124 We also assume that the polarization B field is negligible., We also assume that the polarization $B-$ field is negligible.125 Laving cpt. (Cit and CP. we add a simple. isotropic noise power spectrum where Ato)=bito). bv)=vsln2e(»r) is the beam full width at half maümum (ENLHIM) measurecl in raclians. and o(r)=(AT/T2 is the root mean square noise. por beamresized. pixel.," Having $C^{\rm TT}_{\rm l}$, $C^{\rm TE}_{\rm l}$ and $C^{\rm EE}_{\rm126l}$, we add a simple, isotropic noise power spectrum where $\mathcal{N}_{\rm l}(\nu)=[b(\nu) \sigma(\nu)]^2$, $b(\nu)=\sqrt{8\ln 2} \sigma(\nu)$ is the beam full width at half maximum (FWHM) measured in radians, and $\sigma(\nu)=(\Delta T/T)^2$ is the root mean square noise per beam-sized pixel."127 Assuming uncorrelated noise in the ZZ and T Gelcls. the covariance over realizations is For the channel 9=143€ |o)2οὗ Ix? and (9)=7-laremin(2)...," Assuming uncorrelated noise in the $E$ and $T$ fields, the covariance over realizations is For the channel $\nu=143$, $\mathcal{N}^{\rm TT}_{\rm128 l}(\nu)=\mathcal{N}^{\rm EE}_{\rm l}(\nu)/4=2\times12910^{-4}$ $^{2}$ and $b(\nu)=7.1$."130 These values correspond. to a(vytt=697 and συ)ΕΕοίNytIx. which is roughly the sensitivity expected for after 2 vears (14 months) of a full sky survey (?).," These values correspond to $\sigma(\nu)^{\rm TT}=6.97$ and $\sigma(\nu)^{\rm EE}=9.68$, which is roughly the sensitivity expected for after $\sim 2$ years (14 months) of a full sky survey ."131. We consider two dillerent scenarios relating to forcground CMD. polarization contamination., We consider two different scenarios relating to foreground CMB polarization contamination.132 Firstly. we examine the idealized case where such contamination can be neglected(277?).," Firstly, we examine the idealized case where such contamination can be neglected."133. Secondly. we consider a more conservative scenario where 20 per cent of the sky is irretrievably contaminated by Galactic emission. leaving SO per cent mt can be mocdelled as approximately foregrouncd-free.," Secondly, we consider a more conservative scenario where $\sim 20$ per cent of the sky is irretrievably contaminated by Galactic emission, leaving $\sim 80$ per cent that can be modelled as approximately foreground-free."134 For the second scenario. forecast that will be able to determine the optical depth to reionization to a precision of afr)~0.01. as compared to e(r)~0.005 for the idealized. foreground-free. case(222).," For the second scenario, forecast that will be able to determine the optical depth to reionization to a precision of $\sigma(\tau) \sim1350.01$, as compared to $\sigma(\tau) \sim 0.005$ for the idealized, foreground-free case."136.. Lo account for the elfects of polarization contamination. the DEVE discarded polarization information for multipoles /«30 and imposed a prior on 7 to obtain a(7)=0.01.," To account for the effects of polarization contamination, the DETF discarded polarization information for multipoles $l<30$ and imposed a prior on $\tau$ to obtain $\sigma(\tau)=0.01$."137 For our analysis in the case ofpolarization contamination. we also artificially weaken the constraints on 7 to à precision of στ)~0.01 bv enlarging by an order of magnitude the noise at low multipoles /«30 in the polarization data.," For our analysis in the case of polarization contamination, we also artificially weaken the constraints on $\tau$ to a precision of $\sigma(\tau)\sim 0.01$ by enlarging by an order of magnitude the noise at low multipoles $l<30$ in the polarization data."138 For both scenarios. we use only the data from multipoles 2xd2000.," For both scenarios, we use only the data from multipoles $2\leq l\leq1392000$."140 Por simplicity. we adopt the contamination scenario as our default CMD cata set.," For simplicity, we adopt the zero-contamination scenario as our default CMB data set."141 Given the dark energy model described in Section 2. and the simulated: fii; and CMD data sets described in Section 3.. we use the Metropolis Markov Chain Monte Carlo (AICAIC) algorithm. implemented in the package to examine posterior parameter distributions.," Given the dark energy model described in Section \ref{sec:de} and the simulated $f_{\rm gas}$ and CMB data sets described in Section \ref{sec:simdata}, , we use the Metropolis Markov Chain Monte Carlo (MCMC) algorithm implemented in the package to examine posterior parameter distributions."142 We use a mocilied version of the code to caleulate CAIB power spectra: this accounts for the elfects of dark energy perturbations for evolving dark energy equations of state (see Section 4.5. for details)., We use a modified version of the code to calculate CMB power spectra; this accounts for the effects of dark energy perturbations for evolving dark energy equations of state (see Section \ref{sec:depert} for details).143 Our mocified. version of the code also incorporates the. ἕως analysis method described by??).," Our modified version of the code also incorporates the $f_{\rm144 gas}$ analysis method described by."145. Our choice to forecast. parameter constraints using a ull MOMC analysis has some advantages over the more widelv used Fisher matrix formalism)., Our choice to forecast parameter constraints using a full MCMC analysis has some advantages over the more widely used Fisher matrix formalism.146. Firstly. the shape of the mean log Likelihood see equation (22)) in the MCMC analysis cucapsulates all of the relevant degeneracies between parameters. which is crucial or non-Gaussian distributions.," Firstly, the shape of the mean log likelihood [see equation \ref{eq:logli}) )] in the MCMC analysis encapsulates all of the relevant degeneracies between parameters, which is crucial for non-Gaussian distributions."147 Secondly. the fact that our orecasts are made using the same analysis code used to analyze current data ensures Consistency otween present and future constraints.," Secondly, the fact that our forecasts are made using the same analysis code used to analyze current data ensures consistency between present and future constraints."148 Finally.the ALCALC method. allows us to easily anc clliciently introduce priors and. allowances and thereby study the elfects of svstematic uncertainties.," Finally,the MCMC method allows us to easily and efficiently introduce priors and allowances and thereby study the effects of systematic uncertainties."149The ongoing gasxich spiral spiral merger NGC 1038/39. the Autennac. forms a vich YSC system.,"The ongoing gas-rich spiral – spiral merger NGC 4038/39, the Antennae, forms a rich YSC system."150 It is not possible to tell apart the YSC's into short-lived aud long-lived oues., It is not possible to tell apart the YSCs into short-lived and long-lived ones.151 Iu anv kind of obscrvationally accessible parameter (ass; half-light radius) or parameter combinationflei these YSCs form a coutimmous distribution.," In any kind of observationally accessible parameter (mass, half-light radius) or parameter combination, these YSCs form a continuous distribution."152 Iu a very careful analysis of this SC system du formation. inchicding conservative SC identification. accurate aperturclifuuction correctious for SC sizes aud photometry. careful completeness analvsis. extensive statistical tests aud likelihood evaluatiouslkeut bv Monte Carlo simulations. we could show that the bIuuüunositv fiction of the SC system features a turnover with 99.5 significance (?)..," In a very careful analysis of this SC system in formation, including conservative SC identification, accurate aperture corrections for SC sizes and photometry, careful completeness analysis, extensive statistical tests and likelihood evaluations by Monte Carlo simulations, we could show that the luminosity function of the SC system features a turnover with 99.5 significance \citep{Anders+07}."153 In this respect. the YSC luminosity fiction in this ongonig merecr differs from. Lhunuinositv functions of ¥SCs iu clwart ealaxies. spirals. and isolated starbursts. which all are power laws.," In this respect, the YSC luminosity function in this ongoing merger differs from luminosity functions of YSCs in dwarf galaxies, spirals, and isolated starbursts, which all are power laws."154 It also differs frou the power laws ound for themuss functions of molecular clouds aud uolecular cloud cores in undisturbed ealaxics., It also differs from the power laws found for the functions of molecular clouds and molecular cloud cores in undisturbed galaxies.155" Mass ""uictious of molecular clouds and molecular cloud cores in gas-rich interacting galaxies cannot vet be measured. hev will have to await ALMA."," Mass functions of molecular clouds and molecular cloud cores in gas-rich interacting galaxies cannot yet be measured, they will have to await ALMA."156" Uufortunatelv. it is rot straightforward to transform the YSC luninosity ""uction iuto a mass function. since it is uot clear row to translate the completeness huit iu luninosity into a completeness Πιτ iu mass carving the rapid niuuostv evolution of YSCs."," Unfortunately, it is not straightforward to transform the YSC luminosity function into a mass function, since it is not clear how to translate the completeness limit in luminosity into a completeness limit in mass during the rapid luminosity evolution of YSCs."157 The obvious wav to evaluate the mass function m small age bius suffers roni low statistical significance., The obvious way to evaluate the mass function in small age bins suffers from low statistical significance.158 Repeating our accurate analvsis on the ACS data covering a larecr FoV with etter sunupliug nüght be a promising wav to eo., Repeating our accurate analysis on the ACS data covering a larger FoV with better sampling might be a promising way to go.159 In any case. the clear turi-over in the luminosity function could be a lin that the amount of SF that goes iu nassive SCs relative o the amount of SF that σοςμα into low-ass SC uuelt be higher in this gasrich ucrecr than in other cuviroumeuts.," In any case, the clear turn-over in the luminosity function could be a hint that the amount of SF that goes into massive SCs relative to the amount of SF that goes into low-mass SCs might be higher in this gas-rich merger than in other environments."160" It will be very interesting to check with ALATA our expectation that he molecular cloud structure and mass spectrun i- his major merger are different from what they are in the Milkv. Wax. ie. closer to what is observed iu erus of integrated light frou: higher aud lower density nolecular gas ος, TICN)/L(CO) in ULIRGs."," It will be very interesting to check with ALMA our expectation that the molecular cloud structure and mass spectrum in this major merger are different from what they are in the Milky Way, i.e. closer to what is observed in terms of integrated light from higher and lower density molecular gas L(CS, HCN)/L(CO) in ULIRGs."161 NGC 1038/39 is craveuthly a LIRG (Lgs>Lott L.) aud will xobablv further increase its SFR close to final mereiue., NGC 4038/39 is currently a LIRG ${\rm L_{IR} > 10^{11}~L_{\odot}}$ ) and will probably further increase its SFR close to final merging.162 There is observational evidence for very large amounts of molecular gas at the level of about twice the total eas Inass (III | IIl.) iu the Milkv. Wav (7) and for extremielv massive concentrations of it (7) with low kinetic temperature (7)., There is observational evidence for very large amounts of molecular gas at the level of about twice the total gas mass (HI $+~{\rm H_2}$ ) in the Milky Way \citep{Gao+01} and for extremely massive concentrations of it \citep{Wilson+03} with low kinetic temperature \citep{Schulz+07}.163. Shocked eas. ou the other haud. is found displaced. from the regions of high present SE. i.e. uwost probably due to the collisiou of the two galaxies (?)..," Shocked gas, on the other hand, is found displaced from the regions of high present SF, i.e. most probably due to the collision of the two galaxies \citep{Haas+05}."164 The exceptionally high maguetic field streneth that ? measured over an extended region also suggests compression of the ISAL, The exceptionally high magnetic field strength that \cite*{HummelHulst86} measured over an extended region also suggests compression of the ISM.165 The fraction ofvery dense molecular eas as seen ia Lye is still low. as well as the SF efficiency. wherefrom ? conclude that the bulk of the starburst is vet to come as the two merge. probably driving the Auteunae above the ULIRG threshold in terms of IR. Inninositv.," The fraction of dense molecular gas as seen in ${\rm L_{HCN}}$ is still low, as well as the SF efficiency, wherefrom \cite*{Gao+01} conclude that the bulk of the starburst is yet to come as the two nuclei merge, probably driving the Antennae above the ULIRG threshold in terms of IR luminosity."166 We speculate that if the turnover in the Iuninositv would reflect a turnover in the underline function. then this would tie in nicely with the result obtained ly ?? that the Milkv. Way GC system originally 1uust have had a mass spectrum with a turnover around 107AL...," We speculate that if the turnover in the luminosity function would reflect a turnover in the underlying mass function, then this would tie in nicely with the recent result obtained by \cite*{ParmentierGilmore05,ParmentierGilmore07} that the Milky Way GC system originally must have had a mass spectrum with a turnover around ${\rm 10^5~M_{\odot}}$."167" NGC 7252 is not the oulv example of à merecr that uo doubt has produced a new generation of GCs,", NGC 7252 is not the only example of a merger that no doubt has produced a new generation of GCs.168 The ~d3 Gyr old mereer remnants NGC 3921 (7). NGC 231 (2)... and NGC 1316 (777) as well feature voung GC populations formed during the merecrs.," The $\sim 1 - 3$ Gyr old merger remnants NGC 3921 \citep{Schweizer+96}, NGC 34 \citep{SchweizerSeitzer07}, and NGC 1316 \citep{Goudfrooij+01a,Goudfrooij+01b,Goudfrooij+04,Goudfrooij+07} as well feature young GC populations formed during the mergers."169 The uetallicities of these newly formed GCs agree well with expectations on the basis of spiral ealaxy ISM xoperties., The metallicities of these newly formed GCs agree well with expectations on the basis of spiral galaxy ISM properties.170 Evolutionary svuthesis models predict these SCs to ake on the optical colours of the red-peak GC widely observed in E/SO ealaxies by the time the idal features indicative of the merecr origin will have vanished., Evolutionary synthesis models predict these SCs to take on the optical colours of the red-peak GC widely observed in E/S0 galaxies by the time the tidal features indicative of the merger origin will have vanished.171 They also predict that they should reacdily )e detectable against other populations of red GCs iu combined optical and NIR observations (2) (see also B. Wotulla. this volume).," They also predict that they should readily be detectable against other populations of red GCs in combined optical and NIR observations \citep{Fritze04} (see also R. Kotulla, this volume)."172 No example of a clearly merge gasrich dwarf ealaxy pair. nor of aui accretion of a gas-xicli dwartby an elliptical or S0 has as vet been studied to check whether those would also eive rise to new GC populations.," No example of a clearly merging gas-rich dwarf galaxy pair, nor of an accretion of a gas-rich dwarf by an elliptical or S0 has as yet been studied to check whether those would also give rise to new GC populations."173 When it comes to the first detailed analysis of called Super Star Clusters in normal actively star-forming She Sd type spirals. the situation eects Clubairassing.," When it comes to the first detailed analysis of so-called Super Star Clusters in normal actively star-forming Sbc $-$ Sd type spirals, the situation gets embarrassing."174 ? (LOL) presents eround-based ancl IST multi-baud photometric data for a sample of 17 non-iuteractiugC» actively star formineC» face-on spirals.," \cite*{Larsen04} (L04) presents ground-based and HST multi-band photometric data for a sample of 17 non-interacting actively star forming face-on spirals,"175nid-2018.,mid-2018.176 The current. baseline design. with an elfective mim primary mirror. a ddeg? Ποια of view. ancl a 3.2 Gigapixel camera. will allow about 20.000 square degrees of sky to be covered using pairs of 15-second exposures in (wo out of six SDSS (ugrizy) photometric bands everv tree nights on average. wilh (tvpical 5o depth for point sources of r24.5.," The current baseline design, with an effective m primary mirror, a ${}^2$ field of view, and a 3.2 Gigapixel camera, will allow about 20,000 square degrees of sky to be covered using pairs of 15-second exposures in two out of six SDSS $ugrizy$ ) photometric bands every three nights on average, with typical $\sigma$ depth for point sources of $r\sim24.5$."177 The? (8566.10. pg.," The \citetalias{LSSTbook} 6.10, pg."178 171) includes a discussion on the importance of EBs to the LSST science case. and includes a preliminary estimate of the ED vield.," 171) includes a discussion on the importance of EBs to the LSST science case, and includes a preliminary estimate of the EB yield."179 It proposes a metric based on the number of visits (pairs of 15-s observations) in the eclipses aud provides qualitative results that indicate LSST’s near-perlect efficiency for short-period binaries. ~50% efficiency. Lor periods up to 30 days. and a ον elliciency for the longer periods.," It proposes a metric based on the number of visits (pairs of 15-s observations) in the eclipses and provides qualitative results that indicate LSST's near-perfect efficiency for short-period binaries, $\sim$ efficiency for periods up to 30 days, and a $\sim$ efficiency for the longer periods."180 ere we revise the estimate in sienilicantly greater detail and provide quantitative results., Here we revise the estimate in significantly greater detail and provide quantitative results.181 The paper structure is as follows: in 322 we present the details of the simulation. in 823 we discuss the recoverability rate for the ephemerides and for physical parameters: in 844 we summarize (he results and conclude in 855.," The paper structure is as follows: in 2 we present the details of the simulation, in 3 we discuss the recoverability rate for the ephemerides and for physical parameters; in 4 we summarize the results and conclude in 5."182 In (his section. we describe our procedures to estimate L55T's ED vield., In this section we describe our procedures to estimate LSST's EB yield.183 First we created a set of model ED light curves employing PILOEBE (?).. a? based eclipsing binary modeling suite.," First we created a set of model EB light curves employing PHOEBE \citep{prsa2005}, a \citet{wd1971} based eclipsing binary modeling suite."184 Next. we sampled these light curves according to LSST’s so-called universal cadence (?) over a nominal 10-vear lile span of the mission.," Next, we sampled these light curves according to LSST's so-called universal cadence \citep{cook2009} over a nominal 10-year life span of the mission."185 We then added noise as a [function of apparent magnitude. where the distribution of magnitudes was drawn from the Sloan Digital Skv Survey (8D$5) luminosity function.," We then added noise as a function of apparent magnitude, where the distribution of magnitudes was drawn from the Sloan Digital Sky Survey (SDSS) luminosity function."186 The light curves were then passed to a standaid period finder to determine the ephenmerides. and phased light curves were processed by our neural network-based engine.ebai. (o automatically estimate principal parameters of the svstems.," The light curves were then passed to a standard period finder to determine the ephemerides, and phased light curves were processed by our neural network-based engine, to automatically estimate principal parameters of the systems."187 Finally. we compared these estimated parameters with the ones actually used to create the sample. which provided us with the LSST ellicieney metric for," Finally, we compared these estimated parameters with the ones actually used to create the sample, which provided us with the LSST efficiency metric for"188data for both excitation aud ionization that have been conumnonlv used in nou-LTE caleulatious for Li up to now. agree reasonably with the modern data. ecnerally agreciue withiu a factor of 6. though with a few siguificaut outliers.,"data for both excitation and ionization that have been commonly used in non-LTE calculations for Li up to now, agree reasonably with the modern data, generally agreeing within a factor of 6, though with a few significant outliers."189 This suggests that the estimates of the uncertainties of a factor of 2 for these data are somewhat too low. though the data for the important 25-2p transition doces indeed agree within a factor a two.," This suggests that the estimates of the uncertainties of a factor of 2 for these data are somewhat too low, though the data for the important $2s$ $2p$ transition does indeed agree within a factor a two."190 We fud that these uucertaiuties are not very important when applied to Li Tin cool stars. aud the differences typically result iu unucertainties of less than 0.01 dex.," We find that these uncertainties are not very important when applied to Li I in cool stars, and the differences typically result in uncertainties of less than 0.01 dex."191 The strongest effects are found in FE cdawarts aud extremely Li-vich stars., The strongest effects are found in F dwarfs and extremely Li-rich stars.192 These uncertainties are certainly uceligible compared to those arising frou other sources. especially the atmospheric modelling (?)..," These uncertainties are certainly negligible compared to those arising from other sources, especially the atmospheric modelling \citep{2005ARA&A..43..481A}."193lines measured in the synthesized beam (~95 K).,lines measured in the synthesized beam $\sim$ 95 K).194 The latter corresponds to the surface temperature of the HMC. because the ground state llines are optically thick and. as discussed by BELOS. the temperature inside the HMC ts likely increasing.," The latter corresponds to the surface temperature of the HMC, because the ground state lines are optically thick and, as discussed by BEL05, the temperature inside the HMC is likely increasing."195 The mass obtained is affected by a large uncertainty mostly because of the poorly known dust properties: for example. BELO4 adopted an absorption coefficient of 0.02 em? e!. which would imply a HMC mass of only 420 M...," The mass obtained is affected by a large uncertainty mostly because of the poorly known dust properties: for example, BEL04 adopted an absorption coefficient of 0.02 $^2$ $^{-1}$, which would imply a HMC mass of only 420 $M_\odot$."196 In Fig., In Fig.197 13. we show the same position-velocity plot of the aand llines as in Fig. 12..," \ref{fpvfit} we show the same position-velocity plot of the and lines as in Fig. \ref{fpvmcnco},"198 this time overlaying the pattern outlining the region inside which emission is expected for a Keplerian rotating and free-falling disk., this time overlaying the pattern outlining the region inside which emission is expected for a Keplerian rotating and free-falling disk.199 The latter does not take into account the line-width nor the spectral and angular resolutions and has been obtained assuming that the gas velocity is the vector sum of a tangential component due to Keplerian rotation about a central mass. M. plus a radial component due to free- onto the same mass.," The latter does not take into account the line-width nor the spectral and angular resolutions and has been obtained assuming that the gas velocity is the vector sum of a tangential component due to Keplerian rotation about a central mass, $M$ plus a radial component due to free-fall onto the same mass."200 Under these assumptions the velocity component along the line of sight can be expressed as where x ΑΝ.and z are the coordinates. respectively. along the disk plane and the line of sight. and R=V2—Z is the distance from the center of the disk.," Under these assumptions the velocity component along the line of sight can be expressed as where $x$ and $z$ are the coordinates, respectively, along the disk plane and the line of sight, and $R=\sqrt{x^2+z^2}$ is the distance from the center of the disk."201" We also assume that R lies between the disk radius. R,. and a minimum inner radius. Αι."," We also assume that R lies between the disk radius, $R_{\rm o}$, and a minimum inner radius, $R_{\rm i}$."202 The first term on the right hand side of the equation is the component due to Keplerian rotation. the second that due to free fall.," The first term on the right hand side of the equation is the component due to Keplerian rotation, the second that due to free fall."203 The dashed pattern in Fig., The dashed pattern in Fig.204 12 has been obtained by plotting the maximum and minimum velocities V for z varying across the disk. ie. from JR;—8 and +Rz Απ. taking into account that the region R<R; is forbidden.," \ref{fpvmcnco}205 has been obtained by plotting the maximum and minimum velocities $V$ for $z$ varying across the disk, i.e. from $-\sqrt{R_{\rm o}^2-x^2}$ and $+\sqrt{R_{\rm o}^2-x^2}$ , taking into account that the region $R<R_{\rm i}$ is forbidden."206" In our case. a satisfactory fit is obtained for M=330Μ.. Ry=3"" (or 0.11 pc). and Rj=0715 (or 0.0055 pe)."," In our case, a satisfactory fit is obtained for $M=330~M_\odot$, $R_{\rm o}=3\arcsec$ (or 0.11 pc), and $R_{\rm i}=0\farcs15$ (or 0.0055 pc)."207" Note that the signature of (pseudo-)Keplerian rotation is the ""butterfly"" shape of the plot. determined by the two “spurs” of emission at about +3” aand +4 rrelative to the systemic velocity («96.5 ). plus the presence of high-velocity emission at zero (2009)). CH3OH Μ. (2007)) et al. (2011)."," Note that the signature of (pseudo-)Keplerian rotation is the “butterfly” shape of the plot, determined by the two “spurs” of emission at about $\pm$ and $\pm$ 4 relative to the systemic velocity $\sim$ 96.5 ), plus the presence of high-velocity emission at zero \cite{gira}) $_3$ $M_\odot$ \cite{ppv}) et al. \cite{bel11}) ),"208 these massive. large rotating cores are to be considered transient toroidal structures feeding a cluster of YSOs rather than stable circumstellar accretion disks.," these massive, large rotating cores are to be considered transient toroidal structures feeding a cluster of YSOs rather than stable circumstellar accretion disks."209 In fact. the latter are stabilized by the central star(s). whose mass is greater than that of the disk. whereas the former are dynamically dominated by the gas mass and hence are short-lived.," In fact, the latter are stabilized by the central star(s), whose mass is greater than that of the disk, whereas the former are dynamically dominated by the gas mass and hence are short-lived."210 Although this scenario may be true in most cases. G31.41 might represent an exception.," Although this scenario may be true in most cases, G31.41 might represent an exception."211 We speculate that this HMC could contain a large number of stars tightly packed in the central region., We speculate that this HMC could contain a large number of stars tightly packed in the central region.212 In this case the stars could have a stabilizing effect analogous to that of a single point-like object located at the HMC center. similar to the previously mentioned model by Bertin Lodato (1999)).," In this case the stars could have a stabilizing effect analogous to that of a single point-like object located at the HMC center, similar to the previously mentioned model by Bertin Lodato \cite{belo}) )."213 With all this in. mind. the pseudo-Keplerian pattern recognized in Fig.," With all this in mind, the pseudo-Keplerian pattern recognized in Fig."214 13. suggests that the HMC mass should be comparable to the total mass of the embedded stars that are tightly packed at the center., \ref{fpvfit} suggests that the HMC mass should be comparable to the total mass of the embedded stars that are tightly packed at the center.215 Is this scenario plausible?, Is this scenario plausible?216 Indeed. in the case of G10.62-0.38. a massive star forming region with a luminosity of 9.2x10?L... Sollins et al. (2005))," Indeed, in the case of G10.62–0.38, a massive star forming region with a luminosity of $9.2\times10^5~L_\odot$, Sollins et al. \cite{sollins}) )"217 suggest that within a radius of 0.03 pc. several O stars with a total mass of 175 hhave formed at the center of a flattened disk.," suggest that within a radius of 0.03 pc, several O stars with a total mass of 175 have formed at the center of a flattened disk."218 In our case. the existence of (at least) two high-mass YSOs close to the HMC center andseparated (in projection) by only07119or 1480 AU has been provedbyCesaroniet al. (2010)).," In our case, the existence of (at least) two high-mass YSOs close to the HMC center andseparated (in projection) by only19or 1480 AU has been provedbyCesaroniet al. \cite{cesa10}) ),"219who detected the,who detected the220The main purpose of this paper ids to demonstrate that theories predicting a definite statistical equilibrium. dependent only on the energy and the initial volume τη) at phase-space densities in the range η5|diy. do not predict the same final state when the system undergoes two violent relaxation sessions separated. in time. as they do when the two sessions are treated as onc.,"The main purpose of this paper is to demonstrate that theories predicting a definite statistical equilibrium, dependent only on the energy and the initial volume $\tau(\eta)d\eta$ at phase-space densities in the range $\eta\to \eta+d\eta$, do not predict the same final state when the system undergoes two violent relaxation sessions separated in time, as they do when the two sessions are treated as one."221 This may be called an inconsistency or at best a lack of transitivity., This may be called an inconsistency or at best a lack of transitivity.222 Consider an N-body eravitating system that starts in some state far [rom equilibrium. vibrates violently and settles to a dynamically steady. state 5; that lasts long enough that it may be considered the final product of violent relaxation with energv £1.," Consider an $N$ -body gravitating system that starts in some state far from equilibrium, vibrates violently and settles to a dynamically steady state $s_1$ that lasts long enough that it may be considered the final product of violent relaxation with energy $E_1$."223 Now suppose that this system sullers a significant tidal disturbance from a passing object that causes violent vibrations and leaves out the svstem to relax again but now with energv A»., Now suppose that this system suffers a significant tidal disturbance from a passing object that causes violent vibrations and leaves out the system to relax again but now with energy $E_2$.224 There are now two wavs of predicting the outcome., There are now two ways of predicting the outcome.225 Either we take the function Tol) giving the volume at cach phase-space density. [rom he initial state sy. or we use τι) the predicted outcome or that function after the first relaxation process.," Either we take the function $\tau_0(\eta)$ giving the volume at each phase-space density from the initial state $s_0$, or we use $\tau_1(\eta)$ the predicted outcome for that function after the first relaxation process."226" Of course if we used the fine grained phase-space density both would oe the same. but by hypothesis the system lasted so long in state 8; that is at ""equilibrium"". and only the coarse-grained density can any longer be relevant to the dynamics of the inal relaxation."," Of course if we used the fine grained phase-space density both would be the same, but by hypothesis the system lasted so long in state $s_1$ that is at “equilibrium”, and only the coarse-grained density can any longer be relevant to the dynamics of the final relaxation."227 We show that the outcomes predicted with energy {ο and volume functions 70())) and τι(7p) are certainly diferent in the Lvaden-Dell theory of violent. relaxation (Lynden-Bell1967)... as well as in a more recent theory »v Nakamura (Nakamura2000).," We show that the outcomes predicted with energy $E_2$ and volume functions $\tau_0(\eta)$ and $\tau_1(\eta)$ are certainly different in the Lynden-Bell theory of violent relaxation \citep{ref:Lyn67}, as well as in a more recent theory by Nakamura \citep{ref:Nak00}."228 This paper is organised as follows: in we give a short overview of some of the cdilliculties in the theory of violent relaxation. which we feel complement the main subject of this paper.," This paper is organised as follows: in we give a short overview of some of the difficulties in the theory of violent relaxation, which we feel complement the main subject of this paper."229 Then in we demonstrate the non-transitivitv of the Lynden-Dell theory of violent relaxation. using the thought experiment that was presented above.," Then in we demonstrate the non-transitivity of the Lynden-Bell theory of violent relaxation, using the thought experiment that was presented above."230 In we give a brief description of Nakamuras theory which is based on the information-theory approach., In we give a brief description of Nakamura's theory which is based on the information-theory approach.231 We re-derive his theory using a combinatorial approach that enables us to compare it to. Lynden-DBell's theory., We re-derive his theory using a combinatorial approach that enables us to compare it to Lynden-Bell's theory.232 Then in we demonstrate that also Nakamuras theory is non-transitive. using the thought experiment once again.," Then in we demonstrate that also Nakamura's theory is non-transitive, using the thought experiment once again."233 In we present our conclusions., In we present our conclusions.234 In this section we olfer a short. discussion of other woblems connected: with the process of violent-relaxation and ‘theories’ that aim to predict its outcome., In this section we offer a short discussion of other problems connected with the process of violent-relaxation and `theories' that aim to predict its outcome.235 Let us start rom [first principles., Let us start from first principles.236 Most. large IN-body. systems. governed w long-range forces which are not initially in balance will oscillate with decreasing amplitude before they. settle into a state in which the potential of the long range force xconmies almost steady., Most large $N$ -body systems governed by long-range forces which are not initially in balance will oscillate with decreasing amplitude before they settle into a state in which the potential of the long range force becomes almost steady.237 Such violentrelaxation processes are known to occur in gravitational N-body systems., Such violent-relaxation processes are known to occur in gravitational $N$ -body systems.238 Phereafter evolution may continue due to the shorter range interaction in which the graininess of the individual particles is. of importance. but there is a large class of systems in. which this secondary evolution is on a much longer timescale.," Thereafter evolution may continue due to the shorter range interaction in which the graininess of the individual particles is of importance, but there is a large class of systems in which this secondary evolution is on a much longer timescale."239 Violent relaxation under gravity does not last long., Violent relaxation under gravity does not last long.240 Alter a few oscillations on the timescale (C/p) it is over., After a few oscillations on the timescale $(G\bar{\rho})^{-1/2}$ it is over.241 Thus the whole idea that the interaction of the particles with the mean field. will [ος to some unique detailed. statistical, Thus the whole idea that the interaction of the particles with the mean field will lead to some unique detailed statistical242as ELGs.,as ELGs.243 As the ratio of stars to galaxies decreases with increasing magnitude ?).. (he number of contaminating stars do not dominate the candidate selection ab [nt magnitudes.," As the ratio of stars to galaxies decreases with increasing magnitude \citep[see, for example,244][]{2003MNRAS.343.1013K}, the number of contaminating stars do not dominate the candidate selection at faint magnitudes."245 In anv case. particular care has (ο be taken in (he design or election of the filler set in order (o avoid this source of contamination.," In any case, particular care has to be taken in the design or election of the filter set in order to avoid this source of contamination."246 some (vpes of stellar objects show emission lines in (he wavelength interval where the fillers are defimed., Some types of stellar objects show emission lines in the wavelength interval where the filters are defined.247 Novae. svanbiotie stars. cataclysmic variables (in general. low mass stars with either coronal activity or binaries) can show emission in the line Pad (9229 AJ).," Novae, symbiotic stars, cataclysmic variables (in general, low mass stars with either coronal activity or binaries) can show emission in the line Pa9 (9229 )."248 After a nova explosion there is emission in (he multiplet near 9261-9266 and the line in 8236A., After a nova explosion there is emission in the multiplet near 9261-9266 and the line in 8236.249. Lines of and between 8185 and 8242 (7?) can also be found., Lines of and between 8185 and 8242 \citep{2003ApJ...596.1229R} can also be found.250 Alassive stars. such as some Woll-Ravet. ean exhibit emission lines of Pa9 (9229 A)) and in (8236 A9) (2)..," Massive stars, such as some Wolf-Rayet, can exhibit emission lines of Pa9 (9229 ) and in (8236 ) \citep{2002A&A...392..653C}."251 The equivalent widths of the lines in the range covered by (he narrow-band filters is of the order of tens of Angstroms., The equivalent widths of the lines in the range covered by the narrow-band filters is of the order of tens of Angstroms.252 Although the relative frequency of appearance of these twpes ol stars is very low. thev can be also selected by their color excess.," Although the relative frequency of appearance of these types of stars is very low, they can be also selected by their color excess."253 Further analvsis is needed in other to classify the different objects selected by their narrow-band flix excess., Further analysis is needed in other to classify the different objects selected by their narrow-band flux excess.254 To separate the stars. we can apply morphological methods to the selected candidates.," To separate the stars, we can apply morphological methods to the selected candidates."255 A example of that approach appears in ?.., A example of that approach appears in \citet{2003A&A...410...17M}.256 An alternative. and commonly used. approximation is {ο make use of the artificial neural network of (he source-characterization program SIExtractor (?)..," An alternative, and commonly used, approximation is to make use of the artificial neural network of the source-characterization program SExtractor \citep{1996a&as..117..393b}."257 Nevertheless. (hese classification methods depend on the SNR and seeing of the images.," Nevertheless, these classification methods depend on the SNR and seeing of the images."258 ]t can be difficult to classify candidates morphologically when the overall SNR. is low or the seeing is nol optimal., It can be difficult to classify candidates morphologically when the overall SNR is low or the seeing is not optimal.259 Multicolor photometry can be also used to distinguish stus using a color criterion (we show a simple example in Sect. 4.3.1)), Multicolor photometry can be also used to distinguish stars using a color criterion (we show a simple example in Sect. \ref{sec:contpoli}) )260 Methods (ο classify extragalactic sources range [rom statistical corrections (7). to color-color criteria and photometric redshift determination., Methods to classify extragalactic sources range from statistical corrections \citep{2001ApJ...550..593J} to color-color criteria and photometric redshift determination.261 For example. ?. recomputed the statistical correction of ? to find that the estimated contamination from galaxies ad z>0.24 was negligible.," For example, \citet{2001A&A...379..798P} recomputed the statistical correction of \citet{2001ApJ...550..593J} to find that the estimated contamination from galaxies at $z > 0.24$ was negligible."262 (?) uses three photometric bands (2. Re and Je) and the GISSEL96 models (?) (o develop a color criterion that allow the authors (to select emitters at z—0.24.," \citep{2003ApJ...586L.115F} uses three photometric bands $B$, $R_C$ and $I_C$ ) and the GISSEL96 models \citep{2003MNRAS.344.1000B} to develop a color criterion that allow the authors to select emitters at $z$ =0.24."263 Following, Following264Intermediate polars (IPs) belong to the class of systems known as cataclysmic variables (CVs).,Intermediate polars (IPs) belong to the class of systems known as cataclysmic variables (CVs).265 They occupy the phase space. in terms of magnetic field strength. between the polars and the non-magnetic CVs.," They occupy the phase space, in terms of magnetic field strength, between the polars and the non-magnetic CVs."266 This intermediate strength magnetic field alters the accretion flow from the main sequence donor star to the white dwarf (WD)., This intermediate strength magnetic field alters the accretion flow from the main sequence donor star to the white dwarf (WD).267 Eventually. most of the accreting material is channelled to accretion curtains above the WD magnetic poles.," Eventually, most of the accreting material is channelled to accretion curtains above the WD magnetic poles."268 The temperature and density of this region causes the emission of bremsstrahlung radiation. which varies at the spin period of the WD.," The temperature and density of this region causes the emission of bremsstrahlung radiation, which varies at the spin period of the WD."269 It is this variation that most consider to be the defining characteristics of IPs., It is this variation that most consider to be the defining characteristics of IPs.270 For a review of IPs see e.g. ?.., For a review of IPs see e.g. \citet{warner95}.271 There are at least 30 confirmed IPs!.. ?.. however. have recently pointed out that the commonly used criteria to certify CVs as IPs may be too restrictive.," There are at least 30 confirmed \citet{ramsay08}, however, have recently pointed out that the commonly used criteria to certify CVs as IPs may be too restrictive."272 [t is possible that many of the 84 INTEGRAL//IBIS survey (??)..," It is possible that many of the 84 /IBIS survey \citep{barlow06,bird07}."273 With this in mind we have embarked on a campaign to observe some hard X-ray sources and determine their credentials as potential IPs., With this in mind we have embarked on a campaign to observe some hard X-ray sources and determine their credentials as potential IPs.274 In the first paper in this campaign. was confirmed as an IP (?)..," In the first paper in this campaign, was confirmed as an IP \citep{butters07}."275 Here the results of pointed observations of (hereafter J0056). (hereafter J1719) and (hereafter J1227) are presented.," Here the results of pointed observations of (hereafter J0056), (hereafter J1719) and (hereafter J1227) are presented."276 J0056 was associated with theROSAT source143.. and catalogued as an unidentified object in the RXTE all sky survey (?)..," J0056 was associated with the source, and catalogued as an unidentified object in the all sky survey \citep{revnivtsev04}."277 It was found to have a count rate of 0.7140.04 ct s! PCU! in the 3-8 keV energy band and a photon index of 1.7740.23., It was found to have a count rate of $\pm$ 0.04 ct $^{-1}$ $^{-1}$ in the 3–8 keV energy band and a photon index of $\pm$ 0.23.278 Analysis by ὁ using SWIFT/XRT archive data revealed two X-ray sources in theROSAT error circle., Analysis by \citet{bikmaev06} using /XRT archive data revealed two X-ray sources in the error circle.279 One source was present at low energy. which they presumed to be a chromospherically active star.," One source was present at low energy, which they presumed to be a chromospherically active star."280 The other source showed a typical spectrum of a CV. with an emission feature close to 6.7 keV. ὁ also carried out optical observations with the 1.5 m Russian-Turkish Telescope.," The other source showed a typical spectrum of a CV, with an emission feature close to 6.7 keV. \citet{bikmaev06} also carried out optical observations with the 1.5 m Russian-Turkish Telescope."281 Their photometric data indicated a period of approximately 480 s to be present., Their photometric data indicated a period of approximately 480 s to be present.282 J1719 was detected as an object by ?.. ? found radio galaxies coincident with its error circle and suggested it was extragalactic.," J1719 was detected as an object by \citet{bird04}, \citet{pandey06} found radio galaxies coincident with its error circle and suggested it was extragalactic."283 ? confirmed a tentative association of J1719 with the softer X-ray target using pointed data.," \citet{tomsick06}284 confirmed a tentative association of J1719 with the softer X-ray target using pointed data."285 They also reported variability of JI719 in the 0.3-10 keV band and a flux of 2.555107! eres em7? s7!., They also reported variability of J1719 in the 0.3–10 keV band and a flux of $2.5^{+0.9}_{-0.4}\times10^{-11}$ ergs $^{-2}$ $^{-1}$.286 In calculating this flux they used à power law model and a galactic column density of 0.77x107 em (derived from ?))., In calculating this flux they used a power law model and a galactic column density of $\times10^{22}$ $^{-2}$ (derived from \citet{dickey90}) ).287 ? also reported the spectral properties of J1719 using public data. finding a flux of 107! eres em7? s! in the 20-50 keV energy band.," \citet{tomsick06} also reported the spectral properties of J1719 using public data, finding a flux of $1.9\times10^{-11}$ ergs $^{-2}$ $^{-1}$ in the 20–50 keV energy band."288 ? classifiedJ1719 as a CV based upon its optical spectrum. they also speculated that it may be an IP.," \citet{masetti06}289 classifiedJ1719 as a CV based upon its optical spectrum, they also speculated that it may be an IP."290 J1227 was found in theRXTE all sky survey (?).., J1227 was found in the all sky survey \citep{revnivtsev04}.291 It was classified as a CV and suggested to be an IP by ?.. using optical spectroscopy.," It was classified as a CV and suggested to be an IP by \citet{masetti06}, using optical spectroscopy."292 ? later found J1227 to be an source.," \citet{bird07}293 later found J1227 to be an source."294 Data were obtained from theRXTE satellite (2) with the PCA instrument., Data were obtained from the satellite \citep{bradt93} with the PCA instrument.295In each casemitial data reduction was done with the standard rroors. and the flux was normalised according to,"In each caseinitial data reduction was done with the standard , and the flux was normalised according to"296nunerical results are presented in 833.,numerical results are presented in 3.297 The paper concludes with a summary and cliscussion in SL., The paper concludes with a summary and discussion in 4.298 We consider a magnetized hot Jupiter revolving in a circular orbit on Che equatorial plane of ils parent star., We consider a magnetized hot Jupiter revolving in a circular orbit on the equatorial plane of its parent star.299 As the planet orbits through the open flux tubes emanating [rom the stellar surface. magnetic reconnections occur and generate plasma jets propagating inwards along the flux tubes to the parent star.," As the planet orbits through the open flux tubes emanating from the stellar surface, magnetic reconnections occur and generate plasma jets propagating inwards along the flux tubes to the parent star."300 In the following subsections. we shall describe the model of electron-beam injection aud the stellar atmosphere associated with the flux tube.," In the following subsections, we shall describe the model of electron-beam injection and the stellar atmosphere associated with the flux tube."301 since IID 179949 has been the canonical planetary system highlighted by most previous studies for magnetic interactions. we adopt (the parameters of IID 179949 as an illustrative exanple For our main study.," Since HD 179949 has been the canonical planetary system highlighted by most previous studies for magnetic interactions, we adopt the parameters of HD 179949 as an illustrative example for our main study."302" In other words. we focus on a hot Jupiter orbiting at the radial distance r=7.82, around a central star of mass M,=1.21... radius R,=1.22R.. andelective temperature Zr=GIGS IX (Butlerοἱal. 2006)."," In other words, we focus on a hot Jupiter orbiting at the radial distance $r=7.8R_*$ around a central star of mass $M_*=1.21M_{\odot}$ , radius $R_*=1.22R_{\odot}$, andeffective temperature $T_{\rm eff}=6168$ K \citep{Butler}. ."303". In terms of AM, τν. and Tay. these stellar parameters are noticeably different [rom the solar values. although in (hie broad sense IID 179949 still constitutes a solar-tvpe star."," In terms of $M_*$, $R_*$, and $T_{\rm eff}$, these stellar parameters are noticeably different from the solar values, although in the broad sense HD 179949 still constitutes a solar-type star."304 The (vpical field strength at the plane orbit is 20.1—0.01 G. for the racial field strength ~1—10 G at the stellar surface (ie. Doxr 7).," The typical field strength at the plane orbit is $B\sim 0.1-0.01$ G, for the radial field strength $\sim 1-10$ G at the stellar surface (i.e. $B\propto r^{-2}$ )."305 At rsLOR.. the planet is located inside the Alfvénn radius of the star (see the next subsection) and therefore no Last AIUD shocks form as the stellar winds encounter the planets magnetosphere (c£.," At $r\approx30610R_{\odot}$, the planet is located inside the Alfvénn radius of the star (see the next subsection) and therefore no fast MHD shocks form as the stellar winds encounter the planet's magnetosphere (cf."307 Zarka 2001: Ip et al., Zarka 2001; Ip et al.308 2004: Preussue et al., 2004; Preussue et al.309 2005)., 2005).310" Assuming a dipole field for the planet's magnetic field. we can estimate the radius of the magnetopause 75,5 at which the stellar and the planet's fields are balanced: where DB, and D, are the average surface fields of the planet and the parent star respectively, £2, is the radius of Jupiter. ancl @ is thesemi-major axis."," Assuming a dipole field for the planet's magnetic field, we can estimate the radius of the magnetopause $R_{mp}$ at which the stellar and the planet's fields are balanced: where $B_p$ and $B_*$ are the average surface fields of the planet and the parent star respectively, $R_J$ is the radius of Jupiter, and $a$ is thesemi-major axis."311" As can be clearly seen from the above equation. Ry,<<a— 10R.."," As can be clearly seen from the above equation, $R_{mp}<<a=10R_{\odot}$ ."312" Therefore the magnetic field strengthD, al (hemagnetopause is almost equal to the stellar field strength at r= az ie.D, 0.1—0.01G."," Therefore the magnetic field strength$B_{mp}$ at themagnetopause is almost equal to the stellar field strength at $r=a$ ; i.e.,$B_{mp}\sim 0.1-0.01 G$ ."313"effective at heating gas, and indeed it is.","effective at heating gas, and indeed it is."314 Figure 3 shows the temperature distribution of all gas in the halo A box at z—3.2 the epoch of peak star and the present., Figure \ref{fig:gasall} shows the temperature distribution of all gas in the halo A box at $z=3.2$ (during the epoch of peak star formation) and the present.315" At (duringz—3.2, the No BH model has the formation)coldest gas, with a mean temperature of 6.4x104 K. Adding BH thermal feedback heats the gas 1196 to 7.1x10* K, and adding an X-ray background heats it more to 8.8x10* K. However the two BHX models are more effective by another9%,, giving a mean gas temperature of roughly 9.6x104 K. At 2=0, the effect of feedback X-rays is more pronounced compared to a background: BHX and BHXRP, at a mean temperature of 3x10° K, are hotter than BH+X, which in turn is only hotter than BH and No BH."," At $z=3.2$, the No BH model has the coldest gas, with a mean temperature of $6.4\times10^4$ K. Adding BH thermal feedback heats the gas $11\%$ to $7.1\times10^4$ K, and adding an X-ray background heats it more to $8.8\times10^4$ K. However the two BHX models are more effective by another, giving a mean gas temperature of roughly $9.6\times10^4$ K. At $z=0$, the effect of feedback X-rays is more pronounced compared to a background: BHX and BHXRP, at a mean temperature of $3\times10^5$ K, are hotter than BH+X, which in turn is only hotter than BH and No BH."316" Figure 4 is the same as Figure 3,, except that it shows only virialized gas: gas with a density more than 200 times the mean baryon density."," Figure \ref{fig:gasvir} is the same as Figure \ref{fig:gasall}, except that it shows only virialized gas: gas with a density more than 200 times the mean baryon density."317" Here the effect of the AGN feedback X-rays is more pronounced, as we would expect, since most of the virialized gas is near the central galaxy, where the AGN X-rays are strongest."," Here the effect of the AGN feedback X-rays is more pronounced, as we would expect, since most of the virialized gas is near the central galaxy, where the AGN X-rays are strongest."318" At z=3.2, the three models without X-ray feedback are all within 10% of each other in mean temperature at roughly 9x104 K, while BHX and BHXRP have mean temperatures of 1.6x10° K and 1.3x10? K respectively, higher than the other models."," At $z=3.2$, the three models without X-ray feedback are all within $10\%$ of each other in mean temperature at roughly $9\times31910^4$ K, while BHX and BHXRP have mean temperatures of $1.6\times32010^5$ K and $1.3\times 10^5$ K respectively, higher than the other models."321 At z—0 the picture is even more extreme., At $z=0$ the picture is even more extreme.322" BHX and BHXRP have 2.4x1019 and 3.0x1019M, respectively, of virial X-ray gas >10°-°M. K, more than 4 times the amount that BH+X has, and 6 times the amount of the other models."," BHX and BHXRP have $2.4\times 10^{10} M_\odot$ and $3.0\times 10^{10}323M_\odot$ , respectively, of virial X-ray gas $> 10^{5.5}$ K, more than 4 times the amount that BH+X has, and 6 times the amount of the other models."324" Unlike the Warm-Hot Intergalactic Medium (WHIM), which is usually defined as p<100p;2010),, this gas is dense enough to emit significant soft X-rays."," Unlike the Warm-Hot Intergalactic Medium (WHIM), which is usually defined as $\rho < 100 325\bar{\rho}_b$, this gas is dense enough to emit significant soft X-rays."326" We estimate the (Bremsstrahlung) X-ray luminosities of the various models via for gas above 2x106 K over the virial volume (a 500 kpc radius), and find that all models have logLx£z38—39.5, consistent with the gas luminosities found by for 30 early-type galaxies of similar size."," We estimate the (Bremsstrahlung) X-ray luminosities of the various models via for gas above $2\times 10^6$ K over the virial volume (a 500 kpc radius), and find that all models have $\log L_X 327\approx 38 - 39.5$, consistent with the gas luminosities found by for 30 early-type galaxies of similar size."328" The differences between BH models is modest: averaged over the three ICs, the BH+X, BHX and BHXRP models have increased luminosity by factors of 1.6, 2, and 3, respectively, compared with the models without X-rays."," The differences between BH models is modest: averaged over the three ICs, the BH+X, BHX and BHXRP models have increased luminosity by factors of 1.6, 2, and 3, respectively, compared with the models without X-rays."329" Adding BH feedback also increases the X-ray effective radius: only of the total X-ray luminosity for No BH comes from outside the central 10 kpc, while does for BH and BH+X, for BHXRP and for BHX (again averaging the 3 ICs)."," Adding BH feedback also increases the X-ray effective radius: only of the total X-ray luminosity for No BH comes from outside the central 10 kpc, while does for BH and BH+X, for BHXRP and for BHX (again averaging the 3 ICs)."330 We naturally expect the hotter gas produced by the AGN X-ray feedback to reduce the production of stars., We naturally expect the hotter gas produced by the AGN X-ray feedback to reduce the production of stars.331" The upper panel of Figure ὅ shows the star-formation rate (SFR) over time for galaxy A, out to a radius of 30 kpc."," The upper panel of Figure \ref{fig:sfr-gal-A100} shows the star-formation rate (SFR) over time for galaxy A, out to a radius of 30 kpc."332" We see only modest differences in the initial star- peak below), but BH+X and BHXRP are both effective at (seesuppressing late star formation: BHXRP has a lower SFR than the other models by 0.5 dex for"," We see only modest differences in the initial star-formation peak (see below), but BH+X and BHXRP are both effective at suppressing late star formation: BHXRP has a lower SFR than the other models by 0.5 dex for"333The agreement of our model with the stellar mass functions up to z¥1.5 and with the K-band luminosity functions and counts up to the z&2 is unchanged with respect to Menci et al. (,The agreement of our model with the stellar mass functions up to $z\approx 1.5$ and with the K-band luminosity functions and counts up to the $z\approx 2$ is unchanged with respect to Menci et al. (3342004).,2004).335" Here we present the color distributions of galaxies resulting from our model, and compare them with the most distinctive observational results; these concern the dependence of the local color distributions on the galaxy luminosity and on the environment, and the persistence of the bimodal shape at higher z."," Here we present the color distributions of galaxies resulting from our model, and compare them with the most distinctive observational results; these concern the dependence of the local color distributions on the galaxy luminosity and on the environment, and the persistence of the bimodal shape at higher $z$."336" As for the former, we compare in fig."," As for the former, we compare in fig."337" 2 the color distribution resulting from our model for different luminosity bins with the Gaussian fit to the observational points from the sloan survey (SDSS), given in Baldry et al. ("," 2 the color distribution resulting from our model for different luminosity bins with the Gaussian fit to the observational points from the sloan survey (SDSS), given in Baldry et al. ("3382004) for the u—r colors; details on the SDSS wu and r bands are given by the above authors.,2004) for the $u-r$ colors; details on the SDSS $u$ and $r$ bands are given by the above authors.339" We show our results for three kinds of dust extiction laws (SMC, Galaxy, and Calzetti 1997); the corresponding color distributions are almost identical."," We show our results for three kinds of dust extiction laws (SMC, Galaxy, and Calzetti 1997); the corresponding color distributions are almost identical."340" 'The plot shows that hierarchical galaxy formation may indeed produce a bimodal color distribution, with the fraction"," The plot shows that hierarchical galaxy formation may indeed produce a bimodal color distribution, with the fraction"341"Also displayed in Table 4 are the projected masses computed by aperture densitometry from Eq. 10,,","Also displayed in Table \ref{tab:nfw} are the projected masses computed by aperture densitometry from Eq. \ref{eq:apmass},"342" at a distance from the cluster center r= ryir, and 0?=900"", 65=1000""."," at a distance from the cluster center $r=r_{\rm vir}$ , and $\theta_2=900\arcsec$, $\theta_{\rm out}=1000\arcsec$."343" A good agreement is found between these masses and the values computed from parametric fits, if we take into account the expected ratio Mop/M3p=1.34 (see Sect. 4.2))."," A good agreement is found between these masses and the values computed from parametric fits, if we take into account the expected ratio $M_{\rm 2D}/M_{\rm 3D} = 1.34$ (see Sect. \ref{sec:simulations}) )."344" From the catalog based on photometric redshifts selection (case d), we finallyderived the introduced by ?,, that is: 5=May/om,,, where The map was XXEobtained by defining a grid of points along the image; the tangential components e;; of the lensed galaxy ellipticities were computedtaking as center each point in such grid."," From the catalog based on photometric redshifts selection (case ), we finallyderived the introduced by \citet{aa...420...75s}, that is: $S=M_{\rm ap}/\sigma_{M_{\rm ap}}$, where The map was obtained by defining a grid of points along the image; the tangential components $e_{t,i}$ of the lensed galaxy ellipticities were computedtaking as center each point in such grid."345" The weight w; was defined in Eq. 7,,"," The weight $w_i$ was defined in Eq. \ref{eq:well},"346 and Q is a Gaussian function as in ?:: where 6 and 6; are the center and size of the aperture arcmin)., and $Q$ is a Gaussian function as in \citet{Radovich08}: where $\theta_0$ and $\theta_s$ are the center and size of the aperture $\theta_s \sim 1.5$ arcmin).347" The S-map is displayed in Fig. 10,,"," The S-map is displayed in Fig. \ref{fig:massdist},"348 showing a quite circular mass distribution centered on the BCG., showing a quite circular mass distribution centered on the BCG.349" Several mass measurements of this cluster are available in literature, based on different data and/or methods."," Several mass measurements of this cluster are available in literature, based on different data and/or methods."350" ? used Chandra data and modeled the dark matter halo by a generalized NFW profile, obtaining a mass value My=9.16*}88x10Mg and a concentration value cuc=5.087058, A weak lensing analysis of Abell 383 was done by using CFH12K data in the B, R, I filters."," \citet{Schmidt07} used Chandra data and modeled the dark matter halo by a generalized NFW profile, obtaining a mass value $M_{\rm vir}=9.16^{+1.89}_{-1.85} \times 10^{14} M_\odot$ and a concentration value $c_{\rm vir}=5.08^{+0.55}_{-1.03}$ A weak lensing analysis of Abell 383 was done by \citet{Bardeau07} using CFH12K data in the$B$ , $R$ , $I$ filters."351 For the shape measurements they used a Bayesian method implemented into the IM2SHAPE software., For the shape measurements they used a Bayesian method implemented into the IM2SHAPE software.352 To retrieve the weak lensing, To retrieve the weak lensing353data onto that grid and then locating the densest. cells.,data onto that grid and then locating the densest cells.354 Refinement can be built onto the grid to obtain improve resolution and to increase the speed of the code., Refinement can be built onto the grid to obtain improved resolution and to increase the speed of the code.355 The density peaks that are located on the grid. can then be used. as the seeds for potential structures., The density peaks that are located on the grid can then be used as the seeds for potential structures.356 This technique was usec by. for example. (snollmann&Ixnebe2009)— aux (Planelles&Quilis2010).," This technique was used by, for example, \citep{Knollmann09} and \citep{Planelles10}."357. The variations between these codes comes in the definition. of haloes., The variations between these codes comes in the definition of haloes.358 uses isodensity contours on the grid. while uses spherica overcdensities.," uses isodensity contours on the grid, while uses spherical overdensities."359 Fok and grid based methods are the two main ways for locating structure. but there are alternatives.," FoF and grid based methods are the two main ways for locating structure, but there are alternatives."360 More recen finders. such as (Maciejewskietal.2009).. have tried using phase space to identify subhaloes.," More recent finders, such as \citep{Maciejewski09}, have tried using phase space to identify subhaloes."361 This extends the search based. on. position ancl density το incorporate. the velocity. of the particles., This extends the search based on position and density to incorporate the velocity of the particles.362 Bulk velocities can then also be used to help identify structures., Bulk velocities can then also be used to help identify structures.363 Other finders that have tried dillerent techniques include (Nevrinck.Cinedin&LHlamilton 2005).. which replaced the uniform grid with a Voronoi diagram. and Clormen.Moscardini&Yoshida2004:Ciocolictal. 2010).. which uses knowledge of the structures from one snapshot to help find structure in the next.," Other finders that have tried different techniques include \citep{Neyrinck05}, which replaced the uniform grid with a Voronoi diagram, and \citep{Tormen04, Giocoli10}, which uses knowledge of the structures from one snapshot to help find structure in the next."364 While this summary of halo finders is by no means exhaustive. it does give a Πάνο for the dillerent techniques emploved.," While this summary of halo finders is by no means exhaustive, it does give a flavour for the different techniques employed."365 A thorough review of the cillerent. types of halo linders available and their. ellectiveness will be found. in Ixnebe et al. (, A thorough review of the different types of halo finders available and their effectiveness will be found in Knebe et al. (366in preparation).,in preparation).367 The importance of accurate subhalo detection. has increased in recent vears with the advances in high resolution simulations., The importance of accurate subhalo detection has increased in recent years with the advances in high resolution simulations.368 Various simulations of Milky Way sized haloes rave been produced including (Diemand.Ixublen&Macau2007:Diemandctal. 2008)... (Springeletal.2008) ancl (Stadeletal.2009).," Various simulations of Milky Way sized haloes have been produced including \citep{Diemand07, Diemand08}, \citep{Springel08} and \citep{Stadel09}."369.. As expected. hese haloes contain a wealth of substructure (seeCaoetal. 2004).," As expected, these haloes contain a wealth of substructure \citep[see][]{Gao04}."370. Llowever. it is important to ask how robust the recovered properties of subhaloes are to the choice of subhalo inder.," However, it is important to ask how robust the recovered properties of subhaloes are to the choice of subhalo finder."371 For example. subhaloes are identified: initially as overdensitios in their host haloes.," For example, subhaloes are identified initially as overdensities in their host haloes."372 We expect picking out such overdensities to be more dillicult in the innermost ruts of the host haloes where the background: density is he greatest., We expect picking out such overdensities to be more difficult in the innermost parts of the host haloes where the background density is the greatest.373 H£ one halo finder is less able to pick out these overdensities than another halo finder. we would expect this ialo finder to systematically uncerprecdict the numbers of subhaloes in the inner parts of haloes. which. would have important implications for how we interpret the results of. or example. the racial distribution of subhaloes and subhalo niass loss.," If one halo finder is less able to pick out these overdensities than another halo finder, we would expect this halo finder to systematically underpredict the numbers of subhaloes in the inner parts of haloes, which would have important implications for how we interpret the results of, for example, the radial distribution of subhaloes and subhalo mass loss."374 In this paper we set out to quantify the extent to which our choice of halo finder impacts on the radial distribution of subhaloes that we recover., In this paper we set out to quantify the extent to which our choice of halo finder impacts on the radial distribution of subhaloes that we recover.375 Specifically we focus on (Springeletal.2001). and (Ixnollmann&Ixnebe2009) and ask how well these halo finders can recover the properties of a NEW. subhalo (Navarro.Frenk&White1997) embedded in a more massive host NEW halo., Specifically we focus on \citep{Springel01} and \citep{Knollmann09} and ask how well these halo finders can recover the properties of a NFW subhalo \citep{Navarro97} embedded in a more massive host NFW halo.376 The advantage of this approach is that. unlike using haloes and subhaloes cliawn from cosmological simulations. we know exactly which particles belong to the host and to the subhalo at initial time and we can track their positions and velocities at all subsequent times.," The advantage of this approach is that, unlike using haloes and subhaloes drawn from cosmological simulations, we know exactly which particles belong to the host and to the subhalo at initial time and we can track their positions and velocities at all subsequent times."377 This provides a clean test of the halo finders because any discrepancies found. can be identified easily., This provides a clean test of the halo finders because any discrepancies found can be identified easily.378 The rest of this paper is setout as follows., The rest of this paper is setout as follows.379" In we outline the methods used. including summaries of the halo finders and the process of constructing a niock 6D (Gr. g. ον 6, ry. 02) NEW halo by reproducing the density and velocity. profiles."," In we outline the methods used, including summaries of the halo finders and the process of constructing a mock 6D $x$, $y$, $z$, $v_{x}$, $v_{y}$, $v_{z}$ ) NFW halo by reproducing the density and velocity profiles."380 We then use this construction. in& refmocoel.. to model an infalling subhalo.," We then use this construction, in \\ref{model}, to model an infalling subhalo."381 Vhis is undertaken in two wavs. first by considering how well the halo finders recover the subhalo when simply placed at dilferent. raclii within the main halo.," This is undertaken in two ways, first by considering how well the halo finders recover the subhalo when simply placed at different radii within the main halo."382 “Phe second method is to let. the subhalo fall into the main halo under gravity ancl compare how the different halo finders recover the subhalo., The second method is to let the subhalo fall into the main halo under gravity and compare how the different halo finders recover the subhalo.383 Having established the accuracy of the halo finders. in refstrip we investigate the effect. the trajectory of the subhalo has on stripping as it passes through the halo.," Having established the accuracy of the halo finders, in \\ref{strip} we investigate the effect the trajectory of the subhalo has on stripping as it passes through the halo."384 In we test the reliability of recovering the peak in the circular. velocity. profile., In \\ref{circ} we test the reliability of recovering the peak in the circular velocity profile.385 Finally we sunimarise our results., Finally we summarise our results.386 VPhroughout this work. a standard AC DAL cosmology has been adopted. taking O4=0.3. O4=0.7 and fh=0.73. where appropriate. consistent with observations [rom first vear results (Spergeletal.2003).," Throughout this work, a standard $\Lambda$ CDM cosmology has been adopted, taking $\Omega_{0}=0.3$, $\Omega_{\Lambda}=0.7$ and $h=0.73$, where appropriate, consistent with observations from first year results \citep{Spergel03}."387. For the purpose of this work we focus on two halo finclers that rely on cülferent methods to detect haloes and subhalocs., For the purpose of this work we focus on two halo finders that rely on different methods to detect haloes and subhaloes.388 (Ixnollmann&Ixnebe2009) is an updated version of (GillIxnebe&Gibson2004) and works using an adaptive mesh refinement. method., \citep{Knollmann09} is an updated version of \citep{Gill04} and works using an adaptive mesh refinement method.389 Lt begins by placing a user-defined grid across the box and caleulates the particle density in each cell., It begins by placing a user-defined grid across the box and calculates the particle density in each cell.390 Η this is greater than a user-specified: value. then the cell is refined. with a smaller eric.," If this is greater than a user-specified value, then the cell is refined with a smaller grid."391 The particle density is then recaleulated on this finer eric and. if required. further refinement is carried out.," The particle density is then recalculated on this finer grid and, if required, further refinement is carried out."392 Once al the refinements are carried. out. a hierarchical erid tree of the density distribution has been produced and this can be used to find structure.," Once all the refinements are carried out, a hierarchical grid tree of the density distribution has been produced and this can be used to find structure."393 Throughout this work. we used a gri of 128 cells with refinement being carried out in cells tha contain more than 3 particles.," Throughout this work, we used a grid of 128 cells with refinement being carried out in cells that contain more than 3 particles."394 The most refined and isolated cells are used as potentia alo centres and these are linked to the coarser grids to builc he structure., The most refined and isolated cells are used as potential halo centres and these are linked to the coarser grids to build the structure.395 LE two isolated centres join up on à coarser eric hen these are combined into one structure., If two isolated centres join up on a coarser grid then these are combined into one structure.396 By considering hese separate. isolated points in one structure. substructure can be defined.," By considering these separate, isolated points in one structure, substructure can be defined."397 Once the structures are identified. starting on the lowest level of substructure. they are tested. for roundness in isolation.," Once the structures are identified, starting on the lowest level of substructure, they are tested for boundness in isolation."398 This is conducted by comparing the xuwticles velocity to the local escape velocity obtained. using a spherical potential approximation., This is conducted by comparing the particles velocity to the local escape velocity obtained using a spherical potential approximation.399 Hf. a. particle is found o be unbound it is assigned to the next highest. level of structure until it is dispensed with if not bound to the halo., If a particle is found to be unbound it is assigned to the next highest level of structure until it is dispensed with if not bound to the halo.400 The haloes are then truncated at the virial radius (see refmock)) to define their size., The haloes are then truncated at the virial radius (see \\ref{mock}) ) to define their size.401 For the subhaloes. not all have," For the subhaloes, not all have"402and estimated the values for the cosmological parameter A.,and estimated the values for the cosmological parameter $\Lambda$.403 In a similar line of thinking Iorio(200Sa.b) attempted to investigate secular increase of the Astronomical Unit. perihelion precessions and planetary motions as tests of the Dvali-Gabadadze-Porrati multidimensional braneworld scenario.," In a similar line of thinking \citet{Iorio2005a,Iorio2005b} attempted to investigate secular increase of the Astronomical Unit, perihelion precessions and planetary motions as tests of the Dvali-Gabadadze-Porrati multidimensional braneworld scenario."404 In this connection it is to be noted here that investigations by Liu&Overduin(2000).. along with those of Lim.Overduin&Wes-son(19953). and Kalligas.Wesson&Everitt(1995). are limited to five-dimensional soliton-like space-time only.," In this connection it is to be noted here that investigations by \citet{Liu2000}, along with those of \citet{Lim1995} and \citet{Kalligas1995}, are limited to five-dimensional soliton-like space-time only."405 Therefore. our present attempt is to study more general cases under a spherically symmetric Schwarzschild-like space-time with number of dimensions where Vo=D|2 such that Z2.—2.," Therefore, our present attempt is to study more general cases under a spherically symmetric Schwarzschild-like space-time with$N$ number of dimensions where $N=D+2$ such that $D \geq 2$."406 In this context we discuss the following five cases involved in the solar system experiments to examine the viability of GR with HD. viz.. (," In this context we discuss the following five cases involved in the solar system experiments to examine the viability of GR with HD, viz., ("4071) Perihelion shift (2) Bending of light (3) Gravitational Red-shift (4) Gravitational time delay and (5) Motion of test particle.,1) Perihelion shift (2) Bending of light (3) Gravitational Red-shift (4) Gravitational time delay and (5) Motion of test particle.408 Our present studies show that most of these solar system phenomena do not allow dimensions beyond 4 indicating a gross failure of GR with higher dimensional framework., Our present studies show that most of these solar system phenomena do not allow dimensions beyond $4$ indicating a gross failure of GR with higher dimensional framework.409 Let us consider a spherically symmetric metric which represents a generalized Schwarzschild space-time with higher dimensions (Mayers&Perry1986) where r is a radial coordinate and f£. is a function of r only.," Let us consider a spherically symmetric metric which represents a generalized Schwarzschild space-time with higher dimensions \citep{Mayers1986}410 where $r$ is a radial coordinate and $f$ is a function of $r$ only."411 The line element d£257 on the unit D-sphere is given by with (35=PIMP(CD|1)/2]., The line element ${d{\Omega}_D}^2$ on the unit $D$ -sphere is given by with ${\Omega}_D=2[{\pi}^{(D+1)/2}]/[\Gamma(D+1)/2]$.412 Also. according to Einstein equations we can write f(r)—1nivPol with the constant of integration =16:26AM0Op.," Also, according to Einstein equations we can write $f(r)=1-\mu/r^{D-1}$ with the constant of integration $\mu=16\pi413GM/D c^2 {\Omega}_D$."414 Now. in principle. in Lagrangian mechanics the trajectory of an object is derived by finding the path which minimizes the action. a quantity which is the integral of the Lagrangian over time.," Now, in principle, in Lagrangian mechanics the trajectory of an object is derived by finding the path which minimizes the action, a quantity which is the integral of the Lagrangian over time."415 So. in connection to the solar system problem we would like to adopt the higher dimensional Lagrangian which ean be written as Here dot over any parameter implies differentiation with respect to the affine parameter τς.," So, in connection to the solar system problem we would like to adopt the higher dimensional Lagrangian which can be written as Here dot over any parameter implies differentiation with respect to the affine parameter `s'."416" Now. if we take a cross-section by keeping fixed 6,=#2=6p1 E.sothaté;=0.71.2.3...)| then the Lagrangian takes the form with light-like particle photon. £=0 and for any time-like particle. L=1."," Now, if we take a cross-section by keeping fixed ${\theta}_1={\theta}_2=...={\theta}_{D-1}=\frac{\pi}{2}$ , so that ${{\dot\theta}_i}=0, i=1,2,3,...,D-1$ then the Lagrangian takes the form with light-like particle photon, $L=0$ and for any time-like particle, $L=1$."417 Therefore. in terms of the generalized coordinates g; and generalized velocities q;. the standard Euler-Lagrange equations are By assuming ff=££ and ray=p. Where f£ and p are the energy and momentum of the particle respectively. such that |—Ef and605 =pfi7 and hence with these notations equation (4) becomes which. after simplitication. can be written in the following forms and Again. by substituting 85=ὡ and r=1/U in equation (8). one can write Now. if we write equation (7) in the form then one can easily observe that a vanishes at 5—ry of the closest approach to the sun.," Therefore, in terms of the generalized coordinates $q_i$ and generalized velocities $\dot q_i$, the standard Euler-Lagrange equations are By assuming $f\dot t=E$ and $r^2 \dot{{\theta}_D}=p$, where $E$ and $p$ are the energy and momentum of the particle respectively, such that $\dot t=E/f$ and $\dot{{\theta}_D}=p/r^2$ and hence with these notations equation (4) becomes which, after simplification, can be written in the following forms and Again, by substituting ${\theta}_D=\phi$ and $r=1/U$ in equation (8), one can write Now, if we write equation (7) in the form then one can easily observe that $\frac{dr}{dt}$ vanishes at $r=r_0$ of the closest approach to the sun."418 This at once yields the relationship between momentum and energy of the particle as follows: p/h?=iffo. where fo=f(r ro).," This at once yields the relationship between momentum and energy of the particle as follows: $p^2/E^2 = r_0^2/f_0$, where $f_0 = f(r=r_0)$ ."419" Hence. the equation of photon becomes Thus, the time required for light to travel from ro to r ean be expressed as Following the equation (8). motion of planet in the sun's gravitational field can be written as For r— 1/U. we have The solution to this equation (14) is then given by the following ay D=2 By the use of successive approximation (taking je=O as zeroth approximation) we getthe solution to the above equation (I4) in the form"," Hence, the equation of photon becomes Thus, the time required for light to travel from $r_0$ to $r$ can be expressed as Following the equation (8), motion of planet in the sun's gravitational field can be written as For $r=1/U$ , we have The solution to this equation (14) is then given by the following (i): $D=2$ By the use of successive approximation (taking $\mu=0$ as zeroth approximation) we getthe solution to the above equation (14) in the form"420"on where the CRs are deposited, these powerful AGN outbursts may produce X-ray cavities with different morphologies.","on where the CRs are deposited, these powerful AGN outbursts may produce X-ray cavities with different morphologies."421" In run D1-A, where the CRs are injected into the ICM continuously by a source moving out from the central AGN, the resulting central cavity is elongated in the jet direction and finally breaks up into three pairs of cavities in the same direction Figure 7))."," In run D1-A, where the CRs are injected into the ICM continuously by a source moving out from the central AGN, the resulting central cavity is elongated in the jet direction and finally breaks up into three pairs of cavities in the same direction (see Figure \ref{plot7}) )."422" Interestingly, the morphology seen in this (seerun may have already been detected in cluster observations (e.g., in Hydra A; see Figure 7 and the corresponding discussion)."," Interestingly, the morphology seen in this run may have already been detected in cluster observations (e.g., in Hydra A; see Figure \ref{plot7} and the corresponding discussion)."423" As high-entropy thermal gas flows to the center, the cluster relaxes to the NCC state after t~0.2—0.3 Gyr, as indicated by the long-dashed and dot-short dashed lines in Figure 3.."," As high-entropy thermal gas flows to the center, the cluster relaxes to the NCC state after $t\sim 0.2-0.3$ Gyr, as indicated by the long-dashed and dot-short dashed lines in Figure \ref{plot3}."424" During the NCC state, the cluster has a relatively flat temperature profile and a high entropy (>80 keV cm?) core."," During the NCC state, the cluster has a relatively flat temperature profile and a high entropy $\gtrsim 80$ keV $^{2}$ ) core."425 The central cooling time in the NCC state is quite long (~3 - 4 Gyr) and the cluster profiles do not evolve much from £=0.3 to 0.5 Gyr (dot-long dashed line)., The central cooling time in the NCC state is quite long $\sim 3$ - $4$ Gyr) and the cluster profiles do not evolve much from $t=0.3$ to $0.5$ Gyr (dot-long dashed line).426" In our calculations, we ignore thermal conduction, which may remove irregularities in the temperature distribution and may even provide a strong heating source for the ICM during the CC to NCC transformation (???).."," In our calculations, we ignore thermal conduction, which may remove irregularities in the temperature distribution and may even provide a strong heating source for the ICM during the CC to NCC transformation \citep{guo09,ruszkowski10,parrish10}."427" In cluster cool cores where the gas temperature decreases in the direction of gravity, conduction may be strongly suppressed by the heat flux driven buoyancy instability (hereafter HBI; see ?)), which re-orients the magnetic field to be largely transverse to the radius."," In cluster cool cores where the gas temperature decreases in the direction of gravity, conduction may be strongly suppressed by the heat flux driven buoyancy instability (hereafter HBI; see \citealt{quataert08}) ), which re-orients the magnetic field to be largely transverse to the radius."428" However, it is possible that AGN outbursts counteract the HBI by disturbing the"," However, it is possible that AGN outbursts counteract the HBI by disturbing the"429he cluster center. as oue may expect frou a dissipative settling of the eas iu a selfenrichment process,"the cluster center, as one may expect from a dissipative settling of the gas in a self-enrichment process."430 Similar results were obtained bv Suutzeff Kraft (1996)) who ueasured Cale abundances of & 380 stars and also ound a peak at |Fe/Il|] =1.7 dex and a broad tai o higher aetallicities., Similar results were obtained by Suntzeff Kraft \cite{sunt96}) ) who measured Calcium abundances of $\simeq$ 380 stars and also found a peak at [Fe/H] $= -1.7$ dex and a broad tail to higher metallicities.431 Their data did not support a oimnodal metallicity distribution. but again a weal radial netallicity eradieut.," Their data did not support a bimodal metallicity distribution, but again a weak radial metallicity gradient."432 Both eroups favoured an exteudec oxdod of star formation connected with selteurichlimueut ax the interpretation of their data., Both groups favoured an extended period of star formation connected with self-enrichment as the interpretation of their data.433 A dvnaimical analysis of 100 stars in the Norris ct al. (1996)), A dynamical analysis of 400 stars in the Norris et al. \cite{norr96}) )434 sample reveale a votation of the metal poor component. whereas the metal rich one is not rotating (Norris ct al. 1997)). ↽∕∏∐↴∖↴∐↓," sample revealed a rotation of the metal poor component, whereas the metal rich one is not rotating (Norris et al. \cite{norr97}) )."435⋜↧∙↖↽↴⋈∖↸⊳∪∐∏≻⋜↧↑∏⋝↕↸∖↖↖⇁↕↑∐⋜↧⋯↸∖↥⋅∶↴∙⊾↸∖↥⋅∪↕⋟↑↖↖⇁∪∶↴↜⊾↕∪↴⋝∏↕⋜∐⋅↼↼ clusters with differcut masses. as shown by the model ↸⊳⋜↕↕↸⊳∏⋜↧↑↕∪∐↴∖↴∪↕⋟⋀∖↕⋜↧↘↽↕∐∪↸∖↑⋜↕↕∙∐∩≝∐⊔∙∐∪," This may be compatible with a merger of two globular clusters with different masses, as shown by the model calculations of Makino et al. \cite{maki}) )."436↖↖↽↸∖↖⇁↸∖↥⋅∙↑↕∐∖∐∪↕ ↖↖↽∪∏↕≼↸∖⊼↻↸∖↸⊳↑⋜↧∐∐∖↑⋜↧∐↕↸⊳↕↑⋅↖↽≼∐↴∖↴⊓⋅∏⋝∏⊓∪∐↑∐⋜↧↑↕↴∖↴↻↸∖⋜∐↘↽↸∖≼⇂ ⋜↧↑↑↖↖⇁∪≼∐∖↴↑↕∐↸⊳↑↖↽⋜↧⋯∖↴∖↴∙↖↖⇁↕∐↸⊳∐↕↴∖↴↕∐↸⊳∪∐⊓⋅⋜∥∐↸⊳↑↕∪∐↑∪↑↕ ∖ continous: distribution∙∙∙ shown by the authors.," However, then one would expect a metallicity distribution that is peaked at two distinct values, which is in contradiction to the continuous distribution shown by the authors."437 A recent spectroscopic investigation by Simith et al. (2000)), A recent spectroscopic investigation by Smith et al. \cite{smith00}) )438 shows no strong signatures of curichiment by SNe Ia. but a strong increase of s-process heavy clements with iron abundances. ax las been fouud by Norris Da Costa (1995)) aud other studies as well.," shows no strong signatures of enrichment by SNe Ia, but a strong increase of s-process heavy elements with iron abundances, as has been found by Norris Da Costa \cite{norr95}) ) and other studies as well."439 This can pose a problem. since these elements are believed to come from ACB stars (see Suuith et al.," This can pose a problem, since these elements are believed to come from AGB stars (see Smith et al."440 2000. for a discussion aud references). aud SNe Ta probably also have intermediate-age progenuitors (e.g. MeMillan Ciarcdullo (1996)).," \cite{smith00} for a discussion and references), and SNe Ia probably also have intermediate-age progenitors (e.g. McMillan Ciardullo \cite{mcmi96}) )."441 Because of its peculiar properties. more and nore authors raised the question. whether ο Cen can actually be regarded as a “true” elobular cluster. or whether it is ore likely the stripped uucleus of à dwiuf galaxy that as been accreted by the Alilsv Wav (Majewsii ct al. 1999..," Because of its peculiar properties, more and more authors raised the question, whether $\omega$ Cen can actually be regarded as a “true” globular cluster, or whether it is more likely the stripped nucleus of a dwarf galaxy that has been accreted by the Milky Way (Majewski et al. \cite{maje99b},"442 Lee et al. 1999..," Lee et al. \cite{leey},"443 Tughes Wallerstein 19993)., Hughes Wallerstein \cite{hugh}) ).444 This scenario has also been proposed for M51. one of the most uassive elobular clusters.," This scenario has also been proposed for M54, one of the most massive globular clusters."445 Tt is a candidate for the nucleus of the Sagittarius dwart ealaxy (e.g. Bassino Muzzio —.(1995))., It is a candidate for the nucleus of the Sagittarius dwarf galaxy (e.g. Bassino Muzzio \cite{bass95}) ).446 Three more elobular clusters might have belouged o Sagittarius (Da Costa Armandroff 1995)). now he added to the Milky Way elobular cluster svsteun.," Three more globular clusters might have belonged to Sagittarius (Da Costa Armandroff \cite{daco95}) ), now be added to the Milky Way globular cluster system."447 ⊲⋅⋅ ∺∐⊔∏⋜∐⋅↕⋅↖⇁∙↑∐↸∖∶↴∙⊾↕∪↴⋝∏↕⋜∐⋅↸⊳↕∏↴∖↴↑↸∖↥⋅↴∖↴⋀∖≼∣≼⋅≩∩−≻⋜⋯≼↧⋀∖≼∣≼ ⇁∢⊲∙⋅⊀ ⇁⊲⊲ 6779 müeht∙ have been associated. with| the former; host ⋟⋅⋅⋅ ∖∶↴∙⊾⋜↧↕⋜⋯⋅↖⇁∪↕⊔∩≼↸∖↕∐⋝↸∖↸⊳⋜⋯↴∖↴↸∖∪↕↑∐↸∖∐⋅↴∖↴∐⊔∏⋜∐⋅∙↴∖↴⊓⋅∪∐∶↴∙⊾↥⋅↸∖⊓⋅∪∶↴∙⊾↥⋅⋜∥∐∖ ∪↥⋅↴⋝↕↑↴∖↴≺↕≻↕∐↸∖↴∖↴↸⊳," Similarly, the globular clusters NGC 362 and NGC 6779 might have been associated with the former host galaxy of $\omega$ Cen because of their similar, strong retrograde orbits (Dinescu et al. \cite{dine99b}) )."448∏↸∖↑⋜↧↕∙↕≝↭≝⊔⋟∙ Au orem of w Cen within a dwarf ealaxv outside he Milkv Way could provide a natural explanation for its uuique properties., An origin of $\omega$ Cen within a dwarf galaxy outside the Milky Way could provide a natural explanation for its unique properties.449 Local Group dwarf spheroidals are known to have complex star formation listories (6.8. Ceebel 1997))., Local Group dwarf spheroidals are known to have complex star formation histories (e.g. Grebel \cite{greb97}) ).450 One can imagine that this could also be true for the nuclei of dwart galaxies which cither experienced a extended period of star formation from curiched gas retained in the galaxy potential. or even were built from a merger of two clusters that spiraled iuto the οσο of the cawart galaxy. CMiller et al. 19983).," One can imagine that this could also be true for the nuclei of dwarf galaxies which either experienced a extended period of star formation from enriched gas retained in the galaxy potential, or even were built from a merger of two clusters that spiraled into the center of the dwarf galaxy (Miller et al. \cite{mill98}) )."451 Mediua- spectroscopy of 25 nuclei iu dwarf ellipicals of he Fornuax cluster incicated that all these uuclei have, Medium-resolution spectroscopy of 25 nuclei in dwarf ellipicals of the Fornax cluster indicated that all these nuclei have452"To a second order of approximation, centrifugal effects that disrupt the equilibrium structure of the star are taken into account through an additional frequency perturbation (independent of the sign of m).","To a second order of approximation, centrifugal effects that disrupt the equilibrium structure of the star are taken into account through an additional frequency perturbation (independent of the sign of $m$ )."453" This perturbation in turn scales as the ratio of the centrifugal to the gravitational forces at the stellar surface, i.e., Q?2R?/(GM), where Q denotes the surface angular velocity, R the radius of the star, M its mass, and G the universal gravitational constant."," This perturbation in turn scales as the ratio of the centrifugal to the gravitational forces at the stellar surface, i.e., $\Omega^2R^3/(GM)$ , where $\Omega$ denotes the surface angular velocity, $R$ the radius of the star, $M$ its mass, and $G$ the universal gravitational constant."454" Although negligible in the Sun, these effects may be significant for faster-rotating solar-type stars (e.g.,?).."," Although negligible in the Sun, these effects may be significant for faster-rotating solar-type stars \citep[e.g.,][]{Ballotrot}."455 Large-scale magnetic fields may also introduce further corrections to the oscillation frequencies., Large-scale magnetic fields may also introduce further corrections to the oscillation frequencies.456" The frequency dependence of the mode surface amplitudes is determined both by (i) the frequency dependence of the stochastic process of excitation (mode energies result from a balance between the frequency-dependent energy input and the damping rate) and by (ii) the mode properties in the region of vigorous convection (e.g.,??).."," The frequency dependence of the mode surface amplitudes is determined both by (i) the frequency dependence of the stochastic process of excitation (mode energies result from a balance between the frequency-dependent energy input and the damping rate) and by (ii) the mode properties in the region of vigorous convection \citep[e.g.,][]{Houdek99,Samadi07}."457" The stochastic process of excitation is characterized by a relatively slow variation with frequency, meaning that it excites modes over a large frequency interval to comparable surface amplitudes."," The stochastic process of excitation is characterized by a relatively slow variation with frequency, meaning that it excites modes over a large frequency interval to comparable surface amplitudes."458" At low frequencies modes are evanescent in the region of efficient excitation, leading to small surface amplitudes."," At low frequencies modes are evanescent in the region of efficient excitation, leading to small surface amplitudes."459 At high frequencies — greater than or equal to the acoustic cut-off frequency — modes undergo considerable energy loss through running waves in the atmosphere., At high frequencies – greater than or equal to the acoustic cut-off frequency – modes undergo considerable energy loss through running waves in the atmosphere.460 Excitation is most efficient for those modes whose periods match the timescale of the near-surface convection., Excitation is most efficient for those modes whose periods match the timescale of the near-surface convection.461" Also, the frequency of maximum amplitude, Vmax, is supposed to scale with the acoustic cut-off frequency, Vac (??).."," Also, the frequency of maximum amplitude, $\nu_{\rm{max}}$, is supposed to scale with the acoustic cut-off frequency, $\nu_{\rm{ac}}$ \citep{Brown,KB95}."462 All this gives rise to a characteristic distribution of power with frequency which is a signature of the presence of solar-like oscillations., All this gives rise to a characteristic distribution of power with frequency which is a signature of the presence of solar-like oscillations.463" Substantial changes in the properties of solar-like oscillations occur with stellar evolution, particularly following the exhaustion of hydrogen in the core."," Substantial changes in the properties of solar-like oscillations occur with stellar evolution, particularly following the exhaustion of hydrogen in the core."464" Most noticeable is the occurrence of avoided crossings due to coupling between p and g modes of like degree (??),, which lead to significant departures from the regular frequency spacing described by Eq."," Most noticeable is the occurrence of avoided crossings due to coupling between p and g modes of like degree \citep{Osaki,Aizenman}, which lead to significant departures from the regular frequency spacing described by Eq."465[I] in the case of evolved stars., \ref{asymptotic} in the case of evolved stars.466" The frequencies of non-radial modes, in particular those of /=1 modes, are shifted by avoided crossings when they couple with g modes trapped in the deep stellar interior."," The frequencies of non-radial modes, in particular those of $l\!=\!1$ modes, are shifted by avoided crossings when they couple with g modes trapped in the deep stellar interior."467" At the avoided crossings these modes have a mixed nature, with both p- and g-mode behavior."," At the avoided crossings these modes have a mixed nature, with both p- and g-mode behavior."468" Provided they are excited to observable amplitudes (their high mode inertia reduces their surface amplitude), these so-called mixed modes are of great diagnostic potential because they probe the stellar core and are very sensitive to stellar age."," Provided they are excited to observable amplitudes (their high mode inertia reduces their surface amplitude), these so-called mixed modes are of great diagnostic potential because they probe the stellar core and are very sensitive to stellar age."469 We computed the power density spectrum (PDS) of the time series based on the implementation of the Lomb-Scargle periodogram (??) presented in ?..," We computed the power density spectrum (PDS) of the time series based on the implementation of the Lomb-Scargle periodogram \citep{Lomb,Scargle} presented in \citet{PressRybicki}."470 This algorithm carries out reverse interpolation of the data onto a regular mesh and subsequently employs the fast Fourier transform., This algorithm carries out reverse interpolation of the data onto a regular mesh and subsequently employs the fast Fourier transform.471" The power spectrum was then calibrated so that it satisfies Parseval's theorem, i.e., so that the total power in the positive-frequency side of the spectrum is equal to the variance of the time series (single-sided calibration)."," The power spectrum was then calibrated so that it satisfies Parseval's theorem, i.e., so that the total power in the positive-frequency side of the spectrum is equal to the variance of the time series (single-sided calibration)."472 The effect of the window function is further taken into account when normalizing the PDS., The effect of the window function is further taken into account when normalizing the PDS.473" A total of eleven individual fitters CCR, DDS, A2Z_RRG, AAU, IAS.OOB, PPG, TTA, OCT, ORK, QML and SYD) extracted estimates of the p-mode frequencies for at least one of the two stars and subsequently uploaded their results to the Cat data exchange facility."," A total of eleven individual fitters CR, DS, RG, AAU, OB, PG, TA, OCT, ORK, QML and SYD) extracted estimates of the p-mode frequencies for at least one of the two stars and subsequently uploaded their results to the Cat data exchange facility."474 Different fitting strategies have Basket]been adopted and sometimes the same fitting strategy has been applied in an independent manner., Different fitting strategies have been adopted and sometimes the same fitting strategy has been applied in an independent manner.475" All the fitting strategies adopted are, however, based on Fourier methods, the main idea behind them being either the maximization of the likelihood of a multi-parameter model describing the data or a classic prewhitening method."," All the fitting strategies adopted are, however, based on Fourier methods, the main idea behind them being either the maximization of the likelihood of a multi-parameter model describing the data or a classic prewhitening method."476 A frequency-domain representation of the data aims at modeling the limit PDS of the time series., A frequency-domain representation of the data aims at modeling the limit PDS of the time series.477" Such a model typically includes a sum of symmetric Lorentzian profiles meant to describe the individual p modes, together with a flat term and a number of additional terms describing both instrumental and stellar background noise (?):: where H is the mode height, Τ is the mode linewidth (related to the mode lifetime or amplitude e-folding time, Tmode, through 4I= 1/Tmode), and B(v) represents the background signal."," Such a model typically includes a sum of symmetric Lorentzian profiles meant to describe the individual p modes, together with a flat term and a number of additional terms describing both instrumental and stellar background noise \citep{Anderson}: where $H$ is the mode height, $\Gamma$ is the mode linewidth (related to the mode lifetime or amplitude e-folding time, $\tau_{\rm{mode}}$, through $\pi\Gamma\!=\!1/\tau_{\rm{mode}}$ ), and $B(\nu)$ represents the background signal."478" The components arising from the decay of active regions, granulation and faculae are commonly represented using a Harvey-like model (??):: where (co) are the amplitudes, (τι)are the characteristic timescales, {s,} are the slopes of the individual power laws in the denominator, and W is a constant representing white noise"," The components arising from the decay of active regions, granulation and faculae are commonly represented using a Harvey-like model \citep{Harvey,Aigrain}: where $\{\sigma_k\}$ are the amplitudes, $\{\tau_k\}$are the characteristic timescales, $\{s_k\}$ are the slopes of the individual power laws in the denominator, and $W$ is a constant representing white noise"479Subsequent studies of open cluster Li and Be abundances are revealing a rich variety of stellar Li depletion properties. almost of which can be accounted for by the standard theory (Delivannis2000:Jeffries2000).,"Subsequent studies of open cluster Li and Be abundances are revealing a rich variety of stellar Li depletion properties, almost of which can be accounted for by the standard theory \citep{d00, j00}."480. It is (hus becoming increasinely important (o ascertain what physical mechanisms are really operating inside low mass stars. especially since (here may be critical implications lor interpreting and testing Dig Dang nucleosvnthesis Rvan2004:Pinsonneaultοἱal.1999). and. globular cluster ages (Delivannis.jedini 1996).," It is thus becoming increasingly important to ascertain what physical mechanisms are really operating inside low mass stars, especially since there may be critical implications for interpreting and testing Big Bang nucleosynthesis \citep{DR04, P99}481 and globular cluster ages \citep{DDP89, ddk, CDS}."482". Three classes of models have emerged as possible explanations for the F dwiu Li gap: 1) diffusion (Michaud1936)... where gravitational settling and thermal diffusion clrain Li out of the SCZ and surface. 2) steady main sequence mass loss (Schram.1990.""55D ).. where the Li preservation region is simply lost over time (though the recquired mass loss rates are enormous). and 3) slow mixing driven by instabilities associated with rotation (Pinsonneault.NKawaler.&Demarque1990:Pinsonneault.Delivannis.Demarcque1992:Charbonneletal.1994.hereafter.C94). and/or gravity waves (GarciaLopez&Spruil1991:Talon&Charbonnel 2003)."," Three classes of models have emerged as possible explanations for the F dwarf Li gap: 1) diffusion \citep{michaud86}, where gravitational settling and thermal diffusion drain Li out of the SCZ and surface, 2) steady main sequence mass loss \citep[][``SSD'']{ssd90}, where the Li preservation region is simply lost over time (though the required mass loss rates are enormous), and 3) slow mixing driven by instabilities associated with rotation \citep[][hereafter, C94]{pkd, pdd92, c94}483 and/or gravity waves \citep{gl95, tc03}."484. Rotationally-incucec mixing could include meridional circulation. ancl related. instabilities. and/or instabilities triggered by angular momentum loss.," Rotationally-induced mixing could include meridional circulation and related instabilities, and/or instabilities triggered by angular momentum loss."485 To continue to trv to differentiate between (hese scenarios we pursue here (he novel approach of investigating the differences in the predicted morphology. of the Li eap in its early (and heretofore uninvestigated) stages. (, To continue to try to differentiate between these scenarios we pursue here the novel approach of investigating the differences in the predicted morphology of the Li gap in its early (and heretofore uninvestigated) stages. (486See 82 for previously used diagnostics.),See 3 for previously used diagnostics.)487 The nearby and only moderatelv-reddened (72800 pe. E(B5—V)= 0.20). very rich open cluster M35 has an ideal age (160+20Myr.Delivannisetal.2004a) [or studying possible early stages of Li gap formation. soon alter the age of the Pleiades.," The nearby and only moderately-reddened $\sim$ 800 pc, $E(B-V) = 0.20$ ), very rich open cluster M35 has an ideal age \citep[$160 \pm 20 $Myr,][]{d04}488 for studying possible early stages of Li gap formation, soon after the age of the Pleiades."489 There is also excellent menbership information from the proper motion study. of AleNamara&hereafter.MIS8G6) and WOCS radial velocity data (Meibometal.2004).," There is also excellent membership information from the proper motion study of \citet[][hereafter, MS86]{MS}490 and WOCS radial velocity data \citep{m04}."491. This section provides a brief summary of our methods., This section provides a brief summary of our methods.492 For more details see (2004):: Steinhauer (2003):: ancl Delivannis.Steinhauer. DSJO2)..," For more details see \citet{s04}; \citet{s03}; and \citet[][hereafter, DSJ02]{dsj02}."493 Iheh S/N spectra of 165 dwarl members (P. eenerally >0.90 in MS586) of M35. were taken in the region of the 6708 Li I resonance doublet. using three configurations οἱ WIYN's IIydra/MOS during three observing runs in 1997 November ancl December. and 1998 January.," High S/N spectra of 165 dwarf members (P generally $> 0.90$ in MS86) of M35 were taken in the region of the 6708 Li I resonance doublet using three configurations of WIYN's Hydra/MOS during three observing runs in 1997 November and December, and 1998 January."494 Nearly all MS86 members in the range V.—12.2515 were observed., Nearly all MS86 members in the range $V=12.25-15$ were observed.495 Each, Each496"for three cases (G035.39, G028.37. G024.33; see Cols. (","for three cases (G035.39, G028.37, G024.33; see Cols. ("4979)-(1D) of Table 9)).,9)-(11) of Table \ref{table:separations}) ).498 Figure 8— (bottom) compares the observed nearest-neighbour. distribution in. G304.74 with the. distribution for randomly positioned. clumps., Figure \ref{figure:dist} (bottom) compares the observed nearest-neighbour distribution in G304.74 with the distribution for randomly positioned clumps.499" The mean and median of the nearest-neighbour distribution in. G304.74 are logG)../AU)25083xz0.058 (12171;x10? AU) and log/AU)=5.136 (1.37x10"" AU). respectively."," The mean and median of the nearest-neighbour distribution in G304.74 are $\log(\langle r \rangle_{\rm obs}/{\rm AU})=5.083\pm0.058$ $1.21^{+0.17}_{-0.15}\times10^5$ AU) and $\log(\tilde{r}_{\rm obs}/{\rm AU})=5.136$ $1.37\times10^5$ AU), respectively."500" Again. these values are comparable to those of randomly positioned clumps. for which. the mean and median are log(6)4,/AU)=5.030+OLLI] and log(F/a,/AU)=5.047+0.110. respectively (see Table 10))."," Again, these values are comparable to those of randomly positioned clumps, for which the mean and median are $\log(\langle r \rangle_{\rm ran}/{\rm AU})=5.030\pm0.111$ and $\log(\tilde{r}_{\rm ran}/{\rm AU})=5.047\pm0.110$, respectively (see Table \ref{table:nearest}) )."501 According to the K-S test. there is about probability that the observed and random nearest-neighbour distributions are samples of the same underlying distribution.," According to the K-S test, there is about probability that the observed and random nearest-neighbour distributions are samples of the same underlying distribution."502 We note that the minimum observable separation corresponds to the beam size. ie. 186 or ~4.46x10t AU (log(r/AU)= 4.649) at 2.4 kpe.," We note that the minimum observable separation corresponds to the beam size, i.e, $18\farcs6$ or $\sim4.46\times10^4$ AU $\log(r/{\rm AU})=4.649$ ) at 2.4 kpc."503 Statistics of the nearest-neighbour distributions in other IRDCs are given in Table 10.., Statistics of the nearest-neighbour distributions in other IRDCs are given in Table \ref{table:nearest}.504 Table 10. have the same meaning as in Table 9.. except now for nearest neighbour separations.," Table \ref{table:nearest} have the same meaning as in Table \ref{table:separations}, except now for nearest neighbour separations."505 The observed nearest-neighbour distances are similar to those expected from random distributions., The observed nearest-neighbour distances are similar to those expected from random distributions.506 This is evident from the ratios Gop./Gran and Pops/Fray Which are (within. the erros) about |. and by the high K-S probabilities (~59— 100%) 1 every other case except GO31.97. where this probability ts still ~37% (see Cols. (," This is evident from the ratios $\langle r \rangle_{\rm obs}/\langle r \rangle_{\rm ran}$ and $\tilde{r}_{\rm obs}/\tilde{r}_{\rm ran}$ which are (within the erros) about 1, and by the high K-S probabilities $\sim59-100\%$ ) in every other case except G031.97, where this probability is still $\sim37\%$ (see Cols. ("5076)-(8) of Table 10)).,6)-(8) of Table \ref{table:nearest}) ).508 In summary. the average projected separations betwee clumps in the studied IRDCs range from about 2.6x10? AL to 1.2x10° AU (Le. the minimum and maximum lie withi a factor of five). and the average projected distances betwee the nearest neighbours range from 6.0x107 AU to 3.5xI0? AU (re.. the changes are within a factor of six).," In summary, the average projected separations between clumps in the studied IRDCs range from about $2.6\times10^5$ AU to $1.2\times10^6$ AU (i.e., the minimum and maximum lie within a factor of five), and the average projected distances between the nearest neighbours range from $6.0\times10^4$ AU to $3.5\times10^5$ AU (i.e., the changes are within a factor of six)."509 For most clouds. the distributions of projected separations and distances between the nearest neighbours can be mimicked by clumps placed randomly into the same projected area as occupied by the cloud.," For most clouds, the distributions of projected separations and distances between the nearest neighbours can be mimicked by clumps placed randomly into the same projected area as occupied by the cloud."510 Assuming that the vectors connecting clump pairs are randomly oriented. the average projection factor is (sin6;j)=z/A. where &jj is the angle between the line of sight and the vector pointing from clump i to clump /.," Assuming that the vectors connecting clump pairs are randomly oriented, the average projection factor is $\langle \sin \theta_{ij} \rangle=\pi/4$, where $\theta_{ij}$ is the angle between the line of sight and the vector pointing from clump $i$ to clump $j$."511 Correcting for this projection effect. the grand averages of the separations and distances between the nearest neighbours are about 6.5x10? AU (3.1 pe) and 2.2x10° AU (1.1 pe). respectively.," Correcting for this projection effect, the grand averages of the separations and distances between the nearest neighbours are about $6.5\times10^5$ AU (3.1 pc) and $2.2\times10^5$ AU (1.1 pc), respectively."512 One plausible scenario for the origin of filamentary clouds is that they are formed in shocks occurring in converging flows driven by large-scale turbulence (e.g.. Klessenetal.2000:: Padoanetal. 2001)).," One plausible scenario for the origin of filamentary clouds is that they are formed in shocks occurring in converging flows driven by large-scale turbulence (e.g., \cite{klessen2000}; \cite{padoan2001}) )."513 The chaotic process can give rise to randomly positioned density peaks within filaments. and these can become centres of gravitational collapse.," The chaotic process can give rise to randomly positioned density peaks within filaments, and these can become centres of gravitational collapse."514 On the other hand. supposing that compressionleads to an equilibrium structure. a filament can fragmentthrough the Jeans instability.," On the other hand, supposing that compressionleads to an equilibrium structure, a filament can fragmentthrough the Jeans instability."515" The critical wavelength. οἰς. of perturbations leading to gravitational instability depends on both the gas kinetic tempeture. μμ. and the density. p: εἰς~c,/¥Gp. or. in terms of the surface density. X: 2.~ctGX. where c, is the sound speed. and G is the gravitational constant (e.g.. Larson1985:: Hartmann2002))."," The critical wavelength, $\lambda_{\rm c}$ , of perturbations leading to gravitational instability depends on both the gas kinetic tempeture, $T_{\rm kin}$, and the density, $\rho$: $\lambda_{\rm c} \sim c_{\rm s}/\sqrt{G\rho}$, or, in terms of the surface density, $\Sigma$: $\lambda_{\rm c} \sim c_{\rm s}^2/{G\Sigma}$, where $c_{\rm s}$ is the sound speed, and $G$ is the gravitational constant (e.g., \cite{larson1985}; \cite{hartmann2002}) )."516" The determination of the ""Jeans length’ is not quite straightforward in a study based on dust emission because the cloud mass and therefore also the average density and surface density depend on the assumed dust temperature. Τα."," The determination of the 'Jeans length' is not quite straightforward in a study based on dust emission because the cloud mass and therefore also the average density and surface density depend on the assumed dust temperature, $T_{\rm d}$."517 Furthermore. in the case of G304.74. there Is no independent estimate of Tii. but it is assumed to be equal to Ty.," Furthermore, in the case of G304.74, there is no independent estimate of $T_{\rm kin}$ , but it is assumed to be equal to $T_{\rm d}$."518" The assumption 7)=15 K yields a total mass of ~ Me and an average surface density of 0.05 cem- for G304.74 (within the LABOCA contour 0.1 Jy beam""! ).", The assumption $T_{\rm d}=15$ K yields a total mass of $\sim1000$ $_{\sun}$ and an average surface density of 0.05 $^{-2}$ for G304.74 (within the LABOCA contour 0.1 Jy $^{-1}$ ).519 In these circumstances. the critical wavelength in an isothermal equilibrium filament is te=0.19 pe or 400000 AU (Hartmann2002:; Larson1985)). and the corresponding mass is Μι~5 Mo.," In these circumstances, the critical wavelength in an isothermal equilibrium filament is $\lambda_{\rm c}=0.19$ pc or 000 AU \cite{hartmann2002}; \cite{larson1985}) ), and the corresponding mass is $M_{\rm c}\sim5$ $_{\sun}$."520 The comparison between dust emission at 870 um. 8 ym absorption. and the visual extinction. from 2MASS suggests an elevated temperature in the southern part of the cloud (Table 4.. Col. (," The comparison between dust emission at 870 $\mu$ m, 8 $\mu$ m absorption, and the visual extinction from 2MASS suggests an elevated temperature in the southern part of the cloud (Table \ref{table:extinction}, Col. ("5214)).,4)).522 By assuming Ty=30 K. one would obtain a total cloud mass of ~400 Mo. and an average surface density of X=0.02 gcecm.," By assuming $T_{\rm d}=30$ K, one would obtain a total cloud mass of $\sim400$ $_{\sun}$, and an average surface density of $\Sigma = 0.02$ $^{-2}$."523 These values of temperature anc surface density imply wt.=ΙΙ pe or 2.2x10° AU. and Μι~50 Mo.," These values of temperature and surface density imply $\lambda_{\rm c} = 1.1$ pc or $2.2\times10^5$ AU, and $M_{\rm c} \sim 50$ $_{\sun}$."524 The critical wavelength. Ae. Is not expected to determine a uniform length scale of fragmentation.," The critical wavelength, $\lambda_{\rm c}$, is not expected to determine a uniform length scale of fragmentation."525" According to the analysis of Stodóllkiewiez (1963: see also Curry2000. and references therein). the fastest growing perturbations have a length scale of roughly twice A,."," According to the analysis of Stodóllkiewicz (1963; see also \cite{curry2000} and references therein), the fastest growing perturbations have a length scale of roughly twice $\lambda_{\rm c}$."526 Nevertheless. the fragmentation of a homogenous cloud is likely to result in a preferred length scale and a quasi-periodic structure. as opposed to a random distribution of clumps.," Nevertheless, the fragmentation of a homogenous cloud is likely to result in a preferred length scale and a quasi-periodic structure, as opposed to a random distribution of clumps."527 The projected distances between the nearest neighbours in G304.74 lie in the range 4x107—2.410° AU., The projected distances between the nearest neighbours in G304.74 lie in the range $4\times10^4 - 2.4\times10^5$ AU.528 They are comparable to the characterics length scales indicated above., They are comparable to the characterics length scales indicated above.529 However. the clump masses in the cool northern part (~40—90 Ma) are about ten times larger than Jeans masses at 15 K and the surface density implied by this temperature.," However, the clump masses in the cool northern part $\sim40-90$ $_{\sun}$ ) are about ten times larger than Jeans masses at 15 K and the surface density implied by this temperature."530 Either the Jeans instability has occurred when the cloud has been warmer. Le. ~30 K. and the clumps have cooled during the contraction. or the dense filament is a result of strong compression by external forces.," Either the Jeans instability has occurred when the cloud has been warmer, i.e. $\sim30$ K, and the clumps have cooled during the contraction, or the dense filament is a result of strong compression by external forces."531 We note that the filament is thinner at the northeastern end (cross-sectional diameter @~0.45 pe) than in the southwest (ὁ~[4 pe)., We note that the filament is thinner at the northeastern end (cross-sectional diameter $\phi \sim 0.45$ pc) than in the southwest $\phi \sim 1.4$ pc).532 Moreover. the filament can have accumulated mass through gravitational inflow from the surrounding cloud (Heitschetal. 2009)).," Moreover, the filament can have accumulated mass through gravitational inflow from the surrounding cloud \cite{heitsch2009}) )."533 The present average mass line density in G304.74. ~100 Me pe! exceeds the critical value for a non-magnetic. self- isothermal cylinder in. equilibrium (~25 Mo pc! at 15 K. the critical line density directly proportional to Ti: Ostriker 1964:;;: Curry 2000).," The present average mass line density in G304.74, $\sim 100$ $_{\sun}$ $^{-1}$ exceeds the critical value for a non-magnetic, self-gravitating isothermal cylinder in equilibrium $\sim25$ $_{\sun}$ $^{-1}$ at 15 K, the critical line density directly proportional to $T_{\rm kin}$ ; \cite{ostriker1964}; ; \cite{curry2000}) )."534 Forcomparison. in several filamentary IRDCs studied by Rathborneet al. (," Forcomparison, in several filamentary IRDCs studied by Rathborneet al. ("5352006: G025.04. G028.53.. 002653. G031.97. G033.69.. G034.43. and G035.39). the line densities are in the range ~70— Ma pe.,"2006; G025.04, G028.53, G028.53, G031.97, G033.69, G034.43, and G035.39), the line densities are in the range $\sim70 - 800$ $_{\sun}$ $^{-1}$."536 Supereritical line densities seem to be a common feature in filamentary IRDCs. and they are likely to fragment into smaller cores.," Supercritical line densities seem to be a common feature in filamentary IRDCs, and they are likely to fragment into smaller cores."537 Our observations cannot resolve the possible fragments in G304.74. but the process," Our observations cannot resolve the possible fragments in G304.74, but the process"538This paper belongs to a series. devoted. to the studs of supposedly old open elusters. which represent one of the best possibilities to study the chemical and dynamical evolution of our Galaxy.,"This paper belongs to a series devoted to the study of supposedly old open clusters, which represent one of the best possibilities to study the chemical and dynamical evolution of our Galaxy."539 Open clusters provide unique information on the chemical abuncances and gradients in the disce (e.g.. Janes 1979. Panagia and Γον 1981. Πίο and Janes 1993): on the average stellar ages and radial velocities at. clillerent galactic radii (e.g.. Janes and Phelps 1994. hereinafter JP94): and on the interactions between thin and thick clises (c.g.. Sandage LOSS).," Open clusters provide unique information on the chemical abundances and gradients in the disc (e.g., Janes 1979, Panagia and Tosi 1981, Friel and Janes 1993); on the average stellar ages and radial velocities at different galactic radii (e.g., Janes and Phelps 1994, hereinafter JP94); and on the interactions between thin and thick discs (e.g., Sandage 1988)."540 In addition. they are the only class of objects covering a large range of distances (several kpc around the Sun) and ages (from a few Myr t0. < 10 Cyr) and can. therefore. tightly constrain galactic evolution theories.," In addition, they are the only class of objects covering a large range of distances (several kpc around the Sun) and ages (from a few Myr to $\gsim$ 10 Gyr) and can, therefore, tightly constrain galactic evolution theories."541 Furthermore. in order to avoid misleading ellects. it is mandatory to work with very accurate observational data and to treat them homogeneously (see Section 5.r and e.g.m Carraro and Chiosi 1994a. hereinafter CCO4. Frick 1995)," Furthermore, in order to avoid misleading effects, it is mandatory to work with very accurate observational data and to treat them homogeneously (see Section 5, and e.g, Carraro and Chiosi 1994a, hereinafter CC94, Friel 1995)."542 In order to obtain this kind of homogeneity and to be able to study accurately the metallicity and age distribution of open clusters with ealactocentric distance. we are analyzing svstems of dillerent ages and metallicities. located at. dillerent galactic radii.," In order to obtain this kind of homogeneity and to be able to study accurately the metallicity and age distribution of open clusters with galactocentric distance, we are analyzing systems of different ages and metallicities, located at different galactic radii."543 To this end. we have obtained deep. photometry for several clusters. and have supplemented. these observations with published data of comparable quality to ensure a sample as large as possible of uniformly derived ages. metallicities and distance moduli.," To this end, we have obtained deep photometry for several clusters, and have supplemented these observations with published data of comparable quality to ensure a sample as large as possible of uniformly derived ages, metallicities and distance moduli."544 These quantities are derived. from comparison of the observed. colour-magnituce diagrams (CMDs) to synthetic ones generated by a numerical code based on. stellar evolution tracks and taking into account theoretical and observational uncertainties (Losi et al., These quantities are derived from comparison of the observed colour-magnitude diagrams (CMDs) to synthetic ones generated by a numerical code based on stellar evolution tracks and taking into account theoretical and observational uncertainties (Tosi et al.545 1991)., 1991).546 These simulations are much more powerful than the classical isochrone fitting method to study the evolutionary status of the analyzed region and have been successfully applied both to nearby irregular galaxies (Marconi ct al., These simulations are much more powerful than the classical isochrone fitting method to study the evolutionary status of the analyzed region and have been successfully applied both to nearby irregular galaxies (Marconi et al.547 1995) and to galactic open clusters (Bonifazi et al., 1995) and to galactic open clusters (Bonifazi et al.548 1990. Gozzoli et al.," 1990, Gozzoli et al."549 1996. Dragaelia et al.," 1996, Bragaglia et al."550 1997)., 1997).551 Our sample of old open clusters includes NCGC2243 (age ~ 3 Gyr. metallicity two tenths solar. Bonilazi et al.," Our sample of old open clusters includes NGC2243 (age $\simeq$ 3 Gyr, metallicity two tenths solar, Bonifazi et al."552 1990). Collinder 261 (age << 7 Gyr. almost solar metallicity. CGozzoli οἱ al.," 1990), Collinder 261 (age $\gsim$ 7 Gyr, almost solar metallicity, Gozzoli et al."553 1996) and NGC6253 (age Zi 3 Gyr. metallicity about twice solar. Bragaelia et al.," 1996) and NGC6253 (age $\gsim$ 3 Gyr, metallicity about twice solar, Bragaglia et al."554 1997)., 1997).555 To them we add. now NGC 2506. a moderately old open cluster already studied by AleClure ct al. (," To them we add now NGC 2506, a moderately old open cluster already studied by McClure et al. ("556"1981. hereinafter. AICTE) and Chiu van tena (1981. hereinafter Cv). located toward the galactic anticentre (AlonsoSshei57.6""01030=10739: lj = 231"". by = | 107).","1981, hereinafter MCTF) and Chiu van Altena (1981, hereinafter CvA), located toward the galactic anticentre $\alpha_{1950} = 7^h55757.6^m, \delta_{1950} = -10^{\circ}39^{\prime}$; $_{\rm II}$ = $^{\circ}$, $_{\rm II}$ = $+10^{\circ}$ )."558 In section 2 we describe the observations ane data analysis: in Section 3 we present the derived CALDs involving U.D.G.VICI photometry and discuss the presence of binary stars.," In section 2 we describe the observations and data analysis; in Section 3 we present the derived CMDs involving U,B,G,V,R,I photometry and discuss the presence of binary stars."559 In Section 4 we compare observed and svnthetie CMDs and derive metallicity. age. distance and reddening.," In Section 4 we compare observed and synthetic CMDs and derive metallicity, age, distance and reddening."560 Finally. our findings will be discussed in Section 5.," Finally, our findings will be discussed in Section 5."561Massive stars can lose à significant. fraction of their original mass during. their. short lifetimesp: due to their: strong. radiation-drivenMEN. stellar winds.,"Massive stars can lose a significant fraction of their original mass during their short lifetimes due to their strong, radiation-driven stellar winds."562. Accurate determinations. of these stars’ mass-loss rates are therefore important [rom an evolutionary point of view. as well as for understanding the raciative driving process itself.," Accurate determinations of these stars' mass-loss rates are therefore important from an evolutionary point of view, as well as for understanding the radiative driving process itself."563 Massive star winds are also an important. source of energy. momentum. and (chemically. enriched) matter deposition into the interstellar medium. making accurate mass-loss rate determinations important from a galactic perspective.," Massive star winds are also an important source of energy, momentum, and (chemically enriched) matter deposition into the interstellar medium, making accurate mass-loss rate determinations important from a galactic perspective."564 A consensus appeared to be reached by the late ↓≤⋗≤⋗∪≱∖↥⇂⋯↿∣↓↕⋖⊾⊔↓⋜↧≱∖≱∖−↓∪≱∖≱∖↓⋅⋜⋯⋅≱∖∪⇂↻≱∖↿⋜⊔⋅⊳∖∖∖⊽⋖⋅↓⋅∢⊾⋯⇍≼↛⊔↓⋅⋜⋯⊾↓∙∖⇁ . known observationallv. and theoretically.. using. the moclified» (Pauldrachetal.1986). 6Αν (Castoretal.L975) theory of line-clriven stellar winds.," A consensus appeared to be reached by the late 1990s that the mass-loss rates of O stars were accurately known observationally and theoretically, using the modified \citep{Pauldrach1986} CAK \citep{cak1975} theory of line-driven stellar winds."565 Vhis understanding was thought to be good enough that DUUV observations. of. spectral signatures: of their winds could be used to determine their luminosities with. sullicientD. accuracy to make cxtragalactic. OU stars standard cancdles (Pulsetal.L99G)., This understanding was thought to be good enough that UV observations of spectral signatures of their winds could be used to determine their luminosities with sufficient accuracy to make extragalactic O stars standard candles \citep{Puls1996}.566. This consensus has unraveled in the last few vears. mostly from the observational side. where α growing," This consensus has unraveled in the last few years, mostly from the observational side, where a growing"567'The HLS sample consists of 19 galaxies located behind the Bullet Cluster at redshifts 0.4<z«3.24 (Rexetal.,The HLS sample consists of 19 galaxies located behind the Bullet Cluster at redshifts $0.4 < z < 3.24$ \citep{Rex10}.568 These sources are detected in at least two Herschel 2010)..bands (at 100—500 wm) and many are also observed in LABOCA 870 micron and AzTEC 1.1 mm maps of the field (Wilsonetal.2008;Johansson," These sources are detected in at least two bands (at $100 -569500$ $\micron$ ) and many are also observed in LABOCA 870 micron and AzTEC 1.1 mm maps of the field \citep{Wilson08, Johansson10}."570 These measurements tightly constrain the peak of the 2010)..far-IR SED and therefore provide accurate estimates ofL(TIR)., These measurements tightly constrain the peak of the far-IR SED and therefore provide accurate estimates of.571. We have excluded three galaxies from the original HLS sample 2 of Rex et al., We have excluded three galaxies from the original HLS sample (Table 2 of Rex et al.572" 2010) in our test: HLS12 and HLS13 (Table(z=3.24 and because 24 uum no longer traces PAH emission at their 2.9)redshifts; HLS18, because its large lensing magnification (54x) is not well constrained due to nearby objects (Rexetal.2010)."," 2010) in our test: HLS12 and HLS13 $z = 3.24$ and 2.9) because 24 $\micron$ no longer traces PAH emission at their redshifts; HLS18, because its large lensing magnification $\times$ ) is not well constrained due to nearby objects \citep{Rex10}."573". Otherwise, the lensing magnifications in the final HLS sample of 16 galaxies are small (median 1.1x)."," Otherwise, the lensing magnifications in the final HLS sample of 16 galaxies are small (median $\times$ )."574 These galaxies are shown as stars in Figure 3.., These galaxies are shown as stars in Figure \ref{compare_lir_CDFS}.575" In addition to the HLS galaxies, we have tested the indicator on individual 24 jum-bright lensed star-forming galaxies at 10«z<2.7 for which we obtained near and mid-IR spectroscopic observations with the Large Binocular Telescope andSpitzer, and mm observations from the literature (Rujopakarnfar-IR/sub-etal. 2012).."," In addition to the HLS galaxies, we have tested the indicator on individual 24 $\micron$ -bright lensed star-forming galaxies at $1.0 <576z < 2.7$ for which we obtained near and mid-IR spectroscopic observations with the Large Binocular Telescope and, and far-IR/sub-mm observations from the literature \citep{Rujopakarn12}."577" The sample of five galaxies (Abell 2218b, Abell 2218a, Abell 1835a, cB 58, and the Clone) is unique in that four members are of LIRG luminosity."," The sample of five galaxies (Abell 2218b, Abell 2218a, Abell 1835a, cB 58, and the Clone) is unique in that four members are of LIRG luminosity."578 The gravitational lensing gives us access to objects as low as 1.1x10!! ((at a z of 2.7)., The gravitational lensing gives us access to objects as low as $1.1 \times 10^{11}$ (at a $z$ of 2.7).579" Although small, this sample thus provides an important verification of the accuracy of our method for typical star-forming galaxies at z>2."," Although small, this sample thus provides an important verification of the accuracy of our method for typical star-forming galaxies at $z > 2$."580" Rujopakarnetal.(2012) find that the 24 wm indicator from this work estimates iin good agreement with their far-IR vvalues, with an average difference of L(TIR)0.06 dex (although there is one outlier whose difference is 0.18 dex)."," \citet{Rujopakarn12} find that the 24 $\micron$ indicator from this work estimates in good agreement with their far-IR values, with an average difference of 0.06 dex (although there is one outlier whose difference is 0.18 dex)."581" We have found from the tests using the ECDFS, HDFN, and lensed galaxies data that the systematic mid-IR excess issue discussed in the Introduction is virtually removed."," We have found from the tests using the ECDFS, HDFN, and lensed galaxies data that the systematic mid-IR excess issue discussed in the Introduction is virtually removed."582" Figure 5 uses the ECDFS sample to illustrate the extent of the mid-IR excess when templates for local galaxies are applied directly to z galaxies, as is the case in the formulae given by Riekeal. (2009)."," Figure \ref{compare_lir_rieke} uses the ECDFS sample to illustrate the extent of the mid-IR excess when templates for local galaxies are applied directly to $z$ galaxies, as is the case in the formulae given by \citet{Rieke09}."583". The results from the improved bolometric corrections are shown in comparison, which indicate that the overestimation problem is no longer present."," The results from the improved bolometric corrections are shown in comparison, which indicate that the overestimation problem is no longer present."584" By using the new indicator, the resulting single-band 24 jym-derived hhas an average agreement with the far-IR observations of 0.02 dex in ECDFS (0.03 dex in HDFN) and ac scatter of 0.12 dex in the ECDFS, shown in Figure 3 (0.13 dex in the HDFN, shown in Figure 4))."," By using the new indicator, the resulting single-band 24 $\micron$ -derived has an average agreement with the far-IR observations of 0.02 dex in ECDFS (0.03 dex in HDFN) and a$\sigma$ scatter of 0.12 dex in the ECDFS, shown in Figure \ref{compare_lir_CDFS} (0.13 dex in the HDFN, shown in Figure \ref{compare_lir_HDFN}) )."585 The 0.12—0.13 dex scatters are consistent with the 0.13—dex, The $0.12-0.13$ dex scatters are consistent with the $0.13-$ dex586of small wavelengths perturbations in the radial directions (?)..,of small wavelengths perturbations in the radial directions \citep{1993A&A...267..155D}.587" The final non-linear phase with high amplitude perturbations, shown in Fig. 10,,"," The final non-linear phase with high amplitude perturbations, shown in Fig. \ref{fig:Mach6},"588 appears later than in Fig. 7.., appears later than in Fig. \ref{fig:evolution}.589 The shell is indeed thicker and presents smaller density contrasts than for high Mach numbers., The shell is indeed thicker and presents smaller density contrasts than for high Mach numbers.590 Comparing Fig., Comparing Fig.591" 9 with Fig. 10,,"," \ref{fig:NTSI_KH} with Fig. \ref{fig:Mach6},"592 the amplitude of the variations in shock location or the r.m.s of the fluctuations do not appear to change much but the oscillations in shock location seem to have a longer wavelength., the amplitude of the variations in shock location or the r.m.s of the fluctuations do not appear to change much but the oscillations in shock location seem to have a longer wavelength.593" Finally, we compare the non-linear outcome of simulations with unstable colliding wind regions in the isothermal and adiabatic cases."," Finally, we compare the non-linear outcome of simulations with unstable colliding wind regions in the isothermal and adiabatic cases."594 Figs. 5-, Figs. \ref{fig:KH_eta1}-595-6 and Fig., \ref{fig:KH_eta16} and Fig.596 9 show cases with 7=1 or n=1/16 and Ό]ου=2V20 for both the adiabatic and isothermal cases., \ref{fig:NTSI_KH} show cases with $\eta=1$ or $\eta=1/16$ and $v_{1\infty}=2v_{2 \infty}$ for both the adiabatic and isothermal cases.597 The r.m.s., The r.m.s.598 amplitude is larger for isothermal winds than for adiabatic winds when the same wind parameters are used., amplitude is larger for isothermal winds than for adiabatic winds when the same wind parameters are used.599" The unstable region extends beyond the wings of the contact discontinuity in the case of isothermal winds, unlike the adiabatic case where most of the fluctuations seem to take place within the shocked region of the weaker wind."," The unstable region extends beyond the wings of the contact discontinuity in the case of isothermal winds, unlike the adiabatic case where most of the fluctuations seem to take place within the shocked region of the weaker wind."600 The NTSI creates more small scale structures and higher density contrasts are possible when the winds are isothermal., The NTSI creates more small scale structures and higher density contrasts are possible when the winds are isothermal.601 The weaker wind still propagates freely over a significant fraction of the domain despite the strong perturbations at the interface in the isothermal case., The weaker wind still propagates freely over a significant fraction of the domain despite the strong perturbations at the interface in the isothermal case.602" In contrast, the adiabatic simulations show that the free flowing weaker wind is confined to a very small region refKH))."," In contrast, the adiabatic simulations show that the free flowing weaker wind is confined to a very small region \\ref{KH}) )."603 The wind is still expected to be confined at some distance from the star in the isothermal case (see $33.2) but this happens further away than in the adiabatic case even when the thin shell instabilities develop., The wind is still expected to be confined at some distance from the star in the isothermal case (see 3.2) but this happens further away than in the adiabatic case even when the thin shell instabilities develop.604 We have carried out 2D and 3D hydrodynamical simulations of colliding winds to study the morphology of the interaction region and the instabilities that can affect it when orbital motion can be neglected., We have carried out 2D and 3D hydrodynamical simulations of colliding winds to study the morphology of the interaction region and the instabilities that can affect it when orbital motion can be neglected.605 We first examined the relevance of widely-used analytical estimates., We first examined the relevance of widely-used analytical estimates.606 The position of the standoff point is very well predicted by the standard ram pressure balance on the of-centres., The position of the standoff point is very well predicted by the standard ram pressure balance on the line-of-centres.607" Away from the binary axis, when 7 is close to 1, the opening angle of the contact discontinuity is well approximated by the analytical solution proposed by ?,, which assumes conservation of mass and momentum in a thin shell."," Away from the binary axis, when $\eta$ is close to 1, the opening angle of the contact discontinuity is well approximated by the analytical solution proposed by \citet{Canto:1996jj}, which assumes conservation of mass and momentum in a thin shell."608" The semi-analytical solution of ?,, which assumes balance of the ram pressures normal to the surface, is a better approximation when 7<1."," The semi-analytical solution of \citet{Stevens:1992on}, which assumes balance of the ram pressures normal to the surface, is a better approximation when $\eta\ll 1$."609 This clarifies the range of validity for these approximations that have found widespread practical use in the literature., This clarifies the range of validity for these approximations that have found widespread practical use in the literature.610" Numerical simulations also show that the weaker wind can be fully confined for low η, with the presence of a backward termination (reconfinement) shock, for both isothermal and adiabatic winds."," Numerical simulations also show that the weaker wind can be fully confined for low $\eta$, with the presence of a backward termination (reconfinement) shock, for both isothermal and adiabatic winds."611" The region where the weaker wind propagates freely is reduced when the Mach number of the wind is small, when the KHI develops or when the wind is isothermal."," The region where the weaker wind propagates freely is reduced when the Mach number of the wind is small, when the KHI develops or when the wind is isothermal."612 This may have some observational consequences., This may have some observational consequences.613 One possibility is that the lines from the confined wind show unusual profiles or intensities because the wind terminates very close to the star., One possibility is that the lines from the confined wind show unusual profiles or intensities because the wind terminates very close to the star.614" Another possibility is stronger, variable absorption instead of smooth absorption when"," Another possibility is stronger, variable absorption instead of smooth absorption when"615having a cutoff energy below 200 keV. and confirms that this GRB has a very hard spectrum.,"having a cutoff energy below 200 keV, and confirms that this GRB has a very hard spectrum."616 We analyzed separately the spectra of the first and of the second peak., We analyzed separately the spectra of the first and of the second peak.617 We find evidence that the second peak is at least as hard as the first one., We find evidence that the second peak is at least as hard as the first one.618 This result is different from the hard-to- evolution that seems to be present in most GRBs (Preece et al. 1998))., This result is different from the hard-to-soft evolution that seems to be present in most GRBs (Preece et al. \cite{preece}) ).619 In this respect the properties of GRB971214 are distinct from those observed on the average in GRBs., In this respect the properties of GRB971214 are distinct from those observed on the average in GRBs.620 The burst fluences are 1.9 40.1«10‘creein.? in 2- keV and 8.8 40.8«10°erecin.? in 40-700 keV. The fluence in hard X-rays/> rays is in good agreement with that measured with BATSE (Kippen et al. 1997))., The burst fluences are 1.9 $\pm 0.4 \times 10^{-7} \flux$ in 2-10 keV and 8.8 $\pm 0.8 \times 10^{-6} \flux$ in 40-700 keV. The fluence in hard $\gamma$ rays is in good agreement with that measured with BATSE (Kippen et al. \cite{batse_fluence}) ).621 Assuming a redshift z=3.42 (Kulkarni et al. 1998)), Assuming a redshift z=3.42 (Kulkarni et al. \cite{kulkarni_n}) )622 in a standard Friedmann cosmology (with Hy=65 km ! ! and Qy=0.2) the luminosity distance is «107? em., in a standard Friedmann cosmology (with $_0$ =65 km $^{-1}$ $^{-1}$ and $\Omega_0$ =0.2) the luminosity distance is $\times 10^{29}$ cm.623 At this distance the observed fluences correspond to 6 £1.2«10°! ergs in 2-10 keV and 2.8+0.25«10° eres in 40-700 keV for an isotropically emitting source., At this distance the observed fluences correspond to 6 $\pm 1.2 \times 10^{51} $ ergs in 2-10 keV and $\pm 0.25 \times 10^{53} $ ergs in 40-700 keV for an isotropically emitting source.624" Here we assume that Low,=FyiteD7d|z)! (e. g. Hakkila et al. 1996)).", Here we assume that $_{\rm grb}={\rm F}_{\oplus} 4\pi {\rm D}_{\rm L}^2 (1+{\rm z})^{-1}$ (e. g. Hakkila et al. \cite{hakkila}) ).625" If we assume the measured slope of the GRB spectrum (see Table 1). Lowi,=Γιπο|z)b and the luminosity is a factor 1.6 lower in the hard band."," If we assume the measured slope of the GRB spectrum (see Table 1), $_{\rm grb}={\rm F}_{\oplus} 4\pi {\rm D}_{\rm L}^2 (1+{\rm z})^{-1.3}$ and the luminosity is a factor 1.6 lower in the hard band."626 The energy ranges correspond to 4.4-44 keV and 180-3090 keV at the source., The energy ranges correspond to 4.4-44 keV and 180-3090 keV at the source.627 The X-to- fraction is therefore 0.02., The $\gamma$ fraction is therefore 0.02.628 This can be compared to other fractions measured for other GRBs as reported in Frontera et al. (1999)), This can be compared to other fractions measured for other GRBs as reported in Frontera et al. \cite{frontera_grb}) )629 that range from 0.39 for to 0.01 forGRB980329., that range from 0.39 for to 0.01 for.630. Therefore this GRB shows one of the lowest ratios. i. e. the hardest spectrum. amongst those observed with BeppoSAX.," Therefore this GRB shows one of the lowest ratios, i. e. the hardest spectrum, amongst those observed with BeppoSAX."631 Of course such acomparison is madewithout taking into account possible substantial differences in redshift amongst the different GRBs., Of course such a comparison is made taking into account possible substantial differences in redshift amongst the different GRBs.632 If the emitted X-5 ray spectrum has a break somewhere above 10 keV. the redshift due to the extreme cosmological distance shifts this break to a lower energy in the spectrum as observed at earth. possibly affecting the fluence ratio.," If the emitted $\gamma$ ray spectrum has a break somewhere above 10 keV, the redshift due to the extreme cosmological distance shifts this break to a lower energy in the spectrum as observed at earth, possibly affecting the fluence ratio."633 After the detection of GRB971214 and its positioning using WFCI (Heise et al. 1997)).," After the detection of GRB971214 and its positioning using WFC1 (Heise et al. \cite{heise_grb}) ),"634 BeppoSAX was rescheduled to point the center of the WFC error box., BeppoSAX was rescheduled to point the center of the WFC error box.635 The observation started on December 15.24583 UT (~6.5 hours after the gamma-ray burst) and lasted until December 17.50069. UT for a total elapsed time of 2.25 days., The observation started on December 15.24583 UT $\sim$ 6.5 hours after the gamma–ray burst) and lasted until December 17.50069 UT for a total elapsed time of 2.25 days.636 A faint source. ISAX J1156.446513 at ανυμος 119 56 25° and doy99=+65° 13° 117 (Antonelli et al. 1997)).," A faint source, 1SAX J1156.4+6513 at $\alpha_{2000}$ = $^{\rm h}$ $^{\rm m}$ $^{\rm s}$ and $\delta_{2000}$ $^{\rm o}$ 13' 11” (Antonelli et al. \cite{antonelli}) ),"637 was clearly detected in the center of the MECS/LECS field of view., was clearly detected in the center of the MECS/LECS field of view.638 The accuracy in the position is ]., The accuracy in the position is $\sim$ 1'.639 This accuracy is largely dominated by uncertainties in the reconstructed BeppoSAX attitude in the new |-gyro mode that is implemented since summer 1997., This accuracy is largely dominated by uncertainties in the reconstructed BeppoSAX attitude in the new 1-gyro mode that is implemented since summer 1997.640 The S/N ratio for the entire observation is 12 in the MECS., The S/N ratio for the entire observation is $\sim$ 12 in the MECS.641 Therefore the source is detected with high significance., Therefore the source is detected with high significance.642 The following data analysis was performed using the SAXDAS data reduction. software. version 1.2. and the latest release of the LECS and MECS response matrices.," The following data analysis was performed using the SAXDAS data reduction software, version 1.2, and the latest release of the LECS and MECS response matrices."643 The X-5 decay curve is discussed in more detail in Heise et al. (, The $\gamma$ decay curve is discussed in more detail in Heise et al. (644in preparation).,in preparation).645 The source faded smoothly during the observation., The source faded smoothly during the observation.646 A S/N analysis of the count rates accumulated in twenty time intervals spanning the entire observation shows that the source is visible up to the end of the NFI observation., A S/N analysis of the count rates accumulated in twenty time intervals spanning the entire observation shows that the source is visible up to the end of the NFI observation.647 A X? test against constant count rate gives a chance probability <107 QA=3.7 for 19 dof)., A $\chi^2$ test against constant count rate gives a chance probability $<10^{-5}$ $\chi^2_{\rm dof}= 3.7$ for 19 dof).648" The same test performed on a light curve extracted in a source free region is consistent with a constant count rate (A2,=0.76 for 19 dof)."," The same test performed on a light curve extracted in a source free region is consistent with a constant count rate $\chi^2_{\rm dof}=6490.76$ for 19 dof)."650 The spectrum averaged on the entire observing time is consistent with a single power law with spectral index 1.6+0.2 (see Table 1)., The spectrum averaged on the entire observing time is consistent with a single power law with spectral index $\Gamma = 1.6\pm 0.2$ (see Table 1).651" The measured value of Ny raN 107+) ? is completely consistent with the expected value due to galactic absorption along the line of sight Nyyz10?"" ?."," The measured value of $_{\rm H}$ $^{+2.3}_{-1}\times 10^{21}$ ) $^{-2}$ is completely consistent with the expected value due to galactic absorption along the line of sight $_{\rm H} \approx 1.6\times65210^{20}$ $^{-2}$."653" To have a meaningful upper limit for Nyy at the GRB frame. if the association of GRB971214 with the host galaxy is correct and therefore its redshift is 3.42. the measure of Ny, coming from the formal fit with a non-redshifted function is useless."," To have a meaningful upper limit for $_{\rm H}$ at the GRB frame, if the association of GRB971214 with the host galaxy is correct and therefore its redshift is 3.42, the measure of $_H$ coming from the formal fit with a non-redshifted function is useless."654 We therefore performed also an analysis using a redshifted model., We therefore performed also an analysis using a redshifted model.655 The power law index is obviously unchanged. while the Ny; value is completely not determined.," The power law index is obviously unchanged, while the $_{\rm H}$ value is completely not determined."656good model. te. the data sets are not consistent with one another given this model. and needs to be expanded.,"good model, i.e. the data sets are not consistent with one another given this model, and needs to be expanded."657 Because of the inadequacy of model A6. we no longer assume that the instrument noise is known according to the variances oF but suspect that there could be unknown random variations or biases that differ between the data sets.," Because of the inadequacy of model $\mathcal{M}_{2}$, we no longer assume that the instrument noise is known according to the variances $\sigma_{i}^{2}$ but suspect that there could be unknown random variations or biases that differ between the data sets."658 Therefore. we expand our model set by models where the Gaussian random variable €;; is different for every data set and is assumed to consist of additional random variation caused by the instrument noise and stellar jitter.," Therefore, we expand our model set by models where the Gaussian random variable $\epsilon_{I,l}$ is different for every data set and is assumed to consist of additional random variation caused by the instrument noise and stellar jitter."659 Therefore. in this model. the resulting values σι can only be interpreted as giving the upper limit for the stellar jitter.," Therefore, in this model, the resulting values $\sigma_{I,l}$ can only be interpreted as giving the upper limit for the stellar jitter."660" We denote these models as At,;."," We denote these models as $\mathcal{M}_{I,k}$."661 Using the expanded model set. we receive the model probabilities in Table 2..," Using the expanded model set, we receive the model probabilities in Table \ref{HD217107_probabilities2}."662 These probabilities imply that there are indeed differences in the noise levels of the different data sets and that these differences have to be taken into account when assessing the orbital parameters of the planets., These probabilities imply that there are indeed differences in the noise levels of the different data sets and that these differences have to be taken into account when assessing the orbital parameters of the planets.663 We calculate the model inadequacy Bayes factor BG...m) for the best model Af;j5.," We calculate the model inadequacy Bayes factor $B(m_{1}, ..., m_{4})$ for the best model $\mathcal{M}_{I,2}$."664" This timeBGny..ma)=3.3x41077. which corresponds to an inadequacy probability of 3.010714, a value that clearly states the best model cannot be considered inadequate."," This time$B(m_{1}, ..., m_{4}) = 3.3 \times 10^{12}$, which corresponds to an inadequacy probability of $3.0 \times 10^{-13}$, a value that clearly states the best model cannot be considered inadequate."665" We have listed the solution of the model with the greatest posterior probability. Af,5. in Table 3.."," We have listed the solution of the model with the greatest posterior probability, $\mathcal{M}_{I,2}$, in Table \ref{HD217107_parameters}."666 While consistent with the results of Wrightetal.(2009).. our solution with the best model Aj» has much more uncertain parameter values. especially for the period. RV mass. and RV amplitude of the outer companion. which is also found heavily correlated with the reference velocity parameters.," While consistent with the results of \citet{wright2009}, our solution with the best model $\mathcal{M}_{I,2}$ has much more uncertain parameter values, especially for the period, RV mass, and RV amplitude of the outer companion, which is also found heavily correlated with the reference velocity parameters."667 We show the99%..95%.. and equiprobability contours of RV mass and period of the outer companion in Fig.," We show the, and equiprobability contours of RV mass and period of the outer companion in Fig."668 | (the gap in the contours arises from the numerical inaccuracy of the plot)., \ref{contour_HD217107} (the gap in the contours arises from the numerical inaccuracy of the plot).669 This Fig., This Fig.670 is similar to the Fig., is similar to the Fig.671 8 in Wrightetal.(2009).. but they used the v density for the plot instead of posterior density.," 8 in \citet{wright2009}, but they used the $\chi^{2}$ density for the plot instead of posterior density."672 Also. we note that the jitter of HD 217107 has a level of at most 6.0 ms! based on the noise in the Euler data. which turned out to contain the least noise out of the four data sets.," Also, we note that the jitter of HD 217107 has a level of at most 6.0 $^{-1}$ based on the noise in the Euler data, which turned out to contain the least noise out of the four data sets."673 It is also interesting to see that the Lick data had therefore at least 5 ms7!. but possibly even more than 10.0 ms'. additional uncertainty that can only be caused by the telescopes and the instrument.," It is also interesting to see that the Lick data had therefore at least 5 $^{-1}$, but possibly even more than 10.0 $^{-1}$, additional uncertainty that can only be caused by the telescopes and the instrument."674 Therefore. it cannot be said that the Lick instrument uncertainty is known according to the standard uncertainties of the data reduction pipeline. as reported when publishing Lick. RVs.," Therefore, it cannot be said that the Lick instrument uncertainty is known according to the standard uncertainties of the data reduction pipeline, as reported when publishing Lick RV's."675 This could in fact be one of the reasons the parameter values in our solution (Table 3)) appear to be more uncertain than those reported by Wrightetal.(2009).. though they do not indicate the confidence-level of the reported uncertainties.," This could in fact be one of the reasons the parameter values in our solution (Table \ref{HD217107_parameters}) ) appear to be more uncertain than those reported by \citet{wright2009}, though they do not indicate the confidence-level of the reported uncertainties."676 The Gliese 581 planetary system has been claimed to be a host to as many as six relatively low-mass planets (Bonfilsetal..2005:Udryetal..2007:Mayor2009:Vogt 2010).," The Gliese 581 planetary system has been claimed to be a host to as many as six relatively low-mass planets \citep{bonfils2005,udry2007,mayor2009,vogt2010}."677. Though the most likely number of planetary companions in the system is four (Tuomi.2011) or five (Gregory.201D).. the RV's of Gliese 581 provide a challenging analysis problem because the signals are only barely distinguishable from the relatively noisy Measurements.," Though the most likely number of planetary companions in the system is four \citep{tuomi2011} or five \citep{gregory2011}, the RV's of Gliese 581 provide a challenging analysis problem because the signals are only barely distinguishable from the relatively noisy measurements."678" We start by analysing the combined data set of HARPS and HIRES RV measurements (seee.g.Vogtetal.2010:Gregory.2011:Tuomi.2011) using the models At, and AM, with k=0.....5."," We start by analysing the combined data set of HARPS and HIRES RV measurements \citep[see e.g.][]{vogt2010,gregory2011,tuomi2011} using the models $\mathcal{M}_{k}$ and $\mathcal{M}_{I,k}$ with $k = 0, ..., 5$."679 We choose this model set because we already suspect. based on the analysis of the RVs of HD 217107. that this combined data set may have different noise levels corresponding to the different telescope-instrument combinations.," We choose this model set because we already suspect, based on the analysis of the RV's of HD 217107, that this combined data set may have different noise levels corresponding to the different telescope-instrument combinations."680 The posterior probabilities of the models in our model set are shown in Table 4.., The posterior probabilities of the models in our model set are shown in Table \ref{GJ581_probabilities}. .681 These probabilities. while having the greatest value for model At;s. do not support the conclusion that there are five Keplerian signalsin the data strongly enough because the probability of model Λι 1s highly significant.," These probabilities, while having the greatest value for model $\mathcal{M}_{I,5}$ , do not support the conclusion that there are five Keplerian signalsin the data strongly enough because the probability of model $\mathcal{M}_{I,4}$ is highly significant."682abundances observed in the jet are the product of recent star formation.,abundances observed in the jet are the product of recent star formation.683 Temperature and abundance maps of the poor cluster AWM 4 reveal a high degree of structure in this relatively relaxed poor cluster., Temperature and abundance maps of the poor cluster AWM 4 reveal a high degree of structure in this relatively relaxed poor cluster.684 Features in both temperature and abundance are found to correlate with the jets of the central radio source. with a coo region corresponding to the eastern lobe and cavity. and supersolar abundances extending from the galaxy core along both jets.," Features in both temperature and abundance are found to correlate with the jets of the central radio source, with a cool region corresponding to the eastern lobe and cavity, and supersolar abundances extending from the galaxy core along both jets."685 Testing against normal spectral analysis. and variation of the number of counts and energy band used in the map spectral fits shows the maps to be reliable. and we conclude that the features corresponc to real physical structures within the ICM.," Testing against normal spectral analysis, and variation of the number of counts and energy band used in the map spectral fits shows the maps to be reliable, and we conclude that the features correspond to real physical structures within the ICM."686 The location of high abundances along the jets suggests that material enriched in the inner parts of NGC 6051 has been entrained and is being transported out of the galaxy. roughly along its minor axis.," The location of high abundances along the jets suggests that material enriched in the inner parts of NGC 6051 has been entrained and is being transported out of the galaxy, roughly along its minor axis."687 The mass of iron required to produce such a feature (~L45109LL assuming enrichment by 9) is relatively modest. and it is likely that it could be produced in the central region of NGC 6051 on a timescale comparable to that estimated for the AGN outburst.," The mass of iron required to produce such a feature $\sim1.4\times10^6$, assuming enrichment by ) is relatively modest, and it is likely that it could be produced in the central region of NGC 6051 on a timescale comparable to that estimated for the AGN outburst."688 The energy required to transport the gas to its observed location is ὃςNS«107 erg. depending on the abundance of the uplifted material and the gas it mixes with.," The energy required to transport the gas to its observed location is $\sim3-8\times10^{57}$ erg, depending on the abundance of the uplifted material and the gas it mixes with."689 This is a significant fraction of the estimated total energy required to inflate the lobes of the radio source., This is a significant fraction of the estimated total energy required to inflate the lobes of the radio source.690 An extended region of abundances which extends out to 65 kpe in the ICM is also likely a product of enrichment by the central galaxy. though over timescales much longer than the AGN outburst.," An extended region of near-solar abundances which extends out to $\sim$ 65 kpc in the ICM is also likely a product of enrichment by the central galaxy, though over timescales much longer than the AGN outburst."691 Galaxy motions and previous AGN outbursts may have contributed to transporting metals into this region., Galaxy motions and previous AGN outbursts may have contributed to transporting metals into this region.692 While it is possible that some degree of bias affects the abundance measurements. arising either from the complex temperature structure of the ICM or from non-thermal electron populations associated with the jets. neither possibility seems able to explain the observed abundance structures.," While it is possible that some degree of bias affects the abundance measurements, arising either from the complex temperature structure of the ICM or from non-thermal electron populations associated with the jets, neither possibility seems able to explain the observed abundance structures."693 We therefore conclude that AWM 4 is one of the growing number of systems in which evidence is seen for enrichment of the ICM via entrainment of high-abundance gas by radio jets., We therefore conclude that AWM 4 is one of the growing number of systems in which evidence is seen for enrichment of the ICM via entrainment of high-abundance gas by radio jets.694 The authors thank the anonymous referee for a number of comments which have materially improved the paper., The authors thank the anonymous referee for a number of comments which have materially improved the paper.695 Support for his work was provided by the National Aeronautics and Space Administration through Chandra Award Number GOS8-9127X-R issued by the Chandra X-ray Observatory Center. which is operated by the Smithsonian Astrophysical Observatory for and on behalfof ASA under contract NAS8-03060.," Support for this work was provided by the National Aeronautics and Space Administration through Chandra Award Number GO8-9127X-R issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060."696 E. O'Sullivan acknowledges qe support of the European Community under the Marie Curie Research Training Network., E. O'Sullivan acknowledges the support of the European Community under the Marie Curie Research Training Network.697 We thank the staff of the GMRT for jeir help during the observations., We thank the staff of the GMRT for their help during the observations.698 GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of fundamental Research., GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of fundamental Research.699 We acknowledge the usage of the HyperLeda database rttp://leda.univ-lyon|fr)., We acknowledge the usage of the HyperLeda database (http://leda.univ-lyon1.fr).700hese abrupt transitions. which we refer to as turning points.,"these abrupt transitions, which we refer to as turning points."701 At least four abrupt transitions of drift. directions from »ositive to negative were also noticed by BSS. designated by hem as a runazwas effect. in a sequence of about 2860 single ruses at 645 MlIE," At least four abrupt transitions of drift directions from positive to negative were also noticed by B85, designated by them as a `runaway' effect, in a sequence of about 2860 single pulses at 645 MHz."702: Our data sets suggest that the progress rom turning point to turning point is a repeating pattern. with a time scale ranging from tens to some hunelrecds of »ulsar periods.," Our data sets suggest that the progress from turning point to turning point is a repeating pattern, with a time scale ranging from tens to some hundreds of pulsar periods."703 The drift rate in region HE ranges from about —3.27/P? (late to carly) to about 3.67/P (carly to late). changing continuously. within some tens to several hundreds of pulse »eriods.," The drift rate in region III ranges from about $-3.2^\circ /P$ (late to early) to about $3.6^\circ /P$ (early to late), changing continuously within some tens to several hundreds of pulse periods."704 This range is significantly larger than that [rom 1.5/P to 2.1/P measured by BSS at 645 MlIz: their smaller value for the range may however be due to the lower signal-to-noise ratio of their data.," This range is significantly larger than that from $-1.5^\circ705/P$ to $2.1^\circ /P$ measured by B85 at 645 MHz; their smaller value for the range may however be due to the lower signal-to-noise ratio of their data."706 As shown in Fig., As shown in Fig.707 3 and Fig., 3 and Fig.708 7. the average drift rate of drifting subpulses in region Lis slightly smaller than that in region LLL," 7, the average drift rate of drifting subpulses in region I is slightly smaller than that in region III."709 ln region LL as well as in longitude range 207< 567. the drifting subpulses present a larecr drift rate than others within the whole longitude range.," In region II, as well as in longitude range $20^\circ< l <56^\circ$ , the drifting subpulses present a larger drift rate than others within the whole longitude range."710 Bs5 noted that strong subpulses in region I occurred more frequently when the drift was from carly to later longitudes., B85 noted that strong subpulses in region I occurred more frequently when the drift was from early to later longitudes.711 We lookecl for and found similar ellects in our observations., We looked for and found similar effects in our observations.712 In Fig., In Fig.713 S. we compare the integrated. profiles produced. by single pulses within three drift rate ranges so as to show the variation of average profile intensity in three different cirift states.," 8, we compare the integrated profiles produced by single pulses within three drift rate ranges so as to show the variation of average profile intensity in three different drift states."714 The drift ranges we chose to produce these average xolile are D>0.5/P. Dx.0.5/P and |D|«0.5/P. measured in region Ill," The drift ranges we chose to produce these average profile are $D\geq 0.5^\circ /P$, $D\leq -0.5^\circ /P$ and $|D|<0.5^\circ /P$, measured in region III."715 Relative to the averaec profiles »oduced by pulses with the most negative drift rates (solid ines). the profiles corresponding to the small (dashed) ane most positive (dotted) drift rates have increasingly enhanced intensity in the whole of region L while the profile around the cacing and. trailing edges of region LL is weakened.," Relative to the average profiles produced by pulses with the most negative drift rates (solid lines), the profiles corresponding to the small (dashed) and most positive (dotted) drift rates have increasingly enhanced intensity in the whole of region I, while the profile around the leading and trailing edges of region III is weakened."716 These dilferences are important in our discussion of the possible role of aliasing in our interpretation of the drifting subpulse ULtern., These differences are important in our discussion of the possible role of aliasing in our interpretation of the drifting subpulse pattern.717 The dependence of pulse profile on drift rate can also »e Followed for individual pulses bv integrating the intensity separately over regions Land LIE. as shown in Fig.," The dependence of pulse profile on drift rate can also be followed for individual pulses by integrating the intensity separately over regions I and III, as shown in Fig."718 9., 9.719 Here the wo plots (repeated for the two cats sets A and D) show the intensities of single pulses averaged in regions E and HE as à 'unction of drift rate., Here the two plots (repeated for the two dats sets A and B) show the intensities of single pulses averaged in regions I and III as a function of drift rate.720 Phe average intensities used in these ots are shown on the left and right hand sides respectively of the longitude-time diagrams in Fig., The average intensities used in these plots are shown on the left and right hand sides respectively of the longitude-time diagrams in Fig.721 3., 3.722 The modulation of average Dux density in these regions is clearly associated with the drift rate., The modulation of average flux density in these regions is clearly associated with the drift rate.723 The two top panels in Fig., The two top panels in Fig.724 9 (from the two data sets) confirm the conclusion [from Fig., 9 (from the two data sets) confirm the conclusion from Fig.725 δ that the emission in region Lincereases with the increasing αρ rate. while the two lower panels show a small opposite effect in region IL.," 8 that the emission in region I increases with the increasing drift rate, while the two lower panels show a small opposite effect in region III."726 As we noted in the previous section. the drift behaviour of the pulsar frequently. follows a repeating pattern [rom turning point to turning point.," As we noted in the previous section, the drift behaviour of the pulsar frequently follows a repeating pattern from turning point to turning point."727 Generally. the whole pattern of subpulses crifts from late to earlier longitudes. is stable [or several pulses. and then clrifts from. earlier to. later longitudes.," Generally, the whole pattern of subpulses drifts from late to earlier longitudes, is stable for several pulses, and then drifts from earlier to later longitudes."728 Fig., Fig.729 9 implies that the intensity modulation of the pulsar follows the same evele as the drift., 9 implies that the intensity modulation of the pulsar follows the same cycle as the drift.730 ErequentlIvy. subpulse emission in region LLL rises significantly in pulses immediately before the turning points. and. it drops significantly at the beginning of the next drifting cvele.," Frequently, subpulse emission in region III rises significantly in pulses immediately before the turning points, and it drops significantly at the beginning of the next drifting cycle."731 Previous studies in a number of other drifting pulsars have noticed that the changing of integrated. profile shape is associated with a variation of drift rate., Previous studies in a number of other drifting pulsars have noticed that the changing of integrated profile shape is associated with a variation of drift rate.732 This has been, This has been733 (2). (77).," \citep{wr78}, \citep{sz78,bkw01}."734eedee ↓⋠∖↕⋠↴∙↜↕∏⋯↕⋯⇜↧⋮⋯⋠↴⋝↕⋅↕⋠↰∙↜↕∏↴∖↴↾⋮↕↕∷∖↴⋂↕⋮↕↕⋅≝⋠∖⋠↧↕⋝↾⋮↕↕↓≼⋡⋠∖⋝↕↓⋮↕↖↽⋠∖ LO?E... (oe.2277?T2). (e.c.227?7?)..," $10^9~L_{\sun}$ \citep[e.g.][]{helmi-etal99,majewski-etal03,yanny-etal03,belokurov-etal07,735carollo-etal07,bell-etal08,bell-etal10,xue-etal10,cooper-etal11}. \citep[e.g.][]{beck-etal82,736malin97,zheng-etal99,martinezdelgado-etal08,martinezdelgado-etal10}."737 observations lave identified prominent tidal streams buttress the hicrarchical model of galactic halo thatformation., observations have identified prominent tidal streams that buttress the hierarchical model of galactic halo formation.738 Ilowever. the fundamental Lanits im such studies are flat fielding errors and the of the backeround sEv. which make global halobrightness properties aud UL fante. ws:ace brigh:0 an]d : iE.," However, the fundamental limits in such studies are flat fielding errors and the brightness of the background sky, which make global halo properties and very faint surface brightness features inaccessible \citep{dejong08}."739" Ἡ ox "" MM »nM difficulties. Dunesa vi mie 1ias been eniploved: resolvig niNπα]"" brish stars. recentlyparticularly red eiant branch (ROB) stars which are present 1:! stt|WM populations,. iu' the halos of. external galaxies."," In order to overcome these difficulties, a new technique has recently been employed: resolving individual bright stars, particularly red giant branch (RGB) stars which are present in all stellar populations, in the halos of external galaxies."740 allWithin the past few vears. knowledge of the lshalo of M31 ≻has blossomed↴↴∖⇁⋅ with this⋅↴∖⊳⋅∖ technique. including the discovery of a metallicity eradicut. rich spatial and kinematic substructure. aud a global profile that is remarkably similay to that of the Miülkv Way (UT.," Within the past few years, knowledge of the halo of M31 has blossomed with this technique, including the discovery of a metallicity gradient, rich spatial and kinematic substructure, and a global profile that is remarkably similar to that of the Milky Way \citep{chapman-etal06,kalirai-etal06,ibata-etal07,mcconnachie-etal09,tanaka-etal10}."741 Deteetious of halo Savs du amore distaut ealaxies are now beeiuniug to be achieved. such as in individual small IIST/ACS fields of NGC 5128 (7) and M sl (2). and in NGC 891 using ground-based ΡΕΠΡΠΠ data over a large field of view (7?)..," Detections of halo stars in more distant galaxies are now beginning to be achieved, such as in individual small HST/ACS fields of NGC 5128 \citep{rejkuba-etal05} and M 81 \citep{durrell-etal10}, and in NGC 891 using ground-based Subaru/Suprime-Cam data over a large field of view \citep{mouhcine-etal10}."742 One particularly interesting target is NGC 253., One particularly interesting target is NGC 253.743 This nearly edee-on starburst) galaxy. oue of the largest ealaxies in the “Sculptor eroup” (whichisuottrulyalineofsight: ??7).. is of similar luwinosity to the Milky Wav and M3. allowing direct conrparisous.," This nearly edge-on starburst galaxy, one of the largest galaxies in the “Sculptor group” \citep[which is not744truly a bound group, but rather a filament extended along the line of745sight;][]{jerjen-etal98,karachentsev-etal03-scl}, is of similar luminosity to the Milky Way and M31, allowing direct comparisons."746 Deep optical inages have long shown au optical ilo extending bevoud its disk. with evidence for a shelt-lise feature to the south of the disk (??).. ?..," Deep optical images have long shown an optical halo extending beyond its disk, with evidence for a shelf-like feature to the south of the disk \citep{beck-etal82,malin97}. \citet{fitzgibbons90},"747 in a photographic survey of the ealaxy. also detected exteuded structure to tre south of the galactic disk. particularly in he Z baud.," in a photographic survey of the galaxy, also detected extended structure to the south of the galactic disk, particularly in the $I$ band."748 He found a total light profile in the halo that declines as a powcr law with aniudex of ~2.5 and ~3.5 un tjio Vaud { binds respectively., He found a total light profile in the halo that declines as a power law with anindex of $\sim -2.5$ and $\sim -3.5$ in the $V$ and $I$ bands respectively.749 Resolved nearufrared stellar plotometiy o the, Resolved near-infrared stellar photometry of the750Let us consider a plane-parallel layer in the low chromosphere (~ 800 km above the photosphere) formed by Ba tons and illuminated anisotropically by the photospheric continuum radiation field.,Let us consider a plane-parallel layer in the low chromosphere $\sim$ 800 km above the photosphere) formed by Ba ions and illuminated anisotropically by the photospheric continuum radiation field.751 In a weakly polarizing medium like the solar atmosphere one can safely neglect the contribution of polarization to the excitation of Ba 10ns., In a weakly polarizing medium like the solar atmosphere one can safely neglect the contribution of polarization to the excitation of Ba ions.752 Assuming that the incident radiation has cylindrical symmetry around the local solar vertical through the scattering center. only the multipole orders & = 0 (mean intensity ο)0 and k = 2 (radiation tensor J5J2 associated to the anisotropy) are needed to fully describe the incident radiation.," Assuming that the incident radiation has cylindrical symmetry around the local solar vertical through the scattering center, only the multipole orders $k$ = 0 (mean intensity $J^0_0$ ) and $k$ = 2 (radiation tensor $J^2_0$ associated to the anisotropy) are needed to fully describe the incident radiation."753" For each wavelength. the value of the anisotropy factor Gv=V2Iz/ I"") and of the number of photons per mode (7=Ic?[2hy?» are obtained from Fig."," For each wavelength, the value of the anisotropy factor $w=\sqrt{2}J^2_0/J^0_0$ ) and of the number of photons per mode $\bar{n}=J^0_0(c^2/2h\nu^3)$ ) are obtained from Fig."754 2 of Manso Sainz Landi DeelInnocenti (2002)., 2 of Manso Sainz Landi Degl'Innocenti (2002).755 In particular. for the Ba 4554 line. we obtain w=0.16 and #=2.59x107 which are similar to the values calculated by Belluzzi et al. (," In particular, for the Ba ${\lambda}4554$ line, we obtain $w=0.16$ and $\bar{n}=2.59 \times 10^{-3}$ which are similar to the values calculated by Belluzzi et al. ("7562007).,2007).757 We verified that a reasonable modification of w and 5i (Le. by around 10%)) do not affect the results of the present work., We verified that a reasonable modification of $w$ and $\bar{n}$ (i.e. by around ) do not affect the results of the present work.758 Obviously. a realistic simulation of the line formation conditions requires a careful consideration of the transfer of radiation in à medium that is not optically thin.," Obviously, a realistic simulation of the line formation conditions requires a careful consideration of the transfer of radiation in a medium that is not optically thin."759 This problem ts out of the scope of this paper., This problem is out of the scope of this paper.760 The formulae we use to compute the linear polarization for the case of a tangential observation in a plane-parallel atmosphere is presented. for example. in Sect.," The formulae we use to compute the linear polarization for the case of a tangential observation in a plane-parallel atmosphere is presented, for example, in Sect."761 2 of Derouich et al. (, 2 of Derouich et al. (7622007).,2007).763 A simplified atomic model approximation (Fig. 1)), A simplified atomic model approximation (Fig. \ref{figure1}) )764 can reduce considerably the numerical rald theoretical calculations especially if the transfer of radiation effects are considered., can reduce considerably the numerical and theoretical calculations especially if the transfer of radiation effects are considered.765 However. the hypothesis of neglecting metastable d-sates in the Ba 11954 line modeling is highly questionable.," However, the hypothesis of neglecting metastable $d$ -sates in the Ba ${\lambda}4554$ line modeling is highly questionable."766 We calculate the polarization p=Q// using the simplified atomic model (see Fig. 1)), We calculate the polarization $p=Q/I$ using the simplified atomic model (see Fig. \ref{figure1}) )767 and the 5 levels-5 lines model (see Fig. 2)), and the 5 levels-5 lines model (see Fig. \ref{figure2}) )768 which accounts for the metastable d-levels., which accounts for the metastable $d$ -levels.769 We find that the simplified model overestimates the polarization degree of the Ba 14554: Thus. a more realistic diagnostic of the polarization of this line should be performed im the framework of 5 levels-5 lines model.," We find that the simplified model overestimates the polarization degree of the Ba ${\lambda}4554$: Thus, a more realistic diagnostic of the polarization of this line should be performed in the framework of 5 levels-5 lines model."770 In the description of the Bai. we neglect the contribution of the hyperfine structure.," In the description of the Ba, we neglect the contribution of the hyperfine structure."771 There are no additional conceptual difficulties for including. the contribution of the hyperfine relaxation and polarization transfer rates by isotropic collision., There are no additional conceptual difficulties for including the contribution of the hyperfine relaxation and polarization transfer rates by isotropic collision.772 Our main conclusions concerning the evidence for collisional depolarization of the 14954 line remain unchanged., Our main conclusions concerning the evidence for collisional depolarization of the ${\lambda}4554$ line remain unchanged.773 The collisional evolution of the density matrix components TIEN is due to the gain-terms denoted as polarization transfer rates and to the loss-terms denoted as relaxation rates., The collisional evolution of the density matrix components $\rho_{q}^{k} (J)$ is due to the gain-terms denoted as polarization transfer rates and to the loss-terms denoted as relaxation rates.774 The polarization, The polarization775was somewhat narrower than the true one even though the v; distribution was very closely fitted.,was somewhat narrower than the true one even though the $v_\phi$ distribution was very closely fitted.776 Correspondingly. in the case of the GCS data. the failure of the tit to the v; to adequately populate populate the wings of the distribution is mirrored in the fit to the vj distribution in Fig.," Correspondingly, in the case of the GCS data, the failure of the fit to the $v_\phi$ to adequately populate populate the wings of the distribution is mirrored in the fit to the $v_R$ distribution in Fig."777 9 being least satisfactory in the wings., \ref{fig:GCSfitU} being least satisfactory in the wings.778 The distribution of azimuthal velocities in the dise of a galaxy like ours is very skew and varies systematically with distance from the plane., The distribution of azimuthal velocities in the disc of a galaxy like ours is very skew and varies systematically with distance from the plane.779 Naturally one wants to be able to quantify such a distribution in an ettective way., Naturally one wants to be able to quantify such a distribution in an effective way.780 The traditional approach of fitting it with a superposition of Gaussians (e.g.Bensbyetal.2003:Iveziéetal.2008:MeConnachie2006) is unsatisfactorv. both because there is no physical reasoning behind the use of a Gaussian when the distribution is not dominated by measurement error. and because when a superposition of Gaussians is used. the parameters of the fit are neither unique nor physically informative.," The traditional approach of fitting it with a superposition of Gaussians \citep[e.g.][]{Bensby03,Ivz08,McCo06} is unsatisfactory, both because there is no physical reasoning behind the use of a Gaussian when the distribution is not dominated by measurement error, and because when a superposition of Gaussians is used, the parameters of the fit are neither unique nor physically informative."781 Our formula is based on the approximation that the vertica actions of stars are invariant as stars oscillate radially., Our formula is based on the approximation that the vertical actions of stars are invariant as stars oscillate radially.782 We have refined this approximation by considering anew the impact tha vertical motion has on the radial oscillations. which BMII founc to be a significant effect.," We have refined this approximation by considering anew the impact that vertical motion has on the radial oscillations, which BM11 found to be a significant effect."783 Our treatment of this effect. being based on overall energy conservation. is conceptually much sounder than that of BMII and promises to play a valuable role in the interpretation of stellar velocities with rigorous dynamical models.," Our treatment of this effect, being based on overall energy conservation, is conceptually much sounder than that of BM11 and promises to play a valuable role in the interpretation of stellar velocities with rigorous dynamical models."784 However. we find that the power of our formula is only marginally improved by our more rigorous treatment of how vertical motion affects the radial oscillations.," However, we find that the power of our formula is only marginally improved by our more rigorous treatment of how vertical motion affects the radial oscillations."785 Ultimately. our formula is just a fitting formula rather than a dynamical theory. even though we have derived it from dynamical considerations.," Ultimately, our formula is just a fitting formula rather than a dynamical theory, even though we have derived it from dynamical considerations."786 Something the derivation highlights is how closely the horizontal and vertical motions of stars are intertwined. notwithstanding the adiabatie invariance of actions.," Something the derivation highlights is how closely the horizontal and vertical motions of stars are intertwined, notwithstanding the adiabatic invariance of actions."787 Because both the vertical and horizontal random velocities of stars increase with age. as one moves away from the plane the mix of stars one sees fundamentally changes in the sense of increasing age and decreasing radius of birth.," Because both the vertical and horizontal random velocities of stars increase with age, as one moves away from the plane the mix of stars one sees fundamentally changes in the sense of increasing age and decreasing radius of birth."788 The cleanest way to model this phenomenon is by means of à like those presented by Binney(2010). but a couple of computationally challenging steps are required. to extract observationally testable velocity distribution such as Πο) from üΡΕ: first a connection has to be established between ordinary phase-space coordinates and the isolating integrals upon which the ddepends. and then one has to marginalise over two velocities.," The cleanest way to model this phenomenon is by means of a like those presented by \cite{B10}, but a couple of computationally challenging steps are required to extract observationally testable velocity distribution such as $n(v_\phi)$ from a: first a connection has to be established between ordinary phase-space coordinates and the isolating integrals upon which the depends, and then one has to marginalise over two velocities."789 Evaluation of our formula is trivial by comparison., Evaluation of our formula is trivial by comparison.790 Our derivation makes it plain that no population of stars can simultaneously have scale-height and velocity dispersion that are both independent of radius: the sub-population formed by stars that have a narrow range of angular momenta must inevitably increase in scale-height and decrease in vertical velocity dispersion with increasing A. and if stars of larger angular momenta are added in to hold constant the scale-height. they will have to have an even smaller vertical velocity dispersion. so the vertical dispersion of the entire population will decline steeply outwards.," Our derivation makes it plain that no population of stars can simultaneously have scale-height and velocity dispersion that are both independent of radius: the sub-population formed by stars that have a narrow range of angular momenta must inevitably increase in scale-height and decrease in vertical velocity dispersion with increasing $R$, and if stars of larger angular momenta are added in to hold constant the scale-height, they will have to have an even smaller vertical velocity dispersion, so the vertical dispersion of the entire population will decline steeply outwards."791 Given this situation. it is unwise to seek to detine the thick disc in terms of a given scale-height and velocity dispersion. as some recent papers have done.," Given this situation, it is unwise to seek to define the thick disc in terms of a given scale-height and velocity dispersion, as some recent papers have done."792" We validated our fitting formula by using it to fit the distributions of v, components at several distances from the plane in a model with a well-defined tthat included both thin and thick discs.", We validated our fitting formula by using it to fit the distributions of $v_\phi$ components at several distances from the plane in a model with a well-defined that included both thin and thick discs.793 Excellent fits were obtained., Excellent fits were obtained.794 The values of the fitting parameters varied slightly with the level of sophistication of the model employed. but were broadly in agreement with the values we would expect given the underlyingDF.. especially when the most sophisticated approximations were used.," The values of the fitting parameters varied slightly with the level of sophistication of the model employed, but were broadly in agreement with the values we would expect given the underlying, especially when the most sophisticated approximations were used."795 This exercise implies that physical significance can be attached to the values of parameters derived from fits to real data., This exercise implies that physical significance can be attached to the values of parameters derived from fits to real data.796" Each fit to a v, distribution implies a model of the corresponding vy distribution.", Each fit to a $v_\phi$ distribution implies a model of the corresponding $v_R$ distribution.797 In our tests these models turned out to be very useful although showing a slight tendency to be too narrow at small , In our tests these models turned out to be very useful although showing a slight tendency to be too narrow at small $|z|$.798We fitted the formula to the v4 velocities of GCS stars and obtained good but not perfect fits for plausible values of the parameters., We fitted the formula to the $v_\phi$ velocities of GCS stars and obtained good but not perfect fits for plausible values of the parameters.799 The blemishes in these fits will arise from three causes: (1) the well known presence of pronounced clumping of stars in the (CU.V) plane (Dehnen1998).. (iD) the need to model subtle selection etfects in the GCS sample. and (ii) our formula is derived from an isothermal aand must encounter dithculty fitting data drawn from a system that is a superposition of systems with very disparate dynamical temperatures.," The blemishes in these fits will arise from three causes: (i) the well known presence of pronounced clumping of stars in the $(U,V)$ plane \citep{Dehnen98}, (ii) the need to model subtle selection effects in the GCS sample, and (iii) our formula is derived from an isothermal and must encounter difficulty fitting data drawn from a system that is a superposition of systems with very disparate dynamical temperatures."800 Hence in part the dithculties encountered in fitting the GCS data may reflect the importance at the extremes of the ry. distribution of the thick dise and/or stellar halo., Hence in part the difficulties encountered in fitting the GCS data may reflect the importance at the extremes of the $v_\phi$ distribution of the thick disc and/or stellar halo.801 With a larger body of data. or data taken further from the plane. it might be protitable to fit the data to a sum of two or more instances of our formula.," With a larger body of data, or data taken further from the plane, it might be profitable to fit the data to a sum of two or more instances of our formula."802" Our fit to the v, components yields a model of the v, components that", Our fit to the $v_\phi$ components yields a model of the $v_R$ components that803uncertainties in the measured Uuxes. so this is not the dominant source of uncertainty.,"uncertainties in the measured fluxes, so this is not the dominant source of uncertainty."804 We tabulate our photometric results in Table 2.., We tabulate our photometric results in Table \ref{HSTPhotTable}.805 Since we are measuring counts across a broad. bandpass rather than monochromatic Uuxes. we tabulate the data in two wavs: the corrected. number of electrons. per second. and the average flux per unit wavelength using photometric zero-points estimated. by the ACS pipeline.," Since we are measuring counts across a broad bandpass rather than monochromatic fluxes, we tabulate the data in two ways; the corrected number of electrons per second, and the average flux per unit wavelength using photometric zero-points estimated by the ACS pipeline."806 All have been corrected for CPL. and to a nominal infinite aperture.," All have been corrected for CTI, and to a nominal infinite aperture."807 We obtained simultaneous 2 band observations using the Thomson CCD camera at the mm. LAC'SO [rom 05:51 WY on the night of 2003 July 28/29., We obtained simultaneous $R$ band observations using the Thomson CCD camera at the m IAC80 from 20:50--05:51 UT on the night of 2003 July 28/29.808 We used ss exposures with 52ss readout time between them ancl bias-corrected. and. Hat-fielded: all images in the standard. wav usingIRAE., We used s exposures with s readout time between them and bias-corrected and flat-fielded all images in the standard way using.809" Seeing conditions were not good enough to cleanly separate the contribution of the target and its nearby (1.47)) line-oFsieht star (Udalski&Ixaluzni1991). so we applied: straightforward aperture photometry using a Large aperture of 3.5""which adds the flux [rom both stars. as described by Zuritaetal.(2004)..", Seeing conditions were not good enough to cleanly separate the contribution of the target and its nearby ) line-of-sight star \citep{Udalski:1991a} so we applied straightforward aperture photometry using a large aperture of which adds the flux from both stars as described by \citet{Zurita:2004a}.810 We determine an average magnitude 2=16.63£0.01 in acceptably close agreement with Casaresetal.(1993).. indicating little cilference in the optical brightness of the system compared to earlier data.," We determine an average magnitude $R=16.63\pm0.01$ in acceptably close agreement with \citet{Casares:1993a}, indicating little difference in the optical brightness of the system compared to earlier data."811 To reconstruct the optical SED of the source we use the WAIT data from the program., To reconstruct the optical SED of the source we use the WHT data from the program.812 This covered a Larger range of wavelengths than the Gemini data. and was sipiultaneous with the oobservations.," This covered a larger range of wavelengths than the Gemini data, and was simultaneous with the observations."8131) These observations used the 11 dual-aem spectrograph on the WIIT., These observations used the ISIS dual-arm spectrograph on the WHT.814. To maximise efficiency and minimise readout time and noise. we used the single red-arni mode with the R3IGR. erating and. NLABC'ONI2 CCD.," To maximise efficiency and minimise readout time and noise, we used the single red-arm mode with the R316R grating and MARCONI2 CCD."815 We set exposure times to 200ss. with I7 ss dead-time between exposures.," We set exposure times to s, with $\sim17$ s dead-time between exposures."816 To maximise photometric accuracy. we used a sslit. so our spectral resolution was determined by the secing (median ~L37)). and was typically ~5.5 +).," To maximise photometric accuracy, we used a slit, so our spectral resolution was determined by the seeing (median $\sim1.3$ ), and was typically $\sim5.5$ $^{-1}$ )."817 We performed: bias correction ancl Hat ielding using standard. LRAK techniques., We performed bias correction and flat fielding using standard IRAF techniques.818 “Phe slit was oriented in the same was as in our previous observations and covered the same comparison star., The slit was oriented in the same was as in our previous observations and covered the same comparison star.819 We extracted spectra of xh of these stars. and the nearby blended star. with the same techniques previously described (IEvnes2002:: Hyvnesetal.20023).," We extracted spectra of both of these stars, and the nearby blended star, with the same techniques previously described \citealt{Hynes:2002b}; \citealt{Hynes:2002a}) )."820" We performed wavelength calibration relative o à single observation of a CuNe/CuXr lamp and corrected or time-dependent. variations in the wavelength calibration using ""Tellurie absorption features.", We performed wavelength calibration relative to a single observation of a CuNe/CuAr lamp and corrected for time-dependent variations in the wavelength calibration using Telluric absorption features.821 We calibrated the on-slit comparison star relative to Ixoplf 27 (Stone1977).. and then calibrated all spectra of rrelative to this on-slit comparison.," We calibrated the on-slit comparison star relative to Kopff 27 \citep{Stone:1977a}, and then calibrated all spectra of relative to this on-slit comparison."822 To compare the WIP data with that from the LXC'SO we perform synthetic photometry convolving the spectrum with a R bandpass., To compare the WHT data with that from the IAC80 we perform synthetic photometry convolving the spectrum with a $R$ bandpass.823 We found an olfset between the two. most likely due to svstematic errors in the WIIT calibration.," We found an offset between the two, most likely due to systematic errors in the WHT calibration."824 Since the LACSO photometry agrees well with earlier measures we assume that this calibration is correct ancl rescaled the WIPE data up by a factor of 1.3 to agree with the LACSO /? band data., Since the IAC80 photometry agrees well with earlier measures we assume that this calibration is correct and rescaled the WHT data up by a factor of 1.3 to agree with the IAC80 $R$ band data.825 We used additional optical spectroscopy obtained with the 11521 erating and standard ELV CCDs of the GMOS spectrograph on Gemini-N to extend our continuum lighteurve., We used additional optical spectroscopy obtained with the R831 grating and standard EEV CCDs of the GMOS spectrograph on Gemini-N to extend our continuum lightcurve.826 Exposure times were 40ss and. we binned ancl windowed the images to reduce the dead-time between exposures to ss. With a sslit and mumedian seeing we obtained a spectral resolution of 5)., Exposure times were s and we binned and windowed the images to reduce the dead-time between exposures to s. With a slit and median seeing we obtained a spectral resolution of $^{-1}$ ).827 We performed. data. reduction. spectral extraction. and wavelength and Bux calibration in the same wav as for the WIIT data.," We performed data reduction, spectral extraction, and wavelength and flux calibration in the same way as for the WHT data."828 Waveleneth calibration used a Cur lamp. and we performed. [ux calibration relative to the same on-slit comparison star as used for the WIUE observations. ancl applied the same rescaling to ensure consisteney with LACSO photometry.," Wavelength calibration used a CuAr lamp, and we performed flux calibration relative to the same on-slit comparison star as used for the WHT observations, and applied the same rescaling to ensure consistency with IAC80 photometry."829 We use data taken from two recent Chandra observations of V404 Cve. one on 2000 April 26 for ss (Garciactal. 2001.. Kongetal. 2002)). ancl another on 2003 July 28/29 for a total of 61.200ss (Lvnesetal.2004)..," We use data taken from two recent Chandra observations of V404 Cyg, one on 2000 April 26 for s \citealt{Garcia:2001a}, \citealt{Kong:2002a}) ), and another on 2003 July 28/29 for a total of s \citep{Hynes:2004a}."830 The first observation used L/4 sub-array mode. with time resolution of ss: while the seconc used L/8 sub-uray mode. with a resolution of O.4ss. In the original set. 1587 counts were reported. while the second had. 1941 counts.," The first observation used 1/4 sub-array mode, with time resolution of s; while the second used 1/8 sub-array mode, with a resolution of s. In the original set, 1587 counts were reported, while the second had 1941 counts."831 We reanalyzed the standard pipeline-processed Ievel-2 data from both data sets in CLAO v3.2., We reanalyzed the standard pipeline-processed level-2 data from both data sets in CIAO v3.2.832 The extraction aperture was set to a radius of 6-pixels and we retained only events between kkeV to reduce the background., The extraction aperture was set to a radius of 6-pixels and we retained only events between keV to reduce the background.833 The background can be particularly significant for the S3 chip. so we used [large background regions with a 48-pixecl radius.," The background can be particularly significant for the S3 chip, so we used large background regions with a 48-pixel radius."834 The background: produced approximately 4.6 counts in the source aperture for the 2003 observation. and 0.2 counts in the 2000 observation.," The background produced approximately 4.6 counts in the source aperture for the 2003 observation, and 0.2 counts in the 2000 observation."835the restrietecl three-body problemi ancl it is assumed. that the mass transfer between components of the system occurs through the vicinity of inner Lagrangian point Ly. where pressure eracicnt is not balanced by gravitational force.,"the restricted three-body problem and it is assumed, that the mass transfer between components of the system occurs through the vicinity of inner Lagrangian point $L_1$, where pressure gradient is not balanced by gravitational force."836 The hydrodynamies of mass transfer through the inner Lagrangian point Ly has been investigated by many authors., The hydrodynamics of mass transfer through the inner Lagrangian point $L_1$ has been investigated by many authors.837" The detailed analysis of matter iow in the vicinity of L, was carried out by Lubow Shu (1975).", The detailed analysis of matter flow in the vicinity of $L_1$ was carried out by Lubow Shu (1975).838 Using a perturbation method they evaluated: main characteristics of the flow., Using a perturbation method they evaluated main characteristics of the flow.839 In another approach. based on the analysis of Jernoulli integral. the stream. parameters were specified as well and the dependence of the mass transfer rate upon the degree of Roche lobe overfilling was obtained (Paczvisski Sienkiewiez 1972: Savonije LOTS).," In another approach, based on the analysis of Bernoulli integral, the stream parameters were specified as well and the dependence of the mass transfer rate upon the degree of Roche lobe overfilling was obtained (Paczyńsski Sienkiewicz 1972; Savonije 1978)."840 For adequate deseription of the mass transfer. process in the binary. system besides. determination of stream parameters it is also necessary to consider the further behavior of Lowlines during movement of matter from Ly., For adequate description of the mass transfer process in the binary system besides determination of stream parameters it is also necessary to consider the further behavior of flowlines during movement of matter from $L_1$.841 Lt is the process of mass transfer produces the general How structure and. accordinglv. determines basic observation evidences. therefore the main attention was paid to study of this question.," It is the process of mass transfer produces the general flow structure and, accordingly, determines basic observation evidences, therefore the main attention was paid to study of this question."842" For the first time movement of particles leaving £L, and moving in the gravitational field of binary system was considered by Warner Peters (1972). Lubow Shu (1975) and Flannery (1975)."," For the first time movement of particles leaving $L_1$ and moving in the gravitational field of binary system was considered by Warner Peters (1972), Lubow Shu (1975) and Flannery (1975)."843 These results were obtained using a simplified ballistic approach for analysis of the gas movement without taking into account of hyelroclvnamic elfects., These results were obtained using a simplified ballistic approach for analysis of the gas movement without taking into account of hydrodynamic effects.844 To study the influence of the cireumbinary. envelope on gas movement and. accordingly. for a correct. description of the Dow. the solving of full svstem of hyelrodsynamic equations is required.," To study the influence of the circumbinary envelope on gas movement and, accordingly, for a correct description of the flow, the solving of full system of hydrodynamic equations is required."845 This is possible only in the framework of rather complex mathematical models., This is possible only in the framework of rather complex mathematical models.846 The use of numerical methods. for. investigation of hvdrodynamies of mass transfer in semidetached: binaries was limited by the computer power for a long time so 2D models were used. for the analysis of the Low structure., The use of numerical methods for investigation of hydrodynamics of mass transfer in semidetached binaries was limited by the computer power for a long time so 2D models were used for the analysis of the flow structure.847 Despite the restrictions of 2D) approach. it allowed. to consider some cetails of the Yow structure correctly and to obtain a set of interesting results (see. c.g... Sawacla. Alatsuca Lachisu 1986: Sawada et al.," Despite the restrictions of 2D approach, it allowed to consider some details of the flow structure correctly and to obtain a set of interesting results (see, e.g., Sawada, Matsuda Hachisu 1986; Sawada et al."848 LOST: Taam. Fu Fryxell 1991: Blondin. Bichards Malinowski 1995: Murray 1996).," 1987; Taam, Fu Fryxell 1991; Blondin, Richards Malinowski 1995; Murray 1996)."849 Last vears the possibility of numerical hvdrodynamic simulation of mass transfer in the framework of more realistic 3D models (Nagasawa. Matsuda ]|xuwahara 1991: Lirose. Osaki Minishige 1991: Alolteni. Belvecere Lanzalame L991: Sawada Matsuda 1992: Lanzalame. Belvedere Alolteni 1992. 1994: Belvedere. Lanzafame Aloltent 1993: Aleelicki. Wickramasinghe Bicknell 1903: Armitage Livio 1996) appeared.," Last years the possibility of numerical hydrodynamic simulation of mass transfer in the framework of more realistic 3D models (Nagasawa, Matsuda Kuwahara 1991; Hirose, Osaki Minishige 1991; Molteni, Belvedere Lanzafame 1991; Sawada Matsuda 1992; Lanzafame, Belvedere Molteni 1992, 1994; Belvedere, Lanzafame Molteni 1993; Meglicki, Wickramasinghe Bicknell 1993; Armitage Livio 1996) appeared."850 In particular. these authors considered the formation of accreting disc in semidetached binaries (Nagasawa et al.," In particular, these authors considered the formation of accreting disc in semidetached binaries (Nagasawa et al."851" 1991: Sawada Matsuda. 1992) and investigated the interaction of stream of matter leaving L, with the disc (Hirose et al.", 1991; Sawada Matsuda 1992) and investigated the interaction of stream of matter leaving $L_1$ with the disc (Hirose et al.852 1991: Armitage Livio 1996)., 1991; Armitage Livio 1996).853 Unfortunately. many 3D investigations were carried out during a rather small time-scales and this fact did not allow to consider the real Dow morphology. accordingly. to evaluate the inlluence of forming circumbinary envelope on the flow structure.," Unfortunately, many 3D investigations were carried out during a rather small time-scales and this fact did not allow to consider the real flow morphology, accordingly, to evaluate the influence of forming circumbinary envelope on the flow structure."854 Some progress in the investigation of ecncral How structure in semidetached binaries was achieved in works Molteni ct al. (, Some progress in the investigation of general flow structure in semidetached binaries was achieved in works Molteni et al. (8551991). Lanzaflame et al. (,"1991), Lanzafame et al. ("8561992. 1904). and Belveclere et al. (,"1992, 1994), and Belvedere et al. ("8571993). where 3D. numerical simulations were carried out on the sullicientlv. large time intervals.,"1993), where 3D numerical simulations were carried out on the sufficiently large time intervals."858 A set of interesting results was obtained in these works. however using of method ΕΙ (Smoothed Particle llvdrodsynamics) did not allow to consider the influence of the circumbinary envelope on the [low structure as [ar as the computational restrictions of SPII method did. not permit to investigate [Lows with Large density gradients. and. accordingly. the account of the influence of circumbinary envelope on the mass transfer was not quite correct.," A set of interesting results was obtained in these works, however using of method SPH (Smoothed Particle Hydrodynamics) did not allow to consider the influence of the circumbinary envelope on the flow structure as far as the computational restrictions of SPH method did not permit to investigate flows with large density gradients, and, accordingly, the account of the influence of circumbinary envelope on the mass transfer was not quite correct."859 For the first time the morphology of gaseous Lows in binaries was accurately considered by authors in Bisikalo et al. (, For the first time the morphology of gaseous flows in binaries was accurately considered by authors in Bisikalo et al. (8601997a.b).,"1997a,b)."861 In this work we present the resus of 3D numerica study of the Low structure in semicdetachec non-magnetic binaries., In this work we present the results of 3D numerical study of the flow structure in semidetached non-magnetic binaries.862 TWD (Lotal Variation Diminishing) method. of solving of hvdrodyvnamic equations used in this paper has allowed. to. investigate the morphology of gaseous flows in the system and to consider the influence of forming circumbinary envelope. despite the presence. of significant density &radients.," TVD (Total Variation Diminishing) method of solving of hydrodynamic equations used in this paper has allowed to investigate the morphology of gaseous flows in the system and to consider the influence of forming circumbinary envelope, despite the presence of significant density gradients."863 Phe numerical simulations of mass transfer in semidetached binaries have been conducto on large time intervals that allowed to consider the main features of How structure in steady-state regime., The numerical simulations of mass transfer in semidetached binaries have been conducted on large time intervals that allowed to consider the main features of flow structure in steady-state regime.864 The earlier conclusions on the Dow structure for low-mass X-ray binary (Bisikalo et al., The earlier conclusions on the flow structure for low-mass X-ray binary (Bisikalo et al.865 19972.b) are generalized in present work [or the wider class of objects.," 1997a,b) are generalized in present work for the wider class of objects."866 The paper is structured. as follows., The paper is structured as follows.867 In Section 2. the properties of used. physical. mathematical anc numerical models are. described.," In Section 2, the properties of used physical, mathematical and numerical models are described."868 Section 3 contains the results of numerical simulations., Section 3 contains the results of numerical simulations.869 In this Section. the stream-clise interaction. comparison of svnthetic Leht curves with observations. [low structure in the vicinity of £4. inlluence of accepted boundary conditions. ancl comparison of the results obtained in 2D and 3D models are discussed.," In this Section the stream-disc interaction, comparison of synthetic light curves with observations, flow structure in the vicinity of $L_1$, influence of accepted boundary conditions, and comparison of the results obtained in 2D and 3D models are discussed."870 Our conclusions follow in Section 4., Our conclusions follow in Section 4.871 The semidetached. binaries such as cataclysmic variables (CVs). low-mass X-ray binaries (LAINBs) and. supersoft X-ray sources (888) show a lot of interesting observation evidences.," The semidetached binaries such as cataclysmic variables (CVs), low-mass X-ray binaries (LMXBs) and supersoft X-ray sources (SSS) show a lot of interesting observation evidences."872 The observations of οVs light. curves and X-rav lieht curves of LAINBs olfer bright. evidences of a complex Low structure in these svstems and allow to make assumptions on the structure of gaseous Lows., The observations of CVs light curves and X-ray light curves of LMXBs offer bright evidences of a complex flow structure in these systems and allow to make assumptions on the structure of gaseous flows.873 In particular. in some cataclysmic binaries. the most well stucied of which is Z Cha. the complex picture of eclipse (double eclipse) is observed (see. e.g... Hack La Dous 1993: Cherepashchuk et al.," In particular, in some cataclysmic binaries, the most well studied of which is Z Cha, the complex picture of eclipse (`double eclipse') is observed (see, e.g., Hack La Dous 1993; Cherepashchuk et al."874 1996)., 1996).875" For its explanation the hypothesis of an ""hotspot in interaction zone between the stream and the cise outer", For its explanation the hypothesis of an `hotspot' in interaction zone between the stream and the disc outer876the simulation.,the simulation.877" It must be noted that planetesimal-planetesimal interactions may in reality be important, since they give rise to an effective viscosity in the swarm (Levison, personal communication)."," It must be noted that planetesimal-planetesimal interactions may in reality be important, since they give rise to an effective viscosity in the swarm (Levison, personal communication)."878" Thus, more careful validation of our results should preferentially include these thorny effects."," Thus, more careful validation of our results should preferentially include these thorny effects."879 We used a hybrid Bulisch-Stoer/Wisdom-Holman algorithm of the mercury6 software for all integrations., We used a hybrid Bulisch-Stoer/Wisdom-Holman algorithm of the mercury6 software for all integrations.880" We consistently used a time-step of 7= 300d, and checked all successful simulations with a smaller 7= 60d time-step to ensure that the observed instability is not a numerical artifact."," We consistently used a time-step of $\tau = 300$ d, and checked all successful simulations with a smaller $\tau = 60$ d time-step to ensure that the observed instability is not a numerical artifact."881" In all such checks, the evolutions were practically indistinguishable, which assures that integrals of motion are sufficiently conserved."," In all such checks, the evolutions were practically indistinguishable, which assures that integrals of motion are sufficiently conserved."882" Finally, our simulations only cover a few tens of millions of years, since the focus here is on distinguishing between initial conditions that give rise to gas-giant/ice-giant scattering and ones that don’t."," Finally, our simulations only cover a few tens of millions of years, since the focus here is on distinguishing between initial conditions that give rise to gas-giant/ice-giant scattering and ones that don't."883" As a result, the long-term evolution of the system after the instability is unexplored."," As a result, the long-term evolution of the system after the instability is unexplored."884" Let us first consider a family of initial conditions, listed in table (1), where Jupiter and Saturn are in a 3:2 MMR."," Let us first consider a family of initial conditions, listed in table (1), where Jupiter and Saturn are in a 3:2 MMR."885 'This family of initial conditions was previously studied in some detail by Morbidelli et al. , This family of initial conditions was previously studied in some detail by Morbidelli et al. (886,2007).887"Consequently, this section's results are partially (2007).reproductions."," Consequently, this section's results are partially reproductions."888" Using a hydrodynamical model, Morbidelli et al. ("," Using a hydrodynamical model, Morbidelli et al. ("889"2007) found six multi-resonant configurations, two of which they determined to be long-term stable.","2007) found six multi-resonant configurations, two of which they determined to be long-term stable."890 These are the configurations listed in table (1) where both Jupiter Saturn and Saturn Uranus pairs are in 3:2 MMR’s while Uranus Neptune are in either 4:3 or 5:4 MMR’s., These are the configurations listed in table (1) where both Jupiter Saturn and Saturn Uranus pairs are in 3:2 MMR's while Uranus Neptune are in either 4:3 or 5:4 MMR's.891" There are two more compact configurations listed in table (1) which we determined to be stable, although the counterparts of these configurations put together by Morbidelli et al. w"," There are two more compact configurations listed in table (1) which we determined to be stable, although the counterparts of these configurations put together by Morbidelli et al. ("892ereunstable?.,2007) were.893". These configurations are the two (2007)where Jupiter Saturn are in a 3:2 MMR, Saturn Uranus are in a 4:3 MMR, and Uranus Neptune are either in a 3:2 MMR or 4:3 MMR."," These configurations are the two where Jupiter Saturn are in a 3:2 MMR, Saturn Uranus are in a 4:3 MMR, and Uranus Neptune are either in a 3:2 MMR or 4:3 MMR."894 As discussed in Morbidelli et al. , As discussed in Morbidelli et al. (895"if Jupiter and Saturn start out in a 3:2 MMR, the instability(2007), is triggered by their encounter with the 5:3 MMR.","2007), if Jupiter and Saturn start out in a 3:2 MMR, the instability is triggered by their encounter with the 5:3 MMR."896" While this is 8, second-order resonance, small jumps in Jupiter's and Saturn's eccentricities go a long way, especially in highly compact configurations."," While this is a second-order resonance, small jumps in Jupiter's and Saturn's eccentricities go a long way, especially in highly compact configurations."897" Unfortunately, in this case it is difficult to conclusively determine which configurations will result in evolutions with scattering events a-priori."," Unfortunately, in this case it is difficult to conclusively determine which configurations will result in evolutions with scattering events a-priori."898" Thus, we must rely solely on numerical integrations to explore the various evolutionary outcomes of these initial conditions."," Thus, we must rely solely on numerical integrations to explore the various evolutionary outcomes of these initial conditions."899" After an initial run of 20 integrations for each initial condition of the family listed in table (1), we ruled out the configurations where Saturn Uranus are in a 2:1 MMR as well as the configuration where all planet pairs are in 3:2 MMR’s because all evolutions were characterized by smooth migration."," After an initial run of 20 integrations for each initial condition of the family listed in table (1), we ruled out the configurations where Saturn Uranus are in a 2:1 MMR as well as the configuration where all planet pairs are in 3:2 MMR's because all evolutions were characterized by smooth migration."900 We subjected the remaining four configurations to 30 additional integrations and found that the only configuration which does not result in ice-giant/gas-giant scattering is the one where Saturn Uranus are in a 3:2 MMR and Uranus Neptune are in a 4:3 MMR., We subjected the remaining four configurations to 30 additional integrations and found that the only configuration which does not result in ice-giant/gas-giant scattering is the one where Saturn Uranus are in a 3:2 MMR and Uranus Neptune are in a 4:3 MMR.901" The evolutions of the remaining initial conditions are presented in figures (1) - (3), and their final orbital parameters are entered into table "," The evolutions of the remaining initial conditions are presented in figures (1) - (3), and their final orbital parameters are entered into table (2)."902"For the initial condition in which Saturn and (2).Uranus are in a 3:2 MMR, of the integrations were successful with of them exhibiting close encounters between an ice giant and gas giants."," For the initial condition in which Saturn and Uranus are in a 3:2 MMR, of the integrations were successful with of them exhibiting close encounters between an ice giant and gas giants."903 The same fractions for the two configurations where Saturn and Uranus are initially in a 4:3 MMR are and for the case where Uranus Neptune are in a 3:2 MMR and 4:3 MMR respectively., The same fractions for the two configurations where Saturn and Uranus are initially in a 4:3 MMR are and for the case where Uranus Neptune are in a 3:2 MMR and 4:3 MMR respectively.904 We now move on to the next family of initial, We now move on to the next family of initial905different observing strategies facilitates not only the detection of emission line objects but also to derive photometric spectra of all objects 1n the fields without performing time consuming slit spectroscopy.,different observing strategies facilitates not only the detection of emission line objects but also to derive photometric spectra of all objects in the fields without performing time consuming slit spectroscopy.906 Details of the survey and its calibration will be given in Metsenheimer et al. (, Details of the survey and its calibration will be given in Meisenheimer et al. (907in All observations were performed on Calar Alto. Spain. in the optical wavelength region with the focal reducers CAFOS (Calar Alto Faint Object Spectrograph) at the 2.2 m telescope and MOSCA (Multi Object Spectrograph for Calar Alto) at the 3.5 m telescope. and with the Omega Prime camera for the NIR As a byproduct of the survey we obtain a lot of multi-color data about faint stars in the Galaxy.,"in All observations were performed on Calar Alto, Spain, in the optical wavelength region with the focal reducers CAFOS (Calar Alto Faint Object Spectrograph) at the 2.2 m telescope and MOSCA (Multi Object Spectrograph for Calar Alto) at the 3.5 m telescope, and with the Omega Prime camera for the NIR As a byproduct of the survey we obtain a lot of multi-color data about faint stars in the Galaxy."908" Although for the object classification (see below) exposures in two broadband filters and seven medium-band filters (in the case of the Ohh field eight medium-band filters) are used. the present analysis of the stellar component of CADIS ts based only on exposures in three filters. Re. (central wavelength/width A,f/AA=619 mu/17Onnm). Bee (A.=161um /100nnm) and ης (A.=815111/32 nnm)."," Although for the object classification (see below) exposures in two broadband filters and seven medium-band filters (in the case of the h field eight medium-band filters) are used, the present analysis of the stellar component of CADIS is based only on exposures in three filters, $R_C$ (central wavelength/width $\lambda_c / \Delta\lambda = 649\,{\rm nm}/170$ nm), $B_C$ $\lambda_c =909461\,{\rm nm}/100$ nm) and $I_{815}$ $\lambda_c = 815\,{\rm nm}/32$ nm)."910 Exposure times converted to the mm telescope are given in Table I.., Exposure times converted to the m telescope are given in Table \ref{exptime}.911 The nine CADIS fields measure z1/30LI each and are located at high Galactic latitude to avoid dust absorption and reddening., The nine CADIS fields measure $\approx 1/30~\sq\degr$ each and are located at high Galactic latitude to avoid dust absorption and reddening.912 In all fields the total flux on the IRAS jim maps is less than MMJy/sr which corresponds to Epy0.07. so we do not have to apply any color corrections.," In all fields the total flux on the IRAS $\mu$ m maps is less than MJy/sr which corresponds to $E_{B-V} < 0.07$, so we do not have to apply any color corrections."913 A second selection criterium for the fields was that there should be no star brighter than z16777 in the CADIS 7? band.," A second selection criterium for the fields was that there should be no star brighter than $\approx 91416^{mag}$ in the CADIS $R$ band."915" In fact the brightest star in the two fields under consideration has an R magnitude of 15.127%, Objects are identified on each of the deep images (superposition of 5 to 15 individual exposures) using. the Source Extractor. software SExtractor (Bertin 1996).. and the resulting lists merged into a master Photometry is done using the programEvaluate. which has been developed by Meisenheimer Rósser (1986)."," In fact the brightest star in the two fields under consideration has an $R$ magnitude of $15.42^{mag}$ Objects are identified on each of the deep images (superposition of 5 to 15 individual exposures) using the Source Extractor software xtractor \cite{Bertin}, and the resulting lists merged into a master Photometry is done using the program, which has been developed by Meisenheimer Rösser (1986)."916 Variations in seeing in between individual exposures are taken into account. in order to get accurate colors.," Variations in seeing in between individual exposures are taken into account, in order to get accurate colors."917" For photometric calibration we use a system of ""tertiary"" standard stars in the CADIS fields. which are calibrated with secondary standard stars (Oke1990;Walsh1995) in photometric From the locus of the stars in the 8-dimensional color space we conclude that the relative calibration between each pair of wavebands is better than 3 for all objects with R=22. Since one of the major goals of the survey ts the classification of every object found in all CADIS fields (280.000 to 100000 in total). a classification scheme was developed which is based on template spectral energy distributions (see Wolf 1998)."," For photometric calibration we use a system of ”tertiary” standard stars in the CADIS fields, which are calibrated with secondary standard stars \cite{oke,eso} in photometric From the locus of the stars in the 8-dimensional color space we conclude that the relative calibration between each pair of wavebands is better than 3 for all objects with $R=22$ Since one of the major goals of the survey is the classification of every object found in all CADIS fields $\approx 80\, 000$ to $100\, 000$ in total), a classification scheme was developed which is based on template spectral energy distributions (see Wolf 1998)."918 The observed colors of every object are compared with a color library of known objects. whose colors are obtained. from synthetic photometry performed on our CADIS filterset.," The observed colors of every object are compared with a color library of known objects, whose colors are obtained from synthetic photometry performed on our CADIS filterset."919 The input library for stellar spectra was the Gunn Stryker (1983) catalogue., The input library for stellar spectra was the Gunn Stryker (1983) catalogue.920 For each object the probability to belong to a certain object class (stars — quasars — galaxies) is Objects classified as stars have stellar colors with a likelihood of more than75%.. and images the profile of which does not deviate significantely from that of well defined Details about the performance and reliability of the classification are given in Wolf et al.," For each object the probability to belong to a certain object class (stars – quasars – galaxies) is Objects classified as stars have stellar colors with a likelihood of more than, and images the profile of which does not deviate significantely from that of well defined Details about the performance and reliability of the classification are given in Wolf et al."921" 1999, and Wolf (in With the current filter set and exposure times the classification is reliable down to a limit of ΠΠ.237%,"," 1999, and Wolf (in With the current filter set and exposure times the classification is reliable down to a limit of $R \simeq 23^{mag}$."922" This was checked by spectroscopic follow-up observations of 245 arbitrarily chosen objects (55 stars. 153 galaxies and 20 quasars) with Ro<23°"","," This was checked by spectroscopic follow-up observations of 245 arbitrarily chosen objects (55 stars, 153 galaxies and 20 quasars) with $R<23^{mag}$."923 One galaxy has been classified as a star by it’s colors. two quasars as galaxies and two galaxies as quasars.," One galaxy has been classified as a star by it's colors, two quasars as galaxies and two galaxies as quasars."924" The star counts are not significantly affected by the misclassifications down to Y=23""""""", The star counts are not significantly affected by the misclassifications down to $R=23^{mag}$.925 Thus we restrict our present analysis to stars with 72x23nag To derive distances of the stars from the distance modulus mpAlp. itis essential to know the absolute magnitudes of the stars. Ag. In principle absolute magnitudes of main sequence stars can be obtained from a color-magnitude diagramm.," Thus we restrict our present analysis to stars with $R\le 23^{mag}$ To derive distances of the stars from the distance modulus $m_R-M_R$, it is essential to know the absolute magnitudes of the stars, $M_R$ In principle absolute magnitudes of main sequence stars can be obtained from a color-magnitude diagramm."926" This main sequence approximation is valid for all stars in our sample since we can be sure that it is free from contamination of any non-main sequence stars. as the faint magnitude intervall we observe (16xR< 23) does not allow the detection of a giant We took a mean My, versus (2V.)j relation from Lang (1992)."," This main sequence approximation is valid for all stars in our sample since we can be sure that it is free from contamination of any non-main sequence stars, as the faint magnitude intervall we observe $16 \leq R \leq 92723$ ) does not allow the detection of a giant We took a mean $M_{V_J}$ versus $(B-V)_J$ relation from Lang (1992)."928 A complication arises. because there is no V. filter included in our filter set.," A complication arises, because there is no $V$ filter included in our filter set."929" Thus we have to convert 1 and (2VW), into our filter system. in order to derive the absolute magnitudes from mean main sequence fit in 1j versus () i)."," Thus we have to convert $M_V$ and $(B-V)_J$ into our filter system, in order to derive the absolute magnitudes from mean main sequence fit in $M_R$ versus $(b-r)$ ,"930 (Turner.Ostriker.&andreferencestherein).. (Turner1990:Wanmbsgaanssetal.1995:Porciani&\ladau2000:Keeton2001:lxeeton&Madau2001:LiOstriker2002.hencelorth.LOO2:Gladcdersetal.2003).. Yamamoto2002:Spergel," \citep[and references therein]{tur84,sch92,bar01,cou02}. \citep[henceforth LO02; Gladders et al. 2003]{tur90,wam95,por00,kee01a,kee01,li02}. \citep{ost95,bah99,wan00,pea01,efs02,yam02,spe03}."931etal.2003).. —o. —1 , $- \alpha$ $-1$ 932"Specifically, we performed a detailed asteroseismological study of 44 ZZ Ceti stars extracted from a sample of bright stars for which the surface parameters are accurately known.","Specifically, we performed a detailed asteroseismological study of 44 ZZ Ceti stars extracted from a sample of bright stars for which the surface parameters are accurately known."933 This sample includes the archetypal ZZ Ceti star G117—B15A. The asteroseismological analysis of such a large set of stars has the potential to characterize the common properties of the class., This sample includes the archetypal ZZ Ceti star $-$ B15A. The asteroseismological analysis of such a large set of stars has the potential to characterize the common properties of the class.934" We have employed a large grid of fully evolutionary models characterized by consistent chemical profiles from the centre to the surface and covering a wide range of stellar masses, thicknesses of the H envelope and effective temperatures."," We have employed a large grid of fully evolutionary models characterized by consistent chemical profiles from the centre to the surface and covering a wide range of stellar masses, thicknesses of the H envelope and effective temperatures."935 Our asteroseismological approach represents a significant improvement over previous calculations that rely on the use of DA white dwarf models characterized by simplified chemical profiles at the envelope and/or the core., Our asteroseismological approach represents a significant improvement over previous calculations that rely on the use of DA white dwarf models characterized by simplified chemical profiles at the envelope and/or the core.936 This is the first work aimed at an asteroseismological analysis of ZZ Ceti stars that employsevolutionary white dwarf models., This is the first work aimed at an asteroseismological analysis of ZZ Ceti stars that employs white dwarf models.937" Our main results for G117—B15A are: As for the complete sample of 44 ZZ Ceti stars, our main results are:"," Our main results for $-$ B15A are: As for the complete sample of 44 ZZ Ceti stars, our main results are:"938This source has been measured twice within four months. during which the flux density increased from. 0.93 to 1.44 Jv and the percentage polarisation decreased. from. 4.9 to2.0'4.. Le. they seem to be anti-correlated.,"This source has been measured twice within four months, during which the flux density increased from 0.93 to 1.44 Jy and the percentage polarisation decreased from 4.9 to, i.e. they seem to be anti-correlated."939 The position anele remained largely the same but the orientation of the magnetic field cannot be infered since no VLBI observations of this source have been found in the literature., The position angle remained largely the same but the orientation of the magnetic field cannot be infered since no VLBI observations of this source have been found in the literature.940 ‘This source was observed on eight. different occasions and in terms of its polarisation properties idt ijs the most variable source in the sample., This source was observed on eight different occasions and in terms of its polarisation properties it is the most variable source in the sample.941 The polarisation ranges widely otbween 5.1 and 215'4 averaging to over all epochs., The polarisation ranges widely between 5.1 and $>15\%$ averaging to over all epochs.942 llowever. its measured [ux densitv only varied between 1. and 2.4 Jv.," However, its measured flux density only varied between 1 and 2.4 Jy."943" The milliareseconc jet. position angle has »en determined. from. verv-high-frequeney VLBI maps to ο Ayre,=120°.", The milliarcsecond jet position angle has been determined from very-high-frequency VLBI maps to be $\theta_{VLBI} = -120\degr$.944 Over most epochs. the magnetic field geometry inferred [rom the measurements of the polarisation »osition angle is neither parallel nor perpendicular to the jet.," Over most epochs, the magnetic field geometry inferred from the measurements of the polarisation position angle is neither parallel nor perpendicular to the jet."945 During the last two epochs. however. the polarisation drops rom to while the lux increases from 1.3 to 24 Jv.," During the last two epochs, however, the polarisation drops from to while the flux increases from 1.3 to 2.4 Jy."946 The position angle is clearly seen to rotateby roughly 90. sugeesting that the magnetic field changes from being »erpendieular to the jet (at the high polarisation epoch) o being parallel to it.," The position angle is clearly seen to rotateby roughly $90\degr$, suggesting that the magnetic field changes from being perpendicular to the jet (at the high polarisation epoch) to being parallel to it."947 Over all epochs no correlation is ound between the changes in Dux and degree of polarisation. out if the data are examined. between epochs 5 and 5.8 separately. there is a hint of a positive correlation [first r=0.7 and an anti-correlation later r=0.8 both with he same confidence level.," Over all epochs no correlation is found between the changes in flux and degree of polarisation, but if the data are examined between epochs $-$ 5 and $-$ 8 separately, there is a hint of a positive correlation first $r=0.7$ and an anti-correlation later $r=-0.8$ both with the same confidence level."948 There are four polarisation and five photometric epochs on this source., There are four polarisation and five photometric epochs on this source.949 The variation in polarisation (and (ux) is not as dramatic as seen in other sources. ranging between 3.7 and with measured. position angles spread. over a ~45° range.," The variation in polarisation (and flux) is not as dramatic as seen in other sources, ranging between 3.7 and with measured position angles spread over a $\sim45\degr$ range."950 Llowever. a Uare was recorded. between the last two epochs (taken one month apart) when the flux rose [rom a minimum of 1.1 Jy to a maximum of 2.5 Jv.," However, a flare was recorded between the last two epochs (taken one month apart) when the flux rose from a minimum of 1.1 Jy to a maximum of 2.5 Jy."951 The core's position is uncertain since it remains unresolved with VLBI., The core's position is uncertain since it remains unresolved with VLBI.952 ltelative to a position of —SS for the innermost resolved component. the magnetic field is neither perpendicular nor parallel to the jet. except just. before the Hare where it is found within 15° of the aligned orientation.," Relative to a position of $-88\degr$ for the innermost resolved component, the magnetic field is neither perpendicular nor parallel to the jet, except just before the flare where it is found within $15\degr$ of the aligned orientation."953 Two observations are available on this source. taken almost three vears apart. which are very similar: the polarisation is very high. on average) and the mean Ilux is 1.5 Jy.," Two observations are available on this source, taken almost three years apart, which are very similar: the polarisation is very high on average) and the mean flux is $\sim 1.5$ Jy."954 The magnetic field appears to be exactly. perpendicular to the jet. however the jet position angle (305) was obtained from low-[requeney maps (1.7 611) and it may not represent the true orientation of the milliaresecond jet.," The magnetic field appears to be exactly perpendicular to the jet, however the jet position angle $305\degr$ ) was obtained from low-frequency maps (1.7 GHz) and it may not represent the true orientation of the milliarcsecond jet."955 This source was observed at ten cilferent epochs., This source was observed at ten different epochs.956 The (ux density at. 1.1 mim varied in the range 11 21.2 Jv., The flux density at 1.1 mm varied in the range 11 – 21.2 Jy.957 This unusually high brightness allows polarisation levels as low as to be measured with enough signal to noise. so far not achieved on any other source.," This unusually high brightness allows polarisation levels as low as to be measured with enough signal to noise, so far not achieved on any other source."958 In the last two epochs (in late 1995) this source was caught Daring and the polarisation rose οG., In the last two epochs (in late 1995) this source was caught flaring and the polarisation rose to.959N'.. Except at the epoch of lowest polarisation (and lux) the position angle lies within a small range of 30., Except at the epoch of lowest polarisation (and flux) the position angle lies within a small range of $30\degr$.960 From numerous high-frequency VLBI observations. we estimate he orientation of the milliarsecond. jet to be ~110”. rowever at 100 Cllz the inner jet exhibits a somewhat wigelv morphology.," From numerous high-frequency VLBI observations, we estimate the orientation of the milliarsecond jet to be $\sim -110\degr$, however at 100 GHz the inner jet exhibits a somewhat wiggly morphology."961 The inferred magnetic field. geometry ends. towards alignment with the jet. except at the low x»larisation epoch when it is closer to the perpencicular configuration (although with very low level of ordering).," The inferred magnetic field geometry tends towards alignment with the jet, except at the low polarisation epoch when it is closer to the perpendicular configuration (although with very low level of ordering)."962 There is also a significant correlation. between Lux and degree of polarisation with r=0.8 at the significance level., There is also a significant correlation between flux and degree of polarisation with $r=0.8$ at the significance level.963 This is the most. [frequently observed source in the sample with 11 polarisation epochs., This is the most frequently observed source in the sample with 11 polarisation epochs.964 Lt is very bright. (with Dux densitv in the range 6 13.5 Jv) and very highly polarised (with an average of A))., It is very bright (with flux density in the range 6 – 13.5 Jy) and very highly polarised (with an average of ).965 High-frequeney VLBI maps reveal an inner jet position angle of —135° within0., High-frequency VLBI maps reveal an inner jet position angle of $-135\degr$ within.966lonas. The position angle. varies only by a few degrees between epochs. indicating a highlv-ordered. magnetic field unambiguously perpencicular to the jet.," The position angle varies only by a few degrees between epochs, indicating a highly-ordered magnetic field unambiguously perpendicular to the jet."967 The flux and polarisation are highly correlated with r20.76 at the significance level., The flux and polarisation are highly correlated with $r=0.76$ at the significance level.968 A deo observation was obtained on this source giving a percentage polarisation of ~I0 and a tux density of 1 Jy., A $4\sigma$ observation was obtained on this source giving a percentage polarisation of $\sim 10\%$ and a flux density of 1 Jy.969" Using a VLBI jet position angle of A46"" (obtained at 5 Cllz) the inferred magnetic field orientation is neither parallel nor perpendicular.", Using a VLBI jet position angle of $-46\degr$ (obtained at 5 GHz) the inferred magnetic field orientation is neither parallel nor perpendicular.970 However. the jet curves significantly. within the inner and it is likely to bend further within the unresolved region. casting some doubt on the validity of the AyLer Used.," However, the jet curves significantly within the inner and it is likely to bend further within the unresolved region, casting some doubt on the validity of the $\theta_{VLBI}$ used."971 ‘There are five observations on this source with a Lux density in the range 2.5im 4.9 Js. which overall appears to be anti-correlated with the polarisation that ranges between 2.5 and7.," There are five observations on this source with a flux density in the range 2.5 – 4.9 Jy, which overall appears to be anti-correlated with the polarisation that ranges between 2.5 and."97294... Phe position angle is very steady remaining within a 23 range over all epochs., The position angle is very steady remaining within a $23\degr$ range over all epochs.973 A very tentative jet. orientation of 135° has been obtained from a 5 CGllz VLBI map in which the core is not clearly resolved., A very tentative jet orientation of $135\degr$ has been obtained from a 5 GHz VLBI map in which the core is not clearly resolved.974 This would indicate a magnetic field geometry. perpendicular to jet., This would indicate a magnetic field geometry perpendicular to jet.975 This source has been observed three times. the last. two epochs taken within a month.," This source has been observed three times, the last two epochs taken within a month."976 The [lux density ranges between 1.1 and 1.6 Jv and appears to be anti-correlated with the polarisation that varies in the range 3.7 9.14., The flux density ranges between 1.1 and 1.6 Jy and appears to be anti-correlated with the polarisation that varies in the range 3.7 – .977.. The only VLBI map available is of low resolution but shows a double-sided jet. the most compact sideof which is oriented," The only VLBI map available is of low resolution but shows a double-sided jet, the most compact sideof which is oriented"978"each of these passages, just like the stellar streams.","each of these passages, just like the stellar streams."979" Here, however, liberated stars fan out over a cone of radial orbits."," Here, however, liberated stars fan out over a cone of radial orbits."980" This is the same phenomenon that created the shells at z=2.3, although here the orbital energy of the satellite is much greater and the outer shells are much more extensive."," This is the same phenomenon that created the shells at $z=2.3$, although here the orbital energy of the satellite is much greater and the outer shells are much more extensive."981" As described by (1984),, stars liberated on a given passage have a range of binding energies with respect to their host (determined by the structure of the progenitor and the interaction of the two potentials)."," As described by \citet{Quinn84}, stars liberated on a given passage have a range of binding energies with respect to their host (determined by the structure of the progenitor and the interaction of the two potentials)."982 Stars with low binding energies have longer orbital periods and turn around at larger radii than more tightly-bound stars., Stars with low binding energies have longer orbital periods and turn around at larger radii than more tightly-bound stars.983" Thus, the outermost shell forms first, from the loosely-bound stars that lead the satellite along its orbit."," Thus, the outermost shell forms first, from the loosely-bound stars that lead the satellite along its orbit."984 All shells move outward with time as stars with ever-longer periods reach apocentre., All shells move outward with time as stars with ever-longer periods reach apocentre.985" At any given instant, the edges of the shells are composed of stars that have executed an integer number of orbits (seee.g.&"," At any given instant, the edges of the shells are composed of stars that have executed an integer number of orbits \citep[see986e.g.][]{Merrifield98}."987 They are interleaved in radius on either side of the frifieldKuijken|[1998)..center., They are interleaved in radius on either side of the center.988 Finally note that the companion that was already," Finally, note that the companion that was already"989both the interferometer sensitivity curves and the inferred ? limits.,both the interferometer sensitivity curves and the inferred \citet{bildsten1998} limits.990" In contrast, model E undercuts the ? limit for QPO sources, implying either the natal magnetic fields of these sources are ~10?G, or that these objects are not in GW spin equilibrium."," In contrast, model E undercuts the \citet{bildsten1998} limit for QPO sources, implying either the natal magnetic fields of these sources are $\sim 10^{13.5} \ \mathrm{G}$, or that these objects are not in GW spin equilibrium."991" All the confirmed AMXPs and most of the unconfirmed AMXPs are consistent with model E. They lie below the model E curve either because they have B,«10!??G or because Ohmic diffusion prevents the ellipticity from saturating.", All the confirmed AMXPs and most of the unconfirmed AMXPs are consistent with model E. They lie below the model E curve either because they have $B_{\ast} < 10^{12.5} \ \mathrm{G}$ or because Ohmic diffusion prevents the ellipticity from saturating.992 We note that the current magnetic mountain models are still preliminary., We note that the current magnetic mountain models are still preliminary.993 Effects that have not yet been modelled faithfully in the context of magnetic burial may modify the saturation ellipticities., Effects that have not yet been modelled faithfully in the context of magnetic burial may modify the saturation ellipticities.994" Therefore, it is still premature to quantify the absolute detectability of magnetic mountains as GW sources."," Therefore, it is still premature to quantify the absolute detectability of magnetic mountains as GW sources."995" 'There have been two directed searches for GWs from the accreting neutron star Sco X-1 (??),, which is expected to be the strongest emitter of its class in the GW spin stalling scenario (?).."," There have been two directed searches for GWs from the accreting neutron star Sco X-1 \citep{abbott2007a, abbott2007b}, which is expected to be the strongest emitter of its class in the GW spin stalling scenario \citep{bildsten1998}."996" The first, coherent search computed the F--statistic on 6 h of LIGO $2 data, coincident between the Hanford and Livingston interferometers."," The first, coherent search computed the -statistic on 6 h of LIGO S2 data, coincident between the Hanford and Livingston interferometers."997" Assuming a non-eccentric orbit, it placed a 95 per cent confidence upper limit on the GW strain from Sco X-1 of ho=1.7x10? in the 464-484Hz frequency band, and ho=2.2x10:33 in the 604-624Hz frequency band (?),, which corresponds to an upper limit on the ellipticity of the neutron star of €&4x 107."," Assuming a non-eccentric orbit, it placed a $95$ per cent confidence upper limit on the GW strain from Sco X-1 of $h_{0}=1.7\times10^{-22}$ in the $464$ $484 \ \mathrm{Hz}$ frequency band, and $h_{0}=2.2\times10^{-22}$ in the $604$ $624 \ \mathrm{Hz}$ frequency band \citep{abbott2007a}, which corresponds to an upper limit on the ellipticity of the neutron star of $\epsilon \approx 4\times10^{-4}$ ."998" The second, semicoherent search performed a radiometer analysis of 20 days of triple-coincidence LIGO $4 data."," The second, semicoherent search performed a radiometer analysis of $20$ days of triple-coincidence LIGO S4 data."999 It yielded a 90 per cent confidence upper limit of AO”.223.4x10-2*(f/200Hz) (?)..," It yielded a $90$ per cent confidence upper limit of $h^{90\%}_{\mathrm{RMS}}1000\approx 3.4\times10^{-24} (f/200 \ \mathrm{Hz})$ \citep{abbott2007b}."1001" As required by the non-detection of gravitational emission from accreting neutron stars (??),, adiabatic EOS reduce the GW detectability of magnetic mountains below the current detection threshold of hozz33."," As required by the non-detection of gravitational emission from accreting neutron stars \citep{abbott2007a, abbott2007b}, adiabatic EOS reduce the GW detectability of magnetic mountains below the current detection threshold of $h_{0} \approx 10^{-23}$."1002" In comparison, the saturation ellipticities of ideal isothermal10” magnetic mountains of model A are above this threshold and should have already been detected."," In comparison, the saturation ellipticities of ideal isothermal magnetic mountains of model A are above this threshold and should have already been detected."1003 The models in this paper are not the final word on magnetically confined mountains., The models in this paper are not the final word on magnetically confined mountains.1004" The range of accreted masses investigated here is well below Ma~107'Mo, the typical value for an LMXB (?),, due to numerical breakdown."," The range of accreted masses investigated here is well below $M_{\mathrm{a}}1005\sim 10^{-1} \mathrm{M}_{\sun}$, the typical value for an LMXB \citep{burderi1999}, due to numerical breakdown."1006" If e truly saturates for Λα>>Mc, then this failing is less serious for the GW applications than for understanding L(Ma), but it should be noted that the saturation hypothesis has not been tested rigorously for M4Z10M. (??). "," If $\epsilon$ truly saturates for $M_{\mathrm{a}} \gg M_{\mathrm{c}}$, then this failing is less serious for the GW applications than for understanding $\mu(M_{\mathrm{a}})$, but it should be noted that the saturation hypothesis has not been tested rigorously for $M_{\mathrm{a}} \gtrsim 10 M_{\mathrm{c}}$ \citep{payne2004, vigelius2009b}. ."1007"A precise calculation of mountain equilibria for an exact, depth-dependent nuclear EOS cannot be carried out within our Grad-Shafranov formulation, although a relativistic degenerate electron EOS (model C) is a fair approximation for M4~ Μ.."," A precise calculation of mountain equilibria for an exact, depth-dependent nuclear EOS cannot be carried out within our Grad–Shafranov formulation, although a relativistic degenerate electron EOS (model C) is a fair approximation for $M_{\mathrm{a}} \approx M_{\mathrm{c}}$ ."1008" The models in this paper are constructed on an impenetrable and EOS- and Ma-dependent surface Ri, within the crust, which prevents sinking past this boundary."," The models in this paper are constructed on an impenetrable and EOS- and $M_{\mathrm{a}}$ -dependent surface $R_{\mathrm{in}}$ within the crust, which prevents sinking past this boundary."1009" ? showed that, for isothermal mountains, sinking reduces ε by up to 60 per cent."," \citet{wette2010} showed that, for isothermal mountains, sinking reduces $\epsilon$ by up to $60$ per cent."1010" In the presence of Ohmic diffusion, a balance is achieved after a mass Ma is accreted (Ma depends on magnetic field,temperature, accretion rate and EOS), in which the rate of cross-field mass transport equals the accretion rate (?).."," In the presence of Ohmic diffusion, a balance is achieved after a mass $M_{\mathrm{d}}$ is accreted $M_{\mathrm{d}}$ depends on magnetic field,temperature, accretion rate and EOS), in which the rate of cross-field mass transport equals the accretion rate \citep{melatos2005}."1011" As our model is not time-dependent, the Hall effect is also missing."," As our model is not time-dependent, the Hall effect is also missing."1012" Hall drift acts to break down the magnetic field to shorter scales (77) and may operate in isolated neutron stars (??) but is thought to be relatively unimportant in accreting neutron stars, where it is dominated by Ohmic diffusion (?).."," Hall drift acts to break down the magnetic field to shorter scales \citep{hollerbach2002, hollerbach2004} and may operate in isolated neutron stars \citep{rheinhardt2002, rheinhardt2004} but is thought to be relatively unimportant in accreting neutron stars, where it is dominated by Ohmic diffusion \citep{cumming2004}."1013 The crystalline lattice of the crust is thought to melt in thin layers where electron captures have significantly reduced the nuclear charge (?).., The crystalline lattice of the crust is thought to melt in thin layers where electron captures have significantly reduced the nuclear charge \citep{brown2000}.1014" This is expected to have non-negligible effects on magnetic burial, as the boundary condition on the magnetic field becomesa function of density rather than radius (line-tyingwhere solid, free whereliquid)."," This is expected to have non-negligible effects on magnetic burial, as the boundary condition on the magnetic field becomesa function of density rather than radius (line-tyingwhere solid, free whereliquid)."1015" Finally, the three-dimensional stability of MHD equilibria depends on the EOS (?).."," Finally, the three-dimensional stability of MHD equilibria depends on the EOS \citep{kosinski2006}. ."1016 We leave the investigation of these phenomena to future work., We leave the investigation of these phenomena to future work.1017we restrict our analysis to the 2=3 simulation snapshots. approximately corresponding to the median redshift of the observational| sample that we compare to.,"we restrict our analysis to the $z=3$ simulation snapshots, approximately corresponding to the median redshift of the observational sample that we compare to."1018 Our analysis depends on the identification of the masses ancl locations of gravitationally bound clark matter haloes. which are identified using the spherical overdensity criterion implemented. in the algorithm2001).," Our analysis depends on the identification of the masses and locations of gravitationally bound dark matter haloes, which are identified using the spherical overdensity criterion implemented in the algorithm."1019. Llalo properties quoted in this paper are defined with respect to spheres with radius rogo and mass mooo. centred on the potential minimum. of cach identified halo. defined so that they contain a mean internal density equal to 200 imes the critical density of the Universe at the redshift we are considering.," Halo properties quoted in this paper are defined with respect to spheres with radius $r_{200}$ and mass $m_{200}$, centred on the potential minimum of each identified halo, defined so that they contain a mean internal density equal to 200 times the critical density of the Universe at the redshift we are considering."1020 We note that although we will present. results. only or the reference. implementation of the subericl physics modules. we have repeated the analysis for a range of physics implementations.," We note that although we will present results only for the reference implementation of the subgrid physics modules, we have repeated the analysis for a range of physics implementations."1021 This is important because the cillerent physics prescriptions can allect the density. temperat and velocity fields. of the absorbing eas. changing theure owedieted: ion abundances and optical depths.," This is important because the different physics prescriptions can affect the density, temperature and velocity fields of the absorbing gas, changing the predicted ion abundances and optical depths."1022 We fine. rowever. that using either a simulation with strong. ACN ecdback in the OWLS nomenclature). or a simulation that neelects both supernova feedback. and cooling through metal lines in the OWLS nomenclature) has a negligible effect on our results or conclusions.," We find, however, that using either a simulation with strong, AGN feedback in the OWLS nomenclature), or a simulation that neglects both supernova feedback and cooling through metal lines in the OWLS nomenclature) has a negligible effect on our results or conclusions."1023 In order to predict a synthetic ΤονTHi relation. we require knowledge of both the distribution of metals and the physical state of the absorbing eas.," In order to predict a synthetic $\tauciv-\tauhi$ relation, we require knowledge of both the distribution of metals and the physical state of the absorbing gas."1024 In the simulation. gas metallicities are tracked self-consistentIy. but in the present study we do not make use of this information.," In the simulation, gas metallicities are tracked self-consistently, but in the present study we do not make use of this information."1025" We instead assume that all haloes with a total mass greater than ms; are able to enrich. the surrounding gas out to a proper distance r, to a metallicity Z. and that outside of these Esheres the metallicity of the LGAL is zero."," We instead assume that all haloes with a total mass greater than $\menrich$ are able to enrich the surrounding gas out to a proper distance $\renrich$ to a metallicity $\zenrich$, and that outside of these spheres the metallicity of the IGM is zero."1026 Our moclel for 1e intergalactic metal distribution is therefore completely Es»ecified hy three parameters: my. rz and Z.," Our model for the intergalactic metal distribution is therefore completely specified by three parameters: $\menrich$, $\renrich$ and $\zenrich$."1027" As we wil sec. the parameters rc, and ης determine the shape of the relation between rciv and τη, which is the primary focus of us paper."," As we will see, the parameters $\renrich$ and $\menrich$ determine the shape of the relation between $\tauciv$ and $\tauhi$, which is the primary focus of this paper."1028 Phe metallicity changes only the normalisation. with rciv-x Z. so we simply scale Z in each run to match the normalisation of the observed. τοινTH relation a log(7H)=2.5. the largest optical depth probed. by the observations.," The metallicity changes only the normalisation, with $\tauciv\propto\zenrich$ , so we simply scale $\zenrich$ in each run to match the normalisation of the observed $\tauciv-\tauhi$ relation at $\log_{10}(\tauhi)=2.5$, the largest optical depth probed by the observations."1029 At this point we must note one caveat: we have iniposec metal distributions on to already. completed. simulations. the models are not fully self-consistent in that they do no include the elfect of the winds that carry the metals on the density ancl temperature structure of the gas and in tha they do not include the ellect of the metals on the cooling rates.," At this point we must note one caveat: we have imposed metal distributions on to already completed simulations, the models are not fully self-consistent in that they do not include the effect of the winds that carry the metals on the density and temperature structure of the gas and in that they do not include the effect of the metals on the cooling rates."1030 The Last point is. however. not à major concern as we will show that the metallicities required to match the observations are sullicientlv low (typically 10%18PE Fig. 2)).," The last point is, however, not a major concern as we will show that the metallicities required to match the observations are sufficiently low (typically $10^{-3}-10^{-2}Z_\odot$; Fig. \ref{fig:od}) ),"1031 that metals do not significantly. change the eas cooling rates2009a)., that metals do not significantly change the gas cooling rates.1032. While the hvdrodvnamical simulations that uncerlie our models did include winds. these winds fall short of being able to account for the observed CIV at low 7g. as we will show elsewhere.," While the hydrodynamical simulations that underlie our models did include winds, these winds fall short of being able to account for the observed $\civ$ at low $\tau_{\rm HI}$, as we will show elsewhere."1033 This failure is actually consistent with our results., This failure is actually consistent with our results.1034 Although the simulations have sullicient resolution to identify dark matter haloes to very low niasses (corresponding to 107 dark matter particles). their finite resolution does cause us to strongly underestimate the star formation rates in most of the low-mass haloes that we can identify.," Although the simulations have sufficient resolution to identify dark matter haloes to very low masses (corresponding to $\sim103510^2$ dark matter particles), their finite resolution does cause us to strongly underestimate the star formation rates in most of the low-mass haloes that we can identify."1036 Hence. the simulations underestimate the number and strength of the outllows originating [rom the low-mass haloes that we claim to be responsible for the enrichment of the IGM.," Hence, the simulations underestimate the number and strength of the outflows originating from the low-mass haloes that we claim to be responsible for the enrichment of the IGM."1037 Because not all of the gas that is enriched in our models was touched by winds in the underlying hydro simulation. we cannot exclude the possibility that a self-consistent simulation giving rise to à similar clistribution of bubbles would. predict the enriched gas to be too hot to be visible in €IV.," Because not all of the gas that is enriched in our models was touched by winds in the underlying hydro simulation, we cannot exclude the possibility that a self-consistent simulation giving rise to a similar distribution of bubbles would predict the enriched gas to be too hot to be visible in $\civ$."1038 Reassurinely. we find. as noted above. that post-processing simulations without winds or with much stronger winds leads to identical conclusions.," Reassuringly, we find, as noted above, that post-processing simulations without winds or with much stronger winds leads to identical conclusions."1039 We note that we expect the heating elect of outllows from low-mass galaxies to be smaller than those from the more massive galaxies that our simulations do include., We note that we expect the heating effect of outflows from low-mass galaxies to be smaller than those from the more massive galaxies that our simulations do include.1040 ‘This is because there are already many low-mass galaxies at high redshift. giving the gas more time to cool. and cause they are observed. to drive winds of velocities 10 Kkm/s (this velocity corresponds το post-shock temperatures. of ~2. LOW. assuming the gas is Cully ionized and of »wimordial composition). which leaves the post-shock gas at temperatures for which the cooling time is much shorter han the age of the Universe," This is because there are already many low-mass galaxies at high redshift, giving the gas more time to cool, and because they are observed to drive winds of velocities $\la 10^2$ km/s (this velocity corresponds to post-shock temperatures of $\sim10412\times10^5$ K, assuming the gas is fully ionized and of primordial composition), which leaves the post-shock gas at temperatures for which the cooling time is much shorter than the age of the Universe."1042 The conclusions based on our. simple models will. 1owever. Ultimately need to be confirmed by self-consistent. werodyvnamical simulations.," The conclusions based on our simple models will, however, ultimately need to be confirmed by self-consistent, hydrodynamical simulations."1043 Unfortunately. at the moment such simulations rely on uncertain subgrid models for the ecncration of winds and hey lack the resolution required. to model outllows from ow-nmass galaxies and to simulate the small-scale mixing relevant for the observations2007).," Unfortunately, at the moment such simulations rely on uncertain subgrid models for the generation of winds and they lack the resolution required to model outflows from low-mass galaxies and to simulate the small-scale mixing relevant for the observations."1044". The bulk of our results are derived from a ericl of models in which m. is varied in steps of 0.5 dex from the lowest mass haloes that can be robustly identified in the highest resolution simulation. m,=107M.. which are the least massive halocs that are expected to be able to produce stars alter reionization1996).. up to m;=10M."," The bulk of our results are derived from a grid of models in which $\menrich$ is varied in steps of 0.5 dex from the lowest mass haloes that can be robustly identified in the highest resolution simulation, $\menrich=10^8\,\msun$, which are the least massive haloes that are expected to be able to produce stars after reionization, up to $\menrich=10^{11}\,\msun$."1045 Note that a mass of 107AL. is small compared. with the total masses inferred for observed. galaxies at 2=3.," Note that a mass of $10^{11}\,\msun$ is small compared with the total masses inferred for observed galaxies at $z=3$."1046 For example. find that. Lvman-break ealaxies reside in haloes of mass 1077M...," For example, find that Lyman-break galaxies reside in haloes of mass $\sim10^{12}\,\msun$."1047 However. as we will show. such high-mass galaxies are unimportant for the enrichment of the IGM.," However, as we will show, such high-mass galaxies are unimportant for the enrichment of the IGM."1048 The parameter r4 is changed in factors of 2 [rom 31.25 kpe to 500 kpe., The parameter $\renrich$ is changed in factors of 2 from $31.25$ kpc to 500 kpc.1049 In addition. we investigate à set. of runs in which haloes in the fidiucial simulation are allowed to enrich the IGM out to a fixed multiple oftheir virial radius. rogo.," In addition, we investigate a set of runs in which haloes in the fiducial simulation are allowed to enrich the IGM out to a fixed multiple of their virial radius, $r_{200}$."1050 Galactie winds with velocities up to 400-600 kim/s are frequently detected. in starburst galaxies through the gas absorption lines that are bluc-shiltec relative to their host ealaxies2, Galactic winds with velocities up to 400-600 km/s are frequently detected in starburst galaxies through the gas absorption lines that are blue-shifted relative to their host galaxies.1051011)... Howe assume that winds were ejected. from ealaxies at high redshift (2>> 3) and that their velocities do not decrease with time. thenby z=3 galaxies can enrich out to a maximum radius of 0.9 L4 proper Alpe.," If we assume that winds were ejected from galaxies at high redshift $z\gg3$ ) and that their velocities do not decrease with time, thenby $z=3$ galaxies can enrich out to a maximum radius of $0.9-1.4$ proper Mpc."1052 The assumption of a constant. high outllow velocity and launch," The assumption of a constant, high outflow velocity and launch"1053"In Figure 12,, we present a series of plots that further support the assertion thatMilkomeda resembles an elliptical galaxy and also serve to better quantify its properties.","In Figure \ref{fig:remnant}, we present a series of plots that further support the assertion that resembles an elliptical galaxy and also serve to better quantify its properties."1054" In panel (a), we present the spherically averaged mass profile, decomposed by the three components; dark matter, stellar and gaseous mass."," In panel (a), we present the spherically averaged mass profile, decomposed by the three components; dark matter, stellar and gaseous mass."1055" At radii greater than ~2—3 kpc, the dark matter dominates the mass density, and at radii greater than ~20 kpc, the profile is well-fit by the NFW (?) or Hernquist (?) profile."," At radii greater than $\sim2-3$ kpc, the dark matter dominates the mass density, and at radii greater than $\sim20$ kpc, the profile is well–fit by the NFW \citep{NFW96} or Hernquist \citep{H90} profile."1056 The projected mass distribution shown in panel (b) of Figure 12 presents the first direct evidence thatMilkomeda resembles an elliptical galaxy., The projected mass distribution shown in panel (b) of Figure \ref{fig:remnant} presents the first direct evidence that resembles an elliptical galaxy.1057" Specifically, the stellar surface density is close to a pure RA distribution, with the exception of the inner ~400 pc (2.5x the gravitational softening length), where the surface density flattens to a nearly constant density core."," Specifically, the stellar surface density is close to a pure $^{1/4}$ distribution, with the exception of the inner $\sim400$ pc $\sim2.5\times$ the gravitational softening length), where the surface density flattens to a nearly constant density core."1058 We have also quantified the kinematics and isophotal shape of theMilkomeda galaxy following the methods of ?.., We have also quantified the kinematics and isophotal shape of the galaxy following the methods of \citet{Cox06rot}.1059" Panel (ο) in Figure 12 presents the anisotropy diagram, a measure of the half-mass isophote ellipticity versus the maximum rotation along its major axis divided by the central velocity dispersion."," Panel (c) in Figure \ref{fig:remnant} presents the anisotropy diagram, a measure of the half–mass isophote ellipticity versus the maximum rotation along its major axis divided by the central velocity dispersion."1060" The shaded region represents the distribution of values forMilkomeda if viewed from 195 directions that uniformly sample the unit sphere (withanglesselectedusingHEALPIX, ?).."," The shaded region represents the distribution of values for if viewed from 195 directions that uniformly sample the unit sphere \citep[with1061angles selected using HEALPIX,][]{Gor05}."1062 Also plotted in this figure is the relation expected from an oblate isotropic rotator as a solid line., Also plotted in this figure is the relation expected from an oblate isotropic rotator as a solid line.1063" Owing to the high concentration of projections that closely track the solid line, this analysis demonstrates thatMilkomeda is nearly an oblate isotropic rotator."," Owing to the high concentration of projections that closely track the solid line, this analysis demonstrates that is nearly an oblate isotropic rotator."1064" In addition, the deviations from a perfect ellipse are also quantified and are presented in panel (d) in Figure 12.."," In addition, the deviations from a perfect ellipse are also quantified and are presented in panel (d) in Figure \ref{fig:remnant}."1065" Depending on the viewing direction,Milkomeda may appear to be either disky or boxy, with a slightly larger fraction of views producing disky isophotes."," Depending on the viewing direction, may appear to be either disky or boxy, with a slightly larger fraction of views producing disky isophotes."1066 We have also analyzed the properties of the hotgas in and aroundMilkomeda., We have also analyzed the properties of the hotgas in and around.1067" The evolution of this component was presented in Figure 3 and clearly demonstrates the formation of an extended gaseous halo, primarily accreted from the large reservoir of the intragroup medium."," The evolution of this component was presented in Figure \ref{fig:gasimages} and clearly demonstrates the formation of an extended gaseous halo, primarily accreted from the large reservoir of the intragroup medium."1068" Although the gas temperature was originally 3x10° K, it has been shock-heated to the virial temperature of ~3x10° K inMilkomeda and has a gradient to cooler temperatures at large radii."," Although the gas temperature was originally $3\times10^5$ K, it has been shock-heated to the virial temperature of $\sim3\times10^6$ K in and has a gradient to cooler temperatures at large radii."1069" This hot gas leads to an X-ray surface brightness profile shown in panel (e) of Figure 12 and a total X- luminosity of 1041 ergs s!, which is consistent with present-day elliptical galaxies of equivalent B-band luminosity (~3x10? Lo))."," This hot gas leads to an X-ray surface brightness profile shown in panel (e) of Figure \ref{fig:remnant} and a total X-ray luminosity of $\sim10^{41}$ ergs $^{-1}$, which is consistent with present–day elliptical galaxies of equivalent B-band luminosity $\sim3\times10^{10}$ )."1070" In general,Milkomeda resembles the remnants of gas-rich major mergers, which in-turn resemble the general population of low- and moderate-luminosity elliptical galaxies (??).."," In general, resembles the remnants of gas–rich major mergers, which in–turn resemble the general population of low– and moderate–luminosity elliptical galaxies \citep{NJB06,Cox06rot}."1071" However, there are some systematic differences that likely arise because of the much smaller gas content of the Milky Way and Andromeda when they merge."," However, there are some systematic differences that likely arise because of the much smaller gas content of the Milky Way and Andromeda when they merge."1072" In particular, the inner regions of Milkomeda have a much lower stellar density than present-day ellipticals,"," In particular, the inner regions of have a much lower stellar density than present–day ellipticals,"1073 , 1074is possible to simultancously constrain the gas-to-dust ratio andoco.,is possible to simultaneously constrain the gas-to-dust ratio and.1075 Nev advantages of this approach are that it renuains sensitive to any CO-free euvelopes of aand that the calibration of ac 1s pinned to the wwithin the system being studied.," Key advantages of this approach are that it remains sensitive to any CO-free envelopes of and that the calibration of $\alpha_{\rm1076 CO}$ is pinned to the within the system being studied."1077 This exercise has been applied to several dwarf nreeular galaxies (?7777.Bolattoctal2010.i|prepuation).," This exercise has been applied to several dwarf irregular galaxies \citep[][Bolatto et al. 2010, in1078 preparation]{ISRAEL97,ISRAEL97B,LEROY07,LEROY09,GRATIER10}."1079 In the low-nmetalliitv S1uall Magellanic Cloud. the results sugsest a very— large aco90 270," In the low-metallicity Small Magellanic Cloud, the results suggest a very large $\alpha_{\rm CO} \sim 90$ $270$."1080 An analogous application to the πια Way vields oem~| OAL. citepBLOEMENSO. DAMEOL. roughly compatible with determinations of froin fitting the diffuse οταν backerouned (??)..," An analogous application to the Milky Way yields $\alpha_{\rm CO} \sim10814$ $9$ \\citep{BLOEMEN90, DAME01}, roughly compatible with determinations of from fitting the diffuse $\gamma$ -ray background \citep[][]{STRONG96,ABDOXCO}."1082 Most studies of ace have focused on a single galaxy or high latitudes in the Milky Way. where confusion is uiim," Most studies of $\alpha_{\rm CO}$ have focused on a single galaxy or high latitudes in the Milky Way, where confusion is minimal."1083inial ? worked with a varied galaxy sample but since is work the available IR and CO data for nearby galaxies lave proved dramatically., \citet{ISRAEL97} worked with a varied galaxy sample but since his work the available IR and CO data for nearby galaxies have improved dramatically.1084 This is largely thauks to theSpitzer Space Telescope. which recently finished its cool wission aud produced high quality maps of a number of Local Group galaxies.," This is largely thanks to the Space Telescope, which recently finished its cool mission and produced high quality maps of a number of Local Group galaxies."1085 This is therefore a natural tine to apply this technique to measure aacross the Local Group in a selt-cousisteut way., This is therefore a natural time to apply this technique to measure across the Local Group in a self-consistent way.1086 Iu this paper. we combine maps of CO.IDL aud IR chussion to estimate imn five Local Group galaxies: tle massive spiral M 31. the dwart spiral M 233. the dwarf nregular NGC 6822. aud the Large aud Sinall Magellanic Clouds (the LAC aud SAIC).," In this paper, we combine maps of CO, and IR emission to estimate in five Local Group galaxies: the massive spiral M 31, the dwarf spiral M 33, the dwarf irregular NGC 6822, and the Large and Small Magellanic Clouds (the LMC and SMC)."1087 By treating all five systems self-consisteutIv. we miniuize nucertaity in the “zero poiut of the approach.," By treating all five systems self-consistently, we minimize uncertainty in the ""zero point"" of the approach."1088 With heHerschel uiission now uuderway and the execution of several complementary CO αμα suurvevs. this approach should be readily extensible Πας nearby galaxies in the next few wears.," With the mission now underway and the execution of several complementary CO and surveys, this approach should be readily extensible to many nearby galaxies in the next few years."1089 We and assune that dust aud gas are linearly related wea gas-to-dust ratio. Ócipig. so that where Mayers Sy. and “yy are the mass surface densities of dust. IT. aud aaloug a line of sight.," We and assume that dust and gas are linearly related by a gas-to-dust ratio, $\delta_{\rm GDR}$, so that where $\Sigma_{\rm dust}$, $\Sigma_{\rm H2}$, and $\Sigma_{\rm HI}$ are the mass surface densities of dust, , and along a line of sight."1090 Substituting Myo=acefoo we have where the CO-to-IT» conversion factor. aco. and dust ratio. Ócipg are uuknuown and Nays. foo. aud “yyy are measured.," Substituting $\Sigma_{\rm H2} =1091\alpha_{\rm CO}~I_{\rm CO}$ we have where the $_2$ conversion factor, $\alpha_{\rm CO}$, and gas-to-dust ratio, $\delta_{\rm GDR}$, are unknown and $\Sigma_{\rm dust}$, $I_{\rm CO}$ and $\Sigma_{\rm HI}$ are measured."1092 After asseimibliug Xa. foo. and “yyy over many lines of sight in a region. we will use these data to solve for aco that best allows a single d¢ypR to describe the data.," After assembling $\Sigma_{\rm dust}$, $I_{\rm CO}$, and $\Sigma_{\rm HI}$ over many lines of sight in a region, we will use these data to solve for $\alpha_{\rm CO}$ that best allows a single $\delta_{\rm GDR}$ to describe the data."1093 The literature coutains several working defuitions of aco that apply to differeut scales or phases of the eas., The literature contains several working definitions of $\alpha_{\rm CO}$ that apply to different scales or phases of the gas.1094 Iu this paper aud Equation 2. we define age as the factor to convert from CO cussion totote? molecular eas mass on scales larger than individual clouds., In this paper and Equation \ref{eq:model} we define $\alpha_{\rm CO}$ as the factor to convert from CO emission to molecular gas mass on scales larger than individual clouds.1095 Under this definition. oco includes any IH» associated with C! in the outer. poorly shielded parts of clouds as well as eas inuucdiately mixed with CO.," Under this definition, $\alpha_{\rm CO}$ includes any $_2$ associated with $^{+}$ in the outer, poorly shielded parts of clouds as well as gas immediately mixed with CO."1096 Indeed. our goal is to measure Whether such cuvelopes become douiuaut below sole metallicity.," Indeed, our goal is to measure whether such envelopes become dominant below some metallicity."1097 Because this definition iuteerates over cloud. structure. if is possible to derive a single oc) for a whole ealaxy or part of a galaxy. and to view that aco as a function of large-scale enviroummoenutal factors.," Because this definition integrates over cloud structure, it is possible to derive a single $\alpha_{\rm CO}$ for a whole galaxy or part of a galaxy, and to view that $\alpha_{\rm CO}$ as a function of large-scale environmental factors."1098 We choose this defiuition of ac because it is directly applicable to CO iueasureimeuts of distant galaxies ou slloparsec scales., We choose this definition of $\alpha_{\rm CO}$ because it is directly applicable to CO measurements of distant galaxies on kiloparsec scales.1099 This is distinct from the ratio of CO to II» ouly for nolecular eas mixed with CO., This is distinct from the ratio of CO to $_2$ only for molecular gas mixed with CO.1100 Dynamical iieasurements using CO ciission at lieh spatial resolution may nally probe this quautity with liuited scusitivity o Hl» in au extended cuvelope not mixed with CO., Dynamical measurements using CO emission at high spatial resolution may mainly probe this quantity with limited sensitivity to $_2$ in an extended envelope not mixed with CO.1101 The difference between this quantity aud the quantity hat we study has caused some confusion. leading to apparent coutraclictions between IBR-based iieasurenmenuts and dynamical measurements.," The difference between this quantity and the quantity that we study has caused some confusion, leading to apparent contradictions between IR-based measurements and dynamical measurements."1102 Iu fact these may be areclv attributed to the differeut regions being probed (Section 6))., In fact these may be largely attributed to the different regions being probed (Section \ref{sec:discussion}) ).1103 Sinularh. we donof define eco as the ratio of IT» to CO along a pencil beam.," Similarly, we do define $\alpha_{\rm CO}$ as the ratio of $_2$ to CO along a pencil beam."1104 We have no reason to expect hat this quautity. or any ratio that places many elements across a cloud. romiaius reasonably constant across part of a galaxy.," We have no reason to expect that this quantity, or any ratio that places many elements across a cloud, remains reasonably constant across part of a galaxy."1105" To the contrary comparisons of dust aud CO enission imply dramatic variations in the CO-to-IL, ratio within iudividual clouds (7?)..", To the contrary comparisons of dust and CO emission imply dramatic variations in the $_2$ ratio within individual clouds \citep{PINEDA08}.1106 Our spatial resolution ranges from [5180 pe (Table 1)), Our spatial resolution ranges from 45–180 pc (Table \ref{tab:data}) ).1107 For these resolutions. giant molecular clouds will mostly lie within one or two resolution elements ?)..," For these resolutions, giant molecular clouds will mostly lie within one or two resolution elements \citep[e.g.,][]{HEYER09}."1108 This is ideal for our definition of aco., This is ideal for our definition of $\alpha_{\rm CO}$.1109 We wish to inteerate over the structure of these clouds to make a single oc) a more appropriate assmuption., We wish to integrate over the structure of these clouds to make a single $\alpha_{\rm CO}$ a more appropriate assumption.1110 To carry out this experiment we require maps of IR (to estimate Maya). CO. and cecluission.," To carry out this experiment we require maps of IR (to estimate $\Sigma_{\rm dust}$ ), CO, and emission."1111 Such maps have been publishedfor AL 31. AD 33. NGC 6822.the LAIC aud the SAIC.," Such maps have been publishedfor M 31, M 33, NGC 6822,the LMC and the SMC."1112 We refer to the original papers for details of the observations. reduction. and data.," We refer to the original papers for details of the observations, reduction, and data."1113 For M 31. we use the CO map taken by? using the," For M 31, we use the CO map taken by \citet{NIETEN06} using the"1114"We note also that the implied values for the normalization in our region is (based. on WALAPM best-fit),.TE which: forj our assumed. value ofd Oy givesd { ↽↽−↽ − ⋅∩⋅⋮↽⊰⋖↽∖⋟∣∣∣⋡∣∣↕↓≽⊽⊳↕⋅∙↿∏⋟∖⊽↥∪∖↽≼↲↕⋅↥≀↧↴↕≻↕≻↕∐≸↔↴∖∖⇁↕⊔↥⊔∐↲≺∢↥∏⋟∖⊽∩↲↕⋅∐∐↲≀↕⊔∖⇁⋯⋅≼↲∐∐↲↕∐⋟∖⊽⊔↴↴≤≥∎∎↝∎⋅∶∩⋅≡↽⊰≡↽⊰∶∶∩⋅∩⋮↽⊰⋅","We note also that the implied values for the normalization in our region is $\sigma_8 \sim 0.83^{+0.03}_{-0.05}$ (based on WMAP best-fit), which for our assumed value of $\Omega_0$ gives $\sigma_8\Omega_0^{0.6}=0.38^{+0.015}_{-0.025}$ , just overlapping with the cluster measurements $\sigma_8\Omega^{0.6}=0.33\pm0.03$."1115 The next question is what are the implications as to the implied values of the , The next question is what are the implications as to the implied values of the UV-efficiency?1116Do the efficiencies make sense?, Do the efficiencies make sense?1117 Table 5 shows a number of parameter combinations from the region., Table \ref{tab:parmres} shows a number of parameter combinations from the region.1118" Theimplied efficiency at high redshift is on the order ~10!: a (vansilion occurs al 2=15~20. and the elliciency at low redshift is eo10777ο, "," Theimplied efficiency at high redshift is on the order $\sim 10^{-4}$; a transition occurs at $z = 15\sim20$, and the efficiency at low redshift is $\epsilon_{\rm UV,0} = 10^{-5.5 \sim -5}$."1119"The span of these efficiencies encompasses those (wpically caleulated through population svnthesis of 10στ1, ", The span of these efficiencies encompasses those typically calculated through population synthesis of $10^{-5 \sim -4.5}$.1120Given uncertainties of [actors of a [ew in the gas collapse fraction (our resolution [actor ει). dust absorption (at lower redshift). etc..," Given uncertainties of factors of a few in the gas collapse fraction (our resolution factor $\epsilon_\ast$ ), dust absorption (at lower redshift), etc.,"1121 the values of the efficiencies do not seem unreasonable., the values of the efficiencies do not seem unreasonable.1122 They certainly do not approach the upper bound [ον conversion [rom nuclear reactions of ~107. So, They certainly do not approach the upper bound for conversion from nuclear reactions of $\sim 10^{-3}$.1123kasianetal.(2003) and WivitheandLoeb(2003) discuss further (he star formation efficiency as relating to Population IH and Population ILI stars., \citet{Sok03} and \citet{WL03} discuss further the star formation efficiency as relating to Population II and Population III stars.1124 Our results are consistent with the results of Cen(2003) in that we find that to reach Tor&OLT requires that the spectral index is positively tilted with »z1.02.," Our results are consistent with the results of \citet{Cen03}1125 in that we find that to reach $\tau_{\rm es} \geq 0.17$ requires that the spectral index is positively tilted with $n \gtrsim 1.02$."1126 In this case the ellective UV-efficienev wasat least. LOOx greater at 2>>6., In this case the effective UV-efficiency wasat least $100\times$ greater at $z \gg 6$.1127 However. our caleulations inclicate Chat models with such high » (and hence high power spectrum normalization oy) are inconsistent with quasar transmission measurements at redshift 2<5.," However, our calculations indicate that models with such high $n$ (and hence high power spectrum normalization $\sigma_8$ ) are inconsistent with quasar transmission measurements at redshift $z \lesssim 5$."1128 Like other authors (e.g.. ILaiman and Holder 2003. Cen 2003). we find that a value of T4=Ü.lT is inconsistent with constraints at 2<6 for simple models of reionization. and nmav require more exotic (though not necessarily implausible) methods for creating ionizing photons. such as mini-cquasars or an X-ray. background.," Like other authors (e.g., Haiman and Holder 2003, Cen 2003), we find that a value of $\tau_{\rm es} = 0.17$ is inconsistent with constraints at $z\lesssim 6$ for simple models of reionization, and may require more exotic (though not necessarily implausible) methods for creating ionizing photons, such as mini-quasars or an X-ray background."1129 Iowever. we conclude that WALAP data taken as a whole and quasar observations at zS6 in fact areentirely consistent for reasonable values and Gme-dependence for the UV-eflieney.," However, we conclude that WMAP data taken as a whole and quasar observations at $z\lesssim 6$ in fact $\emph{are entirely}$ consistent for reasonable values and time-dependence for the UV-efficiency."1130" Our analvsis shows the importance of (aking into account the significant degeneracy between 7, aud η determined by WMAD.", Our analysis shows the importance of taking into account the significant degeneracy between $\tau_{\rm es}$ and $n$ determined by WMAP.1131 llaving found a consistent set of evolutionary. models. let us describe their properties in slightly greater detail.," Having found a consistent set of evolutionary models, let us describe their properties in slightly greater detail."1132" We consider the following (wo models: a model with constant with f=0.72. Og=0.27. n=0.99. og=0.64. εν=2.2xLO7. and 7.=0.06): and a model with variable efficiency with f=0.72. O4,=0.27. n=0.96. o,=0.821. εν=7T.7XLO""(14-1706Fel?.. and τις=0.11."," We consider the following two models: a model with constant UV-efficiency with $h=0.72$, $\Omega_0=0.27$, $n=0.99$, $\sigma_8=0.64$, $\epsilon_{\rm UV}=2.2\times 10^{-5}$, and $\tau_{\rm es}=0.06)$; and a model with variable efficiency with $h=0.72$, $\Omega_0=0.27$, $n=0.96$, $\sigma_8=0.827$, $\epsilon_{\rm UV}=7.7\times 10^{-6}(1+17e^{-f_\ast/10^{-4}})$, and $\tau_{\rm es}=0.11$."1133 These are both near peak of the likelihood distiibution lor Qy= 0.27., These are both near peak of the likelihood distribution for $\Omega_0=0.27$ .1134 The Gunn-leterson optical depths are already shown in Figure 3.., The Gunn-Peterson optical depths are already shown in Figure \ref{fig:taueffplot}. .1135 The best-fit models do not show much diflerence. as expected since the parameters were fit to these data.," The best-fit models do not show much difference, as expected since the parameters were fit to these data."1136 Figure shows (he reionization properties lor the (wo models., Figure \ref{fig:bestfitplot} shows the reionization properties for the two models.1137 although the last phase of reionization, although the last phase of reionization1138"This leads to the trascendental equation for the eigenvalue A,,. n=1.2.3... which has the solution for 7<>1 and» =1 It is important to emphasize that the same result for A, is obtained by solving equation (12)) for a slab with total optical depth τι but with reflection condition d.J/dr=0 at 7=7.","This leads to the trascendental equation for the eigenvalue $\lambda_n$ , $n=1,2, 3 ...$ which has the solution for $\tau_0 \gg 1$ and $n=1$ It is important to emphasize that the same result for $\lambda_1$ is obtained by solving equation \ref{eigenval_eq}) ) for a slab with total optical depth $\tau_0$ but with reflection condition $dJ/d\tau=0$ at $\tau=\tau_0$."1139" This is not surprising as such a condition is actually met at the center of a symmetric slab with total optical depth 27, and Q<7<27).", This is not surprising as such a condition is actually met at the center of a symmetric slab with total optical depth $2\tau_0$ and $0 \leq \tau \leq 2\tau_0$.1140 Thus. the same mathematical result is obtained for two different geometrical configurations.," Thus, the same mathematical result is obtained for two different geometrical configurations."1141 In the first case (symmetric slab with total optical depth 27)) it represents. e.g.. an accretion disk (ST85 treatment). in our present case we are dealing with a boundary layer with total optical depth 7). whose asymmetry is due to the presence of a reflector (NS surface) at one of the two boundaries.," In the first case (symmetric slab with total optical depth $2\tau_0$ ) it represents, e.g., an accretion disk (ST85 treatment), in our present case we are dealing with a boundary layer with total optical depth $\tau_0$, whose asymmetry is due to the presence of a reflector (NS surface) at one of the two boundaries."1142 In both cases one obtains Generalizing to the case of arbitrary optical depth τη. the diffusion operator Lig(1/3)07Jfd77 is replaced by the radiative transfer operator L- applied to (7) (see ST85 and TL95) which for the disk geometry is where £4(:) is the exponential integral of the first order.," In both cases one obtains Generalizing to the case of arbitrary optical depth $\tau_0$, the diffusion operator $L_{\rm diff}=(1/3)d^2J/d\tau^2$ is replaced by the radiative transfer operator $L_{\tau}$ applied to $J(\tau)$ (see ST85 and TL95) which for the disk geometry is where $E_1(z)$ is the exponential integral of the first order."1143" In this case. the derived value for ./ is (Titarchuk.1994,TL95) Now having in mind equation. (9)). we introduce the parameter and in Figure 2. we show the values of ./ for the cases reported in formulas (15)). (17)) and (18)) as a function of optical depth 7)."," In this case, the derived value for $\beta$ is \citep[][TL95]{t94}1144 Now having in mind equation \ref{ktetau}) ), we introduce the parameter and in Figure \ref{beta_vs_tau} we show the values of $\beta$ for the cases reported in formulas \ref{beta_as}) ), \ref{beta_general}) ) and \ref{beta_diff}) ) as a function of optical depth $\tau_0$."1145" It is possible to see that actually for 721.5 all values of ./ are practically close each other. but they deviate for 7,ὃς1."," It is possible to see that actually for $\tau_0 \ga 1.5$ all values of $\beta$ are practically close each other, but they deviate for $\tau_0 \la 1$."1146" For example their difference is about for 7,21.", For example their difference is about for $\tau_0$ =1.1147 Using the definition of à (see Eq. 2)).," Using the definition of $\alpha$ (see Eq. \ref{alpha_general}) ),"1148 where > is replaced by aie (Eq. 18)).," where $\beta$ is replaced by $\beta_{\rm diff}$ (Eq. \ref{beta_diff}) ),"1149 and equation (9). we obtain the diffusion spectral index as ⋂∣⋪∩≺∐↕−↥∶↓↖∩∙≺∖∖OdiskQu for OdiskOQeur<i.," and equation \ref{ktetau}) ), we obtain the diffusion spectral index as or $ \alpha_{\rm diff}=1+0.8~ \qd/\qcor$ for $\qd/\qcor<1$."1150 Thus as it follows from Eq. (19)).," Thus as it follows from Eq. \ref{alpha_diff}) ),"1151 in the diffusion regime the TC spectral index can be expressed in terms of Quisk/Qeor (the intercepted disk over coronal fluxes). instead of TL electron temperature &T;. and optical depth 7 (see Eqs. [21] ," in the diffusion regime the TC spectral index can be expressed in terms of $\qd/\qcor$ (the intercepted disk over coronal fluxes), instead of TL electron temperature $kT_e$ and optical depth $\tau_0$ (see Eqs. \ref{alpha_general}] ]"1152and [15]])., and \ref{beta_as}] ]).1153 In Figure 3. we present a plot of agi as a function of μον. Which shows that it ranges from 1 to 1.6 as Quia/Qu increases from 0 to 1.," In Figure \ref{alpha_plot} we present a plot of $\alpha_{\rm diff}$ as a function of $\qd/\qcor$, which shows that it ranges from 1 to 1.6 as $\qd/\qcor$ increases from 0 to 1."1154 One can see the observable values of index a—1 takes place if the energy release in the disk is much less that in TL. namely if Ωωdeorx.," One can see the observable values of index $\alpha\sim1$ takes place if the energy release in the disk is much less that in TL, namely if $Q_{disk}/Q_{cor}\ll1$."1155 In this Paper we compare observational dataof a sample of NS sources (Fig. 1)), In this Paper we compare observational dataof a sample of NS sources (Fig. \ref{alpha_data}) )1156 with the theoretical results which follows from the radiative transfer model in the diffusion. approximation., with the theoretical results which follows from the radiative transfer model in the diffusion approximation.1157" The data show thatstate. which we have parametrized through the measured TL electron temperature AT,;.. the spectral index α=1-70.2."," The data show that, which we have parametrized through the measured TL electron temperature $kT_e$, the spectral index $\alpha= 1\pm 0.2$."1158 We derived anestimate of the energy index a for TC spectra in NS LMXBs using an equation for the diffusion approximation in a slab geometry with the reflection (100 %)) boundary condition. which is valid for optical depth 7)Z 1.5.," We derived anestimate of the energy index $\alpha$ for TC spectra in NS LMXBs using an equation for the diffusion approximation in a slab geometry with the reflection (100 ) boundary condition, which is valid for optical depth $\tau_0 \ga 1.5$ ."1159 In particular. we find that in this approximation it is possible to express the value of," In particular, we find that in this approximation it is possible to express the value of"1160"deviation of the density of NB«20.8 galaxies ina aarcmin? cell is aarcmin?, and aarcmin~? for a aarcmin? cell.","deviation of the density of $NB<20.8$ galaxies ina $^2$ cell is $^{-2}$, and $^{-2}$ for a $^2$ cell."1161" There is a large overdensity of NB-excess objects in the radio galaxy fields, with 5+1 and 6+1 times more objects surrounding aand 11138-262 respectively than the control field."," There is a large overdensity of NB-excess objects in the radio galaxy fields, with $\pm1$ and $6\pm1$ times more objects surrounding and 1138-262 respectively than the control field."1162" The galaxy of the ggalaxies around iis Oyg=4-1, and ὄνη—54:1 in the 11138-262 field."," The galaxy of the galaxies around is $\delta_{\rm NB} =4\pm1$, and $\delta_{\rm NB}=5\pm1$ in the 1138-262 field."1163 The of these overdensities are 50 for aand 86 for the 11138-262proto-cluster., The of these overdensities are $\sigma$ for and $\sigma$ for the 1138-262.1164". The highly significant overdensity around iimplies this radio galaxy also resides in a dense large-scale structure that extends beyond the immediate influence of the radio galaxy, at least out to distances of MMpc (physical)."," The highly significant overdensity around implies this radio galaxy also resides in a dense large-scale structure that extends beyond the immediate influence of the radio galaxy, at least out to distances of Mpc (physical)."1165" pprobably lies within aproto-cluster,, or proto-group environment of a similar density as that of 11138-262."," probably lies within a, or proto-group environment of a similar density as that of 1138-262."1166" In Section 2.3.2 we showed that more than half of the oobjects selected in the control fields were not eemitters at z2, but rather line-emitting contaminants at other redshifts."," In Section \ref{contaminants} we showed that more than half of the objects selected in the control fields were not emitters at $z\sim2$, but rather line-emitting contaminants at other redshifts."1167" To measure the true surface overdensity of eemitters in the radio galaxy fields, the ssources that are not eemitters must be removed."," To measure the true surface overdensity of emitters in the radio galaxy fields, the sources that are not emitters must be removed."1168 Unfortunately we are unable to apply the same colour selection we applied to the control field samples as we do not have the same multi-band data., Unfortunately we are unable to apply the same colour selection we applied to the control field samples as we do not have the same multi-band data.1169 The density of oobjects in the control field that are eemitters is aarcmin~2 (NB<20.8 mmag)., The density of objects in the control field that are emitters is $^{-2}$ $NB<20.8$ mag).1170" Therefore less than 1 ccontaminant is expected in the 6.87aarcmin? field around4-10.48,, and less than 2 ccontaminants in the 12.5 aarcmin? field around 11138-262."," Therefore less than 1 contaminant is expected in the $^{2}$ field around, and less than 2 contaminants in the $12.5$ $^{2}$ field around 1138-262."1171 Whereas we observed 11 and 24 oobjects with NB«20.8 mmag near aand 11138-262 respectively., Whereas we observed 11 and 24 objects with $NB<20.8$ mag near and 1138-262 respectively.1172 Hence less than of these objects are likely to be contaminants., Hence less than of these objects are likely to be contaminants.1173 We ignored this negligible fraction of contaminants and assumed that all the oobjects in the 11138-262 and ffields are eemitters at z2., We ignored this negligible fraction of contaminants and assumed that all the objects in the 1138-262 and fields are emitters at $z\sim2$.1174 This assumption is supported by the spectroscopic data on 2um oobjects near z~2 radio galaxies., This assumption is supported by the spectroscopic data on $2$ objects near $z\sim2$ radio galaxies.1175" ? showed that all spectroscopically confirmed ssources near 11138-262 are likely to be Ha emitters associated with the radio galaxy, as their velocity distribution is much more peaked than the filter response curve."," \citet{Kurk2004b} showed that all spectroscopically confirmed sources near 1138-262 are likely to be $\alpha$ emitters associated with the radio galaxy, as their velocity distribution is much more peaked than the filter response curve."1176" Furthermore, 2um oobjects have recently been studied around the z—2.49 nnear 223.56 (?).."," Furthermore, $2$ objects have recently been studied around the $z=2.49$ near 23.56 \citep{Tanaka2011}. ."1177" All 3 oobjects, for which spectra were obtained, exhibited an emission line withinoof 223.56, indicating they lie in a aassociated with the radio galaxy."," All 3 objects, for which spectra were obtained, exhibited an emission line withinof 23.56, indicating they lie in a associated with the radio galaxy."11781311 exhibits the lareest differeuces certainly because of its large size in relation with the instrmucut FOV.,4314 exhibits the largest differences certainly because of its large size in relation with the instrument FOV.1179 We will not extend further the comparison between the NIR inages presente here aud the optical damages iu the RCS. since the component descomposition is not performed iu the optical images.," We will not extend further the comparison between the NIR images presented here and the optical images in the RC3, since the component descomposition is not performed in the optical images."1180 The reasons for this are to be found iu the nou-nnitormity of the optical images aud the expected spurious effects cue to observational circuustances bevond our control., The reasons for this are to be found in the non-uniformity of the optical images and the expected spurious effects due to observational circunstances beyond our control.1181 However. it is clear that the NIR images more closely represent the rue stear distribution caused by the sunaller value of he extiution.," However, it is clear that the NIR images more closely represent the true stellar distribution caused by the smaller value of the extintion."1182 It is then expected that the ecolctrical features of the nan structural componcuts will be somewhat different in the two specral regimes., It is then expected that the geometrical features of the main structural components will be somewhat different in the two spectral regimes.1183 Using the results of the ellipse fiting. wo have Πασά]ος the integraed iuagnitudes of the sample in both filters (sce table £)) within a circular aperture of the radius at which the surface brightuess from the object equals that of the sky at 30 over its mean value (see tae 3)).," Using the results of the ellipse fitting, we have measured the integrated magnitudes of the sample in both filters (see table \ref{Tab:parametros}) ) within a circular aperture of the radius at which the surface brightness from the object equals that of the sky at $3\sigma$ over its mean value (see table \ref{Tab:limite}) )."1184 These values are in fairly good agrecmenut with those from the 2NTASS data (Skrutskie et al., These values are in fairly good agreement with those from the 2MASS data (Skrutskie et al.1185 1995). taken- from NED (see table 1)).," 1995), taken from NED (see table \ref{Tab:parametros}) )."1186 However. our images extend in ecucral to lareer radii than the fixed scale of 50 arcsec quoted in NED.," However, our images extend in general to larger radii than the fixed scale of 80 arcsec quoted in NED."1187 Iu those galaxies where a clear indication exists of the presence of a large central bar. either from the nuages theniselves and/or from the sudden change in the radial profiles.," In those galaxies where a clear indication exists of the presence of a large central bar, either from the images themselves and/or from the sudden change in the radial profiles."1188 We used au additional method to estimate the gcolctrica paranueters of the bar itself., We used an additional method to estimate the geometrical parameters of the bar itself.1189 The elobal PA and inclination angle of the object galaxy are used to deproject the galaxy inage in order to 1ueasure quantities in the proper galactic plane. Columns 6 aud 7 of table | show the values of ellipticity aud PA for the bar taken frou the ELLIPSE results. after deprojection. aud measured at the ealactic radius spanned by the bar.," The global PA and inclination angle of the object galaxy are used to deproject the galaxy image in order to measure quantities in the proper galactic plane.. Columns 6 and 7 of table \ref{Tab:parametros} show the values of ellipticity and PA for the bar taken from the ELLIPSE results, after deprojection, and measured at the galactic radius spanned by the bar."1190 Ounce the radial profiles have been obtained aud the general parameters calculated. we can now proceed with the decomposition of the averaged brightucss profile iuto different structural compoucuts. each with a separate coutributiou to the observed fiux.," Once the radial profiles have been obtained and the general parameters calculated, we can now proceed with the decomposition of the averaged brightness profile into different structural components, each with a separate contribution to the observed flux."1191 There are a laree nunuber of simular researches in the literature where structural decomposition of external galaxies are attempted iu various wavs (Simica Alicharcd 1990: Pricto et al., There are a large number of similar researches in the literature where structural decomposition of external galaxies are attempted in various ways (Simien Michard 1990; Prieto et al.1192 1990. 1992: Byun Freeman 1995). but lios of them are based on visible data that do not so closely rescluble the true stellar distribution because of their higher value of the extinction.," 1990, 1992; Byun Freeman 1995), but most of them are based on visible data that do not so closely resemble the true stellar distribution because of their higher value of the extinction."1193 Previous NIR decomposition can be found in de Jong (1996). Peleticr Dalcells (1997). Morioudo et al. (," Previous NIR decomposition can be found in de Jong (1996), Peletier Balcells (1997), Moriondo et al. ("11941998). Scigar James (1998) aud references thereiu.,"1998), Seigar James (1998) and references therein."1195 For the different coniponent ideuti&catiou we have followed the teclinical approach of Prieto et al. (, For the different component identification we have followed the technical approach of Prieto et al. (11962001) where the chauges iu the radial profiles of cllip10111.ici PA aud BI are used to identified the radial iuerval over which the eiven component extends.,"2001) where the changes in the radial profiles of ellipticity, PA and B4 are used to identified the radial interval over which the given component extends."1197 Then. the analytical functions. described iu the table 5 and in Aeuerri (1998). are fitted to the brightucss radial xofile within that interval.," Then, the analytical functions, described in the table \ref{Tab:parametros1} and in Aguerri (1998), are fitted to the brightness radial profile within that interval."1198 This technique would be of ittle use in the case of strong vars since these structures ouly occur over a narrow range of azimuthal aneles., This technique would be of little use in the case of strong bars since these structures only occur over a narrow range of azimuthal angles.1199 Deuce. he use of agiuthally averaged profiles. as is the case for he results of the ellipse fitting. could well mask the bar against the averaged backeround.," Hence, the use of azimuthally averaged profiles, as is the case for the results of the ellipse fitting, could well mask the bar against the averaged background."1200 We will come back to hese cases at the eud of this section., We will come back to these cases at the end of this section.

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