ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 We have shown that for cDI models with larger coupling there is a clear cdillerence. between the best. fi ACDAL for the same model but. cliflerent surveys., We have shown that for cDE models with larger coupling there is a clear difference between the best fit $\Lambda$ CDM for the same model but different surveys.3 This dillerence. is due to the dominance of the oll-diagona covariance matrix terms over the diagonal for larger surveys. and shows the importance of including these oll-cliagona terms in weak lensing predictions.," This difference is due to the dominance of the off-diagonal covariance matrix terms over the diagonal for larger surveys, and shows the importance of including these off-diagonal terms in weak lensing predictions."4 We have also caleulatecl the expected signal for a non-constant coupling mocdel and a non-exponential potentia model., We have also calculated the expected signal for a non-constant coupling model and a non-exponential potential model.5 These models could be excluded by :2o for a DISS-like survey and To lor Euclid., These models could be excluded by $\geq2\sigma$ for a DES-like survey and $>7\sigma$ for Euclid.6 However we have no obtained constraints on the parameters of these types of model. since currently. N-body simulations for these moclels have only been run with one parameter set.," However we have not obtained constraints on the parameters of these types of model, since currently N-body simulations for these models have only been run with one parameter set."7 A substantial se of simulations would be required in order to properly sample the parameter space of these more complex scenarios., A substantial set of simulations would be required in order to properly sample the parameter space of these more complex scenarios.8 This will be a worthwhile task. as the ellects of these cosmologies appear to be more dillicult to detect in the background and in the linear regime with respect to standard. interacting dark energy models. making non-linear N-body. simulations vital for realistic lensing predictions.," This will be a worthwhile task, as the effects of these cosmologies appear to be more difficult to detect in the background and in the linear regime with respect to standard interacting dark energy models, making non-linear N-body simulations vital for realistic lensing predictions."9 We have also shown the size of the error on weak lensing predictions if. α ACDAL non-linear fitting formula. such as llalofit. is used to estimate the matter power spectrum. insteack of using simulations.," We have also shown the size of the error on weak lensing predictions if a $\Lambda$ CDM non-linear fitting formula, such as Halofit, is used to estimate the matter power spectrum, instead of using simulations."10 We fined that this Halofit error is larger than the statistical error for the DES and LEuclicl surveys. and for all the models considered here.," We find that this Halofit error is larger than the statistical error for the DES and Euclid surveys, and for all the models considered here."11 This demonstrates the importance of using a full N-body code to estimate the non-linear power spectrum., This demonstrates the importance of using a full N-body code to estimate the non-linear power spectrum.12 DB is supported by an RCUI Academic. Fellowship., DB is supported by an RCUK Academic Fellowship.13 IxIx is supported by the STEC' (grant no., KK is supported by the STFC (grant no.14 ST/11002774/1). a European Research Council Starting Grant and. the Leverhulme trust.," ST/H002774/1), a European Research Council Starting Grant and the Leverhulme trust."15 EB is funced by an ος PhD studentship., EB is funded by an STFC PhD studentship.16" MB acknowledges support by the DEG Cluster of Excellence ""Origin and Structure of the Universe” and by", MB acknowledges support by the DFG Cluster of Excellence “Origin and Structure of the Universe” and by17we refer to the flux immediately. shortward of the Lyman continuum. as opu and immecdiatelv longward of the Lyman continuum. as E ,"we refer to the flux immediately shortward of the Lyman continuum, as $_{o,~\lambda < 912\AA}$, and immediately longward of the Lyman continuum, as $_{o,~\lambda > 912\AA}$."18In the spectra of galaxies. the discontinuitv or “break” between these values is caused by (he enormous optical depth of neutral hydrogen in the interstellar medium.," In the spectra of galaxies, the discontinuity or “break"" between these values is caused by the enormous optical depth of neutral hydrogen in the interstellar medium."19" Fluxes on both sides of the Lyman continuum limit are reddened to the observer. by dust internal to the source galaxy. our. Alilky Wav. and by passage through the IGM. resulting infltures. immediately above aud below ihe Lvman continuum. of F, and F,opa "," Fluxes on both sides of the Lyman continuum limit are reddened to the observer, by dust internal to the source galaxy, our Milky Way, and by passage through the IGM, resulting in, immediately above and below the Lyman continuum, of $_{\lambda < 912\AA}$ and $_{\lambda > 912\AA}$."20Published UDVHRI-band photometry of the galaxies observed. here establishes their baseline continuum strength and shape (in the rest frame mid-UV)., Published UBVRI-band photometry of the galaxies observed here establishes their baseline continuum strength and shape (in the rest frame mid-UV).21 Photometric errors are not quoted in the literature for (hese objects (TamraGarner1991:Cowie.SongailaandHu 1996).," Photometric errors are not quoted in the literature for these objects \citep{tam01,lil91,cow96}."22. We have assumed photometric errors. and made the height of the symbols in Figure 2 equal to this range ol uncertainty.," We have assumed photometric errors, and made the height of the symbols in Figure 2 equal to this range of uncertainty."23 The strength of the dereddened Fux break is shown in the spectral energy distributions (SEDs) of these objects (Figure 2).," The strength of the dereddened $_{o,~\lambda < 912\AA}$ $_{o,~\lambda > 912\AA}$ break is shown in the spectral energy distributions (SEDs) of these objects (Figure 2)."24 The actual escape fraction of photons (hat leak out of a galaxy is dependent upon. among other not well-determined thines. (he spectral shapes and internal reddenines of the sources.," The actual escape fraction of photons that leak out of a galaxy is dependent upon, among other not well-determined things, the spectral shapes and internal reddenings of the sources."25 One previous formulation (e.g.. SPA) is in terms of observed quantities as arelative escape fraction. [pyese = 39.," One previous formulation (e.g., SPA) is in terms of observed quantities as a escape fraction, $_{rel~esc}$ $=$ 3."26 X .," x $_{\nu, 1500\AA}$ $_{\nu, 900\AA}$."27 One (lien uses observations of the ralio. in a model-independent wav. to specily the relative escape fraction.," One then uses observations of the $_{\nu, 1500\AA}$ $_{\nu, 900\AA}$ ratio, in a model-independent way, to specify the relative escape fraction."28 At high redshift.C one should also include anv flux decrement [rom 1500 to 9004 due to the IGAL," At high redshift, one should also include any flux decrement from 1500 to $\AA$ due to the IGM."29 The factor of 3 arises in (he definition trom the anticipatedindrinsie drop in flux from 1500.1 to 900.4. which depends upon assumptions about the IMF and stellar ages.," The factor of 3 arises in the definition from the anticipated drop in flux from $\AA$ to $\AA$, which depends upon assumptions about the IMF and stellar ages."30 We investigated this dependence over à range of Druzual-Charlot stellar svnthesis models 1993).. in which the galaxy originally formed at z ~ 10.," We investigated this dependence over a range of Bruzual-Charlot stellar synthesis models \citep{bc93}, in which the galaxy originally formed at z $\sim$ 10."31 The simulations included. cases with both older (z ~ 1.3). and more recent but smaller. starbursts (z ~ 1.4 - 1.7).," The simulations included cases with both older (z $\sim$ 1.8), and more recent but smaller, starbursts (z $\sim$ 1.4 - 1.7)."32 These starbursts. of duration one gigavear. produced all the O and D stars.," These starbursts, of duration one gigayear, produced all the O and B stars."33 Figure 2 includes two ol these models. one blue and red. al two flux levels which bracket most of our data.," Figure 2 includes two of these models, one blue and red, at two flux levels which bracket most of our data."34 They provide a reasonable match to the published photometry for most of our target. galaxies. and demonstrate the insensitivitv of the Lyman continuum levels to model choices.," They provide a reasonable match to the published photometry for most of our target galaxies, and demonstrate the insensitivity of the Lyman continuum levels to model choices."35 Two extreme stellar population models were generated. using the Druzual Charlot 1995 code.," Two extreme stellar population models were generated, using the Bruzual Charlot 1995 code."36 In both models. the original stellar population is assumed to have formed early. at à redshift of 10.," In both models, the original stellar population is assumed to have formed early, at a redshift of 10."37 Then a second burst of star formation starts at z=1.6., Then a second burst of star formation starts at z=1.6.38 Both bursts are described by the BC95 1 Gyr constant star Formation rate model. wilh an assumed Salpeter IME.," Both bursts are described by the BC95 1 Gyr constant star formation rate model, with an assumed Salpeter IMF."39 No internal reddening has been added., No internal reddening has been added.40 Adding anv reddening to the model would have resulted in an even vounger in(vinsic stellar population. which would have relatively stronger Lyman Init emission than in the models in Figure 2.," Adding any reddening to the model would have resulted in an even younger intrinsic stellar population, which would have relatively stronger Lyman limit emission than in the models in Figure 2."41 The galaxy model is observed at our typical redshift of 1.3., The galaxy model is observed at our typical redshift of 1.3.42 For the II—75 open cosmology, For the H=75 open cosmology43Understanding the properties aud. evolution of the dust eralus contained iu proto-planetarv disks around pre-ain sequence stars is müportant because they are the seeds from which planets may form.,Understanding the properties and evolution of the dust grains contained in proto-planetary disks around pre-main sequence stars is important because they are the seeds from which planets may form.44 We have now stro evidence that erains in disksi are very cifferent Toni the eraius iu the diffuse interstellar medimm aud iu the molecular clouds from which disks form. as reviewed. e.g.àY by Natta et al. (," We have now strong evidence that grains in disks are very different from the grains in the diffuse interstellar medium and in the molecular clouds from which disks form, as reviewed, e.g., by Natta et al. ("452006).,2006).46 I- uauv objects. observations with nuüllineter interferometers have provided stro evidence that the erains iu the outer aud cooler regions of the «isk (further than 5OAU from the star) have CCL hugely processed. and have erown froin sub-auicron sizes to nülluueter and centimeter ones.," In many objects, observations with millimeter interferometers have provided strong evidence that the grains in the outer and cooler regions of the disk (further than 50AU from the star) have been hugely processed, and have grown from sub-micron sizes to millimeter and centimeter ones."47 Closer to the star. however. in the regions were planes are more Likely to formi. observational evidence has been coufined to eraius close to the disk surface.," Closer to the star, however, in the regions were planets are more likely to form, observational evidence has been confined to grains close to the disk surface."48 For these. which however account for a tiny fraction of the total dust mass. emission in the silicate features has shown a correlation between the shape of the feature aud its strength that is interpreted as due to erowth of the exaius from size e~0.1 fu touc Lyra (van Bockel et al.," For these, which however account for a tiny fraction of the total dust mass, emission in the silicate features has shown a correlation between the shape of the feature and its strength that is interpreted as due to growth of the grains from size $a\sim0.1\mu$ m to $a\sim1\mu$ m (van Boekel et al."49 2003. 200[: Moeeus et a.," 2003, 2004; Meeus et al."50 2003)., 2003).51 In this inner isk. the properties of the eraius in the disk uidplaue are still uukuowu.," In this inner disk, the properties of the grains in the disk midplane are still unknown."52 Tu the last few vers. due to the new loug baseline ucar-infrared interferometers. many important steps forward oei the study of the internal regiois of circetuustellar disks have occurred.," In the last few years, due to the new long baseline near-infrared interferometers, many important steps forward in the study of the internal regions of circumstellar disks have occurred."53 The available ucar-intrared mterferomoetric observations of T Tauri (TTS) and IHerbie Ac (ILÀo) stars (Eisner et al., The available near-infrared interferometric observations of T Tauri (TTS) and Herbig Ae (HAe) stars (Eisner et al.54 2003. 2001: \ilau-Cabe et al.," 2003, 2004; Millan-Gabet et al."55 2001: Tutlull et al., 2001; Tuthill et al.56 2001: Monnicr et al., 2001; Monnier et al.57" 2005) confi the idea that the απο disk properties are controlled by the dust evaporation process which produce a -""puffed-up iMer rho at the dust destruction radius (Natta et al.", 2005) confirm the idea that the inner disk properties are controlled by the dust evaporation process which produce a “puffed-up” inner rim at the dust destruction radius (Natta et al.58 2001: Dulleiioud. Donunick Natta 2001. hereafter DDNOL).," 2001; Dullemond, Dominick Natta 2001, hereafter DDN01)."59 Iu these models. the location aud shape of the rim depends ou the properties of exaius located not on the disk surface but on its midplane.," In these models, the location and shape of the rim depends on the properties of grains located not on the disk surface but on its midplane."60" Isella Natta (2005. hereafter INOS) have receutlv proposed inodels of the ""puffed-upiuner rim. which include a selfeonsisteu description of the eran evaporation and its dependence oi the eas density,"," Isella Natta (2005, hereafter IN05) have recently proposed models of the “puffed-up”inner rim which include a self-consistent description of the grain evaporation and its dependence on the gas density."61 INOS have explored a large range of eral properties. and ciseussed how the locatio1 of the vim depends onu erain properties.," IN05 have explored a large range of grain properties, and discussed how the location of the rim depends on grain properties."62 Iit Us paper. we wil use the INOS moclels to analyze the exisine interferometric data of the best 6served ILA&e sars to expore. in practice. the coustraiuts (1 eral pro)erties provied by tus technique aud their ajcertainties.," In this paper, we will use the IN05 models to analyze the existing interferometric data of the best observed HAe stars to explore, in practice, the constraints on grain properties provided by this technique and their uncertainties."63 As a byproduct of the modeling process. oue obtains iso the orieitation of the imuer disk (1e. its mcelination with respect o the ine of sight aud its position angle}: this can be compared witi the orientation of the outer disk. tained from millimeter observations of the molecuar gas id dust cussion and/or scattered liebt in the optical.," As a byproduct of the modeling process, one obtains also the orientation of the inner disk (i.e. its inclination with respect to the line of sight and its position angle); this can be compared with the orientation of the outer disk, obtained from millimeter observations of the molecular gas and dust emission and/or scattered light in the optical."64 The paper is ore:ized as follows., The paper is organized as follows.65 In 822 we describe the available interferometric observations of the tarect stars., In 2 we describe the available interferometric observations of the target stars.66 The INOS model for the iuuer rin ds briefly summarized in $33 and used to fi the observations of tle individual objects i1 811., The IN05 model for the inner rim is briefly summarized in 3 and used to fit the observations of the individual objects in 4.67 A comparison of the results with previous analysis of the same data is preseuted in 855., A comparison of the results with previous analysis of the same data is presented in 5.68 Our results are discussed in 866., Our results are discussed in 6.69 Conclusions follow in 877., Conclusions follow in 7.70 Our sample is composed of six ILÀe stars (AB Aur. CQ Tau. VV Ser. MAVC bso. AIWC 758 and V1295 Aql). for which ucar-intrared interferometric observations exist iu the literature.," Our sample is composed of six HAe stars (AB Aur, CQ Tau, VV Ser, MWC 480, MWC 758 and V1295 Aql), for which near-infrared interferometric observations exist in the literature."71 Table 1 summarizes the physical properties of the tarect stars.," Table \ref{tab.sources}72 summarizes the physical properties of the target stars."73 All the stars are classified as voune PAellar objects with masses ranging from 1.5 to 13 solar mass and a spectral type between A0/DB9 aud AS/F2., All the stars are classified as young stellar objects with masses ranging from 1.5 to 4.3 solar mass and a spectral type between A0/B9 and A8/F2.74 CO Tau and VV Ser beloug to the family of UNORs aud are haracterized by large and regular variability., CQ Tau and VV Ser belong to the family of UXORs and are characterized by large and irregular variability.75" We use visibility nieasurements of the target stars from the literature. obtained with interferometric observations carried out with PTI (Palomar Testhed Iuterferoiueter) iu IX baud (Ay 22,1. AX=Q. Haa) described. in Eisner et al. ("," We use visibility measurements of the target stars from the literature, obtained with interferometric observations carried out with PTI (Palomar Testbed Interferometer) in K band $\lambda_0=2.2\mu$ m, $\Delta\lambda76= 0.4\mu$ m) described in Eisner et al. ("772001).,2004).78 For AB Aur and V1295Aql. IOTA observations are also available (Millan-Ciaboet et al.," For AB Aur and V1295Aql, IOTA observations are also available (Millan-Gabet et al."79 2001) for the N'(Ay= 2.16snu. AA= 0.32¢au}) and II 1.6551. AXA= 0.30/01) bands.," 2001) for the $\lambda_0=2.16\mu$ m, $\Delta\lambda = 0.32\mu$ m) and H $\lambda_0=1.65\mu$ m, $\Delta\lambda = 0.30\mu$ m) bands."80curve in Figure L.,curve in Figure \ref{fig:f2}.81 This model is clearly a poor match to the observed light curve., This model is clearly a poor match to the observed light curve.82 Further. if the two stars have the same mass aid evolutionary state. then there should be no systemic color chauge over the period: as meutioned above. this is contrary to the observed color change.," Further, if the two stars have the same mass and evolutionary state, then there should be no systemic color change over the period; as mentioned above, this is contrary to the observed color change."83 Therefore. we rule out the eqtal-mass contact binary scenario.," Therefore, we rule out the equal-mass contact binary scenario."84 [If we rule out that IRSIGSW is a kuown type of pulsating sar or an eclipsing binary system. hen it must represent a new class of variable object.," If we rule out that IRS16SW is a known type of pulsating star or an eclipsing binary system, then it must represent a new class of variable object."85" ""This iutriguiug possibility is supported by recent work on internal mocels of massive stars.", This intriguing possibility is supported by recent work on internal models of massive stars.86" In. particdar. Dorfi&Cautschy(2000) found that iuearly overstable pulsational modes can develop iuto ""ecοςlar variability in radiation hydrodyuaiie simulations of massive st:us."," In particular, \citet{dg2000} found that linearly overstable pulsational modes can develop into regular variability in radiation hydrodynamic simulations of massive stars."87 Iu particilar. for very high i1lass stars their inodels suggest that these nodes cau cause very regular evelic brightuess variability with ligit curves similar to those of classic »ulsatiig variables.," In particular, for very high mass stars their models suggest that these modes can cause very regular cyclic brightness variability with light curves similar to those of classic pulsating variables."88 The11oclels sugges that this varialol is stable over reasonably loig timescales., The models suggest that this variation is stable over reasonably long timescales.89 ΤΙe highest mass moclel presenteL| by Dorfi&Causchy(2000) is for a 60 M... L = 900.000 L... n=15.000A. sla: (their mode Νορ.," The highest mass model presented by \citet{dg2000} is for a 60 $_\odot$ L $=$ 900,000 $_\odot$, $T_{eff} = 18,000 K$ star (their model M60C)."90 TIe Inocel preclicts a 'egular pulsation with «ays and. peak-to-»eak bolomet‘ic brightuess variation of 0.60 uae., The model predicts a regular pulsation with $P = 4.086$ days and peak-to-peak bolometric brightness variation of 0.66 mag.91 The light. curve ooks qualit:ively lise that we observe for IRSLOSW: areatively steep rise. followed by a somewhat slowel fall.," The light curve looks qualitatively like that we observe for IRS16SW: a relatively steep rise, followed by a somewhat slower fall."92 Tle model predicts no siguilican phase shift between different iter passbauds of feaues in the ight curves. which Dorli&Cautschy(2000). atribute to low heat capacity in the LLOS superficjal stelar layers.," The model predicts no significant phase shift between different filter passbands of features in the light curves, which \citet{dg2000} attribute to low heat capacity in the most superficial stellar layers."93 Color clauges are presei. however. since {ie. ellective temperatur the star char[n]ees during the pulsatious.," Color changes are present, however, since the effective temperature of the star changes during the pulsations."94 These aspects of the moclel are also cousistent witl obse'valionis ο “IRSLOSW., These aspects of the model are also consistent with our observations of IRS16SW.95" Note that Dorli&Catutschy(2000) simulated this ode""s pulsatio a timescale o ‘nore than 20 years without seeing a chiauge iu the pusational properties.", Note that \citet{dg2000} simulated this model's pulsation for a timescale of more than 20 years without seeing a change in the pulsational properties.96 However. Dorli&Gautschy(2000) modelecl variatious ouly inu specific optical passbauds (UBVI) aud heir |ighest mass model lias a perjod less than half that of IRSIGSW.," However, \citet{dg2000} modeled variations only in specific optical passbands (UBVI) and their highest mass model has a period less than half that of IRS16SW."97 Their nxxlels SΙow that the ampμιςe of variability decreases with waveleugth tlroughout tlie oj»tical. witl1 the lareest ampliucles intle ultraviolet.," Their models show that the amplitude of variability decreases with wavelength throughout the optical, with the largest amplitudes in the ultraviolet."98 The amplitide of the AL60C uodel iu the I baud is ~0.2 mae. eeestiug the variidOLs in the near-infrared woid be inuch sinale ‘than we observe in IRSLOSW.," The amplitude of the M60C model in the I band is $\sim$ 0.2 mag, suggesting the variations in the near-infrared would be much smaller than we observe in IRS16SW."99 Eutherimore. all ieir nodels with Af>30AZ. show secondary uaxima caused by shocks waves i1 the atiuosplieres of |e stars (a difference beween the dyuauical timescale of the atinosphliere aud the »ulsationa JeJnxl Causes collapsit& lavers to collide witl already rerising deeper layers): we see nc» evidence fcDu lese secondary maxima iu our IRSIOSW ight curve.," Furthermore, all their models with $M > 30 M_\odot$ show secondary maxima caused by shocks waves in the atmospheres of the stars (a difference between the dynamical timescale of the atmosphere and the pulsational period causes collapsing layers to collide with already rerising deeper layers); we see no evidence for these secondary maxima in our IRS16SW light curve."100 Dori&Gautsclv(2000) point out that there is no observatonal evideuce for pulsating very nDiassive uall-sequence sars witli short pe‘iods., \citet{dg2000} point out that there is no observational evidence for pulsating very massive main-sequence stars with short periods.101 They suggest this may be due to either a missing piece of physies iu their models. which would damp out the ptIsations. or lack of appropriate observational data.whicl would easily confise the pulsatious witli lickering or situply observational," They suggest this may be due to either a missing piece of physics in their models, which would damp out the pulsations, or lack of appropriate observational data,which would easily confuse the pulsations with flickering or simply observational"102Choosing the initial condition VoGe)2.04. we can easily deduce frou: Example 1.6 that equality (1.13)) is also sharp for T>Celloge}.,"Choosing the initial condition $V_{0}(x)=x_{1}$, we can easily deduce from Example \ref{example3} that inequality \ref{1.12}) ) is also sharp for $T\geq C\eps |\log \eps|$."103 Hore. in this application. the vector field a4 is quite special.," Here, in this application, the vector field $a^{\eps}$ is quite special."104 The iuterestedreader could be referred to [?| for some other examples of vector fields in 2D. where a homogenization result is preseuted without any rate of convergence.," The interestedreader could be referred to \cite{HouXin} for some other examples of vector fields in $2$ D, where a homogenization result is presented without any rate of convergence."105 Tn [?].. the author gives some non-explicit error estimates for linear transport equatious in the particular case of periodic vector Ποια «*.," In \cite{Tassa97}, the author gives some non-explicit error estimates for linear transport equations in the particular case of periodic vector field $a^{\eps}$."106 Towever. these eror estimates obtained in |?) may depend strougly on the irrationality of the rotation number wy associated to the vector field o (where wy is nothing else than fin our application).," However, these error estimates obtained in \cite{Tassa97} may depend strongly on the irrationality of the rotation number $\omega_{0}$ associated to the vector field $a^{\eps}$ (where $\omega_{0}$ is nothing else than $-\o{f}$ in our application)."107 Ou the contrary. estimate (1.13)) ouly depends on some bounds of the data ofthe problem. aud are conipletelv mnitorm with respect to the rotation umber.," On the contrary, estimate \ref{1.12}) ) only depends on some bounds of the data ofthe problem, and are completely uniform with respect to the rotation number."108 Remark that when fle.7.αντ) is independent of « aud f. we have a uch better estimate: The proof of Theorcin 1.9 will also be given in Section ??..," Remark that when $f(v,\t,u,t)$ is independent of $u$ and $t$, we have a much better estimate: The proof of Theorem \ref{theo4} will also be given in Section \ref{sec6}."109 The pioneering work (via the theory of viscosity solutious) to periodic homogenization was established in |?].., The pioneering work (via the theory of viscosity solutions) to periodic homogenization was established in \cite{LPV_UnP}.110 Starting from [?].. the homogenization theory for Tamilton-Jacobi equations has received a considerable interest.," Starting from \cite{LPV_UnP}, the homogenization theory for Hamilton-Jacobi equations has received a considerable interest."111 There is a luge literature that we cannot cite in details. but the interested reader cau for mstauce see and the references therein.," There is a huge literature that we cannot cite in details, but the interested reader can for instance see \cite{Alvarez-Bardi03, Barles-Soug01, Barles-Soug00, Evans92,112 Lions-Souga05, Hom-MonneauI, Hom-MonneauII} and the references therein."113 Another aspect concerning homogenization of SDEs (stochastic differeutial equations) has also been studied by several authors (see for instance κ.7. 10).," Another aspect concerning homogenization of SDEs (stochastic differential equations) has also been studied by several authors (see for instance \cite{Pardoux99, GaPa01, BePa07, SOUG99}) )."114 These problems are related to our problem when the SDE reduces to au ODE., These problems are related to our problem when the SDE reduces to an ODE.115 To our knowledec. the question of estimating the rate of convergence in homogenization of PDEs has not been widely tackled up elsewhere in the literature.," To our knowledge, the question of estimating the rate of convergence in homogenization of PDEs has not been widely tackled up elsewhere in the literature."116 We can cite |?]. for several error estimates concerning the rate of convergence of the approximation scheme to the effective Hamiltonian., We can cite \cite{CCG08} for several error estimates concerning the rate of convergence of the approximation scheme to the effective Hamiltonian.117 We can also cite the work in |?]. about the rate of convergence in periodic homogenization of first-order stationary IEuuilton-Jacobi equations. where au error estimate in et? is obtained for Tamiltou-Jacobi equations with Lipschitz effective Huniltoniau.," We can also cite the work in \cite{C.D.-I} about the rate of convergence in periodic homogenization of first-order stationary Hamilton-Jacobi equations, where an error estimate in $\eps^{1/3}$ is obtained for Hamilton-Jacobi equations with Lipschitz effective Hamiltonian."118 For the problems of homogenization of ODEs. we refer the reader to |?. ?]..," For the problems of homogenization of ODEs, we refer the reader to \cite{Picc78,Picc79}. ."119 We also refer the reader to for problems on homogenization of nonlinear first-order ODEs and/or the associated linear trausport equations.," We also refer the reader to \cite{AHZ94,120Dalibard, WeinanE92, Menon02, Peirone96, Petrini99, Tartar89} for problems on homogenization of nonlinear first-order ODEs and/or the associated linear transport equations."121 As mentioned above. we refer the reader to |?| for some other error estimates forlincar transport equations.," As mentioned above, we refer the reader to \cite{Tassa97} for some other error estimates forlinear transport equations."122 The paper is organized as follows., The paper is organized as follows.123 In Section ??.. we preseut the proof of an creodicity result (Proposition 2.1)) that defines f= A.," In Section \ref{sec2}, , we present the proof of an ergodicity result (Proposition \ref{ergo}) ) that defines $\o{f}=\l$ ."124 We also present the proofs of Propositions 1.1. aud 1.L.," We also present the proofs of Propositions \ref{AM7Z}125 and \ref{ganaza}."126 In Section ??.. we give a result of stability of A under additive perturbation (Proposition 3.1)).," In Section \ref{sec3}, we give a result of stability of $\l$ under additive perturbation (Proposition \ref{prop_pert}) )."127 A basic error estimate (Proposition L.1)) is presented in Section ??.., A basic error estimate (Proposition \ref{bef_proof}) ) is presented in Section \ref{sec4}.128 Section ?? is devoted to show our main result of estimating the rate of couvergence (Theorem 1.5))., Section \ref{sec5} is devoted to show our main result of estimating the rate of convergence (Theorem \ref{theo2}) ).129 Iu Section ??.. we give au application to the case of near transport equations (Theorcuis 1.5. and 1.9)).," In Section \ref{sec6}, we give an application to the case of linear transport equations (Theorems \ref{theo3} and \ref{theo4}) )."130 We eud up in Section ?? with an Appendix where we give the proof of Examples 1.3. aud 1.6.., We end up in Section \ref{sec7} with an Appendix where we give the proof of Examples \ref{example2} and \ref{example3}. .131 Tn this section we prescutthe proof of Propositions l.l. and 1.1., In this section we presentthe proof of Propositions \ref{AM7Z} and \ref{ganaza}. .132 We first start with thefollowing ersodicitv result which is a particular case of |?.Proposition L.2].., We first start with thefollowing ergodicity result which is a particular case of \cite[Proposition 4.2]{FIM}. .133 However. we eive the proof in our particular casefor the sake of completcucss.," However, we give the proof in our particular casefor the sake of completeness."134"characterized by mean energies (5,)Ij. where D; is the bulk Loretz factor of the outflow (see.e.g..LhediscussioninWino&Takahara2004;Stawarzetal.2007).","characterized by mean energies $\langle\gamma_{\rm p}\rangle \simeq \Gamma_{\rm j}$, where $\Gamma_{\rm j}$ is the bulk Loretz factor of the outflow \citep[see, e.g., the discussion in][]{kin04,sta07}."135". Llence (he minimum number density of the lobes reads as For (he parameters of (he hypothetical relict lobes of implied by the ""Outer"" model 66). namely Q;=L2xI0 |. /=118 MMyr. D=4.7 MMpe and Ry=6 (giving the total volume of the cocoon V.x1.7LOM cem*). assuming in addition conservatively large-scale jel bulk Lorentz [actor Ijc3 (seeWardle&Aaron1997).. we obtain nyo6xLOI"" ?. or equivalently poo~myMeac10nn» 7."," Hence the minimum number density of the lobes reads as For the parameters of the hypothetical relict lobes of implied by the “Outer” model 6), namely $Q_{\rm j}=1.2\times 10^{46}$ $^{-1}$, $t=178$ Myr, $D=4.7$ Mpc and $R_{\rm T} =6$ (giving the total volume of the cocoon $V \simeq 1.7\times 10^{73}$ $^{3}$ ), assuming in addition conservatively large-scale jet bulk Lorentz factor $\Gamma_{\rm j} \simeq 3$ \citep[see][]{war97}, we obtain $n_{\rm rel} \sim 6 \times 10^{-10}$ $^{-3}$, or equivalently $\rho_{\rm rel} \simeq m_{\rm p} \, n_{\rm rel} \sim 10^{-33}$ $^{-3}$."136 This value is in avery good agreement with the analogous one estimated by Safourisetal.(2008) [or the outer lobes of DDRG DD1545—321 (J1548—3216 in this paper)., This value is in a very good agreement with the analogous one estimated by \citet{saf08} for the outer lobes of DDRG $-$ 321 $-$ 3216 in this paper).137" To sum up. the dvnamical modeling presented in 33 implies that the density of the ambient mecium around (he observed lobes of is pJU>i2x103"" *. Ro"," To sum up, the dynamical modeling presented in 3 implies that the density of the ambient medium around the observed lobes of is $\rho_{\textrm{\scriptsize ``inn''}}^{\rm J1420} \sim 2 \times 10^{-31}$ $^{-3}$."138:The hypothetical. outer lobes. in. the svstem would be. insteadB ⇁− ⇁−↽⊳∣⊔⊇∣∣↴ ⊇∩↽↽⊓ ⋟∖∏∐∪∏∐≼⇂≼↲≺⊓≻∡∖⊔∐↲↖∟↴≺↕⊔∖∖∖↕⊔↥⊔∐↲≺⇂≼↲∐⋟∖∐⋡∖∕↗⋅⋅⋯⊓⊳↼↴∿↓∩↖≺↔↴↖∟↴≺≺∐↓ oE, The hypothetical outer lobes in the system would be instead surrounded by the gas with the density $\rho_{\textrm{\scriptsize ``out''}}^{\rm J1420} \sim 10^{-29}$ $^{-3}$.139 These values can be compared with the densities of (he environment found in the modeling for of the outer lobes in the control sample of DDRG. ηπο(0.3—3)x107 7. and also with the densities of the plasma into which the inner lobes of the studied DDRGs are evolving (ie. with the densities. inside. the outer cocoons in. the svstems).ς namely oblH9M(0.323)NMyx1027 eem.37.," These values can be compared with the densities of the environment found in the modeling for of the outer lobes in the control sample of DDRG, $\rho_{\rm out}^{\rm DDRGs} \sim (0.3-3) \times 10^{-28}$ $^{-3}$, and also with the densities of the plasma into which the inner lobes of the studied DDRGs are evolving (i.e., with the densities inside the outer cocoons in the systems), namely $\rho_{\rm inn}^{\rm DDRGs} \sim (0.3-3) \times 10^{-27}$ $^{-3}$."140 Note that the latter densities are already very. close to/almost (he same as the upper limits for the thermal gas density (pij). provided by the analvsis of the internal depolarization effects within the UI lobes., Note that the latter densities are already very close to/almost the same as the upper limits for the thermal gas density $\langle \rho_{\rm th} \rangle$ provided by the analysis of the internal depolarization effects within the II lobes.141 The comparison indicates (hat even though (the environment of the presumed relicts in was set to resemble (he environments of large-scale structiwesdvuebuves inim DDRGs.DDPCR pL2]20DDRGsSpgs. ihe medium. surrounding the observed. lobes in seems much underdense with respect (ο the medium surrounding inner lobes of DDRGs. pli!apopCSS D," The comparison indicates that even though the environment of the presumed relicts in was set to resemble the environments of large-scale structures in DDRGs, $\rho_{\textrm{\scriptsize ``out''}}^{\rm J1420} \lesssim \rho_{\rm out}^{\rm DDRGs}$, the medium surrounding the observed lobes in seems much underdense with respect to the medium surrounding inner lobes of DDRGs, $\rho_{\textrm{\scriptsize ``inn''}}^{\rm J1420} \ll \rho_{\rm inn}^{\rm DDRGs}$."142ifferent sizes of the structures have to be kept in mind. though.," Different sizes of the structures have to be kept in mind, though."143 MMThe densityeye. pdL120 emerging from (he modeling is however still orders of magnitude above (he minimum censity of the relict cocoon provided by the injection of electron-proton plasma during the hypothetical previous epoch of the jet activity in the source. fey.," The density $\rho_{\textrm{\scriptsize ``inn''}}^{\rm J1420}$ emerging from the modeling is however still orders of magnitude above the minimum density of the relict cocoon provided by the injection of electron-proton plasma during the hypothetical previous epoch of the jet activity in the source, $\rho_{\rm rel}$."144 Thus. a substantial entrainment of matter is required lor the relict lobes of in the framework of the intermitted jet activity scenario (see 2008).," Thus, a substantial entrainment of matter is required for the relict lobes of in the framework of the intermitted jet activity scenario \citep[see the related discussion in][]{kai00,saf08}."145. ]t is worth noting that particularly low density of the gas surrounding the observed lobes in is consistent with the mean density of the barvonic matter in the Universe., It is worth noting that particularly low density of the gas surrounding the observed lobes in is consistent with the mean density of the baryonic matter in the Universe.146 In, In147superburst recurrence times predicted bv the model.,superburst recurrence times predicted by the model.148 Although observations do not constrain recurrence times very well. (he limes are probably shorter (han those in Figure 11.," Although observations do not constrain recurrence times very well, the times are probably shorter than those in Figure 11."149 Neutron star models with hot cores. TigreZ5x105 IX. seem to best match the observational data. rough the A cutolÉ is laveer (see Figure 12).," Neutron star models with hot cores, $T_{\mathrm{core}} \gtrsim 5 \times 10^{8}$ K, seem to best match the observational data, though the $\dot{M}$ cutoff is larger (see Figure 12)."150 Such temperatures correspond (o neutrino ‘ooling that is even less elficient than that from modified URCA reactions., Such temperatures correspond to neutrino cooling that is even less efficient than that from modified URCA reactions.151 One possibility is iab a nonnegligible fraction of the neutron star core consists of superíIuid barvonic matter., One possibility is that a nonnegligible fraction of the neutron star core consists of superfluid baryonic matter.152 The above conclusions about the neutrino emission mechanisin in the core assume that 1ο stellar radius is the canonical 10 km., The above conclusions about the neutrino emission mechanism in the core assume that the stellar radius is the canonical $10$ km.153 The radius of the neutron star is the only other —yaraleler which we have investigated (hat sienilican(ly affects superburst characteristics al je accretion rates al which superbursts are observed., The radius of the neutron star is the only other parameter which we have investigated that significantly affects superburst characteristics at the accretion rates at which superbursts are observed.154 Larger stars produce superbursts with larger energetics and longer recurrence times (see Figure 16)., Larger stars produce superbursts with larger energetics and longer recurrence times (see Figure 16).155 Neutron stars with exceptionally large radii (2216.4 kim) produce extremely. energetic superbursts that are evossly inconsistent wilh observations. even if (he core temperature is verv hieh.," Neutron stars with exceptionally large radii $R \approx 16.4$ km) produce extremely energetic superbursts that are grossly inconsistent with observations, even if the core temperature is very high."156" We cannol make such a definitive statement. about neutron stars with smaller radii because we are unable to dillerentiate between superbursts from neutron stars wilh small radii (4226.5 km) and moderate core temperatures (Zi,23x105 IX) and neutron stars with moderate radii (22210.4 kin) and high core temperatures (Ti,28xLO” KK).", We cannot make such a definitive statement about neutron stars with smaller radii because we are unable to differentiate between superbursts from neutron stars with small radii $R \approx 6.5$ km) and moderate core temperatures $T_{\mathrm{core}} \approx 3 \times 10^{8}$ K) and neutron stars with moderate radii $R \approx 10.4$ km) and high core temperatures $T_{\mathrm{core}} \approx 8 \times 10^{8}$ K).157 Previous theoretical investigations of the superburst phenomenon (Brown Dildsten 1998. Cumming Bildsten 2001. Strohmaver Brown 2002. Brown 2004) generally agree quite well with our results.," Previous theoretical investigations of the superburst phenomenon (Brown Bildsten 1998, Cumming Bildsten 2001, Strohmayer Brown 2002, Brown 2004) generally agree quite well with our results."158 To determine (he physical conditions under which superbursts occur. (he authors use approximate ignition criteria evaluated al the base of the accreted laver.," To determine the physical conditions under which superbursts occur, the authors use approximate ignition criteria evaluated at the base of the accreted layer."159 In (his section. we compare and contrast the results of our rigorous global linear stability analysis with those obtained from these approximate one-zone ignition criteria.," In this section, we compare and contrast the results of our rigorous global linear stability analysis with those obtained from these approximate one-zone ignition criteria."160 According to Brown&Bildsten(1998).. an instability ensues when the carbon nuclear energv generation rale ec al the base of the accreted laver satisfies the criterion where έρωι=plv-T/MaD isB an approximation. to the global cooling. rate and A ro.is the thermal conductivity evaluated at (he base of the accreted Iaver.," According to \citet{BB98}, an instability ensues when the carbon nuclear energy generation rate $\epsilon_{\mathrm{C}}$ at the base of the accreted layer satisfies the criterion where $\epsilon_{\mathrm{cool}} = \rho K T / \Sigma^{2}$ is an approximation to the global cooling rate and $K$ is the thermal conductivity evaluated at the base of the accreted layer."161" Cumming&Bildsten(2001) and Brown(2004) set dInec/dlnf=26 and dlIne;,,/d1nZ'=2 and express the ignition criterion as ec> (2/26)e4,,."," \citet{CB01} and \citet{B04} set $\mathrm{d} \ln \epsilon_{\mathrm{C}} / 162\mathrm{d} \ln T = 26$ and $\mathrm{d} \ln \epsilon_{\mathrm{cool}} / 163\mathrm{d} \ln T = 2$ and express the ignition criterion as $\epsilon_{\mathrm{C}} > (2/26) \epsilon_{\mathrm{cool}}$ ."164 We presume (hat Brown&Bildsten(1993). and Strolimaver caleulate the derivatives numerically., We presume that \citet{BB98} and \citet{SB02} calculate the derivatives numerically.165 Unlike Brown&Bildsten(1993) , Unlike \citet{BB98} 166since the amplitudes of the quite distant and low orbital inclination exo-planets would be only fractions of a meter per second which would be masked by the much larger !) pulsational velocities and is also bevond (he precision allainable by our observations.,since the amplitudes of the quite distant and low orbital inclination exo-planets would be only fractions of a meter per second which would be masked by the much larger $^{-1}$ ) pulsational velocities and is also beyond the precision attainable by our observations.167semi-major axis before the eruptions. and 0.73AU for the semi-major axis after the eruptions.,"semi-major axis before the eruptions, and $\sim 0.73 \AU$ for the semi-major axis after the eruptions."168" For present day A,2151t.=0.35AU. potential overflow does not occur . as fpiPy."," For present day $R_1 \simeq 75~\rm{R_\odot} = 0.35 \AU$, potential overflow does not occur , as $R_{RL1}> R_1$."169 However. during the 17th century eruptions. an expansion. of the LBV radius by a factor of ~2.53 could casily cause the LBV to overllow its potential lobe close to periastron passages. transferring mass to the companion.," However, during the 17th century eruptions, an expansion of the LBV radius by a factor of $\sim 2.5-3$ could easily cause the LBV to overflow its potential lobe close to periastron passages, transferring mass to the companion."170 Weaker acerction probably took place wough the entire. event by wind accretion process Boneli-Llovle accretion), Weaker accretion probably took place through the entire event by wind accretion process (Bondi-Hoyle accretion).171 The acereted mass probably hack high. angular momentum., The accreted mass probably had high angular momentum.172 This might have led to the formation of an accretion disk and jets during the eruption. of P Cvegni., This might have led to the formation of an accretion disk and jets during the eruption of P Cygni.173 Those jets. mixed. with the approximately spherical mass loss from the LBV. may be responsible for the peculiar shape of the nebula. observed by Nota et al. (," Those jets, mixed with the approximately spherical mass loss from the LBV, may be responsible for the peculiar shape of the nebula, observed by Nota et al. ("1741995).,1995).175 Indeed. the observations of the nebula of Smith LHartigan (2006) hint on some axisvnimetry. as expected. from such a scenario.," Indeed, the observations of the nebula of Smith Hartigan (2006) hint on some axisymmetry, as expected from such a scenario."176 In addition to mass transfer. two other ellects act to reduce the orbital period. drag force by the ejected mass that is not accreted. and tidal force by the LBV on the companion.," In addition to mass transfer, two other effects act to reduce the orbital period, drag force by the ejected mass that is not accreted, and tidal force by the LBV on the companion."177 Drag force is exerted on the companion from the LBY ejecta that is influeneecl by its gravity but not accreted., Drag force is exerted on the companion from the LBV ejecta that is influenced by its gravity but not accreted.178 This gas resides between the accretion radius and the maximum inlluence radius of the companion. he cut-olf radius.," This gas resides between the accretion radius and the maximum influence radius of the companion, the cut-off radius."179 Drag force cannot be the only ohvsical process for reducing the orbital period in the case of P €veni for the following reasons. (, Drag force cannot be the only physical process for reducing the orbital period in the case of P Cygni for the following reasons. (1801) The mass oss rate of the LBV is relatively small (in the Great Eruption of η Car it was at least 200 times Larger). (,1) The mass loss rate of the LBV is relatively small (in the Great Eruption of $\eta$ Car it was at least 200 times larger). (1812) The companion passes close to the LDV and may be one to the drag force only close to periastron. where it is small (since the cut-oll distance is proportional to he binary separation).,"2) The companion passes close to the LBV and may be prone to the drag force only close to periastron, where it is small (since the cut-off distance is proportional to the binary separation)."182 Though the tide the companion exerts on the LBV is important. the cllect of the tidal. force. on. the companion is negligible.," Though the tide the companion exerts on the LBV is important, the effect of the tidal force on the companion is negligible."183 Soker (2005) calibrated. the circularization time (Verbunt Phinney 1995) for an eccentric orbit as where Adjsusc10M. is the LDVs envelope mass. and is a climensionless function of the eccentricity (LEut 1982). assuming P Cyeni rotates slowly.," Soker (2005) calibrated the circularization time (Verbunt Phinney 1995) for an eccentric orbit as where $M_{\rm {1,env}} \simeq 10 M_\odot$ is the LBV's envelope mass, and is a dimensionless function of the eccentricity (Hut 1982), assuming P Cygni rotates slowly."184" For the moclel L suggest or P Cvgni e=0.99. f,=O17."," For the model I suggest for P Cygni $e=0.9$, $f_c=0.17$."185 The envelope of Po Cygni is assumed. to. be convective., The envelope of P Cygni is assumed to be convective.186 1n the unlikely case where it is radiative. then the circularization time is longer.," In the unlikely case where it is radiative, then the circularization time is longer."187 Using equation (16)) ] get that he circularization time for our suggested parameters. is 2107vrs. much longer than the duration of the eruptions.," Using equation \ref{eq:taucir}) ) I get that the circularization time for our suggested parameters, is $\sim 2\times 10^5 \yrs$, much longer than the duration of the eruptions."188 Fherefore the companion orbit is not expected. to be alfected. by. tical force during the eruptions., Therefore the companion orbit is not expected to be affected by tidal force during the eruptions.189 lt is expected that the P Cvgni binary system evolve into a Wolf-Itavet. (WR) binary. that would still have an eccentric orbit.," It is expected that the P Cygni binary system evolve into a Wolf-Rayet (WR) binary, that would still have an eccentric orbit."190 The immediate question raised ds whether here exist. WR binary svstenis with eccentric orbits. which might have perviouslv resembled P C€veni.," The immediate question raised is whether there exist WR binary systems with eccentric orbits, which might have perviously resembled P Cygni."191 The Vilth catalogue of galactic WI stars (van der Hucht 2001) clearly shows that long period. WR. binaries and. high eccentricities correlate., The VIIth catalogue of galactic WR stars (van der Hucht 2001) clearly shows that long period WR binaries and high eccentricities correlate.192 The number of very high cecentricity svstemis is not large. but that is expected. as most svstenis are short period and they have time to reduce their eccentricities during their W1t stage.," The number of very high eccentricity systems is not large, but that is expected as most systems are short period and they have time to reduce their eccentricities during their WR stage."193 Eldridge (2009) found. that WR. binaries having an orbital period. longer than 30days are expected to remain with eccentric orbits., Eldridge (2009) found that WR binaries having an orbital period longer than $\sim 30 \days$ are expected to remain with eccentric orbits.194 This usually happens when the mass loss occurs occasionally for short periods. not having enough time to allect the eccentricity.," This usually happens when the mass loss occurs occasionally for short periods, not having enough time to affect the eccentricity."195 The WR 140 massive binary system has an eccentricity of e0:55 ancl a period of P~7.94vrs (Alarchenkoct al., The WR 140 massive binary system has an eccentricity of $e \sim 0.88$ and a period of $P \sim 7.94 \yrs$ (Marchenkoet al.196 2003). and is perhaps the most extraordinary example showing that high eccentricity may survive the LBV stage. assuming all WI stars experience LBV evolution.," 2003), and is perhaps the most extraordinary example showing that high eccentricity may survive the LBV stage, assuming all WR stars experience LBV evolution."197 Though the proposed. model suggests interaction in à binary svstem. luminous x-ray raciation is not expected.," Though the proposed model suggests interaction in a binary system, luminous x-ray radiation is not expected."198 X. detailed: analysis of x-ray luminosity from colliding winds (Akashi et al., A detailed analysis of x-ray luminosity from colliding winds (Akashi et al.199 2006) gives that a collision between the LBV and the MS companion winds. for the parameters used in the model. is likely to produce soft. x-ray at. very. low Luminosity «qoergsI.," 2006) gives that a collision between the LBV and the MS companion winds, for the parameters used in the model, is likely to produce soft x-ray at very low luminosity $< 10^{29} \erg~s^{-1}$."200 Phe reason for that low Luminosity. compared to the strong one observed in other systems (such as 5g Car: Corcoran 2005) is the very small mass loss rate of the ~3.6AL. B-type binary companion. whichmakes the LDV wind dominate ane consequently only very weak shocks are formed.," The reason for that low luminosity, compared to the strong one observed in other systems (such as $\eta$ Car; Corcoran 2005) is the very small mass loss rate of the $\sim 3-6~\rm{M_\odot}$ B-type binary companion, whichmakes the LBV wind dominate and consequently only very weak shocks are formed."201Final point source position and photometry estimation is performed [for all detections on the detection list.,Final point source position and photometry estimation is performed for all detections on the detection list.202 For each point source candidate the data in the input image is fit with the PRF., For each point source candidate the data in the input image is fit with the PRF.203" Fitting is performed by minimizing V: llere (he summation is performed over pixels / from (he fitting area V: 5(7) and o(/) are the pixel values of the input image and uncertainty image. correspondinglv: f, aud R,, are the [lux and the position of the »—/h point source; PREG.R,) is the contribution of the n—lh point source to the /—/h pixel: h is (he constant background wilhin the fitting area that can be used in this formula optionallv."," Fitting is performed by minimizing $\chi^2$: Here the summation is performed over pixels $i$ from the fitting area $W$; $s(i)$ and $\sigma(i)$ are the pixel values of the input image and uncertainty image, correspondingly; $f_n$ and ${\mathbf R}_n$ are the flux and the position of the $n-th$ point source; $PRF(i,{\mathbf204R}_n$ ) is the contribution of the $n-th$ point source to the $i-th$ pixel; $b$ is the constant background within the fitting area that can be used in this formula optionally."205" The number .N,Pp of point sources fit simultaneously is sel (to 1 iniGally if the detection does not belong to a blend. as described in the previous section."," The number $N_p$ of point sources fit simultaneously is set to 1 initially if the detection does not belong to a blend, as described in the previous section."206" For the detections belonging to a blend the number V, is initially set to the size of the blend.", For the detections belonging to a blend the number $N_p$ is initially set to the size of the blend.207 PRE contribution is computed for any fractional position of the point source: a bilinear interpolation is performed [rom the grid points available in the PREF., PRF contribution is computed for any fractional position of the point source; a bilinear interpolation is performed from the grid points available in the PRF.208 The fitting area HV is a combination of rectangle areas centered on the detection positions (Figure 4))., The fitting area $W$ is a combination of rectangle areas centered on the detection positions (Figure \ref{FittingArea}) ).209 The size of each rectangle is specified by the user aud should be set to be on the order of the size of the Airy disk., The size of each rectangle is specified by the user and should be set to be on the order of the size of the Airy disk.210 If set. properly. the fitting areas of the point sources belonging to one blend are partially overlapping.," If set properly, the fitting areas of the point sources belonging to one blend are partially overlapping."211 As a result of detection point sources with the overlapping contributions should belong to one blend., As a result of detection point sources with the overlapping contributions should belong to one blend.212 However. if the detection is done poorly. e.g. if the detection threshold is set too high. then such sources will be erroneously put in (wo separate blends and not fit simultaneously.," However, if the detection is done poorly, e.g. if the detection threshold is set too high, then such sources will be erroneously put in two separate blends and not fit simultaneously."213 If the uncertainty image is nol available. the noise image can used instead.," If the uncertainty image is not available, the noise image can used instead."214 Users have an option of using the background subtracted mosaic. using (he original image and filling the backeround for each point source. or doing both.," Users have an option of using the background subtracted mosaic, using the original image and fitting the background for each point source, or doing both."215 The strategv used [or minimization of A? is a hybrid of a modified simplex algorithm and the 5eradient descent algorithm., The strategy used for minimization of $\chi^2$ is a hybrid of a modified simplex algorithm and the gradient descent algorithm.2165 The simplex algorithimg does not use derivatives of the funcüons involved in minimization., The simplex algorithm does not use derivatives of the functions involved in minimization.217 Ht is a desirable feature since (he world coordinate transformations are very complicated functions of their arguments., It is a desirable feature since the world coordinate transformations are very complicated functions of their arguments.218 We made several modifications ol the algorithm. which are described in Appendix ??..," We made several modifications of the algorithm, which are described in Appendix \ref{app_simplex}."219 Simplex operations are applied to the point sources positions., Simplex operations are applied to the point sources positions.220 On the other hand the derivatives with respect to the [Iuxes οἱ the point sources and the background are taken easily:, On the other hand the derivatives with respect to the fluxes of the point sources and the background are taken easily:221planet or mmeasturing its mass aud orbital parameters as we use for SIM. (,planet or measuring its mass and orbital parameters as we use for SIM. (222Strictly. radial velocities are sensitive to the combinations sin aud w+ rather thau the mass. 1. inclination. 7. argument of pericenter. w. aud longitude of asceudiug uode. 2. iudividually.),"Strictly, radial velocities are sensitive to the combinations $m \sin i$ and $\omega+\Omega$ rather than the mass, $m$, inclination, $i$ , argument of pericenter, $\omega$, and longitude of ascending node, $\Omega$, individually.)"223 We find the use of equation (2.1)) gives reasonable agreement with the simulations of Cunminiugs (2002) assumiug 21 observations over five vears and a [false alarm rate. and are also roughly cousistent with the current radial velocity discoveries (Butler 2002 aid. references therein).," We find the use of equation \ref{EqnSRv}) ) gives reasonable agreement with the simulations of Cummings (2002) assuming 24 observations over five years and a false alarm rate, and are also roughly consistent with the current radial velocity discoveries (Butler 2002 and references therein)."224 The factor of /2 in the denominator of the scaled signal for radial velocity observations accounts for the [act that radial velocity observations are ouly sensitive to oue compouent of the stars velocity. while astrometric observations measure the stars two dimensional position.," The factor of $\sqrt{2}$ in the denominator of the scaled signal for radial velocity observations accounts for the fact that radial velocity observations are only sensitive to one component of the star's velocity, while astrometric observations measure the star's two dimensional position."225 For the teu-vear mission we assume {5 observations and reduce the value of σι by V2., For the ten-year mission we assume 48 observations and reduce the value of $\sigma_K$ by $\sqrt{2}$.226 While this analysis neglects many important [actors that affect the efficiency of racial velocity surveys. Ht allows us to estimate crudely what fraction of planets found by SIM could be iudependently discovered by a radial velocity survey of the same stars.," While this analysis neglects many important factors that affect the efficiency of radial velocity surveys, it allows us to estimate crudely what fraction of planets found by SIM could be independently discovered by a radial velocity survey of the same stars."227 OF course. SIM will allow the mass aud inclination to be measured separately which cannot be done with radial velocity measurements alone.," Of course, SIM will allow the mass and inclination to be measured separately which cannot be done with radial velocity measurements alone."228 We do not cousider the beuelits of combining radial velocity and. astrometric observations (Eisner Ixulkarni 2002)., We do not consider the benefits of combining radial velocity and astrometric observations (Eisner Kulkarni 2002).229 Throughout this paper we attempt to make generous assumptions that teud to overestimate the number of detectious aud measurements SIM will make., Throughout this paper we attempt to make generous assumptions that tend to overestimate the number of detections and measurements SIM will make.230 For example. the simulations of Sozzetti (2002) assume that noue of the reference stars have companions and that tlie measurement Uncertainties are Caussian and uucorrelated.," For example, the simulations of Sozzetti (2002) assume that none of the reference stars have companions and that the measurement uncertainties are Gaussian and uncorrelated."231 Additionally. we assume that multiple planet systems do uot reduce SIMs efficiency for detecting plauets aid measuring orbits.," Additionally, we assume that multiple planet systems do not reduce SIM's efficiency for detecting planets and measuring orbits."232 Finally. we allow [or detectious of planets with orbital periods more than twice the missiou lifetime for which it may be difficult to verify that the astrometric deviations [rom a model with uo planets are Ixepleriau or tliat they are due to the gravitational perturbation of a planetary companion.," Finally, we allow for detections of planets with orbital periods more than twice the mission lifetime for which it may be difficult to verify that the astrometric deviations from a model with no planets are Keplerian or that they are due to the gravitational perturbation of a planetary companion."233 Oue chauge that could significantly increase the number of planets SIM. would find would be that the planetary mass function is much larger for terrestrial-niass. planets than implied by extrapolating the planetary inass function for giant planets., One change that could significantly increase the number of planets SIM would find would be that the planetary mass function is much larger for terrestrial-mass planets than implied by extrapolating the planetary mass function for giant planets.234 We now present the results of our Monte Carlo simulatious., We now present the results of our Monte Carlo simulations.235 lu ackclition to discussing several possible sets of inission parameters. we [requently divide our results into three categories based ou the planet mass.," In addition to discussing several possible sets of mission parameters, we frequently divide our results into three categories based on the planet mass."236 Plauets with ni«91 would be extremely interesting since they have a tnass comparable to the Earth and are likely to be rocky bodies formed by a mechanuisin similar to tliat which formed the Earth., Planets with $m < 3 M_\oplus$ would be extremely interesting since they have a mass comparable to the Earth and are likely to be rocky bodies formed by a mechanism similar to that which formed the Earth.237 This category would include all theterrestrial planets in our solar syste., This category would include all theterrestrial planets in our solar system.238Enropean Space Agency's coruerstone mission Gade ds scheduled for Launch in 2013.,European Space Agency's cornerstone mission $\textit{Gaia}$ is scheduled for launch in 2013.239 It is primarily an astrometric mission. designed to measure precise 3D positions for up to a billion stars in our Galaxy aud other bright objects im the sky.," It is primarily an astrometric mission, designed to measure precise 3D positions for up to a billion stars in our Galaxy and other bright objects in the sky."240 Iu addition to astrometric measurements. spectroscopy and multiiband photometry will be performed. providing radial velocities and additional astrophysical iuformation ou the stars and other objects," In addition to astrometric measurements, spectroscopy and multi-band photometry will be performed, providing radial velocities and additional astrophysical information on the stars and other objects."241 The main scientific goal of Cada mission is to clarity the origin aud formation history of our Galaxy;, The main scientific goal of $\textit{Gaia}$ mission is to clarify the origin and formation history of our Galaxy.242 The goals of the mission are described ina Perrymanetal.(2001).. (2010).. and. more thoroughly. in Turonetal.," The goals of the mission are described in \citet{perryman}, \citet{lindegren}, , and, more thoroughly, in \citet{turon}."243 (2005).. Gaia will continuously. scan the sky covering the whole sky and building its own catalogue of celestial objects.," $\textit{Gaia}$ will continuously scan the sky, covering the whole sky and building its own catalogue of celestial objects."244 Α preliminary catalogue will be released every 6 mouths aud a final catalogue. exploiting all the data recovered durus the nuson. will be released at the cud of the operational time (around 2020) (Laumnuers 2008).," A preliminary catalogue will be released every 6 months and a final catalogue, exploiting all the data recovered during the mission, will be released at the end of the operational time (around 2020) \citep{lammers}."245 Comparing further observations with this catalogue will enable Gee to detect various trausicut sources. with some of them bene cataclysunic variables. superuovae. active galactic nuclei. asteroids. etc.," Comparing further observations with this catalogue will enable $\textit{Gaia}$ to detect various transient sources, with some of them being cataclysmic variables, supernovae, active galactic nuclei, asteroids, etc."246 Since the catalogue of Guia astrometric aud photometric data will be available only late iuto the Gee operation. triggers from transient phenomena will actually be the first Gaia data released to the scientific σοιτν.," Since the catalogue of $\textit{Gaia}$ astrometric and photometric data will be available only late into the $\textit{Gaia}$ operation, triggers from transient phenomena will actually be the first $\textit{Gaia}$ data released to the scientific community."247 Iu order to be prepared for this stream of data and to make sure the alert stream is accurate. reliable. and free from coutamination. the Gare Science Alerts Working Group las beenformed.," In order to be prepared for this stream of data and to make sure the alert stream is accurate, reliable, and free from contamination, the $\textit{Gaia}$ Science Alerts Working Group has been."248 Oue type of possible trausieuts to be detected by Gate is ganuua-rav burst optical afterelows., One type of possible transients to be detected by $\textit{Gaia}$ is gamma-ray burst optical afterglows.249 (αλαταν bursts (CRBs) are extremely energetic explosions occurring at cosmological distances (Piran2005:Mészáros2006).," Gamma-ray bursts (GRBs) are extremely energetic explosions occurring at cosmological distances \citep{piran,meszaros}."250".. They represent the amost luminous events in the gamuna-rav part of the clectromaguetic spectruni known iu the universe,", They represent the most luminous events in the gamma-ray part of the electromagnetic spectrum known in the universe.251" Usualh. the short-term: prompt eanunia-rav Cluission is followed by an afterelow enütted at longer waveleueths frou, N-ravs to radio waves. which cau lastfor several davs"," Usually, the short-term prompt gamma-ray emission is followed by an afterglow emitted at longer wavelengths from X-rays to radio waves, which can lastfor several days."252small.,small.253 We conclude Chat the hard NRB is a largely unbiasecl (racer of the matter distribution on large scales., We conclude that the hard XRB is a largely unbiased tracer of the matter distribution on large scales.254 This is consistent with current moclels of large-scale. late Gime galaxy biasing Benson et al.," This is consistent with current models of large-scale, late time galaxy biasing (Benson et al."255 2000: Tegmark Peebles 1998)., 2000; Tegmark Peebles 1998).256" In addition. the latest studies of the clustering ol L, galaxies on ~LOOApe scales indicates that these objects are also unbiased (racers of matter."," In addition, the latest studies of the clustering of $\sim L_*$ galaxies on $\sim 100~Mpc$ scales indicates that these objects are also unbiased tracers of matter."257 Verde et al. (, Verde et al. (258"2002) found that. on scales of ~Y to ~40AZpe. b=1.04x0.11 for 1.9L, galaxies in the 2dF survev with a mean redshilt of 2=0.17.","2002) found that, on scales of $\sim 7$ to $\sim 40~Mpc$, $b = 1.04 \pm 0.11$ for $1.9~L_*$ galaxies in the $2dF$ survey with a mean redshift of $z = 0.17$."259 Using a different analvsis of the same data. Lahav et al. (," Using a different analysis of the same data, Lahav et al. ("2602002) found that 6=1.200.11 on scales of ~20 to ~150Mpe.,2002) found that $b = 1.20 \pm 0.11$ on scales of $\sim 20$ to $\sim 150~Mpc$.261 Both of these results are consistent with early lindines from the SDSS and 2NLASS survevs that imply linear bias factors on the order of unity (Tegmark et al., Both of these results are consistent with early findings from the SDSS and 2MASS surveys that imply linear bias factors on the order of unity (Tegmark et al.262 2002: Miller et al., 2002; Miller et al.263 2003)., 2003).264" It should not be surprising that the NRB and galaxy. biases are similar since L, galaxies are closely associated with the moderately active AGN that comprise the bulk of the hard XRD (e.g.. Barger et al."," It should not be surprising that the XRB and galaxy biases are similar since $L_*$ galaxies are closely associated with the moderately active AGN that comprise the bulk of the hard XRB (e.g., Barger et al."265 2003: Miller et al., 2003; Miller et al.266 2003)., 2003).267 If these estimates are accurate. then the X-ray. bias factor in the linear regime is now much better determined.," If these estimates are accurate, then the X-ray bias factor in the linear regime is now much better determined."268 The hard XRD background appears to be an excellent tracer of the arge-scale distribution of matter. making it a useful tool for understanding the evolution of structure in the universe.," The hard XRB background appears to be an excellent tracer of the large-scale distribution of matter, making it a useful tool for understanding the evolution of structure in the universe."269 One example of the importance of determining galaxy biases (and indeed the driving motivation for this work) is to ail in the interpretation of recent detections of correlations of galaxies with the cosmic microwave background. (CMD)., One example of the importance of determining galaxy biases (and indeed the driving motivation for this work) is to aid in the interpretation of recent detections of correlations of galaxies with the cosmic microwave background (CMB).270 We («Bouehn Crittenden 2004) have detected a correlation of the 2—10eV. XNRD with UMAP satellite map of the cosmic microwave background (Bennett et al., We (Boughn Crittenden 2004) have detected a correlation of the $2-10~keV$ XRB with $WMAP$ satellite map of the cosmic microwave background (Bennett et al.271 2003). and there iive been correlations observed with a number of other galaxy surveys (Nolta et al.," 2003), and there have been correlations observed with a number of other galaxy surveys (Nolta et al."272 2003: Scranton οἱ al., 2003; Scranton et al.273 2003: Fosalba. Castander 2003: Afshordi. Loh. Strauss 2003).," 2003; Fosalba, Castander 2003; Afshordi, Loh, Strauss 2003)."274 These correlations have been interpreted as (he detection of the integrated Sachs-Wolle (15V) effect (Sachs Wolle 1967)., These correlations have been interpreted as the detection of the integrated Sachs-Wolfe $ISW$ ) effect (Sachs Wolfe 1967).275" If confirmed. they would constitute an important test of the ACDAL cosmological model and provide further evidence of the existence of a substantial amount of ""dark energy” in the universe (Crittenden Turok 1996)."," If confirmed, they would constitute an important test of the $\Lambda CDM$ cosmological model and provide further evidence of the existence of a substantial amount of “dark energy” in the universe (Crittenden Turok 1996)."276Ou the other hand. the charge fluctuations become large for erains appreciably simaller than this size and this makes the treatment of the problem with the Fokkor-Planck equation not precise.,"On the other hand, the charge fluctuations become large for grains appreciably smaller than this size and this makes the treatment of the problem with the Fokker-Planck equation not precise."277 Nevertheless. even takine into account the pilot nature of our estimates it is clear that the process of acceleration is ρουαν very iuportant for small eraius.," Nevertheless, even taking into account the pilot nature of our estimates it is clear that the process of acceleration is potentially very important for small grains."278 We showed that there exists a novel powerful nmechanisni of charec-fluctuation-indiuced acceleration operating iu astrophysical plasmas., We showed that there exists a novel powerful mechanism of charge-fluctuation-induced acceleration operating in astrophysical plasmas.279 This mechanism. which occurs to be more efficicut for smaller eraius. is based ou the charge fluctuations that eraius expericuce during the mutual Couloml collisions.," This mechanism, which occurs to be more efficient for smaller grains, is based on the charge fluctuations that grains experience during the mutual Coulomb collisions."280 As the result. the kinetic cnerey of eraius 1s not conserved in the collisions. which causes the stochastic heating analogous to the second-order Ferm acceleration.," As the result, the kinetic energy of grains is not conserved in the collisions, which causes the stochastic heating analogous to the second-order Fermi acceleration."281 This acceleration iuechanisni is a generic plasma process which cau operate in very differeut euvironuents rangiue from the ISM to laboratory eas discharecs., This acceleration mechanism is a generic plasma process which can operate in very different environments ranging from the ISM to laboratory gas discharges.282 It is a remnarkable manifestation of the iutrinsic nou-equilibrimu (energetic openness) of dusty plasinas (Tsytovich 1997. Fortov 2005): Even if eleetrous and ious themselves were in detailed equilibrium. their absorption aud the subsequent recombination on dust eraius camnot be balauced by the correspoucding iuverse process (of the ionization and enuüssiou frou grains) due to its apparent inefiicicney temperatures necessary for that should be chormously Ligh.," It is a remarkable manifestation of the intrinsic non-equilibrium (energetic openness) of dusty plasmas (Tsytovich 1997, Fortov 2005): Even if electrons and ions themselves were in detailed equilibrium, their absorption and the subsequent recombination on dust grains cannot be balanced by the corresponding inverse process (of the ionization and emission from grains) due to its apparent inefficiency – temperatures necessary for that should be enormously high."283 Therefore. the process of dust chareiue eoes only in one direction. resulting iu the imbalanced asma flux on the erain surface.," Therefore, the process of dust charging goes only in one direction, resulting in the imbalanced plasma flux on the grain surface."284 The dust dvuanuics eots coupled to the chareing process due to charge Huctuatious Gvhlich are inevitable due to the discreteness of the elementary charge)., The dust dynamics gets coupled to the charging process due to charge fluctuations (which are inevitable due to the discreteness of the elementary charge).285 Thus. in terms of the energy valance. the imechanign of charge-diuctuation-duduced acceleration is based ou the conversion of the energy Hux (associated with the plasiua fiux on grains) iuto the sinetic energy ofdust.," Thus, in terms of the energy balance, the mechanism of charge-fluctuation-induced acceleration is based on the conversion of the energy flux (associated with the plasma flux on grains) into the kinetic energy of dust."286 Oue should point out that for typical ISM. conditions he situation is very different from the equilibrium one: The plasma temperature is much larecr that the dust uaterial temperature (Tin) due to efficient radiative cooling of the dust., One should point out that for typical ISM conditions the situation is very different from the equilibrium one: The plasma temperature is much larger that the dust material temperature $T_{d{\rm m}}$ ) due to efficient radiative cooling of the dust.287 Moreover. the ious aud electrous are usually produced by the ISM UV and/or cosnic rav lonization.," Moreover, the ions and electrons are usually produced by the ISM UV and/or cosmic ray ionization."288 Craius themselves cuit photoelectrons interacting with UV photons., Grains themselves emit photoelectrons interacting with UV photons.289 All these non-equilibriu effects can alter charee fluctuations aud therefore additionally contribute to our acceleration mechamisu., All these non-equilibrium effects can alter charge fluctuations and therefore additionally contribute to our acceleration mechanism.290 Tn particular environments. e.g. within quicscent dark clouds and protoplanetary disks with suppressed turbulence. the mechanisua we discussed iu the paper may be dominant for grains substantially lavecr than 10 cm.," In particular environments, e.g., within quiescent dark clouds and protoplanetary disks with suppressed turbulence, the mechanism we discussed in the paper may be dominant for grains substantially larger than $10^{-5}$ cm."291 However. we ποσο the rapid decrease of the mechanisuni efficiency. with the eraiu size.," However, we notice the rapid decrease of the mechanism efficiency with the grain size."292 The treatineut preseuted in this paper is limited iu two respects;, The treatment presented in this paper is limited in two respects.293 First. the Fokker-Plauck approach presuimes relatively σα] energy variation (6)) occurring in cach Coulomb collision due to charge fluctuations.," First, the Fokker-Planck approach presumes relatively small energy variation \ref{25}) ) occurring in each Coulomb collision due to charge fluctuations."294 If this variation becomes larec. such approach (describing the evolution of the velocity distribution function) 1s uo longer applicable.," If this variation becomes large, such approach (describing the evolution of the velocity distribution function) is no longer applicable."295 Ou the other hand. the mean energy evolution which is esseutial for this paper is still described bx Eq. (9)).," On the other hand, the mean energy evolution – which is essential for this paper – is still described by Eq. \ref{0}) )."296 Second. the direct mechanical encounters of eras cannot bo treated within the formalisin.," Second, the direct mechanical encounters of grains cannot be treated within the formalism."297 When such collisions start dominating (af lavee Z4) the additional dissipation associated witli erain deformation. shattering. ete.," When such collisions start dominating (at large $T_d$ ) the additional dissipation associated with grain deformation, shattering, etc."298 should be taken mto account., should be taken into account.299 Tn future. we plan to extend the mechanism for the PAT population of exaius. explicitly taking iuto account the substantial variation of erai charge in the process of individual collision with iu electron or jon (τοια that iu this paper we assumed small charge fluctuations. which allowed us to obtain analytically tractable results).," In future, we plan to extend the mechanism for the PAH population of grains, explicitly taking into account the substantial variation of grain charge in the process of individual collision with an electron or ion (remind that in this paper we assumed small charge fluctuations, which allowed us to obtain analytically tractable results)."300 The fact that the efficiency of grain accelerationincreases with the decrease of grain size makes the process very efficicut., The fact that the efficiency of grain acceleration increases with the decrease of grain size makes the process very efficient.301 Extrapolatiug our results to PAIT particles we lay expect their collisions to be very frequent., Extrapolating our results to PAH particles we may expect their collisions to be very frequent.302 We note that the additional motivation for the PAIT studies comes from the fact that they are responsible for a compoucut of CAMB foreground radiation (Draine Lazariau 1998. see also IHoaug ct al.," We note that the additional motivation for the PAH studies comes from the fact that they are responsible for a component of CMB foreground radiation (Draine Lazarian 1998, see also Hoang et al."303 2010)., 2010).304 Furthermore. we plan to analyze the impact of the charee-fluctuation-induced acceleration on the dus coagulation processes occuring m the ISAL aud other astroplivsical euvironunieuts e.g. protostellar accretion disks.," Furthermore, we plan to analyze the impact of the charge-fluctuation-induced acceleration on the dust coagulation processes occurring in the ISM and other astrophysical environments, e.g. protostellar accretion disks."305 It is alveady clear that the new mechanism can induce coagulation and shattering which have not becu considered in the literature before., It is already clear that the new mechanism can induce coagulation and shattering which have not been considered in the literature before.306 Together with the AIIID turbulence acceleration. our mechanisia testifies that the astrophysical erains achieve velocities much larecr than those arising from the Browian motion.," Together with the MHD turbulence acceleration, our mechanism testifies that the astrophysical grains achieve velocities much larger than those arising from the Brownian motion."307 Our major results can be summarized as 1., Our major results can be summarized as 1.308" The change of the erain charge in the process of the eraierain Coulonib collisious results iu second-order Fermi 2,", The change of the grain charge in the process of the grain-grain Coulomb collisions results in second-order Fermi 2.309 The acceleration is most efficient for small. i.e.. less than 10 cua 3.," The acceleration is most efficient for small, i.e., less than $\sim10^{-6}$ cm 3."310 The process of acceleration should be accounted for correct description of the evolution of the smallest eraius., The process of acceleration should be accounted for correct description of the evolution of the smallest grains.311 AL and ΤΗ acknowledge the support of the NSF-funded Center for Magnetic Self£-Oreauizatiaon (CMSO) and the NSF evant AST O50716L., AL and TH acknowledge the support of the NSF-funded Center for Magnetic Self-Organizatiaon (CMSO) and the NSF grant AST 0507164.312 The interaction of individual dust particles with the background neutral gas is described by the Langevin equation (sce Van Iiauupen 1981).," The interaction of individual dust particles with the background neutral gas is described by the Langevin equation (see Van Kampen 1981),"313tensor.,tensor.314" The parallel and perpendicular conductivities are dominated by the effect of electrons and ions, respectively."," The parallel and perpendicular conductivities are dominated by the effect of electrons and ions, respectively."315 The perpendicular electron conductivity and the parallel ion conductivity are negligible in fully ionized plasmas., The perpendicular electron conductivity and the parallel ion conductivity are negligible in fully ionized plasmas.316" Expressions for the conductivities in MKS units for a hydrogen plasma are (see.¢.g..Parker1953;Spitzer1962:Braginskii1965).. where i, is the proton mass and InA is the Coulomb logarithm, whose value is generally between 5 and 20 and has a weak dependence on temperature and density (see,σ.σ,Priest1982)."," Expressions for the conductivities in MKS units for a hydrogen plasma are \citep[see, e.g.,][]{parker,spitzer,brag}, where $m_{\rm i}$ is the proton mass and $\ln \Lambda$ is the Coulomb logarithm, whose value is generally between 5 and 20 and has a weak dependence on temperature and density \citep[see, e.g.,][]{priest}."317". Finally, the heat-loss function L(T.p) accounts for the balance between radiative cooling and heating."," Finally, the heat-loss function $L(T,\rho)$ accounts for the balance between radiative cooling and heating."318 The determination of an analytical function of the temperature and density that describes radiative losses of the prominence plasma is a very difficult work that requires the numerical solution of nonlocal thermodynamic equilibrium (NLTE) radiative transfer equations., The determination of an analytical function of the temperature and density that describes radiative losses of the prominence plasma is a very difficult work that requires the numerical solution of nonlocal thermodynamic equilibrium (NLTE) radiative transfer equations.319 This is beyond the purpose and scope of the present study., This is beyond the purpose and scope of the present study.320 One reasonable semi-empirical approximation to an expression for the radiative loss function was obtained by Hildner(1974).., One reasonable semi-empirical approximation to an expression for the radiative loss function was obtained by \citet{hildner}.321 This author assumed an optically thin plasma (c.g..Cox&Tucker1969) and performed a piecewise fit of the radiative losses previously computed by several authors as a function of temperature.," This author assumed an optically thin plasma \citep[e.g.,][]{coxtucker} and performed a piecewise fit of the radiative losses previously computed by several authors as a function of temperature."322" Here, we adopt Hildner's approach."," Here, we adopt Hildner's approach."323" The functional expression of L(T.p) considered by Hildner(1974) is where y and a are piccewise constants depending on the temperature, and / is an arbitrary heating function."," The functional expression of $L(T,\rho)$ considered by \citet{hildner} is where $\chi^*$ and $\alpha$ are piecewise constants depending on the temperature, and $h$ is an arbitrary heating function."324" The assumption of an optically thin plasma seems a reasonable approximation for coronal and prominence-corona transition region (PCTR) temperatures, whereas cool prominence plasmas may be considered optically thick."," The assumption of an optically thin plasma seems a reasonable approximation for coronal and prominence-corona transition region (PCTR) temperatures, whereas cool prominence plasmas may be considered optically thick."325" Some authors (c.9..1979) have proposed corrections to the values of y and « in the range of cool prominence temperatures, νο, 7«15,000 K, in order to represent radiation losses in optically thick plasmas using Equation (8))."," Some authors \citep[e.g.,][]{rosner,milne} have proposed corrections to the values of $\chi^*$ and $\alpha$ in the range of cool prominence temperatures, i.e., $T < 15,000$ K, in order to represent radiation losses in optically thick plasmas using Equation \ref{eq:radlosses}) )."326" In the literature, there are more recent parametrizations for γ΄ and @ which update Hildner's values."," In the literature, there are more recent parametrizations for $\chi^*$ and $\alpha$ which update Hildner's values."327" In particular, the so-called Klimchuk-Raymond parametrization Klimchuk&Cargill2001) may be a better representation of the radiative losses in the hotter part of the PCTR and in the solar corona."," In particular, the so-called Klimchuk-Raymond parametrization \citep[see, e.g.,][]{klimchuk} may be a better representation of the radiative losses in the hotter part of the PCTR and in the solar corona."328" On the contrary, the Klimchuk-Raymond function may not be adequate in the cool part of the thread."," On the contrary, the Klimchuk-Raymond function may not be adequate in the cool part of the thread."329 We use the Klimchuk-Raymond function as an alternative to Hildner's parametrization in the hotter part of the equilibrium., We use the Klimchuk-Raymond function as an alternative to Hildner's parametrization in the hotter part of the equilibrium.330 The values of the parameters y and α for various temperature ranges and regimes are given in Table I., The values of the parameters $\chi^*$ and $\alpha$ for various temperature ranges and regimes are given in Table \ref{tab:regimes}. .331M. and M;=0.6 M..,$_{\odot}$ and $M_{\mbox{\scriptsize Ni}} = 0.6$ $_{\odot}$.332" The maximum ejecta velocity is set αἳ Όρων=12210"" em 1.", The maximum ejecta velocity is set at $v_{\mbox{\scriptsize max}} = 1.2 \times 10^{9}$ cm $^{-1}$.333 This is lower than the maximum velocities in real SNe but representative of the velocity regime in which the density is large and is therefore appropriate given our choice of a uniform density protile (see above)., This is lower than the maximum velocities in real SNe but representative of the velocity regime in which the density is large and is therefore appropriate given our choice of a uniform density profile (see above).334 In this model. the “ONG is located in a spherical region at the centre of the ejecta.," In this model, the $^{56}$ Ni is located in a spherical region at the centre of the ejecta."335" The volume of this region is fixed by an adopted """"Ni mass fraction of 0.9.", The volume of this region is fixed by an adopted $^{56}$ Ni mass fraction of 0.9.336 The region outside the central concentration of Ni is assumed to be composed of intermediate mass elements., The region outside the central concentration of Ni is assumed to be composed of intermediate mass elements.337 Model SS has the same geometry and Ni-distribution as Model SC but its densities are everywhere higher by a factor of 1.5., Model SS has the same geometry and Ni-distribution as Model SC but its densities are everywhere higher by a factor of 1.5.338" Thus. this model is ""super-Chandrasekhar"". having Mq.=2.1 M. and AM;=0.9 M.."," Thus, this model is “super-Chandrasekhar”, having $M_{\mbox{\scriptsize T}}=2.1$ $_{\odot}$ and $M_{\mbox{\scriptsize Ni}} = 0.9$ $_{\odot}$."339 This model explores  -ray emission from objects in which τε. is higher than in Model SC., This model explores $\gamma$ -ray emission from objects in which $\tau_C$ is higher than in Model SC.340 Although outside the standard SN Ta paradigm. Super-Chandrasekhar explosions have been proposed for unusually bright events such as SN 1991T (2).. SN 2003fg (2). and SN 2006: (2).," Although outside the standard SN Ia paradigm, Super-Chandrasekhar explosions have been proposed for unusually bright events such as SN 1991T \citep{fisher99}, SN 2003fg \citep{howell06} and SN 2006gz \citep{hicken07}."341 This model isolates the effect of composition., This model isolates the effect of composition.342 It adopts the same geometry. mass and Ni-distribution as Model SC.," It adopts the same geometry, mass and Ni-distribution as Model SC."343 However. it assumes that the majority of the material that is not initially “ONT consists of other heavy nuclei: the photoabsorption and cross-sections are thus different from Model SC.," However, it assumes that the majority of the material that is not initially $^{56}$ Ni consists of other heavy nuclei; the photoabsorption and pair-production cross-sections are thus different from Model SC."344" This model is identical to Model SC ολ=1.4 M.. AA,0.6 . } except that “Ni is distributed uniformly throughout the volume of the ejecta (see panel b of Fig. 13."," This model is identical to Model SC $M_{\mbox{\scriptsize345T}} = 1.4$ $_{\odot}$ , $M_{\mbox{\scriptsize Ni}} = 0.6$ $_{\odot}$ ) except that $^{56}$ Ni is distributed uniformly throughout the volume of the ejecta (see panel b of Fig. \ref{fig:models}) )."346" Recently. ? have argued for a model which may account for most SNe Ia. Analysing spectra of a large sample of SNe. they concluded that the characteristic structure consists of a low-velocity core of stable iron-group material surrounded by a7"" Ni-rich region."," Recently, \citet{mazzali07} have argued for a model which may account for most SNe Ia. Analysing spectra of a large sample of SNe, they concluded that the characteristic structure consists of a low-velocity core of stable iron-group material surrounded by a $^{56}$ Ni-rich region."347 Outside this region. the material underwent incomplete nuclear burning and is dominated by intermediate-mass nuclei.," Outside this region, the material underwent incomplete nuclear burning and is dominated by intermediate-mass nuclei."348 Motivated by their study. we include a model based on such a structure (the geometry is shown in panel ο of Fig. 1).," Motivated by their study, we include a model based on such a structure (the geometry is shown in panel c of Fig. \ref{fig:models}) )."349 The inner stable iron-group core has a mass of 0.2 M.., The inner stable iron-group core has a mass of 0.2 $_{\odot}$.350" A pure """"Ni-region lies immediately above this core and contains 0.6 M...", A pure $^{56}$ Ni-region lies immediately above this core and contains 0.6 $_{\odot}$.351 The outermost region is composed of intermediate-mass elements only., The outermost region is composed of intermediate-mass elements only.352" This model differs from all others as it includes two physically separated ""Ni-rieh regions: a massive core and a thin surface layer.", This model differs from all others as it includes two physically separated $^{56}$ Ni-rich regions: a massive core and a thin surface layer.353" This geometry provides an alternative to the ""super-Chandrasekhar"" scenario (see Section. 3.2) for unusually. bright events.", This geometry provides an alternative to the ``super-Chandrasekhar'' scenario (see Section 3.2) for unusually bright events.354" For this model we retain M4.=1.4 M.. adopt a core ""Ni-mass of 0.9 M. and assume that the outermost 0.1 M. of the ejecta is also pure ""Ni."," For this model we retain $M_{\mbox{\scriptsize T}} = 1.4$ $_{\odot}$, adopt a core $^{56}$ Ni-mass of 0.9 $_{\odot}$ and assume that the outermost 0.1 $_{\odot}$ of the ejecta is also pure $^{56}$ Ni."355 This outer layer is motivated by the early-time spectroscopic behaviour of SNI99IT (2).., This outer layer is motivated by the early-time spectroscopic behaviour of SN1991T \citep{mazzali95}.356 The material sandwiched between the core and the outer Ni-rich shell is taken to be composed of intermediate mass elements., The material sandwiched between the core and the outer Ni-rich shell is taken to be composed of intermediate mass elements.357 This model has the largest M; in our study. as required to account for the brightness of events such as SNI99IT. Here. the basic model is identical to Model SC but the of the Ni ball is displaced along the z-axis by 10 per cent of the outer ejecta radius.," This model has the largest $M_{\mbox{\scriptsize Ni}}$ in our study, as required to account for the brightness of events such as SN1991T. Here, the basic model is identical to Model SC but the centre-of-mass of the Ni ball is displaced along the $z$ -axis by 10 per cent of the outer ejecta radius."358 This leads to an aspherical model. very similar to those discussed by ?..," This leads to an aspherical model, very similar to those discussed by \cite{sim07b}."359 In this model. the maximum ejecta velocity varies with direction. producing an ellipsoidal SN.," In this model, the maximum ejecta velocity varies with direction, producing an ellipsoidal SN."360 This is the same basic geometry as considered by ?.., This is the same basic geometry as considered by \cite{hoeflich02b}.361 Ellipsoidal explosions have been suggested following detection of polarisation in SNe Ta (e.g. ??5).," Ellipsoidal explosions have been suggested following detection of polarisation in SNe Ia (e.g. \citealt{howell01, wang03}) )."362 The maximum velocity (1.5«10 ems +) occurs at the equator., The maximum velocity ( $1.5 \times 10^{9}$ cm $^{-1}$ ) occurs at the equator.363 The UNIS ratio is set to 3-4: therefore the terminal velocity of the ejecta in the polar direction is 1.2.10 em +., The axis ratio is set to 5:4; therefore the terminal velocity of the ejecta in the polar direction is $1.2 \times 10^{9}$ cm $^{-1}$.364 The Ni-distribution is ellipsoidal in the same sense as the total mass distribution and remains centrally concentrated., The Ni-distribution is ellipsoidal in the same sense as the total mass distribution and remains centrally concentrated.365 As in all the other models. the mass-density remains uniform.," As in all the other models, the mass-density remains uniform."366 As discussed above. since the οταν spectrum is primarily determined by Compton scattering. we expect that a highly relevant quantity is the distribution of “°Ni with zc: (see Fig. 29.," As discussed above, since the $\gamma$ -ray spectrum is primarily determined by Compton scattering, we expect that a highly relevant quantity is the distribution of $^{56}$ Ni with $\tau_C$ (see Fig. \ref{fig:taus}) )."367 τε. is a decreasing function of both time and photon energy., $\tau_C$ is a decreasing function of both time and photon energy.368 However. since the energy dependence is universal and. in an homologous flow. the time dependence is very simple (7c:x/. 7). it is sufficient to compare the distribution for one photon energy at one time.," However, since the energy dependence is universal and, in an homologous flow, the time dependence is very simple $\tau_C \propto t^{-2}$ ), it is sufficient to compare the distribution for one photon energy at one time."369 For convenience. the optical depths used in Fig.," For convenience, the optical depths used in Fig."370 2. are computed using the Thompson limit to σε. at time /=50 dy., \ref{fig:taus} are computed using the Thompson limit to $\sigma_C$ at time $t = 50$ dy.371 Fig., Fig.372 2 shows that the models considered quite diverse and reasonably complete. covering a range of plausible single-peaked distributions.," \ref{fig:taus} shows that the models considered quite diverse and reasonably complete, covering a range of plausible single-peaked distributions."373 At the epoch considered. the radioactive material in Model SC is concentrated at moderate optical depths. and its distribution is bracketed by the extremes shown in Model AO.," At the epoch considered, the radioactive material in Model SC is concentrated at moderate optical depths, and its distribution is bracketed by the extremes shown in Model AO."374 Todels SFeC and AE have lower optical depths. but their distributions are still peaked significantly away from το=0.," Models SFeC and AE have lower optical depths, but their distributions are still peaked significantly away from $\tau_C = 0$."375 Todel SM has an extreme distribution. with a significant fraction of the source material at very low optical depths έτει~ 0).," Model SM has an extreme distribution, with a significant fraction of the source material at very low optical depths $\tau_C \sim 0$ )."376 At the opposite limit. Model SS has higher opacities. resulting from the arger density.," At the opposite limit, Model SS has higher opacities, resulting from the larger density."377 Model SNiS differs from the others in having two yeaks in its distribution — most of the Ni lies at moderate optical depths but the thin surface layer provides a distinet peak at very ow optical depth., Model SNiS differs from the others in having two peaks in its distribution – most of the Ni lies at moderate optical depths but the thin surface layer provides a distinct peak at very low optical depth.378 Model SFeR is not shown in Fig. 2:, Model SFeR is not shown in Fig. \ref{fig:taus};379" its distribution of “Ni with τε"" is identical to Model SC so that it can isolate the signatures of photoabsorption.", its distribution of $^{56}$ Ni with $\tau_C$ is identical to Model SC so that it can isolate the signatures of photoabsorption.380 Fig., Fig.381 3 shows a time series of spectra computed from Model SC and spectra from three other spherical models (SS. SFeR and SM) are over-plotted. (," \ref{fig:spec} shows a time series of spectra computed from Model SC and spectra from three other spherical models (SS, SFeR and SM) are over-plotted. ("382For clarity. spectra from the remaining four models are not plotted.,"For clarity, spectra from the remaining four models are not plotted."383 They are. however. included in all the discussions of observable diagnosties in subsequent sections.)," They are, however, included in all the discussions of observable diagnostics in subsequent sections.)"384" At times close to maximum light the 7 -ray spectrumconsists of strong emission lines. mainly due to ""Co. with significant"," At times close to maximum light the $\gamma$ -ray spectrumconsists of strong emission lines, mainly due to $^{56}$ Co, with significant"385"obtained with CoRoT, a space project operated by the French Space Agency, CNES, with participation of the Science Program of ESA, ESTEC/RSSD, Austria, Belgium, Brazil, Germany and Spain.","obtained with CoRoT, a space project operated by the French Space Agency, CNES, with participation of the Science Program of ESA, ESTEC/RSSD, Austria, Belgium, Brazil, Germany and Spain."386 We acknowledge the support of the and of CNES., We acknowledge the support of the and of CNES.387" Computations have been done on theSIGAMM machine, hosted by the Observatoire de la Cotte d""Azur."," Computations have been done on the machine, hosted by the Observatoire de la Côtte d'Azur."388 We present the time-averaged equations for the dynamical evolution of the star-planet system used in this work., We present the time-averaged equations for the dynamical evolution of the star-planet system used in this work.389" These were taken from ? and applied to the case of a planar system (i.e. neglecting possible inclinations of the star and planet), accounting for external forcing of the semi-major axis, eccentricity, and the conservation of angular momentum during the planet’s contraction."," These were taken from \citet{BO09} and applied to the case of a planar system (i.e. neglecting possible inclinations of the star and planet), accounting for external forcing of the semi-major axis, eccentricity, and the conservation of angular momentum during the planet's contraction."390" Given a semi-major axis a and an eccentricy e, the orbital mean motion is n.=(G(m,+mz)/a*)'/? and the angular momentum A=na*(1—e*)'/?."," Given a semi-major axis $a$ and an eccentricy $e$, the orbital mean motion is $n=(G(m_1+m_2)/a^3)^{1/2}$ and the angular momentum $h=na^2(1-e^2)^{1/2}$."391" The equations of secular evolution of h, e, the star's spin € and planet's spin Ω2 under y effect of tides are: In these equations,| µ=mjm/(m,fale]+mz) is the reduced mass of the system, {12 are the moments of inertia of the star and planet, and f; are the tidalfriction timescales, defined as (see??,foradiscussion).. (10--13)) (??):: (23)) (24)) ?,,"," The equations of secular evolution of $h$, $e$ , the star's spin $\Omega_1$ and planet's spin $\Omega_2$ under the effect of tides are: In these equations, $\mu=m_1 m_2/(m_1+m_2)$ is the reduced mass of the system, $I_{1,2}$ are the moments of inertia of the star and planet, and $t_{f1,2}$ are the tidalfriction timescales, defined as \citep[see][for a discussion]{BO09,Eggleton98}. \ref{eq:dhdt}- \ref{eq:do2dt}) \citep{BO09, Hut81}: \ref{eq:H1}) \ref{eq:H2}) \citet{BO09},"392 , 393The collisional de-excitation rates may be computed from the principle of detailed. balance: with 7 expressed in ly. In fig.,The collisional de-excitation rates may be computed from the principle of detailed balance: with $T$ expressed in K. In fig.394 4. we have plotted the population ratio of the excited fine-structure level relatively to the ground state under various physical conditions., \ref{figure:popCII} we have plotted the population ratio of the $^+$ excited fine-structure level relatively to the ground state under various physical conditions.395" As the ion may coexist in both and regions. we sample two cases of interest: a neutral medium at 7=1000 Ix. and an ionized medium at 2=10000 Ix. In the later case. in addition to collisions by electrons. we also consider proton collisions and set nj,= no."," As the ion $^+$ may coexist in both and regions, we sample two cases of interest: a neutral medium at $T=1000$ K, and an ionized medium at $T=10000$ K. In the later case, in addition to collisions by electrons, we also consider proton collisions and set $n_p=n_e$ ."396 However. at Z7=10000 Ix. their ellect on the relative population ratio is only marginal (at the 5 percent level).," However, at $T=10000$ K their effect on the relative population ratio is only marginal (at the 5 percent level)."397 Previous work on the population of the — fine-structure levels taking into account dluorescence and collisions by electrons and hydrogen atoms was accoplished bv Ixeenan et al. (1986)..., Previous work on the population of the $^+$ fine-structure levels taking into account fluorescence and collisions by electrons and hydrogen atoms was accoplished by Keenan et al. \shortcite{KeenanCII}.398 Test calculations showed that our results seem to be in good agreement. with their values. although it is not. possible to make an accurate statement of the discrepancies. since they have published their results only in graphical form.," Test calculations showed that our results seem to be in good agreement with their values, although it is not possible to make an accurate statement of the discrepancies, since they have published their results only in graphical form."399 The ground state of the O atom is comprised of the 2872p! PPSqu triplet levels.," The ground state of the $^0$ atom is comprised of the $^2$ $^4$ $^3\mathrm{P}^e_{2,1,0}$ triplet levels."400 Phe energies. of the fine-structure excited. levels relatively to the ground. state are 158.265 * and 226.977 +., The energies of the fine-structure excited levels relatively to the ground state are 158.265 $^{-1}$ and 226.977 $^{-1}$ .401 The transition probabilities are clin=ο αυ.=127510D&0 and li=L77210s |.," The transition probabilities are $A_{12}=8.865\ 10^{-5}\ \mathrm{s}^{-1}$, $A_{02}=1.275\ 10^{-10}\ \mathrm{s}^{-1}$ and $A_{01}=1.772\ 10^{-5}\ \mathrm{s}^{-1}$ ."402" Our mocel atom includes the five lowest energy. levels: 222p! FPS14, 272p! 1DS and 272p! !S5."," Our model atom includes the five lowest energy levels: $^2$ $^4$ $^3\mathrm{P}^e_{2,1,0}$, $^2$ $^4$ $^1\mathrm{D}^e_2$ and $^2$ $^4$ $^1\mathrm{S}^e_0$."403" ""Ehe energies were taken from Moore (1993) and the transition probabilities [rom the Iron Project caleulation of is. Mendoza and Zeippen (1997)."," The energies were taken from Moore \shortcite{MooreOI} and the transition probabilities from the Iron Project calculation of s, Mendoza and Zeippen \shortcite{AijCI}."404 As the fine-structure levels of atomic oxygen are much more separated Compared to atomic and singly ionized carbon. the CAIBR will not play a major role as one can see from the excitation rates for the first excited level given in table 1. (the excitation rates for the second excited level are even lower).," As the fine-structure levels of atomic oxygen are much more separated compared to atomic and singly ionized carbon, the CMBR will not play a major role as one can see from the excitation rates for the first excited level given in table \ref{table:Kij} (the excitation rates for the second excited level are even lower)."405 The exeited levels may. be populated by collisions with particles present in the medium., The excited levels may be populated by collisions with particles present in the medium.406 Fig., Fig.407 5r shows the collision rates Lor the fine-structure transitions induced by collisions with various particles., \ref{figure:qijOI} shows the collision rates for the fine-structure transitions induced by collisions with various particles.408 The rates for collisional excitation bv electrons were taken from Bell. Berrington Thomas (1998).. by neutral hydrogen from Launay Ποιο (1977a) and by neutral helium from. Monteiro Flower (1987)..," The rates for collisional excitation by electrons were taken from Bell, Berrington Thomas \shortcite{electrons_OI}, by neutral hydrogen from Launay Roueff \shortcite{q_H0_CI} and by neutral helium from Monteiro Flower \shortcite{He_OI}."409 For collisions with protons we have emploved. theanalytic its given by Péqquignot (1990:1996).," For collisions with protons we have employed theanalytic fits given by Péqquignot \shortcite{Peq90,Peq96}."410". For the sake of completeness. we have also considered collisional excitation of the upper ος and tS), levels."," For the sake of completeness, we have also considered collisional excitation of the upper $^1\mathrm{D}^e_2$ and $^1\mathrm{S}^e_0$ levels."411 We mave taken the Mlaxwellian-averaged collision strengths for ransitions induced by electrons involving these levels from Berrington Burke (1981)., We have taken the Maxwellian-averaged collision strengths for transitions induced by electrons involving these levels from Berrington Burke \shortcite{BB81}.412". The rate for the 71"" “py ransition induced by neutral hyelrogen was taken from Federman Shipsev (1983).", The rate for the $^3\mathrm{P}^e$ $^1\mathrm{D}^e$ transition induced by neutral hydrogen was taken from Federman Shipsey \shortcite{FS83}.413.. Phe rates were transformed rom LS coupling to the individual fine-structure levels according to eq. (7))., The rates were transformed from LS coupling to the individual fine-structure levels according to eq. \ref{eq:LSindividual}) ).414" After including 135. UN. allowed. transitions involving he ground 7D"" levels and. upper levels from the work of Vernerct al."," After including 135 UV allowed transitions involving the ground $^3\mathrm{P}^e$ levels and upper levels from the work of Verneret al.,"415" we obtained the indirect excitation rates by he radiation field of the Galaxy: Po,—3.910H«+ and Pao—L110Hs 3", we obtained the indirect excitation rates by the radiation field of the Galaxy: $\Gamma_{21}=3.9\ 10^{-11}\ \mathrm{s}^{-1}$ and $\Gamma_{20}=1.1\ 10^{-11}\ \mathrm{s}^{-1}$ .416" The relative populations of the ground 7I""; levels may", The relative populations of the ground $^3\mathrm{P}^e_J$ levels may4171796À. and HD 988300.,"4796A, and HD 98800."418 TW Ηνα possesses a strong silicate emission band that is generally similar in streugth and shape to many other pre-1nalu seqence stars. such as the Herbig Ae/Be stars (HAEBEsx) aud T Tauri stars (TTs).," TW Hya possesses a strong silicate emission band that is generally similar in strength and shape to many other pre-main sequence stars, such as the Herbig Ae/Be stars (HAEBEs) and T Tauri stars (TTs)."419" However. the feature does not show the unambiguous presence of crystalline material. as evidenced by the 11.2 jun eature, as is observes in some HAEBEs aud i-— some long-period solar system comets."," However, the feature does not show the unambiguous presence of crystalline material, as evidenced by the 11.2 $\mu$ m feature, as is observes in some HAEBEs and in some long-period solar system comets."420 HR L796A has only a very weak excess emission above i0tosplieric levels. aud nothiug cau be said about utlie presetice of a siguificant silicate ad from. these cata.," HR 4796A has only a very weak excess emission above photospheric levels, and nothing can be said about the presence of a significant silicate band from these data."421 HD 98800 is intermediate between these two in terus of the streneth of its silicate baicl. i the data are inadequate to say anytliing about iltlie mineralogy or degree of crystallijty.," HD 98800 is intermediate between these two in terms of the strength of its silicate band, but the data are inadequate to say anything about the mineralogy or degree of crystallinity."422" For the object where we Iave tle best data. TW Hya. tie lack of obvious crystalli""ty ds d eulirely surprising. as it is absent iu all of the votugest pre-ilain sequence stars. aud ii uost b rot all of the older ones."," For the object where we have the best data, TW Hya, the lack of obvious crystallinity is not entirely surprising, as it is absent in all of the youngest pre-main sequence stars, and in most but not all of the older ones."423 It is preseut iu mauy of the long-pelod Comets of our own solar syste jowever. and our failure to detect it so far in a younger star of roughly solar mass is itriguil hough not unexpected.," It is present in many of the long-period comets of our own solar system, however, and our failure to detect it so far in a younger star of roughly solar mass is intriguing, though not unexpected."424 We are lar [rom uuderstaudiug how the crystalline material is »oducecd auc iucorporated iuto the grains of our own solar system and iu the disk systems of soije of the Ueher-tuass stars., We are far from understanding how the crystalline material is produced and incorporated into the grains of our own solar system and in the disk systems of some of the higher-mass stars.425 One of tlie vain obstacles preventing more definitive conclusions is the lack of hieequality uic-IR spectra of TTs., One of the main obstacles preventing more definitive conclusions is the lack of high-quality mid-IR spectra of TTs.426 Many cau ye reached. using grouud-based. instruments. but recure loi fin excess of an hour or two) integation times to achieve the necessary signal-to-noise.," Many can be reached using ground-based instruments, but require long (in excess of an hour or two) integration times to achieve the necessary signal-to-noise."427 A tru comprehensive study will require au instrument like he Space Infrared Telescope Facility (SIRTF)., A truly comprehensive study will require an instrument like the Space Infrared Telescope Facility (SIRTF).428 Support for this work was provied for ML5 throweh NASA's Origins of Solar Systems Progra erant NACOS-9175. aud the University Research Couicil aud Physics Department of the UniversiM7 of Cincinnai.," Support for this work was provided for MLS through NASA's Origins of Solar Systems Program grant NAG5-9475, and the University Research Council and Physics Department of the University of Cincinnati."429 Support for DIXL aiad RWR was p'ovided by the Tje. Aerospace Corporations Iudepeucdeut Research aud Developilent progun., Support for DKL and RWR was provided by the The Aerospace Corporation's Independent Research and Development program.430 We would like to hank Aun Mazuk. aud Ted Tessensolin or techuical support aie Bill Golisch atd Dave Ciriep oftie IRTF for expert telescope operation.," We would like to thank Ann Mazuk, and Ted Tessensohn for technical support and Bill Golisch and Dave Griep of the IRTF for expert telescope operation."431 The authors would also lise to thatk Robert Joseph for beiug flexible in the scheduli18oO ol the IRTF time for this project with our oher prograums., The authors would also like to thank Robert Joseph for being flexible in the scheduling of the IRTF time for this project with our other programs.432 We also thank Carol Gracy for |er comanents on the manuscript., We also thank Carol Grady for her comments on the manuscript.433 The IRAS broadband fIuxes were obtaiied via SIMBAD., The IRAS broadband fluxes were obtained via SIMBAD.434the main sequence.,the main sequence.435 However. the observational data show that ΠΟ 31282 is a highly variable TAcBe star with an active C'S cuviromment.," However, the observational data show that HD 34282 is a highly variable HAeBe star with an active CS environment."436 Coucerming WD 111569. though its disk shares simularities with some debris disk svstenis. which are found to be located below the main sequence. the star does show observational properties which sugecst an eulier evolutionary stage.," Concerning HD 141569, though its disk shares similarities with some debris disk systems, which are found to be located below the main sequence, the star does show observational properties which suggest an earlier evolutionary stage."437 In particular. our data show that he object retains a non-negligible CS activity. as evidenced by he |O i| emission and the variable Πα cluission.," In particular, our data show that the object retains a non-negligible CS activity, as evidenced by the [O ] emission and the variable $\alpha$ emission."438 Taking iuto account these considerations.4. both stars should be located above or ou he main πο1ος in better agreement with normal expectations from their photometric and spectroscopic properties and stellar evolution theory.," Taking into account these considerations, both stars should be located above or on the main sequence, in better agreement with normal expectations from their photometric and spectroscopic properties, and stellar evolution theory."439 In this section we carry out a detailed study of the plivsical paraicters of the stars leacing us to re-consider their location iu the IIR diagram., In this section we carry out a detailed study of the physical parameters of the stars leading us to re-consider their location in the HR diagram.440 The deteriunation of the effective teniperature. gravitv and stellar ποταμοί will allow us. by using the appropriate set of evolutionary tracks aud isochroucs. to estimate the luuimositv. mass and age of the stars. as well as their distances by mcans of the measured stellar fluxes.," The determination of the effective temperature, gravity and stellar metallicity will allow us, by using the appropriate set of evolutionary tracks and isochrones, to estimate the luminosity, mass and age of the stars, as well as their distances by means of the measured stellar fluxes."441 Ikuuez (1993) model atinospheres are used to estimate the phivsical paraüiueters describing the photospheres of TD 31252 and WD 111569., Kurucz (1993) model atmospheres are used to estimate the physical parameters describing the photospheres of HD 34282 and HD 141569.442 We use the following iterative procedure., We use the following iterative procedure.443 First. an initial value of the stellar eravity is obtained from the conrparison of svuthetic profiles. computed with solar metallicity. with the observed IL. IT and Πὸ profiles extracted from the CAFOS observations.," First, an initial value of the stellar gravity is obtained from the comparison of synthetic profiles, computed with solar metallicity, with the observed $\beta$ , $\gamma$ and $\delta$ profiles extracted from the CAFOS observations."444 For this purpose. a tentativo value of Tig. based ou the spectral type of cach star. is taken.," For this purpose, a tentative value of $T_{\rm eff}$, based on the spectral type of each star, is taken."445 The gravity is obtained * nieasuring the width of the observed Baliner profiles at one iunteusitv evel below the normalized coutiumua. uunelv 720.80: lis las been chosen to avoid potential artifacts in the wines near the continua arising from the rormalization of he original spectra.," The gravity is obtained by measuring the width of the observed Balmer profiles at one intensity level below the normalized continuum, namely $I\!=\!0.80$; this has been chosen to avoid potential artifacts in the wings near the continuum arising from the normalization of the original spectra."446 The widths of the Balmer lines are hen compared with those measured on a grid of svuthetic profiles computed for differentjes.., The widths of the Balmer lines are then compared with those measured on a grid of synthetic profiles computed for different.447 A linear interpolation is doue taking the widths of cach Balmer line as incepeudent variables aud the exavitv as the uuknown., A linear interpolation is done taking the widths of each Balmer line as independent variables and the gravity as the unknown.448 The result for loggy. is the mean value of i] the interpolations with iu uncertainty correspouding to the παπαατα deviation., The result for $\log g_*$ is the mean value of all the interpolations with an uncertainty corresponding to the standard deviation.449 With this value of logg fixed. we re-estiuate the efectivo temperatures of the stars and their uctallicitics.," With this value of $\log g_*$ fixed, we re-estimate the efective temperatures of the stars and their metallicities."450 This is done bv meaus of a systematic comparison of svuthetic line profiles. obtained using νο models of different temperatures aud metallicities. with the high resolution. WIIT/UES spectra.," This is done by means of a systematic comparison of synthetic line profiles, obtained using Kurucz's models of different temperatures and metallicities, with the high resolution WHT/UES spectra."451" The regious of effective teiiperatures from 8500 to 9750 Is for ΠΟ 312852. and from, 9750. to 10500 I for TD 11569 were explored. which approximately encompass the values correspondiug to the spectral types reported for both stars."," The regions of effective temperatures from 8500 to 9750 K for HD 34282, and from 9750 to 10500 K for HD 141569 were explored, which approximately encompass the values corresponding to the spectral types reported for both stars."452 For each temperature. different moetallicities were used to svuthesize spectral lines in several selected spectral intervals.," For each temperature, different metallicities were used to synthesize spectral lines in several selected spectral intervals."453 The svuthetic spectra were rotationally broadened with the correspouding cesi; values for each star (Mora ct al., The synthetic spectra were rotationally broadened with the corresponding $v\sin i$ values for each star (Mora et al.454 2001)., 2001).455 A iuicroturbuleuce velocity of 2 lins was used throughout., A microturbulence velocity of 2 km/s was used throughout.456 For ΠΟ 31252 the lines chosen are: [101.75.. 1957.60 (Fe 1). 1508.29. 1515.31. 1583.51. 1629.31 (Fe 11) aud 1501.27 (Ti).," For HD 34282 the lines chosen are: 4404.75, 4957.60 (Fe ), 4508.29, 4515.34, 4583.84, 4629.34 (Fe ) and 4501.27 (Ti )."457 For ΠΟ 111569 the projected rotational velocity is so high that it is difficult to fud. iudividual metallic lines: instead the regions 12601280À.. 13751100. and 15101560.À.. which contain a large ΠΟ of lines. have been selected.," For HD 141569 the projected rotational velocity is so high that it is difficult to find individual metallic lines; instead the regions 4260–4280, 4375--4400 and 4540–4560, which contain a large number of lines, have been selected."458 For both stars the lines 3033.66 (Ca I). EIST.I3 ACMg 1D. and the Si doublet at 6317.11... 6371.27. have also been used (the Si doublet is clearly observed in the ENT spectra).," For both stars the lines 3933.66 (Ca ), 4481.13 (Mg ), and the Si doublet at 6347.11, 6371.37 have also been used (the Si doublet is clearly observed in the INT spectra)."459 It is found. particularly in the case of ΠΟ 31282. that dciffereut (Tig. [Fe/TI]) pairs fit the observed spectra reasonably well.," It is found, particularly in the case of HD 34282, that different $T_{\rm eff}$, [Fe/H]) pairs fit the observed spectra reasonably well."460 The comparison shows that higher effective temperatures require higher inetallieities to ft a eiven spectral line., The comparison shows that higher effective temperatures require higher metallicities to fit a given spectral line.461 This (Tig. |Fo/H]) degeneracy can be solved * usns the observed SEDs. in particular theVARI photometry.," This $T_{\rm eff}$, [Fe/H]) degeneracy can be solved by using the observed SEDs, in particular the photometry."462 For cach (Tag. [Fe/TI]) pair. which providesan apparent satisfactory fit to the observed spectra. we have," For each $T_{\rm eff}$, [Fe/H]) pair, which providesan apparent satisfactory fit to the observed spectra, we have"463"equipartion between magnetic fields and relativistic electrons. these authors showed that the radio light curves could be explained by a svnchrotron sell-absorption model. where the radio emitting material expands al ~0.3 ο, While the fits to the lieht curves were satisfactory. there are some issues left open bx the model.","equipartion between magnetic fields and relativistic electrons, these authors showed that the radio light curves could be explained by a synchrotron self-absorption model, where the radio emitting material expands at $\sim 0.3$ c. While the fits to the light curves were satisfactory, there are some issues left open by the model."464 In particular. the implied optical (hin svunchrotron spectrum is considerably flatter than the observed one.," In particular, the implied optical thin synchrotron spectrum is considerably flatter than the observed one."465 The steeper than expected spectrum could be due (ο svnchrotron cooling., The steeper than expected spectrum could be due to synchrotron cooling.466 If 50. a magnetic field strength nuch in excess of equipartion is required.," If so, a magnetic field strength much in excess of equipartion is required."467 In parallel to (his. there has been several papers discussing NMM observations of SN 2002ap (Sori&&Ixong2002:SutarinChandra.Bhatnagar.Παν2003:Soria.Alazzali 2004).," In parallel to this, there has been several papers discussing XMM observations of SN 2002ap \citep{SK02,SCB03,SPM03}."468. These authors have interpreted (he N-rav emission as coming [rom the thermal electrons behind the shock either directly as [ree-free emission or as inverse Compton scattering of the photospheric SN photons., These authors have interpreted the X-ray emission as coming from the thermal electrons behind the shock either directly as free-free emission or as inverse Compton scattering of the photospheric SN photons.469 For such models to work. the shock velocity has to be fairly low (~10.000—20.000kins| at day 6).," For such models to work, the shock velocity has to be fairly low $\sim 10,000-20,000\kms$ at day 6)."470 As we argue in this paper. there is evience [rom optical line profiles that velociües higher (han this are needed.," As we argue in this paper, there is evience from optical line profiles that velocities higher than this are needed."471 Furthermore. a low shock velocity implies a small size of the radio emission region and. hence. a hieh brightness temperature.," Furthermore, a low shock velocity implies a small size of the radio emission region and, hence, a high brightness temperature."472 In this paper we show that a consistent picture of both the radio ancl X-ray observations can be obtained by a model where inverse Compton cooling of the relativistic electrons by the photospheric photons is important., In this paper we show that a consistent picture of both the radio and X-ray observations can be obtained by a model where inverse Compton cooling of the relativistic electrons by the photospheric photons is important.473 This explains both (he steep radio spectrum. aud ihe X-rav enussion as coming from (he same region. expanding al a velocity. compatible with both optical aud radio observations.," This explains both the steep radio spectrum, and the X-ray emission as coming from the same region, expanding at a velocity compatible with both optical and radio observations."474 The inclusion of the X-ray. constraint also allows a determination of the ratio between the energy deusities in magnetic fields and relativistic electrons., The inclusion of the X-ray constraint also allows a determination of the ratio between the energy densities in magnetic fields and relativistic electrons.475 The paper is organized as follows., The paper is organized as follows.476 In §2 we discuss the constraints on derent cooling processes of (he relativistic electrons. using simple analytical arguments.," In \ref{sec_2} we discuss the constraints on different cooling processes of the relativistic electrons, using simple analytical arguments."477 In 32- we illustrate (his by a detailed model calculation of the observed light curves and radio and X-ray spectra., In \ref{sec_3} we illustrate this by a detailed model calculation of the observed light curves and radio and X-ray spectra.478 The implications of this and a comparison with related papers are given in 84.., The implications of this and a comparison with related papers are given in \ref{sec_disc}.479 In 5 we summarize our conclusions., In \ref{sec_concl} we summarize our conclusions.480 We will in the following use a distance of Dzz7.3 Ape lor M 74 (Sharina.IXarachentsev.&Tikhonov 1996).., We will in the following use a distance of $D\approx 7.3$ Mpc for M 74 \citep{SKT96}. .481" An approximate expression for the optically thin svnehrotron Iuminositv. L,. emitted al a [frequency v trombehind a spherically svmuuetric. non-relativistic shock with velocity"," An approximate expression for the optically thin synchrotron luminosity, $L_{\nu}$, emitted at a frequency $\nu$ frombehind a spherically symmetric, non-relativistic shock with velocity"482lowmass stars with atimosphneric opacities dominated by molecular absorption. we have e2:1 aud bz:0.,"low–mass stars with atmospheric opacities dominated by molecular absorption, we have $a \approx 1$ and $b \approx 0$."483 Therefore We cau now use (1)) together with (9)) iu (7)) and obtain We note that in deriving (10)) we lave applied in (73) the factor Dx ouly to the R dependence comune from the huuinosity Lo., Therefore We can now use \ref{tr1}) ) together with \ref{tr9}) ) in \ref{tr7}) ) and obtain We note that in deriving \ref{tr10}) ) we have applied in \ref{tr7}) ) the factor $D_{\rm N}$ only to the $R$ –dependence coming from the luminosity $L_2$.484 Iudeed. the Ro in the denominator of (7)) conies from the eravitational binding euergv of the star which is related via the Virial theorem to its thermal cnerev. io. essentially to its central temperature.," Indeed, the $R_2$ in the denominator of \ref{tr7}) ) comes from the gravitational binding energy of the star which is related via the Virial theorem to its thermal energy, i.e. essentially to its central temperature."485 Since the central regions of the star are expected to be hardly affected by the distortion of the outer lavers (cf., Since the central regions of the star are expected to be hardly affected by the distortion of the outer layers (cf.486 Fig., Fig.487 3). it is not appropriate to also propagate he factor Dx to the remaining factor Ro.," 3), it is not appropriate to also propagate the factor $D_{\rm N}$ to the remaining factor $R_2$."488 Let us row exanine the conditions at the period Pg., Let us now examine the conditions at the period $P_{\rm turn}$.489 For a polvtope of index NV losing mass the effective mass radius expoucut can be written as (e.g. Ritter 1996) where is the adiabatic mass radius expouent and is the mass loss time scale., For a polytope of index $N$ losing mass the effective mass radius exponent can be written as (e.g. Ritter 1996) where is the adiabatic mass radius exponent and is the mass loss time scale.490 Because at P=Pha the donor star is characterized by N=3/2 aud Gap=|1/3 we obtain from (11)) and (12)) at fuuP=Payy. or With D3;521.06 (cf.," Because at $P = P_{\rm turn}$ the donor star is characterized by $N=3/2$ and $\zeta_{\rm eff}=+1/3$ we obtain from \ref{tr11}) ) and \ref{tr12}) ) at $P=P_{\rm turn}$, or With $D_{3/2} \approx 1.06$ (cf."491 Table 1) (15)) vields Eq. (16)), Table 1) \ref{tr15}) ) yields Eq. \ref{tr16}) )492 meaus that the 3Deffects. Le. he reduces lass loss rate and the lucreased surface huninositv of the more distended sta. result in a smaller deviation from thermal equilibrimu at 7—P.," means that the 3D–effects, i.e. the reduced mass loss rate and the increased surface luminosity of the more distended star, result in a smaller deviation from thermal equilibrium at $P=P_{\rm turn}$."493 Tence he star is systematically less inflated bv the effects of tlierma disequilibriuni. and this. in turn. compensates at least partially for the systematic increase of the orbita perio due to the factor Ds.>1.," Hence the star is systematically less inflated by the effects of thermal disequilibrium, and this, in turn, compensates at least partially for the systematic increase of the orbital period due to the factor $D_{3/2} > 1$."494 A quantitative estimate of the decrease of 444 sugeested from (16)) can be derived by recomputine the evolutionary sequences including the effect of distortion. as done in 83.1. aud by artificially increasing the racliating surface of the donor in the StefanBoltzmann law by a factor Da3ye as sugeested from (10).," A quantitative estimate of the decrease of $\pturn$ suggested from \ref{tr16}) ) can be derived by recomputing the evolutionary sequences including the effect of distortion, as done in 3.1, and by artificially increasing the radiating surface of the donor in the Stefan–Boltzmann law by a factor ${D_{3/2}}^{2.8}$, as suggested from (10)."495 Note that this ix equivalent to increase the radiating surface bv a actor DyD alu to reducing the surface eravitv in he iutegration of the stellar atimnosphere by the same actor.," Note that this is equivalent to increasing the radiating surface by a factor ${D_{3/2}}^2$, and to reducing the surface gravity in the integration of the stellar atmosphere by the same factor."496 The result of such a nmuuerical experiuent is displaved in Fig., The result of such a numerical experiment is displayed in Fig.497 { (dash-dotted lue) and shows a slight decrease of Paya by ~ compared to the case with mre geonmetrical effects (dashed lie)., 4 (dash-dotted line) and shows a slight decrease of $P_{\rm turn}$ by $\sim$ compared to the case with pure geometrical effects (dashed line).498" These results fully confirm the expectation derived frou (16). namely that he value of Z4, is reduced by taking iuto account the effects of the changed thermal relaxation."," These results fully confirm the expectation derived from (16), namely that the value of $P_{\rm turn}$ is reduced by taking into account the effects of the changed thermal relaxation."499 Although reducing the discrepancy between observed and predicted miniuuni period. distortion effects seen insufficient to provide a satisfactory solution of the jetween calculated anc observed. minimuuui period.," Although reducing the discrepancy between observed and predicted minimum period, distortion effects seem insufficient to provide a satisfactory solution of the mismatch between calculated and observed minimum period."500 A combination of distortion effects as estimated in 82 and au augular momentum loss rate of 2.2.5 Fon ui reconcile P4 with the ohserved SO mun value (see otted line in Fie. 1))., A combination of distortion effects as estimated in 2 and an angular momentum loss rate of 2–2.5 $\times \dot J_{\rm GR}$ can reconcile $P_{\rm turn}$ with the observed 80 min value (see dotted line in Fig. \ref{fig4}) ).501 Note that without distortion fects. one would need 1 Jan to reach ~SO mun. as sstimated i Rolb Baratte (1999).," Note that without distortion effects, one would need 4 $\times \dot J_{\rm GR}$ to reach $\sim 80$ min, as estimated in Kolb Baraffe (1999)."502 The amore modes oeacrease of 4 required according to our calculatious is also in better agreement with Patterson's (1998) estimate based on space density considerations., The more modest increase of $\dot J$ required according to our calculations is also in better agreement with Patterson's (1998) estimate based on space density considerations.503 Additional plivsica processes can also result iu an inflation of the secondary. e.g. inradiatiou from the primary (Ritter et al.," Additional physical processes can also result in an inflation of the secondary, e.g. irradiation from the primary (Ritter et al."504 2000) or star spots (Sprui Ritter 1983)., 2000) or star spots (Spruit Ritter 1983).505 A rough estimate of radiation effects or star spots cau be derived by following Ritter et al. (, A rough estimate of irradiation effects or star spots can be derived by following Ritter et al. (506"2000). ie. by reducing the eective radiating surface of the star bv a factor (1s, )","2000), i.e. by reducing the effective radiating surface of the star by a factor $(1-s_{\rm eff}$ )."507 Adopting in our secular evolution calculation a factor sog=1/21 aud Jadqi vields a sequence very similar to the one obtained with deformation (dashed line in Fie. 1))., Adopting in our secular evolution calculation a factor $s_{\rm eff} = 1/2$ and $\dot J =\dot J_{\rm GR}$ yields a sequence very similar to the one obtained with deformation (dashed line in Fig. \ref{fig4}) ).508 I£ 54g=23 the result rescnibles the sequence with deformation and 2.5«Jo (dotted line in Fie. 10)., If $s_{\rm eff} = 2/3$ the result resembles the sequence with deformation and $\dot J = 2.5 \times \dot J_{\rm GR}$ (dotted line in Fig. \ref{fig4}) ).509 Iu order to know whetler such values of sog. Vvielding effects comparable o the distortion effects. are reasonable requires a sophisticatcc treatinent of star spots or irradiation.," In order to know whether such values of $s_{\rm eff}$, yielding effects comparable to the distortion effects, are reasonable requires a sophisticated treatment of star spots or irradiation."510 Au investigation of radiation effects on uou-eray stellar atmospheres is iu progress (Baran 2001)., An investigation of irradiation effects on non-gray stellar atmospheres is in progress (Barman 2001).511 We stress however that even if distortion. irradiation. star spots or additional sources of J are possible solutious for removing the nisuateli between observed aud predicted uini period. the so-calle period spike problem still remains.," We stress however that even if distortion, irradiation, star spots or additional sources of $\dot J$ are possible solutions for removing the mismatch between observed and predicted minimum period, the so-called period spike problem still remains."512 A xoriod. spike which is a consequence of the accumulation of svstenis rear Pan Gvhere P= 0) is iudeed predicted by all models for which J or sag are assed to be the same for all svsteiis.," A period spike which is a consequence of the accumulation of systems near $P_{\rm turn}$ (where $\dot P = 0$ ) is indeed predicted by all models for which $\dot J$ or $s_{\rm513eff}$ are assumed to be the same for all systems."514" Even if they are not. it is very difficult to “sincar out the period spike iu a population of svsteimis with differeut individual bounce periods (Barker Ίος, in preparation)."," Even if they are not, it is very difficult to “smear out” the period spike in a population of systems with different individual bounce periods (Barker Kolb, in preparation)."515 Such a period spike is. however. not observe (sco I&olb Baratte 1999).," Such a period spike is, however, not observed (see Kolb Baraffe 1999)."516 Finally. we note that Ixolb Daraffe (1999) obtained ucelieible effects on the secoudary structure aud evolution when applvius tidal aud rotational correctious to the 1D," Finally, we note that Kolb Baraffe (1999) obtained negligible effects on the secondary structure and evolution when applying tidal and rotational corrections to the 1D"5172004).,.518. Furthermore. NGC 2808 also has a peculiar main sequence where the bluer stars are inferred to have Y~0.4 from fitting theoretical isochrones to the observed data.," Furthermore, NGC 2808 also has a peculiar main sequence \citep{dantona05} where the bluer stars are inferred to have $Y \sim 0.4$ from fitting theoretical isochrones to the observed data."519 To reproduce the CMD. D'Antonaetal.(2005) note the absolute necessitv of including a small population (e20%)) of stus with Y=0.40 and assume a spread of Y between 0.24 0.29 to fit the main fraction (e80%)).," To reproduce the CMD, \citet{dantona05} note the absolute necessity of including a small population $\sim 20$ ) of stars with $Y = 0.40$ and assume a spread of $Y$ between 0.24 – 0.29 to fit the main fraction $\sim 80$ )."520 While the exact maximum value ofY required to reproduce the CMD is dependent on (he color-T;g (transformations used in the analvsis and therefore rather uncertain. il seems (hat the most plausible explanation is that the bluest stars have enhanced amounts of helium with Y=0.35.," While the exact maximum value of $Y$ required to reproduce the CMD is dependent on the $T_{\rm eff}$ transformations used in the analysis and therefore rather uncertain, it seems that the most plausible explanation is that the bluest stars have enhanced amounts of helium with $Y \gtrsim 0.35$."521 Observations by Piottoetal.(2005). show that the blue main-sequence of w Centauri is more metal-rich than the red sequence. contrary (ο what is expected [rom stellar models and showed that isochrones with Y=0.40 best fit the bluest stars.," Observations by \citet{piotto05} show that the blue main-sequence of $\omega$ Centauri is more metal-rich than the red sequence, contrary to what is expected from stellar models and \citet{norris04} showed that isochrones with $Y=0.40$ best fit the bluest stars."522 Until a better explanation for these intriguing observations is found. we take them as motivation to study the ACB sell-pollution scenario [rom a global perspective.," Until a better explanation for these intriguing observations is found, we take them as motivation to study the AGB self-pollution scenario from a global perspective."523 In this paper. we use the Fenneretal.(2004) GC chemical evolution model to follow ihe evolution of helium in the intracluster gas.," In this paper, we use the \citet{fenner04} GC chemical evolution model to follow the evolution of helium in the intracluster gas."524 We probe AGB model uncertainties by using (wo independent sets of vields. including those used in (he previous study which were tailor made for NGC 6752 (with a metallicity [Fe/II] zz—1.42)).," We probe AGB model uncertainties by using two independent sets of yields, including those used in the previous study which were tailor made for NGC 6752 (with a metallicity [Fe/H] $\approx -1.4$ )."525 The evolution of C. N and O is also followed since they. impose important empirical constraints. ie. C4-N2-O % constant. that must be met by the mocel.," The evolution of C, N and O is also followed since they impose important empirical constraints, i.e. $+$ $+$ O $\approx$ constant, that must be met by the model."526 Prior to the AGB both the first and second diredge-up (SDL) mix helium to the surface [rom regions that have undergone some I burning., Prior to the AGB both the first and second dredge-up (SDU) mix helium to the surface from regions that have undergone some H burning.527 During the thermallv-pulsing-AGD phase. partial He-burning results in an abundance ofY~0.75 in the intershell region. and each third dredge-up (TDU) episode increases the tHe abundance of the envelope.," During the thermally-pulsing-AGB phase, partial He-burning results in an abundance of $Y \sim 0.75$ in the intershell region, and each third dredge-up (TDU) episode increases the He abundance of the envelope."528 Hot bottom burning (11121) also produces ‘lle via the CNO evele., Hot bottom burning (HBB) also produces He via the CNO cycle.529 For massive AGB stars the most important mixing phase is the SDU which results in an increase of AY<0.1., For massive AGB stars the most important mixing phase is the SDU which results in an increase of $\Delta Y \lesssim 0.1$.530 The first. dredge-up is inefficient in low-Z stars over 3M. (see Fig., The first dredge-up is inefficient in $Z$ stars over $\Msun$ (see Fig.531 2 in Boothrovd&Sackmann (1999))). and efficient TDU and IIDD result in small increases of at most AY22 0.03. depending on the {ime spent on the AGB and the temperature al the base of the convective envelope.," 2 in \citet{boothroyd99}) ), and efficient TDU and HBB result in small increases of at most $\Delta Y \approx 0.03$ , depending on the time spent on the AGB and the temperature at the base of the convective envelope."532 The helium vields from the AGB models with Z=0.0017 used by are shown in Table 20 as theaverage mass fraction of Y in the winds and the total mass," The helium yields from the AGB models with $Z=0.0017$ used by \citet{fenner04}533 are shown in Table \ref{table1} as theaverage mass fraction of $Y$ in the winds and the total mass"534low latitude field compared to the high latitude field.,low latitude field compared to the high latitude field.535 We have found a methane cdwart from the first night of observations for the I£A-Deep Survey., We have found a methane dwarf from the first night of observations for the IfA-Deep Survey.536 The object las very red optical colors aud relatively blue near-IR colors., The object has very red optical colors and relatively blue near-IR colors.537 Its IH-baud spectiui shows stroug aux modest aabsorptiou., Its $H$ -band spectrum shows strong and modest absorption.538 The iuferred spectral type is T3TL, The inferred spectral type is T3–T4.539 The majority of T chwarts known to date have very. deep aabsorptiou. so TA 0500-21 is au interesting object iu that it lies im a transition region of spectral type (aud hence Tig). where methane is beginuiug to dominate the SED.," The majority of T dwarfs known to date have very deep absorption, so IfA 0230-Z1 is an interesting object in that it lies in a transition region of spectral type (and hence ), where methane is beginning to dominate the SED."540 The colors of carly T-type objects. like IA 0230-Z1. make them difücult to ideutifv in pure near-IR survevs such as 2MÁSS but they are easily distinguished in our deep optical/fu-red. survey.," The colors of early T-type objects, like IfA 0230-Z1, make them difficult to identify in pure near-IR surveys such as 2MASS but they are easily distinguished in our deep optical/far-red survey."541 Such objects are useful to uuderstand the plivsies of ultracool atinosplieres., Such objects are useful to understand the physics of ultracool atmospheres.542 Slightly warler objects. the late L-dwarfs. have extremely red near-IR colors. which have been interpreted as being due to the role of dust.," Slightly warmer objects, the late L-dwarfs, have extremely red near-IR colors, which have been interpreted as being due to the role of dust."543 Towever. the very blue near-IR colors of T dwarfs are consistent with “clear”.ic... dust-frec. atmospheres (e.Tsuji2001)..," However, the very blue near-IR colors of T dwarfs are consistent with “clear”, dust-free, atmospheres \citep[e.g.][]{2001udns.conf....9T}."544 With its high sensitivity in the far-red bands. the TfA-Deep survey will be an excellent means fo search for brown dwarfs.," With its high sensitivity in the far-red bands, the IfA-Deep survey will be an excellent means to search for brown dwarfs."545 Preliminary estimates based on the T dwarf discoveries by SDSS sugeests the IfA survey will fiud a comparable nuuber of T dwarfs as the 2\LASS survey. albeit at aiuuch larger average distance.," Preliminary estimates based on the T dwarf discoveries by SDSS suggests the IfA survey will find a comparable number of T dwarfs as the 2MASS survey, albeit at a much larger average distance."546 The fal survey will go 2100 times fainter than SDSS. raising the possibility of finding isolated brown clwarts much cooler than those found to date.," The final survey will go $\gtrsim$ 100 times fainter than SDSS, raising the possibility of finding isolated brown dwarfs much cooler than those found to date."547 Furthermore. the survey will be sensitive to T cwarfs out to ~300 pc aud L dwarfs out to ~2 kpe alone several lines of sight. at galactic latitudes ranging from |b|z20—GO.," Furthermore, the survey will be sensitive to T dwarfs out to $\sim$ 300 pc and L dwarfs out to $\sim2$ kpc along several lines of sight, at galactic latitudes ranging from $|b|\approx20-60\degs$."548 This raises the possibility of providing the first iusights iuto the vertical scale height of ultracool chvarfs. thereby telling us about their origin iu a ealactic context.," This raises the possibility of providing the first insights into the vertical scale height of ultracool dwarfs, thereby telling us about their origin in a galactic context."549" The authors wish to extend special thauks to those of Hawaiian ancestry ou whose sacred mountain we are privileged to be guests,", The authors wish to extend special thanks to those of Hawaiian ancestry on whose sacred mountain we are privileged to be guests.550 Without their generous hospitality. none of the observatious presented herein would have been possible.," Without their generous hospitality, none of the observations presented herein would have been possible."551 It is a pleasure to acknowlege our collaborators ou the HA-Deep Survev: Herve Aussel Ken Chambers. Pat Παιν Nick Ixaiser. Eugene Maguier. Dave Sauders. and Alan Stockton.," It is a pleasure to acknowlege our collaborators on the IfA-Deep Survey: Herve Aussel, Ken Chambers, Pat Henry, Nick Kaiser, Eugene Magnier, Dave Sanders, and Alan Stockton."552 We are grateful for the support from the stats of the Subaru Telescope. IRTE. aud Keck Observatory. including Yutaka Komivama. Byusuke Oveasawara. Paul Ilirsli. John Ravuer. David Spravbers. and Cary Puniwai.," We are grateful for the support from the staffs of the Subaru Telescope, IRTF, and Keck Observatory, including Yutaka Komiyama, Ryusuke Ogasawara, Paul Hirsh, John Rayner, David Sprayberry, and Gary Puniwai."553 We thank Pete Challis. Alan Tokunaga and Jonathan Leong for help with the Subaru aud Iseck observations: Sunesoo Wim. Lisa Prato. aud Tau MeLean for providing the REDSPEC reduction software and doctuuentation: auc AMamori Doi for SDSS. filter data.," We thank Pete Challis, Alan Tokunaga and Jonathan Leong for help with the Subaru and Keck observations; Sungsoo Kim, Lisa Prato, and Ian McLean for providing the REDSPEC reduction software and documentation; and Mamori Doi for SDSS filter data."554 The Subaru Telescope is operated bv the National Astronomical Observatory of Japan., The Subaru Telescope is operated by the National Astronomical Observatory of Japan.555 The IRTF is operated by the University ο Πανα wider a coutract from National Acronauties and Space Adiministration (NASA)., The IRTF is operated by the University of Hawaii under a contract from National Aeronautics and Space Administration (NASA).556 W.M. Keck Observatory was iade possible by the generous financial support of the WAL neck Foundation aud is operated by Caltech. the University of Califormia. and NASA.," W.M. Keck Observatory was made possible by the generous financial support of the W.M. Keck Foundation and is operated by Caltech, the University of California, and NASA."557 NL. Liu is evateful for rescarch support from the Beatrice Watson Parrent Fellowship at the University of Hawai'i., M. Liu is grateful for research support from the Beatrice Watson Parrent Fellowship at the University of Hawai`i.558in order to confirm (or refute) our findings.,in order to confirm (or refute) our findings.559 Of particular interest will be the issue of what happens when gap opening allows disk material in the vicinity of the planet to become magnetically active., Of particular interest will be the issue of what happens when gap opening allows disk material in the vicinity of the planet to become magnetically active.560 We will address this issue in a future paper., We will address this issue in a future paper.561"(“hh”) for the auto-correlation function of the DG (MH) spectrum, or “hg” for the cross-correlation between the MH and DG spectra.","(“hh”) for the auto-correlation function of the DG (MH) spectrum, or “hg” for the cross-correlation between the MH and DG spectra."562 We plot these correlation functions with solid curves in Fig.2.., We plot these correlation functions with solid curves in \ref{Fig.correlation}.563" From the auto-correlation function of the DG-spectrum, we see little correlation on frequency separations larger than 10kHz, while little correlation on frequency separations larger than 1kHz is seen in the MH-spectrum."," From the auto-correlation function of the DG-spectrum, we see little correlation on frequency separations larger than $10\kHz$, while little correlation on frequency separations larger than $1\kHz$ is seen in the MH-spectrum."564 This is what we could expect for a randomly generated spectrum with only the halo mass function., This is what we could expect for a randomly generated spectrum with only the halo mass function.565 The correlation seen on smaller frequency separations just comes from the point pairs located within the same lines., The correlation seen on smaller frequency separations just comes from the point pairs located within the same lines.566" The DGs have a longer correlation length because of their broader absorption lines or leaks, but the amplitude of the correlation is very low because they are rare."," The DGs have a longer correlation length because of their broader absorption lines or leaks, but the amplitude of the correlation is very low because they are rare."567" In order to illustrate the contribution of those dwarfs with negative absorption, we calculated the auto-correlation function of the DG-spectrum with leaks excluded; the result is shown as the dashed curve in the upper panel of Fig.2.."," In order to illustrate the contribution of those dwarfs with negative absorption, we calculated the auto-correlation function of the DG-spectrum with leaks excluded; the result is shown as the dashed curve in the upper panel of \ref{Fig.correlation}."568" The correlation amplitude is smaller due to the reduced number of signals, and the correlation length is reduced by more than one order of magnitude."," The correlation amplitude is smaller due to the reduced number of signals, and the correlation length is reduced by more than one order of magnitude."569 This shows that the broad signals are caused primarily by those leaks., This shows that the broad signals are caused primarily by those leaks.570" In addition, comparing this dashed curve with the solid curve in the bottom panel, we find that on average, an absorption line of a DG is even narrower than that of a MH."," In addition, comparing this dashed curve with the solid curve in the bottom panel, we find that on average, an absorption line of a DG is even narrower than that of a MH."571" This is because some of these DGs produce HII regions larger than ry;,, and the absorption lines from the gas outside the virial radii but inside the HII region, which has the largest infalling velocities, are erased."," This is because some of these DGs produce HII regions larger than $r_{\rm572vir}$, and the absorption lines from the gas outside the virial radii but inside the HII region, which has the largest infalling velocities, are erased."573 The cross-correlation function between the MHs and DGs can also be obtained in the same way., The cross-correlation function between the MHs and DGs can also be obtained in the same way.574" In this work we have not considered the clustering property of the MHs and DGs arising from large scale structure, so the flux cross-correlation should be zero, except for the Poisson fluctuations."," In this work we have not considered the clustering property of the MHs and DGs arising from large scale structure, so the flux cross-correlation should be zero, except for the Poisson fluctuations."575 Our computation confirms this expectation., Our computation confirms this expectation.576" Directly from the spectrum, we could compute the distribution of equivalent width (EW) of the absorption lines for a specific range of observed frequency corresponding to a specific redshift."," Directly from the spectrum, we could compute the distribution of equivalent width (EW) of the absorption lines for a specific range of observed frequency corresponding to a specific redshift."577 As, As578We start from the spatially uniform model. which estimates the total Lux of gamma-rays ancl radio emission (i.c. integrated over the volume of emission).,"We start from the spatially uniform model, which estimates the total flux of gamma-rays and radio emission (i.e. integrated over the volume of emission)."579 The evolution of positron spectrum can be described by the equation where dE/dé is the rate of svnchrotron losses (see Eq. CO)., The evolution of positron spectrum can be described by the equation where $dE/dt$ is the rate of synchrotron losses (see Eq. \ref{loss}) )).580" In case of instantaneous injection (QE.1)Μο, where No(ie) is the injection spectrum: of positron. the solution of this equation is where and d£di is the rate of svnehrotron or Coulomb losses."," In case of instantaneous injection $Q(E,t) =581N_0(E)\delta(t)$ where $N_0(E)$ is the injection spectrum of positron, the solution of this equation is where and $dE/dt$ is the rate of synchrotron or Coulomb losses."582 In the high energy range. where the svnchrotron losses are essential. the spectrum is We see that independent of the injection spectrum the maximum energy of positrons long after the injection is where / is time after the injection.," In the high energy range, where the synchrotron losses are essential, the spectrum is We see that independent of the injection spectrum the maximum energy of positrons long after the injection is where $t$ is time after the injection."583 If the positrons are secondary. then their. injection spectrum has a cut-olf in the low energy range at ZZ230 MeV. because of the threshold of pp reaction. ancl the energy distribution of positrons leaving the region of strong magnetic fields looks like a succession of separated bunches (sce Fig.4)).," If the positrons are secondary, then their injection spectrum has a cut-off in the low energy range at $E_{\rm cut} \simeq 30$ MeV because of the threshold of $p-p$ reaction, and the energy distribution of positrons leaving the region of strong magnetic fields looks like a succession of separated bunches (see \ref{bunch}) )."584 Here and below we take the injection spectrum of secondary. positrons in the form. where ο25.4-1077. MeV? gives the total number of injected positrons ~3107. where the spectral index equals Bas in the Galactic disk (seeBerezinskiietal.1990).," Here and below we take the injection spectrum of secondary positrons in the form where $A_b\simeq 5.4\cdot 10^{58}$ $^2$ gives the total number of injected positrons $\sim 3\cdot 10^{55}$, where the spectral index equals $-3$ as in the Galactic disk \citep[see][]{ber90}."585". The bunch width is The time duration of the bunch. (characteristic time during which the bunch. crosses any energv ££ under the influence of svnchrotron losses) is independent of £ and for the spectrum (21)) equals that gives Z5=3.6-l0tve for 45,=30 MeV. and 141=3 mG. Subsequent bunches are separated. Lrom each other by the periods of 2;~10° vr. the average periods of star capture."," The bunch width is The time duration of the bunch (characteristic time during which the bunch crosses any energy $E$ under the influence of synchrotron losses) is independent of $E$ and for the spectrum \ref{spectrum}) ) equals that gives $T_b=3.6\cdot 10^4$ yr for $E_{cut}=30$ MeV and $H=3$ mG. Subsequent bunches are separated from each other by the periods of $T_i\sim 10^5$ yr, the average periods of star capture."586 After the capture time equaled LO? vr the maximun energy of positrons in the bunch shifts [rom x to ££—10 AMeN (see Eq. (20)).," After the capture time equaled $10^5$ yr the maximum energy of positrons in the bunch shifts from $\infty$ to $E\simeq 10$ MeV (see Eq. \ref{max}) ),"587 and there are no positrons in the energy range Lo>10 MeV. while the energy range below LO MeV contains permanently a number of bunches moving to the thermal region (see Fie. 4))., and there are no positrons in the energy range $E> 10$ MeV while the energy range below 10 MeV contains permanently a number of bunches moving to the thermal region (see Fig. \ref{bunch}) ).588 Then we conclude that. the spectrum of positrons in the range above 10 MeV is strongly non-stationary (shown by the dashed line in Fig. 4)).," Then we conclude that the spectrum of positrons in the range above 10 MeV is strongly non-stationary (shown by the dashed line in Fig. \ref{bunch}) ),"589 as well as the emission. generated. by these particles., as well as the emission generated by these particles.590 In. contrary. the spectrum of positrons with energies =10 MeV (shown by the solid lines in Fig. 4))," In contrary, the spectrum of positrons with energies $\la 10$ MeV (shown by the solid lines in Fig. \ref{bunch}) )"591 and the radiation produced by these positrons is quasi-stationary., and the radiation produced by these positrons is quasi-stationary.592 When the rate of svnchrotron losses crops down with positron energy. the following evolution of positrons in the range [7«1 MeV occurs under the inlluence of Coulomb losses.," When the rate of synchrotron losses drops down with positron energy, the following evolution of positrons in the range $E<1$ MeV occurs under the influence of Coulomb losses."593 The rate of Coulomb losses is (Ilavakawa1964:Cinzburg1989) where logA is Coulomb logarithm. and 3(42)=vc.," The rate of Coulomb losses is \citep{haya, ginz}594 where $\log \Lambda$ is Coulomb logarithm, and $\beta(E)=v/c$."595 For lorenz-Lactor =| Lin a neutral mediunr while in completely ionized plasma Relativistic positrons with energies higher than 10. MeV e&onerate radio emission due to svnchrotron losses ane IHuxes of in-Hight annihilation and bremsstrahlung emission in the energy range above 10 MeV. From Eqs. (143). (16))," For lorenz-factor $\gamma = \frac{E}{mc^2}+1$ in a neutral medium while in completely ionized plasma Relativistic positrons with energies higher than 10 MeV generate radio emission due to synchrotron losses and fluxes of in-flight annihilation and bremsstrahlung emission in the energy range above 10 MeV. From Eqs. \ref{radio_int}) ), \ref{N_density}) )"596 and (21)) we calculated the time variations of radio emission from the GC at the frequency, and \ref{spectrum}) ) we calculated the time variations of radio emission from the GC at the frequency597Precise stellar parameters for all the stars were determined in the same manner and by the same authors from the same spectra used in our study.,Precise stellar parameters for all the stars were determined in the same manner and by the same authors from the same spectra used in our study.598" For details, we refer to Sousa et al. (2008,2011a, 2011b))."," For details, we refer to Sousa et al. \cite{Sousa_08,Sousa_11,Sousa_11b}) )."599" The typical uncertainties in the atmospheric parameters are of the order of 30 ffor, 0.06 dex for logg, and 0.03 dex for[Fe/H]."," The typical uncertainties in the atmospheric parameters are of the order of 30 for, 0.06 dex for $\log\, g$, and 0.03 dex for."600" The stars in the sample have effective temperatures 4487 € € 7212 (there are only 12 stars with > 6500 and metallicites -1.39 << 0.55 (only 11 stars with < -1 and three stars with > 0.4), and they have surface gravities 2.68 < logg < 4.96 dex (again the number of “outliers” is very small, only 5 stars with logg < 3.8 dex)."," The stars in the sample have effective temperatures 4487 $\leq$ $\leq$ 7212 (there are only 12 stars with $>$ 6500 and metallicites -1.39 $\leq$$\leq$ 0.55 (only 11 stars with $<$ -1 and three stars with $>$ 0.4), and they have surface gravities 2.68 $\leq$ $\log\,g$ $\leq$ 4.96 dex (again the number of “outliers” is very small, only 5 stars with $\log\, g$ $<$ 3.8 dex)."601" Elemental abundances for three a elements (Mg, Si, and Ti) were determined using a differential LTE analysis relative to the Sun (the reference abundances were taken from Anders Grevesse (1989))) with the 2010 revised version of the spectral synthesis code 1973)) 1993)). (2009)) 2011,, 2007)). (2011a)). σ/ VN, o [c/Fe] [a/Fe] 2009;; 2011,, [a@/Fe] x = 2009)). > [c/Fe] +300 to the content of a elements: the “high-a” and the “low-a” stars (thin disk*))."," Elemental abundances for three $\alpha$ elements (Mg, Si, and Ti) were determined using a differential LTE analysis relative to the Sun (the reference abundances were taken from Anders Grevesse \cite{Anders-89}) )) with the 2010 revised version of the spectral synthesis code \cite{Sneden}) \cite{Kurucz}) \cite{Neves}) \cite{Adibekyan}, \cite{Sousa_07}) \cite{Sousa_11}) $\sigma$ $\sqrt{N}$ $\sigma$ $\alpha$ $\alpha$ \cite{Neves}; \cite{Adibekyan}, $\alpha$ $\lesssim$ $\cong$ \cite{Neves}) $>$ $\alpha$ $\pm$ to the content of $\alpha$ elements: the $\alpha$ ” and the $\alpha$ ” stars (thin )."602 This separation highlights the well-known α enhancement of thick disk stars relative to the thin disk found for stars with < 0 (e.g. Fuhrmann 1998;; Bensby et al. 2003. 2005)).," This separation highlights the well-known $\alpha$ enhancement of thick disk stars relative to the thin disk found for stars with $<$ 0 (e.g. Fuhrmann \cite{Fuhrmann}; Bensby et al. \cite{Bensby-03,Bensby-05}) )."603 The blue filled circles in Fig., The blue filled circles in Fig.604 1 are the separation points between low- and high-a stars., 1 are the separation points between low- and $\alpha$ stars.605" A separation into these two “populations” was performed based on [a@/Fe], for the stars with +300 K. We divided the sample into five metallicity bins from =-0.7 to 0.25(see Fig."," A separation into these two “populations” was performed based on $\alpha$, for the stars with $\pm$ 300 K. We divided the sample into five metallicity bins from =-0.7 to 0.25(see Fig."606 2., 2.607 for bin sizes)andidentifiedtheminima in the[o/Fe] histogramsforeachbin., for bin sizes)andidentifiedtheminima in the$\alpha$ histogramsforeachbin.608Theseparation curve in Fig.,Theseparation curve in Fig.609 1 is the simple connectionoftheabove-mentioned separationpoints., 1 is the simple connectionoftheabove-mentioned separationpoints.610Inthe metallicity,Inthe metallicity611values adopted here are representative for tvpical LBLs like BL Lacertae Dóttcher&Bloom2000) or W Cómae (Taglialerriοἱal.2000:Reimer2002).,"values adopted here are representative for typical LBLs like BL Lacertae \citep{madejski99,bb00} or W Comae \citep{tagliaferri00,bmr02}."612. Furthermore. signilicantlv dillerent values of 55. ἐμ. and D would shift the svuchrotron cutoll out of the X-ray regime so that the diagnostics developed here may nol be applicable to the X-ray variability of BL Lac objects. which is (hie focus of (his paper.," Furthermore, significantly different values of $\gamma_2$, $\epsilon_B$, and $D$ would shift the synchrotron cutoff out of the X-ray regime so that the diagnostics developed here may not be applicable to the X-ray variability of BL Lac objects, which is the focus of this paper."613 We have presented a detailed parameter study of the time-dependent electron injection and kinematics and the sell-consistent radiation transport in jets of intermediate and peaked DL Lac objects., We have presented a detailed parameter study of the time-dependent electron injection and kinematics and the self-consistent radiation transport in jets of intermediate and low-frequency peaked BL Lac objects.614 Those objects are currently of great interest as (he steadily improving capabilities of current and future air Ceerenkov detector [acilities might allow the detection of this class of blazars at multi-GeV energies in the near future., Those objects are currently of great interest as the steadily improving capabilities of current and future air Čeerenkov detector facilities might allow the detection of this class of blazars at multi-GeV energies in the near future.615 At the same time. some of these objects exhibit interesting X-ray variability features which can now be studied in detail with the new generation of X-ray telescopes. in particular anclNewton.," At the same time, some of these objects exhibit interesting X-ray variability features which can now be studied in detail with the new generation of X-ray telescopes, in particular and."616 Furthermore. the GLAST mission. scheduled for launch in 2006. is expected to detect many more BL Lac objects at multi-MeV /— GeV energies and bridee the observational gap between the energv ranges previously covered by (he EGRET instrument on boardαπο. and the ground-based air Ceerenkov facilities.," Furthermore, the GLAST mission, scheduled for launch in 2006, is expected to detect many more BL Lac objects at multi-MeV – GeV energies and bridge the observational gap between the energy ranges previously covered by the EGRET instrument on board, and the ground-based air Čeerenkov facilities."617 In our study. we have focused on the impact of various specilic parameter choices and variations on the broadband SEDs. optical and X-ray light curves. and the spectral hysteresis phenomena previously observed in several high-Ireeuency. peaked BL Lac objects. but. also expected to be observable in intermediate and low-frequency peaked BL Lacs.," In our study, we have focused on the impact of various specific parameter choices and variations on the broadband SEDs, optical and X-ray light curves, and the spectral hysteresis phenomena previously observed in several high-frequency peaked BL Lac objects, but also expected to be observable in intermediate and low-frequency peaked BL Lacs."618 Verv important conclusions can be drawn from a comparison of our results concerning s-rayv bright sources dominated by either SSC or external Compton emission., Very important conclusions can be drawn from a comparison of our results concerning $\gamma$ -ray bright sources dominated by either SSC or external Compton emission.619 For a given level of [lux al GeV energies. al a level comprable (ο or exceeding the svnchrotron. pF; peak flux. those (wo scenarios should be clearly disüinguishable by virtue of the X-ray variability. during flaring episodes: Η roughly svametric flare time profiles at soft. N-ravs below the svynchrotron cutoff are observed. and (he local. time-resolved X-ray. spectra. are soll consistent with a case with negligible 5-rav emission ihe 5-rav emission might be dominated by external-Comptou emission (see Figs.," For a given level of flux at GeV energies, at a level comprable to or exceeding the synchrotron $\nu F_{\nu}$ peak flux, those two scenarios should be clearly distinguishable by virtue of the X-ray variability during flaring episodes: If roughly symmetric flare time profiles at soft X-rays below the synchrotron cutoff are observed, and the local, time-resolved X-ray spectra are soft — consistent with a case with negligible $\gamma$ -ray emission — the $\gamma$ -ray emission might be dominated by external-Compton emission (see Figs."620 ὃ 10))., \ref{ext_intspectra} – \ref{ext_hic}) ).621 IIowever. if the N-rav. time profiles show a clear sign of a very rapid rise and more gradual decay. aud (he (ime-resolved spectra are significantly harder (han corresponding to a case without strong y-ray emission. we expect a strong contribution from the SSC mechanism to the 5-rav emission (see Figs.," However, if the X-ray time profiles show a clear sign of a very rapid rise and more gradual decay, and the time-resolved spectra are significantly harder than corresponding to a case without strong $\gamma$ -ray emission, we expect a strong contribution from the SSC mechanism to the $\gamma$ -ray emission (see Figs."622 5 7))., \ref{L_inj_intspectra} – \ref{L_inj_hic}) ).623 Most notably. this diagnose of the ταν emission mechanism does not require a detailed spectral measurement which will be hard to achieve and require long integration," Most notably, this diagnostic of the $\gamma$ -ray emission mechanism does not require a detailed spectral measurement — which will be hard to achieve and require long integration"624"stars (showing for example a flux plateau at the highest flux value) are not described at all by the PSF estimate; such stars are even recognized earlier, since the deconvolution does not yield a point-like structure in these cases.","stars (showing for example a flux plateau at the highest flux value) are not described at all by the PSF estimate; such stars are even recognized earlier, since the deconvolution does not yield a point-like structure in these cases."625 Astrometry in a crowded stellar field necessarily needs as input an estimate for the PSF., Astrometry in a crowded stellar field necessarily needs as input an estimate for the PSF.626" Just using local maxima in the image as position estimates is not sufficient, since essentially all stars are located on the seeing halo of neighboring sources."," Just using local maxima in the image as position estimates is not sufficient, since essentially all stars are located on the seeing halo of neighboring sources."627 This yields a background flux with a gradient and thus biases the positions of local maxima., This yields a background flux with a gradient and thus biases the positions of local maxima.628" Even worse, the background will vary with the AO correction from image to image and lead to a position jitter."," Even worse, the background will vary with the AO correction from image to image and lead to a position jitter."629" Moreover, very faint stars in a seeing halo of a bright star do not produce a local maximum (but only change the shape of the seeing halo) and would be missed by an algorithm looking for local maxima."," Moreover, very faint stars in a seeing halo of a bright star do not produce a local maximum (but only change the shape of the seeing halo) and would be missed by an algorithm looking for local maxima."630" These problems are overcome by using the knowledge of the PSF, which can be obtained from the image itself with an iterative procedure, e.g. using starfinder (?).."," These problems are overcome by using the knowledge of the PSF, which can be obtained from the image itself with an iterative procedure, e.g. using starfinder \citep{Diolaiti:2000p1984}."631" Given a certain PSF estimate, there are two basic options to obtain position estimates."," Given a certain PSF estimate, there are two basic options to obtain position estimates."632" Since both methods use the same input, one does not expect a major difference in astrometric performance."," Since both methods use the same input, one does not expect a major difference in astrometric performance."633 The fact that in figure 4 the starfinder errors are larger than the corresponding deconvolution errors might reflect a non-optimum user choice for the parameters of the starfinder algorithm and/or it might be due to the differences how the non-stellar background is dealt with., The fact that in figure \ref{f4} the starfinder errors are larger than the corresponding deconvolution errors might reflect a non-optimum user choice for the parameters of the starfinder algorithm and/or it might be due to the differences how the non-stellar background is dealt with.634 'The fact that the input PSF is not perfectly known but has to be estimated needs to be accounted for in the error budget., The fact that the input PSF is not perfectly known but has to be estimated needs to be accounted for in the error budget.635" In order to quantify the error, we used various sets of PSF stars and compared the resulting positions."," In order to quantify the error, we used various sets of PSF stars and compared the resulting positions."636" Also, we compared the positions depending on the number of iterations used for the extraction of the PSF."," Also, we compared the positions depending on the number of iterations used for the extraction of the PSF."637 From the scatter of the positions (after having transformed them linearly onto each other) we conclude that the uncertainty of the PSF knowlegde yields a positional error of 50µας.," From the scatter of the positions (after having transformed them linearly onto each other) we conclude that the uncertainty of the PSF knowlegde yields a positional error of $50\,\mu$ as."638 The fact that we need to transform the measured pixel positions with a set of reference stars is an error source because the transformation parameters also have errors., The fact that we need to transform the measured pixel positions with a set of reference stars is an error source because the transformation parameters also have errors.639" Fortunately, the corresponding statistical error can be lowered to a very low level."," Fortunately, the corresponding statistical error can be lowered to a very low level."640" If N stars are used as reference stars, each with a typical position error of oz, the additional error for the target sources due to the transformation is of order c,/V/N."," If $N$ stars are used as reference stars, each with a typical position error of $\sigma_x$, the additional error for the target sources due to the transformation is of order $\sigma_x/\sqrt{N}$."641" By choosing a large enough sample of reference stars, this statistical error can thus be lowered to any desired value as long as a sufficient number of reference stars is available."," By choosing a large enough sample of reference stars, this statistical error can thus be lowered to any desired value as long as a sufficient number of reference stars is available."642" Of course, this holds only if the reference stars can all be chosen from within the field in which the PSF can be treated as constant."," Of course, this holds only if the reference stars can all be chosen from within the field in which the PSF can be treated as constant."643" Recently ? used Νez:100 reference stars in the GC field, which suppresses effectively the transformation error to below 50 µας."," Recently \cite{Gillessen:2009p1117} used $N\approx 100$ reference stars in the GC field, which suppresses effectively the transformation error to below $50\,\mu$ as."644" Fomer studies (7) had used Nz10 reference stars, which hence at the time was contributing at the few level to the errors."," Fomer studies \citep{Schodel:2002p153}645 had used $N\approx 10$ reference stars, which hence at the time was contributing at the few level to the errors."646 We also investigated systematically the number of iterations to be used with our implementation of the Lucy-Richardson algorithm., We also investigated systematically the number of iterations to be used with our implementation of the Lucy-Richardson algorithm.647 Using a set of 66 well isolated stars in the data set from 20 July 2007 we obtained pixel positions for different deconvolution depths., Using a set of 66 well isolated stars in the data set from 20 July 2007 we obtained pixel positions for different deconvolution depths.648" For less than 500 iteration steps, the resulting positions are biased up to 0.5 mas for bright stars compared to the positions in the undeconvolved image and compared to more deeply deconvolved images."," For less than 500 iteration steps, the resulting positions are biased up to $0.5\,$ mas for bright stars compared to the positions in the undeconvolved image and compared to more deeply deconvolved images."649" For different stars the bias acts in different directions, and hence globally it appears to be a scatter of up to 0.5 mas."," For different stars the bias acts in different directions, and hence globally it appears to be a scatter of up to $0.5\,$ mas."650" For 2000 steps, both bias and scatter for bright stars drop below 120 was."," For 2000 steps, both bias and scatter for bright stars drop below $120\,\mu$ as."651 The optimum is reached for ©10000 iterations; also fainter sources are unbiased with that number of iterations., The optimum is reached for $\approx 10000$ iterations; also fainter sources are unbiased with that number of iterations.652" Much larger values (like 50000 steps) tend to put the flux of any star into a single pixel, which of course corresponds to larger positional errors again."," Much larger values (like 50000 steps) tend to put the flux of any star into a single pixel, which of course corresponds to larger positional errors again."653" The optimum depth in practice is between 5000 and 15000 steps, with better data needing less deep deconvolution."," The optimum depth in practice is between 5000 and 15000 steps, with better data needing less deep deconvolution."654 Visual inspection of the deconvolved frames shows that the background in the images is not flat but rather has, Visual inspection of the deconvolved frames shows that the background in the images is not flat but rather has655"Asymptouic⋅ normality ⋅≼for Si,AL) and si AO).for À=x also holds with⋅ an identical⋅ statement to that οἱ. Theorem 5.5 for disunguishable balls.",Asymptotic normality for $S_n^{(1)}$ and $S_n^{(0)}$ for $\lambda=\infty$ also holds with an identical statement to that of Theorem \ref{thm:diballs_r01} for distinguishable balls.656cilferent environments finding that there was no significant trend of galaxy size with local density.,different environments finding that there was no significant trend of galaxy size with local density.657 Pherefore. the effect of aperture bias depends mainly on the spatial distribution of star formation across the galaxy with a lack of strong environment biases.," Therefore, the effect of aperture bias depends mainly on the spatial distribution of star formation across the galaxy with a lack of strong environment biases."658 From galaxies in SDSS. Brinchmann 6 al. (," From galaxies in SDSS, Brinchmann et al. ("6592004) found that there are a still strong aperture 6fects in ΡΑΣ for galaxies with log M?2 10.5.,2004) found that there are a still strong aperture effects in $SFR/M^*$ for galaxies with log $M^* > $ 10.5.660 ‘This is expected since these galaxies often have prominent bulges. in which the specific SER is expected to be low.," This is expected since these galaxies often have prominent bulges, in which the specific SFR is expected to be low."661 TPhis would alfect the star formation rate of the most massive galaxies in our sample. but not the intermediate and low mass svstenis. which dominate our statistics of interacting pairs ( 70%).," This would affect the star formation rate of the most massive galaxies in our sample, but not the intermediate and low mass systems, which dominate our statistics of interacting pairs $\sim$ 70 $\%$ )."662 From these analysis we conclude that this potential bias is not Likely to have a large effect on our analvsis of star formation in pair galaxies in cillerent environments., From these analysis we conclude that this potential bias is not likely to have a large effect on our analysis of star formation in pair galaxies in different environments.663 In order to assess the elfects of incompleteness. we built up a subsample of pairs free (rom incompleteness effects by cross-correlating the spectroscopic and the photometric surveys.," In order to assess the effects of incompleteness, we built up a subsample of pairs free from incompleteness effects by cross-correlating the spectroscopic and the photometric surveys."664" We explored the fields in the photometric SDSS survey around cach spectroscopic pair restricted om,==rτον, searching for those galaxy. pairs without anv extra galaxy companion in the photometric survey within a projected distance of 100kpe at the same limiting magnitude."," We explored the fields in the photometric SDSS survey around each spectroscopic pair restricted to $m_r=17.5$, searching for those galaxy pairs without any extra galaxy companion in the photometric survey within a projected distance of $100 \kpc$ at the same limiting magnitude."665 Dv doing so. we obtain a subsanmple of pairs that is free rom) spectroscopic incompleteness bias and is. therefore. appropriate to test the results for the samples analysed in he paper against incompleteness effects of the spectroscopic survey.," By doing so, we obtain a subsample of pairs that is free from spectroscopic incompleteness bias and is, therefore, appropriate to test the results for the samples analysed in the paper against incompleteness effects of the spectroscopic survey."666 By comparison between both pair saniples (clean and contaminated). we estimated that the spectroscopic catalog i an incompleteness of z 9.54.," By comparison between both pair samples (clean and contaminated), we estimated that the spectroscopic catalog has an incompleteness of $\approx$ $\%$."667 Although this is not a aree fraction. we have examined the possible effects in our analvsis in Section 3 where we conclude that there is not a serious bias in our results.," Although this is not a large fraction, we have examined the possible effects in our analysis in Section 3 where we conclude that there is not a serious bias in our results."668 In order to unveil the effects of interactions in cillerent environments. we constructed. control samples for. the 2dECGIU and SDSS pair catalogs defined by galaxies without a close companion within the adopted. separation and velocity thresholds., In order to unveil the effects of interactions in different environments we constructed control samples for the 2dFGRS and SDSS pair catalogs defined by galaxies without a close companion within the adopted separation and velocity thresholds.669" By using à Monte Carlo algorithm. for each galaxy pair. we selected. (wo other galaxies. without a spectroscopic companion within ry,«1005+kpe and AV«350kms"," By using a Monte Carlo algorithm, for each galaxy pair, we selected two other galaxies without a spectroscopic companion within $r_{\rm p} < 100 \kpc $ and $\Delta V < 350 \ \kms$."670 Aloreover. these galaxies were also required to match the observed redshift) ancl luminosity distributions of the corresponding pair sample.," Moreover, these galaxies were also required to match the observed redshift and luminosity distributions of the corresponding pair sample."671 In this wav thes will also share incompleteness elfects. ancl any other selection bias which may depend on redshift and luminosity., In this way they will also share incompleteness effects and any other selection bias which may depend on redshift and luminosity.672 We did not impose other restriction since the purpose of the control sample is to take into account any possible redshift and luminosity bias while allowing a confrontation of other physical parameters such as colours and star. formation activity as a function of recdshift., We did not impose other restriction since the purpose of the control sample is to take into account any possible redshift and luminosity bias while allowing a confrontation of other physical parameters such as colours and star formation activity as a function of redshift.673 In Fig.2 (panels b and ce) we show the recdshift distributions for SDSS ancl δαο pair samples (solid ines) and their corresponding control catalogs. (dashed ines)., In \ref{histz} (panels $b$ and $c$ ) we show the redshift distributions for SDSS and 2dFGRS pair samples (solid lines) and their corresponding control catalogs (dashed lines).674" Similarly, panels d. and ο show the M, and My, distributions from SDSS and 2dECU."," Similarly, panels $d$ and $e$ show the $M_r$ and $M_{b_j}$ distributions from SDSS and 2dFGRS."675 It can be appreciated hat luminosities and redshift for both pairs and control samples are similarly behaved in SDSS and 2dEGIUS surveys with very small Poisson errors., It can be appreciated that luminosities and redshift for both pairs and control samples are similarly behaved in SDSS and 2dFGRS surveys with very small Poisson errors.676 The characterization of the local environment of galaxies is attained by defining a projected. local density parameter. NS," The characterization of the local environment of galaxies is attained by defining a projected local density parameter, $\Sigma$."677" This parameter is calculated: through the. projected distance d to the 455""H nearest neighbour.. NX5/(id)."," This parameter is calculated through the projected distance $d$ to the $5^{th}$ nearest neighbour, $\Sigma = 5/(\pi d^2)$."678 Neighbours have been chosen to have. luminosities above a certain threshold. anc with a radial velocity dilference lesser than 1000 km s|., Neighbours have been chosen to have luminosities above a certain threshold and with a radial velocity difference lesser than 1000 km $s^{-1}$.679 In a similar way as Balogh et al. (, In a similar way as Balogh et al. (680"2004). we imposed the condition A,<20.5 to select neighbours in SDSS.","2004), we imposed the condition $M_r < -20.5$ to select neighbours in SDSS."681" For the δαο catalog we estimated a corresponding magnitude limit of Ad,=—19.3 by requiring that galaxy. pairs in the common region with the SDSS had a similar density parameter X in both catalogs.", For the 2dFGRS catalog we estimated a corresponding magnitude limit of $M_b = -19.3$ by requiring that galaxy pairs in the common region with the SDSS had a similar density parameter $\Sigma$ in both catalogs.682 This behaviour is illustrated in Fig.3((a.b). where we show the distribution of the derived values of X for both pair catalogs.," This behaviour is illustrated in \ref{histSig}( (a,b), where we show the distribution of the derived values of $\Sigma$ for both pair catalogs."683 We explored if the results obtained in theirs paper could depend on our particular choice of local density estimator., We explored if the results obtained in theirs paper could depend on our particular choice of local density estimator.684 bor that purpose. we also used the local densities given by Ixaulfmann ct al. (," For that purpose, we also used the local densities given by Kauffmann et al. ("6852004).,2004).686 These authors estimated the local density by counting galaxies within evlinders of 2 Alpe in, These authors estimated the local density by counting galaxies within cylinders of 2 Mpc in687"magnificaüons is such thal some microlensing events are observed with a high enough signal-to-noise ratio (S/N) to be reasonably convincing (Alcocketal.1993), even without a good understanding of the variable star background.","magnifications is such that some microlensing events are observed with a high enough signal-to-noise ratio (S/N) to be reasonably convincing \citep{macho-nat93}, even without a good understanding of the variable star background."688" However, many of the conclusions [rom microlensing event samples are statistical in nature, so it is advantageous to idenuly as many microlensing events as possible to improve the statistics."," However, many of the conclusions from microlensing event samples are statistical in nature, so it is advantageous to identify as many microlensing events as possible to improve the statistics."689 This is particularly true for microlensing searches observing the Magellanic clouds where the microlensing optical depth is more than an order of magnitude smaller than it is towards the Galactic bulge., This is particularly true for microlensing searches observing the Magellanic clouds where the microlensing optical depth is more than an order of magnitude smaller than it is towards the Galactic bulge.690 This need for higher staüsties has led to the announcement of microlensing candidates that have since been rejected., This need for higher statistics has led to the announcement of microlensing candidates that have since been rejected.691 Two of the first three MACHO LMC microlensing candidates (Alcocketal.1996a) are no longer considered to be viable microlensing candidates.," Two of the first three MACHO LMC microlensing candidates \citep{macho-lmc1}692 are no longer considered to be viable microlensing candidates."693" MACHO-LMC-? has exhibited additional variations that are appear inconsistent with any reasonable microlensing interpretation, and the MACHO Project has found that candidate MACHO-LMC-3 has a signal-to-noise ratio (S/N) so low that it no longer stands out from the false microlensing-like signals caused by variable stars and/or photometry problems 1997b).."," MACHO-LMC-2 has exhibited additional variations that are appear inconsistent with any reasonable microlensing interpretation, and the MACHO Project has found that candidate MACHO-LMC-3 has a signal-to-noise ratio (S/N) so low that it no longer stands out from the false microlensing–like signals caused by variable stars and/or photometry problems \citep{macho-lmc2}."694" Similarly, the first [our EROS LMC microlensing candidates have also been rejected (Ansariet2005) as likely variable stars."," Similarly, the first four EROS LMC microlensing candidates \citep{eros93,eros-lmc-tau} have also been rejected \citep{eros2-var,eros12-spec,jetz-mil-tiss,tiss-mil} as likely variable stars."695" A major advance in the identification of Magellanic Cloud microlensing events was made by the MACHO Project in Alcocketal.(200005) (herealter A00), where they idenufied background supernovae as the dominant non-microlensing background, and developed a method to remove this background from the microlensing sample."," A major advance in the identification of Magellanic Cloud microlensing events was made by the MACHO Project in \citet{macho-lmc5.7}696 (hereafter A00), where they identified background supernovae as the dominant non-microlensing background, and developed a method to remove this background from the microlensing sample."697" A similar method has also been implemented by EROS (Jetzer2005) to remove supernovae contamination [rom their data, and this has led to the rejection of several previous microlensing candidates."," A similar method has also been implemented by EROS \citep{jetz-mil-tiss,tiss-mil} to remove supernovae contamination from their data, and this has led to the rejection of several previous microlensing candidates."698" The question remains, however, whether there is any additional population of non-microlensing events that sull contaminates the LMC microlensing candidate samples alter the supernovae have been removed."," The question remains, however, whether there is any additional population of non-microlensing events that still contaminates the LMC microlensing candidate samples after the supernovae have been removed."699 There are some reasons to believe that this possible contamination is not large., There are some reasons to believe that this possible contamination is not large.700 There are now a number of events that would be quite difficult to explain with another variability mechanism., There are now a number of events that would be quite difficult to explain with another variability mechanism.701" These include high magnification events, such as MACHO-LMC-5 (Alcocketal.2001b;Drake,Cook,&Keller2004;Gould,Bennett,&Alves2004) and MACHO-99-LMC-? (Bondetal.2002)., caustic crossing binary events such as MACHO-LMC-9 (Bennettetal.1996:Alcock2000ᾳ).. and MACHO-98-SMC-1 (Afonsoetal.2000).. and events with high precision follow-up photometry, such as MACHO-LMC-4, 13, 14 and 15 (AlcockBecker,&Tomaney 2005).."," These include high magnification events, such as MACHO-LMC-5 \citep{macho-hstlmc5,dck-lmc5,lmc5-mass}702 and MACHO-99-LMC-2 \citep{moa-himag-obs}, caustic crossing binary events such as MACHO-LMC-9 \citep{macho-lmc9,macho-binaries}, and MACHO-98-SMC-1 \citep{joint-98smc1}, and events with high precision follow-up photometry, such as MACHO-LMC-4, 13, 14 and 15 \citep{macho-96lmc2,lmc-conf}."703" Also, observations of red clump giant stars in both the LMC and Galactic bulge have revealed no examples of variability resembling microlensing (AlcockAfonsoetal.2003b;Popowski2004:Thomas2004;Sumi 2004).."," Also, observations of red clump giant stars in both the LMC and Galactic bulge have revealed no examples of variability resembling microlensing \citep{macho-blg45,eros-blg-tau,704pop-blgclump,macho-blg-ev,sumi-ogle-tau}."705" Recent observations of microlensing candidate MACHO-LMC-23 by the EROS (Glicenstein2004;Jetzeretal.2004;Tisserand&Milsztajn2005) and OGLE (Udalski, private communication) indicate a subsequent brightening of this star approximately 2500 days alter the one observed by MACHO."," Recent observations of microlensing candidate MACHO-LMC-23 by the EROS \citep{glicens-hawaii,jetz-mil-tiss,tiss-mil} and OGLE (Udalski, private communication) indicate a subsequent brightening of this star approximately 2500 days after the one observed by MACHO."706" This could conceivably be explained with à binary source or binary lens microlens model, but the MACHO data lor the first brightening episode also does not fit à standard microlensing model very well 2005),, and a different modification of standard microlensing would be required to explain the first"," This could conceivably be explained with a binary source or binary lens microlens model, but the MACHO data for the first brightening episode also does not fit a standard microlensing model very well \citep{lmc-conf}, , and a different modification of standard microlensing would be required to explain the first"707the torque acting upon the star. for example via a flux of Alfvénn waves and particles resulting from magnetically-induced (sudden large-scale or persistent small-scale) crustal seismic activity (e.g..Thompsonetal.2000).,"the torque acting upon the star, for example via a flux of Alfvénn waves and particles resulting from magnetically-induced (sudden large-scale or persistent small-scale) crustal seismic activity \citep[e.g.,][]{tdw+00}."708 It is unclear whether any such particular models (seealsoDuncan2001) can explain the magnitude and time scale of the variations in torque currently observed in31810—197.. 4 years after the X-ray outburst.," It is unclear whether any such particular models \citep[see also][]{dun01} can explain the magnitude and time scale of the variations in torque currently observed in, 4 years after the X-ray outburst."709 In any case. substantial variations in magnetospheric plasma densities and/or currents would likely have implications for other observable properties of the pulsar.," In any case, substantial variations in magnetospheric plasma densities and/or currents would likely have implications for other observable properties of the pulsar."710 An interesting comparison is with PSR B1I931+424. an ordinary radio pulsar during intervals of 5-10 days. with P=0.8ss and Bz2«10 GG. which abruptly shuts off for 25-35 days in a pattern that repeats quasi-pertodically (Krameretal.2006).," An interesting comparison is with PSR B1931+24, an ordinary radio pulsar during intervals of 5–10 days, with $P=0.8$ s and $B\approx2\times10^{12}$ G, which abruptly shuts off for 25–35 days in a pattern that repeats quasi-periodically \citep{klo+06}."711. During these turned-off periods. the torque is only two-thirds of its turned-on value.," During these turned-off periods, the torque is only two-thirds of its turned-on value."712 Krameretal.(2006) conclude from this extraordinary behavior that the occasional presence of plasma leads to radio emission and its flow provides the extra braking torque., \citet{klo+06} conclude from this extraordinary behavior that the occasional presence of plasma leads to radio emission and its flow provides the extra braking torque.713 The plasma density calculated from the torque difference is cem. in agreement with the co-rotation value (Goldreich 1969).," The plasma density calculated from the torque difference is $^{-3}$, in agreement with the co-rotation value \citep{gj69}."714. In tthe radio emission has not shut off. but it did diminish and change markedly in character somewhat abruptly in late 2006 July. apparently comeident with a huge reduction in torque (7 changed from —2.96«107 ss on MJD 53933 to -2.65.107 ss* on MID 53949: see 3 and Fig. 4).," In the radio emission has not shut off, but it did diminish and change markedly in character somewhat abruptly in late 2006 July, apparently coincident with a huge reduction in torque $\dot \nu$ changed from $-2.96\times10^{-13}$ $^{-2}$ on MJD 53933 to $-2.65\times10^{-13}$ $^{-2}$ on MJD 53949; see \ref{sec:timing} and Fig. \ref{fig:fdot}) )."715" A calculation such às that by Krameretal.(2006) would suggest for aan ""extra"" plasma density of about eesucem™ prior to the large torque decrease. compared to the source's Goldreich-Julian density of 1350eesucem™."," A calculation such as that by \citet{klo+06} would suggest for an “extra” plasma density of about $^{-3}$ prior to the large torque decrease, compared to the source's Goldreich-Julian density of $^{-3}$."716 Implicit in this calculation is the notion that the radio emission originates from open field lines. which has not been proven forJ1810-197.," Implicit in this calculation is the notion that the radio emission originates from open field lines, which has not been proven for."717. For a magnetar. there is additional plasma due to non-axisymmetric large-scale magnetospheric currents (Thompsonetal.2002).," For a magnetar, there is additional plasma due to non-axisymmetric large-scale magnetospheric currents \citep{tlk02}."718. In any case. the pulse profile and flux variations observed in ooceur on time scales that are apparently too short to be explained by changes in the closed field lines (see.e.g.Beloborodov&Thompson 2007).," In any case, the pulse profile and flux variations observed in occur on time scales that are apparently too short to be explained by changes in the closed field lines \citep[see, e.g.,][]{bt06}."719 Also. interpretation. of polarimetric data for aappears consistent with emission from open field lines (Camiloetal.2007).," Also, interpretation of polarimetric data for appears consistent with emission from open field lines \citep{crj+07}."720. If indeed the measured changes in torque are caused by variations in the magnetospheric plasma density in locations relevant for the production of coherent radio emission. then it should be no surprise that the pulse profiles of cchange so remarkably: ever the “small” torque changes reflected in Figure 4. are ehormous by the standards of ordinary pulsars.," If indeed the measured changes in torque are caused by variations in the magnetospheric plasma density in locations relevant for the production of coherent radio emission, then it should be no surprise that the pulse profiles of change so remarkably: even the “small” torque changes reflected in Figure \ref{fig:fdot} are enormous by the standards of ordinary pulsars."721 And certatnly. the profile variations in ((Figs. 1..," And certainly, the profile variations in (Figs. \ref{fig:profs_nancay},"722" and 5)) are observationally distinct from the ""mode changing""2. of some ordinary pulsars. where the average pulse profile suddenly changes between two of a small set of different configurations (e.g..Barteletal.1982): ddisplays à much greater variety."," \ref{fig:profs_gbt} and \ref{fig:cxo}) ) are observationally distinct from the “mode changing” of some ordinary pulsars, where the average pulse profile suddenly changes between two of a small set of different configurations \citep[e.g.,][]{bmsh82}; displays a much greater variety."723 However. the root cause of mode changing is not well understood and. as we have established that pprofiles can change suddenly (Fig. 5)).," However, the root cause of mode changing is not well understood and, as we have established that profiles can change suddenly (Fig. \ref{fig:cxo}) ),"724 some link may exist between these two phenomena., some link may exist between these two phenomena.725 Other behavior also appears extraordinary. such as the broader pulse components typically observed after MJD 53940 even as the phase separation between components remains fixed (Fig.," Other behavior also appears extraordinary, such as the broader pulse components typically observed after MJD 53940 even as the phase separation between components remains fixed (Fig."726 | and 22)) and the polarimetric properties remain largely unchanged (Camiloetal.2007)., \ref{fig:profs_nancay} and \ref{sec:timing}) ) and the polarimetric properties remain largely unchanged \citep{crj+07}.727. Compared to such extreme radio variability. the X-ray spectrum and pulse profiles of cchange slowly as the flux decays (e.g..Gotthelf&Halpern2007.. on a much longer time scale (~lyyr) than the fluctuations in torque reported here.," Compared to such extreme radio variability, the X-ray spectrum and pulse profiles of change slowly as the flux decays \citep[e.g.,][]{gh06}, on a much longer time scale $\sim 1$ yr) than the fluctuations in torque reported here."728 The alignment of the peaks of the radio and X-ray pulses suggests that the footpoints of the active magnetic field lines on which radio emission is generated are also the locations of concentrated crustal heating that is responsible for the enhanced X-ray emission. at least at the higher energies that apparently come from a relatively small area (seeGotthelf&Halpern2007).," The alignment of the peaks of the radio and X-ray pulses suggests that the footpoints of the active magnetic field lines on which radio emission is generated are also the locations of concentrated crustal heating that is responsible for the enhanced X-ray emission, at least at the higher energies that apparently come from a relatively small area \citep[see][]{gh06}."729. However. even if the energetic particle bombardment that heats the surface hot spot fluctuates on time scales of less than I day. the absence of correlated X-ray variability on similar time scales indicates that most of the X-ray luminosity originated in deeper crustal heating at the time of the X-ray turn on. or from more gradual decay of the magnetic field (Eichler&Cheng1989)..," However, even if the energetic particle bombardment that heats the surface hot spot fluctuates on time scales of less than 1 day, the absence of correlated X-ray variability on similar time scales indicates that most of the X-ray luminosity originated in deeper crustal heating at the time of the X-ray turn on, or from more gradual decay of the magnetic field \citep{ec89a}."730 Among persistent AXPs it is not altogether clear what is the relationship between observed radiative properties (such as pulse shapes and fluxes) and rotational evolution (such as variations in torque)., Among persistent AXPs it is not altogether clear what is the relationship between observed radiative properties (such as pulse shapes and fluxes) and rotational evolution (such as variations in torque).731 Pulse profiles can change following glitches (e.g...Kaspietal.2003).. but otherwise appear to be fairly stable (Gavriil&Kaspi2002).," Pulse profiles can change following glitches \citep[e.g.,][]{kgw+03}, but otherwise appear to be fairly stable \citep{gk02}."732. Quite apart from the phenomenon of X-ray bursts (forburstsinXTEJ1810—197.seeWoodsetal. 2005).. some AXPs have shown substantial variability in X-ray flux (e.g..Gavriil&Kaspi 2004).," Quite apart from the phenomenon of X-ray bursts \citep[for bursts in \xte, see][]{wkg+05}, some AXPs have shown substantial variability in X-ray flux \citep[e.g.,][]{gk04}."733. Nevertheless. with the possible exception of IE 1048.1-5937 (ανν&Kaspi2004).. there has been no reported correlation between X-ray flux and spin-down rate.," Nevertheless, with the possible exception of 1E 1048.1–5937 \citep{gk04}, there has been no reported correlation between X-ray flux and spin-down rate."734 ForJI810-197.. on the other hand. there is an observed correlation between radio flux density and torque over a period of 9 months (Fig. 4)).," For, on the other hand, there is an observed correlation between radio flux density and torque over a period of 9 months (Fig. \ref{fig:fdot}) ),"735 although we know neither whether this correlation is catsal nor whether it holds over longer periods of time., although we know neither whether this correlation is causal nor whether it holds over longer periods of time.736 With observations ofJ1810-197.. we now find ourselves in the curious positio1 of relying upon energetically insignificant radio pulsations exhibiting a remarkably diverse phenomenology to illuminate rather more energetic events on the magnetar.," With observations of, we now find ourselves in the curious position of relying upon energetically insignificant radio pulsations exhibiting a remarkably diverse phenomenology to illuminate rather more energetic events on the magnetar."737 Attempting to understand key aspects of the radio observations may lead to a deeper understanding of both magnetars and radio pulsar emission., Attempting to understand key aspects of the radio observations may lead to a deeper understanding of both magnetars and radio pulsar emission.738 We are grateful to John Sarkissian for help with Parkes observations. Eric Gerard for useful discussions concerning fflux calibration. and David Nice for wisdom on time systems as used in TEMPO.," We are grateful to John Sarkissian for help with Parkes observations, Eric Gerard for useful discussions concerning flux calibration, and David Nice for wisdom on time systems as used in TEMPO."739 The rradio telescope is part of the Paris Observatory. associated with the Centre National de la Recherche Scientifique (CNRS). and partially supported by the Region Centre in France.," The radio telescope is part of the Paris Observatory, associated with the Centre National de la Recherche Scientifique (CNRS), and partially supported by the Region Centre in France."740 The National Radio Astronomy Observatory is a facility of the National Science Foundation. operated under cooperative agreement by Associated Universities. Inc. The Parkes Observatory is part of the Australia Telescope. which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO.," The National Radio Astronomy Observatory is a facility of the National Science Foundation, operated under cooperative agreement by Associated Universities, Inc. The Parkes Observatory is part of the Australia Telescope, which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO."741 FC thanks the NSF for support through grant AST-05-07376., FC thanks the NSF for support through grant AST-05-07376.742 EVG acknowledges, EVG acknowledges743in order to generate relatively more Paschen eunission.,in order to generate relatively more Paschen emission.744 Although Try extends to hotter temperatures. if is consistent with results from the radiative-livdrodynuaiic simuulatiounsfrou: Allredetal.(2006)... which show that material at the base of the transition region cau be heated up to T = 105 Is. Comparing the strengths of the modeled lines to cach other provides strong constraimts on our suite of model atmospheres.," Although $_{TR}$ extends to hotter temperatures, it is consistent with results from the radiative-hydrodynamic simulationsfrom \citet{Allred2006}, which show that material at the base of the transition region can be heated up to T = $^{6}$ K. Comparing the strengths of the modeled lines to each other provides strong constraints on our suite of model atmospheres."745 The line flux ratios with respect to the I> line flux for the best models are shown compared to the median and range of observed line fli ratios in Figure 8.., The line flux ratios with respect to the $\gamma$ line flux for the best models are shown compared to the median and range of observed line flux ratios in Figure \ref{fig:lfluxc}. .746" Iu general. a deeper T,,;, (at logtcol mass) = O or 1). a deeper transition region (at los(col mass) = 3.5 or 1.5). and a hotter chromosphere (with Try = 25 000K. or 300001) better reproduce the line flux ratios observed during the fare."," In general, a deeper $_{min}$ (at log(col mass) = 0 or $-$ 1), a deeper transition region (at log(col mass) = $-$ 3.5 or $-$ 4.5), and a hotter chromosphere (with $_{TR}$ = $25\,000$ K or $30\,000$ K) better reproduce the line flux ratios observed during the flare."747 The line formation regious (where the contribution function for each line is ereater than of its peak value) for oue model are shown in Figure 9.., The line formation regions (where the contribution function for each line is greater than of its peak value) for one model are shown in Figure \ref{fig:hgtfor}.748 Most of the lies are produced over regions that include the outer portion of the chromosphere. at loge(col mass) = 35 aud T = 25000. Is. the strongest eiuissiou line we observed. is formed over the sinallest portion of the chromosphere. with its lighest temperature at T — 20000I. Πο TALITIA and Πο I λΙΟΣΟΟΑ foriu over slightly different regions of the atimosphere. with Ie I ALOS30A tracing slightly higher temperatures.," Most of the lines are produced over regions that include the outer portion of the chromosphere, at log(col mass) = $-$ 3.5 and T = $25\,000$ K. $\gamma$, the strongest emission line we observed, is formed over the smallest portion of the chromosphere, with its highest temperature at T = $20\,000$ K. He I $\lambda$ and He I $\lambda$ form over slightly different regions of the atmosphere, with He I $\lambda$ tracing slightly higher temperatures."749 Durus the fiue observations. the ratio of Πὸ to T+ is relatively. constant.," During the flare observations, the ratio of $\delta$ to $\gamma$ is relatively constant."750 Πὸ is slightly overproduced in the nodels compared to observations. but is similay in each of the models.," $\delta$ is slightly overproduced in the models compared to observations, but is similar in each of the models."751 We IT ALITLA cinission is weak (with a ratio to II5 of ~ 0.1 to 0.3) in both the models aud he observations., He I $\lambda$ emission is weak (with a ratio to $\gamma$ of $\sim$ 0.1 to 0.3) in both the models and the observations.752 The ratios of the Paschen series lines and Brackett ο to each other are relatively coustaut hroughout the dare. and those ratios are well produced in every atinospheric structure.," The ratios of the Paschen series lines and Brackett $\gamma$ to each other are relatively constant throughout the flare, and those ratios are well produced in every atmospheric structure."753" The ratio of the Pascheu ines aud Bre to IIs. however. is matched onulv in the uodels with a log(col iiass)7,,;, = 0."," The ratio of the Paschen lines and $\gamma$ to $\gamma$, however, is matched only in the models with a log(col $_{Tmin}$ = 0."754" Because these lines are sensitive to the hottest regions of the chromosphere. he advantage of the log(tcol 1iass)7,,5, = 0 ds likely an increased amount of material at temperatures near T — 200001 due to a shallower slope in the chromosphere."," Because these lines are sensitive to the hottest regions of the chromosphere, the advantage of the log(col $_{Tmin}$ = 0 is likely an increased amount of material at temperatures near T = $20\,000$ K due to a shallower slope in the chromosphere."755" The ratio of Ca II IK to Us aud to the other hydrogen series lines is best produced in the models with the deepest T,,;,. a deep transition region (log(col ry = 3.45 or -L.5). aud a hot Trj = 25000I& or 30 00019. Iu all other models. Ca II Is is uuderproduced relative to the Paschen series lines."," The ratio of Ca II K to $\gamma$ and to the other hydrogen series lines is best produced in the models with the deepest $_{min}$, a deep transition region (log(col $_{TR}$ = -3.5 or -4.5), and a hot $_{TR}$ = $25\,000$ K or $30\,000$ K. In all other models, Ca II K is underproduced relative to the Paschen series lines."756 As shown in Fieure 9.. the Ca II EK cuuission iu the best-fit model is formed over a larger rauge of log(col mass) than auv other lue.," As shown in Figure \ref{fig:hgtfor}, the Ca II K emission in the best-fit model is formed over a larger range of log(col mass) than any other line."757 The production of Ca II Wo in a τοσο. that includes the upper chromosphere is unusual compared to previous results: typically. Ca II [& cussion during a flare is thought to last longer because it is a lower temperature line (EHoudebine2003:Crespo-Chaconetal.2006).," The production of Ca II K in a region that includes the upper chromosphere is unusual compared to previous results; typically, Ca II K emission during a flare is thought to last longer because it is a lower temperature line \citep{Houdebine2003,Crespo-Chacon2006}."758. Our cooler atinospheres. where Ca II IX emissiou is formed onlv in lower temperature regions. do nof produce enough Ca II KR emission relative to. Pascheu series emission to match our observations.," Our cooler atmospheres, where Ca II K emission is formed only in lower temperature regions, do not produce enough Ca II K emission relative to Paschen series emission to match our observations."759 Te IAIO0830A is underproduced iu nearly every ος]., He I $\lambda$ is underproduced in nearly every model.760 During the flare. its observed ratio compared to II4 increases from 0.1 to 0.5. while all our mocels show line flux ratios of 0.1 or less.," During the flare, its observed ratio compared to $\gamma$ increases from 0.1 to 0.5, while all our models show line flux ratios of 0.1 or less."761 This uuismatch is apparently worse in the one of the other two flares observed: as discussed in Section L. He I ALOs30A is stronecr compared to Pos aud P5 (the two other lines— observed) in the UT 2010 November 27 flare on EV Lac.," This mismatch is apparently worse in the one of the other two flares observed; as discussed in Section \ref{sec:flareall}, He I $\lambda$ is stronger compared to $\beta$ and $\gamma$ (the two other lines observed) in the UT 2010 November 27 flare on EV Lac."762 Simply raising the Try in our models produces too mach Ca II lk but no additional He I AI0830À.., Simply raising the $_{TR}$ in our models produces too much Ca II K but no additional He I $\lambda$.763 Tn the Sun and similar stars. Ho I ATOSOO0A οσο is produced in the upper chromosphlere cing flares as a result of helium ionizationvia backwarnuue from coronal UV flux (Maasetal.2005:Sauz-Forcada&Dupree 2008).," In the Sun and similar stars, He I $\lambda$ emission is produced in the upper chromosphere during flares as a result of helium ionization via backwarming from coronal UV flux \citep{Mauas2005,Sanz-Forcada2008}."764. À similar process could be leading to the Πο I ATOSSO0A e1uissionu during M dwarf flares. but the details of backwarming— from coronal cluission are not vet fully iuiplemented iu the RII atinosphere code.," A similar process could be leading to the He I $\lambda$ emission during M dwarf flares, but the details of backwarming from coronal emission are not yet fully implemented in the RH atmosphere code."765 While onc-dimensional atmosphere models can match the line flux ratios of most of the lines as a sequence of static suapshots. they cannot reproduce the time evolution of the flare.," While one-dimensional atmosphere models can match the line flux ratios of most of the lines as a sequence of static snapshots, they cannot reproduce the time evolution of the flare."766 In our observatious. Ca II Ik. the Paschen lines. Bre. aud Πο I ATIOS8QOA αἱ rise relative to II5 during the decay phase of the flare.," In our observations, Ca II K, the Paschen lines, $\gamma$, and He I $\lambda$ all rise relative to $\gamma$ during the decay phase of the flare."767 The best fitting models inour suite of atinospheres indicate au increase in Ca II Is is always coupled with a decrease of the Paschen aud Brackett lines., The best fitting models inour suite of atmospheres indicate an increase in Ca II K is always coupled with a decrease of the Paschen and Brackett lines.768 The time evolution of flares max involve differeut atmospheric componcuts covering the surface of the star with chaneine filling factors (e.c...Ikowalskictal.2010).," The time evolution of flares may involve different atmospheric components covering the surface of the star with changing filling factors \citep[e.g.,][]{Kowalski2010}."769. It is possible that a linear combination of two or three different onc- ati»osphneres with changius fllius factors would reproduce the tiuuc-evolutiou of this flare., It is possible that a linear combination of two or three different one-dimensional atmospheres with changing filling factors would reproduce the time-evolution of this flare.770 During ucarly 50 hours of suuultaucous plotometric and spectroscopic observations on { active AL dwarts. we saw 16 total fares. 3 of them with accompanying infrared cmiissiou lines.," During nearly 50 hours of simultaneous photometric and spectroscopic observations on 4 active M dwarfs, we saw 16 total flares, 3 of them with accompanying infrared emission lines."771 The strongest flare (Au = 1.02) occurred on EV Lac on UT 2009 October 27., The strongest flare $\Delta u$ = 4.02) occurred on EV Lac on UT 2009 October 27.772 It showed cluission from I. Πὸ Te TALIZA... Calis. Po. P. Po. Bre. and ΠοI ALos30A..," It showed emission from $\gamma$, $\delta$, He I $\lambda$, Ca II K, $\beta$, $\gamma$, $\delta$ $\gamma$ , and HeI $\lambda$."773 A weaker flare (Au = 1.68) on EV Lac on UT 2010 November 27 showed ouly eiission from Po. Ps. and He E ALOs30A..," A weaker flare $\Delta u$ = 1.68) on EV Lac on UT 2010 November 27 showed only emission from $\beta$, $\gamma$, and He I $\lambda$."774 Remarkably. the Πο I ALOS30A emission was twice as strong compared to Pj and Ps asit was in the Aw = 1.02 flare.," Remarkably, the He I $\lambda$ emission was twice as strong compared to $\beta$ and $\gamma$ as it was in the $\Delta u$ = 4.02 flare."775 The weakest flare with infrared emission CAC = 1.38) cecurred on YZ CAL ou UT 2011 February Li: Ps. aud ΠοΤΑΙΟΣΟΟΑ were just above their detection linits.," The weakest flare with infrared emission $\Delta U$ = 1.38) occurred on YZ CMi on UT 2011 February 14; $\beta$, $\gamma$, and He I $\lambda$ were just above their detection limits."776 We estimate a duty cvele of to forobserving the strongest infrared wission line CP.7) durug flares on active nid-M clwarts., We estimate a duty cycle of to forobserving the strongest infrared emission line $\beta$ ) during flares on active mid-M dwarfs.777 These observations confirm that flares are detectable im the infrared. portion of AL chwarf spectra. which is much brighter iu quiescence than the bluer portions of M dwarf spectra which are typically used to detect flares.," These observations confirm that flares are detectable in the infrared portion of M dwarf spectra, which is much brighter in quiescence than the bluer portions of M dwarf spectra which are typically used to detect flares."778 Using a hotter chromosphere than previous static fare models (e.g.Cliistianetal.2010).. the ratios of Ca IT Ix. Ie ΤΑΙΙΤΙΑ.. 6. the Paschen lines. aud Bry to II5 cau be," Using a hotter chromosphere than previous one-dimensional static flare models \citep[e.g.,][]{Christian2003,Fuhrmeister2010},, the ratios of Ca II K, He I $\lambda$ , $\delta$ , the Paschen lines, and $\gamma$ to $\gamma$ can be"779"wonder why more of the bright UCDs have not been found with sizes in the r,~ 30-100 pc range.",wonder why more of the bright UCDs have not been found with sizes in the $r_{\rm h}\sim$ 30–100 pc range.780" Again, a larger number of accurate age estimates would clarify the situation."," Again, a larger number of accurate age estimates would clarify the situation."781" To this end, we have carried out a preliminary analysis using environmental density as a proxy for age, since there appears to be a strong correlation between density and nucleus age (Paudeletal.2010,"," To this end, we have carried out a preliminary analysis using environmental density as a proxy for age, since there appears to be a strong correlation between density and nucleus age \citep{2010ApJ...724L..64P,2011MNRAS.413.1764P}."782" We find indications that the “older” nuclei may 2011)..havefaded by only ~ 1 mag, leaving expansion as a requirement to match the UCD sizes."," We find indications that the “older” nuclei may havefaded by only $\sim$ 1 mag, leaving expansion as a requirement to match the UCD sizes."783" In more detail, the brighter nuclei (M;< —13) show a strong size-luminosity correlation, which flattens out at lower luminosities."," In more detail, the brighter nuclei $M_i \la -13$ ) show a strong size-luminosity correlation, which flattens out at lower luminosities."784" Whether or not the UCDs and GCs follow the same type of trend (with a luminosity offset) is not clear, particularly with the luminosity-dependent selection effects in the current sample."," Whether or not the UCDs and GCs follow the same type of trend (with a luminosity offset) is not clear, particularly with the luminosity-dependent selection effects in the current sample."785" Even with ideal data, the interpretation would be complicated by the current theoretical uncertainty about the size evolution of nuclei after stripping."," Even with ideal data, the interpretation would be complicated by the current theoretical uncertainty about the size evolution of nuclei after stripping."786 Therefore it is difficult at this point to draw firm conclusions about the UCD origins from size-luminosity trends., Therefore it is difficult at this point to draw firm conclusions about the UCD origins from size-luminosity trends.787 Figure 5 also provides a useful point of comparison with the joint size-luminosity and color-magnitude analyses of several GC/UCD systems carried out by Norris&Kannappan(2011).., Figure \ref{fig:cmd} also provides a useful point of comparison with the joint size-luminosity and color-magnitude analyses of several GC/UCD systems carried out by \citet{2011MNRAS.414..739N}.788" They claimed a transition luminosity or “scaling onset mass"" in both parameter spaces, above which strong blue-tilt and size-luminosity relations set in (similar transitions have been found in metallicities, velocity dispersions, and mass-to-light ratios; e.g., Hageganetal.2005;Mieske2006a,2008;Rejkubaetal. 2007))."," They claimed a transition luminosity or “scaling onset mass” in both parameter spaces, above which strong blue-tilt and size-luminosity relations set in (similar transitions have been found in metallicities, velocity dispersions, and mass-to-light ratios; e.g., \citealt{2005ApJ...627..203H,2006AJ....131.2442M,2008A&A...487..921M,2007A&A...469..147R}) )."789" This luminosity of My~—10 corresponds to M;~—10.5 in our plots, where we see no evidence of such a transition in M87."," This luminosity of $M_V \sim -10$ corresponds to $M_i \sim -10.5$ in our plots, where we see no evidence of such a transition in M87."790" It could be that this luminosity is where the proportion of UCDs and GCs varies rapidly (Figure 3)), with neither population on its own having strong trends in size-luminosity, etc."," It could be that this luminosity is where the proportion of UCDs and GCs varies rapidly (Figure \ref{fig:hist}) ), with neither population on its own having strong trends in size-luminosity, etc."791 It is also an open question as to whether or not a significant population of UCDs exists at magnitudes fainter than Mj~—10., It is also an open question as to whether or not a significant population of UCDs exists at magnitudes fainter than $M_i \sim -10$.792" Moving on to another area of parameter space, Figure 6 shows the spectroscopy-based stellar populations analysis of M87 UCDs and Virgo dE nuclei from Paudeletal.(2010, 2011).."," Moving on to another area of parameter space, Figure \ref{fig:amr} shows the spectroscopy-based stellar populations analysis of M87 UCDs and Virgo dE nuclei from \citet{2010ApJ...724L..64P,2011MNRAS.413.1764P}."793" Before comparing these objects, it should be kept in mind that these UCDs are all found in the high-density surroundings of M87, while the nuclei are drawn from a broad range of environmental densities within Virgo."," Before comparing these objects, it should be kept in mind that these UCDs are all found in the high-density surroundings of M87, while the nuclei are drawn from a broad range of environmental densities within Virgo."794" Given the age-density correlation already mentioned for nuclei, the fairest point of comparison is between the UCDs and theolder nuclei."," Given the age-density correlation already mentioned for nuclei, the fairest point of comparison is between the UCDs and the nuclei."795" After taking this aspect into account, and keeping in mind that the luminosity-weighting in such spectroscopic analyses makes comparisons difficult to interpret, we notice a broad correspondence between the UCDs and dE nuclei in their age-metallicity relations (AMRs) and o-element abundance distributions (as a function of mean metallicity)."," After taking this aspect into account, and keeping in mind that the luminosity-weighting in such spectroscopic analyses makes comparisons difficult to interpret, we notice a broad correspondence between the UCDs and dE nuclei in their age-metallicity relations (AMRs) and $\alpha$ -element abundance distributions (as a function of mean metallicity)."796" The AMR for the UCDs and dE nuclei somehow conspires to result in a narrow color-magnitude track for both classes of object 5,, left panel)."," The AMR for the UCDs and dE nuclei somehow conspires to result in a narrow color-magnitude track for both classes of object (Figure \ref{fig:cmd}, , left panel)."797 'These comparisons reinforce the (Figuresuggestion from the CMD that most of the UCDs originate from dE nuclei., These comparisons reinforce the suggestion from the CMD that most of the UCDs originate from dE nuclei.798rere to sunaniarize them iu detail.,here to summarize them in detail.799 The main poiut is that ultimately all of these lossless compression echuiques face the same Shaunon eutropy linüt. and the only wav to achieve greater compression of noisy floating-point images is to use techuiques hat discard some of the noise.," The main point is that ultimately all of these lossless compression techniques face the same Shannon entropy limit, and the only way to achieve greater compression of noisy floating-point images is to use techniques that discard some of the noise."800 These methods are echuically “lossy because they do not exactly oeserve the pixel values. however. if only noise is discarded. then the compression cam still be Csidered lossless from a scientific stanudpoiut )ecause all the useful formation is retained.," These methods are technically “lossy” because they do not exactly preserve the pixel values, however, if only noise is discarded, then the compression can still be considered lossless from a scientific standpoint because all the useful information is retained."801 Tn the remainder of this article we describe a lossy compression technique for floatine-poit astrononucal images that provides au optimal conibination of speed. compression ratio. and preservation of information conteut.," In the remainder of this article we describe a lossy compression technique for floating-point astronomical images that provides an optimal combination of speed, compression ratio, and preservation of information content."802 It is faster and achieves auch higher compression than eeneric lossless fle compression algorithius like CZIP (Cailly&Adler1992).. vet it oxoduces no sjenificaut loss of information in the image when used appropriately.," It is faster and achieves much higher compression than generic lossless file compression algorithms like GZIP \citep{gailly}, yet it produces no significant loss of information in the image when used appropriately."803 Iu 2 wo describe oein detail the quantization aud conrpressiou techuiques that have been inipleimieuted in our publicly avaa.able aud. dnaee COLILDIYCSSIn utilitv programs., In \ref{s:methods} we describe in detail the quantization and compression techniques that have been implemented in our publicly available and image compression utility programs.804 Then iu 3 wedescribe he results of several experiments that demonstrate that astronomical floatiue-poiut nuages ca be compressed by up to a factor of 10 without significant loss of astrometric or photometric precision., Then in \ref{s:tests} we describe the results of several experiments that demonstrate that astronomical floating-point images can be compressed by up to a factor of 10 without significant loss of astrometric or photometric precision.805 Finally. 81 stuunarizes the results and gives recommendations for achieving the best conipressiou of astrouonical Mages.," Finally, \ref{s:discussion} summarizes the results and gives recommendations for achieving the best compression of astronomical images."806 The most coummon lossy compression technique for floating-point inages is to preprocess the pixel values by quantizing them iuto a snaller set of discrete values prior to applying a lossless conrpressionu aleorithiu., The most common lossy compression technique for floating-point images is to preprocess the pixel values by quantizing them into a smaller set of discrete values prior to applying a lossless compression algorithm.807 In the simplest case. the values are rounded into a erid of equally spaced floatiug-poiut levels.," In the simplest case, the values are rounded into a grid of equally spaced floating-point levels."808 This reduces the umber of different bit patterus in the nuage pixels (ic. reduces the cutropy in the image) and improves the efficiency of file compression programs Dike CGZIP which accumulate a dictionary of the most conumnion bit patterns iu the file aud represeut thems. using a shorter code in the compressed file.," This reduces the number of different bit patterns in the image pixels (i.e., reduces the entropy in the image) and improves the efficiency of file compression programs like GZIP which accumulate a dictionary of the most common bit patterns in the file and represent them using a shorter code in the compressed file."809 Watsou(2002) applied an analogous technique to integer nuages., \cite{watson2002} applied an analogous technique to integer images.810 In order to accommodate compression algoritlins. like Rice. that ouly operate on integer arravs. the quautized floating-point values are usually: represeuted by scaled iutegers so that the inage pixel values are approxinated by Note that this integer scaling technique was the ouly wav to represeut floatiug-poit images in the FITS data format (Πάνοetal.2001)/ before support for the IEEE floatine-poiut format was officially added in 1990.," In order to accommodate compression algorithms, like Rice, that only operate on integer arrays, the quantized floating-point values are usually represented by scaled integers so that the image pixel values are approximated by Note that this integer scaling technique was the only way to represent floating-point images in the FITS data format \citep{hanisch2001} before support for the IEEE floating-point format was officially added in 1990."811 As an aside. there are mauv articles iu the literature (c.e..Niecto-Santistebanctal.1999:Bernsteinetal.2010) that advocate using a square roof scaling function. iu part because the DPoissouiui shot uolse scales bv this same factor.," As an aside, there are many articles in the literature \citep[e.g.,][]{nieto1999, gowen2003, nicula2005, seaman2009, bernstein2010} that advocate using a square root scaling function, in part because the Poissonian shot noise scales by this same factor."812 What is usually not stated in these studies is that oxactieallv the same increase iu compression that is obtained after applying a square root scaling junction eau be obtained by linearly scalingel the jXxels iu the image by the same factor as is applied o the background. pixels dung the square root scaling., What is usually not stated in these studies is that practically the same increase in compression that is obtained after applying a square root scaling function can be obtained by linearly scaling the pixels in the image by the same factor as is applied to the background pixels during the square root scaling.813 Since the compression ratio is determined uaiulv by the noise in the backeround areas of the nuage (from equation 3)). the amount of scaling hat is applied to the relatively infrequent xieht jxels usually makes little difference to the overall conirpression ratio of he image.," Since the compression ratio is determined mainly by the noise in the background areas of the image (from equation \ref{eq:ratio2}) ), the amount of scaling that is applied to the relatively infrequent bright pixels usually makes little difference to the overall compression ratio of the image."814"o Iu experiments ou stated astronomical nuages. Derusteinetal.(2010) fouud that usine square-root scaling oulv produced significantly better compression than linear scalingi when more than of tle tageo pixels are affected by isolated bright objects or COSLUC raves,"," In experiments on simulated astronomical images, \cite{bernstein2010} found that using square-root scaling only produced significantly better compression than linear scaling when more than of the image pixels are affected by isolated bright objects or cosmic rays."815 White&Cocenfield(1999)— developed. the technique that forms the basis of the FITS tiled-Huaee compression format that is used here along with a few new refinements., \cite{white1999} developed the technique that forms the basis of the FITS tiled-image compression format that is used here along with a few new refinements.816 Each row of the image (or in principle. anv other rectangular “tile” iu the nuage) is compressed separately to provide fast random access to individual sections of an inage without having to uncompress the cutive image.," Each row of the image (or in principle, any other rectangular “tile” in the image) is compressed separately to provide fast random access to individual sections of an image without having to uncompress the entire image."817 Tn the case of floating-point images. the pixel," In the case of floating-point images, the pixel"818like Fornax ancl Draco where resolved. profiles are available (Mateo 1997: Ixlevna 2002).,like Fornax and Draco where resolved profiles are available (Mateo 1997; Kleyna 2002).819 As we were completing this work. Havashi (2002) posted a preprint addressing simular issues (and with similar conclusions).," As we were completing this work, Hayashi (2002) posted a preprint addressing similar issues (and with similar conclusions)."820 Their approach is complementary to the one we adopt here., Their approach is complementary to the one we adopt here.821 They do not analyse a fully consistent simulation of a Alilky Way halo and. its substructure. nor do they compare in detail with the kinematic structure of the observed. dwarfs.," They do not analyse a fully consistent simulation of a Milky Way halo and its substructure, nor do they compare in detail with the kinematic structure of the observed dwarfs."822 On the other hand. they carry out a much more complete ancl reliable analysis of the structural. evolution of individual satellite substructures mn is possible with our own simulation data.," On the other hand, they carry out a much more complete and reliable analysis of the structural evolution of individual satellite substructures than is possible with our own simulation data."823 We will use reir results below to provide an independent check on the =nost uncertain aspect of our own simulations — whether rev give reliable estimates for the inner 7core structure ol satellite subhalos., We will use their results below to provide an independent check on the most uncertain aspect of our own simulations – whether they give reliable estimates for the inner “core” structure of satellite subhalos.824 In the next section we will give a brief description of 10 simulations we have carried out. the methods we have used to find substructures and to characterise their potential wells. and the checks we have mace on the reliability of these measures.," In the next section we will give a brief description of the simulations we have carried out, the methods we have used to find substructures and to characterise their potential wells, and the checks we have made on the reliability of these measures."825 Section 3 then shows how to predict the line-of-sight. velocity dispersion profile for a chwarf galaxy of given spatial structure within a given. potential well., Section 3 then shows how to predict the line-of-sight velocity dispersion profile for a dwarf galaxy of given spatial structure within a given potential well.826 We apply the technique to the 11. known satellites of the Milky Way and the 20 deepest. satellite potential wells of our highest resolution simulation., We apply the technique to the 11 known satellites of the Milky Way and the 20 deepest satellite potential wells of our highest resolution simulation.827 Section 4 discusses our results. their principal remaining uncertainties and their implications.," Section 4 discusses our results, their principal remaining uncertainties and their implications."828" We work with a μαι A-cominated Cold. Dark Matter universe. with matter density (34,=0.3. cosmological constant O4=0.7. expansion rate 44)—70 km !Mpe. +. index of the initial lluctuation power spectrum »=I. and present-davy IHuctuation amplitude m=0.9."," We work with a flat $\Lambda$ -dominated Cold Dark Matter universe, with matter density $\Omega_{\rm m}=0.3$, cosmological constant $\Omega_{\Lambda}=0.7$, expansion rate $H_{0}=70~$ km $^{-1}$ $^{-1}$ , index of the initial fluctuation power spectrum $n=1$, and present-day fluctuation amplitude $\sigma_8=0.9$."829 We begin with a dark matter simulation of a “typical” region of the Universe (N—610. particle mass ~2107 AZ.) for which the techniques of Springel (2001b. hereafter SWTIX) have been used to follow the formation of the galaxy population (Stoehr 2002. in preparation).," We begin with a dark matter simulation of a “typical” region of the Universe $N\sim 6\times 10^7$, particle mass $\sim 2\times 10^8M_\odot$ ) for which the techniques of Springel (2001b, hereafter SWTK) have been used to follow the formation of the galaxy population (Stoehr 2002, in preparation)."830 We identify a relatively isolated 7Nkv Way like” galaxy. and resimulate its halo at a series of higher resolutions. again using techniques from SWF and the N-body code (Springel. Yoshida White 2001a).," We identify a relatively isolated “Milky Way like” galaxy and resimulate its halo at a series of higher resolutions, again using techniques from SWTK and the $N$ -body code (Springel, Yoshida White 2001a)."831 In the simulations GAO. GAL ancl CAD analvsed. in this paper the resimulatecl halo has 13603. 123775 and 1055083 particles respectively within rego. the radius enclosing a mean density 200 times the critical value.," In the simulations GA0, GA1 and GA2 analysed in this paper the resimulated halo has 13603, 123775 and 1055083 particles respectively within $r_{200}$, the radius enclosing a mean density 200 times the critical value."832 The density profiles of these three. resimulations agree well and are accurately fit by the NEW formula with concentration c=10 (Navarro. Frenk White 1997).," The density profiles of these three resimulations agree well and are accurately fit by the NFW formula with concentration $c=10$ (Navarro, Frenk White 1997)."833 We show the corresponding circular velocity curves in Figure la., We show the corresponding circular velocity curves in Figure 1a.834 ‘These have been scaled down by a factor of 0.91 in velocity and. radius (corresponding to a factor of 0.74 in mass. but unchanged: density ancl time scales) so that they peak at 220 km/s. With this scaling. dark matter particle masses are LS.107. L9.10° and 2.0.10AZ. and Plummer equivalent softening lengths are 1.5. 1.0 and 0.49 kpe in GAO. CAL and GAP. respectively.," These have been scaled down by a factor of 0.91 in velocity and radius (corresponding to a factor of 0.74 in mass, but unchanged density and time scales) so that they peak at 220 km/s. With this scaling, dark matter particle masses are $1.8\times10^8$, $1.9\times10^7$ and $2.0\times10^6 M_\odot$, and Plummer equivalent softening lengths are 1.8, 1.0 and 0.49 kpc in GA0, GA1 and GA2, respectively."835 In all three 72605270 kpc., In all three $r_{200}\approx 270~$ kpc.836 Note hat since the Alilky Way's stars contribute significantly to its measured rotation velocity. our chosen scaling probably xroduces too large a mass for the Milky. Way's halo and thus also for substructures within it.," Note that since the Milky Way's stars contribute significantly to its measured rotation velocity, our chosen scaling probably produces too large a mass for the Milky Way's halo and thus also for substructures within it."837 Fhis is conservative for the »urposes of this paper., This is conservative for the purposes of this paper.838 We identify sclf-bounc substructures within our final jdos using the procedure described. in detail w SWRA., We identify self-bound substructures within our final halos using the procedure described in detail by SWTK.839 In. Figure. lh we compare the number. of substructures found within reo in cach of our simulations., In Figure 1b we compare the number of substructures found within $r_{200}$ in each of our simulations.840 For cach we plot cumulative abuncdances down to a mass corresponding to 20 particles., For each we plot cumulative abundances down to a mass corresponding to 20 particles.841 Clearly the agreement is good., Clearly the agreement is good.842 For example. down to 410A4.. the 20 particle limit for CLAO. we find 5. 7 and 2 subhalos in GAO. COAL and GA. respectively. well within the lluetuations expected for Poisson statistics.," For example, down to $4\times 10^9M_\odot$, the 20 particle limit for GA0, we find 5, 7 and 2 subhalos in GA0, GA1 and GA2, respectively, well within the fluctuations expected for Poisson statistics."843 Down to the 20 particle limit for CAI (4.LOA.) there are 28 and 27 subalos in GAL and CAD., Down to the 20 particle limit for GA1 $4\times 10^8M_\odot$ ) there are 28 and 27 subalos in GA1 and GA2.844 We have also verified that our cumulative function of peak velocities is consistent with that of Font (2001)., We have also verified that our cumulative function of peak velocities is consistent with that of Font (2001).845 For cach subhalo we define the centre as the position of the densest particle. where densities are evaluated. using an SPL smoothing kernel.," For each subhalo we define the centre as the position of the densest particle, where densities are evaluated using an SPH smoothing kernel."846 We then calculate a circular velocity curve as V4(r)=(GALLO)fte where A(r) is the total mass within r of this centre., We then calculate a circular velocity curve as $V_c(r) = (GM(r)/r)^{1/2}$ where $M(r)$ is the total mass within $r$ of this centre.847 In. almost all of the more massive subhalos. these curves rise from the centre. peak at a distance of a few kpc. and then fall for a while before eventually rising again because of the contribution from the smooth halo.," In almost all of the more massive subhalos, these curves rise from the centre, peak at a distance of a few kpc, and then fall for a while before eventually rising again because of the contribution from the smooth halo."848 Fitting such curves we can define a maximum circular velocity and a radius at which it is achieved for each subhalo., Fitting such curves we can define a maximum circular velocity and a radius at which it is achieved for each subhalo.849 In Figure 1c we plot these two quantities against each other for all subhalos in GAL and. GA with more than 100 ancl 300. particles. respectively.," In Figure 1c we plot these two quantities against each other for all subhalos in GA1 and GA2 with more than 100 and 300 particles, respectively."850 There is a weak correlation but no clear tenceney for the GAL subhalos to be less concentrated (ie. to have larger μις al given Vua) than those in CLA2., There is a weak correlation but no clear tendency for the GA1 subhalos to be less concentrated (i.e. to have larger $r_{\rm max}$ at given $V_{\rm max}$ ) than those in GA2.851 By comparing the evolution of the two simulations in detail it is possible to identify counterparts in GA2 for all the eight GAL subhalos plotted in Figure le., By comparing the evolution of the two simulations in detail it is possible to identify counterparts in GA2 for all the eight GA1 subhalos plotted in Figure 1c.852 Four of these lie within soo in CLX2. and the corresponding pairs of points are indicated with ellipses in the plot.," Four of these lie within $r_{200}$ in GA2, and the corresponding pairs of points are indicated with ellipses in the plot."853" Phere is &ood agreement between the (V,Pie.) values measured in the two simulations despite the factor of 10 difference in mass resolution."," There is good agreement between the $(V_{max},r_{max})$ values measured in the two simulations despite the factor of 10 difference in mass resolution."854 In Figure Id we plot circular velocity curves for some of the 20 GA2 subhalos with the largest values of Vias., In Figure 1d we plot circular velocity curves for some of the 20 GA2 subhalos with the largest values of $V_{\rm max}$ .855 Even the least massive of these has more than 300 particles. and we have checked. that they all have maintained their structure with relatively little change since at least 2=0.4.," Even the least massive of these has more than 300 particles, and we have checked that they all have maintained their structure with relatively little change since at least $z=0.4$."856 lt is noticeable that these circular velocity curves have narrower peaks than the NEW form. so we have fitted them with parabolae adjusting the constant e to get a good fit ator<<rua.," It is noticeable that these circular velocity curves have narrower peaks than the NFW form, so we have fitted them with parabolae adjusting the constant $a$ to get a good fit at $r<r_{\rm max}$."857 We find values for @ ranging from0.25 to 0.7 with a median of 0.45., We find values for $a$ ranging from0.25 to 0.7 with a median of 0.45.858" ""Phese fits are shown as dotted curves in Figure ld. and we use themto represent the circular. velocity"," These fits are shown as dotted curves in Figure 1d, and we use themto represent the circular velocity"859The author would like to thank CELA for funding through a National Fellowship.,The author would like to thank CITA for funding through a National Fellowship.860CRES'T is gratefully acknowledged.,CREST is gratefully acknowledged.861 We would like to thank he anonymous referee for constructive comments on the nianuscript., We would like to thank the anonymous referee for constructive comments on the manuscript.862 Funding for the SDSS and SDSS-LE has been provided » the Alfred DP. Sloan Foundation. the Participating Institutions. the National Science. Foundation. the U.S. Department of Energy. the National Acronautics and Space Administration. the Japanese Monbukagakusho. the Max anck Society. and the σος Education Funding Council or England.," Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England."863 Phe SDSS Web Site is httpi/www.scdss.org/., The SDSS Web Site is http://www.sdss.org/.864(c.g. bv starquakes or stellar oscillations) causing particle oecipitation towards the star and hence bursts.,(e.g. by starquakes or stellar oscillations) causing particle precipitation towards the star and hence bursts.865" Besicles external triggers. it has also been suggested (2) that IRIUVIS are old. pulsars approaching the ""death valles (2)... where »ulsar emission is thought to switch olf."," Besides external triggers, it has also been suggested \citep{zhang07} that RRATs are old pulsars approaching the `death valley' \citep{cr93}, where pulsar emission is thought to switch off."866 Of the 56 known RRATSs (2).. 1458 is the most wrolilic. brightest and thus best-stucdied source.," Of the 56 known RRATs \citep{keane10a}, $-$ 1458 is the most prolific, brightest and thus best-studied source."867 1458 las à rotation period of 4.263 s and shows 3 ms pulses every 3 mmin. amounting to 1I s of radio emission per dav.," $-$ 1458 has a rotation period of $4.263$ s and shows $\sim3$ ms pulses every $\sim3$ min, amounting to $\sim1$ s of radio emission per day."868 From its measured. period derivative. 1458 has an inferred magnetic field strength of B=5107 G. jus below that of the magnetars. providing another link between these two classes of neutron stars.," From its measured period derivative, $-$ 1458 has an inferred magnetic field strength of $B=5\times10^{13}$ G, just below that of the magnetars, providing another link between these two classes of neutron stars."869 As well as in the raclio (ος. 2)). 1458 has been observed in N-ravs on severa occasions (2.. 7.. 2)).," As well as in the radio (e.g. \citealt{lyne09}) ), $-$ 1458 has been observed in X-rays on several occasions \citealt{reynolds06}, \citealt{mclaughlin07}, \citealt{rea09}) )."870 The X-ray observations show a therma spectrum Consistent with what is expected [from a cooling neutron star. and the X-ray flux exhibits the same rotation period as derived from. radio observations.," The X-ray observations show a thermal spectrum consistent with what is expected from a cooling neutron star, and the X-ray flux exhibits the same rotation period as derived from radio observations."871 Observations of 31519 1458 at wavelengths other than radio and. X-ray are also highly. desirable in order to measure the spectra enerey distribution and help constrain the pulsar emission mechanism., Observations of $-$ 1458 at wavelengths other than radio and X-ray are also highly desirable in order to measure the spectral energy distribution and help constrain the pulsar emission mechanism.872 Deep infrared observations have revealed very tentative evidence for à counterpart at Aa~21 magnitude (?).., Deep infrared observations have revealed very tentative evidence for a counterpart at $K_{\mathrm{s}}\sim 21$ magnitude \citep{rea10}.873 There is no evidence of an optical counterpart. bu this could. be due to the rather modest magnitude limit of ἐξ το.," There is no evidence of an optical counterpart, but this could be due to the rather modest magnitude limit of $I=17.5$ \citep{reynolds06}."874 ‘Taking longer exposures to £o deeper. however. is no necessarily the best solution. as the IRIUXEsS may have very [aint persistent optical/Ilt emission and only emit strongly. at these wavelengths duringbursts’.," Taking longer exposures to go deeper, however, is not necessarily the best solution, as the RRATs may have very faint persistent optical/IR emission and only emit strongly at these wavelengths during."875 In this case. the bes strategy would be to reduce the contribution of the sky anc take a continuous sequence of extremely short. exposures on a large-aperture telescope covering a number of burs eveles in order to catch a burst in one or two of the frames.," In this case, the best strategy would be to reduce the contribution of the sky and take a continuous sequence of extremely short exposures on a large-aperture telescope covering a number of burst cycles in order to catch a burst in one or two of the frames."876 In paper L (?).. we tried such an approach using the high- CCD camera ULTRACAAL (2) on the 4.2-m William Lerschel Telescope (LUE).," In paper I \citep{dhillon06}, we tried such an approach using the high-speed CCD camera ULTRACAM \citep{dhillon07b} on the 4.2-m William Herschel Telescope (WHT)."877 We found no evidence for bursts brighter than ;=16.6., We found no evidence for bursts brighter than $i'=16.6$.878 This limit may not appear to be particularly deep. but it must be remembered. that. it refers to the burst magnitude. not the persistent magnitucle.," This limit may not appear to be particularly deep, but it must be remembered that it refers to the burst magnitude, not the persistent magnitude."879 In fact. there is only one way in. which it is possible to significantly. improve upon the ULTICACALM|WIPE burst limit: observing in the optical simultaneously with the radio. which would allow just those optical frames coincident with the clispersion-correctecd radio bursts to be searched. for optical bursts.," In fact, there is only one way in which it is possible to significantly improve upon the ULTRACAM+WHT burst limit: observing in the optical simultaneously with the radio, which would allow just those optical frames coincident with the dispersion-corrected radio bursts to be searched for optical bursts."880 In this paper we report on such observations. obtained with ULTILACAM on the WITT and the 3.52m New Technology Telescope (NEL). simultaneously with the 762m Lovell Telescope at Jodrell Bank Observatory (JBO).," In this paper we report on such observations, obtained with ULTRACAM on the WHT and the 3.5-m New Technology Telescope (NTT), simultaneously with the 76-m Lovell Telescope at Jodrell Bank Observatory (JBO)."881 The observations of.J 1458 were obtained on the nights of 2008 August 6 AVIET|ULTIUACAM and BO) and 2010 June 14 (CNTE|UELTILACAAM and JBO)., The observations of $-$ 1458 were obtained on the nights of 2008 August 6 (WHT+ULTRACAM and JBO) and 2010 June 14 (NTT+ULTRACAM and JBO).882 In addition to shot noise from any object Lux. every ULTRACAAL cata frame has noise contributions from the sky and CCD readout noise.," In addition to shot noise from any object flux, every ULTRACAM data frame has noise contributions from the sky and CCD readout noise."883 The sky noise can be reduced bv reducing the exposure time. but the reacout noise cannot.," The sky noise can be reduced by reducing the exposure time, but the readout noise cannot."884 Hence it makes sense to expose each data frame for as long as the readout noise is the dominant noise source. thereby maximising the chances of observing a burst in a single [rame without significantly: degracling the signal-to-noise ratio of the data.," Hence it makes sense to expose each data frame for as long as the readout noise is the dominant noise source, thereby maximising the chances of observing a burst in a single frame without significantly degrading the signal-to-noise ratio of the data."885 ULPRACAAL was hence used in drift mode. which gives the highest frame rate (see 2)). with one window centred on the X-ray position of the RRAT (2). and the other on a nearby comparison star. as shown in the top panel of Fig. 1..," ULTRACAM was hence used in drift mode, which gives the highest frame rate (see \citealt{dhillon07b}) ), with one window centred on the X-ray position of the RRAT \citep{rea09} and the other on a nearby comparison star, as shown in the top panel of Fig. \ref{fig:finding_charts}."886 An SDSS 7 filter and the slow readout. speed: were used. in the red. arm of ULTILACAM on both nights. and the focal-plane mask was used to prevent light. from. bright stars and the sky. from contaminating the windows (see 2)).," An SDSS $i'$ filter and the slow readout speed were used in the red arm of ULTRACAM on both nights, and the focal-plane mask was used to prevent light from bright stars and the sky from contaminating the windows (see \citealt{dhillon07b}) )."887 On 2008 August 6. the CCD windows were unbinned and. of size 60GO pixels. where cach pixel on the ΜΗ is 0.37.," On 2008 August 6, the CCD windows were unbinned and of size $60\times60$ pixels, where each pixel on the WHT is 0.3”."888 A total of 1125588 frames were obtained between 21:11:2:49 UTC on this night. cach of mms exposure time and. maims dead time.," A total of 588 frames were obtained between 21:11–22:49 UTC on this night, each of ms exposure time and ms dead time."889 The data were obtained. in photometric conditions. with no Moon and secing of 0.97.," The data were obtained in photometric conditions, with no Moon and seeing of 0.9”."890 On 2010 June 1H. the CCD windows were binned 2.2 and of size 150.150 pixels. where each unbinned pixel on the NLL is 0.357.," On 2010 June 14, the CCD windows were binned $2\times2$ and of size $150\times150$ pixels, where each unbinned pixel on the NTT is 0.35”."891 A total of 682274 frames were obtained between 01:3202:14. UTC and 03:46 UTC: the gap in the middle of the run was due to a GRB override observation (2)., A total of 274 frames were obtained between 01:32–02:14 UTC and 02:45--03:46 UTC; the gap in the middle of the run was due to a GRB override observation \citep{dhillon10}.892 Each frame had an exposure time of mmis and a dead time of mms., Each frame had an exposure time of ms and a dead time of ms.893" Conditions on this night were not as good as in 2008. with secing of 1.9"" a the start of the run. dropping to 1.27 at the end."," Conditions on this night were not as good as in 2008, with seeing of 1.9” at the start of the run, dropping to 1.2” at the end."894 The nigh was photometric and there was no Moon., The night was photometric and there was no Moon.895 Simultaneous racio observations at JBO were made a an observing frequency. of 1.4 Gilz using a dual-channe cryogenic receiver sensitive to [ο- and righthanded circular polarisation., Simultaneous radio observations at JBO were made at an observing frequency of $1.4$ GHz using a dual-channel cryogenic receiver sensitive to left- and right-handed circular polarisation.896 In 2008 an analogue filterbank (APB) backen was used with an observing bandwidth consisting of 1 MlIz channels and à time sampling of 100 yes. Since 20090. pulsar observations at JBO have upgraded to using a cigita filterbank (DEB) backend.," In 2008 an analogue filterbank (AFB) backend was used with an observing bandwidth consisting of $64\times1$ MHz channels and a time sampling of $100$ $\mu$ s. Since 2009, pulsar observations at JBO have upgraded to using a digital filterbank (DFB) backend."897 Thus the 2010 observations usec the DED with a bandwidth of L024.0.5 AUIz channels. half of which (250 Mllz) were usable. and a time sampling of 1 ms.," Thus the 2010 observations used the DFB with a bandwidth of $1024\times0.5$ MHz channels, half of which $\sim250$ MHz) were usable, and a time sampling of $1$ ms."898 In both cases. the polarisations were summed to eive total intensity. (Stokes D) and the output was either l-bit digitised. (in 2008) or 2-bit digitised (in 2010).," In both cases, the polarisations were summed to give total intensity (Stokes I) and the output was either 1-bit digitised (in 2008) or 2-bit digitised (in 2010)."899 In th radio datasets the zero cispersion-measure subtraction algorithm (27). was used in an attempt to remove sources of broadband: radio frequeney interference. as. described w 7.," In both radio datasets the zero dispersion-measure subtraction algorithm \citep{eatough09} was used in an attempt to remove sources of broadband radio frequency interference, as described by \citet{keane10}."900 Phe 2008 dataset. sulfers less from radio frequency interference than the 2010 observations due to the narrower xixdwidth of the former., The 2008 dataset suffers less from radio frequency interference than the 2010 observations due to the narrower bandwidth of the former.901 Phe pulse times of arrival at JBO were then obtained. by eross-correlating the single-oulse profiles with a smooth single-component template., The pulse times of arrival at JBO were then obtained by cross-correlating the single-pulse profiles with a smooth single-component template.902 In addition to the light travel time [rom the source to the Earth. raclio signals traversing the interstellar medium suller an extra Lrequencey-cdependent delay of the form: ων=4150 sU. where f is the observing frequency in. MlIz. and DAL is the dispersion measure (the integrated electron density along the line of sight to the source measured. by convention in units of cmà pc).," In addition to the light travel time from the source to the Earth, radio signals traversing the interstellar medium suffer an extra frequency-dependent delay of the form: $t_{\mathrm{DM}}=4150\;\mathrm{s}\frac{DM}{f^2}$ , where $f$ is the observing frequency in MHz, and $DM$ is the dispersion measure (the integrated electron density along the line of sight to the source measured by convention in units of $\mathrm{cm}^{-3}\,\mathrm{pc}$ )."903" At 14 Cllz. this delay. is 415 ms for JISIO 1458 (MAL=196.0(4)em"" pe) with respect to a signal at infinite frequency. and cillers bv 38 ms (250 ms) between thetop and bottom of our band for the 2008 (2010) observation."," At $1.4$ GHz, this delay is $415$ ms for $-$ 1458 $DM=196.0(4)\;\mathrm{cm}^{-3}\,\mathrm{pc}$ ) with respect to a signal at infinite frequency, and differs by $38$ ms $250$ ms) between thetop and bottom of our band for the 2008 (2010) observation."904 The optical signal is not subject to such a delay., The optical signal is not subject to such a delay.905 Thus the radio signal is de-dispersed to infinite, Thus the radio signal is de-dispersed to infinite906Cluster (ΟΝΟ see below). there is a spread of radius at a given Tir. Consistent with the luminosity spread. observed.,"Cluster (ONC – see below), there is a spread of radius at a given $T_{\rm eff}$, consistent with the luminosity spread observed."907 Llowever. this paper also cautions that a spread. of radius may not imply a spread in age.," However, this paper also cautions that a spread of radius may not imply a spread in age."908 For example. some models suggest that co-eval stars with dillering carly accretion histories can still have significantly dillerent. radii several million vears later (Tout. Livio Bonnell 1999: Baralle. Chabrier Gallardo 2009).," For example, some models suggest that co-eval stars with differing early accretion histories can still have significantly different radii several million years later (Tout, Livio Bonnell 1999; Baraffe, Chabrier Gallardo 2009)."909 ltesolving this issue is important. because ages from the LR cdiiagrams of voung SEIts are used to investigate different star formation scenarios. calculate star formation rates and set the clock for the clispersal of circumstellar material and the formation of planetary svstems.," Resolving this issue is important because ages from the HR diagrams of young SFRs are used to investigate different star formation scenarios, calculate star formation rates and set the clock for the dispersal of circumstellar material and the formation of planetary systems."910 For example. the inference of a large age spread in SERs has been taken (by some) as evidence against a “fast” mode of star formation governed by the rapid. dissipation of supersonic turbulence (??77).. and used instead to support a “slow” moce of star formation. where collapse is regulated. by the ambipolar cilfusion of strong magnetic fields (?2)..," For example, the inference of a large age spread in SFRs has been taken (by some) as evidence against a “fast” mode of star formation governed by the rapid dissipation of supersonic turbulence \citep{elmegreen00, hartmannsfr01, vazquez05}, and used instead to support a “slow” mode of star formation, where collapse is regulated by the ambipolar diffusion of strong magnetic fields \citep{tassis04, tan06}."911 The ONC is one of the best-stucdied nearby SET (?7).," The ONC is one of the best-studied nearby SFRs \citep{jones88,912hillenbrand97}."913. ? used the LR diagram to deduce that star formation in the ONC began at least MMSyr ago and has acceleratec up to the present day., \citet{palla99} used the HR diagram to deduce that star formation in the ONC began at least Myr ago and has accelerated up to the present day.914 2. extended this work to show that the inferred. star formation history is similar in both the outer and inner parts (the ‘Trapezitun) of the ONC and for stars of all masses., \citet{huff06} extended this work to show that the inferred star formation history is similar in both the outer and inner parts (the Trapezium) of the ONC and for stars of all masses.915 Vhese authors hypothesize that the ONC forme rom a cloud supported by mildly clissipative turbulence. which collapsed globally in a quasi-static. but accelerating ashion over MMyvr.," These authors hypothesize that the ONC formed from a cloud supported by mildly dissipative turbulence, which collapsed globally in a quasi-static, but accelerating fashion over Myr."916 Contrary to this. ? and ? argue tha he close agreement between the kinematies of the stars anc molecular gas in the ONC implies that the ONC is vounger han a crossing time (: 1MMyrb).," Contrary to this, \citet{furesz08} and \citet{tobin09} argue that the close agreement between the kinematics of the stars and molecular gas in the ONC implies that the ONC is younger than a crossing time $\leq9171$ Myr)."918 Phe ONC LR: diagram ias recently been updated ancl improved by 2? (hereafter referred to as DRO). who present. revised determinations of uminosities and Zr aud derive the distribution of members in the massage plane using evolutionary models.," The ONC HR diagram has recently been updated and improved by \citet{dario10b} (hereafter referred to as DR10), who present revised determinations of luminosities and $T_{\rm eff}$ and derive the distribution of members in the mass-age plane using evolutionary models."919 They ound a mean age of 3MMyvr. but with a very similar dispersion in Luminosity. ancl hence inferred age spreads. to he earlier studies.," They found a mean age of Myr, but with a very similar dispersion in luminosity, and hence inferred age spreads, to the earlier studies."920 Ifthe ONC is very voung and undergoing rapid collapse. hat would be dillicult to reconcile with the age spread and mean age found on the basis of the LIC diagram by ? and DRO.," If the ONC is very young and undergoing rapid collapse, that would be difficult to reconcile with the age spread and mean age found on the basis of the HR diagram by \citet{palla99} and DR10."921 In this paper the reality of the ONC age spread is re-examined using the crude. but independent: clock alforded: by the time-dependent: dispersal of cireumstellar material around voung PAIS stars.," In this paper the reality of the ONC age spread is re-examined using the crude, but independent clock afforded by the time-dependent dispersal of circumstellar material around young PMS stars."922 In Section 2 the methoes and the observational material are explained., In Section 2 the methods and the observational material are explained.923 The results are presented in Section 3 and examüned with a simple interpretive model in Section d., The results are presented in Section 3 and examined with a simple interpretive model in Section 4.924 Section 5 discusses the results and their implications for PAIS age determinations., Section 5 discusses the results and their implications for PMS age determinations.925 Section 6 provides a summary., Section 6 provides a summary.926 lt is well known that at the earliest. ages. most. if not all. PAIS stars are surrounded by optically thick cireumstellar discs.," It is well known that at the earliest ages, most, if not all, PMS stars are surrounded by optically thick circumstellar discs."927 These can be revealed. either by the infrared. [ux emitted. by warm dust in the disc. or the signatures of gas accretion [rom the disc onto the star.," These can be revealed either by the infrared flux emitted by warm dust in the disc, or the signatures of gas accretion from the disc onto the star."928 Groups of stars in voung clusters and SERs can be used to determine the timescale for the dispersal of inner disc material. traced by near-infrared. excesses.," Groups of stars in young clusters and SFRs can be used to determine the timescale for the dispersal of inner disc material, traced by near-infrared excesses."929 Plotting the fraction of stars with a Ax-band excess versus the mean age (deduced from the Hi diagram) of clusters. suggests that half of PAIS stars lose their inner discs in about MMyr ane that the timescale for almost all stars to lose their disces is about AlAIve (2)..," Plotting the fraction of stars with a $K$ -band excess versus the mean age (deduced from the HR diagram) of clusters, suggests that half of PMS stars lose their inner discs in about Myr and that the timescale for almost all stars to lose their discs is about Myr \citep{hillenbrand05}."930 Observations at these relatively short wavelengths may not produce a complete census of dises (seethediscussionin?).. however whilst?) found somewhat higher disc frequencies using dyL excess as à disc indicator. the derived. disc dispersal timescale was similar.," Observations at these relatively short wavelengths may not produce a complete census of discs \citep[see931the discussion in][]{lada00}, however whilst \citet{haisch01} found somewhat higher disc frequencies using $K-L$ excess as a disc indicator, the derived disc dispersal timescale was similar."932 This work has now been expanded extensively using more sensitive Spitzer data. but with little change in the overall conclusion.," This work has now been expanded extensively using more sensitive Spitzer data, but with little change in the overall conclusion."933 Fhere is à good. correlation. between WoL excesses at wavelengths of jii and. excesses at the longer pmi wavelengths probed. by Spitzer., There is a good correlation between $K-L$ excesses at wavelengths of $\mu$ m and excesses at the longer $\mu$ m wavelengths probed by Spitzer.934 Additional. data from more clusters (c.g.secτο) has strengthened the conclusion that the fraction of stars with primordial clises declines with age. such that most clises have dispersed. after MMyr. although a few per cent of stars maintain some circumstellar material in clusters with an age of ~LOAIAIve.," Additional data from more clusters \citep[e.g. see][]{hernandez08, kennedy09} has strengthened the conclusion that the fraction of stars with primordial discs declines with age, such that most discs have dispersed after Myr, although a few per cent of stars maintain some circumstellar material in clusters with an age of $\simeq 10$ Myr."935 In principle the declining disc fraction with age seen in an ensemble of clusters could. be used. as a means of constraining any age spread within a single cluster., In principle the declining disc fraction with age seen in an ensemble of clusters could be used as a means of constraining any age spread within a single cluster.936 However. it is not clear to what extent the fraction of stars with discs in a single cluster is determined. by the disc lifetime or a spread of ages within that cluster.," However, it is not clear to what extent the fraction of stars with discs in a single cluster is determined by the disc lifetime or a spread of ages within that cluster."937 dise fraction hat decreases with mean cluster age could. be produced wea range of dise lifetimes in increasinglv elderly but strictly coeval cluster populations., A disc fraction that decreases with mean cluster age could be produced by a range of disc lifetimes in increasingly elderly but strictly coeval cluster populations.938 On the other hand. the rend in dise fraction could. also be explained if the eluster populations had a spread of ages. with clusters of increasing mean age possessing larger proportions of stars older than some unique disc lifetime.," On the other hand, the trend in disc fraction could also be explained if the cluster populations had a spread of ages, with clusters of increasing mean age possessing larger proportions of stars older than some unique disc lifetime."939 These two possibilities: would wave clilferent signatures in the present-day. HII diagram and in the comparative age distributions of stars with and without disces., These two possibilities would have different signatures in the present-day HR diagram and in the comparative age distributions of stars with and without discs.940 For the first. possibility we would expect to see no luminosity spread. in the LR diagram beyond. that contributed. by astrophysical scatter. (παν. variability ete.)," For the first possibility we would expect to see no luminosity spread in the HR diagram beyond that contributed by astrophysical scatter (binarity, variability etc.)"941 and observational uncertainties. and no correlation between the presence of a dise and. HIIS diagram. position.," and observational uncertainties, and no correlation between the presence of a disc and HR diagram position."942 Llowever. for the second possibility we would expect a clear distinction in the LR diagram and inferred age distributions between voung stars with disces ancl older stars that. had lost their clises.," However, for the second possibility we would expect a clear distinction in the HR diagram and inferred age distributions between young stars with discs and older stars that had lost their discs."943 For a more general case between these two extremes (Le. an age spread.and a range of disc lifetimes) we would expect to see a strong correlation. between age determined from the LR diagram and the presence of a disc whenever the age spread becomes comparable to. or exceeds the mean dise lifetime.," For a more general case between these two extremes (i.e. an age spread a range of disc lifetimes) we would expect to see a strong correlation between age determined from the HR diagram and the presence of a disc whenever the age spread becomes comparable to, or exceeds the mean disc lifetime."944 ‘To illustrate this argument. Fig.," To illustrate this argument, Fig."945 1. shows a simulation using a mocel that is explored in more detail in Section 4., \ref{showmodel} shows a simulation using a model that is explored in more detail in Section 4.946 ]t is assumed. (for the purposes of demonstration) that the observed. distribution of ages from the 111. diagram can be represented as log-normal in age (a reasonable approximation for the ONC discussed further in Section +) with a mean log age of 6.2 (in vears). à dispersion a= dex. and that this dispersion. is. formed. from. the quacrature sum of observational uncertainties. binarity. variability (ete.)," It is assumed (for the purposes of demonstration) that the observed distribution of ages from the HR diagram can be represented as log-normal in age (a reasonable approximation for the ONC discussed further in Section 4) with a mean log age of 6.2 (in years), a dispersion $\sigma = 0.4$ dex, and that this dispersion is formed from the quadrature sum of observational uncertainties, binarity, variability (etc.)"947 and a separate contribution due to a, and a separate contribution due to a948 and a separate contribution due to a , and a separate contribution due to a949 and a separate contribution due to a r, and a separate contribution due to a950 and a separate contribution due to a re, and a separate contribution due to a951 and a separate contribution due to a rea, and a separate contribution due to a952 and a separate contribution due to a read, and a separate contribution due to a953 , 954wwhich iuplies. at a distance of 8.5 kpc. a luminosity of 1.2«107 (for 3.1s1079 iu 2-10 keV).,"which implies, at a distance of 8.5 kpc, a luminosity of $1.2\times10^{37}$ (or $3.4\times10^{36}$ in 2-10 keV)."955 The 2-10 keV flux is lower than that measured with WEC four davs earlier., The 2-10 keV flux is lower than that measured with WFC four days earlier.956 The column density ΑΠ is rather mseusitive to the mocel for the contiuuua excep when the Comptonized spectra is considered., The column density $N_{\rm H}$ is rather insensitive to the model for the continuum except when the Comptonized spectrum is considered.957 It lies. between 0.32ον and. 107704022 27., It lies between 0.32 and $\times10^{22}$ $^{-2}$.958 Thisqo range is. consistent with the value resulting from the interstellar reddening to NCC 6110: for Ejy=1.00250.10 (Ortolani et al., This range is consistent with the value resulting from the interstellar reddening to NGC 6440: for $E_{\rm B-V}=1.00\pm0.10$ (Ortolani et al.959 1991). Ay=3.1040.31 aud Ny=(1.79£0.1)x1024.=(5.5£0.6).1073 ? (according to the conversion of sly to Ny by Predehl Schinitt 1995).," 1994), $A_{\rm V}=3.10\pm0.31$ and $N_{\rm H}=(1.79\pm0.1)\times10^{21}A_{\rm V}=(5.5\pm0.6)\times10^{21}$ $^{-2}$ (according to the conversion of $A_{\rm V}$ to $N_{\rm H}$ by Predehl Schmitt 1995)."960 Cliaistian Swank (1997) successfully modeled the 45 to 20 keV spectra of 15 LAINBs by unsaturated Comptonization through a parametrization with a cutoff oower law., Christian Swank (1997) successfully modeled the 0.5 to 20 keV spectra of 45 LMXBs by unsaturated Comptonization through a parametrization with a cutoff power law.961 A comparison of the parameter values for wwith those found by Christian Swank shows that the oower law index is normal for a burster., A comparison of the parameter values for with those found by Christian Swank shows that the power law index is normal for a burster.962 The value for Eg is rather high., The value for $E_{\rm fold}$ is rather high.963 The values for the 8 bursters listed w Chiistian Swank range between 5.3 aud 25.0 keV. However. it should be noted that there is likely to he a selection effect in this parameter range because the upper )oundary in the data is oulv 20 sev. There are a few bursters which have beeu measured up to lhuudreds of keV (e.g... NS 1731-260. Barret et al.," The values for the 8 bursters listed by Christian Swank range between 5.3 and 25.0 keV. However, it should be noted that there is likely to be a selection effect in this parameter range because the upper boundary in the data is only 20 keV. There are a few bursters which have been measured up to hundreds of keV (e.g., KS 1731-260, Barret et al."964 1992: LU 1728-31. Claret et al.," 1992; 4U 1728-34, Claret et al."965 1991: Ταναια Barret 1997)., 1994; Tavani Barret 1997).966 With respect to these bursters. the hiehl-cucrey spectruui of lis uo exceptionally iud.," With respect to these bursters, the high-energy spectrum of is not exceptionally hard."967 The sample of bursters with measured broad-baud spectra is likely to erow iu the near future: a nuniber of NFI observations of bursters are currently beime carried out by various investiseators., The sample of bursters with measured broad-band spectra is likely to grow in the near future; a number of NFI observations of bursters are currently being carried out by various investigators.968 Therefore. in due ueuec. au unanibieuous comparative analysis of all these spectra will be possible.," Therefore, in due time, an unambiguous comparative analysis of all these spectra will be possible."969 Iu the mean ine. he NFI study of the burster LE 1721-308. located in the elobular cluster Terzau 2 (Cmnainazzi et al.," In the mean time, the NFI study of the burster 1E 1724-308, located in the globular cluster Terzan 2 (Guainazzi et al."970 1995) oxovides coniparative material (see also. e.2.. Barret et al.," 1998) provides comparative material (see also, e.g., Barret et al."971 1999)., 1999).972 The ΝΕΤ spectrum of TE 1721-308 was successfully uodcled through the Comptonization model by Titarchux (1991) plus an additional soft component in he form of a L keV black body radiator., The NFI spectrum of 1E 1724-308 was successfully modeled through the Comptonization model by Titarchuk (1994) plus an additional soft component in the form of a $\sim1$ keV black body radiator.973 The Comptonizing plasina las a telverature of ~30 keV aud the seed photons have a temperature of 1 to 2 keV. Comparing the cluperatures ofthe νους photons aud the hot plasia. we 1xte that these are about twice as cool in tthan in 1E 1721-308.," The Comptonizing plasma has a temperature of $\sim30$ keV and the seed photons have a temperature of 1 to 2 keV. Comparing the temperatures of the seed photons and the hot plasma, we note that these are about twice as cool in than in 1E 1724-308."974 Also. no additional soft compoucut is needed in inodeliug the spectrum of18.," Also, no additional soft component is needed in modeling the spectrum of."9759-2021.. We sueeest that the differences between the two sources are due to a twice as low Iuniuositv in wwhich could be a reflection of a differcuce in accretion rate., We suggest that the differences between the two sources are due to a twice as low luminosity in which could be a reflection of a difference in accretion rate.976 Fi, Fig.977s.5 shows the burst profile iu a number of baudpasses from MECS. IIP-GSPC and PDS data.," \ref{figburstlc} shows the burst profile in a number of bandpasses from MECS, HP-GSPC and PDS data."978 There are no observations of the burst with the LECS., There are no observations of the burst with the LECS.979 The 2 to 10 keV peak iuteusitv is about 0.5 Crab units., The 2 to 10 keV peak intensity is about 0.5 Crab units.980 This. as well as the duration. is similar to what was measured for the three bursts detected with WEC.," This, as well as the duration, is similar to what was measured for the three bursts detected with WFC."981 The burst was divided in two time intervals (sce Fig. 5)), The burst was divided in two time intervals (see Fig. \ref{figburstlc}) )982 aud spectra were generated from MECS 10.5 keV). TIP-CSPC (1.0-15.0 keV) aud PDS data (15.0- keV) for the first interval. ancl from MECS data (2.2- keV) for the secoud interval.," and spectra were generated from MECS (2.2-10.5 keV), HP-GSPC (4.0-15.0 keV) and PDS data (15.0-30.0 keV) for the first interval, and from MECS data (2.2-10.5 keV) for the second interval."983 The persistent ciission, The persistent emission984to Αν (Buatetal..2011.andreferencestherein).. and the slope of the UV continuum.,"to $A_{\rm UV}$ \citep[][and references therein]{buat11}, and the slope of the UV continuum."985 We can also compare dust attenuation corrections obtained by applying Eq., We can also compare dust attenuation corrections obtained by applying Eq.986 7 to the various estimates of « defined in section 5.1.1 and 5.1.2., 7 to the various estimates of $\alpha$ defined in section 5.1.1 and 5.1.2.987 The results are reported in Fig., The results are reported in Fig.988 12 and compared to the dust attenuation given by CIGALE: Auv.cigace.," \ref{auv-alphas} and compared to the dust attenuation given by CIGALE: $A_{\rm UV, CIGALE}$."989 A large dispersion is found. as a consequence of the loose relation found initially between Auy and ayer (Fig I1»: <AUaye—AuvceigaLe>=-0.005+0.707 mag.," A large dispersion is found, as a consequence of the loose relation found initially between $A_{\rm UV}$ and $\alpha_{\rm ref}$ (Fig \ref{auv-alpha}) ): $<A_{\rm UV, \alpha_{\rm ref}}- A_{\rm UV,\rm CIGALE} > = -0.005 \pm 0.707$ mag."990 When using ay; the systematic shift remains moderate <Ανα—ÁpvelGALE>=—0.18+0.58 Mag.," When using $\alpha_{13}$ the systematic shift remains moderate $<A_{UV, \alpha_{13}}- A_{UV,\rm CIGALE} > = -0.18\pm 0.58$ mag."991" UGALLX- OI? and ass give worse estimates with substancial shifts and large dispersions: <AUNaaa−⊿−⇘∣↴∖⇁∙⊂⊲∣≺↽∃∧∟∟>=-0.32+0.58 mag. < Atiwe,—AuvewaLe>=—0.73x0.70 mag. <Ανας:−⊿−⇘⋃∖↴∙⊂⊲∣≺↽∃⋅⇥∟∟>=0.37+0.71 Therefore. using UV slopes derived from broad band colours leads to large uncertainties in. the derivation of dust attenuation (~| mag) even if the bump area is avoided and good photometry is available."," $\alpha_{\rm GALEX}$ , $\alpha_{12}$ and $\alpha_{23}$ give worse estimates with substancial shifts and large dispersions: $<A_{\rm UV, \alpha_{\rm GALEX}}- A_{UV,\rm CIGALE} > = -0.32\pm 0.58$ mag, $<A_{\rm UV, \alpha_{12}}- A_{\rm UV, CIGALE} > = -0.73\pm 0.70$ mag, $<A_{\rm UV, \alpha_{23}}- A_{\rm UV,\rm CIGALE} > = 0.37\pm 0.71$ Therefore, using UV slopes derived from broad band colours leads to large uncertainties in the derivation of dust attenuation $\sim 1 $ mag) even if the bump area is avoided and good photometry is available."992 This is due to the intrinsic dispersion found between the slope of the UV continuum and the amount of dust attenuation., This is due to the intrinsic dispersion found between the slope of the UV continuum and the amount of dust attenuation.993 The presence of a bump in one of the filters may add à systematic shift which car reach 0.7 mag for the galaxies of our sample which is likely to be representative of star forming galaxies at redshifts between | and 2., The presence of a bump in one of the filters may add a systematic shift which can reach 0.7 mag for the galaxies of our sample which is likely to be representative of star forming galaxies at redshifts between 1 and 2.994 These results hold for galaxies with a moderate bump in their dust attenuation curve (35% of the mean amplitude found in the MW) and we expect larger effects for larger bumps., These results hold for galaxies with a moderate bump in their dust attenuation curve $35\%$ of the mean amplitude found in the MW) and we expect larger effects for larger bumps.995 We have identified the presence of a UV bump in a sample of galaxies of the CDFS at a redshifts between 0.9<z2.2. selected to be observed in intermediate and broad band optical filters as well as at mid-and far-IR wavelengths by and Herschel.," We have identified the presence of a UV bump in a sample of galaxies of the CDFS at a redshifts between $0.9 < z < 2.2$, selected to be observed in intermediate and broad band optical filters as well as at mid-and far-IR wavelengths by and $Herschel$."996 This study demonstrates the capabilities of intermediate-band photometry to give details on SED of galaxies. and to derive physical properties.," This study demonstrates the capabilities of intermediate-band photometry to give details on SED of galaxies, and to derive physical properties."997 The average dust attenuation curve we deduce Is well described by a modified Calzetti et al., The average dust attenuation curve we deduce is well described by a modified Calzetti et al.998 law slightly steeper than the original one and with a UV bump at 2175 A whose amplitude ts ~ 35% of the MW one., law slightly steeper than the original one and with a UV bump at 2175 $\AA$ whose amplitude is $\sim$ $\%$ of the MW one.999 We propose an analytical expression. of the average attenuation curve which can be used to correct the SEDs of galaxies for dust attenuation., We propose an analytical expression of the average attenuation curve which can be used to correct the SEDs of galaxies for dust attenuation.1000The moderate amplitude of the bump together with the substantial slope of our average attenuation curve in the UV argue for a deficit of UV bump carriers in our sample galaxies as compared to the Our sample contains seven X-ray galaxies.,The moderate amplitude of the bump together with the substantial slope of our average attenuation curve in the UV argue for a deficit of UV bump carriers in our sample galaxies as compared to the Our sample contains seven X-ray galaxies.1001 Five of them are reasonably fitted: a steep attenuation curve is favoured excluding a gray extinction., Five of them are reasonably fitted: a steep attenuation curve is favoured excluding a gray extinction.1002 The sample is too small to draw any firm conclusion about the presence of a UV bump., The sample is too small to draw any firm conclusion about the presence of a UV bump.1003 In any case the amplitude of the bump. if any. is smaller than that found for non X-ray The presence of à bump in the mean dust attenuatio curve has implications for the derivation. of the slope of the UV (rest-frame) continuum of galaxies from broad band datz£2 alone.," In any case the amplitude of the bump, if any, is smaller than that found for non X-ray The presence of a bump in the mean dust attenuation curve has implications for the derivation of the slope of the UV (rest-frame) continuum of galaxies from broad band data alone."1004 The power law modeling of the UV spectral distributio of our galaxies can be extended up to 3000 A but the bump arezο” must be avoided., The power law modeling of the UV spectral distribution of our galaxies can be extended up to 3000 $\AA$ but the bump area must be avoided.1005 When a broad band filter overlaps the bump. despite its moderate amplitude. the error on the determinatio of the slope may reach ~0.5.," When a broad band filter overlaps the bump, despite its moderate amplitude, the error on the determination of the slope may reach $\sim$ 0.5."1006 The use of GALEX filters leads to an underestimation of the slope of only 0.2. even if the NUV filter overlaps the bump.," The use of GALEX filters leads to an underestimation of the slope of only 0.2, even if the NUV filter overlaps the bump."1007 This ts likely to be due to the very large bandpass of this filter., This is likely to be due to the very large bandpass of this filter.1008 However. the proximity of the two central wavelengths of the GALEX filters implies a large uncertainty in the determination of the slope.," However, the proximity of the two central wavelengths of the GALEX filters implies a large uncertainty in the determination of the slope."1009 It is stressed that a larger wavelength baseline would give a better measure., It is stressed that a larger wavelength baseline would give a better measure.1010 Dust attenuation estimated with UV slopes. even when thelatter are reliable. remains uncertain. with an RMS error of 0.7 mag.," Dust attenuation estimated with UV slopes, even when thelatter are reliable, remains uncertain, with an RMS error of 0.7 mag."1011]t is. now accepted that most. ifIp not all. massive. galaxies. lost super-massive. black holes at their. centre.,"It is now accepted that most, if not all, massive galaxies host super-massive black holes at their centre."1012 wsThe observed ight. correlation.. between the mass of⋅ the black hole and he global properties. of. the host galaxy (Magorrian.etal.1998:Gebhardtctal.2000). suggests that the erowth of he black holes at their centres is intimately related to the ormation and assembly of these galaxies.," The observed tight correlation between the mass of the black hole and the global properties of the host galaxy \citep{mtr+98,gkh+00} suggests that the growth of the black holes at their centres is intimately related to the formation and assembly of these galaxies."1013 However. at any one time only ~5% of galaxies are seen as powerful racio sources or show other evidence of an active galactic nucleus (AGN).," However, at any one time only $\sim$ of galaxies are seen as powerful radio sources or show other evidence of an active galactic nucleus (AGN)."1014" ""OMThe question. arises:. are the host galaxies. of⋅ such AGN ⊲⇁⊀⋅cdillerent from⋅ the hosts of ⋅⊀inactive. sources?", The question arises: are the host galaxies of such AGN different from the hosts of inactive sources?10155 1t has been known since the early 1960s that the rosts for⋅ powerful⋅ radio⋠ galaxies. are massive. cllipticalsD. (c.g.Matthewsetal.1964)., It has been known since the early 1960s that the hosts for powerful radio galaxies are massive ellipticals \citep[e.g.][]{mms64}.1016.. Phe trigger for the transition rom quiescence tO an active state has been suggested: to » eravitationalEN interaction. between galaxies., The trigger for the transition from quiescence to an active state has been suggested to be gravitational interaction between galaxies.1017". Signatures"" of . . ⊔⇂⋜↧⇂↓⊔⊓⊾↓⋅⋯∙∣↓∪⊔⊳∖⋜⊔⋅⋖⊾≼∙∪⊔↓⊔↓∪⊔⋜⋯↓∪⊔⋏∙≟⊳∖↿↓−⋯⊔∪⋏∙≟⋜↧⇂⋜∟∖⊓⊾⊳∖↿∖≺⋅⊳⋏∙≟⊳ . . lleckmanetal.. 1986).. which. presumably. result in. a large increase in the amount of material feeding the black hole. hus triggering the radio emission."," Signatures of tidal interactions are common amongst radio galaxies \citep[e.g.][]{hsb+86}, which presumably result in a large increase in the amount of material feeding the black hole, thus triggering the radio emission."1018 Some individual. racio ealaxies also show significant association with voung stellar »opulations (e.g.Arctxagaetal.2001:Tadbiunter2002:Willsetal.2002:Johnstonct 2005): this suggests that he merger process which. triggers. the racio. emissionD. ean also cack tostar formation⋅ Lo.in the host galaxy.," Some individual radio galaxies also show significant association with young stellar populations \citep[e.g.][]{att+01,tdm+02,wtrm02,jhcs05}; this suggests that the merger process which triggers the radio emission can also lead to star formation in the host galaxy."1019 However. numerical. studies. of galaxy interactions. and mergers show that star ormation is not necessarilv enhanced. due to the amount of gas swept out (di.Matteoetal.onn2007).," However, numerical studies of galaxy interactions and mergers show that star formation is not necessarily enhanced, due to the amount of gas swept out \citep{mcms07}."1020. Several questions remain to be answered in this scenario: What is the relationship among mergers. the," Several questions remain to be answered in this scenario: What is the relationship among mergers, the"1021Iu this appoeudix. we present a brief study of three particular coufigurations.,"In this appendix, we present a brief study of three particular configurations."1022 We assume stationaritv — then E cau be expressed in ternis of an electrostatic potential c and nourclativistic velocities. and take B to be a eiven potential field.," We assume stationarity – then $\E$ can be expressed in terms of an electrostatic potential $\psi$ – and nonrelativistic velocities, and take $\B$ to be a given potential field."1023 We use Cartesian coordinates Ge.g.2) aud associated spherical coordinates (Gr.0.47).," We use Cartesian coordinates $(x,y,z)$ and associated spherical coordinates $(r,\theta,\varphi)$."1024 Following Michel 1989.. we consider a ball V. of ceuter O and radius ry containing free clectric charges distributed with the uniform density p.," Following Michel \cite{Mic1989}, we consider a ball $V$ of center $O$ and radius $r_{0}$ containing free electric charges distributed with the uniform density $\mu$."1025 V ds threaded by a uniform magnetic fold 02 (D> 0) aud it is subuutted to au external quadrupolar electric field oricuted iu such a way that the total electric field be given by From now ou. we choose the parameter &=2ryf3.," $V$ is threaded by a uniform magnetic field $B\zu$ $B>0$ ) and it is submitted to an external quadrupolar electric field oriented in such a way that the total electric field be given by From now on, we choose the parameter $k=2\pi\mu/3$."1026 Then E-B=BE. —01iu V. aud the plasiua turus out to be force-free if we take it to move at the dift velocity corresponding. to a Borigid rotation. at the angular velocity Q-2zep/D.," Then $\E\cdot\B=BE_{z}=0$ in $V$, and the plasma turns out to be force-free if we take it to move at the drift velocity corresponding to a rigid rotation at the angular velocity $\Omega=-2\pi c\mu/B$."1027 Of comse. E;=0 on the sphere fr\—rgl0j separatingS the plasiua from the vacuna it ina FFS iudeed.," Of course, $E_{z}=0$ on the sphere $\{r=r_{0}\}$ separating the plasma from the vacuum – it is a FFS indeed."1028 Iu the vacuna. aud jpbeue we recover here in a particular situation our general relation (36)) with 5ο=1.," In the vacuum, and whence we recover here in a particular situation our general relation \ref{dEpar/dl}) ) with $\gamma=\gamma_{n}=1$."1029" Let D, be a void iu coutact with a force-free plasma region D, all along its boundary Sa FES.", Let $D_{v}$ be a void in contact with a force-free plasma region $D_{e}$ all along its boundary ${\cal S}$ – a FFS.1030" D, may be either of", $D_{v}$ may be either of1031that the sharpness of the edge is a stroug functio10f the inclination angle £.,that the sharpness of the edge is a strong function of the inclination angle $\xi$.1032 Given the sharpuess of the observed edge in NCC 1LOL. these derived iucllaion angles a'e uncomfortably large.," Given the sharpness of the observed edge in NGC 1404, these derived inclination angles are uncomfortably large."1033 If we adopt iustead the optical relative radial velocity (y150 measwed by Drinkwater (2001). who identify NCC 1101 as part of a larger. |igl veocity. [αιig Fornax subcluster. the iulerred transverse velocities for NGC 1/01 increase to .292 (179).. respectively. for our two models.," If we adopt instead the optical relative radial velocity $v_r = 450$ measured by Drinkwater (2001), who identify NGC 1404 as part of a larger, high velocity, infalling Fornax subcluster, the inferred transverse velocities for NGC 1404 increase to $\sim 292$ $479$, respectively, for our two models."1034 While improvec. the iuferred inclination angle of 11e motion wlhi respect to the plane of the sky. &—o8 (13°). is still large.," While improved, the inferred inclination angle of the motion with respect to the plane of the sky, $\xi = 58^\circ$ $43^\circ$ ), is still large."1035 There are several possible solutions to his clienmna., There are several possible solutions to this dilemma.1036 First. GC LOL and NGC 1399 may uot both lie in the plane of the sky.," First, NGC 1404 and NGC 1399 may not both lie in the plane of the sky."1037 NGC 1101 uay be uiuergoing[n] a [ly-by of the dominant elliptical. with a non-negligible impact. paratjeter rather than a direct collision. such that the use ol the projected distance between the galaxies unde‘estimates the johysical racial distauce between them aud overestimates the value of the cluster electron deusity at the edge.," NGC 1404 may be undergoing a fly-by of the dominant elliptical, with a non-negligible impact parameter rather than a direct collision, such that the use of the projected distance between the galaxies underestimates the physical radial distance between them and overestimates the value of the cluster electron density at the edge."1038 Thus the deusity jump should be viewed as a lower bouud ou the physical deusity discountituity. Mach nuuber. aud relative," Thus the density jump should be viewed as a lower bound on the physical density discontinuity, Mach number, and relative"1039essentially independent of the resolution used for resolutions in the range 128464.στ512 and overall energy conservation in our simulations at all resolutions is as σους as that of RIB.,essentially independent of the resolution used for resolutions in the range $128\times64\rightarrow512\times512$ and overall energy conservation in our simulations at all resolutions is as good as that of RHB.1040 JEDB is supported. by. the Commonwealth Scholarship Commission in the United. lxingdom., JFB is supported by the Commonwealth Scholarship Commission in the United Kingdom.1041 We thank Helen Drimmer and David Titterington for managing the Beowulf cluster., We thank Helen Brimmer and David Titterington for managing the Beowulf cluster.1042 \We also thank Christian. Waiser and. Malcolm Longair for helpful discussions. and the referee for. helpful comments.," We also thank Christian Kaiser and Malcolm Longair for helpful discussions, and the referee for helpful comments."1043Spherical harmonic transforms (SHTs) have a wide range of applications in science and engineering.,Spherical harmonic transforms (SHTs) have a wide range of applications in science and engineering.1044" In the case of CMB science, which prompted the development of the library presented in this paper, they are an essential building block for extracting the cosmological power spectrum from full-sky maps, and are also used for generating synthesised sky maps in the context of Monte Carlo simulations."," In the case of CMB science, which prompted the development of the library presented in this paper, they are an essential building block for extracting the cosmological power spectrum from full-sky maps, and are also used for generating synthesised sky maps in the context of Monte Carlo simulations."1045" For all recent experiments in this field, the extraction of spherical harmonic coefficients has to be done up to very high multipole moments (up to 105), which makes SHTs fairly costly operation and therefore a natural candidate for aoptimisation."," For all recent experiments in this field, the extraction of spherical harmonic coefficients has to be done up to very high multipole moments (up to $10^4$ ), which makes SHTs a fairly costly operation and therefore a natural candidate for optimisation."1046 It also gives rise to a number of numerical complications that must be addressed by the transform algorithm., It also gives rise to a number of numerical complications that must be addressed by the transform algorithm.1047 The purpose of SHTs is the conversion between functions (or maps) on the sphere and their representation as a set of spherical harmonic coefficients in the spectral domain., The purpose of SHTs is the conversion between functions (or maps) on the sphere and their representation as a set of spherical harmonic coefficients in the spectral domain.1048" In CMB science, such transforms are most often needed for quantities of spin 0 qquantities which are invariant with respect to rotation of the local coordinate system) and spin 2, because the unpolarised and polarised components of the microwave radiation are fields of these respective types."," In CMB science, such transforms are most often needed for quantities of spin 0 quantities which are invariant with respect to rotation of the local coordinate system) and spin 2, because the unpolarised and polarised components of the microwave radiation are fields of these respective types."1049" For applications concerned with gravitational lensing, SHTs of spins 1 and 3 are also sometimes required."," For applications concerned with gravitational lensing, SHTs of spins 1 and 3 are also sometimes required."1050 The paper is organised as follows., The paper is organised as follows.1051" The following section lists the underlying equations anf the motivations for developinglibpsht, as well as the goals of the implementation."," The following section lists the underlying equations anf the motivations for developing, as well as the goals of the implementation."1052" A detailed explanation of the library's inner workings is presentedin refalgorithm,, and refapi contains a high-level overview of the interface it provides."," A detailed explanation of the library's inner workings is presentedin \\ref{algorithm}, and \\ref{api} contains a high-level overview of the interface it provides."1053" Detailed studies regarding libpsht'ss performance, accuracy, and other quality indicatorswere performed, and their results presented in refbenchmarks.."," Detailed studies regarding s performance, accuracy, and other quality indicatorswere performed, and their results presented in \\ref{benchmarks}."1054" Finally, a summary of the achieved (and not completely achieved) goals is given, together with an outlook on planned future extensions."," Finally, a summary of the achieved (and not completely achieved) goals is given, together with an outlook on planned future extensions."1055" A continuous spin-s function f(9,o) with a spectral band limit of iis related to its corresponding set of spin spherical harmonic coefficients ,aj, by the following equations: eqrefana,rueand(2)areknownasbackward (or synthesis)) and (or analysis)) transforms, respectively."," A continuous $s$ function $f(\vartheta,\varphi)$ with a spectral band limit of is related to its corresponding set of spin spherical harmonic coefficients $_sa_{lm}$ by the following equations: and are known as (or ) and (or ) transforms, respectively."1056" For a discretised spherical map consisting of a vector P of Νρικ pixels at locations (9 Q) and with (potentially weighted) solid angles w, they change to: Depending on the choice of/max,, W, and the grid geometry, the P—(αι transform may only be approximate, which is indicated by choosing the identifier à instead of a."," For a discretised spherical map consisting of a vector $\vec p$ of $N_\text{pix}$ pixels at locations $\vec \vartheta, \vec \varphi$ ) and with (potentially weighted) solid angles $\vec w$ , they change to: Depending on the choice of, $\vec w$, and the grid geometry, the ${\vec p} \rightarrow {}_sa_{lm}$ transform may only be approximate, which is indicated by choosing the identifier $\hat a$ instead of $a$."1057 The main purpose of the presented code is the efficient implementation (regarding CPU time as well as memory consumption) of «Bp and (4) for scalars as well as tensor quantities of spins +1 and +2., The main purpose of the presented code is the efficient implementation (regarding CPU time as well as memory consumption) of \ref{eq_syn}) ) and \ref{eq_ana}) ) for scalars as well as tensor quantities of spins $\pm1$ and $\pm2$ .1058" At present, several SHT implementations are in use within the CMBcommunity, like those distributed with the Fortran andC++ implementations of HEALPix|](?),, GLESPP|(?),, radek/s2hat.html,,"," At present, several SHT implementations are in use within the CMBcommunity, like those distributed with the Fortran andC++ implementations of \citep{gorski-etal-2005}, , \citep{doroshkevich-etal-2005}, , ,"1059trend (see Figure 11).,trend (see Figure 11).1060 The run test confirms an underlying trend with a confidence level of approximately95%., The run test confirms an underlying trend with a confidence level of approximately.1061. The intrinsic dispersion as function of the redshift has a similar behaviour when we use the stellar mass., The intrinsic dispersion as function of the redshift has a similar behaviour when we use the stellar mass.1062 In order to characterise the behaviour of the intrinsic dispersion as a function of the redshift. in Figure I] we have fitted the points of the sample with Mia/M.)~11.3 toa straight line whose equation ts: Similarly. the straight line equation obtained from. the sample with Ma/M.J~11.8 is: We must note that the dependence of the intrinsic dispersion of the FJR as a function of redshift has been found for the brightest and more massive galaxies. because in the faint and low mass end we do not have data or the ones that we do have are not of sufficiently good quality.," In order to characterise the behaviour of the intrinsic dispersion as a function of the redshift, in Figure 11 we have fitted the points of the sample with ${\bf M_{virial}}/{\bf M_{\odot}}) \sim 11.3$ to a straight line whose equation is: Similarly, the straight line equation obtained from the sample with ${\bf M_{virial}}/{\bf M_{\odot}}) \sim 11.8$ is: We must note that the dependence of the intrinsic dispersion of the FJR as a function of redshift has been found for the brightest and more massive galaxies, because in the faint and low mass end we do not have data or the ones that we do have are not of sufficiently good quality."1063 On the other hand. the coefficients of equations 6 and 7 are compatible. within the errors. with the coefficients of equations 8 and 9.," On the other hand, the coefficients of equations 6 and 7 are compatible, within the errors, with the coefficients of equations 8 and 9."1064 This behaviour may be understood by means of Figure 2 where we show that the difference between the virial and the stellar mass is smaller for larger values of the mass., This behaviour may be understood by means of Figure 2 where we show that the difference between the virial and the stellar mass is smaller for larger values of the mass.1065 Given that the objects we use for the study of the intrinsic dispersion as a function of the redshift are massive. the differences which might result should be relatively small.," Given that the objects we use for the study of the intrinsic dispersion as a function of the redshift are massive, the differences which might result should be relatively small."1066 The results presented 1n this section. allow us to affirm that. for the brighter and more massive galaxies. the intrinsic dispersion of the FJR changes systematically with distance.," The results presented in this section, allow us to affirm that, for the brighter and more massive galaxies, the intrinsic dispersion of the FJR changes systematically with distance."1067 Those galaxies located further away. have a lower intrinsic dispersion of the FJR than those located closer by.," Those galaxies located further away, have a lower intrinsic dispersion of the FJR than those located closer by."1068 The structural relations of ETGs. in particular the FP. have been studied extensively. over the last 20-30 vears.," The structural relations of ETGs, in particular the FP, have been studied extensively over the last 20-30 years."1069 The physical explanation. for the FP consider that the ETGs are in virial equilibrium and that they are homologous systems., The physical explanation for the FP consider that the ETGs are in virial equilibrium and that they are homologous systems.1070 The term homology means in this context the regular behaviour of both the mass-luminosity ratio and the structure along the entire range of ΕΤΟΣ luminosities., The term homology means in this context the regular behaviour of both the mass-luminosity ratio and the structure along the entire range of ETGs luminosities.1071 However. these assumptions are not sufficient to explain the observational results.," However, these assumptions are not sufficient to explain the observational results."1072 To try to find an explanation to the differences between theory and observation. which refer mainly to the tlt of the FP. several authors have invoked different mechanisms that affect the ETGs along their formation and evolution.," To try to find an explanation to the differences between theory and observation, which refer mainly to the tilt of the FP, several authors have invoked different mechanisms that affect the ETGs along their formation and evolution."1073 One of the most important considerations in trying to explain the tilt is that the ETGs üre non-homologous systems. however. up to the present the results of the different works (e.g. Pahreetal. 1998:; Scodeggioetal.1998:: Robertsonetal. 2006:; Jun&Im 2008)) only explain partially the tilt. and there are no conclusive results.," One of the most important considerations in trying to explain the tilt is that the ETGs are non-homologous systems, however, up to the present the results of the different works (e.g. \cite{pah98}; ; \cite{sco98}; \cite{rob06}; \cite{jun08}) ) only explain partially the tilt, and there are no conclusive results."1074" A recent study (Nigoche-Netroetal. 2009)) has shown that the FP is not a simple plane in the space of parameters log(r,). <pHV logico) and that the distribution of galaxies in this space depends on Juminosity."," A recent study \cite{nig09}) ) has shown that the FP is not a simple plane in the space of parameters $\log(r_{e})$, $<\mu>_{e}$, $\log(\sigma_{0})$ and that the distribution of galaxies in this space depends on luminosity."1075 In the case of the KR and FJR. Nigoche-Netro et al. (," In the case of the KR and FJR, Nigoche-Netro et al. ("10762008: 2010) find the same behaviour.,2008; 2010) find the same behaviour.1077 Fraix-Burnet et al. (, Fraix-Burnet et al. (10782010) have also found that the distribution of galaxies in the space of parameters Is very complex. they established that the FP and other structural relations such as the FJR are formed by 7 different groups of galaxies.,"2010) have also found that the distribution of galaxies in the space of parameters is very complex, they established that the FP and other structural relations such as the FJR are formed by 7 different groups of galaxies."1079 These groups define different separate regions on the graphical planes or space where the structural relations are plotted., These groups define different separate regions on the graphical planes or space where the structural relations are plotted.1080" They also find that each group is truly ""homologous"". where ""homology'. for them. means similarity due to having the same class of progenitor."," They also find that each group is truly `homologous', where `homology', for them, means similarity due to having the same class of progenitor."1081 Each group defines its own structural relation which 15 more loosely defined for less-diversified groups., Each group defines its own structural relation which is more loosely defined for less-diversified groups.1082" The ""diversity! means. in this context. the number and nature of transformation events that affect the galaxies along their life time such as: collapse. accretion. interaction and merging."," The `diversity' means, in this context, the number and nature of transformation events that affect the galaxies along their life time such as: collapse, accretion, interaction and merging."1083 So that the term less-diversified (more-diversified) means that galaxies have suffered fewer (more) transformation events along their life times., So that the term less-diversified (more-diversified) means that galaxies have suffered fewer (more) transformation events along their life times.1084" It is important not to confuse the terms ""diversity and ‘diversification’.", It is important not to confuse the terms `diversity' and `diversification'.1085 “Diversification’. following Fraix-Burnet et al. (," `Diversification', following Fraix-Burnet et al. ("10862006). refers to the number of different classes of objects that are present in a sample.,"2006), refers to the number of different classes of objects that are present in a sample."1087 An illustrative example of the difference between these two concepts is the following: Four identical galaxies when mixed in pairs would produce two different galaxies., An illustrative example of the difference between these two concepts is the following: Four identical galaxies when mixed in pairs would produce two different galaxies.1088 Different among themselves and different from the original ones., Different among themselves and different from the original ones.1089 If these two galaxies would mix again. the mixture would produce a new class of galaxy.," If these two galaxies would mix again, the mixture would produce a new class of galaxy."1090 In this example. along the entire process. 4 different classes of objects have been produced. but the final result is that there is only one class of galaxy and this last object is the more diversified. because is the one that has suffered the lareer number of transformatior events.," In this example, along the entire process, 4 different classes of objects have been produced, but the final result is that there is only one class of galaxy and this last object is the more diversified, because is the one that has suffered the larger number of transformation events."1091 Fraix-Burnet et al. (, Fraix-Burnet et al. (1092"2010) conclude that the FP could be an historical and not a physical correlation. so that. the correlation among log). «ge», and Ιοσίσο) might not be a tilted virial plane due to dissipation or to a particular behaviour of M/Z. but rather a parametric correlation between the evolution of these parameters.","2010) conclude that the FP could be an historical and not a physical correlation, so that, the correlation among $\log(r_{e})$, $<\mu>_{e}$ and $\log(\sigma_{0})$ might not be a tilted virial plane due to dissipation or to a particular behaviour of ${\bf M}/L$, but rather a parametric correlation between the evolution of these parameters."1093 In other words. the FP would be the result of several transforming events such as collapse. accretion. interaction and merging. that is to say. the FP would be the result of the historical sequence of events that affected. one way or another. the physical structure of the galaxies in question.," In other words, the FP would be the result of several transforming events such as collapse, accretion, interaction and merging, that is to say, the FP would be the result of the historical sequence of events that affected, one way or another, the physical structure of the galaxies in question."1094 In previous sections we have characterised the variation of the distribution of the ETGs in the plane of the parameters M and log(co) using the intrinsic dispersion., In previous sections we have characterised the variation of the distribution of the ETGs in the plane of the parameters $M$ and $\log(\sigma_{0})$ using the intrinsic dispersion.1095 We have found that the intrinsic dispersion of the FJR depends on the luminosity and mass of the galaxies and that the distribution of brighter and more massive galaxies has a lower intrinsic. dispersion than that for the fainter and less massive galaxies., We have found that the intrinsic dispersion of the FJR depends on the luminosity and mass of the galaxies and that the distribution of brighter and more massive galaxies has a lower intrinsic dispersion than that for the fainter and less massive galaxies.1096 This result is in agreement with the work of Fraix-Burnet et al. (, This result is in agreement with the work of Fraix-Burnet et al. (10972010). where. in their Figure 7 we can see that the region of the brighter galaxies on the FJR plane is formed by the more diversified groups -only one or two groups populate this . While the region of the fainter galaxies is formed by the less diversified groups -four or five groups populate this region- which occupy à nore ample region.,"2010), where, in their Figure 7 we can see that the region of the brighter galaxies on the FJR plane is formed by the more diversified groups -only one or two groups populate this region-, while the region of the fainter galaxies is formed by the less diversified groups -four or five groups populate this region-, which occupy a more ample region."1098 Put differently. the distribution of galaxies inside the groups and the distribution of the groups on the FJR planemight cause that the distribution," Put differently, the distribution of galaxies inside the groups and the distribution of the groups on the FJR planemight cause that the distribution"1099laving thin convection zones which agree with ILT models using small aap. so we expect o reproduce the white dwarf results.,"having thin convection zones which agree with MLT models using small $\alpha_{ML}$, so we expect to reproduce the white dwarf results."1100" For low uass stars. the surface temperatures will be ower than the solar value. so that the SAR should comprise more mass. Le. we expect arger gajr, to be plysteally correct."," For low mass stars, the surface temperatures will be lower than the solar value, so that the SAR should comprise more mass, i.e., we expect larger $g_{ML}$ to be physically correct."1101 Table 2 indicates that there is a trade off between Gare al GALL: to compensate [or lower gare. 0 must be lower. for the same radius.," Table \ref{tablep} indicates that there is a trade off between $\alpha_{ML}$ and $g_{ML}$ : to compensate for lower $g_{ML}$, $\alpha$ must be lower, for the same radius."1102 For a deep convection zone. aap 1s fixed: then a stronger SAR (larger garz. and more inefficient convection) will give a larger raclius.," For a deep convection zone, $\alpha_{ML}$ is fixed; then a stronger SAR (larger $g_{ML}$, and more inefficient convection) will give a larger radius."1103 This is the seuse of the discrepancy. of the computec radii for low mass eclipsing binaries (Stassun.etal.2008:Morales.2008).. aud we suggest that part of the discrepancy uay be due to the convection algoritlun use.," This is the sense of the discrepancy of the computed radii for low mass eclipsing binaries \citep{stassun,morales}, and we suggest that part of the discrepancy may be due to the convection algorithm used."1104 Unfortunately. direct.i calculation of low tass dwarls (M.zzQ.2NL. ) with aayp7L| exposes imitations in MLT: the SAR is forced upward iuto the photosphere. making 3D atmospheres a necessity for gainingi insight iuto a plausible reatinent in stellar models.," Unfortunately, direct calculation of low mass dwarfs $M \approx 0.2 \rm M_\odot$ ) with $\alpha_{ML} \approx 4$ exposes limitations in MLT: the SAR is forced upward into the photosphere, making 3D atmospheres a necessity for gaining insight into a plausible treatment in stellar models."1105 We have. in fact. sketched ai way to eliminate astronomical calibration from stellar couvectiou theory: Notice that a fit to the present day solar raclius is uot logically necessary.," We have, in fact, sketched a way to eliminate astronomical calibration from stellar convection theory: Notice that a fit to the present day solar radius is not logically necessary."1106 By seriously cousidering MILT. we have determined that no siguilicaut [ree parameters are left to adjust within the framework of the theory.," By seriously considering MLT, we have determined that no significant free parameters are left to adjust within the framework of the theory."1107 We find that the choice of two characteristic leugths. flow. close the system: the turbulent dissipatiou length and the size of the super-adiabatic region. (SAR).," We find that the choice of two characteristic lengths, , close the system: the turbulent dissipation length and the size of the super-adiabatic region (SAR)."1108 Alternatively. the coustral that the observed. micro- aud uacro-turbulent velocities agree with those oredieted using the bulk Richardsou criterion Or surlace couvective mixiug can be used instead of the SAR size.," Alternatively, the constraint that the observed micro- and macro-turbulent velocities agree with those predicted using the bulk Richardson criterion for surface convective mixing can be used instead of the SAR size."1109 ILT is still an incomplete theory. but is suggestive that even modest. changes oward a better physical interpretation. based pon 3D sinulatious auc ou a more complete rbuleuce theory. do give lnnproveiments iu e luodels.," MLT is still an incomplete theory, but it is suggestive that even modest changes toward a better physical interpretation, based upon 3D simulations and on a more complete turbulence theory, do give improvements in the models."1110 MLT. as use here. may. be derived from a more general urbulent kinetic enerey equation by ignoring certain terms (Arnett.Meakin.&Young2009).," MLT, as used here, may be derived from a more general turbulent kinetic energy equation by ignoring certain terms \citep{amy09}."1111. Some of e jenored terius are inportaut. erupliasiziug at MLT is incomplete.," Some of the ignored terms are important, emphasizing that MLT is incomplete."1112 However. the approach sketched above may be generalized. αι inclusion of missiug[n] teris gives a convection jeory that is nonlocal. time «dependent. orovkles robust velocity estimates. aud is yasecl on simulations aud terrestrial experiment. with no astronomical calibration.," However, the approach sketched above may be generalized, and inclusion of missing terms gives a convection theory that is nonlocal, time dependent, provides robust velocity estimates, and is based on simulations and terrestrial experiment, with no astronomical calibration."1113 This moredifficult theory will be presented in detailiu future publicatious., This moredifficult theory will be presented in detailin future publications.11142005).,.1115 This is a large sigual compared to an accuracy in the measurement of the central traut time of order (Ford&Caoudi2006)respectively). amounting to 10s of seconds for iiilliauag photometric accuracy.," This is a large signal compared to an accuracy in the measurement of the central transit time of order \citep{Ford06_2}1116, amounting to 10s of seconds for milli-mag photometric accuracy."1117 The recently oblished ceutral times (Lathamctal.2009:2010:ochetal.2010). are in rough accordance with lus estimate.," The recently published central times \citep{Latham10, Borucki10_4b, Jenkins10, Dunham10, Koch10} are in rough accordance with this estimate."1118 Furthermore. with respect to the xoject. we note that once a transit is detected with sufficient signal-to-noise ratio. the star will be switched roni the lone-cadence (30 minute) to short-cacdeuce (1 uinute) sampling rate (Boruckietal.2008).. innproviug he temporal resolution of the transit even further.," Furthermore, with respect to the project, we note that once a transit is detected with sufficient signal-to-noise ratio, the star will be switched from the long-cadence (30 minute) to short-cadence (1 minute) sampling rate \citep{Borucki08}, improving the temporal resolution of the transit even further."1119 We ake c;y=210! d (m 15 s) as a conservative estimate of accuracy oi the ceutral triuisits.," We take $\sigma_{tr, K} = 2\times 10^{-4}$ d $\approx$ 15 s) as a conservative estimate of accuracy on the central transits."1120 Given a large dataset comprisiug 1 vear or more of continuous transit monitoring. is it possible to infer the mass and elements of the perturbing planet?," Given a large dataset comprising 1 year or more of continuous transit monitoring, is it possible to infer the mass and elements of the perturbing planet?"1121 Recoustructing the properties of the perturber from a noisy TTY signal is a complex. and possibly highly degenerate (Nesvoruv&Alorbidelli 2008).. inverse problemi.," Reconstructing the properties of the perturber from a noisy TTV signal is a complex, and possibly highly degenerate \citep{Nesvorny08}, inverse problem."1122 In this paper. we present a series of simulatious aimed at detecting low-mass perturbers frou realistic central transit and follow-up RV data.," In this paper, we present a series of simulations aimed at detecting low-mass perturbers from realistic central transit and follow-up RV data."1123 To this cud. we produce a large sample of Aepler--like observations and attempt to characterize the perturber using the algoritlin toolset offered by a revised version of the Svsteniüc Console (Aleschiarietal.2009.hereafterPa-per D...," To this end, we produce a large sample of -like observations and attempt to characterize the perturber using the algorithm toolset offered by a revised version of the Systemic Console \citep[][hereafter Paper I]{Meschiari09}."1124 A umuber of differeut planetary realizations were used. in an attempt to fully capture the complexity of TTY fitting. drawing the orbital clemeuts from observed planetary systems.," A number of different planetary realizations were used, in an attempt to fully capture the complexity of TTV fitting, drawing the orbital elements from observed planetary systems."1125 For the sake of simplicity. we focus on two-planct svstems. but the method is fully eeucral within the constraints of CPU time aud measurement CLYOLS.," For the sake of simplicity, we focus on two-planet systems, but the method is fully general within the constraints of CPU time and measurement errors."1126 The plan of the paper is as follows., The plan of the paper is as follows.1127 Iun 877.. we briefly review describe the algorithius used to derive best-fit models aud accompanuving error estinates.," In \ref{sec:Console}, , we briefly review describe the algorithms used to derive best-fit models and accompanying error estimates."1128 Iu 877.. we exanüne the characterization of planets sinuülu to aud.d. which lie close but not quite in a 2:1 AIMB.," In \ref{sec:HD40307}, we examine the characterization of planets similar to and, which lie close but not quite in a 2:1 MMR."1129 Our aualvsis nakes use of the ITARPS dataset (Mavoretal.20094) and a simulated transit timing dataset., Our analysis makes use of the HARPS dataset \citep{Mayor09} and a simulated transit timing dataset.1130 In 877. we fit the svuthetic realization of a planetary system dee yin a 2:1 MMB. with an external perturber (using TAT-P-T as our model system).," In \ref{sec:HATP7} we fit the synthetic realization of a planetary system deep in a 2:1 MMR, with an external perturber (using HAT-P-7 as our model system)."1131 Finally. in 877 owe analyze «ustrauts placed by TTVs on the three-diuensional coi&euration of planctary svstenis. using ILAT-P-13 as a test case. aud conchide in 8??..," Finally, in \ref{sec:HATP13} we analyze constraints placed by TTVs on the three-dimensional configuration of planetary systems, using HAT-P-13 as a test case, and conclude in \ref{sec:conc}."1132 The transit timune variation sigualOo 1s defined as the difference hetweC»en the observed central transit times and the predicted times from a linear regression (corresponding to a sinele-plauct Iseplerian fit with period P): The variations originate by the mutual eravitational interactions with an additional body. chiefly causing short-term oscillations wherein the true anomaly fy trails or leads the Ieplerian value and lone-teriun effects sucht as pericenter precession (Ilevl&Cladiman2007).," The transit timing variation signal is defined as the difference between the observed central transit times and the predicted times from a linear regression (corresponding to a single-planet Keplerian fit with period $P_1$ ): The variations originate by the mutual gravitational interactions with an additional body, chiefly causing short-term oscillations wherein the true anomaly $f_1$ trails or leads the Keplerian value and long-term effects such as pericenter precession \citep{Heyl07}."1133 Iu principle. since the signal will depend on the Newtonian evolution of the planetary svstem. TTVs can provide a sensitive probe for the three-dimenusional orbit of the second planet. in combination with the tight constraints ou the eclipsing planets period aud the time of pericenter passage provided by the ceutral transits themselves.," In principle, since the signal will depend on the Newtonian evolution of the planetary system, TTVs can provide a sensitive probe for the three-dimensional orbit of the second planet, in combination with the tight constraints on the eclipsing planet's period and the time of pericenter passage provided by the central transits themselves."1134 Uowever. solving the inverse problemi of deriving a best-nocdel fit to the TTY obscrvatious cau be daunting.," However, solving the inverse problem of deriving a best-model fit to the TTV observations can be daunting."1135 The computation of the predicted TTY signal requires precise N-body integrations (with .N=3)., The computation of the predicted TTV signal requires precise N-body integrations (with $N \geq 3$ ).1136 Iu the eeneral case. the dependence of the signal ou the set of orbital parameters is not directly clear: unlike. e.g. the RV technique. deviatious from the Keplerian sienal as opposed to the Ieplerian signal itself constitute the bulk ofthe information.," In the general case, the dependence of the signal on the set of orbital parameters is not directly clear; unlike, e.g. the RV technique, deviations from the Keplerian signal – as opposed to the Keplerian signal itself – constitute the bulk of the information."1137 The use of Fourier analvsis to sort out periodicities in the data is eenerallv hampered by the sparseucss of the trausit observations., The use of Fourier analysis to sort out periodicities in the data is generally hampered by the sparseness of the transit observations.1138 Firthermore. given the extreme sensitivity of óf to the model parameters. local minimization routines can casily eet stuck in narrow X7 linia. or fail due to steep eradients in the landscape.," Furthermore, given the extreme sensitivity of $\delta t$ to the model parameters, local minimization routines can easily get stuck in narrow $\chi^2$ minima, or fail due to steep gradients in the landscape."1139 Finally. as shown iu the later sections. there is a degree of non-uniqueness as multiple models can ft the transit timing observations when nmneasurenieut errors are taken into account (seealsoe.g.Nesvoru*&Morbidelli 2008):: these degenerate solutions are characterized by. comparable 4?~1. aud must be taken into account when deriving parameter unicertaities.," Finally, as shown in the later sections, there is a degree of non-uniqueness as multiple models can fit the transit timing observations when measurement errors are taken into account \citep[see also e.g.][]{Nesvorny08}; ; these degenerate solutions are characterized by comparable $\chi^2\sim 1$, and must be taken into account when deriving parameter uncertainties."1140 Direct searches of the parameter space (e.g.Steffen&Ασοι2007) can be extremely expensive in terius of CPU time., Direct searches of the parameter space \citep[e.g.][]{Steffen07} can be extremely expensive in terms of CPU time.1141 A more appealing alternative is represeuted wo the TLV Inversion Method (TTVIALNesvoriuy&Deoaugé2010.andrelated papers)., A more appealing alternative is represented by the TTV Inversion Method \citep[TTVIM; ][and related papers]{Nesvorny10}.1142 TTVIAL combines a fast aleorithin for computing the 2-plauet transit iuiug based on perturbation methods with a downhill simplex unetlod to obtain good convergence towards the oxturbius plauet'* paraueters., TTVIM combines a fast algorithm for computing the 2-planet transit timing based on perturbation methods with a downhill simplex method to obtain good convergence towards the perturbing planet's parameters.1143 However. sonie issues relmain in addressing svsteuis Iviug close to a MMB.," However, some issues remain in addressing systems lying close to a MMR."1144 Tn this paper. we adopt the approach of finding best- models to joint TTV. aud Doppler velocity data scts w driving an cficicnt Dulisclh-Stoer inteerator with he Simulated Anuealine aleorithin integrated iu the Systeme Console (PaperD7.," In this paper, we adopt the approach of finding best-fit models to joint TTV and Doppler velocity data sets by driving an efficient Bulirsch-Stoer integrator with the Simulated Annealing algorithm integrated in the Systemic Console (Paper."1145. SA-type algorithis are wellsuited to exploring the orbital αταποτό space aud convereius. i principle. to global müuunua (subject to appropriate choices of scheduling algorithm and scale parameters).," SA-type algorithms are well-suited to exploring the orbital parameter space and converging, in principle, to global minima (subject to appropriate choices of scheduling algorithm and scale parameters)."1146 Several nuünimuzers can be run in parallel with different initial temperaturesand initial conditions. exploiting moceru multi-core CPUs capabilities.," Several minimizers can be run in parallel with different initial temperaturesand initial conditions, exploiting modern multi-core CPUs capabilities."1147 The stepsize vector is, The stepsize vector is1148In figure Baa we plot the stabilitv threshold defined by rotation estimated fromEq. 3..,"In figure \ref{SFR}a a we plot the stability threshold defined by rotation estimated fromEq. \ref{eq2},"1149 against (he measured star formation rate in those galaxies., against the measured star formation rate in those galaxies.1150 Wilh stars we plot the data taken for normal spirals (INennicutt 1998: IXent. 1987: Pisano et al., With stars we plot the data taken for normal spirals (Kennicutt 1998; Kent 1987; Pisano et al.1151 1998: Giraud 1998: Theis 2001: Braine 2001: Leitherer 2002: Helfer et al., 1998; Giraud 1998; Theis 2001; Braine 2001; Leitherer 2002; Helfer et al.1152 2003: Gallagher 2005: Afanasiey 2005: Davidge 2006: Pérrez-Torres Alberdi 2007; Thilker οἱ al., 2003; Gallagher 2005; Afanasiev 2005; Davidge 2006; Pérrez-Torres Alberdi 2007; Thilker et al.1153 2007). with open circles for the nuclear eas in normal spirals (Jogee 2005; Manersherger et al 1996: Alonso-Ilerrero 2001: IIsieh et al 2008) ancl with full circles for ULIRGs (Downes solomon 1993).," 2007), with open circles for the nuclear gas in normal spirals (Jogee 2005; Mauersberger et al 1996; Alonso-Herrero 2001; Hsieh et al 2008) and with full circles for ULIRGs (Downes Solomon 1998)."1154" Figure 2aa shows a clear correlation between M, and the star lormation rate. in agreement wilh (he scenario outlined in this ο”."," Figure \ref{SFR}a a shows a clear correlation between $\rm M_{rot}$ and the star formation rate, in agreement with the scenario outlined in this $Letter$."1155 Figure 2aa supports the critical role of this threshold mass in the triggering of star lormation., Figure \ref{SFR}a a supports the critical role of this threshold mass in the triggering of star formation.1156 The solid line in figure 2aa represents a star formation law of SFRx[iAL)., The solid line in figure \ref{SFR}a a represents a star formation law of $\rm SFR \propto M_{rot}^{1.4}$.1157 For comparison purposes we also plot in figure 2bb the measured star formation rate against the square of the gas fraction η.," For comparison purposes we also plot in figure \ref{SFR}b b the measured star formation rate against the square of the gas fraction $\rm1158\eta$."1159 Figure 2bb clearly shows that the scatter in this relation is considerably increased. compared to figure 2aa. This means that the gas traction is not a more fundamental parameter in controlling the star formation rate., Figure \ref{SFR}b b clearly shows that the scatter in this relation is considerably increased compared to figure \ref{SFR}a a. This means that the gas fraction is not a more fundamental parameter in controlling the star formation rate.1160 We do not plot the SER against the gas mass. since it is well established that there is no correlation of the total gaseous mass in galaxies with their current star formation rate.," We do not plot the SFR against the gas mass, since it is well established that there is no correlation of the total gaseous mass in galaxies with their current star formation rate."1161 In summary. (he predicted. correlation between (he SFR and the maximum unstable mass defined by rotation is indeed observed in galaxies. in a range thal spans for 5 orders ol magnitude in SER.," In summary, the predicted correlation between the SFR and the maximum unstable mass defined by rotation is indeed observed in galaxies, in a range that spans for 5 orders of magnitude in SFR."1162 This is an strong suggestion that the global threshold for instability indeed (rigeers star formation. by allowing the disk to be in equilibrium configuration with a higher turbulence level.," This is an strong suggestion that the global threshold for instability indeed triggers star formation, by allowing the disk to be in equilibrium configuration with a higher turbulence level."1163 Probably the most straightforward application of the scenario outlined in 82. is (ο check if ils able to explain the observed correlation between (he star formation rate ol a galaxy and the huminosity of its brightest voung stellar cluster (Larsen 2002: Bastian 2008).," Probably the most straightforward application of the scenario outlined in 2, is to check if its able to explain the observed correlation between the star formation rate of a galaxy and the luminosity of its brightest young stellar cluster (Larsen 2002; Bastian 2008)."1164 This is because (he mass-scale studied here and that correlates with the SFR (Fig 1). also corresponds to ihe most massive unstable cloud in a disk. which could lead to the formation of the most massive and luminous voung cluster in such system (Escala Larson 2008).," This is because the mass-scale studied here and that correlates with the SFR (Fig 1), also corresponds to the most massive unstable cloud in a disk, which could lead to the formation of the most massive and luminous young cluster in such system (Escala Larson 2008)."1165 The total luminositw of a cluster. can be computed for a given initial mass function (AIF) ancl mass-Iuminosity relation.," The total luminosity of a cluster, can be computed for a given initial mass function (IMF) and mass-luminosity relation."1166 Assuming a Salpeter IMFE (sxin7) and the usual niass-Iuminosity relation for main sequence stars (Lx m). the total luminositv of a cluster," Assuming a Salpeter IMF $\rm (\frac{dN}{dm} \propto m^{-2.35})$ and the usual mass-luminosity relation for main sequence stars $\rm (L \propto m^{3.5})$ , the total luminosity of a cluster"1167of SNlis. voung and old. in nearby galaxies.,"of SNRs, young and old, in nearby galaxies."1168 Because the timescales for SNR. evolution are short compared to most of the processes that alfect the structure of galaxies. SNB catalogues provide a clean record of the environments where SNe explode. which can be used to put constraints on the properties of their. progenitors (e.g.Bacenesoet.al. 2009).," Because the timescales for SNR evolution are short compared to most of the processes that affect the structure of galaxies, SNR catalogues provide a clean record of the environments where SNe explode, which can be used to put constraints on the properties of their progenitors \citep[e.g.][]{badenes09:SNRs_LMC}."1169. Moreover. by considering the properties of the entire population of SNRs in a galaxy together with the bulk properties of the gas they are expanding into. we can eain insights into the evolutionary phases of SNRs (Woltjer 1972).. the structure of galaxies on scales comparable to the average SNR. size (Cox2005).. and the eveles of matter and energy in the interstellar medium (Ferriere2001)..," Moreover, by considering the properties of the entire population of SNRs in a galaxy together with the bulk properties of the gas they are expanding into, we can gain insights into the evolutionary phases of SNRs \citep{woltjer72:SNR-review}, the structure of galaxies on scales comparable to the average SNR size \citep{cox05:ISM}, and the cycles of matter and energy in the interstellar medium \citep{ferriere01:ISM}."1170 In this paper and in a companion publication (Maoz Badenes 2010. henceforth. Paper LI). we use the SNR population in the Magellanie Clouds to explore some of these issues.," In this paper and in a companion publication (Maoz Badenes 2010, henceforth Paper II), we use the SNR population in the Magellanic Clouds to explore some of these issues."1171 The Magellanic Clouds (AlC's) have the advantage of being close enough to study key aspects of their eloba structure in great. detail. and they also harbor a large anc extensively observed. population of SNRs.," The Magellanic Clouds (MCs) have the advantage of being close enough to study key aspects of their global structure in great detail, and they also harbor a large and extensively observed population of SNRs."1172 Thus. they are he optimal setting to study. the interplay between loca density. star formation. SN explosions. and SNR evolution on a galactic scale.," Thus, they are the optimal setting to study the interplay between local density, star formation, SN explosions, and SNR evolution on a galactic scale."1173" Our ultimate goal. and the focus of ""aper LL is to derive the SN rate and delay time distribution (i.c. the SN rate as a function of time following a brief burs of star formation) in the Magellanic Clouds."," Our ultimate goal, and the focus of Paper II, is to derive the SN rate and delay time distribution (i.e., the SN rate as a function of time following a brief burst of star formation) in the Magellanic Clouds."1174 However. this cannot be done without understanding first the relationship οποσα the Lifetime of SNRs and the properties of their ocal environments.," However, this cannot be done without understanding first the relationship between the lifetime of SNRs and the properties of their local environments."1175 This is the subject of the present. work., This is the subject of the present work.1176 The evolution of SNRs has been the subject of many woretical studies (c.g.Woltjer1972:Chevalier1982:Ciollietal.1988:Blondin1998:Truelove&Melxee 1999)..," The evolution of SNRs has been the subject of many theoretical studies \citep[e.g.,][]{woltjer72:SNR-review,chevalier82:selfsimilar,cioffi88:Radiative_SNRs,blondin98:Radiative_SNRs,truelove99:adiabatic-SNRs}."1177 Because accurate ages are only known lor a handful of voung. often historical objects. any observational tests of jese theoretical models must rely on SNIU size as à proxy or age.," Because accurate ages are only known for a handful of young, often historical objects, any observational tests of these theoretical models must rely on SNR size as a proxy for age."1178 Given that SNRs of equal ages will have cillerent sizes if they expand in dillerent media. this necessarily brings 16 role. of local density into the picture.," Given that SNRs of equal ages will have different sizes if they expand in different media, this necessarily brings the role of local density into the picture."1179 Previous works on the distribution of SNA sizes initially focused on the Milky Way and the MCS (c.g.Alathewsonetal.1984:Greennicutt 1988).. but. more recent elforts have also explored other galaxies in the Local Croup. including M31 (Magnier6al. 1997).. M33 (Longctal.2010).. and M83 (Dopita(al. 2010)..," Previous works on the distribution of SNR sizes initially focused on the Milky Way and the MCs \citep[e.g.][]{mathewson84:SNR-Magellanic-Clouds,green84:SNR_Statistics,hughes84:SNR_N_D,berkhuijsen87:SNRs_N_D,chu88:LMC_SNRs_environments}, but more recent efforts have also explored other galaxies in the Local Group, including M31 \citep{magnier97:M31_SNRs_ROSAT}, M33 \citep{long10:M33_SNRs}, and M83 \citep{dopita10:M83_SNRs}."1180 With few exceptions. these studies gave little consideration to the bulk properties of the gas in the galaxies hosting the SNRs.," With few exceptions, these studies gave little consideration to the bulk properties of the gas in the galaxies hosting the SNRs."1181 In many cases. their samples were also alfected by issues of completeness and. biases from working at à single wavelength.," In many cases, their samples were also affected by issues of completeness and biases from working at a single wavelength."1182 Not surprisingly. these efforts have failecl to produce a unified. physically motivated. picture of the evolution of SNRs in the interstellar medium.," Not surprisingly, these efforts have failed to produce a unified, physically motivated picture of the evolution of SNRs in the interstellar medium."1183 Here. we propose a first approximation to the problem in the contex of the Magellanic Cloucls.," Here, we propose a first approximation to the problem in the context of the Magellanic Clouds."1184 This paper is organized as follows., This paper is organized as follows.1185 In 2.. we presen a compilation of multi-wavelength observations for the 77 known SNRs in the Magellanic Clouds. and we argue tha ib provides a fairly complete record. of all the SNe tha have exploded over the last ~20 kyr.," In \ref{catalog}, we present a compilation of multi-wavelength observations for the 77 known SNRs in the Magellanic Clouds, and we argue that it provides a fairly complete record of all the SNe that have exploded over the last $\sim 20$ kyr."1186 In 3.. we examine the size distribution of SNRs in both galaxies. and we Line that the cumulative distribution is close to linear (i.e.. the clilferential is close to uniform). within the uncertainties associated with the relatively small number of objects. up to a marked cutoll at a physical radius of  30 pc.," In \ref{distribution}, we examine the size distribution of SNRs in both galaxies, and we find that the cumulative distribution is close to linear (i.e., the differential is close to uniform), within the uncertainties associated with the relatively small number of objects, up to a marked cutoff at a physical radius of $\sim$ 30 pc."1187 We also show that the SNR. size distribution in M33 has very similar properties. sugecsting that these features might be widespread.," We also show that the SNR size distribution in M33 has very similar properties, suggesting that these features might be widespread."1188 In 4. we propose a physical model to explain this distribution. based on the assumption that most objects are in the Sedov (adiabatic) stage of their evolution. and that they rapidly fade away once they transition to the radiative stage. at an age that depends on the local density.," In \ref{physics}, we propose a physical model to explain this distribution, based on the assumption that most objects are in the Sedov (adiabatic) stage of their evolution, and that they rapidly fade away once they transition to the radiative stage, at an age that depends on the local density."1189 Under these conditions. the uniform. distribution of SN sizes requires that the gas density in the. Clouds have a probability. distribution described. by a power. [aw with an index of 1 (Le. 8JP/óp~p5)," Under these conditions, the uniform distribution of SNR sizes requires that the gas density in the Clouds have a probability distribution described by a power law with an index of $-$ 1 (i.e., $\delta P / \delta \rho \sim \rho^{-1}$ )."1190 In 5. we test this requirement by examining the distribution of three independent density tracers in the Clouds: neutral hydrogen column density. Ho. surface brightness. ancl star-formation rate based. on resolved. stellar populations.," In \ref{densityestimates}, we test this requirement by examining the distribution of three independent density tracers in the Clouds: neutral hydrogen column density, $\alpha$ surface brightness, and star-formation rate based on resolved stellar populations."1191 We find. that these tracers are indeed: well described by powerlaws with a 1 index., We find that these tracers are indeed well described by powerlaws with a $-$ 1 index.1192 This lends creclence to our model. ancl provides us with the crucial means to estimate the visibility. time of SNRs in cillerent locations. which we review briclly in 6.. and more extensively in Paper H. where we use it to derive the SN rate and delay time distribution in the Clouds.," This lends credence to our model, and provides us with the crucial means to estimate the visibility time of SNRs in different locations, which we review briefly in \ref{sec:disc}, and more extensively in Paper II, where we use it to derive the SN rate and delay time distribution in the Clouds."1193 We conclude by summarizing our main results and outlining avenues for future work in στ., We conclude by summarizing our main results and outlining avenues for future work in \ref{sec:summary}.1194 The population of SNRs in the MCSs has been the object of extensive study for many decades., The population of SNRs in the MCs has been the object of extensive study for many decades.1195 Several catalogues have oen compiled at. dillerent. wavelengths. from the radio to he optical and X-ray.," Several catalogues have been compiled at different wavelengths, from the radio to the optical and X-ray."1196 Because SNRs in the Milky Way and he AIC's are usually cliscovered in the radio. it is the racio catalogues that often. have the largest. number of entries. out. there is some confusion in the literature regarding the otal number of SNRs in the Clouds.," Because SNRs in the Milky Way and the MCs are usually discovered in the radio, it is the radio catalogues that often have the largest number of entries, but there is some confusion in the literature regarding the total number of SNRs in the Clouds."1197 Filipovieetal.(1998) listect all the discrete racio sources in the Parkes survey of he MC's. and found 32 ος and 12 SN] candidates in the LAIC. and 12 SNIS in the SAIC.," \citet{filipovic98:MC_Radio_Discrete} listed all the discrete radio sources in the Parkes survey of the MCs, and found 32 SNRs and 12 SNR candidates in the LMC, and 12 SNRs in the SMC."1198 According to Payneetal. (2008).. a revision of the Parkes survey complemented with Australian Felecope Compact Array (ATCA) data vields 52 confirmed. SNRs and. 20 candidates in the LMC. but these sources are not listed in their paper.," According to \citet{payne08:LMCSNRs}, a revision of the Parkes survey complemented with Australian Telecope Compact Array (ATCA) data yields 52 confirmed SNRs and 20 candidates in the LMC, but these sources are not listed in their paper."1199 Instead. the authors present optical spectroscopy of 25 of the 52 confirmed LMC SNRs.," Instead, the authors present optical spectroscopy of 25 of the 52 confirmed LMC SNRs."1200 Data from ATCA was also collected for the SAIC. where Filipoviéetal.(2005). list 16 confirmed SNRs.," Data from ATCA was also collected for the SMC, where \citet{filipovic05:SMc_SNRs} list 16 confirmed SNRs."

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