source,target
" This is unsurprising, given the obvious relationship between temperature and thermal broadening and between inclination and rotational broadening."," This is unsurprising, given the obvious relationship between temperature and thermal broadening and between inclination and rotational broadening."
" The optically thick CO(3-2) line responds only weakly to variations in density, and the outer radius and position angle of emission should intuitively be unrelated to line broadening, hence the independence of turbulent linewidth from 61, R., and PA."," The optically thick CO(3-2) line responds only weakly to variations in density, and the outer radius and position angle of emission should intuitively be unrelated to line broadening, hence the independence of turbulent linewidth from $c_1$, $R_c$, and PA."
 For the D'Alessio et al., For the D'Alessio et al.
" models, inclination and CO abundance (i and Xco) have the strongest relationships with turbulent linewidth."," models, inclination and CO abundance $i$ and $X_{CO}$ ) have the strongest relationships with turbulent linewidth."
" The contribution of the CO abundance in this case can be understood as a thermal broadening effect: because of the vertical temperature gradient (see Figure 6)), the CO abundance controls the location of the 7—1 surface and therefore the apparent temperature of the CO(3-2) line emission."," The contribution of the CO abundance in this case can be understood as a thermal broadening effect: because of the vertical temperature gradient (see Figure \ref{fig:temp_dens}) ), the CO abundance controls the location of the $\tau$ =1 surface and therefore the apparent temperature of the CO(3-2) line emission."
" To characterize the effects of these variables on the observable properties of the CO(3-2) emission, we investigate their influence on a toy model of optically thick line emission."," To characterize the effects of these variables on the observable properties of the CO(3-2) emission, we investigate their influence on a toy model of optically thick line emission."
" We assume a power-law temperature distribution for a geometrically flat, optically thick, azimuthally symmetric circumstellar disk."," We assume a power-law temperature distribution for a geometrically flat, optically thick, azimuthally symmetric circumstellar disk."
" In the Rayleigh-Jeans approximation, the brightness of the line at a given frequency will be directly proportional to the temperature."," In the Rayleigh-Jeans approximation, the brightness of the line at a given frequency will be directly proportional to the temperature."
" We include two sources of line broadening, thermal and turbulent, implemented by the relationship Av(r)= where Av is the total linewidth, € is the turbulent ./2keT(r)/m+linewidth,£2, and the thermal linewidth is where kg is Boltzmann’s constant, T is the local \/2kgT/mtemperature in the disk, and m is the average mass per particle."," We include two sources of line broadening, thermal and turbulent, implemented by the relationship $\Delta v(r) = \sqrt{2 k_B T(r)/m + \xi^2}$ , where $\Delta v$ is the total linewidth, $\xi$ is the turbulent linewidth, and the thermal linewidth is $\sqrt{2 k_B T/m}$ where $k_B$ is Boltzmann's constant, $T$ is the local temperature in the disk, and $m$ is the average mass per particle."
 Rotational broadening isimplicitly included in the assumed Keplerian rotation, Rotational broadening isimplicitly included in the assumed Keplerian rotation
is to say. the first) ane second. bodies do not collide with cach other or any other bodies than the zeroth.,"is to say, the first and second bodies do not collide with each other or any other bodies than the zeroth."
 In practice. simulations redefine the relative coordinates whenever necessary. according to who is close to whom.)," In practice, simulations redefine the relative coordinates whenever necessary, according to who is close to whom.)"
 For the equations of motion we need. derivatives with respect to quaternion components., For the equations of motion we need derivatives with respect to quaternion components.
" First we have Vo,Q7= 391.", First we have $\nablaQ Q_1^2 = 2\Q_1$ .
" Slightly more subtle is Vg,reQjA]=A il A is independent of Qj.", Slightly more subtle is $\nablaQ \tr{\Q_1^*\A}=\A$ if $\A$ is independent of $\Q_1$.
 Using this last identity. together with the definition (31)) of LL. we derive Hamilton's equations are then and similarly for P».Q..," Using this last identity, together with the definition \ref{dotasPi}) ) of $\Pi$, we derive Hamilton's equations are then and similarly for $\P_2,\Q_2$."
 In dvnamical astronomy the IWS transformation is profound. but may appear mysterious.," In dynamical astronomy the KS transformation is profound, but may appear mysterious."
 This paper attempts to make ib less mysterious. ancl hopefully. therefore more. useful. bv explaining it in three-dimensional ecometric terms.," This paper attempts to make it less mysterious, and hopefully therefore more useful, by explaining it in three-dimensional geometric terms."
 There are several possible directions in which the Ks transformation may turn out to be useful., There are several possible directions in which the KS transformation may turn out to be useful.
 First. one can imagine new orbit integrators specialized to nearlv-Ixeplerian problems.," First, one can imagine new orbit integrators specialized to nearly-Keplerian problems."
 Work on dense stellar systems with near collisions has. alreacky been mentioned. (for.re-viewsseethebooks ??)..," Work on dense stellar systems with near collisions has already been mentioned \citep[for reviews see the
books][]{2003gnbs.book.....A,2003gmbp.book.....H}."
 In the planetary regime. which cilfers from the dense-stellar case in having few bodies bu many more orbital times. time transformations reminiscen of (28)) used. for WS regularization have proved: usefu for highly eccentric orbits (77).. while some integration algorithms (77) apply the time transformation (28)) implicitly.," In the planetary regime, which differs from the dense-stellar case in having few bodies but many more orbital times, time transformations reminiscent of \ref{kepeq}) ) used for KS regularization have proved useful for highly eccentric orbits \citep{1997CeMDA..67..145M,2002CeMDA..84..331E}, while some integration algorithms \citep{1999CeMDA..74..287M,1999AJ....118.2532P} apply the time transformation \ref{kepeq}) ) implicitly."
 C'ould the KS transformation itself be exploitec here?, Could the KS transformation itself be exploited here?
 ? has some further ideas., \cite{2005AJ....129.2496F} has some further ideas.
 Second. it is conceivable that KS variables: coul simply perturbation theory.," Second, it is conceivable that KS variables could simplify perturbation theory."
 Perturbation theory in Classical celestial mechanics (seeforexample?) is algebraically frighteningly complicated. basically because the natural variables for the unperturbecl ancl perturbed parts (being the Weplerian action-angles and real-space coordinate) are related. through an implicit equation.," Perturbation theory in classical celestial mechanics \citep[see for example][]{2000ssd..book.....M} is algebraically frighteningly complicated, basically because the natural variables for the unperturbed and perturbed parts (being the Keplerian action-angles and real-space coordinate) are related through an implicit equation."
= On the other hand. the action-angles of the IxXS-transformed Ixepler problem are explicitly related to space coordinatesthe implicit equation is transferred. to the time variable.," On the other hand, the action-angles of the KS-transformed Kepler problem are explicitly related to space coordinates---the implicit equation is transferred to the time variable."
 Could some major simplication be achieved. through Ks variables?, Could some major simplication be achieved through KS variables?
 Some progress has been mace by ?.., Some progress has been made by \cite{2006NewA...11..366V}.
 Third. the INS transformation might provide new insight into analogous quantum problem.," Third, the KS transformation might provide new insight into analogous quantum problem."
 ?? derive the symmetry groups of the bound and unbound Coulomb problem.," \cite{RevModPhys.38.330,RevModPhys.38.346} derive the symmetry groups of the bound and unbound Coulomb problem."
 These turn out to be the same four-dimensional svmimetries as in IxS theory., These turn out to be the same four-dimensional symmetries as in KS theory.
 Is the KS transformation implicit in that work?, Is the KS transformation implicit in that work?
 Lam grateful to thank Seppo Alikkola for introducing me to WS theory. and to Marcel Zemp. Scott Tremaine. and the referee. JOrre Waldvogel. for suggesting improvements in the nianuscript.," I am grateful to thank Seppo Mikkola for introducing me to KS theory, and to Marcel Zemp, Scott Tremaine, and the referee, Jörrg Waldvogel, for suggesting improvements in the manuscript."
"where e is defined in eq.(1). and (he superscripts Ο ancl S. denote observed image ancl source. respectively,","where $\mathbf{e}$ is defined in eq.(1), and the superscripts 'O' and 'S' denote observed image and source, respectively."
" Then (he noisy convergence &,, including the contamination Iron source elliplicilies follows Considering smoothed quantities. we have (e.g.. van Waerbeke 2000) ancl where X. P. and Avy(0) are the smoothed οἱο). 5 and &,. respectively. WW(4) is the smoothing function. and n», and .N, are. respectively. the surface number density and the nunmber of source galaxies in (he field."," Then the noisy convergence $\kappa_n$ including the contamination from source ellipticities follows Considering smoothed quantities, we have (e.g., van Waerbeke 2000) and where $\mathbf{\Sigma}^{(O)}$ , $\mathbf{\Gamma}$, and $K_N(\vec \theta)$ are the smoothed $\mathbf{e^{(O)}}$, $\gamma$ and $\kappa_n$ , respectively, $W(\vec \theta)$ is the smoothing function, and $n_g$ and $N_g$ are, respectively, the surface number density and the number of source galaxies in the field."
 The noise part of A due to the intrinsic ellipticities is then where HV(&) is the Fourier transformation of the smoothing function with the form Following van Waerbeke (2000). the correlation of NV(4) is caleulated by averaging over both the ellipticities and the positions of source galaxies.," The noise part of $K_N$ due to the intrinsic ellipticities is then where $\tilde W(\vec k)$ is the Fourier transformation of the smoothing function with the form Following van Waerbeke (2000), the correlation of $N(\vec \theta)$ is calculated by averaging over both the ellipticities and the positions of source galaxies."
" Without intrinsic alignments. the correlation of N(@) arises only [rom the smoothing operations. and by ignoring the sampling of source galaxies. we have (van Waerbeke 2000) where o, is the intrinsic dispersion of e). and the factor (27)? comes in to be in accord wilh the definition of W(&) in eq. ("," Without intrinsic alignments, the correlation of $N(\vec \theta)$ arises only from the smoothing operations, and by ignoring the non-uniform sampling of source galaxies, we have (van Waerbeke 2000) where $\sigma_{\epsilon}$ is the intrinsic dispersion of $\mathbf{e}^{(S)}$, and the factor $(2\pi)^2$ comes in to be in accord with the definition of $\tilde W(\vec k)$ in eq. ("
15).,15).
 Including the alignment. theoperation by averaging over (he ellipticiüesof source ealaxies. denoted by ;1 following van Waerbeke (2000). is," Including the alignment, theoperation by averaging over the ellipticitiesof source galaxies, denoted by ${\it {A}}$ following van Waerbeke (2000), is"
 , 
(he solar convection zone than it does al the Earth's tropopause.,the solar convection zone than it does at the Earth's tropopause.
 These differences can have prolound effects on the role of overshoot and. hence. on the scale. frequency. and amplitude of (he waves generated and. so. on the angular momentum transport bv these waves.," These differences can have profound effects on the role of overshoot and, hence, on the scale, frequency and amplitude of the waves generated and, so, on the angular momentum transport by these waves."
 Numerical simulations (Wedi Smolarkiewicz 2005) of the Phumb-MeEswan laboratory experiment attempting to reproduce (he QDO. have shown (hat the (wpe and period of an oscillation in the differential rotation profile depend sensitively on the lorcing.," Numerical simulations (Wedi Smolarkiewicz 2005) of the Plumb-McEwan laboratory experiment attempting to reproduce the QBO, have shown that the type and period of an oscillation in the differential rotation profile depend sensitively on the forcing."
 In particular. ib is found that random forcing rarely produces a periodic oscillation.," In particular, it is found that random forcing rarely produces a periodic oscillation."
 Given the turbulent nature of the sun. it is likely that the forcing is fairly random.," Given the turbulent nature of the sun, it is likely that the forcing is fairly random."
 For reasons stated above. it is unlikely (hat there is à QBO-like oscillation associated with the solar tachcocline.," For reasons stated above, it is unlikely that there is a QBO-like oscillation associated with the solar tachcocline."
 Lowever. QDO-like oscillations may occur in stars will radiative envelopes because of the inelliciency of overshoot into an overlving stable region. and because ol more similar geometry.," However, QBO-like oscillations may occur in stars with radiative envelopes because of the inefficiency of overshoot into an overlying stable region, and because of more similar geometry."
 We have presented self-consistent numerical simulations of convective overshoot ancl eravily wave generation and (he angular momentum (ransport by these processes in a 2D model of the dynamics in the solar equatorial plane., We have presented self-consistent numerical simulations of convective overshoot and gravity wave generation and the angular momentum transport by these processes in a 2D model of the dynamics in the solar equatorial plane.
 We find (hat angular velocity variations in (he tachocline are driven by angular momentum t(rausported by overshooting plumes rather (han nonlinear interaction of low amplitude waves., We find that angular velocity variations in the tachocline are driven by angular momentum transported by overshooting plumes rather than nonlinear interaction of low amplitude waves.
 These overshooting plumes are strongly nonlinear disturbances. which can not be accurately represented as an increased fIux of linear waves.," These overshooting plumes are strongly nonlinear disturbances, which can not be accurately represented as an increased flux of linear waves."
 We observe a semi-periodic oscillation in amplitude. but not in direction. of (he mean flow in the tachocline because of an asvimnietry in the driving of prograde and retrograde motions.," We observe a semi-periodic oscillation in amplitude, but not in direction, of the mean flow in the tachocline because of an asymmetry in the driving of prograde and retrograde motions."
 Since we find that linear gravity waves are not dominant in the tachocline it is unlikely Chat thev are responsible for the 1.3 vear oscillation or the 11 vear solar cvele., Since we find that linear gravity waves are not dominant in the tachocline it is unlikely that they are responsible for the 1.3 year oscillation or the 11 year solar cycle.
 It is no surprise (hat overshooting motions plav a dominant role in the tachocline aud we expect these results will persist in three-dimensions., It is no surprise that overshooting motions play a dominant role in the tachocline and we expect these results will persist in three-dimensions.
 In the deep radiative interior the continual deposition of angular momentum by the Yonlinear interaction of gravity waves produces a radiallv banded differential rotation., In the deep radiative interior the continual deposition of angular momentum by the nonlinear interaction of gravity waves produces a radially banded differential rotation.
 However. il remains {ο be seen whether this pattern persists in 3D. considering its verv low amplitude.," However, it remains to be seen whether this pattern persists in 3D, considering it's very low amplitude."
 In the models core. the amplitude of the differential rotation (ie.. angular velocitv) is arger. about (vo orders of magnitude larger than that in the bulk of the radiative region and similar to the magnitude within the convection zone.," In the model's core, the amplitude of the differential rotation (i.e., angular velocity) is larger, about two orders of magnitude larger than that in the bulk of the radiative region and similar to the magnitude within the convection zone."
 We observe retrograde motion in (he core reversing (o prograde motion in step with the counter-reversal (prograde (o retrograde) at the tachocline., We observe retrograde motion in the core reversing to prograde motion in step with the counter-reversal (prograde to retrograde) at the tachocline.
 When (here is predominantly prograde flow at the base of, When there is predominantly prograde flow at the base of
 1 (IXomossactal.2003.seeColpi& ~ (ATaness," $\lsim 1$ \citep[][see Colpi \& Dotti 2009 for
 a recent review]{komossa2003}."
etal.2001:Rodriguez2006).," $\sim$ \citep{maness2004,rodriguez2006}."
 z7 (2=0.055) (seeValtonenetal.2008.andreferencestherein).. zz12 (Bee," $\approx 7$ $z = 0.055$ \citep[see][and references
 therein]{valtonen2008}."
chnan.Dlaudford&Rees1980)., $\approx 12$ \citep{begelman1980}.
 stripped by the eravitational poteutial of the companion. resulting iu peculiar flux ratios between DLs with different ionization potential (Montuorietal.2010).," stripped by the gravitational potential of the companion, resulting in peculiar flux ratios between BLs with different ionization potential \citep{montuori2010}."
. This spectroscopic approach does not suffer any aueular resolution limitations: Actually. the closer (aud more massive} the binary is. the more shifted/deforined the DLs are.," This spectroscopic approach does not suffer any angular resolution limitations: Actually, the closer (and more massive) the binary is, the more shifted/deformed the BLs are."
" Thaulss to the existence of large spectroscopic survevs, such as the Sloan Digital Skv Survey (SDSS). a laree region of the skv can be probed."," Thanks to the existence of large spectroscopic surveys, such as the Sloan Digital Sky Survey (SDSS), a large region of the sky can be probed."
 Up to date five spectroscopically identified candidates have Όσοι preseuted: J0927|2913 (Ixoiossa.Zhou&Lu2008:Dos-dauovic.Eracleous&Sigurdsson2009:Dottietal. 2009). J1536|0111. CBorosoun&Lauer2009).. J1050|3156 (Shieldsetal.2009)... 1€|22.25 (J1000|2233per.Decarlietal. 201053... and JO9320318 (Barrowsctal. 2011)..," Up to date five spectroscopically identified candidates have been presented: J0927+2943 \citep{komossa08,bogdanovic09,dotti09}, J1536+0441 \citep{boroson09}, J1050+3456 \citep{shields09}, 4C+22.25 \citep[J1000+2233 in this paper,][]{decarli_4c2225}, and J0932+0318 \citep{barrows11}. ."
 Such à simall umber of objects| is mareiually compatible with the theoretically predicted. umber of sub-parsec BUBs at τς0.7 (510.eiventhemergerrateandobservabilitv:seeVolouterietal. 2009).," Such a small number of objects is marginally compatible with the theoretically predicted number of sub-parsec BHBs at $z \lsim 0.7$ \citep[5--10, given the merger rate and
under reasonable assumptions on the binary lifetime and observability; 
see][]{volonteri09}."
. The spectroscopic approach las an obvious drawback: a peculiar spectrum does not euarantee the presence of a DIID iu the uucleus of the host., The spectroscopic approach has an obvious drawback: a peculiar spectrum does not guarantee the presence of a BHB in the nucleus of the host.
 As an example. an nnobscirecdk BIB with both DIIs active could resaiid5 the spectrum of a double peaked. emitter (see.e.g..Er-acleous&Παρα 1991).. where broad doublepeaked lines are cluitted because of the almost οσοon. disklike structure of the DL region ofa single BIT.," As an example, an unobscured BHB with both BHs active could resamble the spectrum of a double peaked emitter \citep[see,
 e.g.,][]{eracleous1994}, where broad double–peaked lines are emitted because of the almost edge–on, disk–like structure of the BL region of a single BH."
 A binary with a single accreting DIT would show a single shifted BL., A binary with a single accreting BH would show a single shifted BL.
 It the shift corresponds to a relatively small velocity along the line of sightCZ1000 kun s +). the same signature could be emitted by a remnant ofa binary coalescence. recoiling because of anisotropicgravitational wave cussion (e.g.," If the shift corresponds to a relatively small velocity along the line of sight$\lsim 4\,000$ km $^{-1}$ ), the same signature could be emitted by a remnant of a binary coalescence, recoiling because of anisotropicgravitational wave emission \citep[e.g.][]{komossa08}"
QPOs possidv. observed from £U 155030 (Zhaue 11998) a signature of the preseuce of the innermost stable circular orbit 15600). a crucial prediction of stroug-eravitv general relativity.,"QPOs possibly observed from 4U 1820–30 (Zhang 1998) a signature of the presence of the innermost stable circular orbit (ISCO), a crucial prediction of strong-gravity general relativity."
 σος only iu BFAIs cau one infer a Hel gravitational mass M>ολ. for this source. which constraius strouglv the equation of state of the high-density matter in fre core of neutron stars.," Hence only in BFMs can one infer a high gravitational mass $M>2.1M_\odot$ for this source, which constrains strongly the equation of state of the high-density matter in the core of neutron stars."
 The chawine separation frequency observed iu several sources provided part of the motivation for t16 development of other models of the silohertz QPOs. iu utieular the relativisic precession models (e.g.. Stella Vietzii 1998).," The changing separation frequency observed in several sources provided part of the motivation for the development of other models of the kilohertz QPOs, in particular the relativistic precession models (e.g., Stella Vietri 1998)."
 In these nodels the close match between t16 separation frequency aud the spin frequency interred from burst brielitucss oscilations is a coincideice. but they do precict the qualitative effect ofa searation frequency hat drops with increasing kilohertz QPO YOequencev.," In these models the close match between the separation frequency and the spin frequency inferred from burst brightness oscillations is a coincidence, but they do predict the qualitative effect of a separation frequency that drops with increasing kilohertz QPO frequency."
 Tere we discuss the beat-frequeACY nocclin helt of hese new developeits ancl contrast it with alternate pictures., Here we discuss the beat-frequency model in light of these new developments and contrast it with alternate pictures.
 Ins 2 we describe tιο observaional trends that notivated the development of bea-frequeicv models., In 2 we describe the observational trends that motivated the development of beat-frequency models.
 We then οaborate oi these uodels; iu particular the souic-poiut beat-frequency model.," We then elaborate on these models, in particular the sonic-point beat-frequency model."
 In 3Pa we ¢iscuss the evicence for a changine difference yequenc wodmn the four sources Sco X-1. IU IT 172831. aud. IU 1735|ο," In 3 we discuss the evidence for a changing difference frequency in the four sources Sco X-1, 4U 1608--52, 4U 1728–34, and 4U 1735–44."
" Wes row that an aspect of the sonic-poiut veat-frequency iiocdel. iucluded iu the ανiuues but originally onuittec from the yequency estimates, naturally accomunodates the changing difference frecποιον axd can quautitative vt he data."," We show that an aspect of the sonic-point beat-frequency model, included in the dynamics but originally omitted from the frequency estimates, naturally accommodates the changing difference frequency and can quantitatively fit the data."
 Finally. in Lie contrast some of he predictions of he beat-frequency uodoel with the predictions of he relativistic precession model. aud cliscuss analysis that ασ! be doue with ctirent data to help discriminate vetween the two iteroxetatious.," Finally, in 4 we contrast some of the predictions of the beat-frequency model with the predictions of the relativistic precession model, and discuss analysis that might be done with current data to help discriminate between the two interpretations."
 We also explore fje inurpact of future observations. oth with the u»voniues eeneration of Ligh spectral resolution satellites (such as Chandra and NMBM) aid with louger-terii projecs such as Constellation-N. aud a wpothetical ligarea follow-on toXTE.," We also explore the impact of future observations, both with the upcoming generation of high spectral resolution satellites (such as Chandra and XMM) and with longer-term projects such as Constellation-X and a hypothetical high-area follow-on to."
 As discussed iu the iitroductiou. soon after the discovery of kiloverte QPOs it was established tha these oscilations have (1) higoh frequency. (2) high amplitide. aud (3) high colereicc. àid that there are always two or fewer kiohertz QPOs iu a eiveu oer density spectrmu.," As discussed in the introduction, soon after the discovery of kilohertz QPOs it was established that these oscillations have (1) high frequency, (2) high amplitude, and (3) high coherence, and that there are always two or fewer kilohertz QPOs in a given power density spectrum."
 T1 addition. the separation frequency a»peared Consistct with constant mi many solrees and close to the spin frequeicy interred frou burst xiehtuess oscillatious iu he four sources where this coud be tested.," In addition, the separation frequency appeared consistent with constant in many sources and close to the spin frequency inferred from burst brightness oscillations in the four sources where this could be tested."
 Tt is LOW shown (see 23) tha in several. aud perhaps all. sources. tιο separation frequency is coustant (although 1 is still close to the interred spin frequency). ai in fact decreases systenati‘ally with increasing lower peak frequency.," It is now known (see 3) that in several, and perhaps all, sources, the separation frequency is constant (although it is still close to the inferred spin frequency), and in fact decreases systematically with increasing lower peak frequency."
 In 3 owe diseuss row this new result nay be interpreted within the beat-frequeney model., In 3 we discuss how this new result may be interpreted within the beat-frequency model.
 The Hel freqcacy indicates that the source of the brightucss oscillations is close to the neutron star., The high frequency indicates that the source of the brightness oscillations is close to the neutron star.
 A natural candidate for these oscillations is the orbital yequency at sole special radius., A natural candidate for these oscillations is the orbital frequency at some special radius.
 Caven that the burst oscillation frequency is most convincingly iutermeted as the stellar spin frequeney or its first overtone (sec. e.g.. Strolunaver AMarkwardt 1999). the close match of the separation frequency," Given that the burst oscillation frequency is most convincingly interpreted as the stellar spin frequency or its first overtone (see, e.g., Strohmayer Markwardt 1999), the close match of the separation frequency"
Radio galaxies. with linear sizes reaching up to several neeaparsecs. are possibly the largest individual objects in the Universe.,"Radio galaxies, with linear sizes reaching up to several megaparsecs, are possibly the largest individual objects in the Universe."
 It is widely accepted that thev originate roni highly energetic unou-theriial processes occurring iun he nucleus of the so-called active galaxies (Blandford Rees 197E: Rees 1978))., It is widely accepted that they originate from highly energetic non-thermal processes occurring in the nucleus of the so-called active galaxies (Blandford Rees \cite{blandford}; Rees \cite{rees1}) ).
 According to the standard model of active galactic nuclei. (ACNs). a super-massive black role with a nass between 109 and ΤοAL. resides iu he ceuter of the active galaxy. powered by an accretion disk STLPOUMLICed by a torus formed by eas aud dust.," According to the standard model of active galactic nuclei (AGNs), a super-massive black hole with a mass between $10^6$ and $10^9 M\odot$, resides in the center of the active galaxy, powered by an accretion disk surrounded by a torus formed by gas and dust."
" Iu about of these Ανα, there is intense svuchrotrou radio enissiou produced iu a bipolar ottfow of relativistic particles expelled perpendicularly to the plane of the disk aud extending to distances reaching the meeaparsec scales."," In about of these AGNs, there is intense synchrotron radio emission produced in a bipolar outflow of relativistic particles expelled perpendicularly to the plane of the disk and extending to distances reaching the megaparsec scales."
 The reason why an ACN prescuts or not powerful radio enüssion is matter of strong debate., The reason why an AGN presents or not powerful radio emission is matter of strong debate.
 While there is Increasing evidence about the existence of superanassive black holes in the center of AGNs. iux even at the uuclei of nou active galaxies (Macchetto. 1999:: I&onueudy. Gebhardt 2001)). if has been argued tiat the preseuce or uot of iuteuse radio emission might be due to the rotatiou velocity of the black hole (e.g. Wilson Colbert 1995: Cavaliere D'Elia 20023). or to its total mass aud the efficiency. of accretion (àcLure Duulop 2001:: Dunlop et al. 2003).," While there is increasing evidence about the existence of super-massive black holes in the center of AGNs, and even at the nuclei of non active galaxies (Macchetto \cite{macchetto}; Kormendy Gebhardt \cite{kormendy}) ), it has been argued that the presence or not of intense radio emission might be due to the rotation velocity of the black hole (e.g. Wilson Colbert \cite{wilson}; Cavaliere D'Elia \cite{cavaliere}) ), or to its total mass and the efficiency of accretion (McLure Dunlop \cite{mclure}; Dunlop et al. \cite{dunlop2}) )."
 Considering a natural evolutionary sequence of radio ealaxies. jets clmanating from the couter of activity start boring their way fwoueh the iuterstellar mediuu first. reaching the ealactic halo aud in some large cases the intergalactic uediunu.," Considering a natural evolutionary sequence of radio galaxies, jets emanating from the center of activity start boring their way through the interstellar medium first, reaching the galactic halo and in some large cases the intergalactic medium."
 Finally. the lobes of radio galaxies which have ceased them central activity expand aud disappear in the external medium.," Finally, the lobes of radio galaxies which have ceased their central activity expand and disappear in the external medium."
 Badio sources represcuting these differeut pliases of evolution are currently known adding support to this scenario: compact svuunetrie objects (CSOs: Wilkinson ct al. 1991)), Radio sources representing these different phases of evolution are currently known adding support to this scenario: compact symmetric objects (CSOs; Wilkinson et al. \cite{wilkinson}))
" are thought to be voung radio eaaxies (ος, Owsianilk Comvay 1998)). while the eianut radio galaxies (GRCGs: defined as those with a projected linear > 1 Mpc) are probably old objects at the latter stages of evolution (slovara-Chancdra Saikia 1999))."," are thought to be young radio galaxies (e.g. Owsianik Conway \cite{owsianik}) ), while the giant radio galaxies (GRGs; defined as those with a projected linear $\ge$ 1 Mpc) are probably old objects at the latter stages of evolution (Ishwara-Chandra Saikia \cite{ishwara}) )."
 Relic radio sources found in clusters of galaxies ποτ correspond to the last detectable cussion from “dead” radio galaxies (e.g. TNomissarov Cubanov 1991: Slee et al. 2001))., Relic radio sources found in clusters of galaxies might correspond to the last detectable emission from “dead” radio galaxies (e.g. Komissarov Gubanov \cite{komissarov}; Slee et al. \cite{slee}) ).
 However. the degree of influence of parameters other than the age (e.g. source power. conditions of the external mediun)iu the evolution of radio galaxies is not clear.," However, the degree of influence of parameters other than the age (e.g. source power, conditions of the external medium) in the evolution of radio galaxies is not clear."
 For example. although there is observational evidence supporting the voune source scenario for CSOs. it has also been argued that CSOs are short lived objects which never reach the size of their bie relatives (Reacdhead et al. 1991)).," For example, although there is observational evidence supporting the young source scenario for CSOs, it has also been argued that CSOs are short lived objects which never reach the size of their big relatives (Readhead et al. \cite{readhead}) )."
 At he other extreme. GRGs could be the result of normal Yaio galaxies expanding in very low density environments permitting them to reach their overwhehuing sizes.," At the other extreme, GRGs could be the result of normal radio galaxies expanding in very low density environments permitting them to reach their overwhelming sizes."
 But they could also result from very powerful core activity. or both concditious must apply for a radio galaxy to become a eiut.," But they could also result from very powerful core activity, or both conditions must apply for a radio galaxy to become a giant."
 Complicating the previously outlined. evolutionary sequence. sole radio galaxies secu. to wake up after a dormant phase of absence or much lower activity (c.g. Lara et al. 1999a)).," Complicating the previously outlined evolutionary sequence, some radio galaxies seem to wake up after a dormant phase of absence or much lower activity (e.g. Lara et al. \cite{lara}) )."
 Moreover. the presence of super-auassive objects in inanv nonactive galaxies argue im favor of activity as a short trausition period in most. if not all. (elliptical) galaxies. aud that the “menace” for future activity is present at the ceuter of every. galaxy.," Moreover, the presence of super-massive objects in many non–active galaxies argue in favor of activity as a short transition period in most, if not all, (elliptical) galaxies, and that the “menace"" for future activity is present at the center of every galaxy."
 This paper is the last of a series of three devoted to the study of a sample of large augular size radio galaxies which try to address some of these open questions., This paper is the last of a series of three devoted to the study of a sample of large angular size radio galaxies which try to address some of these open questions.
 Definition of the sample and radiomaps in one side. and tages and spectroscopic data on the other. were preseuted by Lara ct al. (2001a.. ," Definition of the sample and radiomaps in one side, and images and spectroscopic data on the other, were presented by Lara et al. \cite{paperI}, ,"
hereafter Paper I) auc (2001b.. Paper," hereafter Paper I) and \cite{paperII}, , Paper"
"boundary conditions (e.g. existence of a planetary surface), chemistry, and the properties of the condensating species, such that a direct comparison with these atmospheres is difficult.","boundary conditions (e.g. existence of a planetary surface), chemistry, and the properties of the condensating species, such that a direct comparison with these atmospheres is difficult."
" Nonetheless, effective cloud formation in these atmospheres can, for example, also significantly alter the thermal emission and reflection spectra of these objects by means of both the scattering and absorption of radiation caused by cloud particles."," Nonetheless, effective cloud formation in these atmospheres can, for example, also significantly alter the thermal emission and reflection spectra of these objects by means of both the scattering and absorption of radiation caused by cloud particles."
" In this paper, we study the influence of low- and high-level clouds on the reflectance spectra and spectral albedos of Earth-like planets in the visible and NIR wavelength range at low resolution."," In this paper, we study the influence of low- and high-level clouds on the reflectance spectra and spectral albedos of Earth-like planets in the visible and NIR wavelength range at low resolution."
 A one-dimensional (1D) steady-state radiative-convective atmospheric model is used in the model calculations., A one-dimensional (1D) steady-state radiative-convective atmospheric model is used in the model calculations.
 The model accounts for two different cloud layers (low-level water droplet and high-level ice particle clouds) and for the partial overlap of these two layers., The model accounts for two different cloud layers (low-level water droplet and high-level ice particle clouds) and for the partial overlap of these two layers.
 A more detailed model description is given in Sect. 2.., A more detailed model description is given in Sect. \ref{sec_model}.
" To verify the applicability of our modelling approach, this coupled cloud-atmosphere model is applied to the modern Earth atmosphere and its spectral appearance, as described in Sect. 3.."," To verify the applicability of our modelling approach, this coupled cloud-atmosphere model is applied to the modern Earth atmosphere and its spectral appearance, as described in Sect. \ref{sec_earth_ref}."
 The resulting reflection spectra and spectral albedos of Earth-like planets orbiting different types of central stars and their implications for the detectability of characteristic molecular signatures are presented in Sect. 4.., The resulting reflection spectra and spectral albedos of Earth-like planets orbiting different types of central stars and their implications for the detectability of characteristic molecular signatures are presented in Sect. \ref{sec_spectra}.
 The impact of clouds on the thermal IR emission spectra was investigated in detail by ? (henceforth called Paper II) for Earth-like planets around different types of stars., The impact of clouds on the thermal IR emission spectra was investigated in detail by \citet{Kitzmann2011A&A531} (henceforth called Paper II) for Earth–like planets around different types of stars.
" However, clouds also affect the reflected incident stellar radiation in the short wavelength range, from the NUV to NIR, of the planetary spectrum."," However, clouds also affect the reflected incident stellar radiation in the short wavelength range, from the NUV to NIR, of the planetary spectrum."
" We study here the influence of clouds on planetary reflection spectra at low resolution using a 1D steady-state radiative-convective atmospheric model developed to account for the radiative effects of multi-layered clouds and their impact on the surface temperature in atmospheres of Earth-like planets (see?,PaperI,fordetails).."," We study here the influence of clouds on planetary reflection spectra at low resolution using a 1D steady-state radiative-convective atmospheric model developed to account for the radiative effects of multi-layered clouds and their impact on the surface temperature in atmospheres of Earth-like planets \citep[see][Paper I, for details]{Kitzmann2010}."
" We adopt a parameterised description of two different cloud layers, low-level droplet and high-level ice particle clouds, that is derived from in-situ measurements of the respective cloud type in the atmosphere of Earth."," We adopt a parameterised description of two different cloud layers, low-level droplet and high-level ice particle clouds, that is derived from in-situ measurements of the respective cloud type in the atmosphere of Earth."
" This cloud model is included into the originally cloud-free atmospheric model of ?,, in its form developed by ? and ?.."," This cloud model is included into the originally cloud-free atmospheric model of \citet{Kasting1984}, in its form developed by \citet{Pavlov00} and \citet{Segura03}."
" To limit the number of cloud parameters, the minimal possible partial overlap of both cloud layers is assumed in the calculations unless otherwise stated."," To limit the number of cloud parameters, the minimal possible partial overlap of both cloud layers is assumed in the calculations unless otherwise stated."
" The altitude of each cloud layer is not simply fixed in height, but iteratively adjusted to match the corresponding measured Earth pressure values (low-level water cloud: 0.83bar, high-level ice cloud: 0.27 bar)."," The altitude of each cloud layer is not simply fixed in height, but iteratively adjusted to match the corresponding measured Earth pressure values (low-level water cloud: $0.83~\mathrm{bar}$, high-level ice cloud: $0.27~\mathrm{bar}$ )."
 The freezing limit of the water droplets and the limiting temperature for liquefying the ice particles determine the range of temperatures for which our method is valid (cf., The freezing limit of the water droplets and the limiting temperature for liquefying the ice particles determine the range of temperatures for which our method is valid (cf.
 PaperD)., Paper.
".. For all calculations, the same chemical composition of the atmosphere is assumed, which is chosen to represent modern Earth conditions (see?).."," For all calculations, the same chemical composition of the atmosphere is assumed, which is chosen to represent modern Earth conditions \citep[see][]{Grenfell07}."
 The treatment of the radiation transfer problem in the atmospheric model is optimised for the energy transport in Earth-like atmospheres (e.g.?).., The treatment of the radiation transfer problem in the atmospheric model is optimised for the energy transport in Earth-like atmospheres \citep[e.g.][]{Mlawer97}.
" As usual, the calculation of the radiation transport is divided into two spectral parts."," As usual, the calculation of the radiation transport is divided into two spectral parts."
" The first part treats the absorption and scattering of incident solar radiation in the short wavelength regime, the second handles the absorption and emission of thermal radiation from the planetary surface and atmosphere, including the multiple scattering caused by cloud particles."," The first part treats the absorption and scattering of incident solar radiation in the short wavelength regime, the second handles the absorption and emission of thermal radiation from the planetary surface and atmosphere, including the multiple scattering caused by cloud particles."
" The plane-parallel radiative transfer equation in the short wavelength regime is solved by applying a 6-two-stream quadrature approach (?)., which uses 38 broad spectral intervals between 0.238 um and 4.55 um with variable spectral resolution (10 <R<100)."," The plane-parallel radiative transfer equation in the short wavelength regime is solved by applying a $\delta$ -two-stream quadrature approach \citep{Toon89}, which uses 38 broad spectral intervals between 0.238 $\mu$ m and 4.55 $\mu$ m with variable spectral resolution $10 \leq$ $\leq 100$ )."
" These intervals define the spectral resolution of the planetary spectra presented here, which are obtained directly from the radiative transfer calculations of the atmospheric model."," These intervals define the spectral resolution of the planetary spectra presented here, which are obtained directly from the radiative transfer calculations of the atmospheric model."
" The molecular absorption of HzO, CO», O2, O3, and CH, is treated with four- correlated-k coefficients (cf.?).."," The molecular absorption of $_2$ O, $_2$, $_2$, $_3$, and $_4$ is treated with four-term $k$ coefficients \citep[cf.][]{Segura03}."
" Rayleigh scattering is considered for O5», No, and CO; in this wavelength region."," Rayleigh scattering is considered for $_2$, $_2$, and $_2$ in this wavelength region."
 A description of the IR radiation transport treatment and the resulting thermal emission spectra is given in Paper II., A description of the IR radiation transport treatment and the resulting thermal emission spectra is given in Paper II.
" In addition to the gas opacities, the frequency-dependent optical properties of the cloud particles were previously introduced into the radiative transfer schemes including multiple scattering (Paper I)."," In addition to the gas opacities, the frequency-dependent optical properties of the cloud particles were previously introduced into the radiative transfer schemes including multiple scattering (Paper I)."
" To account for different coverages of multi-layered clouds and their partial overlap (being non uni-dimensional quantities) in a 1D atmospheric model, we use a flux-averaging procedure, where the radiative transfer problem is solved for every distinct cloud configuration separately."," To account for different coverages of multi-layered clouds and their partial overlap (being non uni-dimensional quantities) in a 1D atmospheric model, we use a flux-averaging procedure, where the radiative transfer problem is solved for every distinct cloud configuration separately."
" By averaging these radiation fluxes weighted with the respective cloud cover values, the mean radiative flux is obtained, which then enters into the atmospheric model calculations (see Paper I for details)."," By averaging these radiation fluxes weighted with the respective cloud cover values, the mean radiative flux is obtained, which then enters into the atmospheric model calculations (see Paper I for details)."
an assumed effective temperature of 2500 K. The values given in Table 1 for the systemic velocity of the source and the terminal velocity of the outflow were based upon Herschel/HIFI observations of the CO J=6—5 transition at 691.473 GHz (Schmidt et 22010) and are in excellent agreement with previous determinations by BWO1.,an assumed effective temperature of 2500 K. The values given in Table 1 for the systemic velocity of the source and the terminal velocity of the outflow were based upon /HIFI observations of the CO $J=6-5$ transition at 691.473 GHz (Schmidt et 2010) and are in excellent agreement with previous determinations by BW01.
" To obtain an estimate of the total mass-loss rate in the outflow, we have modeled the fluxes observed by Herschel/HIFI for the CO J= 6-5, J=10-9 and J=16—15 transitions."," To obtain an estimate of the total mass-loss rate in the outflow, we have modeled the fluxes observed by /HIFI for the CO $J=6-5$ , $J=10-9$ and $J=16-15$ transitions."
 Full details of the observations and modeling of CO will be given by Schmidt et ((2010)., Full details of the observations and modeling of CO will be given by Schmidt et (2010).
" Our best estimate of the gas mass-loss rate in the inner envelope is 4.6x10°°Moyr, a factor ~3 larger than that obtained by Schóiier Olofsson (2000) from a fit to the CO J=2—I transition, and the derived CO/H> ratio is 10-3."," Our best estimate of the gas mass-loss rate in the inner envelope is $4.6 \times 10^{-6} M_\odot\, \rm yr^{-1},$ a factor $\sim 3$ larger than that obtained by Schöiier Olofsson (2000) from a fit to the CO $J=2-1$ transition, and the derived $_2$ ratio is $^{-3}$."
" Indeed, we find that a constant mass- rate model that fits the CO J=6—5, J=10—9 and J=16—15 transitions substantially overpredicts the flux in the CO J=2-1 transition."," Indeed, we find that a constant mass-loss rate model that fits the CO $J=6-5$, $J=10-9$ and $J=16-15$ transitions substantially overpredicts the flux in the CO $J=2-1$ transition."
" This discrepancy suggests some variability in the mass-loss rate, with a larger value applying to the inner envelope where the higher-lying transitions of CO originate."," This discrepancy suggests some variability in the mass-loss rate, with a larger value applying to the inner envelope where the higher-lying transitions of CO originate."
" We obtained a satisfactory fit to both the CO rotational line fluxes and the continuum spectrum by assuming a gas and dust density that decreases as , instead of the radius? density profile expected for an envelope with a constant mass loss rate and outflow velocity."," We obtained a satisfactory fit to both the CO rotational line fluxes and the continuum spectrum by assuming a gas and dust density that decreases as $^{-2.15}$, instead of the $^{-2}$ density profile expected for an envelope with a constant mass loss rate and outflow velocity."
 The gas-to-dust mass ratio in this model is 510., The gas-to-dust mass ratio in this model is 510.
" Fortunately, given the significant uncertainties in many of the assumed parameters listed in Table 1, the derived water outflow rate is not strongly dependent upon any of them."," Fortunately, given the significant uncertainties in many of the assumed parameters listed in Table 1, the derived water outflow rate is not strongly dependent upon any of them."
" As discussed in GNM, unless the mass-loss rate is extremely large, the excitation of water is dominated by radiative pumping via the 64m v» band."," As discussed in GNM, unless the mass-loss rate is extremely large, the excitation of water is dominated by radiative pumping via the $\,\mu$ m $\nu_2$ band."
" Thus, for a given water outflow rate, the observed water line fluxes scale linearly with the observed 6m continuum flux."," Thus, for a given water outflow rate, the observed water line fluxes scale linearly with the observed $\,\mu$ m continuum flux."
" Since the latter is an observed (rather than a derived) quantity, our estimate of the water outflow rate is largely independent of the distance or total outflow rate assumed for the source."," Since the latter is an observed (rather than a derived) quantity, our estimate of the water outflow rate is largely independent of the distance or total outflow rate assumed for the source."
" In modeling the water line strength and profile observed toward V Cygni, we have investigated two models for the spatial distribution of the observed water."," In modeling the water line strength and profile observed toward V Cygni, we have investigated two models for the spatial distribution of the observed water."
" In Model A, we assume that water is present at radii as small as 4.5x1014 cm, while in Model B, we adopt an inner radius Ri,=2X10cm at which the water is injected into the outflow."," In Model A, we assume that water is present at radii as small as $4.5 \times 10^{14}$ cm, while in Model B, we adopt an inner radius $R_{\rm in} = 2 \times 10^{15} \, \rm cm$ at which the water is injected into the outflow."
" In both cases, we assume an outer radius of Rout=1x10!°cm, the estimated photodissociation radius for The distribution assumed in Model B is expected if the vapourisation of icy objects is the origin ofthe observed water vapour, since all such objects at smaller distances from the star will have been vapourised already (Ford Neufeld"," In both cases, we assume an outer radius of $R_{\rm out} = 1 \times 10^{16} \, \rm cm$, the estimated photodissociation radius for The distribution assumed in Model B is expected if the vapourisation of icy objects is the origin ofthe observed water vapour, since all such objects at smaller distances from the star will have been vapourised already (Ford Neufeld"
of this diagram as an alternative to the BPT diagrams and N2 ratio to classify galaxies.,of this diagram as an alternative to the BPT diagrams and N2 ratio to classify galaxies.
 As explained in Section 3. the BPT and other optical emission lines diagnostic diagrams have become important in. the classification of galaxies.," As explained in Section 3, the BPT and other optical emission lines diagnostic diagrams have become important in the classification of galaxies."
 In this section. our aim ts to investigate the effects of the evolution of galaxies from the three BPT diagrams.," In this section, our aim is to investigate the effects of the evolution of galaxies from the three BPT diagrams."
 For this purpose. and with the objective of increase our number of galaxies. we did not take any restriction in magnitude. as detailed in the sample selection.," For this purpose, and with the objective of increase our number of galaxies, we did not take any restriction in magnitude, as detailed in the sample selection."
 In Fig., In Fig.
 5 we show the three BPT diagrams for the four redshift samples., 5 we show the three BPT diagrams for the four redshift samples.
 As redshift increases. we observe that ni] A5007/HB goes toward higher values.," As redshift increases, we observe that ] $\lambda$ goes toward higher values."
 In order to explain this shift. in Fig.," In order to explain this shift, in Fig."
 6 we plotted the ratio [Om] 415007/H8. versus redshift and metallicity only for SF galaxies selected with the Kauf03 criterion., 6 we plotted the ratio ] $\lambda$ versus redshift and metallicity only for SF galaxies selected with the Kauf03 criterion.
 The gap observed around ς~ 0.145 (see Fig., The gap observed around $z\sim$ 0.145 (see Fig.
 6a. c) is due to theHf line falling nearby the 5577 sky line. because the residuals are significant and. as a consequence. measurements of around this redshift were lost.," 6a, c) is due to the line falling nearby the 5577 sky line, because the residuals are significant and, as a consequence, measurements of around this redshift were lost."
 As shown in Fig., As shown in Fig.
 6b. there is a clear tendencyof the ui] 25007/H6 ratio towards higher values with redshift. which 1s explained by examining the same ratio against 12+log(O/H).," 6b, there is a clear tendencyof the ] $\lambda$ ratio towards higher values with redshift, which is explained by examining the same ratio against 12+log(O/H)."
 The ratio [Om] 5007/HB has demonstrated to correlate linearly with metallicity (see. for example. Liang et al.," The ratio ] $\lambda$ has demonstrated to correlate linearly with metallicity (see, for example, Liang et al."
 2006)., 2006).
 Then. a decrement in 12+log(O/H) will result in higher values of πι A5007/H (see Fig.," Then, a decrement in 12+log(O/H) will result in higher values of ] $\lambda$ (see Fig."
 6b)., 6b).
 We observe a decrement of «0.2 dex in [Om] 45007/HB. and a decrement of «0.1 dex in 12+log(O/H) for the z redshift range with respect to the zo range.," We observe a decrement of $\sim$ 0.2 dex in ] $\lambda$, and a decrement of $\sim$ 0.1 dex in 12+log(O/H) for the $z_3$ redshift range with respect to the $z_0$ range."
 In previous papers (Lara-Lóppez et al., In previous papers (Lara-Lóppez et al.
 2009a. b) we reported a decrement in. 12+log(O/H) of «0.1 dex for the redshift range 0.3«c<0.4 comparing galaxies in the same range of luminosity at different redshift intervals.," 2009a, b) we reported a decrement in 12+log(O/H) of $\sim$ 0.1 dex for the redshift range $0.3 < z < 0.4$ comparing galaxies in the same range of luminosity at different redshift intervals."
 Since the possible bias. such as Iuminosity. mass and aperture effects of those samples were carefully studied. we demonstrated there that this decrement in metallicity is due to an intrinsic evolution of the galaxies.," Since the possible bias, such as luminosity, mass and aperture effects of those samples were carefully studied, we demonstrated there that this decrement in metallicity is due to an intrinsic evolution of the galaxies."
 Although our z; sample corresponds to luminous galaxies. if we compare galaxies with the same luminosity. taking as a reference our previous papers. the metallicity decrement will be again of ~O.1 dex. and as consequence. the effects on the BPT diagrams will be the same.," Although our $z_3$ sample corresponds to luminous galaxies, if we compare galaxies with the same luminosity, taking as a reference our previous papers, the metallicity decrement will be again of $\sim$ 0.1 dex, and as consequence, the effects on the BPT diagrams will be the same."
 Therefore. the evolution observed in the in] 45007/H lines ratio toward higher values in the three BPT diagrams. could be attributed to a metallicity evolution.," Therefore, the evolution observed in the ] $\lambda$ lines ratio toward higher values in the three BPT diagrams, could be attributed to a metallicity evolution."
 On the other hand. we analyze the ratio against redshift and metallicity (see Fig.6c. d).," On the other hand, we analyze the ratio against redshift and metallicity (see Fig.6c, d)."
 The ratio is also a metallicity index. commonly known as N2. and it has been widely studied since it 15 not severely affected by dust extinction. (see Pettini & Pagel 2004).," The ratio is also a metallicity index, commonly known as N2, and it has been widely studied since it is not severely affected by dust extinction (see Pettini $\&$ Pagel 2004)."
 Among the calibrations of the N2 index. we have for example those of Raimann et al. (," Among the calibrations of the N2 index, we have for example those of Raimann et al. ("
2000). Denicoló et al. (,"2000), Denicoló et al. ("
2002). and Liang et al. (,"2002), and Liang et al. ("
2006).,2006).
 In Fig., In Fig.
 6d we observe a clear increasing trend of metallicity following the increase of the N2 index up to 12+log(O/H) «9.0., 6d we observe a clear increasing trend of metallicity following the increase of the N2 index up to 12+log(O/H) $\sim$ 9.0.
 The galaxies with 12+log(O/H) >9 show a flattening and a slightly decrease of the N2 index with metallicity (see Fig., The galaxies with 12+log(O/H) $>$ 9 show a flattening and a slightly decrease of the N2 index with metallicity (see Fig.
 6d)., 6d).
 This trend was explained by Kewley et al. (, This trend was explained by Kewley et al. (
2002) using photoionization models as follows: when the secondary production of nitrogen dominates. at somewhat higher metallicity. the line ratio continues to increase. despite the decreasing electron temperature.,"2002) using photoionization models as follows: when the secondary production of nitrogen dominates, at somewhat higher metallicity, the line ratio continues to increase, despite the decreasing electron temperature."
 Eventually. at still higher metallicities. nitrogen becomes the dominant coolant in the nebula. and the electron temperature falls sufficiently to ensure that the nitrogen line weakens with increasing metallicity.," Eventually, at still higher metallicities, nitrogen becomes the dominant coolant in the nebula, and the electron temperature falls sufficiently to ensure that the nitrogen line weakens with increasing metallicity."
 Liang et al. (, Liang et al. (
2006). using SDSS galaxies with redshifts 0.04<20.25. observed a small decrement of the N2 index against metallicity: this turnover of the N2 index is more evident for the higher redshifts z» and zi in our sample (see Fig.,"2006), using SDSS galaxies with redshifts $0.04 < z < 0.25$, observed a small decrement of the N2 index against metallicity; this turnover of the N2 index is more evident for the higher redshifts $z_2$ and $z_3$ in our sample (see Fig."
 6d)., 6d).
 The turnover of the N2 ratio will produce in the 45007/HB vs. BPT diagram. the turnover zone around N2 ~—0.4. which is more evident in a density plot (see Fig.," The turnover of the N2 ratio will produce in the ] $\lambda$ vs. BPT diagram, the turnover zone around N2 $\sim-0.4$, which is more evident in a density plot (see Fig."
 2)., 2).
 Regarding the two left BPT diagrams of Fig., Regarding the two left BPT diagrams of Fig.
 5b and c. since they share the ratio [Om] 45007/Hf. the evolutionary effects due to a decrement in metallicity will be the same as discussed above.," 5b and c, since they share the ratio ] $\lambda$, the evolutionary effects due to a decrement in metallicity will be the same as discussed above."
 The ratio has never been used before as a metallicity indicator because it is far more sensitive to ionization than to metallicity (Liang et al., The ratio has never been used before as a metallicity indicator because it is far more sensitive to ionization than to metallicity (Liang et al.
 2006)., 2006).
 Moreover. it is double-valued with metallicity (see Fig.," Moreover, it is double–valued with metallicity (see Fig."
 +). whereas the ratio is not a metallicity indicator.," 4), whereas the ratio is not a metallicity indicator."
 Therefore. after analyzing allthe ratios involved in the three BPT diagrams. we concluded that the evolution of galaxies in the three BPT diagrams is shown through the i1] 25007/HB8 ratio.," Therefore, after analyzing allthe ratios involved in the three BPT diagrams, we concluded that the evolution of galaxies in the three BPT diagrams is shown through the ] $\lambda$ ratio."
 Since this ratio is a metallicity indicator. any decrement in metallicity will result in higher values of the ui] 25007/H6 ratio.," Since this ratio is a metallicity indicator, any decrement in metallicity will result in higher values of the ] $\lambda$ ratio."
separated by less than100.! kpe. which is significantly smaller than the scales studied herein.,"separated by less than$h^{-1}$ kpc, which is significantly smaller than the scales studied herein."
" In each case. we also constructed catalogues of random data points (containing SLO"" points) over the same area of the sky and with the same selection function as discussed in Popeetal.(2004)."," In each case, we also constructed catalogues of random data points (containing $8\times10^5$ points) over the same area of the sky and with the same selection function as discussed in \cite{Pope2004}."
. These random catalogues are then used to calculate edge effects on the N-point correlation functions using the estimators presented in Szapudi&Szalay(1998)., These random catalogues are then used to calculate edge effects on the N–point correlation functions using the estimators presented in \cite{SS1998}.
 There are two common parametrizations of ().., There are two common parametrizations of $Q_z$ .
" One detines where sj». s»; and sy, are the three sides of a triangle in redshift space."," One defines where $s_{12}$, $s_{23}$ and $s_{31}$ are the three sides of a triangle in redshift space."
 Then Q(s.i.0) is defined by the ratio of the 3PCF QUS12.523.534 ). to sums of productsof 2PCFs (e.g. €(512)€(815) and permutations}:," Then $Q(s,u,v)$ is defined by the ratio of the 3PCF $\zeta(s_{12}, s_{23}, s_{31})$ , to sums of productsof 2PCFs (e.g. $\xi(s_{12})\xi(s_{13})$ and permutations):"
Wangetal.(2001a)/ outlined a method to decompose the observed polarimetry into two components.,\citet{Wang:2001} outlined a method to decompose the observed polarimetry into two components.
 On the Q - U plot. the two components correspond to the polarized vectors projected onto the so-called dominant axis and (he axis perpendicular to the dominant axis.," On the Q - U plot, the two components correspond to the polarized vectors projected onto the so-called dominant axis and the axis perpendicular to the dominant axis."
 The dominant axis can be defined rom (he aspherical distribution of the data points on the Q - U plane., The dominant axis can be defined from the aspherical distribution of the data points on the Q - U plane.
 The dominant axis is derived by a linear fit to the data points weighted bv the observational errors in the Q - U plane., The dominant axis is derived by a linear fit to the data points weighted by the observational errors in the Q - U plane.
 The spectropolarimetry projected to the dominant axis represents global geometric deviations Irom spherical svannietry. whereas the vector perpendicular to the dominant axis represents deviations from the dominant axis., The spectropolarimetry projected to the dominant axis represents global geometric deviations from spherical symmetry whereas the vector perpendicular to the dominant axis represents deviations from the dominant axis.
 The same niethod will be applied in (his study. as well., The same method will be applied in this study as well.
 We show in Figures 3 to 7 the observed data points in the Q - U plane., We show in Figures 3 to 7 the observed data points in the Q - U plane.
 Each point represent a data pair of the Q - U vector at a different wavelength., Each point represent a data pair of the Q - U vector at a different wavelength.
 The wavelength of the data points in important intervals are encoded in color., The wavelength of the data points in important intervals are encoded in color.
 The data show remarkable evolution during the five epochs of observation., The data show remarkable evolution during the five epochs of observation.
 The polarization also shows spectral features. (hal can be identified with features in the flux spectra., The polarization also shows spectral features that can be identified with features in the flux spectra.
 This firmly establishes (hat SN 2001el is intrinsically polarized. αἱ least at certain epochs alter explosion.," This firmly establishes that SN 2001el is intrinsically polarized, at least at certain epochs after explosion."
 SN 2001el exhibits some remarkable features that are unlike (hose of previously observed SN ΠΠ aad the subluminous SN Ia 1999bv (Wangetal.1996:Wang.Wheeler.&Hollich1997:Waneetal.2001a:Leonard&Filippenko2001:Howell2001 ).," SN 2001el exhibits some remarkable features that are unlike those of previously observed SN II and the subluminous SN Ia 1999by \citep{Wang:1996, WWH:1997, Wang:2001, Leonard:2001a, Leonard:2001b,
Howell:99by}."
. On the Q - U plot. SN 19955 and SN 1999by showed well-defined linear features (WangοἱILowelletal. 2001).," On the Q - U plot, SN 1998S and SN 1999by showed well-defined linear features \citep{Wang:2001,Howell:99by}."
. This is indicative of a relatively well-defined svmunetiy axes., This is indicative of a relatively well-defined symmetry axes.
 The SN 2001el data. however. show large scatter around (the dominant axis.," The SN 2001el data, however, show large scatter around the dominant axis."
 In. particular. a sharp increase of the degree of polarization is seen in the Ca 1I IK. triplet in the Sept. 26 and Oct. 1 data.," In particular, a sharp increase of the degree of polarization is seen in the Ca II IR triplet in the Sept. 26 and Oct. 1 data."
 Other strong polarized spectral features are also observed during Sept. 26 and Oct. 1., Other strong polarized spectral features are also observed during Sept. 26 and Oct. 1.
 The polarized features becomes much weaker in the data taken on Oct. 18 and afterwards., The polarized features becomes much weaker in the data taken on Oct. 18 and afterwards.
 To derive the intrinsic polarization due to the supernova atmosphere. we first need to deduce the component due to interstellar dist.," To derive the intrinsic polarization due to the supernova atmosphere, we first need to deduce the component due to interstellar dust."
 A simple approach is to assume that the resonance-scattered photons are unpolarized (Trammelletal.1993)., A simple approach is to assume that the resonance-scattered photons are unpolarized \citep{Trammell:1993}.
. This method attempts to disünguish continuum and scattered photons ancl use that separation to derive interstellar extinction (Jeffrey1991:Trammelletal.1993:Hoflich1996:WangTranetal.1997:Leonard&Filippenko 2001)..," This method attempts to distinguish continuum and scattered photons and use that separation to derive interstellar extinction \citep{Jeffrey:1991,Trammell:1993,Hoeflich:1996w,
Wang:1996, Tran:1997, Leonard:2001a}. ."
 This technique implicitly assumes a unique intrinsic, This technique implicitly assumes a unique intrinsic
pulse-heights of greater than 3.3 photoelectrons. and Cherenkov photon arrival (mes within +50 nns of the median arrival time.,"pulse-heights of greater than 3.3 photoelectrons, and Cherenkov photon arrival times within $\pm$ ns of the median arrival time."
 Clusters of at least five adjacent triggered pixels (rather than the usual four-pixel eut) were required in each event (to minimize the effects of the bright star field., Clusters of at least five adjacent triggered pixels (rather than the usual four-pixel cut) were required in each event to minimize the effects of the bright star field.
 After these pre-selection cuts. which reduced events due to background light were reduced by99%... the shower rate was stable on a run-to-run basis for observations in (he same vear.," After these pre-selection cuts, which reduced events due to background light were reduced by, the shower rate was stable on a run-to-run basis for observations in the same year."
 The systematic difference of the run-by-run acceptance within (he same vear is expected to be less than124., The systematic difference of the run-by-run acceptance within the same year is expected to be less than.
.. The ON/OFF shower rate differences in 2002 and 2003 were —8415% and —1+134... respectively.," The ON/OFF shower rate differences in 2002 and 2003 were $-8\pm15$ and $-1\pm13$, respectively."
 By examining the event rates within each run we were able to reject periods affected by cloud. dew. forming on the mirrors. instrumental abnormalities. etc.," By examining the event rates within each run we were able to reject periods affected by cloud, dew forming on the mirrors, instrumental abnormalities, etc."
 Only data taken at elevation angles greater than 607 were accepted., Only data taken at elevation angles greater than $^{\circ}$ were accepted.
 After these cuts. 4300 oof ON- and 3900 oof OFF-source data survived.," After these cuts, 4300 of ON- and 3900 of OFF-source data survived."
 ‘Trigger rates for each pixel per 700ji were monitored by a scaler circuit in real-time and recorded. each second., Trigger rates for each pixel per $\mu$ s were monitored by a scaler circuit in real-time and recorded each second.
 These data were used to exclude ‘hot’ pixels (generally due to the passage of a star through the FOV of a pixel) in off-Iime analvsis., These data were used to exclude `hot' pixels (generally due to the passage of a star through the FOV of a pixel) in off-line analysis.
 Hillas parameters were then calculated to discriminate gamnma-ravs from cosmic ravs based on the image shape aud orientation (Ilillas1985)., Hillas parameters were then calculated to discriminate gamma-rays from cosmic rays based on the image shape and orientation \citep{hillas85}.
. Further. in each νους data. we masked a small number of pixels which showed celormed ADC spectra. possibly due to a hardware fault.," Further, in each year's data, we masked a small number of pixels which showed deformed ADC spectra, possibly due to a hardware fault."
 Discrimination of the cosmic rav background from gamima-ravs was carried out using the likelihood method of Enomotoetal.(2002a)., Discrimination of the cosmic ray background from gamma-rays was carried out using the likelihood method of \cite{enomoto02a}.
. The resulting distributions of the image orientation angle. a. for the combined data in 2002 and 2003 are shown in Fig. 5..," The resulting distributions of the image orientation angle, $\alpha$, for the combined data in 2002 and 2003 are shown in Fig. \ref{fig1}."
 The normalizations between the ON- ancl were carried out using data with a>27°., The normalizations between the ON- and OFF-distributions were carried out using data with $\alpha>27^\circ$.
 The numbers of excess events 187) were 530)-120 (in an observation time of 2100 min.).," The numbers of excess events $\alpha <18^\circ$ ) were $530\pm120$ (in an observation time of 2100 min.),"
 540+140 (2200 min.).," $540\pm140$ (2200 min.),"
 and 1080X180 (4300 min.), and $1080\pm180$ (4300 min.)
" in 2002. 2003. and the combined data. respectively,"," in 2002, 2003, and the combined data, respectively."
 The excess rates for 2002 and 2003 were similar to each other., The excess rates for 2002 and 2003 were similar to each other.
 Nightly signal rates were also checked during both vears., Nightly signal rates were also checked during both years.
" The largest deviations occurred with a rate 2.50.9 times larger than the average for 2002 and 3.0£1.0 times [or 2003. respectively,"," The largest deviations occurred with a rate $2.5\pm 0.9$ times larger than the average for 2002 and $3.0\pm 1.0$ times for 2003, respectively."
 These are not unexpected statistically. and therefore there is no evidence of time-variability in the TeV emission.," These are not unexpected statistically, and therefore there is no evidence of time-variability in the TeV emission."
" To check on the spatial distribution of the signal we derived (he ""significance map. shown by the blue contours in Fig. 4.."," To check on the spatial distribution of the signal we derived the “significance map”, shown by the blue contours in Fig. \ref{fig2}."
 The contours were calculated [rom the distribution of the detection significance determined at each location [rom the difference in the a plots minus OFF-source histogram) divided by the statistical errors., The contours were calculated from the distribution of the detection significance determined at each location from the difference in the $\alpha$ plots (ON- minus OFF-source histogram) divided by the statistical errors.
 The centroid is consistent with position of the X-ray maxinmnmn. within our possible svstematic uncertainty of 0.17.," The centroid is consistent with position of the X-ray maximum, within our possible systematic uncertainty of $^\circ$ ."
,.
zIH/Ecolh(izH/E). Wi >>E. there will be a significant increase in the pair production rale.," If $H>>E$, there will be a significant increase in the pair production rate."
" The electric field of the electrosphere could be as high as E—40E,.,;;zz120 MeV?.", The electric field of the electrosphere could be as high as $E=40E_{crit}\approx 120$ $^2$.
 On the other hand (he estimated magnetic fields at the surface of the quark stars could be οἱ the order of 1210— 10G x20—2000 MeV? (1G =1.953x10.!! MeV?).," On the other hand the estimated magnetic fields at the surface of the quark stars could be of the order of $H\approx
10^{15}-10^{17}$ G $\approx 20-2000$ $^2$ (1G $=1.953\times
10^{-14}$ $^2$ )."
 Magnetic fields with such high values may be present in very voung quark stars., Magnetic fields with such high values may be present in very young quark stars.
 Assuming ecquipartition of energy. (he energy of (he differential rotation can be converted into magnetic energy. so that 0?((NO/O)zz(40/3)RCLIP/8). where 7 is the moment of inertia of the star. A its radius and Ὁ and AQ are the angular velocity and the variation of the angular velocity. respectively.," Assuming equipartition of energy, the energy of the differential rotation can be converted into magnetic energy, so that $I\Omega ^{2}\left( \Delta \Omega /\Omega \right) \approx
\left( 4\pi /3\right) R^{3}\left( H^{2}/8\pi \right) $, where $I$ is the moment of inertia of the star, $R$ its radius and $\Omega $ and $\Delta \Omega $ are the angular velocity and the variation of the angular velocity, respectively."
" Therefore the magnetic field of a voung quark star can be approximated as LIzz10!(NQ/O)!> MeV?,"," Therefore the magnetic field of a young quark star can be approximated as $H\approx
10^{4}\left( \Delta \Omega /\Omega \right) ^{1/2}$ $^{2}$."
 By assuming that AQ/Ozz0.03. we can obtain values of the magnetic field as high as 44zz2000 MeV?.," By assuming that $\Delta \Omega /\Omega \approx 0.03$, we can obtain values of the magnetic field as high as $H\approx 2000$ $^{2}$."
 Of course magnetic fields of such strength are nol stable. because thev will be pushed to and through the surface by buovant forces ancl then reconnect (IxInzniakandRuclerman1998).," Of course magnetic fields of such strength are not stable, because they will be pushed to and through the surface by buoyant forces and then reconnect \citep{Klu98}."
. For à magnetic field of the order of LFzz2000 MeV?E we have ὃμ-22.53., For a magnetic field of the order of $H\approx 2000$ $^{2}$ we have $\delta _H\approx 53$.
 Therefore strong magnetic fields can significantly increase the electron-positron pair production rate. and. consequently the Iuminositv of the electrosphere of quark stars.," Therefore strong magnetic fields can significantly increase the electron-positron pair production rate, and, consequently the luminosity of the electrosphere of quark stars."
 In the present paper we have re-considered the electron-positron pair enission from the electrosphere of quark stars. as originally proposed by Usov(1998a.b).. bv pointing out the important role (he boundary effects and (he inhomogeneity in the distribution of the electric field may play in the pair creation process.," In the present paper we have re-considered the electron-positron pair emission from the electrosphere of quark stars, as originally proposed by \citet{Us98a,Us98b}, by pointing out the important role the boundary effects and the inhomogeneity in the distribution of the electric field may play in the pair creation process."
 At zero temperature. there are no available free enerev states in (he electron. plasma at the strange stars surface.," At zero temperature, there are no available free energy states in the electron plasma at the strange star's surface."
" Therefore. at low temperatures 7'<T,220.1 MeV (corresponding to a quark star surface electric potential of V,—5 MeV). the pair production mechanism by the strong electric field of the electrosphere is severely limited bv the quantum effects aud (he exclusion principle specific to the statistics."," Therefore, at low temperatures $T\leq T_{cr}\approx 0.1$ MeV (corresponding to a quark star surface electric potential of $V_q=5$ MeV), the pair production mechanism by the strong electric field of the electrosphere is severely limited by the quantum effects and the exclusion principle specific to the Fermi-Dirac statistics."
 At high temperatures 77/77;220.1 MeV. the pair creation rate is controlled bv the electric field £ and not by the temperature. because such a process is essentially a «quantum process.," At high temperatures $T\geq T_{cr}\approx 0.1$ MeV, the pair creation rate is controlled by the electric field $E$ and not by the temperature, because such a process is essentially a quantum process."
 Once the munber of available electron states becomes higher than the schwinger pair production rate. electron-positron pairs can be freely created by (he electric field at Che surface of strange stars.," Once the number of available electron states becomes higher than the Schwinger pair production rate, electron-positron pairs can be freely created by the electric field at the surface of strange stars."
 This happens at a critical temperature {νο which strongly depends on the electrostatic properties of the quark star surface.," This happens at a critical temperature $T_{cr}$, which strongly depends on the electrostatic properties of the quark star surface."
 The critical temperature increases with the increase of the electrostatic potential Ἐν., The critical temperature increases with the increase of the electrostatic potential $V_q$.
 At high enough temperatures. the pair creation process is almost independent of the temperature and is controlled exclusively bv the electric field.," At high enough temperatures, the pair creation process is almost independent of the temperature and is controlled exclusively by the electric field."
 On the other hand. (he actual thermalized pair creation rate. which.," On the other hand, the actual thermalized pair creation rate, which,"
WOOL MNis an exteuded (~. 17) radio. source located at the tangential point (/2 197) of the Sagittarius ari.,W51 is an extended $\sim 1^\circ$ ) radio source located at the tangential point $l=49^\circ$ ) of the Sagittarius arm.
 It is composed of two complex ID II regions. W51A and W51D. and the supernova remaut (SNR) ας (es. Bicging 1975: Koo 1997).," It is composed of two complex H II regions, W51A and W51B, and the supernova remant (SNR) W51C (e.g., Bieging 1975; Koo 1997)."
 W51A forms the northern part of WL. and is separated frou the other two sources.," W51A forms the northern part of W51, and is separated from the other two sources."
 It coutains two major coniponeuts. cach composed of several compact IL II reisons.," It contains two major components, each composed of several compact H II reigons."
 W51D ids composed of at least ‘ II : scattered m area of six~DS commpacsize., W51B is composed of at least six compact H II regions scattered over an area of $\sim 15'$ size.
 W5LBHu regionssources are associatedover with a stream of atomic and molecular gases. with lue-of-sieght velocitics significauth ercater than the maxinuun velocity peruütted by Galactic rotation alone.," W51B sources are associated with a stream of atomic and molecular gases, with line-of-sight velocities significantly greater than the maximum velocity permitted by Galactic rotation alone."
 The stream is thought to be eas flowine along the Sagittarius spiral arm in response fo the perturbation the spiral poteutial (e.g... Burton 1971).," The stream is thought to be gas flowing along the Sagittarius spiral arm in response to the perturbation due to the spiral potential (e.g., Burton 1971)."
 dueSuperimposedfo ou W51D.- there is⋅ an extended structure ll.W51C which. is à SNB.," Superimposed on W51B, there is an extended structure W51C which is a SNR."
 W51C€ appears iu radio contiuuuun as an incomplete shell of ~30 extent with its upper portion open (Copetti&Schinidt1991:Subrahmanuvan&Coss 1995).," W51C appears in radio continuum as an incomplete shell of $\sim 30'$ extent with its upper portion open \citep{cop91, sub95}."
. Shocked atomic and molecular eases have Όσοι detected iu the western part of the SNR. which indicates that the SNR is interacting with a laree molecular cloud (hoo&Teiles1991:ΊνουMoon19972.b).," Shocked atomic and molecular gases have been detected in the western part of the SNR, which indicates that the SNR is interacting with a large molecular cloud \citep{koo91, koo97a, koo97b}."
. The complex. structure of W51 is partly due tfo. the inclination of the Sagittarius arii. so that we look down the leugth of the axi a distance of 5 kpc along the linc-of-sighit.," The complex structure of W51 is partly due to the inclination of the Sagittarius arm, so that we look down the length of the arm a distance of 5 kpc along the line-of-sight."
 Soft 52 keV) N-ray emission associated with N51 has been detected by aud ROSAT (Seward1990:Ίουetal.1995.hereafter.IIÍSS).," Soft $\simlt 2$ keV) X-ray emission associated with W51 has been detected by and ROSAT \citep[hereafter KKS]{sew90, koo95}."
. Diffuse N-ravs come from a region sumoundius W5ID aud W51C. whereas W51AÀ has essentially no soft N-rav eunission associated with it.," Diffuse X-rays come from a region surrounding W51B and W51C, whereas W51A has essentially no soft X-ray emission associated with it."
 The soft N-ray cutting region is elongated (50« 38) along the east-west direction. aud mav be divided into three parts: a ceutral structure composed of two," The soft X-ray emitting region is elongated $50'\times 38'$ ) along the east-west direction, and may be divided into three parts; a central structure composed of two"
axis ratio 22.,axis ratio $\simgeq \ 2$.
 Such a disk would eet quickly wound up due to differeutial rotation., Such a disk would get quickly wound up due to differential rotation.
 For these reasous we regard it unlikely that GBSN's velocity field is due to pure rotation., For these reasons we regard it unlikely that GR8's velocity field is due to pure rotation.
 Aanore likely inodoel is one iu wuch the kinematics of CRS can be described as a combination of radial aud circular notions., A more likely model is one in which the kinematics of GR8 can be described as a combination of radial and circular motions.
 Such a model provides a reasonable fit to the observed velocity field., Such a model provides a reasonable fit to the observed velocity field.
 In this interpretation. iu case the radial motions are outwards. then they could be dviven by he star formation in GR&: a previous study (Elineereenu IIunter 2000) las shown that the pressure in the TI regions in this galaxy is af least 55 times greater than he average pressure in the disk.," In this interpretation, in case the radial motions are outwards, then they could be driven by the star formation in GR8; a previous study (Elmegreen Hunter 2000) has shown that the pressure in the HII regions in this galaxy is at least $55$ times greater than the average pressure in the disk."
 The measured expansion velocity is considerably less than the estimated escape velocity. so even in this iuterpretation the cold eas is still vound to the ealaxy.," The measured expansion velocity is considerably less than the estimated escape velocity, so even in this interpretation the cold gas is still bound to the galaxy."
 Finally. the radial motions could also ve immterpreted as iufall. in which case CRS is either iu the xocess of formation. or the ISM is falling |ck after a ouevious pase of expansion.," Finally, the radial motions could also be interpreted as infall, in which case GR8 is either in the process of formation, or the ISM is falling back after a previous phase of expansion."
half maximum of 0.5ddex. in the stellar. radii around an isochronal value.,"half maximum of dex, in the stellar radii around an isochronal value."
" ""This result is almost. independent of which. evolutionary models are. considered.", This result is almost independent of which evolutionary models are considered.
 An obvious interpretation is that this is caused by a spread in ages and this is investigated in the next subsection., An obvious interpretation is that this is caused by a spread in ages and this is investigated in the next subsection.
 Two separate models for an age spread. were tested., Two separate models for an age spread were tested.
" The first was a Gaussian distribution of log), age around a central. isochrone.", The first was a Gaussian distribution of $\log_{10}$ age around a central isochrone.
" The free parameters were the central age and the age dispersion (in logarithmic units). 0,."," The free parameters were the central age and the age dispersion (in logarithmic units), $\sigma_a$."
 The second model was an age distribution which is zero up to some starting age. jumps to a maximum and then decays exponentially with à decay constant. A. expressed in Myr.," The second model was an age distribution which is zero up to some starting age, jumps to a maximum and then decays exponentially with a decay constant, $\lambda_a$, expressed in Myr."
 This latter model. with a suitably small starting age. represents the exponentially accelerating star formation model advocated by Palla Stahler (1999).," This latter model, with a suitably small starting age, represents the exponentially accelerating star formation model advocated by Palla Stahler (1999)."
 The lowest starting age considered was 0.03 δλδνε., The lowest starting age considered was $0.03$ Myr.
 Ages drawn randomly from the Gaussian. age distribution were transformed into radii using the appropriate stellar models (at. the Zi of each star in the observational dataset) ancl these radii were perturbed according {ο the I50KK Zr uncertainties and then subjected to the measurement. uncertainies. random axial orientations and. selection ellects before comparing the observed and modelled clistribution of 2sinz/Itasis.," Ages drawn randomly from the Gaussian age distribution were transformed into radii using the appropriate stellar models (at the $T_{\rm eff}$ of each star in the observational dataset) and these radii were perturbed according to the K $T_{\rm eff}$ uncertainties and then subjected to the measurement uncertainties, random axial orientations and selection effects before comparing the observed and modelled distribution of $R\sin i/R_{{\rm 3Myr}}$."
 A grid of models covering a wide range of cenral ages and age dispersion was calculated. for both. the DAMOT7 ancl SOO models., A grid of models covering a wide range of central ages and age dispersion was calculated for both the DAM97 and S00 models.
 Assuming that the correct solution lay within this erid. | normalised the Ίντο probabilities ancl this gave a pair of relative probability. grids. which are shown in," Assuming that the “correct” solution lay within this grid, I normalised the K-S probabilities and this gave a pair of relative probability grids which are shown in"
no simultaneous CCD 2 observations had. been obtained. were utilized.,"no simultaneous CCD $B$ observations had been obtained, were utilized."
 Vhe datasets of the variables used. for. the »eriod. change study are listed in Table 4.., The datasets of the variables used for the period change study are listed in Table \ref{felhasznalt}.
 For each star. the dataset that defines the mean (master) light curve is marked ον an asterisk.," For each star, the dataset that defines the mean (master) light curve is marked by an asterisk."
 Phe complete table is available as supporting information in the electronic version of this article., The complete table is available as supporting information in the electronic version of this article.
 The mean light curves were constructed in the form of ifth and seventh order Fourier series for the Rite and RRab stars. respectively.," The mean light curves were constructed in the form of fifth and seventh order Fourier series for the RRc and RRab stars, respectively."
 In case of noisy and/or strongly variable ight curves. lower order fits were applied to avoid. unreal. wavy mean light-curve shapes.," In case of noisy and/or strongly variable light curves, lower order fits were applied to avoid unreal, wavy mean light-curve shapes."
 As the first step. cach dataset was. magnitude iomogenized by fitting the mean light curve.," As the first step, each dataset was magnitude homogenized by fitting the mean light curve."
 In the second step. the mean light curve was fitted in phase to 24 vears ong segments of the magnitude homogenized. combined ight curve.," In the second step, the mean light curve was fitted in phase to 2–4 years long segments of the magnitude homogenized, combined light curve."
 By default. the data were divided. into 19 segments. and their phase-shift. values corresponded to the OC for the mean epoch of the data subsets.," By default, the data were divided into 19 segments, and their phase-shift values corresponded to the $O-C$ for the mean epoch of the data subsets."
 Some of the xns were divided into shorter segments in case of very fast »eriod. changes. or they were merged together if insullicient number of cata points were available in one of the bins. and no significant period change occurred in the given time interval.," Some of the bins were divided into shorter segments in case of very fast period changes, or they were merged together if insufficient number of data points were available in one of the bins, and no significant period change occurred in the given time interval."
 The O—C values. derived in this way. were used to construct the phase-shift diagrams (O6 diagrams).," The $O-C$ values, derived in this way, were used to construct the phase-shift diagrams $O-C$ diagrams)."
 Since there were gaps in the coverage of the observations. evele count ambiguities occurred. in some cases. especially for stars showing irregular. Large period. changes.," Since there were gaps in the coverage of the observations, cycle count ambiguities occurred in some cases, especially for stars showing irregular, large period changes."
 These οC points were adjusted. upward or downward. by integer evele numbers to obtain the most acceptable period-change solution (see details in the next section)., These $O-C$ points were adjusted upward or downward by integer cycle numbers to obtain the most acceptable period-change solution (see details in the next section).
 Then. he magnitude homogenization was refined. as described in section 2.3 of Szeidletal.(2011).," Then, the magnitude homogenization was refined as described in section 2.3 of \citet{m5}."
. For the stars with abrupt »eriod changes. this step greatly improved. the magnitude 10mogenization.," For the stars with abrupt period changes, this step greatly improved the magnitude homogenization."
 The determination of the O6 points and he construction of the O—C' diagrams were finalized on the refined. version of the magnitude-homogenized data., The determination of the $O-C$ points and the construction of the $O-C$ diagrams were finalized on the refined version of the magnitude-homogenized data.
 The O6 diagrams were fitted bv polynomials. and the xeriod-change rates of the variables were measured by the cocllicients of these functions.," The $O-C$ diagrams were fitted by polynomials, and the period-change rates of the variables were measured by the coefficients of these functions."
 The reliability of the OC its were checked by the comparison of the results of direct »eriod determinations with the derivative of the O6 fits. and by the construction of folded light curves corrected. for he period change.," The reliability of the $O-C$ fits were checked by the comparison of the results of direct period determinations with the derivative of the $O-C$ fits, and by the construction of folded light curves corrected for the period change."
 Table 5. gives an example of the results for VI., Table \ref{ocvalues} gives an example of the results for V1.
 The ime interval. the corresponding mean epoch. the number of datapoints of the subsets and the O or temporal »eriod. values and their errors are given in the columns.," The time interval, the corresponding mean epoch, the number of datapoints of the subsets and the $O-C$ or temporal period values and their errors are given in the columns."
 The complete table. including the O6) values and instantaneous »eriods for all the analvzed stars is available in the electronic version of the article as supporting information.," The complete table, including the $O-C$ values and instantaneous periods for all the analyzed stars is available in the electronic version of the article as supporting information."
 The results of the period-change analysis are documentec in Fig., The results of the period-change analysis are documented in Fig.
 1. for 129 Ht Lyrae stars., \ref{oc} for 129 RR Lyrae stars.
 The variables are shown in the order of the length of their periods., The variables are shown in the order of the length of their periods.
 Decause of their extremely strong phase modulations (Blazhko effect). ane abrupt changes of the pulsation period. no period-change solution could be obtained. for three RRab variables (V5. V50 and V130).," Because of their extremely strong phase modulations (Blazhko effect) and abrupt changes of the pulsation period, no period-change solution could be obtained for three RRab variables (V5, V50 and V130)."
 The strong changes of their modal conten made the analysis of V79 and. VOO impossible using our method., The strong changes of their modal content made the analysis of V79 and V99 impossible using our method.
 Thus. οC' diagrams have not been constructec for five of the studied: 134 variables.," Thus, $O-C$ diagrams have not been constructed for five of the studied 134 variables."
 Three panels are shown for each variable., Three panels are shown for each variable.
 The lelt-harn panels show the O6 diagrams ancl their polynomial fits., The left-hand panels show the $O-C$ diagrams and their polynomial fits.
" Variables showing Blazhko effect or double-mocde pulsations are denoted as ""DE. and cdm. respectively."," Variables showing Blazhko effect or double-mode pulsations are denoted as `Bl' and `dm', respectively."
 The dillerences. between temporal period values (P?) etermined by direct period analysis of the data subsets and 10 mean period (41) adopted to caleulate O—C' values are Xotted in the middle panels (2P.)107 d]., The differences between temporal period values $P$ ) determined by direct period analysis of the data subsets and the mean period $P_a$ ) adopted to calculate $O-C$ values are plotted in the middle panels $(P-P_a)\times 10^5$ d].
 Phe variations X the instantaneous periods {0} predicted from the OC ata using Eq., The variations of the instantaneous periods $P(t)$ ] predicted from the $O-C$ data using Eq.
 3 of Juresiketal.(2001) are also shown or comparison., 3 of \citet{ocen} are also shown for comparison.
 When evele-count ambiguity of the ο6 Pvalues occurred. that solution was accepted. which vielded 1e smallest. cdillerence of the directly observed. period values rom the 2) function.," When cycle-count ambiguity of the $O-C$ values occurred, that solution was accepted, which yielded the smallest difference of the directly observed period values from the $P(t)$ function."
 The errorbars shown for the ο6 points and the observed: period values indicate. 20 formal uncertainties etermined. by least-squares fitting method., The errorbars shown for the $O-C$ points and the observed period values indicate $2\sigma$ formal uncertainties determined by least-squares fitting method.
 The right-hand panels show the folded. light curves of 1e time-transformec (Iq., The right-hand panels show the folded light curves of the time-transformed (Eq.
 4 of Juresiketal. (2001))) data. which are corrected for the period. variations according to 16 polynomial fits of the O—C' diagrams.," 4 of \citet{ocen}) ) data, which are corrected for the period variations according to the polynomial fits of the $O-C$ diagrams."
 The OC solutions are shown in two separate plots using different periods for V13 anc ΝΕ. as the period anges of these stars are too large to be shown in a single plot.," The $O-C$ solutions are shown in two separate plots using different periods for V13 and V41, as the period changes of these stars are too large to be shown in a single plot."
 The very irregular O—C' variations of thirteen stars (V12. V17T. VIS. Ves. V34. V35. V43. V44. V4T. V54. V1O. Vso and ΧΙΟ) could be fitted. only by two consecutive. separate polvnomials.," The very irregular $O-C$ variations of thirteen stars (V12, V17, V18, V28, V34, V35, V43, V44, V47, V54, V70, V80 and V110) could be fitted only by two consecutive, separate polynomials."
 The period-change and light-curve characteristics of the analyzed stars are summarized in Table 6.., The period-change and light-curve characteristics of the analyzed stars are summarized in Table \ref{tabla}.
 The first three columns list the designation. the tvpe of the variable. anc the period. used for the construction of the O6 diagram.," The first three columns list the designation, the type of the variable, and the period used for the construction of the $O-C$ diagram."
 The next two columns give photometric information on the light curves: Vi is the intensityv-averaged mean 1. magnitude. and zd is the full amplitude in the V band.," The next two columns give photometric information on the light curves: $V_\mathrm{i}$ is the intensity-averaged mean $V$ magnitude, and $A_V$ is the full amplitude in the $V$ band."
"are the Alaxwell-Boltzmann distribution. the Ixnudsen number. and Aj""in=ey,fy, ts. a thermal electron. collision_ mean [ree path.","are the Maxwell-Boltzmann distribution, the Knudsen number, and $\lambda_{e}^{th}=v_{th}/\nu_{th}$ is a thermal electron collision mean free path."
 Note that only /ALB is still dimensional but all other quantities- are cimiensionless., Note that only $f^{MB}$ is still dimensional but all other quantities are dimensionless.
. ⊳∖⋠⋠To eliminate £4“De! [rom eq., To eliminate $E^{DC}$ from eq.
 12 we need to relate it to the spatial variability of /MMOBO-, \ref{eq:fir_or} we need to relate it to the spatial variability of $f^{MB}$.
 cqToward that goal one uses the current free. condition., Toward that goal one uses the current free condition.
nc In astrophysical conditions. thermoelectric fields. would cause the plasma to settle down to à zero current. state.," In astrophysical conditions, thermoelectric fields would cause the plasma to settle down to a zero current state."
 Vhe current free condition reads: Using eq. 12..," The current free condition reads: Using eq. \ref{eq:fir_or},"
 in eq., in eq.
 14. and substituting the result into eq., \ref{eq:day_kvar} and substituting the result into eq.
 12. we find after some algebra that the current [ree distribution function is: and the ratio of Y2/Y* should be evaluated once the value of £ has been determined.," \ref{eq:fir_or}
 we find after some algebra that the current free distribution function is: where and the ratio of $Y^{2}/Y^{1}$ should be evaluated once the value of $\tilde{\nu}$ has been determined."
 For a collision dominated plasma the value of @ is given by eq. 2.., For a collision dominated plasma the value of $\tilde{\nu}$ is given by eq. \ref{eq:coll_coll}.
 Thus. the value of Y7/Y! can be evaluated.," Thus, the value of $Y^{2}/Y^{1}$ can be evaluated."
 However. if the plasma is whistler dominated. fis a functional of ο. and not a simple function obit.," However, if the plasma is whistler dominated, $f$ is a functional of $\tilde{\nu}$, and not a simple function of it."
 Substituting 2=ὃ into eq. 16.," Substituting $\tilde{\nu}=\tilde{v}^{-3}$ into eq. \ref{eq:cur_ints},"
 one linds 37/1!=4 and using this in eq. 15..," one finds $Y^{2}/Y^{1}=4 $ and using this in eq. \ref{eq:tcur_free},"
 one obtains MM ⋠⋠ . . T∐∐⊳∖⊳∖∪↓⋯↓∪⊔↓⊳∖∖⇁⋜↧↓⊓⇂↓≻↓⋅∪∖⇁⊔⇂⋖⊾∠⇂↿⇂⋯↥↙∣∶↙ ⇉↓∪∶↿∖∠⇂⋯⋅↥⇂↥∢⋅∖⇁∢⊾↓⋯⋰↓↿∙∖⇁ dependence of the collisions mean free path: Grav Willkenny 1980).," one obtains This solution is valid provided that $\epsilon^{th} =\epsilon^{coll}(v^{th})
\le 2 \times 10^{-2}$ (due the velocity dependence of the collisions mean free path; Gray Killkenny 1980)."
" Note that if (L210? then [or =2c""0.32ας1. for P=4 the uncerlving assumptions of the expansion do not hold."," Note that if $\epsilon^{th}=2\times10^{-2}$ then for $\tilde{v}=2\Rightarrow\epsilon^{coll}=0.32\not\ll 1$, for $\tilde{v}=4$ the underlying assumptions of the expansion do not hold."
 The aim of this section is to a) calculate when eq., The aim of this section is to a) calculate when eq.
 17 gives rise to whistlers. b) to find the angular dependence of the whistler spectrum. and ο) with this whistler spectrum to estimate the mocified steady state cistribution function (to which the collision dominated plasma distribution function evolves). from which follows the heat [lux inhibition factor.," \ref{eq:knud} gives rise to whistlers, b) to find the angular dependence of the whistler spectrum, and c) with this whistler spectrum to estimate the modified steady state distribution function (to which the collision dominated plasma distribution function evolves), from which follows the heat flux inhibition factor."
 Consistency checks of the assumptions made are carried out as we progress., Consistency checks of the assumptions made are carried out as we progress.
 “Lo obtain these goals we consider approximate solutions to the equations given in 7? under the assumption that whistlers pervade the plasma.," To obtain these goals we consider approximate solutions to the equations given in \ref{sec:gov}
 under the assumption that whistlers pervade the plasma."
 However. before we do so we need to establish when this situation would occur and what the qualitative nature of it is.," However, before we do so we need to establish when this situation would occur and what the qualitative nature of it is."
 The formal expression for the distribution function has been found via the Knudsen expansion and is given by eq. 15.., The formal expression for the distribution function has been found via the Knudsen expansion and is given by eq. \ref{eq:tcur_free}.
 To calculate when whistlers are present in the plasma we need to use eq., To calculate when whistlers are present in the plasma we need to use eq.
 15 in eq. LO., \ref{eq:tcur_free} in eq. \ref{eq:wisgro0}.
 Ht proves mathematically convenient to formulate all expressions in terms of Ay=hy and X as the independent variables rather than & ancl y., It proves mathematically convenient to formulate all expressions in terms of $k_{\parallel}=k\chi$ and $\chi$ as the independent variables rather than $k$ and $\chi$.
 After some algebra we obtain the following schematic form for the quasilincar growth rate: ⋜⋯∠⇂∫↗↴⊲↓⊳∖⇂↓↥∢⊾∢⊾↓⋖⋅≼⇍↿↓⋅∪⊔⊳∖↓≻↓⋅∢⊾⊳∖⊳∖⊔↓⋅⋖⋅⊳⋜⋃⊔⇂∫↗⇂↓↕∢⋅⋯⋯↓⋏∙≟∥⊳∖ pressure.," After some algebra we obtain the following schematic form for the quasilinear growth rate: where and $P_{e}$ is the electrons pressure, and $P$ the total gas pressure."
 We have chosen the magnetic field. pointing from hot to cold., We have chosen the magnetic field pointing from hot to cold.
 For this choice whistler propagation is parallel to field lines. in the coldward direction.," For this choice whistler propagation is parallel to field lines, in the coldward direction."
 Thus. for wave growth we must have y20 (or hy> 0).," Thus, for wave growth we must have $\chi>0$ (or $\tilde{k}_{\parallel}>0$ )."
 This point is taken into account in the expression written above., This point is taken into account in the expression written above.
 Lhe terms QUmU aud PUv) in eq.," The terms $Q(\tilde{k}_{\parallel},\chi)$ and $P(\tilde{k}_{\parallel},\chi)$ in eq."
 19. represent a growth term due to the OlOe term. and the damping term due to the erpορ term in eq. LO.," \ref{eq:P_Q}
 represent a growth term due to the ${\partial {F} \over \partial \mu}$ term, and the damping term due to the ${\partial {F} \over \partial
p}$ term in eq. \ref{eq:wisgro0},"
 respectively., respectively.
 llore we show that under a wide range of conditions. a distribution function. were it. &overned. only by collisions. would be unstable to whistler waves which. of course. mocitv the distribution function.," Here we show that under a wide range of conditions, a distribution function, were it governed only by collisions, would be unstable to whistler waves which, of course, modify the distribution function."
 Using eq., Using eq.
 18 we first establish when a collision dominated. plasma becomes unstable., 18 we first establish when a collision dominated plasma becomes unstable.
" Using 1Y7/Y*=+ ancl p=IEPETI""= ὰ eg. 19."," Using $Y^{2}/Y^{1}=4 $ and $\tilde{\nu}^{w,s}=\tilde{\nu}^{w,a}=0$ in eq. \ref{eq:P_Q},,"
 we have:, we have:
"range 107?—10-?, and imply that a planet can open a gap at 1 AU only if its mass is larger than about 0.1 M.","range $10^{-2}-10^{-3}$, and imply that a planet can open a gap at 1 AU only if its mass is larger than about 0.1 $M_J$."
" To open a gap at 30 AU, the mass must be larger than about 0.5 Mj."," To open a gap at 30 AU, the mass must be larger than about 0.5 $M_J$."
" To investigate the effects that a planet more massive than 0.1 M; might have on the observations of the dust continuum emission, we simulated the presence of a planet in the DG Tau disk by opening a gap in the surface density distribution corresponding to the best fit models discussed above."," To investigate the effects that a planet more massive than 0.1 $M_J$ might have on the observations of the dust continuum emission, we simulated the presence of a planet in the DG Tau disk by opening a gap in the surface density distribution corresponding to the best fit models discussed above."
" For simplicity, we assumed that the planet describes a circular orbit and that the gap can be represented by a circular ring."," For simplicity, we assumed that the planet describes a circular orbit and that the gap can be represented by a circular ring."
" To be compatible with numerical simulations of planet-disk interaction, the half-width of the ring A is assumed to be equal to twice the Hill radius Ry=Rp*/Mp/(3M,) (e.g.Brydenetal.1999;Wolfetal. 2007)."," To be compatible with numerical simulations of planet-disk interaction, the half-width of the ring $\Delta$ is assumed to be equal to twice the Hill radius $R_H = R_p \sqrt[3]{M_P/(3M_{\star})}$ \citep[e.g.][]{br99,wo07}."
". In the region between R,+A the surface density is depleted by a fraction f that depends on the mass of the planet and on the disk viscosity.", In the region between $R_p \pm \Delta$ the surface density is depleted by a fraction $f$ that depends on the mass of the planet and on the disk viscosity.
" For a= 10-3, we can assume f—0 for planet masses M,>1M;, f=0.1 for M,=0.5 My, f=0.17 for M,=0.3M; and f=0.6 for M,=0.1M; (Wolfetal.2007)."," For $\alpha = 10^{-3}$ , we can assume $f=0$ for planet masses $_{p} > 1 M_J$, $f=0.1$ for $M_p=0.5$ $M_J$, $f=0.17$ for $M_p=0.3~M_J$ and $f=0.6$ for $M_p=0.1~M_J$ \citep{wo07}."
". Therefore, only planets more massive than 1 M; will produce completely cleaned gaps."," Therefore, only planets more massive than 1 $M_J$ will produce completely cleaned gaps."
 We simulated gaps corresponding to planets in the mass range 0.3-5 M; and with orbital radii between 1 and 90 AU., We simulated gaps corresponding to planets in the mass range 0.3-5 $M_J$ and with orbital radii between 1 and 90 AU.
 For each model we calculated the residuals as the difference between the observations of DG Tau at 1.3 mm and the model image., For each model we calculated the residuals as the difference between the observations of DG Tau at 1.3 mm and the model image.
 If the gap istoo small compared to, If the gap istoo small compared to
accurate measure of the PN content of the Galaxy is important in determining the relative importance of the various routes to PN formation and the role of binary interaction (see de Marco (2009) for a review).,accurate measure of the PN content of the Galaxy is important in determining the relative importance of the various routes to PN formation and the role of binary interaction (see de Marco \cite{2009PASP..121..316D} for a review).
" It has been noted that --emitting PN tend to lie at low Galactic latitude, with a scale height of ppc (Kastner et al. (1996)))"," It has been noted that -emitting PN tend to lie at low Galactic latitude, with a scale height of pc (Kastner et al. \cite{1996ApJ...462..777K}) )"
" and the same trend exists for the pre-PN eemitters, which tend to be bipolar (Kelly Hrivnak (2005)))."," and the same trend exists for the pre-PN emitters, which tend to be bipolar (Kelly Hrivnak \cite{2005ApJ...629.1040K}) )."
" A deep Galactic plane ssurvey, such as UWISH2, has the potential to uncover a significant population of evolved objects and its contiguous areal coverage will provide important constraints on their space density and any variation along the plane."," A deep Galactic plane survey, such as UWISH2, has the potential to uncover a significant population of evolved objects and its contiguous areal coverage will provide important constraints on their space density and any variation along the plane."
" The UWISH2 survey also provides a unique study of PN morphologies (note the considerable improvement in spatial resolution over Spitzer evident in refirdc)), particularly when complemented by IPHAS optical and CORNISH radio survey data."," The UWISH2 survey also provides a unique study of PN morphologies (note the considerable improvement in spatial resolution over Spitzer evident in \\ref{irdc}) ), particularly when complemented by IPHAS optical and CORNISH radio survey data."
 Point-symmetric structure is seen in many post-AGB objects and PN; this is thought to result from the interaction of a precessing jet with the remnant AGB shell (Kwok (2000)))., Point-symmetric structure is seen in many post-AGB objects and PN; this is thought to result from the interaction of a precessing jet with the remnant AGB shell (Kwok \cite{2000eaa..bookE5200K}) ).
" In many ways the physics of post-AGB evolution mimics that seen in pre-main-sequence objects, something that could be investigated further with these simultaneous observations of both classes of object."," In many ways the physics of post-AGB evolution mimics that seen in pre-main-sequence objects, something that could be investigated further with these simultaneous observations of both classes of object."
 Observations of the near-IR aand CO bandhead emission in the post-AGB object 118276-1431 show striking similarities with emission features in Herbig, Observations of the near-IR and CO bandhead emission in the post-AGB object 18276-1431 show striking similarities with emission features in Herbig
"Sincee Tig1XR7 2rfor coustan Iuniuosity. his ""Mis also a scaling to the Newtonian gravity of the models.","Since $\Teff ^4 \propto R_*^{-2}$ for constant luminosity, this is also a scaling to the Newtonian gravity of the models."
" Figure 8 shows the normalized gi, of Fe for he moclels A (top) and B (bottom).", Figure \ref{f_ABFe} shows the normalized $g_{\rm L}$ of Fe for the models A (top) and B (bottom).
 The right hand figures show au chlarecinent of the region near the sonic poit., The right hand figures show an enlargement of the region near the sonic point.
 It shows that for model D gy of Fe around the sonic point is more than a factor two larger than for nodel A (see Fies. S((, It shows that for model B $g_{\rm L}$ of Fe around the sonic point is more than a factor two larger than for model A (see Figs. \ref{f_ABFe}( (
b) aud (dj).,b) and (d)).
 This extra amount of Fe din model Bcauses an increase in the tote? gp m the subsonic part of the wind also. as cau be secu in Fie. 9((," This extra amount of Fe in model Bcauses an increase in the $total$ $g_{\rm L}$ in the subsonic part of the wind also, as can be seen in Fig. \ref{f_ABCABC}( ("
b).,b).
 Now the effect of gp ou ex will be examined., Now the effect of $g_{\rm L}$ on $\vinf$ will be examined.
" Therefore. Model D is compared to model €. We remind that mocels D aud € have the sameZig.. aud hence the same radiative flux aud gravity. but model € las a twice as small value of Vaγιος 05 model D. Figure 9((a) slows the normalized gr, for models A. Baud €. As expected. gp(re) for model € is significantly smaller than gi(7) for models A aud B. This is Obviously due to the simaller value of."," Therefore, Model B is compared to model C. We remind that models B and C have the same, and hence the same radiative flux and gravity, but model C has a twice as small value of $\ratio$ as model B. Figure \ref{f_ABCABC}( (a) shows the normalized $g_{\rm L}$ for models A, B and C. As expected, $g_{\rm L}(r)$ for model C is significantly smaller than $g_{\rm L}(r)$ for models A and B. This is obviously due to the smaller value of."
. The iuteeral Γι)de in Fig. 9((, The integral $\int g_{\rm L}(r)~dr$ in Fig. \ref{f_ABCABC}( (
"a) for model A and D is larger than for model C. The values of fgi(r)dr for the models are 2.31 1010 aud 1.92 & 1010 ene 7 for models A aud D respectively,. aud 6.12Lae « 10175 cm?2 7 2ofor model C. Using7 Eq.","a) for model A and B is larger than for model C. The values of $\int g_{\rm L}(r)~dr$ for the models are 2.34 $\times$ $^{16}$ and 1.92 $\times$ $^{16}$ $^2$ $^{-2}$ for models A and B respectively, and 6.12 $\times$ $^{15}$ $^2$ $^{-2}$ for model C. Using Eq."
 7 mx the values of ffrom cohuun (61) iu Table 1.. the output values for cean be obtained from the values of the iutegral of gr.," \ref{eq:vinfty} and the values of from column (4) in Table \ref{t:parameters}, the output values for can be obtained from the values of the integral of $g_{\rm L}$."
 The derived output values for ffor the moclels are == 2050. 1860 aud 920 kaw | respectively for the models A.D and C. These values are equal within 10 to the oeiput values for Ισ were indicated in column (5) of Table 1..," The derived output values for for the models are = 2050, 1860 and 920 km $^{-1}$ respectively for the models A,B and C. These values are equal within 10 to the input values for which were indicated in column (5) of Table \ref{t:parameters}."
 We can conclude that a smaller value for Hs indeed cousistent with a smaller value of the integral {ο(ή) dr., We can conclude that a smaller value for is indeed consistent with a smaller value of the integral $\int g_{\rm L}(r)~dr$ .
 However. this is not au independent check. since the calculated line acceleration of optically thick lines (in the Sobolev approximation) is iuversely proportional to the Sobolev optical depth which is," However, this is not an independent check, since the calculated line acceleration of optically thick lines (in the Sobolev approximation) is inversely proportional to the Sobolev optical depth which is"
has modeled the distance of the termination shock (TS) in the direction of the Vovager 1 motion. and found that 1.5 vvields a TS distance of 94 AU. which agrees with the recently measured Vovager 1 value (81)).,"has modeled the distance of the termination shock (TS) in the direction of the Voyager 1 motion, and found that $\sim$ 1.5 yields a TS distance of 94 AU, which agrees with the recently measured Voyager 1 value \ref{sec:intro}) )."
 I argued that aat (he Sun should be similar to the uniform component οἱ iinferred from pulsar data. Biy|~ 1.6G.. which dominates low density interarm regions such as surrounding the Sun1990).," I argued that at the Sun should be similar to the uniform component of inferred from pulsar data, $\sim$ 1.6, which dominates low density interarm regions such as surrounding the Sun."
. ILowever stronger fields are indicated. 2.6 [IG if equipartition between thermal and magnetic pressure applies.," However stronger fields are indicated, $\sim$ 2.6, if equipartition between thermal and magnetic pressure applies."
 The value 11.5 wwill be used in the following discussions., The value 1.5 will be used in the following discussions.
 The interaction between ISDGs and the heliosphere depends on the dust charge. mass. and composition.," The interaction between ISDGs and the heliosphere depends on the dust charge, mass, and composition."
 In this section the results of radiative transfer models of the local ISM are compared wilh a reference abundance lor the ISM. here assume to be solar abundances. to determine the dust composition.," In this section the results of radiative transfer models of the local ISM are compared with a reference abundance for the ISM, here assume to be solar abundances, to determine the dust composition."
 The following section gives the gas-to-dust mass ratio calculated from the same assumptions., The following section gives the gas-to-dust mass ratio calculated from the same assumptions.
 Unfortunately. both solar abundances aud (he ISM composition. generally assumed to be (he summed abundances of the gas and dust. ave highly uncertain.," Unfortunately, both solar abundances and the ISM composition, generally assumed to be the summed abundances of the gas and dust, are highly uncertain."
 For instance. estimates of the solar ratio for Ο/Η vary by 230542005).," For instance, estimates of the solar ratio for O/H vary by $\sim$."
.. Also. eas and grains may decouple in transient violent interstellar phenomena2004).," Also, gas and grains may decouple in transient violent interstellar phenomena."
. The predicted LIC gas-phase abundanees of C. N. ο. Ale. Al. Si. and Fe are listed in Table 1 for the best-fitting RT models 2 and 8 (SE02).," The predicted LIC gas-phase abundances of C, N, O, Mg, Al, Si, and Fe are listed in Table \ref{tab:dust} for the best-fitting RT models 2 and 8 (SF02)."
 Comparisons between the gaseous Fe. Me. Si. and O abundances and solar abundances then vield underabuncances of Fe. Meg. Si. and O in the eas within ~1 pe of the Sun towards e CMa," Comparisons between the gaseous Fe, Mg, Si, and O abundances and solar abundances then yield underabundances of Fe, Mg, Si, and O in the gas within $\sim$ 1 pc of the Sun towards $\epsilon$ CMa."
 For this discussion. (the abundances presented in are utilized.," For this discussion, the abundances presented in are utilized."
 The short length of the local ISM towards € CMa (1 pe) contains two velocity components separated bv ~8 , The short length of the local ISM towards $\epsilon$ CMa $\sim$ 1 pc) contains two velocity components separated by $\sim 8$ 
Although these secondary GeV eamuna-ravs are not taken iuto account here aud it is beyond the scope of this paper. it is naportaut to study how laree is this spectral distortion iu future work.,"Although these secondary GeV gamma-rays are not taken into account here and it is beyond the scope of this paper, it is important to study how large is this spectral distortion in future work."
 We here discuss the expected properties of gamma-ray clusters of galaxies., We here discuss the expected properties of gamma-ray clusters of galaxies.
" Perhaps the most natural question in this regard would be ""Are they already observed iu other wavebauds such as x-rays or optical surveys?”", Perhaps the most natural question in this regard would be “Are they already observed in other wavebands such as x-rays or optical surveys?”
 We have checked that there is no statistically significant association of the ROSAT Brightest Cluster Sample (RBCS. Ebeliug et al.," We have checked that there is no statistically significant association of the ROSAT Brightest Cluster Sample (RBCS, Ebeling et al."
 1998). within the error circles of the nnideutified sources with |b]230° in the EGRET catalog.," 1998), within the error circles of the unidentified sources with $|b|>30^\circ$ in the EGRET catalog."
 We have also checked the correlation with the clusters in the revised Abell catalog (Abell Corwin. Olowin 1989). and uo statistically significant associations are found. either.," We have also checked the correlation with the clusters in the revised Abell catalog (Abell, Corwin, Olowin 1989), and no statistically significant associations are found, either."
 ILlowever. iu the following[m] we argueOo that the Ooσαταν clusters proposed in this paper are very difficult to detect in xaavs or optical bands compared with ordinary clusters ideuti&ed in these wavebands. and heuce our scenario 1s uot rejected bv these results.," However, in the following we argue that the gamma-ray clusters proposed in this paper are very difficult to detect in x-rays or optical bands compared with ordinary clusters identified in these wavebands, and hence our scenario is not rejected by these results."
 We first estimate the expected. xay flux from gamuna-rav clusters., We first estimate the expected x-ray flux from gamma-ray clusters.
 Barvouic gas in most clusters of galaxies observed in X-ravs seenmis to be in approximate livdrostatic equilibrimu with the surface brightuess well fitted by a density profile. pear)x|ld(en|Ἐ (ee. Sarazin 1988). where r. is the core radius that is typically about ~10 times smaller than the virial radius.," Baryonic gas in most clusters of galaxies observed in x-rays seems to be in approximate hydrostatic equilibrium with the surface brightness well fitted by a density profile, $\rho_{\rm gas}(r) \propto
[1+(r/r_c)^2]^{-1}$ (e.g., Sarazin 1988), where $r_c$ is the core radius that is typically about $\sim 10$ times smaller than the virial radius."
 Since the x-ray cuussivity ds proportional to D the x-ray cussion is strongly concentrated into the central region.," Since the x-ray emissivity is proportional to $\rho_{\rm
gas}^2$, the x-ray emission is strongly concentrated into the central region."
 Asstuning the above density profile and the sclfsimilar model as described in Kitavama Suto (1996b). ba typical gamma-ray cluster detectable by the ECRET with AL~WAL. ane 0.05 would have the x-ray flux 2.]«10Heyeeni28 bin 02.1 keV. The inverse-Compton flux is also expected to be conrparable with the thermal enussiou.," Assuming the above density profile and the self-similar model as described in Kitayama Suto (1996b), a typical gamma-ray cluster detectable by the EGRET with $M \sim 10^{15} M_\odot$ and $z \sim
0.05$ would have the x-ray flux $2.4 \times 10^{-11} \rm \ erg \
cm^{-2} \ s^{-1}$ in 0.1–2.4 keV. The inverse-Compton flux is also expected to be comparable with the thermal emission."
 By equating fe: aud faa; du 2.. we eet the cooling photon euergv €-cool=2.0(1|CO keV. below which the electron cooling time is longer than the dvuamical time.," By equating $t_{IC}$ and $t_{\rm shock}$ in \ref{section:flux}, we get the cooling photon energy $\epsilon_{\rm \gamma, cool}
= 2.0 (1+z)^{-5}$ keV, below which the electron cooling time is longer than the dynamical time."
" Then the IC spectrum extends down to around x-ray band withH dN.-/de.XDie.. whileB it becomes harder at waveleusths longer than x-ays with VN.Πε.~e,1."," Then the IC spectrum extends down to around x-ray band with $dN_\gamma/d\epsilon_\gamma \propto \epsilon_\gamma^{-2}$, while it becomes harder at wavelengths longer than x-rays with $dN_\gamma/d\epsilon_\gamma \propto \epsilon_\gamma^{-1.5}$."
 T£ the eamumacrav flux at LOO MeV. is —10©photonsc7s+ that is the EGRET threshold. the IC xav flux (FL) is —1.6«10Hergcni2.41," If the gamma-ray flux at 100 MeV is $\sim 10^{-7} \rm \ photons \ cm^{-2} s^{-1}$ that is the EGRET threshold, the IC x-ray flux $\nu F_\nu$ ) is $\sim 1.6 \times 10^{-11} \rm \ erg \ cm^{-2} \ s^{-1}$."
 Therefore. the thermal and IC fluxes are well above the Bux linüt —bs10Perecmὃν+ of the RBCS.," Therefore, the thermal and IC fluxes are well above the flux limit $\sim 4 \times 10^{-12} \rm
\ erg \ cm^{-2} \ s^{-1}$ of the RBCS."
 However. it takes nearly the ανασα. time for the cluster gas to reach livdrostatic equilibrium after the collapse. aud seanuna-rayvs from the shock generated bv the gravitational collapse are radiated away within that period.," However, it takes nearly the dynamical time for the cluster gas to reach hydrostatic equilibrium after the collapse, and gamma-rays from the shock generated by the gravitational collapse are radiated away within that period."
 Then it is likely that the deusity profile of eanumnia-rav cluitting clusters is more nregular aud extended than ordinary x-ray clusters., Then it is likely that the density profile of gamma-ray emitting clusters is more irregular and extended than ordinary x-ray clusters.
 Iu fact. if the unidentified eur sources in the EGRET catalog are actually extended. they iust have typical angular size of about degree. from the source location accuracy of the EGRET.," In fact, if the unidentified `em' sources in the EGRET catalog are actually extended, they must have typical angular size of about degree, from the source location accuracy of the EGRET."
 As we lave shown. augular size of about 1? is theoretically reasonable if the emission is exteuded to the virial radius.," As we have shown, angular size of about $^\circ$ is theoretically reasonable if the emission is extended to the virial radius."
 When the density profile is not concentrated into the central region but rather constant within the virial radius. the x-ray hinunosity becomes lower than the selfsimilar model by a factor of ~3.7 because of the lower ceutral deusity.," When the density profile is not concentrated into the central region but rather constant within the virial radius, the x-ray luminosity becomes lower than the self-similar model by a factor of $\sim 3.7$ because of the lower central density."
 Furthermore. the surface brieltucss of such loose clusters should be drastically cünuuer than ordinary x-ray clusters.," Furthermore, the surface brightness of such loose clusters should be drastically dimmer than ordinary x-ray clusters."
 In the selfsimular model with ma.2αι the core eas density iS pase~(1/3)GarepassisoDÜPaassis where pan=(Qp/Qulpair is the virial gas density hat is the average gas deusitv within ma.," In the self-similar model with $r_{\rm vir} \gg r_c$, the core gas density is $\rho_{\rm gas, c} \sim (1/3)(r_{\rm vir}/r_{c})^2 
\rho_{\rm gas, vir} \sim 50 \rho_{\rm gas, vir}$, where $\rho_{\rm gas, vir} = (\Omega_B/\Omega_0) \rho_{\rm vir}$ is the virial gas density that is the average gas density within $r_{\rm vir}$."
 Ou the other iud. if the eas density profile of gamma-ray clusters is roughly constant at pai; out to ri. the x-ray surface xiehtuess of such a loose cluster is dinuner than the central surface brightuess of the sclfsimilar model bv a ‘actor of ~(rfras)pssse/Passi)ce200. since the x-rav cluissivity is proportional to Pons," On the other hand, if the gas density profile of gamma-ray clusters is roughly constant at $\rho_{\rm gas, vir}$ out to $r_{\rm vir}$, the x-ray surface brightness of such a loose cluster is dimmer than the central surface brightness of the self-similar model by a factor of $\sim (r_c/r_{\rm vir})(\rho_{\rm gas, c}/
\rho_{\rm gas, vir})^2 \sim 200$, since the x-ray emissivity is proportional to $\rho_{\rm gas}^2$."
 Tt crucially affects he detectability of x-ravs from eamunaray clusters., It crucially affects the detectability of x-rays from gamma-ray clusters.
 The detectability of x-rays should be described by the sigual-o-noise ratio (9/.N) against the x-ray backgrouud fiux, The detectability of x-rays should be described by the signal-to-noise ratio $(S/N)$ against the x-ray background flux.
" The noise level is proportional to (image yee,1/2 and rence SYNxFr where Fo and r are the flux aud the oenage radius. respectively,"," The noise level is proportional to (image $^{1/2}$, and hence $S/N \propto F/r$, where $F$ and $r$ are the flux and the image radius, respectively."
 We have compared the value of Fr of the extended ganuna-ray clusters detectable by the EGRET aud those of the clusters in the RBCS., We have compared the value of $F/r$ of the extended gamma-ray clusters detectable by the EGRET and those of the clusters in the RBCS.
 We fouud that the Fr of gamunarav clusters is by a factor of 3 sunaller than the mium Fr of the RBCS clusters., We found that the $F/r$ of gamma-ray clusters is by a factor of 3 smaller than the minimum $F/r$ of the RBCS clusters.
 The absence of association between the RBCS aud the ECRET sources is therefore not in contracliction to our scenario., The absence of association between the RBCS and the EGRET sources is therefore not in contradiction to our scenario.
 Ou the other haud. deeper observation of candidate gamiuna-rav clusters by Newton. for example. wight detect the x-rav Cluission extended to about 17 with the flux estimated above. that would provide a clear test of our scenario.," On the other hand, deeper observation of candidate gamma-ray clusters by Newton, for example, might detect the x-ray emission extended to about $1^\circ$ with the flux estimated above, that would provide a clear test of our scenario."
 Such x-ray cluission should reflect the structure of shocks in dvuaimically forming clusters. aud nauagiug study is of eyoat interest.," Such x-ray emission should reflect the structure of shocks in dynamically forming clusters, and imaging study is of great interest."
 Tere we again curphasize that the gamma-ray clusters are expected to be more exteuded than clusters that have already stabilized., Here we again emphasize that the gamma-ray clusters are expected to be more extended than clusters that have already stabilized.
" It is known that the surface deusitv profile of galaxies ina cluster cau well be deseribed by the Ising profile. v(r)x[1leer,M lowith the core radius of ~ LOO kpe that is comparable with the core radius of x-ray profile (e.g... Adami et al."," It is known that the surface density profile of galaxies in a cluster can well be described by the King profile, $\sigma(r) \propto [1 +
(r/r_c)^2]^{-1}$ with the core radius of $\sim$ 100 kpc that is comparable with the core radius of x-ray profile (e.g., Adami et al."
 1998)., 1998).
 If we assume a roughly constant surface deusity out to ~rq rather than the Ning profile for gamuna-ray clusters. the average surface deusity," If we assume a roughly constant surface density out to $\sim r_{\rm
vir}$ rather than the King profile for gamma-ray clusters, the average surface density"
"Since the astrometric signature is hidden iu the second derivative of £(2). the computationally most appealing expansion of R aud £ is a Tavlor series around some reference value of :: We define refractivity iutegrals as a short-cut to the notation. covering ((8)) as a special case: A stable nunerical scheme for these iuteerals is proposed in retsec.Ru αν,","Since the astrometric signature is hidden in the second derivative of $L(z)$, the computationally most appealing expansion of $R$ and $L$ is a Taylor series around some reference value of $z$: We define refractivity integrals as a short-cut to the notation, covering \ref{eq.RofnInt}) ) as a special case: A stable numerical scheme for these integrals is proposed in \\ref{sec.Rnum} ."
 Insertion of the series (32)) into the oof (S)) aud iuto the aremments τρτΠο the sines at the vields the expansion cocticicuts with the doublvi-udexed shorthiuds Iu ((33)) C12)) aud refsec.IRuun.. the subscripts of Π are the expoucutial j of the definition (33)): elsewhere they indicate the telescope uumuboer/site.," Insertion of the series \ref{eq.rtayl}) ) into the of \ref{eq.RofnInt}) ) and into the arguments $z_0=z-R$ of the sines at the yields the expansion coefficients with the doubly-indexed shorthands In \ref{eq.RofnInt2}) \ref{eq.Renddef}) ) and \\ref{sec.Rnum}, the subscripts of $R$ are the exponential $j$ of the definition \ref{eq.RofnInt2}) ); elsewhere they indicate the telescope number/site."
 e din ((032)) is of the order of b/(2p) if the reference azimuth + is chosen close to the uiddle between the telescopes. and therefore uot larger than 1.6-10' ad for b«200 un. Because the £j are approximately of the same maguitude refRtavl.ps)). collecting the terms up to j=3 ought establish a relative accuracy of ~5-101 in the anele of refraction.," $x$ in \ref{eq.rtayl}) ) is of the order of $b/(2\rho)$ if the reference azimuth $z$ is chosen close to the middle between the telescopes, and therefore not larger than $1.6\cdot 10^{-5}$ rad for $b<200$ m. Because the $\xi_j$ are approximately of the same magnitude \\ref{Rtayl.ps}) ), collecting the terms up to $j=3$ ought establish a relative accuracy of $\approx 5\cdot 10^{-14}$ in the angle of refraction."
 The expansion proceeds via insertion of ((32)) iuto the sines of ((26)). aud employs an auxiliary. set of iuteerals," The expansion proceeds via insertion of \ref{eq.rtayl}) ) into the sines of \ref{eq.LInt}) ), and employs an auxiliary set of integrals"
For a prolate or oblate ellipsoid we know that where &>1 for a prolate ellipsoid. aud «4<1 for an oblate ellipsoid.,"For a prolate or oblate ellipsoid we know that where $u>1$ for a prolate ellipsoid, and $u<1$ for an oblate ellipsoid."
 So in zx plane iFrom standard trigonometryFrom figure l we can see where n ds the eradieut. aud will uccessarily be the opposite sign to cj.," So in z-x plane >From standard trigonometry>From figure \ref{ellipse} we can see where m is the gradient, and will necessarily be the opposite sign to $x_0$."
 This gives the z value for the z-axis/tangent intercept., This gives the z value for the z-axis/tangent intercept.
 Using (17)) we ect We define the apparcut axial ratio (4) to be less than 1 for both prolate aud oblate ellipsoids., Using \ref{cot}) ) we get We define the apparent axial ratio $q$ ) to be less than 1 for both prolate and oblate ellipsoids.
 Thus for oblate ellipsoids 4=ee and for prolate cllipsoids 4= Z7., Thus for oblate ellipsoids $q=\frac{uA}{a}$ and for prolate ellipsoids $q=\frac{a}{uA}$ .
 Se, So
For many vears there have been theoretical predictions that accretion discs can undergo outbursts which start. either close to their inner edge. or their outer edge (Meyer MaverHofmeister 1984: Mineshige Osaki 1985: Ludwig Mover 1998).,"For many years there have been theoretical predictions that accretion discs can undergo outbursts which start either close to their inner edge, or their outer edge (Meyer Mayer–Hofmeister 1984; Mineshige Osaki 1985; Ludwig Meyer 1998)."
" In this and the following paper we use the eclipsing dwarf novae to resolve spatially their outbursts. and prove that. one. outburst is ""outsidein. the other ""insideout” (Webbetal1999)."," In this and the following paper we use the eclipsing dwarf novae to resolve spatially their outbursts, and prove that one outburst is “outside–in”, the other “inside–out” \cite{Webb99}."
". This is the first time an ""insideoul” outburst has been resolved. anc should be viewed as a major vindication of dise instability. theories."," This is the first time an “inside–out” outburst has been resolved, and should be viewed as a major vindication of disc instability theories."
 1n both cases we find that the discs have extensive vertical structure. which is shown to be the cause of. problems of interpretation in the only other observation of an in” outburst (Vogt. 1983: Rutten 1992).," In both cases we find that the discs have extensive vertical structure, which is shown to be the cause of problems of interpretation in the only other observation of an ``outside--in'' outburst (Vogt 1983; Rutten 1992)."
 The dwarf nova observed in this paper is the SU UAla star IUE Cas. whose orbital period is about LOG min. (," The dwarf nova observed in this paper is the SU UMa star HT Cas, whose orbital period is about 106 min. ("
Patterson 1981: Zhang. Robinson Nather 1986: Wood. llorne Vennes 1992) The observations of LEE Cas. from the 1995. November erüption were carried out with the CCD system. on the 0(.95m James Gregory ‘Telescope (JOUR) at the University of St. Andrews (Bell. Lilditeh Eclwin (1993))). the Thornton Rellector at Ixeele Observatory (Somersctal.1996b) and with a 0.3m Newtonian rellector in Essex.,"Patterson 1981; Zhang, Robinson Nather 1986; Wood, Horne Vennes 1992) The observations of HT Cas, from the 1995 November eruption were carried out with the CCD system on the 0.95m James Gregory Telescope (JGT) at the University of St. Andrews (Bell, Hilditch Edwin \shortcite{Bell93}) ), the 0.6-m Thornton Reflector at Keele Observatory \cite{Somers96b} and with a 0.3m Newtonian reflector in Essex."
 ‘Table 1 lists all the observations., Table \ref{tab:observation_log} lists all the observations.
 Timings are in Darycentric Dynamical Julian Date (BDJD)., Timings are in Barycentric Dynamical Julian Date (BDJD).
 The raw images whicre processed intje standard wav for the instruments in question. as outlines in Somersctal.(1996b) and Bell (1993).," The raw images where processed in the standard way for the instruments in question, as outlined in \scite{Somers96b} and Bell \shortcite{Bell93}."
. The data [rom Essex were dark subtractecl and. [la ficlelecl in the sandard wav [for CCD photometry., The data from Essex were dark subtracted and flat fielded in the standard way for CCD photometry.
 The data were extracted using an optimal extraction technique by avlor (1998)., The data were extracted using an optimal extraction technique by Naylor \shortcite{Naylor98}.
. Eve values for the visual magnitudes for the standard stars were adopted [rom Misselt.(1996)., The values for the visual magnitudes for the standard stars were adopted from \scite{Misselt96}.
. The overall outburst light curve is depicted on Fig. 1.., The overall outburst light curve is depicted on Fig. \ref{fig:alllcvs}.
 The rise to outburst looks very steep with a linear decline., The rise to outburst looks very steep with a linear decline.
 Our coverage of the outburst rise phase starts at a point, Our coverage of the outburst rise phase starts at a point
Following the initial selection of 2>0.9 AMIS8G6 members. stars were rejected if. a) thev are photometric nonmembers inany of our six CMDs. b) they are radial velocity from our spectra or from those spectra used in the Vig study. or ο) they appear to be probable binaries based on a photometric and spectroscopic analyses.,"Following the initial selection of $P>0.9$ MS86 members, stars were rejected if, a) they are photometric nonmembers in of our six CMD's, b) they are radial velocity non-members from our spectra or from those spectra used in the $V_{rad}$ study, or c) they appear to be probable binaries based on a photometric and spectroscopic analyses."
 Figure 1 shows A(Li) as a function of T;jy for the Pleiades. M35 (this study). and the AI35 data from BDSOL are also shown.," Figure 1 shows $A(Li)$ as a function of $T_{eff}$ for the Pleiades, M35 (this study), and the M35 data from BDS01 are also shown."
 All data [vom the literature have been reanalvzed using our methods and photometry. where available. (ο give the most consistent picture possible.," All data from the literature have been reanalyzed using our methods and photometry, where available, to give the most consistent picture possible."
 Several aspects of the 7;;; morphology in M35 are worthy of notice., Several aspects of the $T_{eff}$ morphology in M35 are worthy of notice.
 First. it is clear (hat. as compared to the nominal upper bound plateau between 6300 and 6800Ix with A(Li) = 3.2. many stars between 6000 and 6700 Ix (or bevond) have depleted their surface Li abundances.," First, it is clear that, as compared to the nominal upper bound plateau between 6300 and 6800K with A(Li) = 3.2, many stars between 6000 and 6700 K (or beyond) have depleted their surface Li abundances."
 Although a small amount of Li depletion cannot be ruled. out for the Pleiades. the Li eap hasdefinitely begun to Form in M35.," Although a small amount of Li depletion cannot be ruled out for the Pleiades, the Li gap has begun to form in M35."
 This is clearly illustrated in Figure 2. which shows the continuum-nornmalized spectra in the Li region for four pairs of stars.," This is clearly illustrated in Figure 2, which shows the continuum-normalized spectra in the Li region for four pairs of stars."
 The stars in each pair have similar {ντε and (hus it is not surprising that their Fe I and Ca I line strengths (which depend primarily on 7;;; and intrinsic abundance) are identical: the Li abundances. however. are strikinglv disparate. (," The stars in each pair have similar $T_{eff}$, and thus it is not surprising that their Fe I and Ca I line strengths (which depend primarily on $T_{eff}$ and intrinsic abundance) are identical; the Li abundances, however, are strikingly disparate. ("
Note that where necessary. spectra of slowly rotating stars were artificially. broadened to match their pair.),"Note that where necessary, spectra of slowly rotating stars were artificially broadened to match their pair.)"
 Although the errors listed in Table 1 are internal (see 82). we stress again that svstematic errors due to uncertainties in E(B—V) or T;jy scale do not allect a differential analvsis of stars ad the same νε," Although the errors listed in Table 1 are internal (see 2), we stress again that systematic errors due to uncertainties in $E(B-V)$ or $T_{eff}$ scale do not affect a differential analysis of stars at the same $T_{eff}$."
 Formally. the Li differences are significant at the 5—10e level: the depth of the depletion far exceeds our errors.," Formally, the Li differences are significant at the $5-10\sigma$ level; the depth of the depletion far exceeds our errors."
 The upper aud lower envelope of stars in the gap region of M35 differ by more (han 0.5 dex. which corresponds to to a factor of more than 3 in abundance (and in line strength).," The upper and lower envelope of stars in the gap region of M35 differ by more than 0.5 dex, which corresponds to to a factor of more than 3 in abundance (and in line strength)."
" Thus. M35 illustrates (hat the Li gap begins to form early,"," Thus, M35 illustrates that the Li gap begins to form early."
 second. the Li depletion region is quite wide in Tell.," Second, the Li depletion region is quite wide in Teff."
 The same four pairs illustrate that its width exceeds 700Ix. (from 6000 to 6700IxX2-). which is clearly wider than the canonical llvades Li gap (the region 6550-67001Ix that contains the most extreme Ivacl depletions).," The same four pairs illustrate that its width exceeds 700K (from 6000 to 6700K+), which is clearly wider than the canonical Hyades Li gap (the region 6550-6700K that contains the most extreme Hyad depletions)."
 Bul perhaps this canonical IHvades gap should be viewed as being part of a wider depletion structure: after all. να Li abundances in the region 6300-6550Ix. show Li dispersions of," But perhaps this canonical Hyades gap should be viewed as being part of a wider depletion structure: after all, Hyad Li abundances in the region 6300-6550K show Li dispersions of"
LDNIG621 is a region ofdiffuse emission =25 arcmin to the north of LDNI1622.,LDN1621 is a region of diffuse emission $\approx 25$ arcmin to the north of LDN1622.
 Observations with the CBI at 31 Cllz show a broken ring of emission. that is stronely correlated with PIR emission at 1200100 jim. with Pearson correlation coellicients in the range =0.6 0.5. Optical and Ilo. data show absorption of a strong background. of emission. from warm ionized gas in the Eastern arm of Orion.," Observations with the CBI at 31 GHz show a broken ring of emission, that is strongly correlated with FIR emission at $12-100~\mu$ m, with Pearson correlation coefficients in the range $\approx 0.6-0.8$ Optical and $\alpha$ data show absorption of a strong background of emission from warm ionized gas in the Eastern arm of Orion."
 This suggests that LDNI621 and LDN1622 are in the foreground of Orion (al à distance un500 parsec). possibly as close as 120 pc (Wilsonetal.2005).," This suggests that LDN1621 and LDN1622 are in the foreground of Orion (at a distance of $\sim 500$ parsec), possibly as close as 120 pc \citep{Wilson05}."
.. No Lla emission. associated. clürectlv with LDNIG2I. aseen.," No $\alpha$ emission, associated directly with LDN1621, is seen."
 “This suggests that LDNI621 itself is not emitting significant [rec-free. emission. although the ellects of dust. extinction do not allow a strong constraint to be placed.," This suggests that LDN1621 itself is not emitting significant free-free emission, although the effects of dust extinction do not allow a strong constraint to be placed."
 Low frequency. radio data also do not show evidence of dilfuse emission associated with LDNIG621., Low frequency radio data also do not show evidence of diffuse emission associated with LDN1621.
 The 31 CGllz emission is at z20—30 mJy while an analvsis of the GBG6 map at 4.85 CGllz provides a strong (30) upper limit of 7.2 mJv Lau 31 Guz for frec-[ree emission., The 31 GHz emission is at $\approx 20-30$ mJy $^{-1}$ while an analysis of the GB6 map at 4.85 GHz provides a strong $3\sigma$ ) upper limit of 7.2 mJy $^{-1}$ at 31 GHz for free-free emission.
 The FlR-corrclated emission at 31 Gllz therefore appears to be mostly due to radiation associated with dust., The FIR-correlated emission at 31 GHz therefore appears to be mostly due to radiation associated with dust.
 IRAS data alone do not allow a reliable extrapolation of the RayleighJeans thermal dust tail to 31 Gilz., IRAS data alone do not allow a reliable extrapolation of the Rayleigh-Jeans thermal dust tail to 31 GHz.
WAZAP data at 95 mGllz combined with HUXS data allowed the Dux density to estimatedin an aperture of diameter 30 arcmin at an angular resolution of 13 arcmin., data at 93.5 GHz combined with IRAS data allowed the flux density to be estimated in an aperture of diameter 30 arcmin at an angular resolution of 13 arcmin.
 A single moclified blackbody indicates that the thermal dust is 10 per cent ofthe total 31 CLIz us. corresponding to an excess of 1.524 Jv (2.30).," A single modified blackbody indicates that the thermal dust is $\sim 10$ per cent of the total 31 GHz flux, corresponding to an excess of $1.52\pm0.66$ Jy $2.3\sigma$ )."
 The dust-correlated emission has a coupling coelIicient. relative to LOO pim. of 18.12354.4 pls |. consistent. with that observed from LDN1622.," The dust-correlated emission has a coupling coefficient, relative to $100~\mu$ m, of $18.1\pm4.4~\mu$ K $^{-1}$, consistent with that observed from LDN1622."
 Orion East(consisting of both LDNI621 and LDN1622) appear to be part of the same svstem of dust clouds. emitting significant anomalous emission at [requencies ~30 Cillz.," Orion East (consisting of both LDN1621 and LDN1622) appear to be part of the same system of dust clouds, emitting significant anomalous emission at frequencies $\sim 30$ GHz."
 Spinning dust is an obvious candidate for the physical mechanism responsible for the bulk of the emission., Spinning dust is an obvious candidate for the physical mechanism responsible for the bulk of the emission.
 Ligh sensitivity data. covering a wide range of frequencies. (~5300 Cllz). is required to study such clouds in. more detail.," High sensitivity data, covering a wide range of frequencies $\sim5-300$ GHz), is required to study such clouds in more detail."
 Data from thePlanck satellite will be particularly useful in constraining the Iavleigh-Jeans dust tail. which niv be responsible for a significant fraction of the 31 12 if the emissivity index llattens at longer wavelengths.," Data from the satellite will be particularly useful in constraining the Rayleigh-Jeans dust tail, which may be responsible for a significant fraction of the 31 GHz if the emissivity index flattens at longer wavelengths."
 This work was supported by the Strategic Alliance for the Implementation. of New Technologies. (SAINT. - see wwwsastro.caltech.edu/chajnantorsaint/index.html) and we are most grateful to the SAINT partners for their strong support., This work was supported by the Strategic Alliance for the Implementation of New Technologies (SAINT - see www.astro.caltech.edu/chajnantor/saint/index.html) and we are most grateful to the SAINT partners for their strong support.
 We gratefully acknowledge support from the Ixavli Operating Institute and thank D. Rawn and S. Rawn Jr. Phe CBL was supported by NSE grants 9802089. 0008734 anc 0206416. and a Roval Society Small Research rant.," We gratefully acknowledge support from the Kavli Operating Institute and thank B. Rawn and S. Rawn Jr. The CBI was supported by NSF grants 9802989, 0098734 and 0206416, and a Royal Society Small Research Grant."
 We are particularly indebted to the engineers who maintainec and operated the CBL: Cristobbal Achermann. José Cortéss. Cristóbbal Jara. Nolberto Ovarace. Martin. Shepherd anc Carlos Verdugo.," We are particularly indebted to the engineers who maintained and operated the CBI: Cristóbbal Achermann, José Cortéss, Cristóbbal Jara, Nolberto Oyarace, Martin Shepherd and Carlos Verdugo."
 CD acknowledges an SPEC Xdvanceec Fellowship and ERC erant. under the PPT., CD acknowledges an STFC Advanced Fellowship and ERC grant under the FP7.
 We acknowledge the use of the Legacy Archive for Microwave. Dackgrounc Data Analvsis (LAAIBDA)., We acknowledge the use of the Legacy Archive for Microwave Background Data Analysis (LAMBDA).
 Support. for LAAIBDA is provided by the NASA Ollice of Space Science., Support for LAMBDA is provided by the NASA Office of Space Science.
We used data from the Southern L-Alpha Sky Survey Atlas (SLLASSA). which is supported by the National Science Foundation.,"We used data from the Southern H-Alpha Sky Survey Atlas (SHASSA), which is supported by the National Science Foundation."
MLC was supported by theCajal Programme of the Spanish science ministry.,MLC was supported by the Programme of the Spanish science ministry.
 We have used (he following online databases: Sloan Digital Sky Survey (http://www.sdss.org/). ihe Atomic Line List (http://www.pa.ukv.edu/ peter/atomic/). and NIST Atomic Spectra Database (http://physies.nist.gov/PhvsBRefData/ASD).," We have used the following online databases: Sloan Digital Sky Survey (http://www.sdss.org/), the Atomic Line List (http://www.pa.uky.edu/ peter/atomic/), and NIST Atomic Spectra Database (http://physics.nist.gov/PhysRefData/ASD)."
Smoothec Particle Hvdrodynamiecs (SPLHI) was firs introduced. as a tool for studying stellar structure (7. 2: 7 7)). but has since found. wide application in all areas of theoretical astrophysics (?).. in engineering (2).. and bevonc (c.g. ? ?)).,"Smoothed Particle Hydrodynamics (SPH) was first introduced as a tool for studying stellar structure \bcite{1977MNRAS.181..375G}; ; \bcite{1977AJ.....82.1013L}) ), but has since found wide application in all areas of theoretical astrophysics \citep{1992ARA&A..30..543M}, , in engineering \citep{1993JCoPh.109...67L}, , and beyond (e.g. \bcite{2008JCoPh.227.9195H}) )."
 Although there are many varieties of SPLIT. the centra idea is to represent a fIuid. by discrete particles that move with the Dow (?2: 7 2)).," Although there are many varieties of SPH, the central idea is to represent a fluid by discrete particles that move with the flow \bcite{1992ARA&A..30..543M}; \bcite{2005astro.ph..7472P}) )."
 Dvpically these particles represen the [uid exactly. though in some variants the Bui is advected: on top of the particles (27: ? 73).," Typically these particles represent the fluid exactly, though in some variants the fluid is advected on top of the particles \bcite{1999Dilts}; \bcite{2003ApJ...595..564M}) )."
 Phe kev advantages over Eulerian are its Lagrangian nature that makes it Galilean invariant. and its particle nature that makes it easy to couple to the fast multipole method for gravity that scales as O(N) (22: 7? 2)).," The key advantages over Eulerian are its Lagrangian nature that makes it Galilean invariant, and its particle nature that makes it easy to couple to the fast multipole method for gravity that scales as $O(N)$ \bcite{2000ApJ...536L..39D}; \bcite{1987JCoPh..73..325G}) )."
 However. SPL has problems correctly integrating ΕΙ instabilities ancl mixing at boundariesTu YTTu Tu PP 7 PV).," However, SPH has problems correctly integrating fluid instabilities and mixing at boundaries; \bcite{1999Dilts}; \bcite{2001MNRAS.323..743R}; \bcite{2003MNRAS.345..561M}; ; \bcite{2006astro.ph.10051A}) )."
 Several different reasons have been sugeested for this in the literature so far., Several different reasons have been suggested for this in the literature so far.
 7 and ? argue that the problem owes to errors in the SPL gradients that do not show good. convergence for irregular. particle distributions., \citet{1996PhDMorris} and \citet{1999Dilts} argue that the problem owes to errors in the SPH gradients that do not show good convergence for irregular particle distributions.
 ? argue that the problem. owes to the fact that entropies are discontinuous at boundaries. while the densities are smooth.," \citet{2007arXiv0709.2772P} argue that the problem owes to the fact that entropies are discontinuous at boundaries, while the densities are smooth."
 This gives spurious pressure blips at boundaries that drive Duids of dillerent entropy. apart., This gives spurious pressure blips at boundaries that drive fluids of different entropy apart.
 ον find that adding thermal conductivity at. boundaries to smooth the entropies gives improved mixing in SP, They find that adding thermal conductivity at boundaries to smooth the entropies gives improved mixing in SPH.
ILL. ? make a similar argument. phrasing the problem in terms of an inability for SPILL particles to mix ancl generate entropy on the kernel scale.," \citet{2008MNRAS.387..427W} make a similar argument, phrasing the problem in terms of an inability for SPH particles to mix and generate entropy on the kernel scale."
 They. find that adding a heat diffusion term to model subericl turbulence gives improved. mixing in SPI., They find that adding a heat diffusion term to model subgrid turbulence gives improved mixing in SPH.
 Finally. 2. suggest that the problem lies in the SPL density estimate.," Finally, \citet{2001MNRAS.323..743R} suggest that the problem lies in the SPH density estimate."
 They. introduce a new temperature weighted density estimate that is designed to give smoother pressures at. [low boundaries. thus combating the spurious boundary. pressure blip.," They introduce a new temperature weighted density estimate that is designed to give smoother pressures at flow boundaries, thus combating the spurious boundary pressure blip."
 In this paper. we perform an error ancl stability analysis Of SPILL in its most general form to understand why mixing fails.," In this paper, we perform an error and stability analysis of SPH in its most general form to understand why mixing fails."
 In doingthis. weshowthat all of the above authors correctly identified one of twodistinet problems with mixing," In doingthis, weshowthat all of the above authors correctly identified one of twodistinct problems with mixing"
"the initial mass fractions for!?C,,'*N,, and the alpha elements, and a look-up table for the true data block.","the initial mass fractions for, and the alpha elements, and a look-up table for the true data block."
" The final file consists of 63 rectangular data arrays, where logκι is tabulated as a function of logT and logR."," The final file consists of 63 rectangular data arrays, where $\log \kappa_\mathrm{R}$ is tabulated as a function of $\log T$ and $\log R$."
 The tables are ordered such that the mass fraction Χ(12Ο) varies the most rapidly followed by the hydrogen mass fraction and X(!N)., The tables are ordered such that the mass fraction $X(\mbox{\element[][12]{C}})$ varies the most rapidly followed by the hydrogen mass fraction and $X(\mbox{\element[][14]{N}})$.
" For future compatibility, a data field for the alpha element enhancement factor was introduced into the look-up table."," For future compatibility, a data field for the alpha element enhancement factor was introduced into the look-up table."
 We compare our tables based on a scaled solar metal mixture with data from F05 based on the same abundances as in this work., We compare our tables based on a scaled solar metal mixture with data from F05 based on the same abundances as in this work.
" A direct comparison with AF94 is not possible because there are, of course, no tables based on the Lodders(2003) abundances."," A direct comparison with AF94 is not possible because there are, of course, no tables based on the \citet{2003ApJ...591.1220L} abundances."
 We refer to F05 for a comparison of AF94 and FOS., We refer to F05 for a comparison of AF94 and F05.
" In the figures, we always depict data from our database as Kcoma, while the respective comparison values are labelled κκ."," In the figures, we always depict data from our database as $\kappa_\mathrm{COMA}$ , while the respective comparison values are labelled $\kappa_\mathrm{R}$."
" Despite the numerous differences between the COMA and F05 approach, we find reasonable agreement between both sets of data."," Despite the numerous differences between the COMA and F05 approach, we find reasonable agreement between both sets of data."
 For the case shown in Fig., For the case shown in Fig.
" 4 (Z= 0.02), the difference between the COMA and ΕΟ5 values does not exceed 15 per cent for temperatures as low as logT=3.5."," \ref{fig:coma-f05-full-sc} $Z=0.02$ ), the difference between the COMA and F05 values does not exceed 15 per cent for temperatures as low as $\log T=3.5$."
 The discrepancies at lower temperatures are higher (up to 35 per cent) and can in fact be ascribed to several things., The discrepancies at lower temperatures are higher (up to 35 per cent) and can in fact be ascribed to several things.
" First and foremost, the use of different sets of molecular data in the calculations (cf."," First and foremost, the use of different sets of molecular data in the calculations (cf."
 our Table 2 and their Tables 3 and 4) produces a deviation in the resulting mean opacity coefficients., our Table \ref{table:molecules} and their Tables 3 and 4) produces a deviation in the resulting mean opacity coefficients.
" Second, we adopt a microturbulent velocity of 2.5kms!, while FOS use 20kms!."," Second, we adopt a microturbulent velocity of $2.5\,\mathrm{km\,s^{-1}}$, while F05 use $2.0\,\mathrm{km\,s^{-1}}$."
" The choices for this parameter are (within a certain range that is found for atmospheres of low mass giants) somewhat arbitrary and cause perceptible changes in Kg, especially at lower temperatures."," The choices for this parameter are (within a certain range that is found for atmospheres of low mass giants) somewhat arbitrary and cause perceptible changes in $\kappa_\mathrm{R}$, especially at lower temperatures."
" Third, F05 use a denser wavelength grid for the evaluation of xg."," Third, F05 use a denser wavelength grid for the evaluation of $\kappa_\mathrm{R}$ ."
 We discuss these issues in more detail in Sect. ??.., We discuss these issues in more detail in Sect. \ref{sec:uncertainties}.
 From a comparison of Fig., From a comparison of Fig.
 4 with Figs., \ref{fig:coma-f05-full-sc} with Figs.
" 10 (showing a comparable order of magnitude of the deviations) and 11, it is, however, clear that the numerous differences in the physical input data are responsible for the major part of the discrepancies."," \ref{fig:coma-h2o-c2-relative-logT} (showing a comparable order of magnitude of the deviations) and \ref{fig:coma-xi-f05res-relative-logT}, it is, however, clear that the numerous differences in the physical input data are responsible for the major part of the discrepancies."
 The resolution and microturbulent velocity influence kg not quite as much., The resolution and microturbulent velocity influence $\kappa_\mathrm{R}$ not quite as much.
" The large deviations in the data at the lowest temperatures are due to grain opacity that we do not take into account in our calculations, but dust is usually not formed under equilibrium conditions (as assumed by F05, see Introduction)."," The large deviations in the data at the lowest temperatures are due to grain opacity that we do not take into account in our calculations, but dust is usually not formed under equilibrium conditions (as assumed by F05, see Introduction)."
" Moreover, FOS adopted a finer grid in logT below 3.5."," Moreover, F05 adopted a finer grid in $\log T$ below 3.5."
" For the oxygen-rich case, a cubic spline interpolation (see Fig. 4,,"," For the oxygen-rich case, a cubic spline interpolation (see Fig. \ref{fig:coma-f05-full-sc},"
 dotted lines) on the coarser grid we adopted (and also used by AF94) provides reasonably accurate values., dotted lines) on the coarser grid we adopted (and also used by AF94) provides reasonably accurate values.
 The comparison with high temperature data such as that from OPAL or OP is limited to the temperature regions where the tables overlap., The comparison with high temperature data such as that from OPAL or OP is limited to the temperature regions where the tables overlap.
" Moreover, it is this region where a transition between low and high temperature opacities has to be made for applications covering a wide temperature range."," Moreover, it is this region where a transition between low and high temperature opacities has to be made for applications covering a wide temperature range."
" OP data stretch down to logT3.5, whereas the OPAL tables end at logT3.75."," OP data stretch down to $\log T=3.5$, whereas the OPAL tables end at $\log T=3.75$."
 The comparison for a standard scaled solar composition in Fig., The comparison for a standard scaled solar composition in Fig.
 5 shows a growing deviation for lower temperatures because both OPAL and OP do not include molecular absorbers (except H5)., \ref{fig:coma-op-opal-full} shows a growing deviation for lower temperatures because both OPAL and OP do not include molecular absorbers (except $_2$ ).
" This plot indicates that in the region between logT=3.8 and the high temperature end of the COMA data, a smooth transition to high temperature data is possible."," This plot indicates that in the region between $\log T=3.8$ and the high temperature end of the COMA data, a smooth transition to high temperature data is possible."
" Again, from the dimension of the differences, we conclude that these are due to different physical input data ratherthan other parameters (see Sect. ??))."," Again, from the dimension of the differences, we conclude that these are due to different physical input data ratherthan other parameters (see Sect. \ref{sec:uncertainties}) )."
 To assess which temperature region renders itself tosuch a crossover we plot the logarithmic difference between our, To assess which temperature region renders itself tosuch a crossover we plot the logarithmic difference between our
Because of very effective tidal truncation on Be disks in the relatively narrow and low eccentric svstems. the flow of the matter towards the DII will be effectively blocked during almost the whole orbital evele.,"Because of very effective tidal truncation on Be disks in the relatively narrow and low eccentric systems, the flow of the matter towards the BH will be effectively blocked during almost the whole orbital cycle."
 In such episode. the accretion could be mainly from the polar wind of the donor star.," In such episode, the accretion could be mainly from the polar wind of the donor star."
 As suggested by Waters&vanNerkwijk(1989).. the polar wind of the Be star probably resembles that in OD stars.," As suggested by \citet{wat89}, the polar wind of the Be star probably resembles that in OB stars."
 Such low-clensity high-velocity wind can hardly form accretion disks around the BIIs. and the accretion would follow the classical Bondi-IHovle-Littleton. (BILL) approximation.," Such low-density high-velocity wind can hardly form accretion disks around the BHs, and the accretion would follow the classical Bondi-Hoyle-Littleton (BHL) approximation."
" For a typical main-sequence 15AL. main-sequence star in the svstem of 2,=10d. if the mass loss rate M.—10""M.vr! and the terminal wind velocity ος=2000kms+ exist. the accreting compact star would have luminosity of about L;~LOeres+."," For a typical main-sequence $15 \, M_{\sun}$ main-sequence star in the system of $\Porb=10 \, {\rm d}$, if the mass loss rate $\Mwdot=10^{-9} \, M_{\sun}\ {\rm yr}^{-1}$ and the terminal wind velocity $v_{\infty}=2000 \, {\rm km \, s}^{-1}$ exist, the accreting compact star would have luminosity of about $\Lx\sim
10^{33} \, \rm{erg \, s^{-1}}$."
 For the De/DII binaries. the luminosity would be still less. since the polar wind just takes a small fraction of the mass loss from the donor star.," For the Be/BH binaries, the luminosity would be still less, since the polar wind just takes a small fraction of the mass loss from the donor star."
 The wind plasma accumulates in the outer rings of the decretion disc 41 one-armed oscillaàton instabilitv - probably responsible for the V/I variability seen in the Be stars - occurs. Which causes the almost total disruption of the Be disk.," The wind plasma accumulates in the outer rings of the decretion disc till one-armed oscillaiton instability - probably responsible for the V/R variability seen in the Be stars - occurs, which causes the almost total disruption of the Be disk."
 The resulted. large onto the black hole would lead (o very. luminous outbursts., The resulted large mass-infall onto the black hole would lead to very luminous outbursts.
 However. no aspect of the truncation model implies (hat the large mass transfer must occur (Okazakiοἱal.2002).," However, no aspect of the truncation model implies that the large mass transfer must occur \citep{oka02}."
.. II the collapsed disk due to the ανπάσα} instability falls back on to the more massive Be star. such narrow and low-eccentricitv transients would be almost out. of detection even lor the most sensitive instruments. so it should be careful to deal with the Be stars unrelated to the X-raw SOTIECES.," If the collapsed disk due to the dynamical instability falls back on to the more massive Be star, such narrow and low-eccentricity transients would be almost out of detection even for the most sensitive instruments, so it should be careful to deal with the Be stars unrelated to the X-ray sources."
 For systems in which effective (uneation occurs. e.g. NTE J1543—568 and 25 1553—542. the burst activities are very rare (see Okazakietal.(2002) ancl reference therein).," For systems in which effective truncation occurs, e.g. XTE $1543-568$ and 2S $1553-542$, the burst activities are very rare (see \citet{oka02} and reference therein)."
 During the long quiescent stage. De stars could be identified [rom (he Balmer (and sometimes other) line emission and the associated strong infrared excess.," During the long quiescent stage, Be stars could be identified from the Balmer (and sometimes other) line emission and the associated strong infrared excess."
 In the IIMXD catalogue of Liu.ParaclijsHeuvel (2000).. there are probably 24 De/X-ray systems where the nature of the compact star and (he orbital period are undetermined.," In the HMXB catalogue of \citet{liu00}, there are probably 24 Be/X-ray systems where the nature of the compact star and the orbital period are undetermined."
 They are signed as ΠοΝταν binaries because of their highly variable X-ray. characteristics analogous to those of the well studied Be/NS transients. or the optical identification of the donor stars.," They are signed as Be/X-ray binaries because of their highly variable X-ray characteristics analogous to those of the well studied Be/NS transients, or the optical identification of the donor stars."
 Most of them have been observed once during the burst states. and (hen disappeared [roi X-ray detection because ol verv low Iuminositv.," Most of them have been observed once during the burst states, and then disappeared from X-ray detection because of very low luminosity."
 Among these undetermined De/X-rav svstems. NTE J1739—302 and AX J0052.9—7158 (SAIC 32) can be excluded now since the donor star of the former has been identified as an O supereiant (Smithetal.2003) ancl 167.8 seconds pulsations have been found in the latter (Yokogawaetal.2001).," Among these undetermined Be/X-ray systems, XTE $1739-302$ and AX $0052.9-7158$ (SMC 32) can be excluded now since the donor star of the former has been identified as an O supergiant \citep{smi03}
 and 167.8 seconds pulsations have been found in the latter \citep{yok01}."
. To look for Be/DII binaries in the left svstenis. optical observations in the quiescent stage become important. from which we can confinn the nature of the donor star and get information of the orbital period aud (the velocity. curve of the donor.," To look for Be/BH binaries in the left systems, optical observations in the quiescent stage become important, from which we can confirm the nature of the donor star and get information of the orbital period and the velocity curve of the donor."
 The latter (wo are useful in estimating the dynamical mass of the compact star - (he common wav to determine whether the compact star is a black hole. though the," The latter two are useful in estimating the dynamical mass of the compact star - the common way to determine whether the compact star is a black hole, though the"
the beeinning of a evele and then progressively move to lower latitudes.,the beginning of a cycle and then progressively move to lower latitudes.
 This plot looks verv much like the plots presented by Durnev (1997) especiallv his Figure 7., This plot looks very much like the plots presented by Durney (1997) — especially his Figure 7.
 This is cerlainly very reassuring. since (he numerical techniques emploved by us aud by Durney (1997) are completely different.," This is certainly very reassuring, since the numerical techniques employed by us and by Durney (1997) are completely different."
 Apart from the production of the double rings. our code allows lor the toroidal flux to be brought to the surface bv meridional circulation and then to be acted upon by a-coefficient (an effect not present in Durneys calculations).," Apart from the production of the double rings, our code allows for the toroidal flux to be brought to the surface by meridional circulation and then to be acted upon by $\alpha$ -coefficient (an effect not present in Durney's calculations)."
" However. when A""is made as large as 1000. this effect is insignificant."," However, when $K'$ is made as large as 1000, this effect is insignificant."
 In fact. we made some runs with a=0 and found that the results for zero or non-zero a are virtually indistinguishable when A’=1000.," In fact, we made some runs with $\alpha = 0$ and found that the results for zero or non-zero $\alpha$ are virtually indistinguishable when $K' = 1000$."
 For example. the plots of eruption latitude against time ancl the butterfly diagrams look identical in both the cases.," For example, the plots of eruption latitude against time and the butterfly diagrams look identical in both the cases."
" We have already mentioned that a positive A"" is like a positive a-elleet concentrated near the surface.", We have already mentioned that a positive $K'$ is like a positive $\alpha$ -effect concentrated near the surface.
 Choudhunr. Sehüsssler. Dikpati (1995) showed that a positive a concentrated near the surface leads to a poleward propagation of the dynamo wave when the meridional flow is switched off.," Choudhuri, Schüsssler, Dikpati (1995) showed that a positive $\alpha$ concentrated near the surface leads to a poleward propagation of the dynamo wave when the meridional flow is switched off."
" We find exactly the same result in the double ring approach with positive A"" if we switch off the meridional flow.", We find exactly the same result in the double ring approach with positive $K'$ if we switch off the meridional flow.
 Figure 5 shows a time-latitude plot of the toroidal field al the bottom of the convection zone with meridional flow for the case A!=1000. fy=0.5. whereas Figure 6 is a similar plot without meridional flow. keeping all the other parameters (he same.," Figure 5 shows a time-latitude plot of the toroidal field at the bottom of the convection zone with meridional flow for the case $K'=1000$, $f_d = 0.5$, whereas Figure 6 is a similar plot without meridional flow keeping all the other parameters the same."
 We see clear indication of poleward migration in Figure 6., We see clear indication of poleward migration in Figure 6.
 For contrast. we now present results obtained by the method described in 2.2.," For contrast, we now present results obtained by the method described in 2.2."
 As we have seen. the control parameter in (his problem is /(«1). which measures the strength of magnetic buovaneyv.," As we have seen, the control parameter in this problem is $f (<1)$, which measures the strength of magnetic buoyancy."
 Figure 7 shows how the dvnamo period changes on increasing f., Figure 7 shows how the dynamo period changes on increasing $f$.
 As in Figure 2. we begin with a period of 66 vrs in the limit /=0 corresponding to the CSD model.," As in Figure 2, we begin with a period of 66 yrs in the limit $f= 0$ corresponding to the CSD model."
 On making the effect of buovancy stronger (by increasing |). the flix transport," On making the effect of buoyancy stronger (by increasing $f$ ), the flux transport"
those of Seyferts and. QSOs.,those of Seyferts and QSOs.
" Lowe consider the ""wash out” fact for LLAGNs. the correlation should be tighter."," If we consider the “wash out” fact for LLAGNs, the correlation should be tighter."
 One may notice that NGC3227 deviates from the main trend in Figure L.., One may notice that NGC3227 deviates from the main trend in Figure \ref{fig-1}.
 This object is unusual by virtue of its very [at soft. X-ray spectrum which may. be caused by a clusty warm absorber (Georecetal.1998:Ixomassa&Fink 1991).," This object is unusual by virtue of its very flat soft X-ray spectrum which may be caused by a dusty warm absorber \cite{george,kf}."
. Probably its variability is enhanced by some changes in the absorber., Probably its variability is enhanced by some changes in the absorber.
 In addition. Schinnerer. Eckart Tacconi (2000) reported that the enclosed mass in the inner 25 pe of NGC3221 is about 210AZ. based on a detection of molecular gas at a clistance from nucleus of only ~15 pc.," In addition, Schinnerer, Eckart Tacconi \shortcite{set} reported that the enclosed mass in the inner 25 pc of NGC3227 is about $2\times10^7M_{
\odot}$ based on a detection of molecular gas at a distance from nucleus of only $\sim15$ pc."
 Although this mass approximately agrees with the Virial mass of 3.94.0«10AL; measured by using reverberation mapping cata with larger uncertainty. it may suggest that the mass of the central black hole is lower than the measured Virial mass.," Although this mass approximately agrees with the Virial mass of $3.9-4.9\times10^7M_{\sun}$ measured by using reverberation mapping data with larger uncertainty, it may suggest that the mass of the central black hole is lower than the measured Virial mass."
 Wothe central black hole mass of NGC3227 is really lower than the estimated. Virial mass (sav. by a factor of 2). NGC€C3227 would join the main trend.," If the central black hole mass of NGC3227 is really lower than the estimated Virial mass (say, by a factor of 2), NGC3227 would join the main trend."
 Furthermore. we ga10uld caution that some systematic error may exist because je adopted masses are measured. by cilferent techniques for LLAGNs and Sevfert 1 ealaxies/OQSOs.," Furthermore, we should caution that some systematic error may exist because the adopted masses are measured by different techniques for LLAGNs and Seyfert 1 galaxies/QSOs."
 This svstematic error should not be very large since the measured masses by 1ese two methods follow the same relation with the galaxies rulge potential (Gebhardtctal.2000b:Nelson2000).. and 1 trend still remains even i we exclude those points for LLAGNs in Figure 1..," This systematic error should not be very large since the measured masses by these two methods follow the same relation with the galaxies bulge potential \cite{g2000b,nelson}, and the trend still remains even if we exclude those points for LLAGNs in Figure \ref{fig-1}."
" 1n Figure L.. the trend seems to be the case that there is. a linear. relationship.. στιµ..2xMdb,"," In Figure \ref{fig-1}, the trend seems to be the case that there is a linear relationship, $\sigma^2_{\rm rms}\propto M^{-1}_{\rm bh}$."
" As we can sec. it can be represented by a line logez,Lus435log(Myun/M.) in both Figure 1 A and. B. All the objects are localized. in the region between the lines logaz.=3.75log(AlinM.) and loge,2—5.55log(Ady/M.) except NGC3227."," As we can see, it can be represented by a line $\log\sigma^2_{\rm rms}=4.75-\log(
M_{\rm bh}/M_{\odot})$ in both Figure \ref{fig-1} A and B. All the objects are localized in the region between the lines $\log\sigma^2_{\rm 
rms}=3.75-\log(M_{\rm bh}/M_{\odot})$ and $\log\sigma^2_{\rm rms}=5.75-\log(M_{\rm bh}/M_{\odot})$ except NGC3227."
" More quantitatively, a Spearman rank test gives the correlation coelficients of -0.70 and -0.65 for the points in Figure 1 A and D. respectively: and rejects the possibility that στης and Ady, are uncorrelated at 2299.94 confidence."," More quantitatively, a Spearman rank test gives the correlation coefficients of -0.70 and -0.65 for the points in Figure \ref{fig-1} A and B, respectively; and rejects the possibility that $\sigma^2_{\rm rms}$ and $M_{\rm bh}$ are uncorrelated at $>$ confidence."
 Vhe robust nature of a rank test means that the significance of this correlation does not depend on the outlying point λος2291., The robust nature of a rank test means that the significance of this correlation does not depend on the outlying point NGC3227.
 Η we include NCGC3227 in the test. the corresponding correlation coefficient are -0.68 and. -0.64 with almost the same confidence for the points in Figure 1. X and 0. respectively.," If we include NGC3227 in the test, the corresponding correlation coefficient are -0.68 and -0.64 with almost the same confidence for the points in Figure \ref{fig-1} A and B, respectively."
" In the present paper. we found that the ""excess variance"" is significantly anti-correlated. with the central black hole mass for a combined sample of Sevfert 1 galaxies. QSOs anc LLAGNs."," In the present paper, we found that the “excess variance” is significantly anti-correlated with the central black hole mass for a combined sample of Seyfert 1 galaxies, QSOs and LLAGNs."
 The most plausible explanation is that the “excess variance is caused by some global coherent changes in the X-ray emitting region. and this region scales with the size of black hole.," The most plausible explanation is that the “excess variance” is caused by some global coherent changes in the X-ray emitting region, and this region scales with the size of black hole."
" Phe light curves are known to be characterize by à steep power-Iaw PDS (PCP)xf"".wheree —L5.2) in some ACGNs. such as NG€4051. NGC3516. NGC€CB5AS ane ALCC-6-30-15 (Lawrence&Papaclakis1993:NowakChi-ang2000)."," The light curves are known to be characterized by a steep power-law PDS $P(f)\propto f^{-\alpha}$, where $\alpha
\sim 1.5-2$ ) in some AGNs, such as NGC4051, NGC3516, NGC5548 and MCG-6-30-15 \cite{lp,nch}."
". Assuming self similar scaling and hence a direc connection between time scales and the size of sources. the observed. ""excess variance” can be related to the size of the central black hole as στ.=IDPODdfxfi©Al. ""s where fi; and az1."," Assuming self similar scaling and hence a direct connection between time scales and the size of sources, the observed “excess variance” can be related to the size of the central black hole as $\sigma^2_{\rm rms} = \int_{f_1}^{f_2}P(f)df \propto f^{1-\alpha}_{1}
\propto R^{1-\alpha} \propto M^{1-\alpha}_{\rm bh}$ , where $f_1\ll f_2$ and $\alpha\neq 1$."
" One can readily get the observed. correlation ez,xAd, lcillustrated in. Figurem 1 by assuming à~2."," One can readily get the observed correlation $
\sigma^2_{\rm rms} \propto M^{-1}_{\rm bh}$ illustrated in Figure \ref{fig-1}
 by assuming $\alpha \sim 2$."
" This fundamental relationship can self-consistently explain the previous finding of the relationship between oz, and Luminosity. which has been proposed.by many authors (Nandraetal.LOOT:Turner.1999:Leighlv1999:Xlmainietal."," This fundamental relationship can self-consistently explain the previous finding of the relationship between $\sigma^2_{\rm rms}$ and luminosity, which has been proposedby many authors \cite{nandra,turner,leighly,alm}."
" 2000).. ltecentIs. some investigations have been performed. on the relationship between of, and Luminosity for a sample of LLAGNs (Ptakctal.1998). anc a deep flux. limited sample of QSOs selected (rom deep ROSAT survey CAlmainietal. 2000). which greatly extend the luminosity range and redshift range."," Recently, some investigations have been performed on the relationship between $\sigma^2_{\rm rms}$ and luminosity for a sample of LLAGNs \cite{ptak}
 and a deep flux limited sample of QSOs selected from deep ROSAT survey \cite{alm}, which greatly extend the luminosity range and redshift range."
 Ptak et al., Ptak et al.
 (1998). found. that LLAGNs tend to show little or no significant short termi variability. and there is a break from the trend of increased variability in Sevfert 1 galaxies with decreased Luminosity.," \shortcite{ptak} found that LLAGNs tend to show little or no significant short term variability, and there is a break from the trend of increased variability in Seyfert 1 galaxies with decreased luminosity."
 They proposed that this is cue to the lower aceretion rates in LLACGNs., They proposed that this is due to the lower accretion rates in LLAGNs.
 Vhey arguedὃν that this results in a largero characteristic size of the X-ray emission region in LLAGNs than in Sevfert 1 ealaxies because the lower accretion rate is probably causing the accretion Llow to be advection-dominated., They argued that this results in a larger characteristic size of the X-ray emission region in LLAGNs than in Seyfert 1 galaxies because the lower accretion rate is probably causing the accretion flow to be advection-dominated.
 However. most of the X-ray emission should originate in an inner volume probably with a radius less than 10/22: (Ptakοἱal. 1998).. which is similar to the typical X-ray emission region size ( LORS) of a normal Sevfert. 1 galaxies.," However, most of the X-ray emission should originate in an inner volume probably with a radius less than $R_{\rm Sch}$ \cite{ptak}, which is similar to the typical X-ray emission region size $\sim 10R_{\rm Sch}$ ) of a normal Seyfert 1 galaxies."
 Lf the X-ray variability is caused by some global coherent oscillation for both LLAGNs and normal Sevfert 1 galaxies. then similar variability should be observed in both svystenis with similar black holes.," If the X-ray variability is caused by some global coherent oscillation for both LLAGNs and normal Seyfert 1 galaxies, then similar variability should be observed in both systems with similar black holes."
 Indeed. those LLACNs and AGNs follow the same trend in Figure 1.. though LLACGNs have," Indeed, those LLAGNs and AGNs follow the same trend in Figure \ref{fig-1}, , though LLAGNs have"
Recently. there has been much interest generated by the observation of ubiquitous propagating Alfvénnic waves in the solar corona detected by Tomcezyketal.(2007) using the innovative Coronal Multi-Channel Polarimeter (CoMDP) instrument.,"Recently, there has been much interest generated by the observation of ubiquitous propagating Alfvénnic waves in the solar corona detected by \citet{tomczetal07} using the innovative Coronal Multi-Channel Polarimeter (CoMP) instrument."
 The Alfvénnic properties of (hese waves are undeniable since thev have a phase speed of about 1 Mam Ll (he velocity components are perpendicular to the direction of magnetic field lines and," The Alfvénnic properties of these waves are undeniable since they have a phase speed of about 1 Mm $^{-1}$, the velocity components are perpendicular to the direction of magnetic field lines and"
wind density and velocity and the ionization front parameters.,wind density and velocity and the ionization front parameters.
 Their numerical calculations also assume a hemispherical proplyd head and a cylindrical tail., Their numerical calculations also assume a hemispherical proplyd head and a cylindrical tail.
" Studying the interaction between these two winds, they have successfully reproduced the arc emission for the proplyds near 6! Ori C. Richling&Yorke(2000) performed 2D, axisymmetric hydrodynamical simulations of photoevaporating disks including both ionizing (hv>13.6 eV) and dissociating (6 eV < hy< 13.6 eV) radiation."," Studying the interaction between these two winds, they have successfully reproduced the arc emission for the proplyds near $\theta^1$ Ori C. \cite{rich..00} performed 2D, axisymmetric hydrodynamical simulations of photoevaporating disks including both ionizing $\nu \geq 13.6$ eV) and dissociating (6 eV $<$ $\nu <$ 13.6 eV) radiation."
" In their models, disk structures are formed through collapse simulations of 1 and 2 Mo molecular clumps (Yorke&Bodenheimer,1999),, which are then exposed to the radiation field by switching on the external UV radiation field in the calculation."," In their models, disk structures are formed through collapse simulations of 1 and 2 $M_{\odot}$ molecular clumps \citep{yorke..99}, which are then exposed to the radiation field by switching on the external UV radiation field in the calculation."
" They studied the effects of distance from the UV photon source on emission line maps and the effect of the presence of a spherical wind from the proplyd star, which promotes the appearance of collimated, bipolar microjets."," They studied the effects of distance from the UV photon source on emission line maps and the effect of the presence of a spherical wind from the proplyd star, which promotes the appearance of collimated, bipolar microjets."
" Instead of calculating the dissociation of the H5 molecule, they followed the ionization of C. They took into account photoelectric heating and cooling by fine-structure lines such as [CII] 158 um, [OT] 63 um and [OT] 145 um. An important point in their work is the inclusion of the diffuse radiation field,which is responsible for the tails of the proplyds (see Figure 1))."," Instead of calculating the dissociation of the $_2$ molecule, they followed the ionization of C. They took into account photoelectric heating and cooling by fine-structure lines such as ] 158 $\mu$ m, ] 63 $\mu$ m and ] 145 $\mu$ m. An important point in their work is the inclusion of the diffuse radiation field,which is responsible for the tails of the proplyds (see Figure \ref{f1}) )."
 In this work we present the first fully three-dimensional numerical simulations of disks exposed to FUV and EUV radiation fields., In this work we present the first fully three-dimensional numerical simulations of disks exposed to FUV and EUV radiation fields.
" As discussed in Johnstoneetal.(1998),, the diffuse ionizing and dissociating radiation field is important for determining the shape of the ionization front behind the (directly) illuminated disk surface."," As discussed in \cite{john..98}, the diffuse ionizing and dissociating radiation field is important for determining the shape of the ionization front behind the (directly) illuminated disk surface."
" Our present simulations do not include the diffuse field, resulting in the tails that do not have the correct morphology (see Cerqueira et al."," Our present simulations do not include the diffuse field, resulting in the tails that do not have the correct morphology (see Cerqueira et al."
 2006b)., 2006b).
" We concentrate on obtaining a description of the head of the proplyd flow, and study the effect of different orientations of the disks with respect to the impinging UV photon field (and the stellar wind)."," We concentrate on obtaining a description of the head of the proplyd flow, and study the effect of different orientations of the disks with respect to the impinging UV photon field (and the stellar wind)."
 The present paper is organized as follows., The present paper is organized as follows.
" In §2,, we describe the code and the simulations."," In \ref{simulations}, we describe the code and the simulations."
" In §3,, we present our results."," In \ref{results}, we present our results."
" Finally, in $4,, we draw our main conclusions."," Finally, in \ref{conclusions}, we draw our main conclusions."
" The 3D numerical simulations have been carried out with the YGUAZÜ-A adaptive grid code (Ragaetal,2000,2002) using a 5-level binary adaptive grid."," The 3D numerical simulations have been carried out with the YGUAZÚ–A adaptive grid code \citep{raga..00,raga..02} using a 5-level binary adaptive grid."
 The YGUAZU- code integrates the gasdynamic equations employing the flux vector splitting scheme of vanLeer(1982) together with a system of rate equations for atomic/ionic species.," The YGUAZ\'U--A code integrates the gasdynamic equations employing the flux vector splitting scheme of \cite{vanleer82}
 together with a system of rate equations for atomic/ionic species."
" In our simulations, we consider 4 species:HI, HII, and CII."," In our simulations, we consider 4 species:, , and ."
" This code has been extensively employed for simulating different astrophysical flows such as jets (Masciadrietal.,2002;Cerqueiraetal., 2006a),, interacting winds (Gonzálezetal., 2004),, photoevaporating clumps (Cerqueiraetal.,2006b) and supernova remnants (Velázquezetal.,20012,2004)."," This code has been extensively employed for simulating different astrophysical flows such as jets \citep{masciadri..02, dri..06a}, interacting winds \citep{ricardo..04}, photoevaporating clumps \citep{dri..06b} and supernova remnants \citep{pablo..01a,pablo..04}."
". It was also tested with laser generated plasma laboratory experiments (Sobraletal.,2000;Raga2001;Velázquez2001b)."," It was also tested with laser generated plasma laboratory experiments \citep{sobral..00,raga..01,pablo..01b}."
". In this work, instead of solving an energy equation, we prescribe a temperature law, given by where T,=10000 K, is the characteristic temperature of an region, T?=1000 K, the typical PDR temperature, K, the temperature of the molecular gas, xy is the hydrogen ionization fraction and xcy is the carbon ionization fraction (xcg=1 when all the CI is CID)."," In this work, instead of solving an energy equation, we prescribe a temperature law, given by where $T_1 = 10\,000$ K, is the characteristic temperature of an region, $T_2 = 1\,000$ K, the typical PDR temperature, $T_3 = 10$ K, the temperature of the molecular gas, $x_\mathrm{H II}$ is the hydrogen ionization fraction and $x_\mathrm{C
II}$ is the carbon ionization fraction $x_\mathrm{C II}=1$ when all the $\mathrm{C I}$ is $\mathrm{C II}$ )."
" This prescription is justified if the thermal equilibrium time scale is much smaller than the dynamical time scale (Lefloch&Lazareff,1994),, which is the case here, for both the ionized and the molecular gas."," This prescription is justified if the thermal equilibrium time scale is much smaller than the dynamical time scale \citep{lefloch..94}, which is the case here, for both the ionized and the molecular gas."
" It is clear from equation (1)), that we have possible temperatures ranging from 10 K to 10 K. In order to study the dependence of the PDR geometry with temperature, we also compute models in which we set 7;=3000 K. Following Richling&Yorke(2000) we do not treat thedissociation of Ho, but consider that the dissociation front and the carbonionization front coincide."," It is clear from equation \ref{temp}) ), that we have possible temperatures ranging from 10 K to $10^4$ K. In order to study the dependence of the PDR geometry with temperature, we also compute models in which we set $T_2 = 3\,000$ K. Following \cite{rich..00} we do not treat thedissociation of $_2$ but consider that the dissociation front and the carbonionization front coincide."
 We then solve rate equations for hydrogen and carbon takinginto, We then solve rate equations for hydrogen and carbon takinginto
"from the kinetic energv in a buller region nine cells (2935.tkpe) thick outside of ri; where the stun is over the jV; cells in the buffer region rj,<ry«rv,+9f.",from the kinetic energy in a buffer region nine cells $h^{-1}$ kpc) thick outside of $r_{vir}$: where the sum is over the $N_{b}$ cells in the buffer region $r_{vir}<r_k<r_{vir}+9l$.
 Now suppose the gas is allowed to rearrange itself within the DM potential such that ibis in hydrostatic equilibrium and has a polvtropic equation of state with index P—1.2., Now suppose the gas is allowed to rearrange itself within the DM potential such that it is in hydrostatic equilibrium and has a polytropic equation of state with index $\Gamma=1.2$.
 There is much support for such a model— see (he discussion and Fie., There is much support for such a model— see the discussion and Fig.
 1 in Drvan).. and also Ascasibaretal.(2006).," 1 in \citet[][comparing the polytropic model with a full, high resolution 
cosmological simulation by G. Bryan]{OstrikerBB05}, and also \citet{AscasibarSYMG06}."
. We will treat the gas as a tracer such that the potential. set bv the DM. does not change.," We will treat the gas as a tracer such that the potential, set by the DM, does not change."
" Defining as in Ostrikerοἱal.(2005).. the resulting gas pressure 7 and density p are given by llere 0,4 is a nonthermal component of pressure. assumed to be proportional to thermal pressure such that the total 2,=(12-9,,)P."," Defining as in \citet{OstrikerBB05}, the resulting gas pressure $P$ and density $\rho$ are given by Here $\delta_{rel}$ is a nonthermal component of pressure, assumed to be proportional to thermal pressure such that the total $P_{tot}=(1+\delta_{rel})P$."
" To specify the final gas distribution given (hese assumptions. two quanliGes still need to be determined. namely the pressure 71, and densitv py at the potential minimum."," To specify the final gas distribution given these assumptions, two quantities still need to be determined, namely the pressure $P_0$ and density $\rho_0$ at the potential minimum."
 This can be done with (wo equations of constraint. derived bv requiring conservation of energv and by matching the external surface pressure. as follows.," This can be done with two equations of constraint, derived by requiring conservation of energy and by matching the external surface pressure, as follows."
"For a given choice of [η and po. the final radius ry of the gas initially inside μις CAL be found by summing outwards [rom the cluster center until the initial mass M, is enclosed: This implies that eas mav expand or contract. changing (he gas [fraction inside rj.","For a given choice of $P_0$ and $\rho_0$, the final radius $r_f$ of the gas initially inside $r_{vir}$ can be found by summing outwards from the cluster center until the initial mass $M_g$ is enclosed: This implies that gas may expand or contract, changing the gas fraction inside $r_{vir}$."
 Assuming the external surface pressure changes little with radius. there will be mechanical work done. causing a change in energy proportional to the change in volume. M. The equation lor conservation of energy is (hus," Assuming the external surface pressure changes little with radius, there will be mechanical work done, causing a change in energy proportional to the change in volume, $\Delta E_p=(4\pi/3)(r_{vir}^3-r_f^3)P_s$ The equation for conservation of energy is thus"
determined by the current conditions in the star-disk interaction and independent of any initial conditions.,determined by the current conditions in the star-disk interaction and independent of any initial conditions.
" MP05 described the method of computing the stellar spin rate in this hypothetical equilibrium state for their torque formulation, which uses equations (23)-(27) of that work."," MP05 described the method of computing the stellar spin rate in this hypothetical equilibrium state for their torque formulation, which uses equations (23)–(27) of that work."
" In presenting our results below, we compare the actual spin rates to the equilibrium values to gain insight into these systems."," In presenting our results below, we compare the actual spin rates to the equilibrium values to gain insight into these systems."
" The coupled equations (1)), (2)), and (3)) describe the evolution of the system."," The coupled equations \ref{eq_mdot}) ), \ref{eq_rstar}) ), and \ref{eq_angmom}) ) describe the evolution of the system."
" We wrote a computational code that solves these simultaneously, using the fourth-order Runge-Kutta scheme of Pressetal.(1994),, starting from ty=3x104 yr and ending at 3 Myr."," We wrote a computational code that solves these simultaneously, using the fourth-order Runge-Kutta scheme of \citet{pressea94}, starting from $t_0=3\times10^4$ yr and ending at 3 Myr."
" For computational efficiency and numerical stability, we use a dynamic timestep."," For computational efficiency and numerical stability, we use a dynamic timestep."
" At each step, we compute the next timestep by requiring that none of the three main variables, Ὡς, R,, M,, change by more than per step."," At each step, we compute the next timestep by requiring that none of the three main variables, $\Omega_{*}$, $R_{*}$, $M_{*}$, change by more than per step."
 This gives results converged to three significant figures and typically requires a few hundred timesteps for the entire evolution., This gives results converged to three significant figures and typically requires a few hundred timesteps for the entire evolution.
" In order to compute the torque at each timestep, the code first solves equation to determine the magnetic connection state of the system."," In order to compute the torque at each timestep, the code first solves equation \ref{eq_fcrit}) ) to determine the magnetic connection state of the system."
"(8)) Then, depending on the state, the code solves either equation (10)) or (11)) to determine the disk truncation radius."," Then, depending on the state, the code solves either equation \ref{eq_rt1}) ) or \ref{eq_rt2}) ) to determine the disk truncation radius."
" We enforce a minimum value of R;=R,.", We enforce a minimum value of $R_t=R_*$.
" Finally, the code calculates the accretion torque using equation (12)) and the magnetic torque using either equation (13)) or "," Finally, the code calculates the accretion torque using equation \ref{eq_ta}) ) and the magnetic torque using either equation \ref{eq_tmag2}) ) or \ref{eq_tmag1}) )."
The torque is assumed to be constant during each timestep., The torque is assumed to be constant during each timestep.
"(14)). We also enforce a maximum on the spin rate, corresponding to f=1 (see §2.3))."," We also enforce a maximum on the spin rate, corresponding to $f=1$ (see \ref{sec_spin}) )."
 This section contains results from several models., This section contains results from several models.
" Table 1 lists the parameters for all cases, in order of their presentation and grouped by the figures in which the results appear."," Table \ref{tab_parms} lists the parameters for all cases, in order of their presentation and grouped by the figures in which the results appear."
" All models have the same initial stellar radius and effective temperature (Τε=4280 K; see (8E)reffig, starand§ 2.2)).", All models have the same initial stellar radius $8R_\odot$ ) and effective temperature $T_e=4280$ K; see \\ref{fig_rstar} and \ref{sec_rstar}) ).
" Also, all models end with a mass of Mo, so that the initial mass depends on the accretion rate (see 2.1))."," Also, all models end with a mass of $M_\odot$, so that the initial mass depends on the accretion rate (see \ref{sec_mdot}) )."
" For each case in table 1,, we ran four models, one for each combination of two different initial spin rates (see 82.3)) and two different mass accretion rates (see 2.1)."," For each case in table \ref{tab_parms}, we ran four models, one for each combination of two different initial spin rates (see \ref{sec_spin}) ) and two different mass accretion rates (see \ref{sec_mdot}) )."
 These parameters are intended to represent a range that is appropriate for accreting T Tauri stars., These parameters are intended to represent a range that is appropriate for accreting T Tauri stars.
" Section 3.1 includes two simplified cases with no magnetic fields: one in which T;=0, so that there is no star-disk interaction; and one in which B,=0 so that there are no magnetic effects, just disk accretion."," Section \ref{sec_t0} includes two simplified cases with no magnetic fields: one in which $T_*=0$, so that there is no star-disk interaction; and one in which $B_*=0$ so that there are no magnetic effects, just disk accretion."
" Section 3.2 contains the main results, models that include magnetic fields with realistic field line opening = 1) and different values of 8, for two different field strengths."," Section \ref{sec_gam1} contains the main results, models that include magnetic fields with realistic field line opening $\gamma_c=1$ ) and different values of $\beta$, for two different field strengths."
"(ye For comparison, and as a verification of our model and computations, the appendix contains results for cases with the classical assumption of a fully closed magnetic field (9.= oo) and 8—1."," For comparison, and as a verification of our model and computations, the appendix contains results for cases with the classical assumption of a fully closed magnetic field $\gamma_c=\infty$ ) and $\beta=1$."
" 'To begin, it is useful to examine few simplified cases."," To begin, it is useful to examine a few simplified cases."
" The main goal is to understand aindividually how the stellar contraction and accretion alone affects the spin evolution, before adding the effects of magnetic fields."," The main goal is to understand individually how the stellar contraction and accretion alone affects the spin evolution, before adding the effects of magnetic fields."
" We will consider two cases here: one in which the net torque on the star is forced to be zero; and one in which there are no magnetic fields, so that the only torque on the star is due to the accretion of material from the disk."," We will consider two cases here: one in which the net torque on the star is forced to be zero; and one in which there are no magnetic fields, so that the only torque on the star is due to the accretion of material from the disk."
 Figure 4 shows the evolution of stellar spin for the case of zero torque (Τε=0 in [3]])., Figure \ref{fig_t0} shows the evolution of stellar spin for the case of zero torque $T_*=0$ in ]).
 The figure shows both, The figure shows both
Dased on the IRACI colour (lower panel). we find four sources. 771. 660. and SOri665 / with >30 colour excesses. which we consider to be primary disk In all [our cases the excess increases significantly in IRAC channel 4 compared with channel 3. indicating rising flux levels towards longer wavelengths. a clear signature of disk emission.,"Based on the IRAC4 colour (lower panel), we find four sources – 71, J053949.5-023130, 60, and 65 – with $>3\sigma$ colour excesses, which we consider to be primary disk In all four cases the excess increases significantly in IRAC channel 4 compared with channel 3, indicating rising flux levels towards longer wavelengths, a clear signature of disk emission."
 With the exception of SO011665. these objects have been published previously as disk-bearing verv low mass sources (Caballeroetal. 2007)..," With the exception of 65, these objects have been published previously as disk-bearing very low mass sources \citep{2007A&A...470..903C, 2007A&A...472L...9Z}."
 This gives a disk fraction of 4 out of 14 or 29-054..., This gives a disk fraction of 4 out of 14 or $29\pm ^{16}_{13}$.
 Here we do not count the three objects with upper limits well-above the photospheric level. for which we cannot decide if they have disk excess or not.," Here we do not count the three objects with upper limits well-above the photospheric level, for which we cannot decide if they have disk excess or not."
 Disk frequencies derived Irom IRACS and IRAC are thus consistent; since the value determined from [RACH is likely to be more robust. we pul more emphasis on this result.," Disk frequencies derived from IRAC3 and IRAC4 are thus consistent; since the value determined from IRAC4 is likely to be more robust, we put more emphasis on this result."
 We note that the disk fraction in our sample might still be somewhat higher than given here. due to the combined effects of photometric uncertainties and contaminating field objects (seethedicussioninCaballeroetal.2007)..," We note that the disk fraction in our sample might still be somewhat higher than given here, due to the combined effects of photometric uncertainties and contaminating field objects \citep[see the dicussion in][]{2007A&A...470..903C}."
 We now compare our disk detection rate will previous results for more massive objects in c OOri. as given by Hernándezetal.(2007). based on IRAC! data: for ILXeDe stars. [or intermediate-mass T. Tauri stars. for T Tauri stars. for brown dwarfs.," We now compare our disk detection rate with previous results for more massive objects in $\sigma$ Ori, as given by \citet{2007ApJ...662.1067H} based on IRAC data: for HAeBe stars, for intermediate-mass T Tauri stars, for T Tauri stars, for brown dwarfs."
 The value for brown chwarls is in agreement with the disk fraction of lderived by. Javawardhana [rom ground-based. L’-band imaging., The value for brown dwarfs is in agreement with the disk fraction of derived by \citet{2003AJ....126.1515J} from ground-based L'-band imaging.
 A higher brown dwarf disk fraction of has been published by Caballeroetal.(2007).., A higher brown dwarf disk fraction of has been published by \citet{2007A&A...470..903C}.
 For the IMPO range (objects with ALS201 μμ). we now derive a disk fraction of29%... which is compatible with the values for T Tauri stars and brown dwarls within (he lo uncertainties.," For the IMPO range (objects with $M\lesssim 20\,M_{\mathrm{Jup}}$ ), we now derive a disk fraction of, which is compatible with the values for T Tauri stars and brown dwarfs within the $\sigma$ uncertainties."
 We do not see a trend to hieher disk [requencies in the IPMO range. as claimecl by ZapateroOsorioetal.(2007).. instead the evidence points to comparable disk fractions for planetary mass objects. brown cdwarfs. and T Tawi stus. Le. over more (han (wo orders of magnitude in object mass (0.008...2M. ).," We do not see a trend to higher disk frequencies in the IPMO range, as claimed by \citet{2007A&A...472L...9Z}, instead the evidence points to comparable disk fractions for planetary mass objects, brown dwarfs, and T Tauri stars, i.e. over more than two orders of magnitude in object mass $0.008\ldots 2\,M_{\odot}$ )."
 We note that two of the objects with disk excess. 666 and 771. stand out [rom the rest of (he sample. as they show excessively strong Io. emission with equivalent widths ol ~100 and ~TOOA.. respectively (Darradov.Navaseuésοἱal.2001.2002)..," We note that two of the objects with disk excess, 66 and 71, stand out from the rest of the sample, as they show excessively strong $\alpha$ emission with equivalent widths of $\sim 100$ and $\sim 700$, respectively \citep{2001A&A...377L...9B,2002A&A...393L..85B}."
 This indicates that the presence of a dusty disks is likely accompanied by ongoing gas accretion. causing intense Ila emission. as observed in T Tauri stars and brown clwarts.," This indicates that the presence of a dusty disks is likely accompanied by ongoing gas accretion, causing intense $\alpha$ emission, as observed in T Tauri stars and brown dwarfs."
where L(r.8) is (he amplitude ofthe A effect and A is the inclination of the flux vector wilh respect to the rotational axis.,"where $L(r,\theta)$ is the amplitude ofthe $\Lambda$ effect and $\lambda$ is the inclination of the flux vector with respect to the rotational axis."
 We use for (he amplitude of the A effect the expressions where d=0.025..., We use for the amplitude of the $\Lambda$ effect the expressions where $d=0.025R_\odot$.
 À aud Ag are lree-parameters., $\lambda$ and $\Lambda_0$ are free-parameters.
" The value of / needs to be equal to or larger than 2 (o ensure regularitv near the pole. so we set /=2. The X effect does nol depend on ce,. ej or O4. meaning il is a stationary elfect."," The value of $l$ needs to be equal to or larger than 2 to ensure regularity near the pole, so we set $l=2$ The $\Lambda$ effect does not depend on $v_r$, $v_\theta$ or $\Omega_1$, meaning it is a stationary effect."
 We emphasize that the A ellect depends on stellar angular velocity. ο since (he X effect is generated by turbulence and Coriolis force.," We emphasize that the $\Lambda$ effect depends on stellar angular velocity $\Omega_0$, since the $\Lambda$ effect is generated by turbulence and Coriolis force."
 The more rapidly the star rotates. the more angular momentum the A effect can transport.," The more rapidly the star rotates, the more angular momentum the $\Lambda$ effect can transport."
 The dependence of Ay anc A on stellar angular velocity is discussed in 8??.., The dependence of $\Lambda_0$ and $\lambda$ on stellar angular velocity is discussed in \ref{variation}.
 Using the moclifiecl Las-Wendroll seheme with TVD artificial viscosity (Davis1984).. we solve Equations (1))-(5)) numerically for the northern hemisphere of the meridional plane in 0.652.«r0.934. and 0«9<7/2.," Using the modified Lax-Wendroff scheme with TVD artificial viscosity \citep{davis1984tvd}, we solve Equations \ref{continuity}) \ref{se1}) ) numerically for the northern hemisphere of the meridional plane in $0.65R_\odot < r <0.93R_\odot$ and $0 < \theta < \pi/2$."
 We use a uniform resolution of 200 points in the radial direction and 400points in the Iatitudinal direction in all of our simulations., We use a uniform resolution of $200$ points in the radial direction and $400$points in the latitudinal direction in all of our simulations.
 Each simulation run is conducted until it reaches a stationary state., Each simulation run is conducted until it reaches a stationary state.
" All the variables py. v. ry. O4 and s, are equal to zero in the initial condition."," All the variables $\rho_1$, $v_r$ , $v_\theta$ , $\Omega_1$ and $s_1$ are equal to zero in the initial condition."
At the top boundary (r=0.9322. ) we adopt stress-Iree boundary conditions for ος. eg aud O4 and set thederivative of δι to,"At the top boundary $r=0.93R_\odot$ ) we adopt stress-free boundary conditions for $v_r$ , $v_\theta$ and $\Omega_1$ and set thederivative of $s_1$ to"
"and 4 ryd, respectively, will propagate at the same (photon flux-limited) velocity for a critical spectral index, corresponding to our adopted He/H abundance, y= 0.0823.","and 4 ryd, respectively, will propagate at the same (photon flux-limited) velocity for a critical spectral index, corresponding to our adopted He/H abundance, $y = 0.0823$ ."
" The agreement with the HS'T--observed mean spectral index of AGN at 1-2 ryd, (as)=1.76+0.12 22002),(Telfer suggests that aand iionization fronts normally propagate together."," The agreement with the -observed mean spectral index of AGN at 1–2 ryd, $\langle \alpha_s \rangle = 1.76 \pm 0.12$ (Telfer 2002), suggests that and ionization fronts normally propagate together."
" In photoionization equilibrium in regions of high ionization, zgry«1 and wen<1, the aabundance ratio is (Fardal 11998; Shull 22004), 'The numerical coefficient has been increased from 1.70 to 1.77, reflecting an updated value of the primordial"," In photoionization equilibrium in regions of high ionization, $x_{\rm HI} \ll 1$ and $x_{\rm HeII} \ll 1$, the abundance ratio is (Fardal 1998; Shull 2004), The numerical coefficient has been increased from 1.70 to 1.77, reflecting an updated value of the primordial"
the neutron star interiors. (,the neutron star interiors. (
This is not to be confused with the global length-scale of neutron stars (o10Η) for which M/R~0.3 depending on the stars mass (in uniisec— G=1 so that M.71.475/).),This is not to be confused with the global length-scale of neutron stars $\sim 10km$ ) for which $M/R\sim 0.3$ depending on the star's mass (in units $c=G=1$ so that $M_{\sun}\approx 1.475km$ ).)
 In other words. eravily curves space-time only on a macroscopic scale but to a verv good approximation leaves it [lat on a microscopic scale.," In other words, gravity curves space-time only on a macroscopic scale but to a very good approximation leaves it flat on a microscopic scale."
 To achieve an appreciable curvature on a microscopic level at which the strong interactions dominate the particle dvnanmics mass densities greater than ~107g10em? would be necessary (WeberThorne 1966)..," To achieve an appreciable curvature on a microscopic level at which the strong interactions dominate the particle dynamics mass densities greater than $\sim 10^{40} g\hspace{1mm}cm^{-3}$ would be necessary \citep{Weber:1999a,Thorne1966a}."
 Under this circumstances the problem of constructing models of neutron stars separates into (wo distinct tasks., Under this circumstances the problem of constructing models of neutron stars separates into two distinct tasks.
 First. the short-range effects of the nuclear forces are described by (he principles of many-body nuclear physics in a local inerGal Irae. proper relerence frame) in which space-time is flat.," First, the short-range effects of the nuclear forces are described by the principles of many-body nuclear physics in a local inertial frame (co-moving proper reference frame) in which space-time is flat."
 Second. the coupling between the long-range gravitational [orce and matter is accounted for by solving the general relativistic equations for the gravitational field described by the curvature of space-time. leading to the global structure of stellar configurations.," Second, the coupling between the long-range gravitational force and matter is accounted for by solving the general relativistic equations for the gravitational field described by the curvature of space-time, leading to the global structure of stellar configurations."
 In (he case of spherically svinnetric static (non-rotating) stars the metric has (he famous Schwarzschild form: with For a static star Einsteins field equations (eq. (1))), In the case of spherically symmetric static (non-rotating) stars the metric has the famous Schwarzschild form: $(c=G=1)$ where the metric functions $\phi(r)$ and $\Lambda(r)$ are given by: with For a static star Einstein's field equations (Eq. \ref{eq.1}) ))
 reduce then to the familiar Tolman- equation (TOV) (Tolman1939:Oppenheimer&Volkolf 1939):," reduce then to the familiar Tolman-Oppenheimer-Volkoff equation (TOV) \citep{Tolman:1939jz,PhysRev.55.374}: :"
Suppose that the true redshifts 2 are available for a subset of the objects: for now. assume that the subset is a random subsample of he objects in a magnitude limited. catalog.,"Suppose that the true redshifts $z$ are available for a subset of the objects; for now, assume that the subset is a random subsample of the objects in a magnitude limited catalog."
 Ideally. this stibset would have the same geometry as the full survey. as Cross-correlating the objects with spectra and those witrout allows the use of other methods. (e.g. Calor ο al.," Ideally, this subset would have the same geometry as the full survey, as cross-correlating the objects with spectra and those without allows the use of other methods (e.g. Caler et al."
 2009)., 2009).
 In practice. this may be clillicult to achieve and this is not required. for the analysis which follows. provied that the photometric redshift estimator does not have spatially dependent. biases (ee. as a result of photometric calibrations varving across the survey).," In practice, this may be difficult to achieve – and this is not required for the analysis which follows, provided that the photometric redshift estimator does not have spatially dependent biases (e.g., as a result of photometric calibrations varying across the survey)."
 lor the οjects with spectroscopic redshifts. one can study 1ο joint distribution of ς and : (see Figure 1)).," For the objects with spectroscopic redshifts, one can study the joint distribution of $\zeta$ and $z$ (see Figure \ref{pzzeta}) )."
 Typically. most photometric redshift’ codes are constructed to return. ic]zzz2.," Typically, most photometric redshift codes are constructed to return $\langle\zeta |z\rangle \approx z$."
 The codes which do so are sometimes said to be unluased. but they are not. perfect: the scatter around the unbiased. mean is of order ay.στ0.05(1|z).," The codes which do so are sometimes said to be unbiased, but they are not perfect: the scatter around the unbiased mean is of order $\sigma_{\zeta|z} \approx 0.05\,(1+z)$."
 This scatter. ¢ombinedwith the fact that £C[z)zx2 means that £z]4¢: the fact that 2 isguaranteed to be biased is not widely appreciated.," This scatter, combinedwith the fact that $\langle\zeta |z\rangle \approx z$ means that $\langle z|\zeta\rangle \ne \zeta$: the fact that $\langle z|\zeta\rangle$ is to be biased is not widely appreciated."
 However. we show below that it matters Little whether ([z) or (z|O) are unbiased what matters is that the bias is accurately quantified.," However, we show below that it matters little whether $\langle\zeta |z\rangle$ or $\langle z|\zeta\rangle$ are unbiased – what matters is that the bias is accurately quantified."
 In particular. af ANde and ANας denote the clistribution of C and z values in the subset of he data where both z and care available. then what matters is that p(C|z) and p(z]C). where ave known.," In particular, if ${\rm d}{\cal N}/{\rm d}\zeta$ and ${\rm d}N/{\rm d}z$ denote the distribution of $\zeta$ and $z$ values in the subset of the data where both $z$ and $\zeta$ are available, then what matters is that $p(\zeta|z)$ and $p(z|\zeta)$, where are known."
 Note that The algorithm in Sheth (2007) assumes that p(c|z). measured in the subset for which both z and ¢ are available. also applies to the full sample for which z is not available.," Note that The algorithm in Sheth (2007) assumes that $p(\zeta|z)$, measured in the subset for which both $z$ and $\zeta$ are available, also applies to the full sample for which $z$ is not available."
 Since dAfede is measured in the full dataset. ancl p(c[z) is known. a deconvolution is then. used to estimate the true cLNας.," Since ${\rm d}{\cal N}/{\rm d}\zeta$ is measured in the full dataset, and $p(\zeta|z)$ is known, a deconvolution is then used to estimate the true ${\rm d}N/{\rm d}z$."
 Suppose. however. that one measured. p(z|C). instead.," Suppose, however, that one measured $p(z|\zeta)$ instead."
 Then. because one could estimate the quantity on the left hand. side by cconvolving the two measurables on the right hand side.," Then, because one could estimate the quantity on the left hand side by `convolving' the two measurables on the right hand side."
 Lor the data-subset in which both z and & are available. this is correct by definition.," For the data-subset in which both $z$ and $\zeta$ are available, this is correct by definition."
 Clearly. to use this method on the larger dataset for which only ¢ is available. one must assume that p(z|) in the subset rom which it was measured remains accurate in the larger dataset.," Clearly, to use this method on the larger dataset for which only $\zeta$ is available, one must assume that $p(z|\zeta)$ in the subset from which it was measured remains accurate in the larger dataset."
 Rossi et al. (, Rossi et al. (
2010) ave shown that the deconvolution method accurately reconstructs the true Ας distribution [rom LAY dé.,2010) have shown that the deconvolution method accurately reconstructs the true ${\rm d}N/{\rm d}z$ distribution from ${\rm d}{\cal N}/{\rm d}\zeta$ .
 Figure 2 shows that the convolution approach also works well. even when only a random of the full dataset is used to calibrate p(z|) as displaved. in," Figure \ref{Nzconv} shows that the convolution approach also works well, even when only a random of the full dataset is used to calibrate $p(z|\zeta)$ – as displayed in"
moclels in disagreement witLa distauce of dzzLs6pc.,models in disagreement with a distance of $d\approx 186$ pc.
 Án important point is he sigtificance of the two-temperature WD it over the siugle WD fit., An important point is the significance of the two-temperature WD fit over the single WD fit.
 A change in chi-squared from 1.55 o 1.38 (for theSE fits) aid. even nore so. [roi13.73 t0 3.56 (for the+IUE fits) is al bes a modest improvement iu he fi quaity with tle adcditiou of he second temperature coriponen.," A change in chi-squared from 1.58 to 1.38 (for the fits) and, even more so, from 3.73 to 3.56 (for the fits) is at best a modest improvement in the fit quality with the addition of the second temperature component."
 However. addiug the second coiiporent results in a better fit o the bottom « ‘the Ly liue aroud 1025À.. aud improves he fit to the left. winees of Ly? (the Ἱθη wing is contamüuatecd N the OVI etjlssiou feature).," However, adding the second component results in a better fit to the bottom of the $\beta$ line around 1025, and improves the fit to the left wing of $\beta $ (the right wing is contaminated by the OVI emission feature)."
 Iu that region le lmprovelrent of the fit is the actual ing of the blue wit go“tl e Lys iu the spectruil., In that region the improvement of the fit is the actual fitting of the blue wing of the $\beta$ in the spectrum.
 We remark here that there coid some instrumeut backeroutd contamination contributiug o the flux. s that the Ly wotld :willy never go to zero.," We remark here that there could be some instrument background contamination contributing to the flux, such that the $\beta$ would actually never go to zero."
" However. since we have discarded all the noisy [ions of the channels {Islally the edges). the actual coutri»utiou of the instruiient containinatio 1ould be less than z5x1015 tem 7A! («505€ of the Πιν which is the excess enmisslon a (this is an ove""esimate. since the region A«010A. is near the edge where the noise is maximal)."," However, since we have discarded all the noisy portions of the channels (usually the edges), the actual contribution of the instrument contamination should be less than $\approx 5 \times 10^{-15}$ $~$ $^{-1}$ $^{-2}$ $^{-1}$ $<$ of the flux) which is the excess emission at (this is an overestimate, since the region $\lambda < 910$ is near the edge where the noise is maximal)."
 Iu the wavelenehi rauge A«9 he iiuiprovement ofthe fit does no fit any actual feature but only reduces the discrepancy between he model aud the oervation., In the wavelength range $\lambda <$ the improvement of the fit does not fit any actual feature but only reduces the discrepancy between the model and the observation.
 Therefore the need aud importance of the secoud component does ot originate [rom fittiug that pa1 of the spectrum where there is emission but rather it comes rou [ittiug a feature in the continuum., Therefore the need and importance of the second component does not originate from fitting that part of the spectrum where there is emission but rather it comes from fitting a feature in the continuum.
 At this stage the “belt” is really a flat continuum added to improve the fit and i should be regarded as a featureless blue spectruu., At this stage the “belt” is really a flat continuum added to improve the fit and it should be regarded as a featureless blue spectrum.
 So far the belt is probably ot the best physica description of the data but it is the best availae model compoient. to help improve e fit., So far the belt is probably not the best physical description of the data but it is the best available model component to help improve the fit.
 La fact. the two-temperature WD fit does not provide the lowest X7.> tle disk+WD oes.," In fact, the two-temperature WD fit does not provide the lowest $\chi^2_{\nu}$, the disk+WD does."
 However. this lowest disk+WD model. while fittiug better ii theIUE (lower resolution) spectral ange. does uot provide a good fit ain theFUSE (higher resoution) range of the combined spectrum al is inconsistant with the clistauce of the system.," However, this lowest disk+WD model, while fitting better in the (lower resolution) spectral range, does not provide a good fit a in the (higher resolution) range of the combined spectrum and is inconsistant with the distance of the system."
 As we stated previously. we do uot chose bliidly the lowest V7 model. but we chose one of the lowest \7 uodels that provides a better Π to so110 Ἡyecilic parts aud features of the spectruu.," As we stated previously, we do not chose blindly the lowest $\chi^2_{\nu}$ model, but we chose one of the lowest $\chi^2_{\nu}$ models that provides a better fit to some specific parts and features of the spectrum."
 The [act that both the WD-belt. aud he WD-+disk provide the lowest. V7 models. reflects he fact that the secoud Component cannot. oesently. be uodeled accurately.," The fact that both the WD+belt and the WD+disk provide the lowest $\chi^2_{\nu}$ models, reflects the fact that the second component cannot, presently, be modeled accurately."
 Trere are broad. emissior lines which are probaby due to a ho eas. aud theOVI recd-shiltect eature inay luidicate the possibility that the maerial is llowing away [rom the observer.," There are broad emission lines which are probably due to a hot gas, and the red-shifted feature may indicate the possibility that the material is flowing away from the observer."
 However. he other eiisslou features a‘e not resolved. enctela o confirm or 'efute such a scenario.," However, the other emission features are not resolved enough to confirm or refute such a scenario."
 We cdo 100 discuss here the origin or he possible scenariOs of such a flow. tlough the mechanisms at work could ye as varied as the ones discussed in Hoa«|οἱal.(2003) [9]1 the FUYV observation of the complex system DW UMa.," We do not discuss here the origin or the possible scenarios of such a flow, though the mechanisms at work could be as varied as the ones discussed in \citet{hoa03} on the FUV observation of the complex system DW UMa."
 I melt be worth iotiug that the supra-solar Nitrogen abundauce. albeit uncertain (as it. could well be from intersellar origin). togetler with the sub-solar Carbon abundance. could be a result of CNO-processiug. either from a past nova or from CNO processed," It might be worth noting that the supra-solar Nitrogen abundance, albeit uncertain (as it could well be from interstellar origin), together with the sub-solar Carbon abundance, could be a result of CNO-processing, either from a past nova or from CNO processed"
D) js dsed that encodes replicated observations for hi calilxator and tarect.,(OB) is used that encodes replicated observations for both calibrator and target.
 Raod star acquisition Wwuch is iuportaut for ensuring eood calibration — cau be angleited by usine a simple offset o* the telescope without liaving to preset the telescope and perform a ful (iustameutal) re-acquisitiou., Rapid star acquisition -- which is important for ensuring good calibration – can be augmented by using a simple offset of the telescope without having to preset the telescope and perform a full (instrumental) re-acquisition.
" In this 110do. which las been chisched ""star hopping”. t1ο adaptive optics loop is opened. while the template orders a dither to bring a different sar into the AO field selector."," In this mode, which has been christened “star hopping”, the adaptive optics loop is opened, while the template orders a dither to bring a different star into the AO field selector."
 The AO is then closed iuamally by the operator without incurring the tine peatv for re-optimization., The AO is then closed manually by the operator without incurring the time penalty for re-optimization.
 Star hopping therefore onv works ou objects of conrpirable brightucss in the wavetroit SCLISOL., Star hopping therefore only works on objects of comparable brightness in the wavefront sensor.
 As t1e observation progresses. the repetition of the template collects cight datacubes of multiple frames (typically a hundred). cach at a differcut dither position on the ¢ctector.," As the observation progresses, the repetition of the template collects eight datacubes of multiple frames (typically a hundred), each at a different dither position on the detector."
 For these observations. the detector was windowed ο 512«511 pixels.," For these observations, the detector was windowed to $512\times 514$ pixels."
 A siele snapshot observation vields Fourier coverage of 21 sdalial frequencies., A single snapshot observation yields Fourier coverage of 21 spatial frequencies.
 IHowewer. the pupiltrackiug mode POSIts in sky rotation on the detector as the parallacic anele changes.," However, the pupil-tracking mode results in sky rotation on the detector as the parallactic angle changes."
 This variation with time results sweeps the baselines iuto circular Fourier tracks aud permits roational aperture svuthesis tecliniques to assist with the fllius of the spatial frequency UV-plane plane. as illustrated in Fig. 2..," This variation with time results sweeps the baselines into circular Fourier tracks and permits rotational aperture synthesis techniques to assist with the filling of the spatial frequency UV-plane plane, as illustrated in Fig. \ref{uv}."
 To the authors knowledge. two ¢ata reduction software libraries-. are preseutly oreuce SAM daa.," To the author's knowledge, two data reduction software libraries are presently to reduce SAM data."
 One pipeline las been developed w Svney University. Cornell University. and Caltech from 20H ouwards. based on an earlier pix‘line from Berkeley.," One pipeline has been developed by Sydney University, Cornell University, and Caltech from 2004 onwards, based on an earlier pipeline from Berkeley."
 It iis already beenused for several pa])ers arising predomunatly youn Keck aperture nasking data (7)., It has already been used for several papers arising predominantly from Keck aperture masking data \citep{2000PASP..112..555T}.
 This reduction algorithin is based on fast Emer traustfonu (FFT)., This reduction algorithm is based on fast Fourier transform (FFT).
 The daa presented in this Po have been reduced by the sparse aIOLTULC uode pip¢‘line (SAMD) developed at the Observatoire de Paris., The data presented in this paper have been reduced by the sparse aperture mode pipeline (SAMP) developed at the Observatoire de Paris.
 This software is similar to that Toni Svduev university. ando nunnerous tests ando cross-checks have xoduced similar results.," This software is similar to that from Sydney university, and numerous tests and cross-checks have produced similar results."
 For voth pipelines. data reduction follows a similar oath:," For both pipelines, data reduction follows a similar path:"
The first billion vears after the Big Bang represents a period of great. interest Lor studies of both galaxy. formation and he evolution of the Universe as à whole.,The first billion years after the Big Bang represents a period of great interest for studies of both galaxy formation and the evolution of the Universe as a whole.
 Εις period. sees he formation of the first galaxies (2). and. consequently. he beginning and completion of the process of reionizing he Universe (77) as a result. of the copious number of ionizing photons emitted. by these sources.," This period sees the formation of the first galaxies \citep{wise_resolving_2008} and, consequently, the beginning and completion of the process of reionizing the Universe \citep{loeb_reionization_2001,loeb_frontier_2009} as a result of the copious number of ionizing photons emitted by these sources."
" Current and uture facilities aim to probe this epoch of the Universe roth using traditional methods such as surveying [faint galaxies (e.g. the James Webb Space ""Telescope: ?2)) and using novel techniques such as 210m cosmology (7) to probe he distribution of neutral hydrogen during the process of reionization.", Current and future facilities aim to probe this epoch of the Universe both using traditional methods such as surveying faint galaxies (e.g. the James Webb Space Telescope; \citealt{gardner_james_2009}) ) and using novel techniques such as 21cm cosmology \citep{furlanetto06a} to probe the distribution of neutral hydrogen during the process of reionization.
 Understanding this epoch of the Universe from a theoretical perspective therefore requires an understanding both of the sources of ionizing photons and of the thermal and ionization state of the intergalactic medium (16M) at these times., Understanding this epoch of the Universe from a theoretical perspective therefore requires an understanding both of the sources of ionizing photons and of the thermal and ionization state of the intergalactic medium (IGM) at these times.
 Additionally. the thermal and ionization history of the IGAL as a function of cosmic redshift. z. strongly alfects the visibility of the most distant galaxies ancl quasars (??7).. and the feedback exerted on the formation of new galaxios (222727272727272727727)..," Additionally, the thermal and ionization history of the IGM as a function of cosmic redshift, $z$, strongly affects the “visibility” of the most distant galaxies and quasars \citep{madau_radiative_1995,meiksin_colour_2006,dayal_visibility_2011}, and the feedback exerted on the formation of new galaxies \citep{efstathiou_suppressing_1992,quinn_photoionization_1996,navarro_effects_1997,barkana_photoevaporation_1999,bullock_reionization_2000,somerville_can_2002,
Benson:02a,Benson:02b,koposov_quantitative_2009,munoz_probing_2009,busha_impact_2010,maccio_luminosity_2010}."
 Phe process of reionization is expected. to begin with the formation of ionized bubbles around Luminous sources in the redshift range z=10 , The process of reionization is expected to begin with the formation of ionized bubbles around luminous sources in the redshift range $z=10$ --20.
These bubbles will eventually erow in size and number, These bubbles will eventually grow in size and number
"For heterodyne interferometry, one gets: ACTIWe noisecan see that the ratio Neg/Np is ΝΕΤΗΙalways less than one, which gives a clear advantage to direct imaging from the strict point of view of the noise.","For heterodyne interferometry, one gets: We can see that the ratio $N_\mathrm{eq}/N_h$ is always less than one, which gives a clear advantage to direct imaging from the strict point of view of the noise."
" This ratio appears squared in the ratio of imaging to bolometric interferferometry and without power in the ratio of imaging to heterodyne interferometry but in the latter case, the NET ratio is also less than one, penalising heterodyne interferometry."," This ratio appears squared in the ratio of imaging to bolometric interferferometry and without power in the ratio of imaging to heterodyne interferometry but in the latter case, the NET ratio is also less than one, penalising heterodyne interferometry."
" The number of equivalent baselines for a square horn array is: If one averages over directions in the baseline plane at a given |u|, a good approximation of Neg as a function of £ is given by (see Fig. 1)):"," The number of equivalent baselines for a square horn array is: If one averages over directions in the baseline plane at a given $|\vec{u}|$, a good approximation of $N_\mathrm{eq}$ as a function of $\ell$ is given by (see Fig. \ref{uapprox}) ):"
 One finally finds that a good approximation of the sensitivity ratio is: AC;and:noise These approximate formulae have been NETurcompared with actual calculations of the number of equivalent baselines for square arrays., One finally finds that a good approximation of the sensitivity ratio is: and: These approximate formulae have been compared with actual calculations of the number of equivalent baselines for square arrays.
" We have chosen 256 horns for the comparison and we compare bolometric and heterodyne interferometers with imagers having a low angular resolution of one degree, BICEP-like (Yoonetal, 2006)) and a high one of 10 arcminutes, Clover-like (Northetal, 2008))."," We have chosen 256 horns for the comparison and we compare bolometric and heterodyne interferometers with imagers having a low angular resolution of one degree, BICEP-like \cite{bicep}) ) and a high one of 10 arcminutes, Clover-like \cite{clover}) )."
 The results are shown in Fig. 2.., The results are shown in Fig. \ref{comparison}.
" We have chosen to only consider the multipole region between 0 and 200 as for higher multipoles, interferometers are less sensitive due the loss of coherence between largely separated horns."," We have chosen to only consider the multipole region between 0 and 200 as for higher multipoles, interferometers are less sensitive due the loss of coherence between largely separated horns."
 Note that the effect of coherence loss for the long baselines and the bandwidth smearing have not been taken into account here and might have a significant effect., Note that the effect of coherence loss for the long baselines and the bandwidth smearing have not been taken into account here and might have a significant effect.
 The sensitivities of the three different techniques only differ in the way the instrument filters the multipoles observed in the sky., The sensitivities of the three different techniques only differ in the way the instrument filters the multipoles observed in the sky.
 An imager is affected by its resolution on the sky while an interferometer is affected by the ratio between the number of equivalent baselines and the number of horns as a function of multipoles., An imager is affected by its resolution on the sky while an interferometer is affected by the ratio between the number of equivalent baselines and the number of horns as a function of multipoles.
 All of these filtering factors are less than one., All of these filtering factors are less than one.
" However, imagers are usually operated in such a way that they are not limited by their angular resolution in the multipole region of interest, in that case By~1, and the imager is always more sensitive than an interferometer (bolometric or heterodyne)."," However, imagers are usually operated in such a way that they are not limited by their angular resolution in the multipole region of interest, in that case $B_\ell\simeq 1$, and the imager is always more sensitive than an interferometer (bolometric or heterodyne)."
" From the strict point of view of sensitivity, interferometers can therefore only compete with low angular resolution imagers."," From the strict point of view of sensitivity, interferometers can therefore only compete with low angular resolution imagers."
 There is a large difference in sensitivity between bolometric and heterodyne interferometers compared to an imager: the ratio Neg/Nn acts quadratically on the variance for a bolometric interferometer while it acts linearly for a heterodyne instrument., There is a large difference in sensitivity between bolometric and heterodyne interferometers compared to an imager: the ratio $N_\mathrm{eq}/N_h$ acts quadratically on the variance for a bolometric interferometer while it acts linearly for a heterodyne instrument.
" This is due to the fact that with a heterodyne interferometer, equivalent baselines are averaged after their measurement, resulting in a 1/Neq factor on the variances."," This is due to the fact that with a heterodyne interferometer, equivalent baselines are averaged after their measurement, resulting in a $1/N_\mathrm{eq}$ factor on the variances."
" In a bolometric interferometer, the signals from all N; horns are added together multiplying the noise variance by N; while the coherent summation of equivalent baselines performs an efficient 1/N2, reduction of the noise."," In a bolometric interferometer, the signals from all $N_h$ horns are added together multiplying the noise variance by $N_h$ while the coherent summation of equivalent baselines performs an efficient $1/N_\mathrm{eq}^2$ reduction of the noise."
 This finally results in a factor N;/2N.q for the variance of a bolometric interferometer relative to a heterodyne one., This finally results in a factor $N_h/2N_\mathrm{eq}$ for the variance of a bolometric interferometer relative to a heterodyne one.
 This is largely compensated by the difference in NET between bolometric instruments and coherent ones., This is largely compensated by the difference in NET between bolometric instruments and coherent ones.
" When comparing them, the ratio of their NET also appears quadratically and favours bolometric instruments that are dominated by the photon noise rather than by that of the amplifiers."," When comparing them, the ratio of their NET also appears quadratically and favours bolometric instruments that are dominated by the photon noise rather than by that of the amplifiers."
 This situation may change in the future with the improvements of the HEMT technologies but at frequencies around and above 100 GHz we are unlikely to face photon noise limited HEMTs in the near future., This situation may change in the future with the improvements of the HEMT technologies but at frequencies around and above 100 GHz we are unlikely to face photon noise limited HEMTs in the near future.
 The difference between the NET would be even greater in space where the bolometers NET would drop as the background temperature while that of the coherent instruments would remain roughly constant., The difference between the NET would be even greater in space where the bolometers NET would drop as the background temperature while that of the coherent instruments would remain roughly constant.
" With the present technologies of bolometers and coherent amplifiers, the hierarchy in terms of sensitivity between the three techniques (and layout) studied here is very clear for the multipole range 25«€200 where the primordial B-mode signal is expected to be maximal."," With the present technologies of bolometers and coherent amplifiers, the hierarchy in terms of sensitivity between the three techniques (and layout) studied here is very clear for the multipole range $25<\ell<200$ where the primordial B-mode signal is expected to be maximal."
" Imagers are the most sensitive, bolometric interferometers have a lower sensitivity, the ratio dropping quadratically with the multipole considered."," Imagers are the most sensitive, bolometric interferometers have a lower sensitivity, the ratio dropping quadratically with the multipole considered."
 Heterodyne interferometers have an even lower sensitivity but the ratio with an imager drops less rapidly., Heterodyne interferometers have an even lower sensitivity but the ratio with an imager drops less rapidly.
" They remain however less sensitive than bolometric interferometers in the range of multipoles considered here, where the largest primordial B-mode signal is expected and where the lensing"," They remain however less sensitive than bolometric interferometers in the range of multipoles considered here, where the largest primordial B-mode signal is expected and where the lensing"
Cluster major mergers are among5 the most energetic5 phenomena in the Universe.,Cluster major mergers are among the most energetic phenomena in the Universe.
"ὃν They release a total energy. of the order of 10510"".1 erg. and it Mis nowadays accepte that they are the key ingredient to explain the origin and rarity of radio halos in galaxy clusters: shocks anc turbulence are generated during such energetic events. anc they deeply alfect the thermal and nonthermal properties of the intracluster medium (ICM)."," They release a total energy of the order of $10^{63}-10^{64}$ erg, and it is nowadays accepted that they are the key ingredient to explain the origin and rarity of radio halos in galaxy clusters: shocks and turbulence are generated during such energetic events, and they deeply affect the thermal and non–thermal properties of the intracluster medium (ICM)."
 Radio halos are the signposts of the nontherma components in galaxy clusters., Radio halos are the signposts of the non–thermal components in galaxy clusters.
 They are diffuse racio sources. whose size and morphology are similar to those of the underlving hot ICM (e.g. Ferrari et al.," They are diffuse radio sources, whose size and morphology are similar to those of the underlying hot ICM (e.g. Ferrari et al."
 2008. Cassano 2009 ancl Venturi 2011 for recent reviews).," 2008, Cassano 2009 and Venturi 2011 for recent reviews)."
" Their spectrum (defined. as Sxf£ "") is steep. with typical values of the spectral index o in the range 1.2.1.4."," Their spectrum (defined as $\propto\nu^{-\alpha}$ ) is steep, with typical values of the spectral index $\alpha$ in the range 1.2–1.4."
 However. recent highsensitivity low frequency. imaging led to the discovery. of racio halos with much steeper spectra (Venturi 2011). with spectral index à~LS2 (e.g. 5521. Brunetti et al.," However, recent high--sensitivity low frequency imaging led to the discovery of radio halos with much steeper spectra (Venturi 2011), with spectral index $\alpha \sim 1.8-2$ (e.g. 521, Brunetti et al."
 2008. Dallacasa ct al.," 2008, Dallacasa et al."
 2000: 66907 Macario ct al., 2009; 697 Macario et al.
 2010)., 2010).
 Combined radio anc Xrav studies. provide strong support to the idea that radio halos are found only in unrelaxed clusters., Combined radio and X–ray studies provide strong support to the idea that radio halos are found only in unrelaxed clusters.
" Buote (2001). first showed a correlation between the 1.4 Gllz radio power of halos. Piocu. and the dipole power ratio P, /Po in the hosting cluster: based on temperature maps. Govoni ct al."," Buote \cite{buote01} first showed a correlation between the 1.4 GHz radio power of halos, $_{\rm 1.4~GHz}$, and the dipole power ratio $_{\rm 1}$ $_{\rm 0}$ in the hosting cluster; based on temperature maps, Govoni et al."
 (2004). found evidence for merging activity in clusters with radio halos.," \cite{govoni04}
 found evidence for merging activity in clusters with radio halos."
 Venturi et al. (, Venturi et al. (
2008. hereinafter. VOS) showed that all racio halos in the GMIEE (Giant. Metrewave Radio Telescope) radio halo survey are located in clusters with signs of dynamical clisturbances.,"2008, hereinafter V08) showed that all radio halos in the GMRT (Giant Metrewave Radio Telescope) radio halo survey are located in clusters with signs of dynamical disturbances."
 More recently. Cassano ct al. (," More recently, Cassano et al. ("
2010. hereinafter. C10) carried out a quantitative analysis of the radio halocluster merger scenario.,"2010, hereinafter C10) carried out a quantitative analysis of the radio halo–cluster merger scenario."
 μον. used all clusters in. the GMBIRE radio halo cluster sample (Venturi et al., They used all clusters in the GMRT radio halo cluster sample (Venturi et al.
 2007. hereinafter VOT. and. VOS) with available high quality images (a total of 32. clusters) to characterize the presence of substructures by three cillerent methods.," 2007, hereinafter V07, and V08) with available high quality images (a total of 32 clusters) to characterize the presence of substructures by three different methods."
 Γον showed that clusters with and without radio halos are well segregated according to all parameters indicating substructure: raclio halos are associated with clusters currently undergoing a merger. while clusters without radio halo are usually more “relaxed”.," They showed that clusters with and without radio halos are well segregated according to all parameters indicating substructure: radio halos are associated with clusters currently undergoing a merger, while clusters without radio halo are usually more “relaxed”."
 Four clusters. however. are noticeable outliers in the correlations. being disturbed systems with no detectable radio halo at the sensitivity limit of the 610. MlIIz GAIRT survey (VOT and VOS).," Four clusters, however, are noticeable outliers in the correlations, being disturbed systems with no detectable radio halo at the sensitivity limit of the 610 MHz GMRT survey (V07 and V08)."
 One o£ the outliers. Abell 781," One of the outliers, Abell 781"
heir coalescence driven by the emission of eravitational waves. and the recoil associated with the non-zero uct Inear momentum carried away by CAVs in the coalescence of two unequal mass black holes (the veravitational rocket,"their coalescence driven by the emission of gravitational waves, and the recoil associated with the non-zero net linear momentum carried away by GWs in the coalescence of two unequal mass black holes (the “gravitational rocket”)."
 Major halo mergers lead to MDII fueling aud rigecr ).quasar activity., Major halo mergers lead to MBH fueling and trigger quasar activity.
 In this paper we use the same uodel to provide a more detailed characterization of the CV. sienal from iuspiraliug MDIIDs., In this paper we use the same model to provide a more detailed characterization of the GW signal from inspiraling MBHBs.
 Their coutributiou o the data stream is twofold: unresolved. sources will eive origin to confusion noise to be compared to instrumental noise aud other astrophysical stochastic vackerounds (e.g. from white dwarf binaries. Financer Phinney 2003). while resolved iuspialiug binaries will xobe eravitv in extreme conditions (e.e.. Vecchio 2001).," Their contribution to the data stream is twofold: unresolved sources will give origin to confusion noise to be compared to instrumental noise and other astrophysical stochastic backgrounds (e.g. from white dwarf binaries, Farmer Phinney 2003), while resolved inspiraling binaries will probe gravity in extreme conditions (e.g., Vecchio 2004)."
 Confusion noise aud resolved sources should provide different cosmological information., Confusion noise and resolved sources should provide different cosmological information.
 The former. produced wea large nuniber of unresolved MDIIDs. will trace light AIBIIDs at very high redshift. placing coustraiuts ou black tole formation scenarios prior to the reionization epoch: he latter will be a formidable tool to follow the cosmic evolution of MDIIs aud the formation and dvnamics of MBI binaries following galaxy mergers.," The former, produced by a large number of unresolved MBHBs, will trace light MBHBs at very high redshift, placing constraints on black hole formation scenarios prior to the reionization epoch; the latter will be a formidable tool to follow the cosmic evolution of MBHs and the formation and dynamics of MBH binaries following galaxy mergers."
 The plan is as follows., The plan is as follows.
 In 2 we review the basics of the detection of CAV from MBIIDs. defining observable quantities such as the characteristic stram amplitude. signal-to-noise ratio. aud source detection rate.," In 2 we review the basics of the detection of GW from MBHBs, defining observable quantities such as the characteristic strain amplitude, signal-to-noise ratio, and source detection rate."
 In 3 we briefliv sunmnuarize our scenario for the cosmological evolution of ealaxy halos aud associated holes., In 3 we briefly summarize our scenario for the cosmological evolution of galaxy halos and associated holes.
 In £ we preseut confusion noise levels aud source uuuber counts., In 4 we present confusion noise levels and source number counts.
 Finally. in 85 we discuss our results.," Finally, in 5 we discuss our results."
" Following Thorne (1996). an interferometer can be characterized by two different sensitivitv curves. cepending ou the type of signal one expects to detect. 10. a ""burst? or a “periodic” GW source."," Following Thorne (1996), an interferometer can be characterized by two different sensitivity curves, depending on the type of signal one expects to detect, i.e. a “burst"" or a “periodic"" GW source."
" A burst. a short-lived VAignal whose waveform can be utterly complicated. cau be escribed in terms of a characteristic strain amplitude /, at the observed frequency f.c L/At.. where Af, is the uration of the signal (Thorne 1987)."," A burst, a short-lived signal whose waveform can be utterly complicated, can be described in terms of a characteristic strain amplitude $h_c$ at the observed frequency $f_c \sim 1/\Delta
t_s$ , where $\Delta t_s$ is the duration of the signal (Thorne 1987)."
 The spread of the power spectruni around £F. will be Af~f., The spread of the power spectrum around $f_c$ will be $\Delta f \sim f_c$.
 At the other xtreme. a perfectly periodic source cuits. for the cutire uration of the observation. at a fixed frequency f.," At the other extreme, a perfectly periodic source emits, for the entire duration of the observation, at a fixed frequency $f$."
 The power spectrum will be peaked at £. with a spread Af FN. where N is the umber of wave cveles clipped iuto he observation.," The power spectrum will be peaked at $f$, with a spread $\Delta f \simeq f/N$ , where $N$ is the number of wave cycles clipped into the observation."
 Iu this respect. a burst cau be thought as a sinele complete waveform with f£=f...," In this respect, a burst can be thought as a single complete waveform with $f=f_c$."
 In the case of a seriodic signal. the iuterferomieter sensitivity is increased w the fact that. across the observing interval r. the signal is repeated f7 times.," In the case of a periodic signal, the interferometer sensitivity is increased by the fact that, across the observing interval $\tau$, the signal is repeated $f\tau$ times."
 The seusitivitv to bursts (5) aud to periodic signals (hp) axe related by: Iu Fieure 1 the two curves fip aud δρ are colmpared for an assed Devear observation., The sensitivity to bursts $h_B$ ) and to periodic signals $h_P$ ) are related by: In Figure \ref{sensitivity} the two curves $h_B$ and $h_P$ are compared for an assumed 3-year observation.
 The curves are obtained combining the sinele-ain Michelson seusitivity curve (taken from the URL www.srlealtecliiedu/-shaue/seusitivitv) with the recent analysis of the instrumental noise below 10! Tz (Beuder 2003. extended from 3.«109 IIz to 1«10.5 Tz with a constant slope).," The curves are obtained combining the single-arm Michelson sensitivity curve (taken from the URL $\sim$ shane/sensitivity) with the recent analysis of the instrumental noise below $10^{-4}$ Hz (Bender 2003, extended from $3\times 10^{-6}$ Hz to $1\times 10^{-6}$ Hz with a constant slope)."
 Consider now a periodic signal of finite duration. with strain amplitude 5.," Consider now a periodic signal of finite duration, with strain amplitude $h$."
 The total energy carried by the wave will be proportional to the nuuiber of wave cycles à speut at that particular frequency., The total energy carried by the wave will be proportional to the number of wave cycles $n$ spent at that particular frequency.
" The quantity to be compared with 5j is then the ""characteristic strain Jh.—hn."," The quantity to be compared with $h_B$ is then the “characteristic"" strain $h_c \equiv h\sqrt{n}$ ."
 Note that for a periodic signal at frequency. f lasting for a time interval longer than the observation time 7. we have simply (9=fr.," Note that for a periodic signal at frequency $f$ lasting for a time interval longer than the observation time $\tau$ , we have simply $n=f\tau$."
 Then. the signal-to-noise ratio S/N increases by the same factor one would obtain comparing h to hp in equation (1)).," Then, the signal-to-noise ratio $S/N$ increases by the same factor one would obtain comparing $h$ to $h_P$ in equation \ref{eqburstperiodic}) )."
 The former approach. io. comparing ὃς top rather than / to fp. is more general. as it allows us to characterize the S/N not only for perfectly xeriodie signals (7= fr). or for bursts (0= 1). but also for events in which the emitted frequeucy shifts to iucreasiuglv arecr values during the spiral-in phase of the binary system.," The former approach, i.e. comparing $h_c$ to $h_B$ rather than $h$ to $h_P$, is more general, as it allows us to characterize the $S/N$ not only for perfectly periodic signals $n=f\tau$ ), or for bursts $n=1$ ), but also for events in which the emitted frequency shifts to increasingly larger values during the spiral-in phase of the binary system."
" Iu the latter case. 0=of) represeuts the nuuber of eveles spent in a frequency interval Af~f around yequency f£. aud hence fi, is the strain in a logarithnunic requeucyv interval (Flanagan Hughes 1998)."," In the latter case, $n=n(f)$ represents the number of cycles spent in a frequency interval $\Delta f \simeq f$ around frequency $f$, and hence $h_c$ is the strain in a logarithmic frequency interval (Flanagan Hughes 1998)."
 Typically. he timescale for frequency shift is long compared to he wave period. aud short compared to the duration of the observation.," Typically, the timescale for frequency shift is long compared to the wave period, and short compared to the duration of the observation."
 Onlv close to the innuenuoststable circular. orbit (CISCO). the CW frequency changes at a rate comparable to the frequency itself η~1 aud lence h.c h)," Only close to the innermoststable circular orbit (ISCO), the GW frequency changes at a rate comparable to the frequency itself $n\sim 1$ and hence $h_c \sim h$ )."
 Tu Figure dlowe also show 7L audbh. for two representative binary svstenis., In Figure \ref{sensitivity} we also show $h$ and$h_c$ for two representative binary systems.
" One should uote that the true observable CAV signal is. for f2ne/r (the ""kuec"," One should note that the true observable GW signal is, for $f> n/\tau$ (the “knee"""
of which stellar populations are detected at cach wavelength is essential to obtain the full picture.,of which stellar populations are detected at each wavelength is essential to obtain the full picture.
 Nevertheless. we are somewhat limited by the sensitivity. quality and field-of-view of the existing observations.," Nevertheless, we are somewhat limited by the sensitivity, quality and field-of-view of the existing observations."
 Star formation tends to be localised and varies within galaxies., Star formation tends to be localised and varies within galaxies.
 While the nuclear region ancl inner spiral arms of a galaxy are generally locations of significant star ormation. we also find new stars forming in other areas such as interaction zones and occasionally in isolated clumps (presumably. of high molecular gas density) in the zw outskirts of galaxies.," While the nuclear region and inner spiral arms of a galaxy are generally locations of significant star formation, we also find new stars forming in other areas such as interaction zones and occasionally in isolated clumps (presumably of high molecular gas density) in the far outskirts of galaxies."
 Vhe NGC 1512/1510 system is an xcellent. laboratory to study the locations ancl properties of its many star forming regions. from the galaxy. nuclei out o the largest racii where detached eclouds are found. (see Section 3.3) as well as in the interaction zone between the two galaxies.," The NGC 1512/1510 system is an excellent laboratory to study the locations and properties of its many star forming regions, from the galaxy nuclei out to the largest radii where detached clouds are found (see Section 3.3) as well as in the interaction zone between the two galaxies."
 llere we use a range of tracers to study the global SER of both NGC 1512 and. NGC 1510. (results. are summarised in Table 5. and Fig., Here we use a range of tracers to study the global SFR of both NGC 1512 and NGC 1510 (results are summarised in Table \ref{tab:sfr} and Fig.
 14). before investigating he local star formation activity within various parts of the GC 1512/1510 system (see Section 4.4).," 14), before investigating the local star formation activity within various parts of the NGC 1512/1510 system (see Section 4.4)."
 From our 20-cm radio continuum data we derive a recent global SER o£ Tor NGC 1512 and for NGC 1510. (see Section. 3.4)., From our 20-cm radio continuum data we derive a recent global SFR of for NGC 1512 and for NGC 1510 (see Section 3.4).
 Another. extinction-ree SER. estimate is derived. [rom the far-infrared. (£41) uminositv., Another extinction-free SFR estimate is derived from the far-infrared $FIR$ ) luminosity.
 Using the HtAS flux densities (Moshir οἱ al., Using the IRAS flux densities (Moshir et al.
 1990) together with the relations given by Sanders Alirabel (1996) and Ixennicutt (1998). we derive z012M.s [for NGC 1512 and [for NGC 1510.," 1990) together with the relations given by Sanders Mirabel (1996) and Kennicutt (1998), we derive $\approx$ for NGC 1512 and for NGC 1510."
 FIR emission comes from the thermal continuum re-radiation of dust. grains which absorb the visible and CY. radiation emitted by massive voung stars., $FIR$ emission comes from the thermal continuum re-radiation of dust grains which absorb the visible and $UV$ radiation emitted by massive young stars.
 In contrast. racio continuum emission is mainlv due to svnchrotron radiation from relativistic electrons. accelerated. in the remnants of core-collapse supernovae. therefore also associated with the presence of massive stars.," In contrast, radio continuum emission is mainly due to synchrotron radiation from relativistic electrons accelerated in the remnants of core-collapse supernovae, therefore also associated with the presence of massive stars."
 Both estimates trace the star formation activity in the last 100 Alvr., Both estimates trace the star formation activity in the last $\sim$ 100 Myr.
 However. as relativistic electrons have lifetimes of ~L00 Alvr (Conclon οἱ al.," However, as relativistic electrons have lifetimes of $\sim$ 100 Myr (Condon et al."
 2002). we should expect that the 20-em radio continuum emission traces SLRs with somewhat extended ages.," 2002), we should expect that the 20-cm radio continuum emission traces SFRs with somewhat extended ages."
 comission traces the most massive. ionising stars. ancl imescales of ~1O Myr. ic. the most recent events of star ormation in the galaxy.," emission traces the most massive, ionising stars, and timescales of $\sim$ 10 Myr, i.e. the most recent events of star formation in the galaxy."
 Lhe flux given by Meurer. ct al. (, The flux given by Meurer et al. (
2006) was corrected [for Galactic extinction. but not for internal extinction or for he contribution of the eemission lines adjacent to ((sec Lóppez-Sánnchez Esteban2008).,2006) was corrected for Galactic extinction but not for internal extinction or for the contribution of the emission lines adjacent to (see Lóppez-Sánnchez Esteban.
. Using the relation by Ixennicutt (1998). we find == 0.19 and for NGC 1512 and NGC 1510. respectively.," Using the relation by Kennicutt (1998), we find = 0.19 and for NGC 1512 and NGC 1510, respectively."
 Slighter lower values. == 0.13 and i. result when using the more recent Calzetti οἱ al. (," Slighter lower values, = 0.13 and , result when using the more recent Calzetti et al. ("
2007) calibration.,2007) calibration.
 UVemission. probes star formation over timescales of ~100 Mr. the life-time of the massive OB stars.," $UV$ -emission probes star formation over timescales of $\sim$ 100 Myr, the life-time of the massive OB stars."
 Using the extinetion-corrected CLALIZN. CV-magnitude. πριν. as eiven by Gil de Paz et al. (," Using the extinction-corrected GALEX $UV$ -magnitude, $m_{\rm FUV}$ , as given by Gil de Paz et al. ("
2007a). we derive the CV-MIux as follows: fpes teem 7 d = 140e10Dosohsft ,"2007a), we derive the $UV$ -flux as follows: $f_{\rm FUV}$ $^{-1}$ $^{-2}$ $^{-1}$ ] = $1.40 \times 10^{-15} \times 10^{0.4 \times (18.82 - m_{\rm FUV})}$."
We have Corrected mypvy for extinction assuming the Galactic value provided by Schlegel et al. (, We have corrected $m_{\rm FUV}$ for extinction assuming the Galactic value provided by Schlegel et al. (
1998). οV) = 0.011. and elpey=7.9EXG(D1.,"1998), $E(B-V)$ = 0.011, and $A_{\rm FUV} = 
7.9~E(B-V)$."
 Applying the Salim et al. (, Applying the Salim et al. (
2007) relation between the £UCV luminosity and the SER. we obtain == 0.12 and for NGC 1512 and NGC 1510. respectively.,"2007) relation between the $FUV$ luminosity and the SFR, we obtain = 0.12 and for NGC 1512 and NGC 1510, respectively."
 For comparison. applving the Ixennicutt (1998) relation results in values that are a 1.3 times higher.," For comparison, applying the Kennicutt (1998) relation results in values that are a 1.3 times higher."
 Here we prefer to use Salim οἱ al. (, Here we prefer to use Salim et al. (
2007) relation because it was derived. using CCALIZX data.,2007) relation because it was derived using GALEX data.
 The SINGS Legacy project lxennicutt et al., The SINGS Legacy project (Kennicutt et al.
 2003) provides Spitzer mic-infrarecd (ALL) images of GO 15191510., 2003) provides Spitzer mid-infrared $MIR$ ) images of NGC 1512/1510.
 ΑΙ emission. which traces the dust distribution. within galaxies. also agrees well with the »xosition of the C V-rieh star clusters in the svstem.," $MIR$ emission, which traces the dust distribution within galaxies, also agrees well with the position of the $UV$ -rich star clusters in the system."
 Because of its higher intrinsic. brightness. the MZ? emission. is mainlv detected. in the cores of both galaxies and in the inner ring of NGC 1512.," Because of its higher intrinsic brightness, the $MIR$ emission is mainly detected in the cores of both galaxies and in the inner ring of NGC 1512."
 Using the Spitzer 24jun. Hux density measurements of NGC 1512 (Dale et al., Using the Spitzer $\mu$ m flux density measurements of NGC 1512 (Dale et al.
 2007) and GC 1510 (obtained by us: see Table 5) together with the relations by Calzetti et al. (, 2007) and NGC 1510 (obtained by us; see Table 5) together with the relations by Calzetti et al. (
2007) we derive. SPisa = for NGC 1512 and forNGC 1510.,2007) we derive $SFR_{24\mu m}$ = for NGC 1512 and forNGC 1510.
" Combining the 24/2. luminosity (which.traces. the clust-absorbeck star formation) with the luminosity (which probes the unobscured. star formation) we derive. S£-Hg,", Combining the $\mu$ m luminosity (whichtraces the dust-absorbed star formation) with the luminosity (which probes the unobscured star formation) we derive $SFR_{\rm H\alpha+24\mu m}$ =
A system response function for both regions was needed to account for the contribution from the system setup (e.g. windows. beamsplitter. lens. filler aud detector) which alters the strength of the lines observed.,"A system response function for both regions was needed to account for the contribution from the system setup (e.g. windows, beamsplitter, lens, filter and detector) which alters the strength of the lines observed."
 This was achieved by recording the blackbody spectrum emitted from a solid graphite rod placed at the center of the Al3O tube: the end facing the speclrometer was machined into a concave cone to allow only blackbody emissions to be detected., This was achieved by recording the blackbody spectrum emitted from a solid graphite rod placed at the center of the $_{2}$ $_{3}$ tube; the end facing the spectrometer was machined into a concave cone to allow only blackbody emissions to be detected.
 The spectrum was then compared with a theoretical blackbody spectrum at the same temperature and normalized., The spectrum was then compared with a theoretical blackbody spectrum at the same temperature and normalized.
 The detector response curve for Region 2 and the effect on (he line intensities can be seenin Figure 4.., The detector response curve for Region 2 and the effect on the line intensities can be seenin Figure \ref{fig4}. .
"As an example. in Figure (4)) we consider the expected constraints on the BAO scale [rom a hypothetical galaxy survey with 10"" galaxies and bias of 1.5. spread over à volume of 0.8 Cpe? at small redshifts ?.","As an example, in Figure \ref{BAO_chi2}) ) we consider the expected constraints on the BAO scale from a hypothetical galaxy survey with $10^6$ galaxies and bias of 1.5, spread over a volume of 0.8 $^3$ at small redshifts ."
. In Figure (faa). we show the expected power spectrun--errors. normalized to a smooth power spectrum without BAO oscillations. using the fit to the transfer [unction.," In Figure \ref{BAO_chi2}a a), we show the expected power spectrum+errors, normalized to a smooth power spectrum without BAO oscillations, using the \citet{Eisenstein:1997jh} fit to the transfer function."
 The solid curve in Figure (4bb) shows NA? for fitting this spectrum with a different BAO (or sound horizon) scale. marginalizing over the amplitude of the oscillations.," The solid curve in Figure \ref{BAO_chi2}b b) shows $\Delta\chi^2$ for fitting this spectrum with a different BAO (or sound horizon) scale, marginalizing over the amplitude of the oscillations."
 Here. we only include linear scales. conservatively defined as &<0.1Mpe.t. and assume gaussian errors for ACh)—[|àPQ)/(222)]ol?.," Here, we only include linear scales, conservatively defined as $k<0.1 ~{\rm Mpc}^{-1}$, and assume gaussian errors for $\Delta(k) = \left[k^3P(k)/(2\pi^2)\right]^{1/2}$."
 While (he eaussian approximation to (he likelihood (dashed curve in Figure 4bb). is a good approximation-. close to the minimum.H itH grows indefinitely.B. while- the real A\>> saturates al c(S/N7.," While the gaussian approximation to the likelihood (dashed curve in Figure \ref{BAO_chi2}b b), is a good approximation close to the minimum, it grows indefinitely, while the real $\Delta\chi^2$ saturates at $\sim (S/N)^2$."
 In order to reflect this. we propose a simple analytic [function to approximate the (rue difference.B between 4L7 and ils. minimum. value: As shown in Figure (4bb). this takes the quadratie shape of the gaussian approximation close to the minimum since the denominator is then negligible. but Eq. ())," In order to reflect this, we propose a simple analytic function to approximate the true difference between $\chi^2$ and its minimum value: ^2 As shown in Figure \ref{BAO_chi2}b b), this takes the quadratic shape of the gaussian approximation close to the minimum since the denominator is then negligible, but Eq. \ref{dchi}) )"
 guarantees (hat A\? remains smaller than 65/.N)?. of the detection. [far from its minimum. which limits the statistical power of low signal-to-noise detections in constraining parameters.," guarantees that $\Delta\chi^2$ remains smaller than $(S/N)^2$ of the detection, far from its minimum, which limits the statistical power of low signal-to-noise detections in constraining parameters."
 While the interpolating function ()) is in good agreement with the actual A\7. we should note that it is only an approximation. and ideally one should use the full likelihood of the model fitting the data the [ull galaxy power spectrum) for an accurate statistical analvsis.," While the interpolating function \ref{dchi}) ) is in good agreement with the actual $\Delta\chi^2$, we should note that it is only an approximation, and ideally one should use the full likelihood of the model fitting the data the full galaxy power spectrum) for an accurate statistical analysis."
 Finally. Figure (5)) demonstrates (he effect of non-gaussian. posteriors on cosmological constraints.," Finally, Figure \ref{BAO_percival}) ) demonstrates the effect of non-gaussian posteriors on cosmological constraints."
 Here. we compare the eaussian approximation to likelihood «distribution [or distances (o 2=0.2 and :=0.35 in Sloan Digital Skv Survey 2010).. with our expectation from Equation ()).," Here, we compare the gaussian approximation to likelihood distribution for distances to $z=0.2$ and $z=0.35$ in Sloan Digital Sky Survey \citep[SDSS;][]{dr7}, with our expectation from Equation \ref{dchi}) )."
 Given that total S/N for BAO detection in Percivaletal.(2010) is ν10.1 for two degrees of [reedom.we see significant deviations from gaussian likelihoods bevond 99%. confidence level ?..," Given that total $S/N$ for BAO detection in \citet{dr7} is $\sqrt{13.1}$ for two degrees of freedom,we see significant deviations from gaussian likelihoods beyond $99\%$ confidence level ."
"As part of this effort to understand the nature of the evolution of dwarf galaxies, we present (Pilbratt 2010) photometric observation of the nearby (5.1 + 0.6 Mpc (Tosi et al.","As part of this effort to understand the nature of the evolution of dwarf galaxies, we present (Pilbratt 2010) photometric observation of the nearby (5.1 $\pm$ 0.6 Mpc (Tosi et al."
" 2001)) dwarf starburst galaxy, NGC 1705."," 2001)) dwarf starburst galaxy, NGC 1705."
 The galaxy is dominated optically by a massive central super star cluster (SSC) NGC 1705-1 (Meurer et al., The galaxy is dominated optically by a massive central super star cluster (SSC) NGC 1705-1 (Meurer et al.
" 1995), whilst studies in the mid and far-IR (Cannon et al."," 1995), whilst studies in the mid and far-IR (Cannon et al."
 2006; Galametz et al., 2006; Galametz et al.
" 2009) reveal the presence of two bright infrared regions flanking the central SSC, offset by ~250 pc from the SSC, with these off-nuclear regions dominating the global IR emission of NGC 1705."," 2009) reveal the presence of two bright infrared regions flanking the central SSC, offset by $\sim$ 250 pc from the SSC, with these off-nuclear regions dominating the global IR emission of NGC 1705."
" This galaxy provides an ideal environment for exploring the effects of ongoing, massive star formation on the environment within a dwarf galaxy (Cannon et al."," This galaxy provides an ideal environment for exploring the effects of ongoing, massive star formation on the environment within a dwarf galaxy (Cannon et al."
" 2006), given its sub-solar nebular metallicity (Z ~35% Zo; (Lee et al."," 2006), given its sub-solar nebular metallicity (Z $\sim$ $_{\odot}$; (Lee et al."
 2004) and large reservoir of gas (Meurer et al., 2004) and large reservoir of gas (Meurer et al.
" 1998), as we can trace the effects of the SSC on the surrounding interstellar medium, and in particular, can characterize the nature of dust and PAH emission."," 1998), as we can trace the effects of the SSC on the surrounding interstellar medium, and in particular, can characterize the nature of dust and PAH emission."
 NGC 1705 was observed as part of the Dwarf Galaxy Survey programme (PI., NGC 1705 was observed as part of the Dwarf Galaxy Survey programme (PI.
" S. Madden), a Guaranteed Time (GT) key program with the objective of mapping the dust and gas in 51 nearby dwarf galaxies, sampling a broad metallicity range of 1/50 to 1/3 Zo."," S. Madden), a Guaranteed Time (GT) key program with the objective of mapping the dust and gas in 51 nearby dwarf galaxies, sampling a broad metallicity range of 1/50 to 1/3 $_{\odot}$."
 The galaxy was observed by SPIRE (Griffin et al., The galaxy was observed by SPIRE (Griffin et al.
" 2010) at 250, 350 and 500 um for a total of 733 seconds."," 2010) at 250, 350 and 500 $\mu$ m for a total of 733 seconds."
" in scan-map mode with scanning rate 30""/sec, with the final map covering roughly 16 x 16 arcmin."," in scan-map mode with scanning rate 30""/sec, with the final map covering roughly 16 x 16 arcmin."
" The measured 1 o noise level are 5, 6 and 7 mJy beam""! at 250, 350 and 500 um respectively; the noise levels in the images are dominated by confusion."," The measured 1 $\sigma$ noise level are 5, 6 and 7 mJy $^{-1}$ at 250, 350 and 500 $\mu$ m respectively; the noise levels in the images are dominated by confusion."
 The data were processed using the HIPE pipeline (see Pohlen et al. (, The data were processed using the HIPE pipeline (see Pohlen et al. (
"2010) for a detailed description, Swinyard et al. (","2010) for a detailed description, Swinyard et al. ("
2010) for calibration accuracy and Bendo et al. (,2010) for calibration accuracy and Bendo et al. (
2010b) for details on the destriper).,2010b) for details on the destriper).
" The pipeline produces maps with a pixel size of 6.0, 10.0 and 14.0"" at 250, 350 and 500 um respectively."," The pipeline produces maps with a pixel size of 6.0, 10.0 and 14.0"" at 250, 350 and 500 $\mu$ m respectively."
 The ICC has released some interim small correction factors to improve the preliminary calibration., The ICC has released some interim small correction factors to improve the preliminary calibration.
" All flux values derived using the current standard calibration file for the flux conversion, are multiplied by 1.02, 1.05, and 0.94, for the 250um, 350um,"," All flux values derived using the current standard calibration file for the flux conversion, are multiplied by 1.02, 1.05, and 0.94, for the $\mu$ m, $\mu$ m,"
plane is 20°.,plane is $20\degr$.
 The equatorial scattering region is assumed to be at least partly ionised and we therefore assume pure electron scattering with a Thomson optical depth of unity between the inner and outer radius of the wedge., The equatorial scattering region is assumed to be at least partly ionised and we therefore assume pure electron scattering with a Thomson optical depth of unity between the inner and outer radius of the wedge.
 When showing modelling results we take into account existing (anti-)symmetries between the two hemispheres above and below the equatorial plane., When showing modelling results we take into account existing (anti-)symmetries between the two hemispheres above and below the equatorial plane.
 We therefore only discuss the results for viewing directions 0?<i90° (or 1>cosi 0) with i being measured with respect to the symmetry axis of the disk and the torus., We therefore only discuss the results for viewing directions $0\degr < i < 90\degr$ (or $1 > \cos{i} > 0$ ) with $i$ being measured with respect to the symmetry axis of the disk and the torus.
" The spectral modelling of the accretion disc irradiated by an elevated X-ray source confirms previous results, as is shown in Fig. 2.."," The spectral modelling of the accretion disc irradiated by an elevated X-ray source confirms previous results, as is shown in Fig. \ref{fig:disc}."
" The reprocessed spectra reveal iron Ka and Kf fluorescence lines, the associated iron K absorption edge and the broad Comptonised hump centred around 30 keV. Absorption effects mainly due to hydrogen and helium produce an overall positive slope of the normalised reprocessed spectrum."," The reprocessed spectra reveal iron $\alpha$ and $\beta$ fluorescence lines, the associated iron K absorption edge and the broad Comptonised hump centred around 30 keV. Absorption effects mainly due to hydrogen and helium produce an overall positive slope of the normalised reprocessed spectrum."
" Note that in the figure we have omitted the contribution of the directly visible, unpolarised primary radiation to have spectral features in the flux and polarisation spectrum come out more clearly."," Note that in the figure we have omitted the contribution of the directly visible, unpolarised primary radiation to have spectral features in the flux and polarisation spectrum come out more clearly."
" In this modelling case, the polarisation vector, w, is always aligned with the projected symmetry axis."," In this modelling case, the polarisation vector, $\psi$, is always aligned with the projected symmetry axis."
" At on view, when 7 is low, P does not exceed 1 per cent because the scattering geometry is almost symmetric."," At face-on view, when $i$ is low, $P$ does not exceed 1 per cent because the scattering geometry is almost symmetric."
 The polarisation degree then rises with increasing 7 and the scattering medium appears less symmetric with respect to the line-of-sight., The polarisation degree then rises with increasing $i$ and the scattering medium appears less symmetric with respect to the line-of-sight.
" The polarisation degree drops sharply across the iron K lines, which is due to dilution by the unpolarised fluorescent emission."," The polarisation degree drops sharply across the iron K lines, which is due to dilution by the unpolarised fluorescent emission."
" Across the Compton hump the relation between P and i differs from the soft X-ray band, which is due to the Compton scattering phase function that favours forward over backward scattering at higher photon energies."," Across the Compton hump the relation between $P$ and $i$ differs from the soft X-ray band, which is due to the Compton scattering phase function that favours forward over backward scattering at higher photon energies."
 It is instructive to compare these results to the non-relativistic calculations by Matt (1993).., It is instructive to compare these results to the non-relativistic calculations by \citet{matt1993}. .
" Qualitatively, we find the same behaviour of the polarisation degree and angle but the absolute values of P obtained here are lower than for comparable cases shown in fig."," Qualitatively, we find the same behaviour of the polarisation degree and angle but the absolute values of $P$ obtained here are lower than for comparable cases shown in fig."
 4 of Matt(1993)., 4 of \cite{matt1993}.
. This can be explained when considering that the net polarisation degree of the reprocessed radiation results from integrating the reprocessed Stokes flux over the whole disc., This can be explained when considering that the net polarisation degree of the reprocessed radiation results from integrating the reprocessed Stokes flux over the whole disc.
" After one scattering event, the polarisation of the outgoing radiation is directed perpendicularly to the scattering plane, and thus the central parts of the disc produce polarisation angles around i=0? (perpendicular to the symmetry axis) while the outer regions of the disc rather give rise to i)=90? (parallel to the projected symmetry axis)."," After one scattering event, the polarisation of the outgoing radiation is directed perpendicularly to the scattering plane, and thus the central parts of the disc produce polarisation angles around $\psi = 0\degr$ (perpendicular to the symmetry axis) while the outer regions of the disc rather give rise to $\psi = 90\degr$ (parallel to the projected symmetry axis)."
 The net Stokes flux is dominated by the outer parts of the disc but still influenced also by the perpendicular polarisation state coming from the disc centre., The net Stokes flux is dominated by the outer parts of the disc but still influenced also by the perpendicular polarisation state coming from the disc centre.
" Since Matt(1993) included a centralhole in the disc, the impact of the disc centre"," Since \cite{matt1993} included a centralhole in the disc, the impact of the disc centre"
ido.,halo.
 The latter would therelore give an even poorer fit than the spherical case. aud hence is 100 (θά here.," The latter would therefore give an even poorer fit than the spherical case, and hence is not tried here."
 Therefore. in addition to the above parameters. (he axis ratio q is varied as well between 0.1 and 0.9 in steps of 0.1.," Therefore, in addition to the above parameters, the axis ratio $q$ is varied as well between 0.1 and 0.9 in steps of 0.1."
 This gives a total of 47250 grid points to be scanned or each value of p., This gives a total of 47250 grid points to be scanned for each value of $p$.
 We first thoroughly scan this grid to locate the region of mininnun V7., We first thoroughly scan this grid to locate the region of minimum ${\chi}^2$.
 In retrospect. Naravan et al. (," In retrospect, Narayan et al. ("
2005) had pinned the rotation curve at a single point only ie the solar point with Ro — 8.5 kpc) using the local Oort constants “land D. for which the values are available for (he Galaxy.,"2005) had pinned the rotation curve at a single point only (i.e the solar point with R = 8.5 kpc) using the local Oort constants $A$ and $B$, for which the values are available for the Galaxy."
 This effectively fixed the rotation curve locally. with respect to shape as well.," This effectively fixed the rotation curve locally, with respect to shape as well."
 Also. the global trends exhibited by the observed curve was used as (he final criterion to choose the best fit density index (p = 2).," Also, the global trends exhibited by the observed curve was used as the final criterion to choose the best fit density index $p$ = 2)."
 Here. on the other haud. we apply a more rigorous (treatinent by pinning the rotation curve at all the observed points.," Here, on the other hand, we apply a more rigorous treatment by pinning the rotation curve at all the observed points."
 This. in fact. was imperative since the Oort A and £D constants for M31 are not known.," This, in fact, was imperative since the Oort $A$ and $B$ constants for M31 are not known."
 For each of the above eric points. we evaluate (he galactic rotation curve using our (disc plus bulge plus halo) model as follows.," For each of the above grid points, we evaluate the galactic rotation curve using our (disc plus bulge plus halo) model as follows."
" For an exponential disk. (he rotation velocity. 094,02) is given by (Dinnev Tremaine where My is the disk central surface density. £2; the disc scale leneth and yv. =R/2Ry. li being the galactocentric radius."," For an exponential disk, the rotation velocity $v_{disk}(R)$ is given by (Binney Tremaine where $\Sigma_{0}$ is the disk central surface density, $R_{d}$ the disc scale length and y =, R being the galactocentric radius."
" J, and A, (where n=O and 1) are the modified. Bessel functions of the first aud second kind respectively.", $I_{n}$ and $K_{n}$ (where n=0 and 1) are the modified Bessel functions of the first and second kind respectively.
 The above relation is for an infinitesimally (hin disk which we use here for simplicitv., The above relation is for an infinitesimally thin disk which we use here for simplicity.
 For a thick disk. a separate result has to be used (as given in Beequaert Combes 1997). which we check gives à value within <14 of the value given by eq.(10). hence we are justified in using (he above simpler form.," For a thick disk, a separate result has to be used (as given in Becquaert Combes 1997), which we check gives a value within $< 1 \% $ of the value given by eq.(10), hence we are justified in using the above simpler form."
 For the spherical bulge. rotation velocity Crag.(1?) is given by," For the spherical bulge, rotation velocity $v_{bulge}(R)$ is given by"
"potential, we solve the nuclear network locally and then transfer generated energy on the multi-dimensional mesh.","potential, we solve the nuclear network locally and then transfer generated energy on the multi-dimensional mesh."
 The transport of angular momentum may be also approximated by diffusion., The transport of angular momentum may be also approximated by diffusion.
" Since the resultant distributions of thermodynamical quantities and elements will in general be non-uniform on the surface of constant effective potential, we will take their angular averages on the surface and solve the new rotational equilibrium for the obtained equations of state and rotation law."," Since the resultant distributions of thermodynamical quantities and elements will in general be non-uniform on the surface of constant effective potential, we will take their angular averages on the surface and solve the new rotational equilibrium for the obtained equations of state and rotation law."
 This completes the single cycle and the iteration of this process will give the temporal evolution of rotational stars., This completes the single cycle and the iteration of this process will give the temporal evolution of rotational stars.
 We hope that this procedure is feasible and that the formulation presented in this paper will contribute to the study of the influences of non-sphericity on the evolution of rapidly rotating massive stars., We hope that this procedure is feasible and that the formulation presented in this paper will contribute to the study of the influences of non-sphericity on the evolution of rapidly rotating massive stars.
" Numerical computations were in part carried on XT4 and general common use computer system at the center for Computational Astrophysics, CfCA, the National Astronomical Observatory of Japan and on NEC-SX8 at Yukawa Institute for Theoretical Physics in Kyoto University."," Numerical computations were in part carried on XT4 and general common use computer system at the center for Computational Astrophysics, CfCA, the National Astronomical Observatory of Japan and on NEC-SX8 at Yukawa Institute for Theoretical Physics in Kyoto University."
" This study was supported in part by the Grants-in-Aid for the Scientific Research from the Ministry of Education, Science and Culture of Japan (Nos."," This study was supported in part by the Grants-in-Aid for the Scientific Research from the Ministry of Education, Science and Culture of Japan (Nos."
 80251403 and 19104006)., 80251403 and 19104006).
iu Stokes I rom ?..,in Stokes I from \cite{hks+81}.
" The simulator generates visibilities as they would be produced by the MWA correlator. :uxl the array parameters cal be couti«ος, by the user."," The simulator generates visibilities as they would be produced by the MWA correlator, and the array parameters can be controlled by the user."
 In this case the caliration is perfect. tiere js Πο lonosplieric refraction. aud al the poi| sources and diffuse bacseround are intriisically uupolarized.," In this case the calibration is perfect, there is no ionospheric refraction, and all the point sources and diffuse background are intrinsically unpolarized."
 The integration le weΡΕ λα)ely 2 hours aid ouly a siigle kkHz channel cenered at 160.02 MHz was sinulated., The integration time was approximately 2 hours and only a single kHz channel centered at 160.02 MHz was simulated.
 The full obse‘vation has no been similated as the computatio1ial clemmauds are large aud a 'epresentaive inteeation is 'equi‘eck to test the fidelity of le Stokes conversion., The full observation has not been simulated as the computational demands are large and a representative integration is required to test the fidelity of the Stokes conversion.
 The two hour itteeration is sullicie| 1ο enstre 1att je. doibait nolse SOLree in the simulated inap is from sidelobes., The two hour integration is sufficient to ensure that the dominant noise source in the simulated map is from sidelobes.
 Tje linages were producecL by exactly tle salue pipeine as produced the real sky images. except that these 1ages we'e georeratect offine and not in 'eal time.," The images were produced by exactly the same pipeline as produced the real sky images, except that these images were generated offline and not in real time."
 The FOV imaged was also slightly wicler: closer to ., The FOV imaged was also slightly wider: closer to $^\circ$.
 AA has been peeled out he simulated images.e due to perfect calibratio there are no residtals 'emailning.," A has been peeled out the simulated images, due to perfect calibration there are no residuals remaining."
 Figures 1. and 2 contaiu siguilicautly more poi sources than thes lmulation (Figure 7 )., Figures \ref{fig:StokesI_low} and \ref{fig:StokesI_mid} contain significantly more point sources than the simulation (Figure \ref{fig:mapsI}) ).
 These sources are actually in the catalog., These sources are actually in the catalog.
 However the siuation is very consealive when iichucling catalog sources. aud has only iucluded those soi‘ces With [lux meastwemeuts near the MWA observing baud aud that are predicted to be larger than ον.," However the simulation is very conservative when including catalog sources, and has only included those sources with flux measurements near the MWA observing band and that are predicted to be larger than Jy."
 Nevertheless this sinulation gives a good indication of the performance of the systen under more controlled coucitious than the ineasured dataset., Nevertheless this simulation gives a good indication of the performance of the system under more controlled conditions than the measured dataset.
 The RMS brightness of the polarization observatious is approximately of the Stoses { observatious. the point source polarized residual is cousicerably ess than thiS. of J0522-36027 at the very edge of the Q map. and only at the saue poln in the U uap.," The RMS brightness of the polarization observations is approximately of the Stokes I observations, the point source polarized residual is considerably less than this, of J0522–3627 at the very edge of the Q map, and only at the same point in the U map."
 The residial is also a function of position «itlin the primary beam. near the center of the map the residual in QO is nearer and in the U 1laps there is almost no heasttlale association between Stoses { sources and polarized structure in the beam center - except as poarized residuals from tle peeling of AA. The polarized 'eslduals are a feature of üunperfect. calibration of the iicdiviclual antennas.," The residual is also a function of position within the primary beam, near the center of the map the residual in Q is nearer and in the U maps there is almost no measurable association between Stokes I sources and polarized structure in the beam center - except as polarized residuals from the peeling of A. The polarized residuals are a feature of imperfect calibration of the individual antennas."
 The fact that the residuals deteriorate away from |Canu center lends further weight to thus claim: as differences betwee le primary beams become more apparent futher froin tlie beam center., The fact that the residuals deteriorate away from beam center lends further weight to this claim; as differences between the primary beams become more apparent further from the beam center.
 The simulated point sotJyCes lave no intrinsic polarization aud as the calibration js perfect here should be no polarized j»oiut sources in tlie iutegrated maps. uulike the images of je true sky which do display some polarized point source sienals due to 1uperlect «alibration of le primary jeans.," The simulated point sources have no intrinsic polarization and as the calibration is perfect there should be no polarized point sources in the integrated maps, unlike the images of the true sky which do display some polarized point source signals due to imperfect calibration of the primary beams."
 Figures 8 and 9 are featureless in this 'egard. with litle evideice of the exiseuce of any j»oint source features in the uaps.," Figures \ref{fig:mapsQ} and \ref{fig:mapsU} are featureless in this regard, with little evidence of the existence of any point source features in the maps."
 The maps from simulation possess dMfuse polarization despite he fact that the iuput sky is uupolarized., The maps from simulation possess diffuse polarization despite the fact that the input sky is unpolarized.
 This is due to tle polarized sidelobes o ‘the οokes ] emission., This is due to the polarized sidelobes of the Stokes I emission.
 The polarized biehtuess in a elven pixel contaiis contribions from 1ot only the j»olarized sky at that position. but all the sideloyes of the οine and point source eiuissiou in the sky.," The polarized brightness in a given pixel contains contributions from not only the polarized sky at that position, but all the sidelobes of the diffuse and point source emission in the sky."
 The sidelobes are generated with lustrumeual polarization couuneisurate with he position, The sidelobes are generated with instrumental polarization commensurate with the position
"where #=1/3 if! <7, and &2-p/2 otherwise.",where $\kappa = 1/3$ if $\nu' < \nu'_m$ and $\kappa = -p/2$ otherwise.
 Numerically speaking the integration procedure ts as follows., Numerically speaking the integration procedure is as follows.
 First we tabulate A(t.) for à given set of physical parameters. so that we do not need to estimate it analytically but can use its exact dependence on the fluid Lorentz factor instead.," First we tabulate $R(t_e)$ for a given set of physical parameters, so that we do not need to estimate it analytically but can use its exact dependence on the fluid Lorentz factor instead."
 We integrate over ( before we integrate over o. , We integrate over $\theta$ before we integrate over $\phi$ 
is equal to the smoothing scale.,is equal to the smoothing scale.
 Using cluster analysis we have detected two clusters in this sample a triplet and a quintet (8 out of a total of 21 quasars)., Using cluster analysis we have detected two clusters in this sample – a triplet and a quintet (8 out of a total of 21 quasars).
 The z-sizes of both clusters are ~35h.1 Mpce., The $z$ -sizes of both clusters are $\sim 35h^{-1}$ Mpc.
 The estimated. probability to be random is 0.05 and 0.01. respectively.," The estimated probability to be random is $0.05$ and $0.01$, respectively."
 Both of these clusters contribute to the excess of quasar pairs at. separations of 30.40h! Ape., Both of these clusters contribute to the excess of quasar pairs at separations of $30-40h^{-1}$ Mpc.
 ltesults for the BJS2 sample are shown in figs., Results for the BJS2 sample are shown in figs.
 2c and d. The decay of BO) at ic<30h+ Mpe is caused by the Lact that the number density of quasars in this sample is considerably lower than in WI and (ZANDTB and even lower than in BIS] and BJS., 2c and d. The decay of $\Xi(r)$ at $r<30h^{-1}$ Mpc is caused by the fact that the number density of quasars in this sample is considerably lower than in KK and $^2$ B and even lower than in BJS1 and BJS3.
 Εις sample therefore just lacks close pairs., This sample therefore just lacks close pairs.
 The correlation Function Ductuates considerably at scales 1502005 Alpe (there is a significant excess of pairs at these separations as compared to the random distribution)., The correlation function fluctuates considerably at scales $\sim 150-200h^{-1}$ Mpc (there is a significant excess of pairs at these separations as compared to the random distribution).
 These Huetuations correspond to the positive and negative peaks in AGU) at150h| Alpe and ~1805.7 Alpe., These fluctuations correspond to the positive and negative peaks in $\Delta\Theta(r)$ at $\sim 150h^{-1}$ Mpc and $\sim 180h^{-1}$ Mpc.
 Using cluster analysis we have found a triplet (s-size ~205| Ape). à quartet (z-size 20h1 Alpe). and a sextet (z-size 75h Alpe).," Using cluster analysis we have found a triplet $z$ -size $\sim 20h^{-1}$ Mpc), a quartet $z$ -size $\sim 20h^{-1}$ Mpc), and a sextet $z$ -size $\sim 75h^{-1}$ Mpc)."
 The probability that eachindividual cluster is random is smaller than 0.05., The probability that eachindividual cluster is random is smaller than $0.05$.
 Our analysis has shown that the excess of pairs at separations 150200h Alpe is explained by the distance between the quartet and the sextet (Lsof1 Alpe)., Our analysis has shown that the excess of pairs at separations $150-200h^{-1}$ Mpc is explained by the distance between the quartet and the sextet $\sim 180h^{-1}$ Mpc).
 The correlation function for this sample (lig., The correlation function for this sample (fig.
 2e) has two broad “humps” at seales ~LOOM1 Alpe and ~2005.+ Alpe., 2e) has two broad “bumps” at scales $\sim 100h^{-1}$ Mpc and $\sim 200h^{-1}$ Mpc.
 There are two negative peaks in the z;AO(r) corresponding to these fluctuations (Lig., There are two negative peaks in the $\Delta\Theta(r)$ corresponding to these fluctuations (fig.
 21)., 2f).
 Statistical significance of both peaks is 2a., Statistical significance of both peaks is $\sim 2\sigma$.
 The cluster analysis failed to detect any large clusters in this sample., The cluster analysis failed to detect any large clusters in this sample.
 However. the distribution of quasars in this sample is quite interesting.," However, the distribution of quasars in this sample is quite interesting."
 Phere are seven relatively close pairs (distances between quasars in 5 of then are less than 305.+ Mpe and in the other two —407.+ Alpe) separated.olher by either SO.—1005.+ Alpe or 1802005+ Alpe., There are seven relatively close pairs (distances between quasars in 5 of them are less than $30h^{-1}$ Mpc and in the other two $\sim 40h^{-1}$ Mpc) separated by either $80-100h^{-1}$ Mpc or $180-200h^{-1}$ Mpc.
 This causes the [luctuations in Z(r) at the corresponding scales., This causes the fluctuations in $\Xi(r)$ at the corresponding scales.
 The results presented in the previous section suggest that the distribution of quasars in the analvzed. samples is not homogencous at scales of a [ον tens of megaparsecs., The results presented in the previous section suggest that the distribution of quasars in the analyzed samples is not homogeneous at scales of a few tens of megaparsecs.
 Alany quasars belong to clumps of sizes 30TOh5 Alpe., Many quasars belong to clumps of sizes $30-70h^{-1}$ Mpc.
 The clumps are often separated. hy 100200h4 Alpe. which creates a pair excess at the corresponding scales.," The clumps are often separated by $100-200h^{-1}$ Mpc, which creates a pair excess at the corresponding scales."
 Qualitatively this quasar distribution is very similar to that of CIV. absorption svstenmis discussed. in the recent paper by Williger et al. (, Qualitatively this quasar distribution is very similar to that of CIV absorption systems discussed in the recent paper by Williger et al. (
1996).,1996).
 They have found that their CIV sample contains two groups of 7 and 5 absorbers of sizes ~43511e69h7 Ape? and ~25453b% Alpe? (comoving) located at z2.3 and 2~2.5. respectively.," They have found that their CIV sample contains two groups of $7$ and $5$ absorbers of sizes $\sim43\times17\times69h^{-3}$ $^3$ and $\sim25\times4\times53h^{-3}$ $^3$ (comoving) located at $z\sim2.3$ and $z\sim2.5$, respectively."
" The distance between these two groups (~501205+ Alpe) results in ""beating"" (the pair excess) giving rise to the correlation signal at these separations (3.5 significance level).", The distance between these two groups $\sim 50-120h^{-1}$ Mpc) results in “beating” (the pair excess) giving rise to the correlation signal at these separations $3.5\sigma$ significance level).
 A number of smaller clumps were also detected., A number of smaller clumps were also detected.
 The similar clusters of CIV. absorbers were also found in earlier studies bv Jakobsen Perryman (1992). Foltz et al. (," The similar clusters of CIV absorbers were also found in earlier studies by Jakobsen Perryman (1992), Foltz et al. ("
1993). and Dinshaw Impoey (1996).,"1993), and Dinshaw Impey (1996)."
 Recently. Lespine Petitjean (1996) presented evidences for a coherent structure extende over ~SOP54 Alpe at zo2 in the distribution of meta absorption svstems.," Recently, Lespine Petitjean (1996) presented evidences for a coherent structure extended over $\sim80h^{-1}$ Mpc at $z\approx2$ in the distribution of metal absorption systems."
 Although the numbers of CIV systems are also small. the similarity of the results may suggest tha both quasars ancl CIV. absorbers may. trace the same kin of underlying structures in the matter distribution.," Although the numbers of CIV systems are also small, the similarity of the results may suggest that both quasars and CIV absorbers may trace the same kind of underlying structures in the matter distribution."
 Unlike Deng et al. (, Unlike Deng et al. (
1994) we did. not observe any evidence for a periodic signal in the function Or)..,1994) we did not observe any evidence for a periodic signal in the function $\Delta\Theta(r)$.
. This may be cause bv the small number statistics., This may be caused by the small number statistics.
 The clumps. distribution of quasars in the analvze samples is consistent. with the recent studies of the quasar distribution in the larger samples (Crampton. Cowley Hartwick LOST. 1989: Clowes Campusano 1991a. 1991b: Graham. Clowes Campusano 1995: Ixomboerg et al.," The clumpy distribution of quasars in the analyzed samples is consistent with the recent studies of the quasar distribution in the larger samples (Crampton, Cowley Hartwick 1987, 1989; Clowes Campusano 1991a, 1991b; Graham, Clowes Campusano 1995; Komberg et al."
 1996)., 1996).
 These samples were found to contain several relatively rich (~1025 QSOs) groups of quasars with sizes in the redshift clireetion of 70160b+ Mpe., These samples were found to contain several relatively rich $\sim10-25$ QSOs) groups of quasars with sizes in the redshift direction of $\sim70-160h^{-1}$ Mpc.
 Ehe small extent of the pencil-bcam samples perpendicular to the line of sight prevents detection of such large groups., The small extent of the pencil-beam samples perpendicular to the line of sight prevents detection of such large groups.
 However. the detected. smaller clumps can casily be parts of larger systems.," However, the detected smaller clumps can easily be parts of larger systems."
 Lt would be very interesting to check this by studying larger deep samples which are currently. underway (e.g. Hall et al., It would be very interesting to check this by studying larger deep samples which are currently underway (e.g. Hall et al.
 1996)., 1996).
 If quasars anc CIV. absorption systems trace the matter distribution at high redshifts as galaxies or galaxy clusters co at. low redshifts. their clunmipy distribution suggests that. large-scale. inhomogeneitics similar to the nearby superclusters were already. distinct at 2—2.," If quasars and CIV absorption systems trace the matter distribution at high redshifts as galaxies or galaxy clusters do at low redshifts, their clumpy distribution suggests that large-scale inhomogeneities similar to the nearby superclusters were already distinct at $z\sim1-2$."
 This information may provide some useful insights into the physics of high. redshift Universe., This information may provide some useful insights into the physics of high redshift Universe.
 “Phe fact that we see structures at redshifts z~1.2 similar to the superclusters ab o2cO (dxomberg et al., The fact that we see structures at redshifts $z\sim1-2$ similar to the superclusters at $z\sim0$ (Komberg et al.
 1996). for instance. favors low-clensity ACDAL or low-density CDM. models in. which perturbation amplitude at large. scales stops growing at 2cl.," 1996), for instance, favors low-density $\Lambda$ CDM or low-density CDM models in which perturbation amplitude at large scales stops growing at $z\geq 1$."
 On the other hand. rather high ctuasar-quasar correlations at small separations and high number density contrasts in the detected quasar groups may indicate that o. distribution of quasars is highly biased. with respect to re matter distribution.," On the other hand, rather high quasar-quasar correlations at small separations and high number density contrasts in the detected quasar groups may indicate that the distribution of quasars is highly biased with respect to the matter distribution."
 Although present available surveys we too small to provide a statistically reliable estimate X the power spectrum. 264). in the future. with bigger uasar samples and better models for both QSOs and CIV thsorbers. we will be able to ect useful constraints on the μα»eetrum. and thus on the theories of structure formation.," Although present available surveys are too small to provide a statistically reliable estimate of the power spectrum $P(k)$ , in the future, with bigger quasar samples and better models for both QSOs and CIV absorbers, we will be able to get useful constraints on the spectrum, and thus on the theories of structure formation,"
varving between 36.000 ancl 000001 Gn steps of 100019) and AL varving over the [ull range ol the disk moclel grid. (here was no improvement in the fitting and the scale lactor-cderivecl distance was still grossly too large.,"varying between 36,000 and 60,000K (in steps of 1000K) and $\dot{M}$ varying over the full range of the disk model grid, there was no improvement in the fitting and the scale factor-derived distance was still grossly too large."
 Next. we tested. (wo-lemperature fits with a cooler. slowly rotating photosphere and a hot. rapidly spinning. equatorial on as spe from disk accretion.," Next, we tested two-temperature fits with a cooler, slowly rotating photosphere and a hot, rapidly spinning, equatorial belt as expected from disk accretion."
" In (his experiment. we varied the WD Τι"" between 42.000Ix. ancl 60.00Ix."" the accretion belt temperature between 50.000Ix. ancl 60.000Ix. in steps of 1000Ix. and the C and Si abundances of the white dwarl fixed."," In this experiment, we varied the WD $T_{eff}$ between 42,000K and 60,00K, the accretion belt temperature between 50,000K and 60,000K in steps of 1000K and kept the C and Si abundances of the white dwarf fixed."
 Once again. as in the white dwarf plus disk case. there was no improvement in the 47 value.," Once again, as in the white dwarf plus disk case, there was no improvement in the $\chi^2_{\nu}$ value."
 The quality of the model fits to the FUSE spectra of the (wo svstenis is «quite different., The quality of the model fits to the FUSE spectra of the two systems is quite different.
 The fit to SS Aur is verv much in agreement with a model white dwarf atmosphere with log g — 9.0 and Tipp = 33.000Ix. This fit to the FUSE spectrum provides independent confirmation of the results of Lake&Sion(2001) who also found that the [ar UV IUE spectra were dominated bv a hot. massive white dwaif.," The fit to SS Aur is very much in agreement with a model white dwarf atmosphere with log $g$ = 9.0 and $T_{eff}$ = 33,000K. This fit to the FUSE spectrum provides independent confirmation of the results of \citet{lak01} who also found that the far UV IUE spectra were dominated by a hot, massive white dwarf."
 The 7;;; they derived with IUE for the white dwarf in SS Aur was 30.000IX. .--This is surprising because it was widelv felt that the white dwarf in SS Aur was not the svstem was clisk-dominated in the lar UV. auc could not be analvzed unambiguously.," The $T_{eff}$ they derived with IUE for the white dwarf in SS Aur was 30,000K. This is surprising because it was widely felt that the white dwarf in SS Aur was not exposed, the system was disk-dominated in the far UV and could not be analyzed unambiguously."
 In SS Aur. it dis also highly significant that there is little evidence of an additional hot component other (han a single temperature white dwar! photosphere.," In SS Aur, it is also highly significant that there is little evidence of an additional hot component other than a single temperature white dwarf photosphere."
 The absence of (1175 À)) absorption in the FUSE spectrum suggests the possibility that the white dwarl is deficient in carbon., The absence of (1175 ) absorption in the FUSE spectrum suggests the possibility that the white dwarf is deficient in carbon.
 If so. (his could be an indication (hat past thermonuclear processing (ancient novae) depleted the carbon.," If so, this could be an indication that past thermonuclear processing (ancient novae) depleted the carbon."
 This possibility is supported by the indication that the N-abundance in the SS Aur WD surface lavers is elevated above solar., This possibility is supported by the indication that the N-abundance in the SS Aur WD surface layers is elevated above solar.
 An alternative picture discussed by Gausickeetal.(2003). suggest that theN/C anomaly seen in the cbwarf novae BZ UMa. EY Cvg. IRNS J232953.9--062814. and now CIIUMa may have its origin ina CV with an originally more massive donor star (Alo>1.5M. ) which survived thermal time scale mass transfer (Schenkeretal.(2002) and references (herein).," An alternative picture discussed by \citet{gan03} suggest that the N/C anomaly seen in the dwarf novae BZ UMa, EY Cyg, 1RXS J232953.9+062814, and now CH UMa \citep{dul02,dul04} may have its origin in a CV with an originally more massive donor star $M_{2} > 1.5 M_{\odot}$ ) which survived thermal time scale mass transfer \citet{sch02} and references therein)."
 In such asvstem. the white cdwarl would be accreting from the peeled away CNO-processed core stripped of its outer lavers during the (thermal timescale mass transfer.," In such a system, the white dwarf would be accreting from the peeled away CNO-processed core stripped of its outer layers during the thermal timescale mass transfer."
 Ou FUSE spectrum of RU Peg likewise reveals à very hot white dwarf in agreement with the analvsis of the IUE archival spectra of RU Peg in quiescence., Our FUSE spectrum of RU Peg likewise reveals a very hot white dwarf in agreement with the analysis of the IUE archival spectra of RU Peg in quiescence.
 We find that Τε = 49.000Ix for the white dwarf. is very close to the νε derived by Sion&Urban (2002)..," We find that $T_{eff}$ = 49,000K for the white dwarf, is very close to the $T_{eff}$ derived by \citet{sio02}. ."
2000 by FGMO03.,2000 by FGM03.
 Outside of the flare the spectral parameters do not vary significantly and their average values (see below) are similar to the 2000 values (FGMO3). as is the X-ray luminosity (1.510 η).," Outside of the flare the spectral parameters do not vary significantly and their average values (see below) are similar to the 2000 values (FGM03), as is the X-ray luminosity $1.5\times 10^{30}$ )."
 To derive the flaring emission spectral parameters. we applied the same procedure as for V827 Tau.," To derive the flaring emission spectral parameters, we applied the same procedure as for V827 Tau."
 The quiescent spectral parameters are N(H)=2.43x107 επι. KT= keV. EM=140xI0? em. and Z=0.6Zs. and the resulting spectral parameters for the flaring component are listed in Table 5..," The quiescent spectral parameters are $=2.43 \times 10^{22}~{\rm cm^{-2}}$ , $kT=3.10$ keV, $E\!M= 1.40
\times 10^{53}$ $^{-3}$, and $Z=0.6~Z_{\odot}$, and the resulting spectral parameters for the flaring component are listed in Table \ref{tab:hl_flare}."
 The event shows a peculiar evolution. with a monotonically decaying light curve associated with a highly irregular temperature evolution.," The event shows a peculiar evolution, with a monotonically decaying light curve associated with a highly irregular temperature evolution."
 The temperature has two well-defined peaks above 7 keV separated by a deep minimum at about 3 keV. The temperature evolution suggests that this 1s the combination of two flares. probably physically related to each other but occurring in independent coronal structures.," The temperature has two well-defined peaks above 7 keV separated by a deep minimum at about 3 keV. The temperature evolution suggests that this is the combination of two flares, probably physically related to each other but occurring in independent coronal structures."
 This kind of evolution has been predicted by modeling two independent flares by Reale.Güdel.Peres.&Audard(2004)., This kind of evolution has been predicted by modeling two independent flares by \cite*{rgp+2004}.
. In order to support this hypothesis. we modeled the event by combining two flares computed with detailed hydrodynamie modeling of plasma confined in a coronal loop.," In order to support this hypothesis, we modeled the event by combining two flares computed with detailed hydrodynamic modeling of plasma confined in a coronal loop."
 The light curve decay time suggests long flaring structures citealpsrj+91)). so that we considered each model flare to be identical to the one used to describe one of the flares observed during the COUP campaign (Favataetal.. 2005)) in detail.," The light curve decay time suggests long flaring structures \\citealp{srj+91}) ), so that we considered each model flare to be identical to the one used to describe one of the flares observed during the COUP campaign \citealp{ffr+2005}) ) in detail."
 We assumed that each flare occurs in a coronal loop with à constant cross-section anc half-length L=107 em. symmetric around the loop apex.," We assumed that each flare occurs in a coronal loop with a constant cross-section and half-length $L = 10^{12}$ cm, symmetric around the loop apex."
 Both flares were triggered by injecting a heat pulse in the loop. which was initially at à temperature of =20 MK.," Both flares were triggered by injecting a heat pulse in the loop, which was initially at a temperature of $\simeq 20$ MK."
" This heat pulse is symmetrically deposited at the loop footpoints with a Gaussian spatial distribution of intensity 10 ergem ""land width 10!"" em (1/100 of the loop half-length).", This heat pulse is symmetrically deposited at the loop footpoints with a Gaussian spatial distribution of intensity 10 erg $^{-3}$ $^{-1}$ and width $10^{10}$ cm (1/100 of the loop half-length).
 After 20 ks the heat pulse was switched off completely., After 20 ks the heat pulse was switched off completely.
 From the evolution of the plasma density and temperature along the loop computed with the Palermo-Harvard hydrodynamic loop model (Peresetal..1982.. Bettaetal..1997)). we synthesized the corresponding EPIC spectra of the loop throughout the flare. deriving a light curve and the evolution of temperature.," From the evolution of the plasma density and temperature along the loop computed with the Palermo-Harvard hydrodynamic loop model \citealp{psv+82}, \citealp{bpr+97}) ), we synthesized the corresponding EPIC spectra of the loop throughout the flare, deriving a light curve and the evolution of temperature."
 To model the HL Tau event we duplicated. the resulting light curve and temperature evolution with à time shift.," To model the HL Tau event we duplicated, the resulting light curve and temperature evolution with a time shift."
 The two flares are identical flares. except for a normalization factor. which represents the loop cross-section and does not enter explicitly in the hydrodynamic modeling.," The two flares are identical flares, except for a normalization factor, which represents the loop cross-section and does not enter explicitly in the hydrodynamic modeling."
 The second flare has a normalization factor of 0.3 aa correspondingly smaller cross-section) and it starts 60 ks after the first., The second flare has a normalization factor of 0.3 a correspondingly smaller cross-section) and it starts 60 ks after the first.
 We summed the resulting two asynchronous sequences of flare spectra and obtained a single sequence of spectra. which we integrated to derive a single light curve and fit with single temperature EPIC model spectra.," We summed the resulting two asynchronous sequences of flare spectra and obtained a single sequence of spectra, which we integrated to derive a single light curve and fit with single temperature EPIC model spectra."
 Figure 14 shows the resulting light curve and temperature evolution as compared to those obtained from the data., Figure \ref{fig:hlflare} shows the resulting light curve and temperature evolution as compared to those obtained from the data.
 The model temperatures in the first flare are somewhat higher than the observed one. but the main flare characteristics. tthe monotonic light curve and the temperature dip. are reproduced by the double-flare model well — although the model is not unique.," The model temperatures in the first flare are somewhat higher than the observed one, but the main flare characteristics, the monotonic light curve and the temperature dip, are reproduced by the double-flare model well – although the model is not unique."
 Since no constraint can be derived from the data. each of the two flares was modeled with no significant residual heating present during the flare decay citealprbp+97)).," Since no constraint can be derived from the data, each of the two flares was modeled with no significant residual heating present during the flare decay \\citealp{rbp+97}) )."
 Such modeling implies very large flaring structures. similar to the ones found in ONC YSOs by Favataetal.(2005) — where the data allowed investigation of the presence of sustained heating.," Such modeling implies very large flaring structures, similar to the ones found in ONC YSOs by \cite{ffr+2005} – where the data allowed investigation of the presence of sustained heating."
 Such large structures. with L= 5R.. have only been found in YSOs. and were interpreted by Favataetal.(2005) as linking the star to the aceretion disk. aas being the magnetic structures supporting the magnetospheric accretion.," Such large structures, with $L \simeq
5\,R_*$ , have only been found in YSOs, and were interpreted by \cite{ffr+2005} as linking the star to the accretion disk, as being the magnetic structures supporting the magnetospheric accretion."
 In addition to the evidence from the ONC YSOs. HL Tau is the first Taurus YSO in which such large flaring structures have been detected.," In addition to the evidence from the ONC YSOs, HL Tau is the first Taurus YSO in which such large flaring structures have been detected."
 We cannot a priori exclude that shorter loops with sustained heating in the decay may also reproduce the features of this flare., We cannot a priori exclude that shorter loops with sustained heating in the decay may also reproduce the features of this flare.
 However. the long delay of the model flares required to reproduce the distant temperature peaks suggests that very large structures must be involved in the flare (Realeetal.. 2004)).," However, the long delay of the model flares required to reproduce the distant temperature peaks suggests that very large structures must be involved in the flare \citealp{rgp+2004}) )."
 Unlike the other stars in the present study. 2285845 (an active binary system) is not à member of the star-forming region. on the basis of its radial velocity and. proper motion (Walteretal.. 1988)).," Unlike the other stars in the present study, 285845 (an active binary system) is not a member of the star-forming region, on the basis of its radial velocity and proper motion \citealp{wbm+88}) )."
 The primary spectral type is G8. and Schneideretal.(1998) report a separation of 73 mas and a magnitudedifference of 1.19 mag.," The primary spectral type is G8, and \cite{shw98}
 report a separation of 73 mas and a magnitudedifference of 1.19 mag."
 In the 2000 observation. 2285845 showed significant variability. and similar behavior is present in. the present data set (Fig. 15))," In the 2000 observation, 285845 showed significant variability, and similar behavior is present in the present data set (Fig. \ref{fig:hdall}) )."
 Table 12— summarizes the best-fit, Table \ref{tab:hd_all11pn} summarizes the best-fit
"The joint distribution in z and. /. in presenceof the M—L luminosity (equation (16)]) ls The mean red-shift is The number clensitv of galaxies per unit [Iux interval is The number of galaxies as given bv formula (38)) has à maximum al 2,4, where A comparison between the observed and theoretical number of galaxies as given by the M—-L [function is reported in Figure 13. where the 2dF Galaxy. Redshift Survey is considered ancl in Figure 14 where the 6dE Galaxy Survey is considered.","The joint distribution in $z$ and $f$, in presenceof the ${\mathcal M}-L$ luminosity (equation \ref{equation_schechter_mia}) )) is The mean red-shift is The number density of galaxies per unit flux interval is The number of galaxies as given by formula \ref{nfunctionz_mia}) ) has a maximum at $z_{max}$ where A comparison between the observed and theoretical number of galaxies as given by the ${\mathcal M}-L$ function is reported in Figure \ref{maximum} where the 2dF Galaxy Redshift Survey is considered and in Figure \ref{maximum_6d} where the 6dF Galaxy Survey is considered."
 One method to deduce the mass of a star by its absolute visual magnitude is presented: ihe mass of a galaxy is deduced by analogy., One method to deduce the mass of a star by its absolute visual magnitude is presented; the mass of a galaxy is deduced by analogy.
 In the case of the galaxies. the bolometric correction of the stus will be replaced bv the sun's absolute magnitude and mass-Inninosity ratio different in each selected band.," In the case of the galaxies, the bolometric correction of the stars will be replaced by the sun's absolute magnitude and mass-luminosity ratio different in each selected band."
 In the case of the stars il is possible to parameterise (he mass of the star. My . as a [unction of the observable colour (23—V). see Zaninetli (2005)..," In the case of the stars it is possible to parameterise the mass of the star , ${\mathcal M_S}$ , as a function of the observable colour $(B-V)$, see \cite{zaninetti05} ."
. The first equation connectsthe (5—V) colour with the temperature, The first equation connectsthe $(B-V)$ colour with the temperature
»220 ms7!. of which 43 exhibit significant periodicities.,"20 m$^{-1}$, of which 43 exhibit significant periodicities."
coniplicate processes is far bevoud the scope of this Letter.,complicate processes is far beyond the scope of this Letter.
 Nonetheless. the actual flux may uot be far dinuuer than our prediction since averagelv speaking. the LFs of the slow u-shells aud the i-shells are significantly different. but their masses are comparable.," Nonetheless, the actual flux may not be far dimmer than our prediction since averagely speaking, the LFs of the slow n-shells and the i-shells are significantly different, but their masses are comparable."
 So the interaction of them can power a bright UV flash iu the range ~Lot1050., So the interaction of them can power a bright UV flash in the range $\sim 10^{13}-10^{15}{\rm cm}$.
 Y. Z. F thanks T. Lu aud Z. Li for their long-term chcouragcinent on the subject of ueutrou-fed CRBs., Y. Z. F thanks T. Lu and Z. Li for their long-term encouragement on the subject of neutron-fed GRBs.
 We also thauk the anomvmous referee for herμας coustructive conunents., We also thank the anonymous referee for her/his constructive comments.
 This work is supported by the National Natural Scicuce Foundation (erauts 1052325011 and 10233010). the National 973 Project ou Fundamental Researches of China (NINBRSF C19990751).," This work is supported by the National Natural Science Foundation (grants 10225314 and 10233010), the National 973 Project on Fundamental Researches of China (NKBRSF G19990754)."
 This work is in memory of Chanehu. Zhang (Chaneanu University. Clina). Y. Z. Fos university plivsics teacher. who has passed away ou 2001 September 6.," This work is in memory of Changlin, Zhang (Chang'an University, China), Y. Z. F's university physics teacher, who has passed away on 2004 September 6."
a gravitationally unstable disk (e.g.Vorobyov or by the core accretion mechanism (e.g.Pollacketal.1996).,a gravitationally unstable disk \citep[e.g.][]{vorobyov10} or by the core accretion mechanism \citep[e.g.][]{pollack96}.
". Indeed for both scenarios the disks would need to be unusually large and massive, but even then, the formation timescale by core accretion would be prohibitively long while the efficiency of disk instability to produce such companions is highly uncertain (Vorobyov&Basu2010;Kratteretal. 2010)."," Indeed for both scenarios the disks would need to be unusually large and massive, but even then, the formation timescale by core accretion would be prohibitively long while the efficiency of disk instability to produce such companions is highly uncertain \citep{vorobyov10, kratter10}."
". Nevertheless, it is possible that these companions did form in a planet-like manner much closer to the star, but were subsequently kicked outward through gravitational interactions (e.g.Scharf&Menou2009;Verasetal.2009)."," Nevertheless, it is possible that these companions did form in a planet-like manner much closer to the star, but were subsequently kicked outward through gravitational interactions \citep[e.g.][]{scharf09,veras09}."
". In this scenario, according to the simulations of Verasetal. (2009),, the timescale for instabilities to develop and send planets on large orbits may be quite short (0.01-1 Myr), with significant dynamical evolution occurring within the first few Myr."," In this scenario, according to the simulations of \citet{veras09}, the timescale for instabilities to develop and send planets on large orbits may be quite short (0.01-1 Myr), with significant dynamical evolution occurring within the first few Myr."
" However, owing to further evolution, planets quickly scattered on large orbits are to be ejected from the system after a few tens of Myr."," However, owing to further evolution, planets quickly scattered on large orbits are likely to be ejected from the system after a few tens of Myr."
" likelyAlternatively, these wide and low mass ratio companions could form like stellar binaries, through the fragmentation of a pre-stellar core (e.gBate2009;Bateetal. 2003)."," Alternatively, these wide and low mass ratio companions could form like stellar binaries, through the fragmentation of a pre-stellar core \citep[e.g][]{bate09,bate03}."
". Numerical simulations indicate that very low mass ratio companions can indeed be produced by this process, albeit rarely, and that they preferentially have large separations and are generally found in high order multiple systems."," Numerical simulations indicate that very low mass ratio companions can indeed be produced by this process, albeit rarely, and that they preferentially have large separations and are generally found in high order multiple systems."
 Future observations may provide constraints to exclude or support the various formation possibilities of these wide low mass companions., Future observations may provide constraints to exclude or support the various formation possibilities of these wide low mass companions.
" For instance, if they formed in a planet-like manner closer to the star and were subsequently kicked outward through gravitational interactions, then it would be expected that additional companions of similar mass or even heavier should be present in the systems, at smaller separations."," For instance, if they formed in a planet-like manner closer to the star and were subsequently kicked outward through gravitational interactions, then it would be expected that additional companions of similar mass or even heavier should be present in the systems, at smaller separations."
" In addition, as mentioned above, distant companions produced through this process would likely be eventually ejected from the system, such that they should be found more in than around older stars."," In addition, as mentioned above, distant companions produced through this process would likely be eventually ejected from the system, such that they should be found more frequently in star-forming regions than around older stars."
" In our frequentlyoverall survey of star-formingUpper regionsScorpius that led to the discovery of aand IRXS J1609-2105b, we observed 91 stars (masses 0.15-5 Mo)), so taken at face value, our two discoveries imply that companions with mass ratios below 0.01 and separations of hundreds of AUs exist in credibility) of stellar systems."," In our overall survey of Upper Scorpius that led to the discovery of and 1RXS J1609-2105b, we observed 91 stars (masses 0.15-5 ), so taken at face value, our two discoveries imply that companions with mass ratios below 0.01 and separations of hundreds of AUs exist in $_{-1.9}^{+5.5}$ credibility) of stellar systems."
" Considering that we 2.243%did not achieve the same sensitivity for all targets as well as our incompleteness to lower mass ratio companions, this number is only a lower limit."," Considering that we did not achieve the same sensitivity for all targets as well as our incompleteness to lower mass ratio companions, this number is only a lower limit."
 The statistics are not yet sufficient to tell whether there exists a difference for older , The statistics are not yet sufficient to tell whether there exists a difference for older objects.
"For the of Lafreniéreetal.(2007),, which objects.targeted ~200 exampleMyr-old studyGKM stars, enabled placing upper limits of ~6% credibility) for companions of ~10 ((i.e. mass ratio ~0.01); Mjupsee also Chauvinetal.(2010) and Nielsen&Close(2010)."," For example the study of \citet{lafreniere07}, which targeted $\sim$ 200 Myr-old GKM stars, enabled placing upper limits of $\sim$ credibility) for companions of $\sim$ 10 (i.e. mass ratio $\sim$ 0.01); see also \citet{chauvin10} and \citet{nielsen10}."
. Improving the statistics for both young and older systems would thus be a good way to investigate further the importance of gravitational scattering in accounting for distant companions., Improving the statistics for both young and older systems would thus be a good way to investigate further the importance of gravitational scattering in accounting for distant companions.
" This approach is valid as long as the internal dynamics of the multiple planets dominates over interactions with other stars or giant molecular clouds as the travels the galaxy, as these interactions can also systemstrip out wide throughcompanions."," This approach is valid as long as the internal dynamics of the multiple planets dominates over interactions with other stars or giant molecular clouds as the system travels through the galaxy, as these interactions can also strip out wide companions."
 This can be roughly checked using the results of Weinbergetal. (1987)., This can be roughly checked using the results of \citet{weinberg87}.
". Based on their figure 2, with a/Mi~ pc M, the disruption lifetime of HIP 78530AB due to encounters with stars and giant molecular clouds is larger than 10 Gyr; this is also the case for IRXS J160929.1—210524Ab."," Based on their figure 2, with $a/M_{\rm tot}\sim0.0014$ pc $^{-1}$, the disruption lifetime of HIP 78530AB due to encounters with stars and giant molecular clouds is larger than 10 Gyr; this is also the case for 1RXS J160929.1--210524Ab."
" In other words, stellar and molecular clouds encounters have little impact on the evolution of companions such as the ones we have found."," In other words, stellar and molecular clouds encounters have little impact on the evolution of companions such as the ones we have found."
" The new companion reported in this paper joins a growing list of low-mass substellar companions (S25 in wide orbit (2100 AU) around stars, which now Mjup))counts about ten objects (see Lafreniéreetal.(2010) for a recent compilation, see also Fig. 9))."," The new companion reported in this paper joins a growing list of low-mass substellar companions $\la$ 25 ) in wide orbit $\ga$ 100 AU) around stars, which now counts about ten objects (see \citet{lafreniere10} for a recent compilation, see also Fig. \ref{fig:qvssep}) )."
 These companions are found around primaries covering a wide range of masses and even around primaries that are themselves binaries., These companions are found around primaries covering a wide range of masses and even around primaries that are themselves binaries.
" Thus, while the statistics on their may not be accurate, it seems likely that wide frequencylow-mass substellar verycompanions are not an unusual outcome of the star formation process, yet they remain hard to explain within current theoretical frameworks."," Thus, while the statistics on their frequency may not be very accurate, it seems likely that wide low-mass substellar companions are not an unusual outcome of the star formation process, yet they remain hard to explain within current theoretical frameworks."
" Over the next few years, additional searches for new companions and continued efforts to characterize the known ones should allow us to make good progress toward explaining their formation."," Over the next few years, additional searches for new companions and continued efforts to characterize the known ones should allow us to make good progress toward explaining their formation."
 We thank the Gemini staff for help and support with the observations., We thank the Gemini staff for help and support with the observations.
" The authors also wish to thank Marten van Kerkwijk, Alexis Brandeker, Christian Marois and Ettienne Artigau for useful discussion or help regarding some aspects of this work."," The authors also wish to thank Marten van Kerkwijk, Alexis Brandeker, Christian Marois and Éttienne Artigau for useful discussion or help regarding some aspects of this work."
 RJ acknowledges support from NSERC grants and a Royal Netherlands Academy of Arts and Sciences, RJ acknowledges support from NSERC grants and a Royal Netherlands Academy of Arts and Sciences
In addition. when at a given step we have different extrapolation procedures depending of the flux of the source. we do not switeh abruptly from one regime to the other. but we adopt a linear transition between the two with a width which is the greater of LOOmJy and 10% of the threshold flux.,"In addition, when at a given step we have different extrapolation procedures depending of the flux of the source, we do not switch abruptly from one regime to the other, but we adopt a linear transition between the two with a width which is the greater of $100$ mJy and $10\%$ of the threshold flux."
 Moreover. we do not consider polarization.," Moreover, we do not consider polarization."
" This approach provides both the probability that a source with an VSS flux 5,4 will have a 94 GHz flux σος Le. (S01)S101). as well as the complementary distribution 205)ασ)."," This approach provides both the probability that a source with an NVSS flux $S_{1.4}$ will have a 94 GHz flux $S_{94}$, i.e. $P(S_{94}|S_{1.4})$, as well as the complementary distribution $P(S_{1.4}|S_{94})$."
" In figure 3 we plot the distribution of the initial 1.4 GHz fluxes for sources with tinal 94 GHz fluxes of So,~0.01.—0.10 and —1.0 Jy. which wovides an estimate of (9,4|S64)."," In figure \ref{fig:backhist} we plot the distribution of the initial 1.4 GHz fluxes for sources with final 94 GHz fluxes of $S_{94} \sim 0.01, \sim 0.10$ and $\sim 1.0$ Jy, which provides an estimate of $P(S_{1.4}|S_{94})$."
 The plots refer to the full set of 800 simulations., The plots refer to the full set of 800 simulations.
 Figure 4 shows instead {σοιση)., Figure \ref{fig:frwdhist} shows instead $P(S_{94} | S_{1.4})$.
 A general expectation is that for flux levels relevant to CMB experiments. the iigh frequency population of sources is dominated by objects with flat spectral indexes.," A general expectation is that for flux levels relevant to CMB experiments, the high frequency population of sources is dominated by objects with flat spectral indexes."
 We recover this behaviour in the simulations. as shown in figures 3. and 4.," We recover this behaviour in the simulations, as shown in figures \ref{fig:backhist}
 and \ref{fig:frwdhist}."
" In particular, according to the discussion of section 2.. the residual contamination in WMAP maps will be dominated by sources with S=0.1 Jy in the frequency range 600 GHz. and we expect the majority of these sources to have Syz I00mlv."," In particular, according to the discussion of section \ref{sec:ped}, the residual contamination in WMAP maps will be dominated by sources with $S \gtrsim 0.1$ Jy in the frequency range $60-90$ GHz, and we expect the majority of these sources to have $S_{1.4} \gtrsim 100$ mJy."
 Inaccuracy in the extrapolations of sources with lower Sy.) will have a minimal impact on estimates of the residual contamination in WMAP maps., Inaccuracy in the extrapolations of sources with lower $S_{1.4}$ will have a minimal impact on estimates of the residual contamination in WMAP maps.
 For each simulation. we compute the corresponding differentia number counts dS)/dS and then average over the whole set of simulations.," For each simulation, we compute the corresponding differential number counts $dn(S)/dS$ and then average over the whole set of simulations."
 In figure 5. we compare the incomplete counts from WMAPS source catalog with the ensemble average differentia counts at the frequencies of 33.41.61 and 94 GHz. approximately corresponding to the central frequencies of WMAP Ka. Q. V anc W bands.," In figure \ref{fig:eucl_counts} we compare the incomplete counts from WMAP5 source catalog with the ensemble average differential counts at the frequencies of $33, 41, 61$ and $94$ GHz, approximately corresponding to the central frequencies of WMAP Ka, Q, V and W bands."
 At 33 GHz we compare our estimation also with results from CBI. VSA. and DASI surveys. while at 94 GHz we also plo prediction from earlier works (deZottietal.2005:Waldram 2007)..," At 33 GHz we compare our estimation also with results from CBI, VSA, and DASI surveys, while at 94 GHz we also plot prediction from earlier works \citep{2005A&A...431..893D,2007MNRAS.379.1442W}."
 Comparison with lower flux data at 35 GHz. shows that the methods discussed here tends to underestimate source counts below S~0.02.0.03 Jy.," Comparison with lower flux data at $33$ GHz, shows that the methods discussed here tends to underestimate source counts below $S \sim
0.02-0.03$ Jy."
 These sources do not provide a relevant contribution to the total residual contamination to WMAP spectra. but will play a more relevant role for Planck data analysis.," These sources do not provide a relevant contribution to the total residual contamination to WMAP spectra, but will play a more relevant role for Planck data analysis."
 Since, Since
The anisotropy parameter of the expiusiou and thus the anisotropy energv deusity are found to be nou-cynical. The deviation-free EoS parameter of the fluid is obtained as follows: The skewness paramcter of the EoS paruneter is obtained as follows: One can check that this solutiou vields (19).,"The anisotropy parameter of the expansion and thus the anisotropy energy density are found to be non-dynamical, The deviation-free EoS parameter of the fluid is obtained as follows: The skewness parameter of the EoS parameter is obtained as follows: One can check that this solution yields (19)."
 The directional IIubble parameters. the anisotropy of the expansion (thus. the anisotropy cucrey density) aud the directional EoS paramicters are all constants throughout the historv of the universe.," The directional Hubble parameters, the anisotropy of the expansion (thus, the anisotropy energy density) and the directional EoS parameters are all constants throughout the history of the universe."
 It is obvious that px 3h. thus paxAA? and A<2.," It is obvious that $\rho\leq3k^{2}$ , thus $\rho_{\beta}\leq3k^{2}$ and $\Delta\leq2$."
 We recover the conventional vacuuu energy and isotropic expansion when p=347. because iw= 1. ~=0Oaund A=0 in that case.," We recover the conventional vacuum energy and isotropic expansion when $\rho=3k^{2}$, because $w=-1$ , $\gamma=0$ and $\Delta=0$ in that case."
 However. when p«347. both the expansion and the fluid deviate frou isotropy. because dq0m Ls«UO or uw« Ls>0 aud 0 in this case.," However, when $\rho<3k^{2}$, both the expansion and the fluid deviate from isotropy, because $w>-1$, $\gamma<0$ or $w<-1$, $\gamma>0$ and $\Delta>0$ in this case."
 It can be observed that. while the EoS pariter on the ος axis is in the quiutessence region (ue2 l1) the oues on the y aud : axes are in the phantom region (w|5κ— 1) or vice versa.," It can be observed that, while the EoS parameter on the $x$ axis is in the quintessence region $w>-1$ ), the ones on the $y$ and $z$ axes are in the phantom region $w+\gamma<-1$ ), or vice versa."
 According to this. while the expansion of the wv axis acts so as to decrease the energy deusitv of the fluid. the expansion of the yz plane acts so as to increase the energv density of the fuid or vice versa.," According to this, while the expansion of the $x$ axis acts so as to decrease the energy density of the fluid, the expansion of the $yz$ plane acts so as to increase the energy density of the fluid or vice versa."
 However. iu total. the decrements aud. increments comipeusate for each other aud the energy density of the fluid does not change.," However, in total, the decrements and increments compensate for each other and the energy density of the fluid does not change."
 Ou inotivatiug from the increasing evidence for the need of a geometry that resembles Bianchi morphology to explain the observed anisotropy in the WALAP data. we have discussed some features of the Bianchi type-I universes iu the presence of a fiuid that wields an anisotropic equation of state (EoS) parameter iu eeneral relativity.," On motivating from the increasing evidence for the need of a geometry that resembles Bianchi morphology to explain the observed anisotropy in the WMAP data, we have discussed some features of the Bianchi type-I universes in the presence of a fluid that wields an anisotropic equation of state (EoS) parameter in general relativity."
 We have focused ou those 11odels that exhibit de Sitter volumetric expansion iu the presence of a hypothetical fluid obtained bv distorting the EoS paraiueter of the couventional vactuun energy in a way so ax to wield anisotropy., We have focused on those models that exhibit de Sitter volumetric expansion in the presence of a hypothetical fluid obtained by distorting the EoS parameter of the conventional vacuum energy in a way so as to wield anisotropy.
 We have also given two exact solutious within the locally rotationally svauinetrie Biauchi tvpe-I framework, We have also given two exact solutions within the locally rotationally symmetric Bianchi type-I framework.
 Iu both models the effective euergv deusity (the sum of the energv density of the πια aud the anisotropy energv density) has been assumed to be constant so as o secure the de Sitter volumetric expansion., In both models the effective energy density (the sum of the energy density of the fluid and the anisotropy energy density) has been assumed to be constant so as to secure the de Sitter volumetric expansion.
 Iu the firs uodel. the directional EoS parameter on je c axis las been assumed to be -1.," In the first model, the directional EoS parameter on the $x$ axis has been assumed to be -1."
 The anisotropy of 1e expansion. the energy density aud the anisotropy of ie fiuid. have been found to be dynamical.," The anisotropy of the expansion, the energy density and the anisotropy of the fluid have been found to be dynamical."
 While the anisotropv of the expansion aud the anisotropy of the Huid decrease and teud to null as the uuiverse expands. 1e enerev deusity of the fluid increases aud approaches ο. its inaxinuni value.," While the anisotropy of the expansion and the anisotropy of the fluid decrease and tend to null as the universe expands, the energy density of the fluid increases and approaches to its maximum value."
" The finid approximates the conventional vactuun energy as the universe evolves,", The fluid approximates the conventional vacuum energy as the universe evolves.
 Iu the second model. the energy deusitv of the fid das been asstuned to be coustaut.," In the second model, the energy density of the fluid has been assumed to be constant."
 The anisotropy. of he expansion aud the anisotropy of the fiuid have Όσοι ound to be non-dvuanucal., The anisotropy of the expansion and the anisotropy of the fluid have been found to be non-dynamical.
 When the αλαπια value of the cucrey density of the fluid (342. where kis a yositive constant) is considered. the universe expands isotropically aud the τις ήος the conventional vacunuu enerev.," When the maximum value of the energy density of the fluid $3k^{2}$, where $k$ is a positive constant) is considered, the universe expands isotropically and the fluid mimics the conventional vacuum energy."
 Lower values of the euergv density of he fluid eive rise to an anisotropy both iu the expansion and Eos parameter of the fluid., Lower values of the energy density of the fluid give rise to an anisotropy both in the expansion and EoS parameter of the fluid.
 Ozzeün Akagsu was supported iu part by The Scicutific and Technological Research Council of Turkey (TUBBITTAL)., Özzgürr Akarsu was supported in part by The Scientific and Technological Research Council of Turkey (TÜBBİTTAK).
 Some of this work was carried out while O.. Akarsu was visiting the Department of Applied Mathematics audTheoretical Physics (DAMTP) University ofCambridge.," Some of this work was carried out while Ö.. Akarsu was visiting the Department of Applied Mathematics andTheoretical Physics (DAMTP), University ofCambridge."
 O.. Alausu would also like to thauk Jonathan Middleton for the discussions he had with lim., Ö.. Akarsu would also like to thank Jonathan Middleton for the discussions he had with him.
The fraction of the total (stellar + cliffuse) FUWV light emitted as diffuse radiation in the SAIC! provides important information in context to the regional distribution of dust.,The fraction of the total (stellar + diffuse) FUV light emitted as diffuse radiation in the SMC provides important information in context to the regional distribution of dust.
 We found the total fux in each of theCYT fields by summing the fluxes in all pixels in that fiel., We found the total flux in each of the fields by summing the fluxes in all pixels in that field.
 We then used the catalog of Cornettοἱal.(1997). to caleulate the total stellar [lux in each field., We then used the catalog of \citet{Cornett97} to calculate the total stellar flux in each field.
 The diffuse flux in the(77 field was the difference between the two., The diffuse flux in the field was the difference between the two.
 We extended the stellar flux into theFUSE bands using Ixurucz (Ixuruez1992) model spectra and calculated their flux inFUSE bands., We extended the stellar flux into the bands using Kurucz \citep{Kurucz92} model spectra and calculated their flux in bands.
 Finally. we extrapolated the diffuse flux into theFUSE bands using the observedFUÜUSE/UIT diffuse {hax ratios i.e.. the slope of the best fit line (Figure 2)). obtained separately for each of theFUSE bands [rom their correlation withCIT baud.," Finally, we extrapolated the diffuse flux into the bands using the observed diffuse flux ratios i.e., the slope of the best fit line (Figure \ref{Fig2}) ), obtained separately for each of the bands from their correlation with band."
 Cornettetal.(1997). predicted that of the diffuse flix was due to faint unresolved stars which we subtracted from each of theCIT andFUSE diffuse f[Iuxes., \citet{Cornett97} predicted that of the diffuse flux was due to faint unresolved stars which we subtracted from each of the and diffuse fluxes.
 The dilluse lraction defined. as the diffuse emission divided by the total emission was then calculated for each region and over the entire SAIC! Dar (Figure 3)). with an estimated uncertainty of about30%.," The diffuse fraction defined as the diffuse emission divided by the total emission was then calculated for each region and over the entire SMC Bar (Figure \ref{Fig3}) ), with an estimated uncertainty of about."
.. In all cases. the behavior of the diffuse fraction is almost the same. rising by from 1000 ito 1150 aand a further from 1150 {to 1615A.," In all cases, the behavior of the diffuse fraction is almost the same, rising by from 1000 to 1150 and a further from 1150 to 1615."
. The albedo of the dust obtained from the theoretical predictions of for a mix of spherical carbonaceous and silicate eraims increases by about the same factor over the considered wavelength range and the consequent increase in scattered light may be responsible lor the increased diffuse fraction at longer wavelengths., The albedo of the dust obtained from the theoretical predictions of \citet{Weingartner01} for a mix of spherical carbonaceous and silicate grains increases by about the same factor over the considered wavelength range and the consequent increase in scattered light may be responsible for the increased diffuse fraction at longer wavelengths.
 Integrating over the entire SAIC Dar. we find that of the total radiation that escapes the SMC Bar at 1004 iis diffuse rising to al 1615A.," Integrating over the entire SMC Bar, we find that of the total radiation that escapes the SMC Bar at 1004 is diffuse rising to at 1615."
. The scattered light in the SAIC has been modeled by Witt&Gordon(2000) using multiple scattering in a clumpy mediun., The scattered light in the SMC has been modeled by \citet{Witt00} using multiple scattering in a clumpy medium.
 They found that the dilfuse radiation is to of the total (Figure 3)) depending on different. dust eeomelries., They found that the diffuse radiation is to of the total (Figure \ref{Fig3}) ) depending on different dust geometries.
 Considering only IHE regions of the SAIC. we found that around of the total radiation at iis diffuse rising to at 1615 A.," Considering only H regions of the SMC, we found that around of the total radiation at is diffuse rising to at 1615 ."
". Studies for the Orion nebula (Bohlinetal.1982). and NGC 595 (Alalumuthetal.1996) (ind similar results with of the total radiation being dilfuse at 1400 iin Orion and at L700 iin NGC 595,", Studies for the Orion nebula \citep{Bohlin82} and NGC 595 \citep{Malumuth96} find similar results with of the total radiation being diffuse at 1400 in Orion and at 1700 in NGC 595.
 Pradhanοἱal.(2010) found significantly smaller values for the diffuse fraction in (he LMC (Figure 4)) perhaps due to the difference in erain size ancl composition between the two galaxies (Pei1992:Weingartner&Draine2001:Gordonetal.2003).," \citet{Pradhan10} found significantly smaller values for the diffuse fraction in the LMC (Figure \ref{Fig4}) ) perhaps due to the difference in grain size and composition between the two galaxies \citep{Pei92,Weingartner01, Gordon03}."
. The albedo of the SMC dust is about higher (Weingartner&Draine2001) compared to the LAIC dust (Figure 4)) and (his may explain the increaseddiffuse [Traction in the SAIC., The albedo of the SMC dust is about higher \citep{Weingartner01} compared to the LMC dust (Figure \ref{Fig4}) ) and this may explain the increaseddiffuse fraction in the SMC.
The most important point about these plots is the/ack of anv pattern.,The most important point about these plots is the of any pattern.
 The deviation of any particular galaxy from a model appears to be quite random in space (wilh exceptions to be pointed oul)., The deviation of any particular galaxy from a model appears to be quite random in space (with exceptions to be pointed out).
 Consiler in detail. for example. (he Supergalactic X plots.," Consider in detail, for example, the Supergalactic X plots."
 There is clearly a lack of galaxies al negative X values. reflecting the uneven clistribution of data.," There is clearly a lack of galaxies at negative X values, reflecting the uneven distribution of data."
 There is no clear trend of error with postion. though the total width of the error is reduced somewhat in the anisotropic solution.," There is no clear trend of error with postion, though the total width of the error is reduced somewhat in the anisotropic solution."
 The isolated point with a -400 to -500 km/sec.! error is UGC 7857. a dwarl galaxy with only a brightest-star distance. in the general direction of the Virgo cluster.," The isolated point with a -400 to -500 ${\rm sec}^{-1}$ error is UGC 7857, a dwarf galaxy with only a brightest-star distance, in the general direction of the Virgo cluster."
 The distance may be in error. or the redshift could be affected by a superimposed star (a problem noted several times in Whiting.Wau&Irwin (2002))): or. just. possibly. it could represent a very high-velocitw tail of the peculiar velocity distribution (a matter discussed below).," The distance may be in error, or the redshift could be affected by a superimposed star (a problem noted several times in \citet{WHI02}) ); or, just possibly, it could represent a very high-velocity tail of the peculiar velocity distribution (a matter discussed below)."
 Note also that. in areas with points. the density is approximately constant.," Note also that, in areas with points, the density is approximately constant."
 That is. (here is no apparent concentration around any given value.," That is, there is no apparent concentration around any given value."
 This important observation will be expanded below., This important observation will be expanded below.
 The 98-galaxy Supergalactie Z. isotropic plot does show interesting svsteniatic behavior.," The 98-galaxy Supergalactic Z, isotropic plot does show interesting systematic behavior."
 Recall that these are (he residual racial velocities after (he average expansion of the cloud of ealaxies has been subtracted., Recall that these are the residual radial velocities after the average expansion of the cloud of galaxies has been subtracted.
 There appears to be a trend [or galaxies with Z«—2 to line up from lower left to upper right. which would indicate a lower effective IIubble constant normal to the Supergalactic Plane.," There appears to be a trend for galaxies with ${\rm Z} < -2$ to line up from lower left to upper right, which would indicate a lower effective Hubble constant normal to the Supergalactic Plane."
 This was noted by Ixarachentsev&AMlakarov(1996) in (heir similar plot.," This was noted by \citet{KMa96}
 in their similar plot."
 This flow is easily interpreted as the expected lower effective Hubble constant normal to the Plane., This flow is easily interpreted as the expected lower effective Hubble constant normal to the Plane.
 llowever. it disappears in the plot of higher-quality data (in. part. it must be noted. because (he hieh-quality coverage of high-Iatitude galaxies is poor).," However, it disappears in the plot of higher-quality data (in part, it must be noted, because the high-quality coverage of high-latitude galaxies is poor)."
 More important. it does not show up in the IIubble Censor calculation in the form of a low eigenvalue in the direction of the Superealactic Pole. (he nearest eigenvector being 45°Hr away.," More important, it does not show up in the Hubble tensor calculation in the form of a low eigenvalue in the direction of the Supergalactic Pole, the nearest eigenvector being $45\arcdeg$ away."
 It is not. then. a sign of anv slower Hubble flow out of the Plane.," It is not, then, a sign of any slower Hubble flow out of the Plane."
 Going to (he coordinate svstem delined by (he eigenvectors of the caleulated. tensors. first we note that the 98-ealaxy U plots look much like the Supergalactic Y plots.," Going to the coordinate system defined by the eigenvectors of the calculated tensors, first we note that the 98-galaxy U plots look much like the Supergalactic Y plots."
 This is no surprise. since (he respective axes are only a [ew degrees apart.," This is no surprise, since the respective axes are only a few degrees apart."
 There is no clear ivend in (he other plots., There is no clear trend in the other plots.
 In. particular. the dvnamical behavior discerned above in the 98-ealaxv. Supergalactic Z plot (Figure 3)) has [faded or disappeared.," In particular, the dynamical behavior discerned above in the 98-galaxy, Supergalactic Z plot (Figure \ref{99Z}) ) has faded or disappeared."
 The fact that the caleulated eigenvectors might actually conceal information on the kinematies of the svstem is an indication that (hev are not useful in its description., The fact that the calculated eigenvectors might actually conceal information on the kinematics of the system is an indication that they are not useful in its description.
 This reinforces (he conclusion of (he previous section: the anisotropic flow models tell more about a given cata set than about the underlving galaxy motions., This reinforces the conclusion of the previous section: the anisotropic flow models tell more about a given data set than about the underlying galaxy motions.
"the derived results are consistent with those from the oxygen triplet, however they do not add further information.","the derived results are consistent with those from the oxygen triplet, however they do not add further information."
 The analysis of emission lines reinforces the picture derived from the study of the light curves and the global spectra., The analysis of emission lines reinforces the picture derived from the study of the light curves and the global spectra.
 We find that in the most likely scenario the coronal structures on Altair are quite compact compared to the stellar dimensions and their typical size is about one to a few percent of the stellar radius., We find that in the most likely scenario the coronal structures on Altair are quite compact compared to the stellar dimensions and their typical size is about one to a few percent of the stellar radius.
" The coronal plasma is cool, at relatively low densities and fills up to a few percent of the available coronal volume."," The coronal plasma is cool, at relatively low densities and fills up to a few percent of the available coronal volume."
" As a whole, Altair is rather sparsely covered with X-ray emitting structures, with the X-ray emission mainly originating from the cooler surface areas, i.e. equatorial regions or intermediate latitudes."," As a whole, Altair is rather sparsely covered with X-ray emitting structures, with the X-ray emission mainly originating from the cooler surface areas, i.e. equatorial regions or intermediate latitudes."
" Over the last years there has been some debate on the true neon content of the Sun and other stars (seee.g.?,and therein)..", Over the last years there has been some debate on the true neon content of the Sun and other stars \citep[see e.g.][and therein]{rob08}.
 The controversy arose due to a disagreement between helioseismology and a downward revision of solar abundances., The controversy arose due to a disagreement between helioseismology and a downward revision of solar abundances.
 We previously studied Ne/O ratios in a sample of low and moderately active stars of later spectral type (mid-F to mid-K)., We previously studied Ne/O ratios in a sample of low and moderately active stars of later spectral type (mid-F to mid-K).
" The basic outcome was that, first the coronal Ne/O ratio is activity dependent with more active stars showing a higher Ne/O ratio, and that second stars with solar-like activity level show roughly solar-like Ne/O abundance ratios."," The basic outcome was that, first the coronal Ne/O ratio is activity dependent with more active stars showing a higher Ne/O ratio, and that second stars with solar-like activity level show roughly solar-like Ne/O abundance ratios."
" Since Altair also has a very low activity level, our data is well suited to extend the stellar sample towards hotter photospheric temperatures."," Since Altair also has a very low activity level, our data is well suited to extend the stellar sample towards hotter photospheric temperatures."
" Beside the global fit result derived above, we determined the Ne/O ratio by utilizing linear combinations of emission lines from neon and oxygen that should provide a roughly EMD independent abundance ratio."," Beside the global fit result derived above, we determined the Ne/O ratio by utilizing linear combinations of emission lines from neon and oxygen that should provide a roughly EMD independent abundance ratio."
" We used two different line ratios as in our previous work to derive the Ne/O ratio, i.e. the energy flux ratio (1): vs. NeIX+0.15xNex and thephoton flux ratio (2): 0.67xOvir—0.17OVII vs. NeIx+0.02xx."," We used two different line ratios as in our previous work to derive the Ne/O ratio, i.e. the energy flux ratio (1): vs. $\ion{Ne}{ix}+0.15\times\ion{Ne}{x}$ and thephoton flux ratio (2): $0.67\times\ion{O}{viii}-0.17\times\ion{O}{vii}$ vs. $\ion{Ne}{ix}+0.02\times\ion{Ne}{x}$."
 We note that for the coronal properties of Altair the ratios from the two linear combinations of emission lines rather supply lower and upper boundary values for the true Ne/O ratio; a full discussion of the systematic errors of these methods can also be found in ?.., We note that for the coronal properties of Altair the ratios from the two linear combinations of emission lines rather supply lower and upper boundary values for the true Ne/O ratio; a full discussion of the systematic errors of these methods can also be found in \cite{rob08}.
 We thus derived the Ne/O ratios for Altairand compared these to the solar abundance ratios., We thus derived the Ne/O ratios for Altairand compared these to the solar abundance ratios.
" ? give a solar ratio of +0.04, we derived for Altair from the global fit x0.05 and with RGS data only -0.07, from the two emission line ratios we derived Ne/O==00.17+0.04 (1) and x0.07 (2)."," \cite{grsa} give a solar ratio of $\pm 0.04$, we derived for Altair from the global fit $\pm 0.05$ and with RGS data only $\pm 0.07$, from the two emission line ratios we derived $\pm 0.04$ (1) and $\pm 0.07$ (2)."
" Altogether this gives a mean coronal ratio for Altair of +0.03, slightly above but fully consistent with the ‘classical’ solar one."," Altogether this gives a mean coronal ratio for Altair of $\pm 0.03$, slightly above but fully consistent with the `classical' solar one."
" The Altair result and the ratios from our sample stars of later spectral type are shown in refneo,, the respective linear regressions are overlaid."," The Altair result and the ratios from our sample stars of later spectral type are shown in \\ref{neo}, the respective linear regressions are overlaid."
" Altair's low Ne/O ratio fits well in the trend derived from the cooler stars, suggesting similar chemical fractionation processes and coronal abundance patterns."," Altair's low Ne/O ratio fits well in the trend derived from the cooler stars, suggesting similar chemical fractionation processes and coronal abundance patterns."
 The onset of magnetic activity in late A-type stars as well as the regime of very inactive stars are only poorly studied at X-ray wavelengths., The onset of magnetic activity in late A-type stars as well as the regime of very inactive stars are only poorly studied at X-ray wavelengths.
" Its spectral type and very low activity level place Altair into both categories at once, making suitable objects for comparison rare."," Its spectral type and very low activity level place Altair into both categories at once, making suitable objects for comparison rare."
" Nevertheless, given its repeated X-ray detections over several decades, a very inefficient but quite stable dynamo mechanism needs to operate somewhere in the thin outer convective layer of this fast rotating star."," Nevertheless, given its repeated X-ray detections over several decades, a very inefficient but quite stable dynamo mechanism needs to operate somewhere in the thin outer convective layer of this fast rotating star."
 As a tentative approach for comparison with late-type stars we adopt a solar-like dynamo to generate the observed X-ray emission from Altair and discuss its possible implications., As a tentative approach for comparison with late-type stars we adopt a solar-like dynamo to generate the observed X-ray emission from Altair and discuss its possible implications.
" When assuming an oΩ dynamo, the correlation of magnetic activity with rotation or more precisely dynamo efficiency in the non-saturated regime is usually described by the Rossby number, ie. Ρ/τε with P being the rotation period and το the convective turnover time."," When assuming an $\alpha\,\Omega$ dynamo, the correlation of magnetic activity with rotation or more precisely dynamo efficiency in the non-saturated regime is usually described by the Rossby number, i.e. $P/\tau_{c}$ with $P$ being the rotation period and $\tau_{c}$ the convective turnover time."
 Its validity has been shown over a broad range of stellar activity for chromospheric emission (?) and coronal X-ray emission (e.g. ?).., Its validity has been shown over a broad range of stellar activity for chromospheric emission \citep{noy84} and coronal X-ray emission \citep[e.g.][]{ran00}. .
" However, in both cases the region of weakly active stars with log ,O.5isnearlyunexploredand f urtherthesamplesaredominatedbyle: 1M) stars."," However, in both cases the region of weakly active stars with log $>0.5$ is nearly unexplored and further the samples are dominated by less massive $\lesssim 1{\rm M}_{\sun}$ ) stars."
" Adopting the relation Lx/Lpo1«Ro with a«2 that is valid for large Rossby numbers (log Roz —0.8), we can derive the dynamo efficiency for Altair and compare the expected with the observed activity level."," Adopting the relation $L_{\rm X}/L_{\rm bol} \propto {\rm Ro}^{-\alpha}$ with $\alpha \approx 2$ that is valid for large Rossby numbers (log $\gtrsim -0.8$ ), we can derive the dynamo efficiency for Altair and compare the expected with the observed activity level."
" To obtain a rough estimate of Altair’s convective turnover time, we adopt an empirical formula, although derived from less massive late-F to late-K stars, that relates το with B-V color as given in ?.."," To obtain a rough estimate of Altair's convective turnover time, we adopt an empirical formula, although derived from less massive late-F to late-K stars, that relates $\tau_{c}$ with B-V color as given in \cite{noy84}."
" For Altair’s 00.22, corresponding to Τεῃ=77650 KK, we obtain τε= 1.3hh and when adopting a period of hh we finally get log Ro==00.88."," For Altair's 0.22, corresponding to $T_{\rm eff}=$ K, we obtain $\tau_{c}= 1.3$ h and when adopting a period of h we finally get log 0.88."
" Inspecting the correlation shown in ?,, derived from a stellar sample that includes many ROSAT field stars, we obtain for large Ro the empirical relation logLx/Lpo.=—4.9—2.1x Ro."," Inspecting the correlation shown in \cite{ran00}, , derived from a stellar sample that includes many ROSAT field stars, we obtain for large Ro the empirical relation $\log L_{\rm X}/L_{\rm bol} = -4.9 -2.1\times {\rm log~Ro}$ ."
" With the values for Altair we then expect logLx/Lpo1~—6.8, a value of the"," With the values for Altair we then expect $\log L_{\rm X}/L_{\rm bol}\approx -6.8$, a value of the"
A general lesson learned from theAcck expericuce is that high-resolution spectroscopy is one of the most powerful tools iu astrophysics.,A general lesson learned from the experience is that high-resolution spectroscopy is one of the most powerful tools in astrophysics.
 That power should be extended to other wavelength bauds., That power should be extended to other wavelength bands.
 Large instrmucuts are needed: Abu of the talks at this mecting worked within the new cosmological paradigu for the Lye clouds., Large instruments are needed: Many of the talks at this meeting worked within the new cosmological paradigm for the $\alpha$ clouds.
 Over the past five vears. numerical models have increased their accuracy and predictive power muuenuselhv. to the poiut where they are now able to provide coustraiuts on O5. ην aud galaxy formation.," Over the past five years, numerical models have increased their accuracy and predictive power immensely, to the point where they are now able to provide constraints on $\Omega_b$, $J_{\nu}$, and galaxy formation."
 There is still sole wavs to eo. however. aud 1 offer the following wishes:," There is still some ways to go, however, and I offer the following wishes:"
Recent oobservations have shown that the iron. lines commonly observed in Sevfert 1 galaxies. (Nanedra Pounds 1994) are extremely broad. with EWLIM of order 50.0000 km s (Mushotzky 11995: Tanaka 11995: Yaqoob 11995: Nancdra 11996b. hereafter. N96).,"Recent observations have shown that the iron lines commonly observed in Seyfert 1 galaxies (Nandra Pounds 1994) are extremely broad, with FWHM of order $50,0000$ km $^{-1}$ (Mushotzky 1995; Tanaka 1995; Yaqoob 1995; Nandra 1996b, hereafter N96)."
 These observations alone provide strong evidence for a black hole/accretion disk system. the line widths beinge extremely dillicult to account for in any other geometry (Fabian 11995).," These observations alone provide strong evidence for a black hole/accretion disk system, the line widths being extremely difficult to account for in any other geometry (Fabian 1995)."
 A specific prediction of the disk-line model is that the line should respond rapidly to changes in the continuum. as it is excited by Duorescence in a region close to the central black hole.," A specific prediction of the disk-line model is that the line should respond rapidly to changes in the continuum, as it is excited by fluorescence in a region close to the central black hole."
 Evidence for such line variability in Sevlert 1 galaxies has proved surprisingly. elusive., Evidence for such line variability in Seyfert 1 galaxies has proved surprisingly elusive.
 The well-studied case of the bright Sevfert galaxy NGC 4151 failed to provide conclusive evidence. despite over LO vears worth of quality cata Warwick 11989).," The well-studied case of the bright Seyfert galaxy NGC 4151 failed to provide conclusive evidence, despite over 10 years worth of high-quality data Warwick 1989)."
 Phe best cases reported to date have been those of AIC-6-30-15 and NGC 7314. for which Dvasawa ((1996) ancl Yaqoob ((1996) have shown changes in the iron Ίνα profile.," The best cases reported to date have been those of MCG-6-30-15 and NGC 7314, for which Iwasawa (1996) and Yaqoob (1996) have shown changes in the iron $\alpha$ profile."
 Interestingly. in the former case. the variations were such hat the narrow and broad. components of the linc were anti-correlated. meaning that the evidence for variability of the total [lux of the line was weak.," Interestingly, in the former case, the variations were such that the narrow and broad components of the line were anti-correlated, meaning that the evidence for variability of the total flux of the line was weak."
 This is contrary o the predictions of simple accretion clisk models. where he line should. track the continuum. variations in a linear ashion. even on short time scales.," This is contrary to the predictions of simple accretion disk models, where the line should track the continuum variations in a linear fashion, even on short time scales."
 Thus it is clearly essential o examine the variations in other sources. to investigate whether or not such behaviour is common.," Thus it is clearly essential to examine the variations in other sources, to investigate whether or not such behaviour is common."
 Llere we present two SCA observations of the bright Sevfert 1 galaxy NGC 3516. separated by à L1 vear baseline.," Here we present two ASCA observations of the bright Seyfert 1 galaxy NGC 3516, separated by a 1 year baseline."
 This source has shown strong continuum variability in the past. allowing us to search for the associated: variations expected in the emission line.," This source has shown strong continuum variability in the past, allowing us to search for the associated variations expected in the emission line."
 NGC 3516 was observed by (CEanaka. Inoue Lolt 1994) on 1994-Xpr-02. (hereafter observation 1) and 1995-March-12 (hereafter observation 2)," NGC 3516 was observed by (Tanaka, Inoue Holt 1994) on 1994-Apr-02 (hereafter observation 1) and 1995-March-12 (hereafter observation 2)"
Newtoniaan dark matter halos are more concentrated than in spirals.,an dark matter halos are more concentrated than in spirals.
Aleol-type close biua‘les are semi-detached interacting systems iu which one type of interaction is ass trausler between the compolet stars by meats of a gas stream.,Algol-type close binaries are semi-detached interacting systems in which one type of interaction is mass transfer between the component stars by means of a gas stream.
 They have been know1 as good astrophysical la)Olatorles or studying acereion processes because a number of them are bright., They have been known as good astrophysical laboratories for studying accretion processes because a number of them are bright.
 They are in he slow phase of mass trauser with dM/dlz10+—10° M. and do not undergo violeut eruptions that interfere wihi the accretion process., They are in the slow phase of mass transfer with $dM/dt \simeq 10^{-11}-10^{-7}$ $_\odot$ $^{-1}$ and do not undergo violent eruptions that interfere with the accretion process.
 The circumstellar structures produced by 1le lnass-trausler process in tlese systems lave been sorted according t« orbital perio« by Richards Albriglt (1999) bu clo no depeud upon it significantly., The circumstellar structures produced by the mass-transfer process in these systems have been sorted according to orbital period by Richards Albright (1999) but do not depend upon it significantly.
 Rather. their natures cau be easily ulderstood fro ntle posijon ol tje mnass-galning component 1 the so-called r-q diagram in whicl mue [Tactional radius + (Ria) of a gainer is plottedverses he mass ratio q aud compared with |e semianalytica comptations of the gas stream νογούναnics of Lubow Shu (1975).," Rather, their natures can be easily understood from the position of the mass-gaining component in the so-called $r$ $q$ diagram in which the fractional radius $r$ = $R/a$ ) of a gainer is plotted the mass ratio $q$ and compared with the semianalytical computations of the gas stream hydrodynamics of Lubow Shu (1975)."
 In the slort-period Algos locaed above the wy curve of the diagraii (cl, In the short-period Algols located above the $\omega_d$ curve of the diagram (cf.
 Figure'e 2 of Richards Alblell. the hot. detacied. prinary slar is large relative to the orbital radius aud the two coniponuent 'e too close to eac1 othe “to form ar accretion disk or even a sable accretion annulus.," Figure 2 of Richards Albright), the hot, detached primary star is large relative to the orbital radius and the two components are too close to each other to form an accretion disk or even a stable accretion annulus."
 Lbusteacd. j»ossible that an impact reeico). and hence a lxM Ἡ501. can be formed on the surface of the prinary slar soniewijt displaced fron1 the line of centers due o the Coriolis acceleratioi imposed oi the flowing gas.," Instead, it is possible that an impact region, and hence a hot spot, can be formed on the surface of the primary star somewhat displaced from the line of centers due to the Coriolis acceleration imposed on the flowing gas."
" If the seconda""wo stars are sπμently cool. they liκοιν display. enllanced maguetic activity due to deep outer convective lavers aid rapid rotation."," If the secondary stars are sufficiently cool, they likely display enhanced magnetic activity due to deep outer convective layers and rapid rotation."
 This inagnetic ijechanisim αν contribute to the period aud ight variations [or systems with spectra later than F-type (Hall 1989)., This magnetic mechanism may contribute to the period and light variations for systems with spectra later than F-type (Hall 1989).
 CL Atr (GSC 2393-1155. HV 6886. TYC 2393-1155-1L) was cliscove'ed ο bea variable star by Hollleit (1939) based ou pliotographic plate estimates.," CL Aur (GSC 2393-1455, HV 6886, TYC 2393-1455-1) was discovered to be a variable star by Hoffleit (1935) based on photographic plate estimates."
 Ixurochkiu (1951) presented the first (partial) photographic light €uve of the star aud the original ight elements. Mit," Kurochkin (1951) presented the first (partial) photographic light curve of the star and the original light elements, Min."
 ΕΞ Π.Ο 2.132.967.262 + 1.211366GE.," I = HJD 2,432,967.262 + $E$."
 The value of the period positions tliis olject toward the slort-period limit [or Aleols., The value of the period positions this object toward the short-period limit for Algols.
 The spectral type o. the prilary star was classifiec to be AO by διiz Wenzel (1963)., The spectral type of the primary star was classified to be A0 by Göttz Wenzel (1968).
 Since then. times of miniinun light have been published assiduously by uulerotis workers but. to our kuowledege. a couplete light ¢uve and the fundaimenual parameters [or he binary system have uot been made so far.," Since then, times of minimum light have been published assiduously by numerous workers but, to our knowledge, a complete light curve and the fundamental parameters for the binary system have not been made so far."
 Clanges of he orb=.al period have been cousidered by Hegecüss (LOSS) ancl Wolf et al. (, Changes of the orbital period have been considered by Hegedüss (1988) and Wolf et al. (
1999).,1999).
" Hegedtüss selectecl this ""bem as a possible candidate for tle sttcy of apsidal motion.", Hegedüss selected this system as a possible candidate for the study of apsidal motion.
 However. the later ithors ruecd out this possibility rou CCD timiuegs for prinary and secoudary eclipses.," However, the later authors ruled out this possibility from CCD timings for primary and secondary eclipses."
 They sugeroestecl the cause of pe‘iod variation to be a light-travel-titje (LTT) effect. due to the presence o Sa third body in l ebinary system., They suggested the cause of period variation to be a light-travel-time (LTT) effect due to the presence of a third body in the binary system.
 Most recently. Wolf et al. (," Most recently, Wolf et al. ("
2007. hereafter WOT) reported tlat a loug-teriu period iCrease is superimposed ou an LTT o‘bit with a period of 21.7 yrs. a seui-amplitude of A =0.0!LE d. and an eccentricity of e=0.32.,"2007, hereafter W07) reported that a long-term period increase is superimposed on an LTT orbit with a period of $P_3 $ =21.7 yrs, a semi-amplitude of $K$ =0.014 d, and an eccentricity of $e$ =0.32."
 In the Sinb:id database-.. the sysenr is described as au eclipsing binary of 5? Lyr type.," In the Simbad data, the system is described as an eclipsing binary of $\beta$ Lyr type."
 BWJHly maguittes are listed for the star but these are [rom heterogeneous sources aud are not, $BVJHK$ magnitues are listed for the star but these are from heterogeneous sources and are not
ΤΟΝΙ line at 128.75 for the reference nou-coufiuecd model.,FeXXI line at 128.75 for the reference non-confined model.
 This kind of prediction may not provide significant indications when looking at rea fiue observations for various reasons: bue-shifts are expected only if the flaring reeion is favourabv oriceited to the observer: shifts of few iuucdreds kms are εαν detectadle even with AAAT anced Chandra high rexution erating spectrometers: alhough ess persistent. sigUficaut bluc-shifted componcuts nav be esent even durinο confined flares iu long loops.," This kind of prediction may not provide significant indications when looking at real flare observations for various reasons: blue-shifts are expected only if the flaring region is favourably oriented to the observer; shifts of few hundreds km/s are hardly detectable even with XMM and Chandra high resolution grating spectrometers; although less persistent, significant blue-shifted components may be present even during confined flares in long loops."
 A] these uitaions nia niae anv cdiaguosics of confinement frou ine shifts rather «ifficult., All these limitations may make any diagnostics of confinement from line shifts rather difficult.
 Recent works have pointed the attention o the derivation of the distribution of ciission ueasure with enperature 2) troM the analysis of N-rav stellar data (e.g. Drake ct al., Recent works have pointed the attention to the derivation of the distribution of emission measure with temperature ) from the analysis of X-ray stellar data (e.g. Drake et al.
" 200, Liuskv Cagne 2001)."," 2000, Linsky Gagne 2001)."
 Noirconfned flare models: predict a flare CUSSION nüeasure distribution monotoically decreasing with temperature diving the heating pphase aud then losing the highest temperature coniponeuts and sole intermediate temperature conipoueuts 1 itje decay phase., Non-confined flare models predict a flare emission measure distribution monotonically decreasing with temperature during the heating phase and then losing the highest temperature components and some intermediate temperature components in the decay phase.
 These distributions are quite different from those tvpically derived from flaving aud non-flaring soar (e.c. Peres et al., These distributions are quite different from those typically derived from flaring and non-flaring solar (e.g. Peres et al.
 2000. Reale ct al.," 2000, Reale et al."
 2001) axl nou-flariie stellar data. which iustead shiwv well-defi1ος EM )eadks.," 2001) and non-flaring stellar data, which instead show well-defined EM peaks."
 This may be a discrinünatiuο feature. whenever medium resolulon spectra provide reliable cinissio1 measure distri»utions during stellar flares (6.8. Oste ret al.," This may be a discriminating feature, whenever medium resolution spectra provide reliable emission measure distributions during stellar flares (e.g. Osten et al."
 2000)., 2000).
 As a final diagnostic couskeration. we poiut out tlat. if data show cvidence of a flare ocecmring dà a non-confined plasima. then accordi18o o our mocdoeliug the soft A-av light curve would faitifiIv trace the evolulon of the heating. au nuportaut diagnostics for coronal physics 2).," As a final diagnostic consideration, we point out that, if data show evidence of a flare occurring in a non-confined plasma, then according to our modeling the soft X-ray light curve would faithfully trace the evolution of the heating, an important diagnostics for coronal physics )."
 Au cquivalent informalon is eenerallv derived from hare A-ravs dm solar flares (e.g. Golub DPasachotf 1997)., An equivalent information is generally derived from hard X-rays in solar flares (e.g. Golub Pasachoff 1997).
 We nav wonder whether our results; such as t1ο helt curves presented in Fig. 7..," We may wonder whether our results, such as the light curves presented in Fig. \ref{fig:lc},"
 are affected by tle Nou Equilibrium of Ionization (NET) couditious of the plasima., are affected by the Non Equilibrium of Ionization (NEI) conditions of the plasma.
 Iu eeneral. im fact. he N-vay cluissivity depends onu f thermal history of the oemittiug plasma parcel. which unfortunately not straightforward to evaluate.," In general, in fact, the X-ray emissivity depends on the thermal history of the emitting plasma parcel, which is unfortunately not straightforward to evaluate."
 Bocchi ot al. (, Bocchino et al. (
1997) show that the 0.1-2.0 keV N-vay cunissivity an dupulsively heated plasma (a situation similar to t rise of the flare in our iocels) approaches the equilibrit value for ionization ne loger~ llinscm >.,1997) show that the 0.1-2.0 keV X-ray emissivity of an impulsively heated plasma (a situation similar to the rise of the flare in our models) approaches the equilibrium value for ionization time $\log\tau \sim 11$ in s $^{-3}$.
 This isa true in the ASCA/SIS bardwidth., This is also true in the ASCA/SIS bandwidth.
 In the initial phase the flare the typical deusiv of the bright X-ray etti18o pluuia is in excess of 10? 5 correspouding to au equilibriua tine scale of t1e order of 100 s: we may expect a imodification of the ligit curve before 100 s. cousistiug in a higher NET value reached at the cud of the rising phase aud a slow descend to the sustained rate.," In the initial phase of the flare the typical density of the bright X-ray emitting plasma is in excess of $10^9$ $^{-3}$, corresponding to an equilibrium time scale of the order of 100 s: we may expect a modification of the light curve before 100 s, consisting in a higher NEI value reached at the end of the rising phase and a slow descend to the sustained rate."
 Iu the fast decay at the eud of the heatiis phase the NET conditions may have some importance aud bring to variations of the light curve in this phase., In the fast decay at the end of the heating phase the NEI conditions may have some importance and bring to variations of the light curve in this phase.
 However. these effects will be reduced for hotter aud hotter eveuts. Le. typical iuteuse stellar flares. because the continui eniüssion dominates more aud more on the lue enissioii," However, these effects will be reduced for hotter and hotter events, i.e. typical intense stellar flares, because the continuum emission dominates more and more on the line emission."
 Later on. in the eradual decay. most of the enussion Comes roni the expanding shock. iu whicl1 we have oulv a slight decrease of the teniperaUre. aid therefore tli! plaga ix onv mareinally overionized.," Later on, in the gradual decay, most of the emission comes from the expanding shock, in which we have only a slight decrease of the temperature, and therefore the plasma is only marginally overionized."
 Tιο staal deviation from equiibriun gives quasi-equilibrini conditions duriug most of the decav phase. thus we do not expec substantial modifications of the elobal tine scales we have worsed out.," The small deviation from equilibrium gives quasi-equilibrium conditions during most of the decay phase, thus we do not expect substantial modifications of the global time scales we have worked out."
 Iu stnuuarv. there are two basic features that may characterize invariably flares 1 non-coufined regions aud may be relatively easy to trace in stelar N-rav data: light curves with very fast ¢ecays and svuchronous evolution of deusity and temperature.," In summary, there are two basic features that may characterize invariably flares in non-confined regions and may be relatively easy to trace in stellar X-ray data: light curves with very fast decays and synchronous evolution of density and temperature."
 Both these features are in coutrast with evidence from sella flares., Both these features are in contrast with evidence from stellar flares.
 Then we come to an incresting couchsou: This d somewhat unexpected. because lore-lasting stellar flares have been vpically associated to very laree coronal structures (see Sect. 1)).," Then we come to an interesting conclusion: This is somewhat unexpected, because long-lasting stellar flares have been typically associated to very large coronal structures (see Sect. \ref{sec:intro}) ),"
 which have the uoirconfmned configuration as ali asvlutotic extreme., which have the non-confined configuration as an asymptotic extreme.
" This work shows that most likely ie long-lasting flares. such as those in active stars. PAil occur in cosed. alhough larec, structures aud that i0 role of confinementni of the coronal magnetic. field nust be inviriabVv sigüficant in frose events."," This work shows that most likely the long-lasting flares, such as those in active stars, still occur in closed, although large, structures and that the role of confinement of the coronal magnetic field must be invariably significant in those events."
 In other words. the magneic fields must always be strong and/or le lnaenetic structure never breaks open.," In other words, the magnetic fields must always be strong and/or the magnetic structure never breaks open."
 Iu the same lirection. notice also that norconfned fares appear to luvolveo huge anuouuts o ‘heating (see Table 1)) whic1 ΑΝ iof be entielv realistic whei colmpared to the euergv midget of stellar coronae.," In the same direction, notice also that non-confined flares appear to involve huge amounts of heating (see Table \ref{tab:sim}) ) which may not be entirely realistic when compared to the energy budget of stellar coronae."
 If loug-duration stellar flares aro unlikely to he described as breaking the maeietic Confinement. are there auv other observed events wwüch instead could le?," If long-duration stellar flares are unlikely to be described as breaking the magnetic confinement, are there any other observed events which instead could be?"
 As mentioned in Sect., As mentioned in Sect.
 1 long stelay flares are prefereutialv detected mio N-rav observations., \ref{sec:intro} long stellar flares are preferentially detected in X-ray observations.
 However there is a class of coronal variations which occur on small time scaCR aud which have been detectec on dMe star UV. Ceti »* ROSAT (Schinitt et al., However there is a class of coronal variations which occur on small time scales and which have been detected on dMe star UV Ceti by ROSAT (Schmitt et al.
 1993)., 1993).
 The possibility tat such short eveuts may be interpreted as simall but very intense non-confined events should be explored., The possibility that such short events may be interpreted as small but very intense non-confined events should be explored.
 This study duo some wavslows an dnuterestiug theoretical perspective to he colpared with SNB inodels and Coronal Mass. Ejections {CME) models., This study in some way shows an interesting theoretical perspective to be compared with SNR models and Coronal Mass Ejections (CME) models.
 Our model shows al OvCTreated plasiua whic1 expards uuder the ffect of heating πι a hot aud lhermalv conduceine stratified atuosphere. axd we xovide for i characteristic scalines of οσοreral validity (Eqs. 10.. 11.. 13).," Our model shows an overheated plasma which expands under the effect of heating in a hot and thermally conducting stratified atmosphere, and we provide for it characteristic scalings of general validity (Eqs. \ref{eq:rtvn}, \ref{eq:tauc}, , \ref{eq:tauf}) )."
 For lustance. since the time scale ο the ate decay zy (Eq. 139) ," For instance, since the time scale of the late decay $\tau_f$ (Eq. \ref{eq:tauf}) )"
depends practically oulv ο1 the spec oft1ο evaporation frout aud ou he therual pasta condilous far from the flaring region. it is itt]e dependent on the flare heating and on other moel »uanneters if is a seneraldecav time scale for shell frous expanding in a stratified," depends practically only on the speed of the evaporation front and on the thermal plasma conditions far from the flaring region, it is little dependent on the flare heating and on other model parameters: it is a generaldecay time scale for shell fronts expanding in a stratified"
In summary. we found (hat rapid stellar rotation causes (wo opposing effects on the speed of meridional flow.,"In summary, we found that rapid stellar rotation causes two opposing effects on the speed of meridional flow."
 The speed is reduced by the suppression of Ag. while it is enhanced bv the angular momentum transport along the axial direction with a smaller A.," The speed is reduced by the suppression of $\Lambda_0$, while it is enhanced by the angular momentum transport along the axial direction with a smaller $\lambda$."
 Although the results of the three-dimensional caleulation suggest that meridional flow becomes slower with a larger stellar angular velocity. our model caunot draw a conclusion about the speed of meridional flow in rapidly rotating stars.," Although the results of the three-dimensional calculation suggest that meridional flow becomes slower with a larger stellar angular velocity, our model cannot draw a conclusion about the speed of meridional flow in rapidly rotating stars."
 Next we investigate (he influence of superadiabaticitwv in (he convection zone., Next we investigate the influence of superadiabaticity in the convection zone.
" In cases 13-17. superadiabaticitv in the convection zone 0,=1x10°."," In cases 13-17, superadiabaticity in the convection zone $\delta_\mathrm{c} = 1\times 10^{-6}$."
 The differences of the NTP parameters with adiabatic and superadiabatic convection zones (Pup ave shown in Fig. 15.., The differences of the NTP parameters with adiabatic and superadiabatic convection zones $(P_{\mathrm{ntp}(\delta_\mathrm{c}=0)}-P_{\mathrm{ntp}(\delta_\mathrm{c}=10^{-6})})/P_{\mathrm{ntp}(\delta_\mathrm{c}=0)}$ are shown in Fig. \ref{super}.
 The NTP parameter values with a superachabatic convection zone are smaller (han (hose with an adiabatic convection zone. since meridional flow in the superadiabatic convection zone makes (he entropy gradient small.," The NTP parameter values with a superadiabatic convection zone are smaller than those with an adiabatic convection zone, since meridional flow in the superadiabatic convection zone makes the entropy gradient small."
 This result is suggested by Rempel(2005a).., This result is suggested by \cite{2005ApJ...631.1286R}.
 Note that the dillerence between the values of the NTP parameters with an adiabatie and those with a superadiabatic convection zone decreases as the stellar angular velocity. increases. since (he generation of entropy eradient by the subaciabtic laver becomes ineffective with a larger stellar angular velocity.," Note that the difference between the values of the NTP parameters with an adiabatic and those with a superadiabatic convection zone decreases as the stellar angular velocity increases, since the generation of entropy gradient by the subadiabtic layer becomes ineffective with a larger stellar angular velocity."
 We have investigated differential rotation in rapidly rotating stars using a mean field model., We have investigated differential rotation in rapidly rotating stars using a mean field model.
 This work is significant because it can be used as a base for further research on stellar activity eveles. which are most likely caused by the dvnamo action of differential rolation in the stellar convection zone.," This work is significant because it can be used as a base for further research on stellar activity cycles, which are most likely caused by the dynamo action of differential rotation in the stellar convection zone."
 First. we investigated the morphology of dillerential rotation in rapiclly rotating stars.," First, we investigated the morphology of differential rotation in rapidly rotating stars."
 Although more angular momentum is transported by convection with larger stellar, Although more angular momentum is transported by convection with larger stellar
Following the suggestion of Paezviiski(1986).. several collaborations. notably NLACIIO and EROS. began to search for gravitational microlensing towards the \lagellanie Clouds as an indicator of compact objects in the halo of the Milky Way (Alcock 1993).,"Following the suggestion of \citet{Paczynski86}, several collaborations, notably MACHO and EROS, began to search for gravitational microlensing towards the Magellanic Clouds as an indicator of compact objects in the halo of the Milky Way \citep{Alcock93, Aubourg93}."
. AC about the same time. the OGLE collaboration began a survey in the direction ol the Galactic bulge (Udalskietal.1992.1993).," At about the same time, the OGLE collaboration began a survey in the direction of the Galactic bulge \citep{Udalski92,Udalski93}."
. It was soon ound that a much higher event rate occurred in fields towards the Galactic bulge relative to the rate towards the Magellanic Clouds (Udalskietal.1994a:Alcockοἱ1905.1997a).," It was soon found that a much higher event rate occurred in fields towards the Galactic bulge relative to the rate towards the Magellanic Clouds \citep{Udalski94a,
Alcock95,Alcock97a}."
. Gince 1990. approximatelv 1000 such events have been detected (Aleocketal.2000:Udalski2000).," Since 1990, approximately 1000 such events have been detected \citep{Alcock00,Udalski00}."
. Several groups including PLANET (Probing Lensing A1j0:3nalies NETwork. Albrowet 2002)). MIPS (Microlensing Planet Search. Rhieetal. 1999)) and. pEUN (Microlensing Follow-Up Network. Yooetal. 2004)) monitor," Several groups including PLANET (Probing Lensing Anomalies NETwork, \citealt{Albrow98,Albrow01,Dominik02,Gaudi02}) ), MPS (Microlensing Planet Search, \citealt{Rhie99}) ) and $\mu$ FUN (Microlensing Follow-Up Network, \citealt{Yoo03}) ) monitor"
The models just described make predictions for the halo two-»ont. correlation function on any length scale r.,The models just described make predictions for the halo two-point correlation function on any length scale $r$.
 Since the shape ofthe halo correlation function is not well constrained ον current observations. most authors have focused just on he amplitude. quantified in terms of the correlation length ro.," Since the shape of the halo correlation function is not well constrained by current observations, most authors have focused just on the amplitude, quantified in terms of the correlation length $r_0$."
 L now compare the predictions of cach of the models or ry with the values observed in large collisionless N-bocly simulations (comparison between models. and. simulations or the full halo correlation function is bevond the scope of he current paper. but deserves future investigation).," I now compare the predictions of each of the models for $r_0$ with the values observed in large collisionless N-body simulations (comparison between models and simulations for the full halo correlation function is beyond the scope of the current paper, but deserves future investigation)."
 The simulations have been carried out by Colberg et al. (, The simulations have been carried out by Colberg et al. (
1998 hereafter. COS) and Governato ct al. (,1998 – hereafter C98) and Governato et al. (
1999 hereafter 699).,1999 – hereafter G99).
 For each simulation the power spectrum has been taken to have a CDM form (Dardoen et 1986. eq.," For each simulation the power spectrum has been taken to have a CDM form (Bardeen et \markcite{BBKS}~ 1986, eq."
 63) parameterized. by a shape parameter E. (vhere PoxOf. and fis the Hubble constant in units of 100 Alpe |) and normalization ax. where ex is therms [uctuation in an Sh IMpe sphere.," G3) parameterized by a shape parameter $\Gamma$ (where $\Gamma
\simeq
\Omega h$, and $h$ is the Hubble constant in units of 100 $^{-1}$ $^{-1}$ ) and normalization $\sigma_8$, where $\sigma_8$ is the fluctuation in an $8h^{-1}$ Mpc sphere."
" The power spectrum: parameters. for each simulation are summarized in Table 1.. together with the box length. ἐν. particle number ;N, and. background cosmology."," The power spectrum parameters for each simulation are summarized in Table \ref{tab-simulation}, , together with the box length $L$, particle number $N_p$ and background cosmology."
 Fig., Fig.
 1. compares the ryd relation observed in the simulations (data points) with that. predicted by the AIW (clotted lines) and. SN. (solid Lines) formalisms.," \ref{fig-simulation}
 compares the $r_0-d$ relation observed in the simulations (data points) with that predicted by the MW (dotted lines) and SMT (solid lines) formalisms."
 In computing these predictions. L use p(MIA)=0(MAL) where ὁ denotes the Dirac delta function. since in this case the richness property by which the halos are ranked is just the true mass.," In computing these predictions, I use $p({\cal
M}|M)=\delta({\cal M}-M)$ where $\delta$ denotes the Dirac delta function, since in this case the richness property by which the halos are ranked is just the true mass."
 Clearly the SMT model gives much better agreement with the cluster correlation length as observed. in. the simulations., Clearly the SMT model gives much better agreement with the cluster correlation length as observed in the simulations.
 E quantify the goodness of fit by defining anrins error ££ via ∖∖⋎↓↥∢⊾↓⋅⋖⋅∣↓↕⋖⊾⊳∖⊔⊔↓∣⊽↓⋅⊔⊔⊳∖∪∖⇁⋖⊾↓⋅⋜↧∐∠⇂⋜∐⋜↧↓≻∪⊲↓⊔∣⊳∖↿∖↙∣∣⊳∣⋮⊏∣⊳∃⊔⊔∠⇂⋖⋅↓⋅ ≼⇍∪⊔⊳∖⊲⊓⇂∢⋅↓⋅⋜∐⊀↓∪⊔⊳⋜⋯∠⇂∣⋅⊏↽⊁↿∖↙∣⊐∠⇂∢⋅⊔∪⋖⋅⊳∖⇂↓↥∢⊾≼↛∢≱↓⋅↓⋅⋖⋅↓⋜↧⇂↕⋖≱↓↥↓⋖⊾⊔⋏∙≟⇂↓↕ prediction for model X at separation d.," I quantify the goodness of fit by defining an error $E$ via where the sum $i$ runs over all datapoints $d^i$ $r^i_0$ ) under consideration, and $r^{\rm X}_0(d)$ denotes the correlation length prediction for model X at separation $d$."
 For the combined datapoints from all four simulations. the SALE model gives IL=0.08. while errors for the AIW model are much larger. with £=0.22.," For the combined datapoints from all four simulations, the SMT model gives $E=0.08$, while errors for the MW model are much larger, with $E=0.22$."
 The goodness of fit for each of the mocoels is given in Tab 2.., The goodness of fit for each of the models is given in Tab \ref{tab-fits}.
 Phe left column shows results using the non- correlation function to compute ry. while the right column shows results using the linear correlation function.," The left column shows results using the non-linear correlation function to compute $r_0$, while the right column shows results using the linear correlation function."
 Use of the non-linear correlation function improves the fit in cach case., Use of the non-linear correlation function improves the fit in each case.
 ] conclude from this analysis that the SAVE model gives a good fit (tvpical errors less than S per cent) to the halo correlation length arising from a full treatment of the non- gravitational evolution., I conclude from this analysis that the SMT model gives a good fit (typical errors less than 8 per cent) to the halo correlation length arising from a full treatment of the non-linear gravitational evolution.
 The MW model docs worst of all the models. considered. with typical errors of order 25 per cent.," The MW model does worst of all the models considered, with typical errors of order 25 per cent."
 In. particular. the MW. model systematically overestimates the halo correlation length for fixed separation d. à result also found in COS.," In particular, the MW model systematically overestimates the halo correlation length for fixed separation $d$, a result also found in C98."
 It is worth noting that the iscrepaney between the NW model and the simulations is much larger than might be inferred. from. previous studies., It is worth noting that the discrepancy between the MW model and the simulations is much larger than might be inferred from previous studies.
 For instance. Mo. Jing (1996 - hereafter NLJW) and (1999) suggest that the AIW formula agrees at better than the five per cent level with the rare halo bias observed in their simulations.," For instance, Mo, Jing \markcite{MJW} (1996 - hereafter MJW) and \markcite{Jing} (1999) suggest that the MW formula agrees at better than the five per cent level with the rare halo bias observed in their simulations."
 Closer examination of the rarest mass atapoints in Fig., Closer examination of the rarest mass datapoints in Fig.
 3 of Jing (1999) illustrate that the error is actually much larger., 3 of Jing (1999) illustrate that the error is actually much larger.
 Figs., Figs.
 7 and S of Governato ct al., 7 and 8 of Governato et al.
 also imply extremely good: agreement between the MW. formula and correlation lengths observed in their simulations., also imply extremely good agreement between the MW formula and correlation lengths observed in their simulations.
 In fact. the MN. prediction has been computed incorrectly in these Ligures. and the true agreement is much worse (as illustrated in Fie.," In fact, the MW prediction has been computed incorrectly in these figures, and the true agreement is much worse (as illustrated in Fig."
 1 of this paper)., \ref{fig-simulation} of this paper).
 A final source of confusionas to the accuracy of the MW formula is that the curves showing the ΑΝ prediction in Fig., A final source of confusionas to the accuracy of the MW formula is that the curves showing the MW prediction in Fig.
 S of MJW have also been computed, 8 of MJW have also been computed
{from the central star as seen in ΠΙΟΣ (Schóieretal.2007) and SiO (Schóier.Olofsson.Lunderen2006).. and modeled by Corniner&Millar(2009).,"from the central star as seen in $^{13}$ CN \citep{schoier2007} and SiO \citep{schoier2006}, , and modeled by \citet{cordiner2009}."
.. Radiation from the central star. as well as [rom local dust. contribute significantly to the molecular excitation.," Radiation from the central star, as well as from local dust, contribute significantly to the molecular excitation."
 We therefore consider the ICI abundance and [CT//*CH] abundance ratio for IRC+10216 as listed in Table 3. highly uncertain.," We therefore consider the HCl abundance and ] abundance ratio for IRC+10216 as listed in Table \ref{tab:radex-fit}
 highly uncertain."
 More sophisticated modeling efforts such as Schoier&(2001) and Wvrowskiοἱal.(2006) are required to correctly interpret the results for IRC+10216., More sophisticated modeling efforts such as \citet{schoier2001} and \citet{wyrowski2006} are required to correctly interpret the results for IRC+10216.
 Cernicharoοἱal...(2010b) recently reported an LIC! abundance of 5x10.7 [rom their ILerschel SPIRE and PACS observations of IRC+10216., \citet{Cernicharo2010b} recently reported an HCl abundance of $5\times10^{-8}$ from their Herschel SPIRE and PACS observations of IRC+10216.
 It max be interesting to note that we derive an upper limit o£ 8x10* for the HCL abundance in CITG by treating the low signal-to-noise detection as a 0.2 IN line with 20 iin line width., It may be interesting to note that we derive an upper limit of $8\times10^{-8}$ for the HCL abundance in CIT6 by treating the low signal-to-noise detection as a 0.2 K line with 20 in line width.
 Similar to the procedure used in Ser À* and GI.6-0.025. the resulting HCl column density. is. 5xLOL7 L77. with. an adopted gas temperature ofB 40 IX- and an ccolumn density of 6.3xLol!’ ? (Zhang.Kwok.&Trung.2009).," Similar to the procedure used in Sgr $^*$ and G1.6-0.025, the resulting HCl column density is $5\times10^{12}$ $^{-2}$, with an adopted gas temperature of 40 K and an column density of $6.3\times10^{19}$ $^{-2}$ \citep{zhang2009}."
. As listed in Table 3.. the aabundance ratio is rather varied from around unity to around 3 and over.," As listed in Table \ref{tab:radex-fit}, the abundance ratio is rather varied from around unity to around 3 and over."
" Cernicharo.(2000) reported an X[PC1//""CH] ratio of 3.12:0.6 from line intensity ratios of NaCl. NCI. ancl AIC] in IRC+10216."," \citet{Cernicharo2000} reported an ] ratio of $\pm$ 0.6 from line intensity ratios of NaCl, KCl, and AlCl in IRC+10216."
 Recent Herschel LUFI observations show an N[9CI//*CH] ratio of 2.7 in NGCG63341 (Lisetal.2010) and 2.12:0.5 in W3A 2010a)., Recent Herschel HIFI observations show an ] ratio of 2.7 in NGC6334I \citep{Lis2010} and $2.1\pm0.5$ in W3A \citep{Cernicharo2010a}.
. These compare to the terrestrial value of ~3.1., These compare to the terrestrial value of $\sim$ 3.1.
 It is interesting to note that the aabundance ratio comes in a good agreement with the integration line intensity ratio of the HC]and lime. as predicted by the modeling efforts of Cernicharoοἱal.(2010a) for their Herschel," It is interesting to note that the abundance ratio comes in a good agreement with the integration line intensity ratio of the HCland line, as predicted by the modeling efforts of \citet{Cernicharo2010a} for their Herschel"
 , 
The host ealaxy of CRB 980703 is at an intermediate redshift of +=0.966 (Figure A1).,The host galaxy of GRB 980703 is at an intermediate redshift of $z = 0.966$ (Figure A1).
 The Is /ILJ ratio in this ealaxy gives us an ECBV) = 0. and thus no correction for extinction is applied.," The $\gamma$ $\beta$ ratio in this galaxy gives us an $B-V$ ) = 0, and thus no correction for extinction is applied."
 We cau apply the IKobuluickv. Ikewley (2001) Ros metallicity diagnostic to this galaxy. but without a detection of the Ta aud A658 | features we cannot determine whether it lies on the lower or upper branches of the diagnostic.," We can apply the Kobulnicky Kewley (2004) $_{23}$ metallicity diagnostic to this galaxy, but without a detection of the $\alpha$ and $\lambda$ 6584 features we cannot determine whether it lies on the lower or upper branches of the diagnostic."
 Calculating[NIT| metallicities for both branches.we find log(O/II) | 12 = 8.31 4 0.1 (lower: log qg = 7.51) and los(tO/II) | 12 = 8.65 + 0.1 (upper: log 4 = 7.66).," Calculating metallicities for both branches,we find log(O/H) + 12 = 8.31 $\pm$ 0.1 (lower; log $q$ = 7.51) and log(O/H) + 12 = 8.65 $\pm$ 0.1 (upper; log $q$ = 7.66)."
 We also determine a voung stellar population age for this host ealaxy of [7 + 0.1 Myr for the lower-brauch unctallicity and LL + 0.2 Myr for the upper-branch metallicity., We also determine a young stellar population age for this host galaxy of 4.7 $\pm$ 0.1 Myr for the lower-branch metallicity and 4.4 $\pm$ 0.2 Myr for the upper-branch metallicity.
 Using the flax of the |OITJA2727 line and the Kewley et ((2001) metallicity-depeudent relation. we determine SFRs of 9.9 AZ. 1 for the lower-brauch metallicity aud 13.6AL. vy3 for the upper-brauch metallicity.," Using the flux of the $\lambda$ 3727 line and the Kewley et (2004) metallicity-dependent relation, we determine SFRs of 9.9 $M_{\odot}$ $^{-1}$ for the lower-branch metallicity and $M_{\odot}$ $^{-1}$ for the upper-branch metallicity."
 These SFRs agree with the lower limit of >7AL. + determined by Djorgovski et ((1998) and the 8-13 AZ. | range found by. Holland et (2001)., These SFRs agree with the lower limit of $>7 M_{\odot}$ $^{-1}$ determined by Djorgovski et (1998) and the 8-13 $M_{\odot}$ $^{-1}$ range found by Holland et (2001).
" Finally, withphotometry from Savaglio et ((2009) and thePhare code we find a stellar mass for the host galaxy of M,/M ,.) = 9.83 4 0.13."," Finally, withphotometry from Savaglio et (2009) and the code we find a stellar mass for the host galaxy of $M_{\star}/M_{\odot}$ ) = 9.83 $\pm$ 0.13."
 The host ealax of GRB 991208 is an intermediateredshitt (2=0.706) host galaxy that was originally published iu Paper 1. We previously applied the Iobuluickv Ἱνοπιο (2001) Ro; metallicity diagnostic to our LRIS observations of this host. but were unable to established whether the host metallicity was on the lower or upper brauch of the double-valued diagnostic.," The host galax of GRB 991208 is an intermediate-redshift $z = 0.706$ ) host galaxy that was originally published in Paper I. We previously applied the Kobulnicky Kewley (2004) $_{23}$ metallicity diagnostic to our LRIS observations of this host, but were unable to established whether the host metallicity was on the lower or upper branch of the double-valued diagnostic."
 Here we preseut our NIRSPEC data for this host. which show a detection of the Ta cussion feature and an upper limit on the [NIJA65s8 feature (Figure A2).," Here we present our NIRSPEC data for this host, which show a detection of the $\alpha$ emission feature and an upper limit on the $\lambda$ 6584 feature (Figure A2)."
 Based on the Πα ratio determined from this data. and following the criteria of Icwlev EEllison (2008). we can now conclude [NUthat the host galaxy of CRB 991208 falls on the lower branch of the Ro; diagnostic. vielding a host metallicity of los(O/II) | 12 = 8.02 and an ionization paramcter of log g = 7.38 according to Iobuluicky Kewley (2001).," Based on the $\alpha$ ratio determined from this data, and following the criteria of Kewley Ellison (2008), we can now conclude that the host galaxy of GRB 991208 falls on the lower branch of the $_{23}$ diagnostic, yielding a host metallicity of log(O/H) + 12 = 8.02 and an ionization parameter of log $q$ = 7.38 according to Kobulnicky Kewley (2004)."
 We also derive a young stellar population age of 12+ 0.2 Mov. aud a metallicity-dependeut SFR = 3.17 AL. | based on the Newley et ((2001) [OTI]diagnostic.," We also derive a young stellar population age of 4.2 $\pm$ 0.2 Myr, and a metallicity-dependent SFR = 3.47 $M_{\odot}$ $^{-1}$ based on the Kewley et (2004) [OII]diagnostic."
" Using photometry from Savaglio et ((2009) and the codo. we deterimine a stellar 1ass for this host galaxy of M, /AL.) = 88h + O17."," Using photometry from Savaglio et (2009) and the code, we determine a stellar mass for this host galaxy of $M_{\star}/M_{\odot}$ ) = 8.85 $\pm$ 0.17."
 The host ealaxy of CRB 010921 is an iutermeciate-redshitt (2=0.151) host that was previously examined in Paper IL We originally applied the Nobulnicky Ixewley (2001) Ros mectallicity diagnostic to these host observations. but were unable to determune whether this host was ou the lower or upper brauch of the diagnostic.," The host galaxy of GRB 010921 is an intermediate-redshift $z = 0.451$ ) host that was previously examined in Paper I. We originally applied the Kobulnicky Kewley (2004) $_{23}$ metallicity diagnostic to these host observations, but were unable to determine whether this host was on the lower or upper branch of the diagnostic."
 Here we present our observation of the Πο cinission feature aud an upper Init ou the [NIT|AG58 feature (Figure À3)., Here we present our observation of the $\alpha$ emission feature and an upper limit on the $\lambda$ 6584 feature (Figure A3).
" Based ou the Cluission-lne ratio determiued from this observation and the criteria of Iowley LEEllison (2008). we can now conclude that the host of CRB 010921 lies ou the lower brauch of the Ros diagnostic. with a ietallicitv of los(O/II) | 12 2 8.21 + 0.1. an ionization parameter of log 4 = T.LI. a young stellar population age of 8.0 + 0.2 Mya. aud à SER = 0.70 M, | based ou the metallicity-dependeut [OI] diagnostic of Iewlev et (2001)."," Based on the emission-line ratio determined from this observation and the criteria of Kewley Ellison (2008), we can now conclude that the host of GRB 010921 lies on the lower branch of the $_{23}$ diagnostic, with a metallicity of log(O/H) + 12 = 8.24 $\pm$ 0.1, an ionization parameter of log $q$ = 7.44, a young stellar population age of 8.0 $\pm$ 0.2 Myr, and a SFR = 0.70 $M_{\odot}$ $^{-1}$ based on the metallicity-dependent [OII] diagnostic of Kewley et (2004)."
" Adopting photometry from Savaglio et ((2009) and using the code. we also determine a stellar mass for the host galaxy of logM,/AL.) = 9,5610.110-09."," Adopting photometry from Savaglio et (2009) and using the code, we also determine a stellar mass for the host galaxy of $M_{\star}/M_{\odot}$ ) = $^{+0.09}_{-0.11}$."
 For a detailed discussion of the unusual host galaxy of GRB 020819. see Levesque ct ((2010b): for this work we adopt the ISM properties derived for the uucleus of the host galaxy.," For a detailed discussion of the unusual host galaxy of GRB 020819, see Levesque et (2010b); for this work we adopt the ISM properties derived for the nucleus of the host galaxy."
" We adopt photometry from Savaglio et ((2009) and use the code to deteriiue a stellar mass for the host galaxy of logCAM,/M ..) = 10.65 + 0.19.", We adopt photometry from Savaglio et (2009) and use the code to determine a stellar mass for the host galaxy of $M_{\star}/M_{\odot}$ ) = 10.65 $\pm$ 0.19.
 Rau et ((2005) publish enission-line fluxes. uncorrected for extinction. for the [OIT|A3727. Πο. |OITI[A 1959. aud OII[A5Q007 features in the +=0.782 host galaxy of GRB 030528.," Rau et (2005) publish emission-line fluxes, uncorrected for extinction, for the $\lambda$ 3727, $\beta$, $\lambda$ 4959, and $\lambda$ 5007 features in the $z = 0.782$ host galaxy of GRB 030528."
 They also include upper limits on the |NeTIT|A3869. Id. aud T+ cimission features.," They also include upper limits on the $\lambda$ 3869, $\delta$, and $\gamma$ emission features."
 Ran et ((2005) propose a total line-ofsielt y-<2.5 for this host. correspondiug oa Galactic E(B V) « 0.62 from Schlegel et ((1998) aud an additional host extinction of ELB V) < 0.19.," Rau et (2005) propose a total line-of-sight $A_V < 2.5$ for this host, corresponding to a Galactic $B-V$ ) $<$ 0.62 from Schlegel et (1998) and an additional host extinction of $B-V$ ) $<$ 0.19."
 However. Dutra ct ((2003) Sugeest a lower line-ofsight ECB V) = 0.16. following a rescaling of the Schlegel ct ((1998) extinction.," However, Dutra et (2003) suggest a lower line-of-sight $B-V$ ) = 0.46, following a rescaling of the Schlegel et (1998) extinction."
 We consider both of these proposed E(B WW) values in our analysis. aud &ud that iu both cases he Ros value places the host metallicity on the log(O/IID) | 12 ~ 8.1 c 0.1 turnover of the Nobulnicky Kewley (2001) diagnostic.," We consider both of these proposed $B-V$ ) values in our analysis, and find that in both cases the $_{23}$ value places the host metallicity on the log(O/H) + 12 $\sim$ 8.4 $\pm$ 0.1 turnover of the Kobulnicky Kewley (2004) diagnostic."
 We also find a lower limit of SFR >12.1Af. + based on the metallicity-depeudeut [OT] relation of Ixewlev et ((2001)., We also find a lower limit of SFR $> 12.1 M_{\odot}$ $^{-1}$ based on the metallicity-dependent [OII] relation of Kewley et (2004).
 Using photometry frou Savagho et ((2009) and the Phare code. we find a stellar 11ass or the host ealaxy of M. /AL.) 9 941 03. ," Using photometry from Savaglio et (2009) and the code, we find a stellar mass for the host galaxy of $M_{\star}/M_{\odot}$ ) = $9.11^{+0.23}_{-0.26}$ ."
Sollcrman et (2007) publish ffuxes for the |OIT|A3727. Πο. |OITI[A 1959. aud ABOUT. c1ission features in the 2=0.828 host galaxy of GRB 050821.," Sollerman et (2007) publish fluxes for the $\lambda$ 3727, $\lambda$ 3869, $\beta$ , $\lambda$ 4959, and $\lambda$ 5007 emission features in the $z = 0.828$ host galaxy of GRB 050824."
 These fluxes are [NeII[A3869.uncorrected forGalactic extinction[DITE] (E(B V) = 0.035 from Schlegel et 11998) or host extinction: however. they estimate a lost extinction of E(B V) « 0.16.," These fluxes are uncorrected forGalactic extinction $B-V$ ) = 0.035 from Schlegel et 1998) or host extinction; however, they estimate a host extinction of $B-V$ ) $<$ 0.16,"
conclusion in de ας et al. (,conclusion in de Grijs et al. (
2005) that we can retrieve prominent features in the cluster age distribution to within Adlog(Xge/vr)?x0.35. we have now also shown that theinbrinsic statistical uncertainties involved. in cluster age determinations based. on. broad-band. SEDs are of a very similar magnitude.,"2005) that we can retrieve prominent features in the cluster age distribution to within $\Delta \langle \log( {\rm Age /
yr} ) \rangle \le 0.35$, we have now also shown that the statistical uncertainties involved in cluster age determinations based on broad-band SEDs are of a very similar magnitude."
 Using the newly determined and improved age estimates for the largest LMC cluster sample spanning the most extensive age and mass ranges to date. we now have the means to constrain the past cluster formation rate (CER). as well as the effects of cluster disruption. to unprecedented detail.," Using the newly determined and improved age estimates for the largest LMC cluster sample spanning the most extensive age and mass ranges to date, we now have the means to constrain the past cluster formation rate (CFR), as well as the effects of cluster disruption, to unprecedented detail."
 In Fig., In Fig.
 Gaa we display the number of clusters formed. per unit age range., \ref{agemasshist.fig}a a we display the number of clusters formed per unit age range.
 Evolutionary fading. as predicted by stellar population synthesis models. will cause this number to slowly decline from. the voungest ages upward.," Evolutionary fading, as predicted by stellar population synthesis models, will cause this number to slowly decline from the youngest ages upward."
 This cllect is shown by the dashed line in Fig., This effect is shown by the dashed line in Fig.
 62a. of which the slope is entirely. determined. by the details of stellar population svnthesis: we have only shifted. this line to best. match the data points for log(Xge/sr).8.," \ref{agemasshist.fig}a a, of which the slope is entirely determined by the details of stellar population synthesis; we have only shifted this line to best match the data points for $\log({\rm Age/yr}) \le 8$."
 Both internal and external cllects. such as two-body relaxation. disk ancl bulge shocking. and the tidal cllects caused by the underlving galactic gravitational potential (even in the low-clensity environment of the LMC: cf," Both internal and external effects, such as two-body relaxation, disk and bulge shocking, and the tidal effects caused by the underlying galactic gravitational potential (even in the low-density environment of the LMC; cf."
 Lamers. Gieles Portegies Zwart 2005). leaciing to tidal stripping and to evaporation of a fraction of the low-mass cluster stars. will result in the (eradiual) dissolution of star clusters.," Lamers, Gieles Portegies Zwart 2005), leading to tidal stripping and to evaporation of a fraction of the low-mass cluster stars, will result in the (gradual) dissolution of star clusters."
 Simple (instantaneous) disruption theory (Boutloukos Lamers 2003). predicts that. assuming a constant CER and that the characteristic," Simple (instantaneous) disruption theory (Boutloukos Lamers 2003) predicts that, assuming a constant CFR and that the characteristic"
 Péquiguot&Daluteau(1991). ideutify cussion lines frou a wmuuber of heavy clements with Z>30 i for the first time., \citet{pequignotba1994} identify emission lines from a number of heavy elements with $Z>30$ in for the first time.
 As expected. many of these lines have extremely low intensities |~10ΤΠ j|.," As expected, many of these lines have extremely low intensities $\sim 10^{-5}I({\rm H}\beta)$ ]."
 Table AL lists cuiission lines from heavy elemieuts of Z>30 ideutified by Péquignot&Daluteau(1991). (PB) that have also been detected in our optical spectrum., Table \ref{rs} lists emission lines from heavy elements of $Z>30$ identified by \citet{pequignotba1994} (PB) that have also been detected in our optical spectrum.
 The measured fiuxes are in general consistent with those reported by 1).., The measured fluxes are in general consistent with those reported by \citet{pequignotba1994}.
 These emission features should provide vital information about r- aud s-processes in late evolution stages of ACB stars., These emission features should provide vital information about r- and s-processes in late evolution stages of AGB stars.
 Table Bl and Table B2 list references of atomic data for CEL and ORL analyses. respectively.," Table \ref{refcel} and Table \ref{reforl} list references of atomic data for CEL and ORL analyses, respectively."
is assembled bv taking the median οἱ all images ancl is then subtracted.,is assembled by taking the median of all images and is then subtracted.
 We then rotate (he images (o put North up and median combine them., We then rotate the images to put North up and median combine them.
 We apply an unsharp mask to the resulting image (median in a +x 4A/D box) to remove the low spatial frequency noise and convolve ii by a 0.5A/D width Gaussian (o average the high frequency pixel-to-pixel noise., We apply an unsharp mask to the resulting image (median in a $4\times4 \lambda/$ D box) to remove the low spatial frequency noise and convolve it by a $0.5 \lambda$ /D width Gaussian to average the high frequency pixel-to-pixel noise.
 We finally average the Nov. 1 and 2 images (Fig. 2))., We finally average the Nov. 1 and 2 images (Fig. \ref{fig : f2}) ).
 Without the LOCI background subtraction. none of the planets would have been detected (right panel. signal-to-noise ratio (SNR) for dis less than 2).," 	 Without the LOCI background subtraction, none of the planets would have been detected (right panel, signal-to-noise ratio (SNR) for d is less than $2$ )."
 With the LOCI background subtraction.8799b.. ¢ and d are detected. (left. panel. 3 to 8 SNR).," With the LOCI background subtraction, c and d are detected (left panel, $3$ to $8$ SNR)."
 Planet e non-detection is probably due to. both sequences not being acquired through transit. thus limiting the amount of speckle noise being removed at small separations from the median subtraction.," Planet e non-detection is probably due to both sequences not being acquired through transit, thus limiting the amount of speckle noise being removed at small separations from the median subtraction."
 We tried toapply a more advanced LOCI algorithm (Lafreniereetal.2007:Marolsal.2003b.2010b) {ο improve the speckle reduction. but as the FOV rotation ranges were small for both nights. no contrast gain was achieved.," We tried toapply a more advanced LOCI algorithm \citep{lafreniere07,marois08b,marois10b} to improve the speckle reduction, but as the FOV rotation ranges were small for both nights, no contrast gain was achieved."
 Planet (hixes aud positions were obtained bv sublractine the planets prior (o the speckle reduction using the stellar insaturated PSF as the template., Planet fluxes and positions were obtained by subtracting the planets prior to the speckle reduction using the stellar unsaturated PSF as the template.
 We also (riecl subtracting the companions prior to the LOCHI-background algorithm and we have confirmed that no bias is introduced by this technique (final flux variations smaller than 0.07%)., We also tried subtracting the companions prior to the LOCI-background algorithm and we have confirmed that no bias is introduced by this technique (final flux variations smaller than $0.07\%$ ).
 The subtraction was iterated by moving the planet template and changing ils intensity until a minimal noise residual αἱ the planets location was achieved (inside a 1.5 A/D radius area; Tab., The subtraction was iterated by moving the planet template and changing its intensity until a minimal noise residual at the planet's location was achieved (inside a 1.5 $\lambda$ /D radius area; Tab.
 1 for the resulting magnitudes)., \ref{tab : tab1} for the resulting magnitudes).
 Photometric error bars were calculated in A/D width annulus., Photometric error bars were calculated in $\lambda/D$ width annulus.
 As expected [rom other wavelengths (Alaroisetal.2008).. flux. is roughly a third of that of planets c and d. The planets positions are included in Tab. 1..," As expected from other wavelengths \citep{marois08}, flux is roughly a third of that of planets c and d. The planet's positions are included in Tab. \ref{tab : tab1}."
 The low SNRs and the large M-band PSF core result in large astrometric errors., The low SNRs and the large M-band PSF core result in large astrometric errors.
 A fultwe astrometric IER. 8799 paper using shorter wavelength astrometry is in preparation., A future astrometric HR 8799 paper using shorter wavelength astrometry is in preparation.
 Contrast plots (central panel of Fig. 2)), Contrast plots (central panel of Fig. \ref{fig : f2}) )
 were obtained by caleulating the noise in an annulus having a A/D width normalized bv the stellar PSF flux (alter performing (he same unsharp mask and convolution of a 0.5 A/D Gaussian)., were obtained by calculating the noise in an annulus having a $\lambda/$ D width normalized by the stellar PSF flux (after performing the same unsharp mask and convolution of a 0.5 $\lambda/$ D Gaussian).
 The contrast. plots were (hen normalized at each separation bv the estimated point source throughput using simulated ADI mecian process planets., The contrast plots were then normalized at each separation by the estimated point source throughput using simulated ADI median process planets.
 Fig., Fig.
 2 shows that the LOCI background subtraction (black full line) is up to ~3 times better than a classical background median subtraction (red dotted line)., \ref{fig : f2} shows that the LOCI background subtraction (black full line) is up to $\sim 3$ times better than a classical background median subtraction (red dotted line).
 If a classical backeround subtraction routine is used. an integration time of up to 9 times longer is required to reach (he same LOCI background. subtraction contrast.," If a classical background subtraction routine is used, an integration time of up to 9 times longer is required to reach the same LOCI background subtraction contrast."
 This new highly efficient LOCI-based backeroundoO subtvaction routine can be used on anv data where the background is non-negligible and evolving with time., This new highly efficient LOCI-based background subtraction routine can be used on any data where the background is non-negligible and evolving with time.
 It has been shown that the planets are an L-type extension towards lower effective temperatures and lower surface gravities (Maroisetal.2008:Dowler 2011)..," It has been shown that the planets are an L-type extension towards lower effective temperatures and lower surface gravities \citep{marois08,bowler10,currie11,barman11}. ."
 The planets have also been, The planets have also been
"by the LAT non-detections on the ratio R of the 100 MeV to 1 MeV fluences. vF,=vfdrfar for hv=1.100 MeV. during the prompt emission.","by the LAT non-detections on the ratio $R$ of the 100 MeV to 1 MeV fluences, $\nu F_\nu=\nu\int dt f_\nu(t)$ for $h\nu=1,100$ MeV, during the prompt emission."
" The upper limits on R obtained assuming dN,/dE«E at E>100 MeV (see fig.", The upper limits on $R$ obtained assuming $dN_\gamma/dE\propto E^{-2}$ at $E>100$ MeV (see fig.
" 2). also imply upper limits on the 0.1-1 GeV fluence. which is approximately given by IncIO)Rv£,|iyi;v. (the upper limit on the 1-10 GeV fluence is few times higher and depends on the assumed spectrum). and on the ratio of the 0.1—1 GeV fluence and the 0.1-1 MeV fluence. which is =Δ."," 2), also imply upper limits on the 0.1–1 GeV fluence, which is approximately given by $\ln(10)R\nu F_\nu|_{1\rm MeV}$ (the upper limit on the 1–10 GeV fluence is few times higher and depends on the assumed spectrum), and on the ratio of the 0.1–1 GeV fluence and the 0.1–1 MeV fluence, which is $\approx R$."
 The upper limits on R are more stringent for brighter bursts (see fig., The upper limits on $R$ are more stringent for brighter bursts (see fig.
 2). with R«(0.1.0.3.1} for (5.30.6016€ of the bursts (see fig.," 2), with $R<\{0.1,0.3,1\}$ for $\{5,30,60\}\%$ of the bursts (see fig."
 4)., 4).
 This implies that for most bursts the prompt ~1 GeV emission may be comparable to the ~1 MeV emission. but can not dominate it.," This implies that for most bursts the prompt $\sim1$ GeV emission may be comparable to the $\sim1$ MeV emission, but can not dominate it."
 For several bright bursts with reliable determination of the photon spectral index at ~1 MeV. the LAT non detection implies an upper limit to the ~100 MeV flux which is <0.1 of the flux obtained by extrapolating the ~| MeV flux to high energy (see fig.," For several bright bursts with reliable determination of the photon spectral index at $\sim1$ MeV, the LAT non detection implies an upper limit to the $\sim100$ MeV flux which is $<0.1$ of the flux obtained by extrapolating the $\sim1$ MeV flux to high energy (see fig."
 5)., 5).
 Examining figs., Examining figs.
 2 and 4. we conclude that the ratio R is not universal among GRBs.," 2 and 4, we conclude that the ratio $R$ is not universal among GRBs."
 The detections and non-detection upper limits imply a spread in R over at least an order of magnitude., The detections and non-detection upper limits imply a spread in $R$ over at least an order of magnitude.
 The upper limits we obtain are similar to those inferred for the fluence at lower energy. 30-200 MeV. from EGRETs non-detections of BATSE bursts (see 49).," The upper limits we obtain are similar to those inferred for the fluence at lower energy, 30–200 MeV, from EGRET's non-detections of BATSE bursts (see \ref{sec:EGRET}) )."
 The upper limits on Α provide constraints on models for the prompt GRB emission., The upper limits on $R$ provide constraints on models for the prompt GRB emission.
 Models where the prompt ~| MeV emission ts produced by inverse-Compton scattering of optical synchrotron photons (e.g. Stern Poutanen 2004. Panaitescu Kumar 2007). typically predict R>1.," Models where the prompt $\sim1$ MeV emission is produced by inverse-Compton scattering of optical synchrotron photons (e.g. Stern Poutanen 2004, Panaitescu Kumar 2007), typically predict $R\ge1$."
 This is not supported by the data., This is not supported by the data.
 Such models are not necessarily ruled out by the current data. as they might be modified to include a suppression of the ~1 GeV flux by pair production.," Such models are not necessarily ruled out by the current data, as they might be modified to include a suppression of the $\sim1$ GeV flux by pair production."
 Such modification may be required for all (widely discussed) models. in which the ~| MeV power-law photon spectrum reflects the power-law energy distribution of fast cooling electrons.," Such modification may be required for all (widely discussed) models, in which the $\sim1$ MeV power-law photon spectrum reflects the power-law energy distribution of fast cooling electrons."
 The suppression of the ~100 MeV flux. compared to that expected from an extrapolation of the -1 MeV power-law spectrum. suggests that either the electron energy distributior does not follow a power-law over a wide energy range. or that the high energy photons are absorbed. probably by pair production.," The suppression of the $\sim100$ MeV flux, compared to that expected from an extrapolation of the $\sim1$ MeV power-law spectrum, suggests that either the electron energy distribution does not follow a power-law over a wide energy range, or that the high energy photons are absorbed, probably by pair production."
 Requiring an optical depth of ~1 at 100 MeV sets an upper limit to the expansion Lorentz factor Γς107?[(LJI0erg/s)/(./10msj|'/? (e.g. eq.," Requiring an optical depth of $\sim1$ at $100$ MeV sets an upper limit to the expansion Lorentz factor $\Gamma\lsim10^{2.5}[(L/10^{52}{\rm erg/s})/(t_v/10\,{\rm ms})]^{1/6}$ (e.g. eq."
 7 of Waxman 2003)., 7 of Waxman 2003).
 Significant compactness of the emission region has been suggested by several authors (e.g. Guetta et al., Significant compactness of the emission region has been suggested by several authors (e.g. Guetta et al.
 2001. Peer Waxman 2004).," 2001, Pe'er Waxman 2004)."
 The spectrum is modified in this case. compared to the optically thin case. with 100 MeV to 1 MeV flux ratios in the range 0.01<R<0.1 obtained for typical parameters (e.g. figs.," The spectrum is modified in this case, compared to the optically thin case, with 100 MeV to 1 MeV flux ratios in the range $0.01\lsim R\lsim0.1$ obtained for typical parameters (e.g. figs."
 8 11 of Pe'er Waxman 2004)., 8 11 of Pe'er Waxman 2004).
 This research was supported in part by ISF. AEC and Minerva grants.," This research was supported in part by ISF, AEC and Minerva grants."
 DG EP thank the Benoziyo center for Astrophysics at the Weizmann institute for hospitality during the time at which this research was initiated., DG EP thank the Benoziyo center for Astrophysics at the Weizmann institute for hospitality during the time at which this research was initiated.
 We thank Nicola Omodei. David Coward for their useful advices.," We thank Nicola Omodei, David Coward for their useful advices."
"more realisic cases considering (he non-radial expansion of fina,=5 cannot explain the observations. which implies (hat other mechanisms of heating (ancl acceleration) necessarily work cooperatively,","more realistic cases considering the non-radial expansion of $f_{\rm max}=5$ cannot explain the observations, which implies that other mechanisms of heating (and acceleration) necessarily work cooperatively."
 We would like to study in detail why (Προ)c has an upper limit on fixed 7 and i., We would like to study in detail why $(n_{\rm p}v)_{\rm 1AU}$ has an upper limit on fixed $\tau$ and $f_{\rm max}$.
" Figure 6. displavs the ratios of the main three (vpes of energy loss: downward thermal conduction from the coronal base. radiative escape in the corona. and total amount of enerev converted to the flow (mass loss) at rou. respectively. normalized by F4 lor the cases adopting 7= 120s and fia,=5."," Figure \ref{fig:fwfrc} displays the ratios of the main three types of energy loss: downward thermal conduction from the coronal base, radiative escape in the corona, and total amount of energy converted to the flow (mass loss) at $r_{\rm out}$, respectively normalized by $F_{\rm w,0}$ for the cases adopting $\tau=120$ s and $f_{\rm max}=5$."
" The values for downward thermal conduction in fie.6 ave taken from maximum conductive [αν Fea, in lower corona (see fig.7)) and the values for (he radiative escape are derived by (he integration of the radiative cooling hunction from points with F.,444 lo fou."," The values for downward thermal conduction in \ref{fig:fwfrc} are taken from maximum conductive flux $F_{\rm c, max}$ in lower corona (see \ref{fig:egtr}) ) and the values for the radiative escape are derived by the integration of the radiative cooling function from points with $F_{\rm c, max}$ to $r_{\rm out}$."
 Che region not labeled between radiative escape ancl “Low denotes οποιον carried out of roa by thermal conduction., The region not labeled between 'radiative escape' and 'flow' denotes energy carried out of $r_{\rm out}$ by thermal conduction.
 According to fig.6.. (he main source ol coronal energv loss is downward thermal conduction within our range of Fy.4 (striclly speaking. most of the conducted energy. finally radiates away). whereas radiative escape Comes {ο play a significant role lor larger £44 since clensily in (he corona becomes higher. being subject to eq.(24)).," According to \ref{fig:fwfrc}, , the main source of coronal energy loss is downward thermal conduction within our range of $F_{\rm w,0}$ (strictly speaking, most of the conducted energy finally radiates away), whereas radiative escape comes to play a significant role for larger $F_{\rm w,0}$ since density in the corona becomes higher, being subject to \ref{eq:fwptr}) )."
 Although a ratio of enerey trausfered to (he flow is as small as <3% throughout the range. it has a bimodal tendency.," Although a ratio of energy transfered to the flow is as small as $\lesssim 3\%$ throughout the range, it has a bimodal tendency."
" In Fi<6x10""erg 7s | it increases. which implies that the larger Fy. is. the more effectively the energy is transfered to the flow."," In $F_{\rm w,0}<6\times 10^5$ erg $^{-2}$ $^{-1}$ it increases, which implies that the larger $F_{\rm w,0}$ is, the more effectively the energy is transfered to the flow."
 However. in Fio>6x LOerg em7s |. it decreases because of the abrupt dominance of radiative cooling.," However, in $F_{\rm w,0}>6\times 10^5$ erg $^{-2}$ $^{-1}$, it decreases because of the abrupt dominance of radiative cooling."
" As a result. the predicted Ga,e)yr increases rapidly on increasing Fab first ancl eventually decreases as seen in fig.5.."," As a result, the predicted $(n_{\rm p}
v)_{\rm 1AU}$ increases rapidly on increasing $F_{\rm w,0}$ at first and eventually decreases as seen in \ref{fig:fwmd}."
 To examine these differences in terms of enerev transfer. we show variations of energy [αν of four components. per flow tube with a cross section of sf =lem? atthe inner boundary.," To examine these differences in terms of energy transfer, we show variations of energy flux of four components, per flow tube with a cross section of $A=$ $^2$ atthe inner boundary."
 The flow term of eq.(27)) contains three ingredients. kinetic enerev of the solar wind. enthalpy. aud," The 'flow' term of \ref{eq:flx3}) ) contains three ingredients, kinetic energy of the solar wind, enthalpy, and"
beeiuuiug of this flare coiucides with the X-rav spike within less than 300s.,beginning of this flare coincides with the X-ray spike within less than 300s.
 On & and p classes; we lack the sensitivity to confirm or reject a simular behavior.," On $\kappa$ and $\rho$ classes, we lack the sensitivity to confirm or reject a similar behavior."
 Finally. @ classes παν also follow this scheme with. however. radio flares siguificautlv siualler than diuvine aud » dips of conrparable duration.," Finally, $\theta$ classes may also follow this scheme with, however, radio flares significantly smaller than during $\beta$ and $\nu$ dips of comparable duration."
 Using the available 3. A aud v observations. a trend is visible between the leneth of the X-ray dips aud the characteristics of the following flare: the longer the N-rav dip is. the bieecr the following radio flare will be.," Using the available $\beta$, $\lambda$ and $\nu$ observations, a trend is visible between the length of the X-ray dips and the characteristics of the following flare: the longer the X-ray dip is, the bigger the following radio flare will be."
 This result does uot directly depend ou the plasmon model used to characterize the radio data., This result does not directly depend on the plasmon model used to characterize the radio data.
 Indeed. this model we chose was used mainly to distinguish between the energy cluitted during each individual flare i a sequence of racio flares. rather than as a precise description of cach fare.," Indeed, this model we chose was used mainly to distinguish between the energy emitted during each individual flare in a sequence of radio flares, rather than as a precise description of each flare."
 Therefore. every “realistic” function with a fast rise aud slow decay able to fit the shape of the radio flares would lead to the same result.," Therefore, every “realistic"" function with a fast rise and slow decay able to fit the shape of the radio flares would lead to the same result."
 Ta particular. cussion from a conical jet or a shock-leated compact jet would have almost the same temporal shape. and thus lead to similar results concerning the basic paraiaeters explored here.," In particular, emission from a conical jet or a shock-heated compact jet would have almost the same temporal shape, and thus lead to similar results concerning the basic parameters explored here."
 This link seems to be related to the leneth of lard N-ray clips: longer dips lead to more energetic ejections., This link seems to be related to the length of hard X-ray dips: longer dips lead to more energetic ejections.
 Although the data are scarce. this link does not secu to be linear. and can be deseribed. for iustauce. by a power-law or exponential relatiouship.," Although the data are scarce, this link does not seem to be linear, and can be described, for instance, by a power-law or exponential relationship."
 Cüveu the lnieh uncertainties on the data. if is uot possible to discriminate between these fuuctions.," Given the high uncertainties on the data, it is not possible to discriminate between these functions."
 Yot. in the second case. one could think of au attractive scenario to explain the relationship.," Yet, in the second case, one could think of an attractive scenario to explain the relationship."
 Observations slow that the begimniug of the dip is marked by a quick increase In the accretion disk mner radius., Observations show that the beginning of the dip is marked by a quick increase in the accretion disk inner radius.
 Then. during the dip itself. the disk draws closer to the BU (Belloui 2008b).," Then, during the dip itself, the disk draws closer to the BH \citep{Belloni:1997, Migliari:2003, Rodriguez:2008b}."
. This evolution briugs more eravitational energy close to the DII., This evolution brings more gravitational energy close to the BH.
 Let us suppose that. during the Tard X- dip. energv is somehow extracted from the accretion disk. and accumulated iu the surrounding medium.," Let us suppose that, during the Hard X-ray dip, energy is somehow extracted from the accretion disk, and accumulated in the surrounding medium."
 Thus. the huninosity of the disk aud corona slowly increase.," Thus, the luminosity of the disk and corona slowly increase."
" At t1ο sale time. the amount of cnerev lost by the corona 1 La given time erows as the energy density of the corona 1icreases,"," At the same time, the amount of energy lost by the corona in a given time grows as the energy density of the corona increases."
" Thus. the total energy stored inside the corona saturates after. sav, ~LO00s."," Thus, the total energy stored inside the corona saturates after, say, $\sim$ 1000s."
 Then. at some point. this energv ds released iu the formu of a quickly expanding blob of matter.," Then, at some point, this energy is released in the form of a quickly expanding blob of matter."
 In the A-rav lighteurve. this ejection is marked bv a short N-rav spike (Mirabeletal.1998:Ro-driguezetal. 2008a).," In the X-ray lightcurve, this ejection is marked by a short X-ray spike \citep{Mirabel:1998, Rodriguez:2008a}."
. Note that the ejected material can conie from the corona itself. or from the iuner accreting disk: either way. after the spike the corona is not visible auvinore. and the disk is closer to the DII.," Note that the ejected material can come from the corona itself, or from the inner accreting disk; either way, after the spike the corona is not visible anymore, and the disk is closer to the BH."
 Iu the case of a jet (either steady or shock-heatec). the scenario is similar: during the dips an injection of material iuto the jet from the corona takes place (xleiu-Woltetal.2002).," In the case of a jet (either steady or shock-heated), the scenario is similar: during the dips an injection of material into the jet from the corona takes place \citep{KleinWolt:2002}."
. Ássuniug a amore or less constant injection rate. longer N-vav dips will thus be radio-briehter. as more material is ejected.," Assuming a more or less constant injection rate, longer X-ray dips will thus be radio-brighter, as more material is ejected."
 Furthermore. during the dip. as the disk moves back in towards the compact object. one can assunie that it reduces the injection rate. which would explain the apparent saturation iu the flare fiueuce.," Furthermore, during the dip, as the disk moves back in towards the compact object, one can assume that it reduces the injection rate, which would explain the apparent saturation in the flare fluence."
 Then. at some point. the disk is so close to the DIT that it stppresses the injection of particles.," Then, at some point, the disk is so close to the BH that it suppresses the injection of particles."
 The N-rav dip euds. aud radio eniüssion is detected afterwards.," The X-ray dip ends, and radio emission is detected afterwards."
 Iowever. the jet interpretation suffers from an Huportant caveat: it predicts lightcirves different frou he observed radio flares.," However, the jet interpretation suffers from an important caveat: it predicts lightcurves different from the observed radio flares."
 Tudeed. using the conical jet roni Wjelhning&Johustou(1988). itf is possible to uodel the radio cussion from a transieut jet.," Indeed, using the conical jet from \citet{Hjellming:1988}, it is possible to model the radio emission from a transient jet."
 During a eiven dip. the jet would be active for ~30 min.," During a given dip, the jet would be active for $\sim$ 30 min."
" With a velocity of about cho,=Oe. the jet would have a otal extension of ~LOM em. or about ~10Rs."," With a velocity of about $v_{exp}=0.8c$, the jet would have a total extension of $\sim4.10^{13}$ cm, or about $\sim10^7 R_S$."
 The resulting svuchrotron chussion would thus emanate from clectrous at very differeut teniperatures. due to adiabatic expansion.," The resulting synchrotron emission would thus emanate from electrons at very different temperatures, due to adiabatic expansion."
 When looking at a fixed radio frequency. the ichteurve would then be broader than that of a single asnon.," When looking at a fixed radio frequency, the lightcurve would then be broader than that of a single plasmon."
 Besides. the radio cussion would be detected roni the beeiunius of the N-rav dip. or with a coustaut nue-lag with it.," Besides, the radio emission would be detected from the beginning of the X-ray dip, or with a constant time-lag with it."
 Since the data show that the radio Cluission begins within a few minutes frou the N-rav spike at the end of the dip. with no dependance ou the cheth of the dip. this iuterpretation seenis less probable han the discrete ejection model.," Since the data show that the radio emission begins within a few minutes from the X-ray spike at the end of the dip, with no dependance on the length of the dip, this interpretation seems less probable than the discrete ejection model."
 It is interesting to note that the distribution of width of the radio flares is quite peaked while that of the auplitude not., It is interesting to note that the distribution of width of the radio flares is quite peaked while that of the amplitude not.
 In the framework of the plasiion mode (vanderLaan1966).. the width of the flare is related to he initial physical size of the plasmon.," In the framework of the plasmon model \citep{vanderLaan:1966}, the width of the flare is related to the initial physical size of the plasmon."
 Thus. the relative sharpness of this distribution means that the initia radius of the plasmon is roughly always the same.," Thus, the relative sharpness of this distribution means that the initial radius of the plasmon is roughly always the same."
 It is cClupting to interpret that this radius may be constraiec o» the iuuer radius of the disk., It is tempting to interpret that this radius may be constrained by the inner radius of the disk.
 On the other haud. he mnaxiuuni amplitude of the flare is related to the initial temperature and energy distribution of the ejectec asna.," On the other hand, the maximum amplitude of the flare is related to the initial temperature and energy distribution of the ejected plasma."
 Thus the relative broaducss of the amplitude distribution could mean that the amount of energy store inside the plasiua prior to the ejection is more variable.," Thus, the relative broadness of the amplitude distribution could mean that the amount of energy stored inside the plasma prior to the ejection is more variable."
 If we asstune that the amount of energy stored inside the plasina depeuds on the duration of the preceding A-rav dip. then this relative broaduess can be casily explained.," If we assume that the amount of energy stored inside the plasma depends on the duration of the preceding X-ray dip, then this relative broadness can be easily explained."
 Indeed. during shorter dips the iuput of energy would be shorter. thus the amplitude of the following flare would be smaller.," Indeed, during shorter dips the input of energy would be shorter, thus the amplitude of the following flare would be smaller."
 Since the duration of the X-ray dips is highly variable. the amplitude of the flares will also be variable.," Since the duration of the X-ray dips is highly variable, the amplitude of the flares will also be variable."
 Ou the other hand. the medimu which stores this cucrey will always be located in the same reeion. close to the inner radius ofthe disk: ifits plivsical size is constrained by the disk. then the width of tle flares will be roughly constant.," On the other hand, the medium which stores this energy will always be located in the same region, close to the inner radius of the disk; if its physical size is constrained by the disk, then the width of the flares will be roughly constant."
" Oue possible interesting. model which could provide a inore precise interpretation of this behavior is the ""Magnetic Flood” model (Tagecretal.2001."," One possible interesting model which could provide a more precise interpretation of this behavior is the “Magnetic Flood"" model \citep{Tagger:2004}."
 This model was proposed to account for the behavior of dduring the .} class., This model was proposed to account for the behavior of during the $\beta$ class.
 It relies ou the Accretion-Ejection Tustability (Tageer&Pellat1999).. which would develop during the X-ray dip.," It relies on the Accretion-Ejection Instability \citep{Tagger:1999}, which would develop during the X-ray dip."
 This instability relics on the presence of a moderate maenetic field in the inner parts of the disk. and can produce Low-Frequency Quasi-Periodic Oscillations (LFQPOs). as well as feed a corona with matter frou the disk.," This instability relies on the presence of a moderate magnetic field in the inner parts of the disk, and can produce Low-Frequency Quasi-Periodic Oscillations (LFQPOs), as well as feed a corona with matter from the disk."
 Then. if the maguetic configuration is favorable. a sudden recomuection event can occur between maguetic fields of opposite polaritics in the accretion disk.," Then, if the magnetic configuration is favorable, a sudden reconnection event can occur between magnetic fields of opposite polarities in the accretion disk."
 This reconuectiou eveut would produce the spike seen im X-rays. aud power the ejection of matter.," This reconnection event would produce the spike seen in X-rays, and power the ejection of matter."
"with the electron density », (in ?) and the electron temperature Το, in units of 10° K. In a collisionless plasma the diffusion approximation for the heat flux breaks down because the mean free path of electrons becomes comparable to or even larger than the temperature scaleheight.","with the electron density $n_e$ (in $^{-3}$ ) and the electron temperature $T_{6,e}$ in units of $10^6$ K. In a collisionless plasma the diffusion approximation for the heat flux breaks down because the mean free path of electrons becomes comparable to or even larger than the temperature scaleheight."
 In this so-called saturated regime described by a collisionless plasma. CM77 used a flux-limited heat flux.," In this so-called saturated regime described by a collisionless plasma, CM77 used a flux-limited heat flux."
 This takes charge conservation into account anc ylelds results in good agreement with more sophisticated treatments (e.g. Max et al. 1980)), This takes charge conservation into account and yields results in good agreement with more sophisticated treatments (e.g. Max et al. \cite{mmm80}) )
 and with numerical simulations of laser heated plasmas (Morse Nielsen 1973:: Mannhhetmer Klein 1975))., and with numerical simulations of laser heated plasmas (Morse Nielsen \cite{mn73}; heimer Klein \cite{mk75}) ).
 The saturated heat flux as an upper limit takes the form (CM77)) with the sound speed ο., The saturated heat flux as an upper limit takes the form \cite{cm77}) ) with the sound speed $c$.
" d, is an efficiency factor less thai or of the order of unity. which embodies some uncertainties connected with the flux-limited treatment and flux suppresstor by magnetic fields (0,=] in our calculations)."," $\Phi_s$ is an efficiency factor less than or of the order of unity, which embodies some uncertainties connected with the flux-limited treatment and flux suppression by magnetic fields $\Phi_s =1$ in our calculations)."
 For an abrupt change of the conductivity from the classical to the saturated regime this leads to an envelope around the clouc consisting of three layers: a saturated zone embedded in ar inner and outer classical zone., For an abrupt change of the conductivity from the classical to the saturated regime this leads to an envelope around the cloud consisting of three layers: a saturated zone embedded in an inner and outer classical zone.
" CM77 obtain a classical loss rate of where 5, 1s 25kpnthe conductivity evaluated for the unperturbed hot medium far away from the cloud.", CM77 obtain a classical mass-loss rate of where $\kappa_f$ is the conductivity evaluated for the unperturbed hot medium far away from the cloud.
 @ is the cloud radius anc iH the mean molecular weight., $R$ is the cloud radius and $\mu$ the mean molecular weight.
 The mass-loss rate is lower for the saturated case., The mass-loss rate is lower for the saturated case.
 In McKee Cowie (1977)) they includec radiative losses in their studies., In McKee Cowie \cite{mc77}) ) they included radiative losses in their studies.
" As a criterion. to. separate the classical and the saturated case for à cloud of radius & embedded in a hot gas with temperature 7, and electroi density ρε. CM77 introduced a global saturation parameter συ Which is the ratio of the electron mean free path to the clouc radius For συD.ipreth-0.027/,. material condenses onto the cloud because radiative losses exceed the conductive heat input."," As a criterion to separate the classical and the saturated case for a cloud of radius $R$ embedded in a hot gas with temperature $T_f$ and electron density $n_{ef}$, \cite{cm77} introduced a global saturation parameter $\sigma_0$ which is the ratio of the electron mean free path to the cloud radius For $\sigma_0 < 0.027/\Phi_s$ material condenses onto the cloud because radiative losses exceed the conductive heat input."
" For 0027/0,<ay1 the cloud suffers classical evaporation. while for oj.—1 the evaporation is saturated."," For $0.027/\Phi_s < \sigma_0 \le 1$ the cloud suffers classical evaporation, while for $\sigma_0 > 1$ the evaporation is saturated."
 McKee Begelman (1990)) found similar results introducing the called Field length in which the |cooling or heating is comparable to the conductive energy exchange., McKee Begelman \cite{mb90}) ) found similar results introducing the so-called Field length in which the cooling or heating is comparable to the conductive energy exchange.
" For R>A, condensation occurs. otherwise the cloud will be evaporated."," For $R > \lambda_{\mbox{\tiny F}}$ condensation occurs, otherwise the cloud will be evaporated."
 η is the particle density. X the cooling rate. Τ the heating rate.," $n$ is the particle density, $\Lambda$ the cooling rate, $\Gamma$ the heating rate."
 These studies concluded that cold clouds in a dilute medium at à temperature of some million Kelvin always experience evaporation. but one of them examined more realistic phase clouds or 1cluded self-gravity.," These studies concluded that cold clouds in a dilute medium at a temperature of some million Kelvin always experience evaporation, but none of them examined more realistic multi-phase clouds or included self-gravity."
 In a seperate paper (Vieser Hensler 2005: hereafter: Paper D) we studied the differences caused by heat conduction on the evapporattion/conddenssation competition between the fixed analytical deseription and the more realistic approach of flux saturation that adopts flexibly to the temporal physical state., In a seperate paper (Vieser Hensler 2005; hereafter: \cite{vh05}) ) we studied the differences caused by heat conduction on the sation competition between the fixed analytical description and the more realistic approach of flux saturation that adopts flexibly to the temporal physical state.
 The main results of these investigations are as follows: The analytical mass loss rates of a cloud at rest in a hot and rarefied medium can be reproduced in numerical simulations for the pure classical case. because the evaporated material is pushed away with supersonic speed.," The main results of these investigations are as follows: The analytical mass loss rates of a cloud at rest in a hot and rarefied medium can be reproduced in numerical simulations for the pure classical case, because the evaporated material is pushed away with supersonic speed."
 The initial large density and temperature jump at the edge of the cloud remains unaltered during the calculation., The initial large density and temperature jump at the edge of the cloud remains unaltered during the calculation.
 Taking the more realistic saturatec heat flux into account. a transition zone forms at the cloud edgePad in which the steep temperature and density gradients are reduced.," Taking the more realistic saturated heat flux into account, a transition zone forms at the cloud edge in which the steep temperature and density gradients are reduced."
 This results in a lower evaporation rate than predicted., This results in a lower evaporation rate than predicted.
 Simulations that include additional heating and cooling show an even more dramatic effect., Simulations that include additional heating and cooling show an even more dramatic effect.
 The clouds can even gain material if radiative cooling exeeds the energy input by heat conduction., The clouds can even gain material if radiative cooling exeeds the energy input by heat conduction.
 Here we examine the evolution of molecular clouds in the stream of a hot. dilute medium.," Here we examine the evolution of molecular clouds in the stream of a hot, dilute medium."
 The treatment of heat conduction in the context of hydrodynamical simulations is described in 822., The treatment of heat conduction in the context of hydrodynamical simulations is described in 2.
 Analytical estimates of the influence of heat conductio are compared with the results of dynamical models with and without heat conduction in $33., Analytical estimates of the influence of heat conduction are compared with the results of dynamical models with and without heat conduction in 3.
 Conclusions are draw! in S44., Conclusions are drawn in 4.
 The evolution of clouds in the subsonic stream of a hot plasma is studied by two-dimensional hydrodynamic simulations., The evolution of clouds in the subsonic stream of a hot plasma is studied by two-dimensional hydrodynamic simulations.
 The hydro-part of this Eulerian. explicit code is based on the prescription of Rozyezka (1985) and has been extensively tested and used by different authors (e.g. Yorke Welz 1996)).," The hydro-part of this Eulerian, explicit code is based on the prescription of Rozyczka (1985) and has been extensively tested and used by different authors (e.g. Yorke Welz \cite{yw96}) )."
 The hydrodynamic equations have been formulated in cylindrical coordinates (r. z). assuming axial symmetry around the z-axis that is also the flow direction.," The hydrodynamic equations have been formulated in cylindrical coordinates (r, z), assuming axial symmetry around the z-axis that is also the flow direction."
 The cloud's center is located on the z-axis., The cloud's center is located on the z-axis.
 The differencing scheme used to discreticize the equations is second-order accurate in space because a “staggered erid™ is used, The differencing scheme used to discreticize the equations is second-order accurate in space because a “staggered grid” is used.
 We applied operator splitting for time integration. because numerical experiments have shown that a multi-step solution procedure is more accurate than a single integration step based on preceding values (Stone&Norman 1992)).," We applied operator splitting for time integration, because numerical experiments have shown that a multi-step solution procedure is more accurate than a single integration step based on preceding values \cite{sn92}) )."
 The advection scheme of vat Leer (1977)) is employed., The advection scheme of van Leer \cite{vl77}) ) is employed.
 Since the basic code is explicit. the Courant-Friedrichs-Lewy (CFL) condition determines the maximum time step for the hydro-part.," Since the basic code is explicit, the Courant-Friedrichs-Lewy (CFL) condition determines the maximum time step for the hydro-part."
 Because the conductior time step is smaller than the CFL one. the temperature distribution has to be calculated several times in one hydro time step.," Because the conduction time step is smaller than the CFL one, the temperature distribution has to be calculated several times in one hydro time step."
 Von Neumann-Richtmyer artificial viscosity 18 usec for the treatment of shocks., Von Neumann-Richtmyer artificial viscosity is used for the treatment of shocks.
 In order to prevent the cloud from moving out of the computational domain due to drag forces. the cloud center of mass ts re-adjusted at each time step.," In order to prevent the cloud from moving out of the computational domain due to drag forces, the cloud center of mass is re-adjusted at each time step."
 The grid parameters. the resulting physical domain and the resolution are listed in Table 1. for three representative models.," The grid parameters, the resulting physical domain and the resolution are listed in Table \ref{t1} for three representative models."
 The grid resolution is 28 - 33 zones per initial cloud radius., The grid resolution is 28 - 33 zones per initial cloud radius.
 The boundary conditions on the upper and right-hand sides are semi-permeable to allow for an outflow of gas from the computational domain., The boundary conditions on the upper and right-hand sides are semi-permeable to allow for an outflow of gas from the computational domain.
 The physical parameters at the lower, The physical parameters at the lower
"obtained by averaging the emission of three different CO isotopomers over a square region, iin size, centered at the HMC position.","obtained by averaging the emission of three different CO isotopomers over a square region, in size, centered at the HMC position."
" While the aand pprofiles are double-peaked with a dip at ~97s!,, the optically thin(ner) C""O((2-1) line (Cesaroni, unpublished data) is Gaussian and peaks right at the velocity of the dip in the other two lines."," While the and profiles are double-peaked with a dip at $\sim$ 97, the optically thin(ner) (2–1) line (Cesaroni, unpublished data) is Gaussian and peaks right at the velocity of the dip in the other two lines."
 This is an indication of self-absorption and thus of high optical depth in the aand ttransitions., This is an indication of self-absorption and thus of high optical depth in the and transitions.
 An apparent feature of the '*CO((2-1) profile is the presence of broad wings., An apparent feature of the (2–1) profile is the presence of broad wings.
 From Fig., From Fig.
 8 one sees that this high-velocity emission originates from 2—3 compact structures located roughly to the E (red-shifted) and W (blue-shifted) of the HMC., \ref{fchm12co} one sees that this high-velocity emission originates from 2–3 compact structures located roughly to the E (red-shifted) and W (blue-shifted) of the HMC.
 Whether this morphology is consistent with that of a bipolar outflow cannot be trivially decided on the basis of the evidence presented so far and requires a detailed analysis and discussion that we postpone to Sect. 4.2.., Whether this morphology is consistent with that of a bipolar outflow cannot be trivially decided on the basis of the evidence presented so far and requires a detailed analysis and discussion that we postpone to Sect. \ref{svgr}.
 The main purpose of the present study is to shed light on the nature of the velocity gradient observed in this HMC, The main purpose of the present study is to shed light on the nature of the velocity gradient observed in this HMC
 ~ 5.|! ~ 5.1 (Dahcall&Soneira1983:IXIvpinIopvlov19823.. Baheall1983:IIuchra.οἱ Dahcall&Soneira(1983). (Ixaiser1934:Governatoetal.1999:Colberg2000:Moscardini2001:Baheall20036: 2<0.5. itis (Mann.Heavens&Peacock1993:White1996.2002:Sheth.Mo.&Tormen2001:Moscardinietal.2001)..," $\sim$ $h^{-1}$ $\sim$ $h^{-1}$ \citealt{bah83, kly83}, \citealt{bah88, huc90, 
pos92, bah92, pea92, dal94, cro97, aba98, lee99, bor99, col00, gon02, bah03c}; \citet{bah83} \citealt{kai84, bah92a, moh96, gov99, colb00, mos01, bah03c}; $z \la 0.5$ \citep{man93, moh96, moh02, she01, mos01}."
by Carretta et al. (,by Carretta et al. (
"2010, based on the stars’ sodium abundance) and Martell and Grebel (2010, based on CN and CH bandstrengths).","2010, based on the stars' sodium abundance) and Martell and Grebel (2010, based on CN and CH bandstrengths)."
" For comparison, of globular cluster stars are identified as SG when the same classification criteria are adopted (Kraft 1994, Carretta et al."," For comparison, of globular cluster stars are identified as SG when the same classification criteria are adopted (Kraft 1994, Carretta et al."
" 2010, Martell Grebel 2010)."," 2010, Martell Grebel 2010)."
" We note that for these estimates of fsc,u, using, for example, a power- IGCMF with a=1.8 as a reference model, our calculations reffig:fsg2)) with a K01 IMF (K93 IMF) imply that a fraction ranging from about to about to about 60%)) of the Galactic stellar halo must(30% be composed of stars originally formed in globular clusters."," We note that for these estimates of $\fsge$, using, for example, a power-law IGCMF with $\alpha=1.8$ as a reference model, our calculations \\ref{fig:fsg2}) ) with a K01 IMF (K93 IMF) imply that a fraction ranging from about to about to about ) of the Galactic stellar halo must be composed of stars originally formed in globular clusters."
" Although this estimate is very uncertain and both more calculations and further observational studies of SG stars in the halo will be required to refine it, it is interesting to note how the fractions of SG stars in globular clusters and in the Galactic stellar halo connect and constrain both models for the formation and dynamical evolution of multiple stellar generations in globular clusters and the formation history of the Galactic halo."," Although this estimate is very uncertain and both more calculations and further observational studies of SG stars in the halo will be required to refine it, it is interesting to note how the fractions of SG stars in globular clusters and in the Galactic stellar halo connect and constrain both models for the formation and dynamical evolution of multiple stellar generations in globular clusters and the formation history of the Galactic halo."
" EV and SM were supported in part by NASA grants NNX07AG95G, NNX08AH15G and NNX10AD86G and by NSF grant AST-0708299."," EV and SM were supported in part by NASA grants NNX07AG95G, NNX08AH15G and NNX10AD86G and by NSF grant AST-0708299."
 AD acknowledges financial support from italian MIUR through grant PRIN 2007 (prot., AD acknowledges financial support from italian MIUR through grant PRIN 2007 (prot.
 2007JJC53X)., 2007JJC53X).
" FD was supported by PRIN MIUR 2007 ""Multiple Stellar Populations in Globular Clusters: Census, Characterization and Origin’ (prot."," FD was supported by PRIN MIUR 2007 'Multiple Stellar Populations in Globular Clusters: Census, Characterization and Origin' (prot."
 n. 20075TP5K9)., n. 20075TP5K9).
Lt has been proposed. that powerful. ΕΠ] (see. Fanaroll Riley 1974) radio galaxies ancl radio Loud. quasars are intrinsically the same objects. with all observed. dilferences being a result of the angle between the line of sieht and the radio axis (Scheuer LOST: Barthel 1989).,"It has been proposed that powerful II (see Fanaroff Riley 1974) radio galaxies and radio loud quasars are intrinsically the same objects, with all observed differences being a result of the angle between the line of sight and the radio axis (Scheuer 1987; Barthel 1989)."
" While objects Classified as ""narrow-line radio galaxies"" do not clisplay obvious broad lines in their optical spectra. broad lines have been seen either in the near-infrared. Hill. €oocdrich DePov 1996) or in polarized light) Young et 11996)."," While objects classified as “narrow-line radio galaxies” do not display obvious broad lines in their optical spectra, broad lines have been seen either in the near-infrared Hill, Goodrich DePoy 1996) or in polarized light Young et 1996)."
 In. addition. the detection. of unresolved nuclei in near-infrared observations of radio galaxies DDjorgovski et 11991: Simpson. Ward Wilson 1995). where the optical depth is lower. indicates the presence of a quasar-like nucleus in the centres of these objects.," In addition, the detection of unresolved nuclei in near-infrared observations of radio galaxies Djorgovski et 1991; Simpson, Ward Wilson 1995), where the optical depth is lower, indicates the presence of a quasar-like nucleus in the centres of these objects."
 Since quasars can outshine their host galaxies by factors ranging from a few DDunlop et 11993: Tavlor et 11996. hereafter T96) to more than LOO in extreme cases PPDS 456: Simpson et 11999). even if only a few. per cent of the nuclear light is transmitted it can still make a major contribution to the integrated. Luminosity.," Since quasars can outshine their host galaxies by factors ranging from a few Dunlop et 1993; Taylor et 1996, hereafter T96) to more than 100 in extreme cases PDS 456; Simpson et 1999), even if only a few per cent of the nuclear light is transmitted it can still make a major contribution to the integrated luminosity."
 lt has long been known that the brightest radio galaxies. tthose in the 3CRR catalogue of Laing. Riley Longair (1983). are brighter in the near-infrared. by about a magnitude at zc1 than they are at low redshift.," It has long been known that the brightest radio galaxies, those in the 3CRR catalogue of Laing, Riley Longair (1983), are brighter in the near-infrared by about a magnitude at $z \approx 1$ than they are at low redshift."
 This amount of dimming as cosmic time increases is consistent with passive evolution of their stellar populations (Lilly Loneair 1984: Lilly. Longair Allineton-Smith 1985b).," This amount of dimming as cosmic time increases is consistent with passive evolution of their stellar populations (Lilly Longair 1984; Lilly, Longair Allington-Smith 1985b)."
 While some 3€ radio galaxies at z71 suller significant contamination [rom non-stellar radiation (Rawlings ct 11995: Simpson. Rawlings Lacy 1999). this does not have a significant impact on the locus of the A z relation.," While some 3C radio galaxies at $z \approx 1$ suffer significant contamination from non-stellar radiation (Rawlings et 1995; Simpson, Rawlings Lacy 1999), this does not have a significant impact on the locus of the $K$ $z$ relation."
 However. racio galaxies from the fainter 6C and B2 radio surveys are mmag fainter at A than the 3€ objects at these redshifts (Eales οἱ 11997). whereas there is no correlation between racio and host galaxy luminosities locally.," However, radio galaxies from the fainter 6C and B2 radio surveys are mag fainter at $K$ than the 3C objects at these redshifts (Eales et 1997), whereas there is no correlation between radio and host galaxy luminosities locally."
 Furthermore. the ος{295 galaxies lie the no-evolution curve.," Furthermore, the 6C/B2 galaxies lie the no-evolution curve."
 The possibility that there is significant non-stcllar contamination at redshift is one that therefore. needs, The possibility that there is significant non-stellar contamination at redshift is one that therefore needs
where τις is given by Eq. (1)).,where $\tau_{dn}^{-1}$ is given by Eq. \ref{tau_fr}) ).
" The random Langevin force has zero average. (L(t))=0. aud is properly noriualized. (ο|ry)=27ΗμT,T). fo safisfv the fluctuatiou-dissipation theoren."," The random Langevin force has zero average, $\langle{\bf
L}(t)\rangle=0$, and is properly normalized, $\langle{\bf L}(t){\bf L}(t+\tau)\rangle=2\tau_{dn}^{-1}m_dk_{\rm
B}T_n\delta(\tau)$, to satisfy the fluctuation-dissipation theorem."
 The formatlisin of the Langevin equation is equivalent to the Fokker-Plauck approach which describes evolution of the velocity distribution function (Lifshitz Pitaevskii 1951. Vau Iampcu 1981).," The formalism of the Langevin equation is equivalent to the Fokker-Planck approach which describes evolution of the velocity distribution function (Lifshitz Pitaevskii 1981, Van Kampen 1981)."
",lhe latter approach is solely determined by the first audsecoud Fokker-Plank cocfficieuts. A=(δρ)δὲ and B=((9p)23/26f (where 6.) denotes the averaging over may collisions occurring over the time period f)."," The latter approach is solely determined by the first andsecond Fokker-Plank coefficients, ${\cal A}=\langle\delta{\bf p}\rangle/\delta t$ and ${\cal B}=\langle(\delta{\bf
p})^2\rangle/2\delta t$ (where $\langle\ldots\rangle$ denotes the averaging over many collisions occurring over the time period $\delta t$ )."
 They play the role of the miobility and diffusion coefficients iu the velocity space. respectively. aud for processes that allow stable equilibrium (c.g... for dust-ueutral collisions) they are interrelated.," They play the role of the mobility and diffusion coefficients in the velocity space, respectively, and for processes that allow stable equilibrium (e.g., for dust-neutral collisions) they are interrelated."
" The resulting collision operator for dust-ueutral collisions has the following differcutial form (Lifshitz Pitaevski 1981. Vau Ixkauipen 1981). where B,nomak, is the second. Fokker-Plank coeffücieut for dust-neutral collisions."," The resulting collision operator for dust-neutral collisions has the following differential form (Lifshitz Pitaevskii 1981, Van Kampen 1981), where ${\cal B}_{dn}=\tau_{dn}^{-1}m_dk_{\rm B}T_n$ is the second Fokker-Plank coefficient for dust-neutral collisions."
 The iuteeration nunediately vields We employ the most general form of the collision operator for binary This form allows for the enerey uon-couservation in the mutual cast collisions aud therefore does not require the unitaritv to satisfied [which reduces Eq. (D1)), The integration immediately yields We employ the most general form of the collision operator for binary This form allows for the energy non-conservation in the mutual dust collisions and therefore does not require the unitarity relation to be satisfied [which reduces Eq. \ref{St_n}) )
 to the canonical Boltzumaun form (Lifshitz Pitaevskii 151]., to the canonical Boltzmann form (Lifshitz Pitaevskii 1981)].
 Iere. Mand'(p.hep'.pi) is a probability function for a pair of colliding particles with momenta p aud py to acquire 1nonienuta p' pj. pirespectively. after the collision.," Here, $w({\bf p},{\bf p}_1;\:{\bf p}',{\bf p}_1')$ is a probability function for a pair of colliding particles with momenta ${\bf p}$ and ${\bf p}_1$ to acquire momenta ${\bf p}'$ and ${\bf p}_1'$, respectively, after the collision."
 Equation (B1)) counts for all possible transitions (p>(p.pi) and then is averaged over pj.," Equation \ref{St_n}) ) counts for all possible transitions $({\bf p}',{\bf p}_1')\to({\bf p},{\bf p}_1)$ and then is averaged over ${\bf p}_1$."
 Function « can be determined by solving a mechanical problem of the binarypi) scattering with given interaction between the particles., Function $w$ can be determined by solving a mechanical problem of the binary scattering with given interaction between the particles.
 Assunmiug the Maswellian distribution. f(p})fp). it--- is couvenieut to introduce the “binary” distrilnition function of dust. Ερι.pi)=fFutpilhutpo).," Assuming the Maxwellian distribution, $f({\bf p})=f_{\rm M}({\bf p})$, it is convenient to introduce the “binary” distribution function of dust, $F({\bf p}_{\rm c},{\bf p}_{\rm r})\equiv f_{\rm M}({\bf p}_1)f_{\rm M}({\bf p}_2)$."
 We also define the probability fiction W(Di:Q)wp.pi:p.pi) for the relative moment exchange py>»|q aud after the integration of Eq. (0111 Pe ," We also define the probability function $W({\bf p}_{\rm c},{\bf p}_{\rm r};\:{\bf q})\equiv w({\bf p},{\bf p}_1;\:{\bf p}',{\bf
p}_1')$ for the relative momentum exchange ${\bf p}_{\rm r}\to{\bf p}_{\rm r}+{\bf q}$ and after the integration of Eq. \ref{St_n}) )"
"obtain (105).= Iu a homogeneous and isotropic medi. the collision probability depeuds only ou the absolute value of the relative molmentiun. p, and does not depend on pe."," obtain (I05), In a homogeneous and isotropic medium, the collision probability depends only on the absolute value of the relative momentum, $p_{\rm r}$, and does not depend on ${\bf p}_{\rm c}$."
" Thus. HW.=Wy:àq). where we introduced the absolute value for the inclastic momentum exchange. 64=|p,αἱpr."," Thus, $W=W(p_{\rm r};\:\delta q)$, where we introduced the absolute value for the inelastic momentum exchange, $\delta q=|{\bf p}_{\rm r}+{\bf q}|-p_{\rm r}$."
" For weakly inclastic collisions with dq«p, we have Furthenuore. the iutegraud in Eq. (B2))"," For weakly inelastic collisions with $\delta q\ll p_{\rm r}$ we have Furthermore, the integrand in Eq. \ref{7}) )"
 can be expanded iuto a series over dq., can be expanded into a series over $\delta q$.
 Retaining the linear iud quadratic ternis and iutegratiug in parts. we obtain where Ayia.)=|ogdóq and Burl)=ifflog?déq aye analogous to the Fokker-Plauck coefficients for dust-dust collisions (105).," Retaining the linear and quadratic terms and integrating in parts, we obtain where ${\cal A}_{dd}(p_{\rm r})=\int\delta qWd\delta q$ and ${\cal B}_{dd}(p_{\rm r})=\frac12\int(\delta q)^2Wd\delta q$ are analogous to the Fokker-Planck coefficients for dust-dust collisions (I05)."
" The coctfficicuts can he expressed in terms of thebinary collision cross section X iu the followine form: Using Eqs (6)) and (B3)) we obtain that 6g=Oc3""m", The coefficients can be expressed in terms of the binary collision cross section $\Sigma$ in the following form: Using Eqs \ref{25}) ) and \ref{20a}) ) we obtain that $\delta q=O(\sigma_Q^2)$.
" Therefore. Ay,=Ol05) aud B=Ot(od). lo. for weakly fluctuating charges the mean energy. variation 1s dete rmiued1o coefficient Au only."," Therefore, ${\cal A}_{dd}=O(\sigma_Q^2)$ and ${\cal B}_{dd}=O(\sigma_Q^4)$, i.e., for weakly fluctuating charges the mean energy variation is determined by coefficient ${\cal A}_{dd}$ only."
 Iu order to calculate the kinetic coefficient Ay; we asstume the Coulomb interaction between cliarged erains (the main contribution to Au; comes frou the interaction at shorter distances. sec 105).," In order to calculate the kinetic coefficient ${\cal A}_{dd}$, we assume the Coulomb interaction between charged grains (the main contribution to ${\cal A}_{dd}$ comes from the interaction at shorter distances, see I05)."
 By substituting dog/dr=/—Qui? in Eq. ⋅ (6)), By substituting $d\varphi_0/dr=-Q_0/r^2$ in Eq. \ref{25}) )
" and integratingB along the trajectory. r(f)=VPoppp?| Go).pA we obtain+ the energy variation. de,~(7,05PV)D (here pis the impact parameter of colliding particles. for simplicity we consider the scattering at μα] angles) aud the corresponding momentu variation dg [using Eq. (B3))|."," and integrating along the trajectory $r(t)=\sqrt{\rho^2+(v_{\rm r}t)^2}$ , we obtain the energy variation $\delta\varepsilon_{\rm r}\sim(\sigma_Q^2Q_0^2/\rho^3\nu_{\rm ch}p_{\rm r})$ (here $\rho$ is the impact parameter of colliding particles, for simplicity we consider the scattering at small angles) and the corresponding momentum variation $\delta q$ [using Eq. \ref{20a}) )]."
 Finally. we substitute the result in the first equation (B5)).," Finally, we substitute the result in the first equation \ref{FP_coeff}) ),"
as products frou both JF events aud.low-frequency Fe-producing £ events were mixed in the ISAL,as products from both $H$ events andlow-frequency Fe-producing $L$ events were mixed in the ISM.
 The Fe abundance resulting from an £ event is |Fe/TII|;=2.ls ΝΟ)., The Fe abundance resulting from an $L$ event is $_L\approx -2.48$ (WQ).
 Iu adcditiou to 77 and E eveuts. an initial or prompt (P) inventory of Clements is assumed to explain abundances of Fe and other associated clements in stars with [Fe/T] « 3.," In addition to $H$ and $L$ events, an initial or prompt $P$ ) inventory of elements is assumed to explain abundances of Fe and other associated elements in stars with [Fe/H] $< -3$ ."
 The P-uveutorv was attributed to production by the first very massive (LOO AJ.) stars prior to formation of normal stars (AL~1 6037.) and onset of regular SNIT associated with the process.," The $P$ -inventory was attributed to production by the first very massive $\gtrsim 100\,M_\odot$ ) stars prior to formation of normal stars $M\sim 1$ $60\,M_\odot$ ) and onset of regular SNII associated with the $r$ -process."
 It was argued that formation of normal stars could not occur until a “metallicitw” corresponding to |Fe/H] =3 was achieved in the ISM (WO)., It was argued that formation of normal stars could not occur until a “metallicity” corresponding to [Fe/H] $\approx -3$ was achieved in the ISM (WQ).
 The P-inventory was considered to represeut tlic earliest stages of chemical evolution that need not be specifically associated with our Galaxy., The $P$ -inventory was considered to represent the earliest stages of chemical evolution that need not be specifically associated with our Galaxy.
 Data on Ba at Lo[Fe/Il)«03 (AlcWilliaun et al., Data on Ba at $-4\lesssim {\rm [Fe/H]}<-3$ (McWilliam et al.
 1995: ALcWilliam 1998: Norris Ryan. Beers 2001) iuclicate that the P- inventory of heavy r-clements is ucgligihle.," 1995; McWilliam 1998; Norris, Ryan, Beers 2001) indicate that the $P$ -inventory of heavy $r$ -elements is negligible."
 As |Fe/II| for UAIP stars reflect only the P-inveutory of Fe Πρzm 3) and no £-coutributions. we cousider that abundauces of heavy r-clements from Ba aud above in these stars only resulted from J events.," As [Fe/H] for UMP stars reflect only the $P$ -inventory of Fe $_P\approx -3$ ) and no $L$ -contributions, we consider that abundances of heavy $r$ -elements from Ba and above in these stars only resulted from $H$ events."
 Observations by Sucdeu et al. (, Observations by Sneden et al. (
1996. 2000) audWestin et al. (,"1996, 2000) andWestin et al. ("
2000) show that abundances of these elements in UMP stars very closely follow the solar r-patteru.,2000) show that abundances of these elements in UMP stars very closely follow the solar $r$ -pattern.
 Thus their f-vields can be directly calculated from the solar i;-abuudauces., Thus their $H$ -yields can be directly calculated from the solar $r$ -abundances.
 Over the Galactic history of τς10 Civr before solar svstei formation z=LO ΠΠ events contributed to the solu abundances., Over the Galactic history of $\approx 10$ Gyr before solar system formation $\approx 10^3$ $H$ events contributed to the solar abundances.
" The H-vield of c.g.. Os CA~ 190) is then logey(Os)zxloge..fOs)3=1.66 where loge(E)=log(E/II)|12 for an clement E and loge...,.(Os)=1.31 Uxapppeler. Beer. Wisshal 1989: Arlandini et al."," The $H$ -yield of e.g., Os $A\sim 190$ ) is then $\log\epsilon_H({\rm Os})\approx\log\epsilon_{\odot,r}({\rm Os})-3=-1.66$ where $\log\epsilon({\rm E})\equiv\log({\rm E/H})+12$ for an element E and $\log\epsilon_{\odot,r}({\rm Os})=1.34$ (Käpppeler, Beer, Wisshak 1989; Arlandini et al."
 1999) for the solar r-inveutorv of Os., 1999) for the solar $r$ -inventory of Os.
 Lf-vields of heavy r-clemeuts from Da and above are given in Table 1., $H$ -yields of heavy $r$ -elements from Ba and above are given in Table 1.
 By comparing the observed abundances of Sr. Y. and Zr with those of the heavy οσοι in the UMP stars CS 22892-052 (Sneden ot al.," By comparing the observed abundances of Sr, Y, and Zr with those of the heavy $r$ -elements in the UMP stars CS 22892-052 (Sneden et al."
 2000) aud ΠΟ 115411 (Westin et al., 2000) and HD 115444 (Westin et al.
 2000). QW found that the Sr. Y. aud Zr abundances in these two stars received siguificaut to dominant contributions from a common source. the P-inventory.," 2000), QW found that the Sr, Y, and Zr abundances in these two stars received significant to dominant contributions from a common source, the $P$ -inventory."
 The logep values for the P-iuveutory of Sr. Y. aud Zr and the corresponding Zf-xields (veprescuted bv logeg) calculated by QW are eiven in Table 1.," The $\log\epsilon_P$ values for the $P$ -inventory of Sr, Y, and Zr and the corresponding $H$ -yields (represented by $\log\epsilon_H$ ) calculated by QW are given in Table 1."
 The observed Os abundance of loge(Os)=0.05 in CS 22892-052 (Sneden et al., The observed Os abundance of $\log\epsilon({\rm Os})=-0.05$ in CS 22892-052 (Sneden et al.
 2000) indicates that this star received contributions from ay2LL ZI eveuts., 2000) indicates that this star received contributions from $n_H\approx 41$ $H$ events.
 A slightly different value for yy is obtained by using the observed Eu abundance as in QW., A slightly different value for $n_H$ is obtained by using the observed Eu abundance as in QW.
 The Z-coutributious to the Sr. Y. and Zr abuudances in CS 22892-052 are larger than the P-inventory.," The $H$ -contributions to the Sr, Y, and Zr abundances in CS 22892-052 are larger than the $P$ -inventory."
 We assume that the observed abunudauces iu CS 22892-052 for the light +clemeuts Nb. Ru. Rl. Pd. Ag. and Cd (A=93 116) are clominated by the ZI-coutiibutious.," We assume that the observed abundances in CS 22892-052 for the light $r$ -elements Nb, Ru, Rh, Pd, Ag, and Cd $A=93$ –116) are dominated by the $H$ -contributions."
" ""Their fZ-viclds are given in Table 1.", Their $H$ -yields are given in Table 1.
 IH -xiekds of r-clemeuts and the P-uveutorv of Sr. Y. and Zr are shown in Figure 1.," $H$ -yields of $r$ -elements and the $P$ -inventory of Sr, Y, and Zr are shown in Figure 1."
 As the U-star is à UMP star with uo L-coutributious. L-vields caleulated by OW are not eiven.," As the U-star is a UMP star with no $L$ -contributions, $L$ -yields calculated by QW are not given."
 In 822 we discuss abundances of stable elements in the U-star based on the above three-component model., In 2 we discuss abundances of stable elements in the U-star based on the above three-component model.
 The abundances of 77Th aud 77U in this star and inplicatious for cosiunochronology are discussed in 8233., The abundances of $^{232}$ Th and $^{238}$ U in this star and implications for cosmochronology are discussed in 3.
 Data for the U-star clearly show an extremely larec chhancement of heavy r-clemeuts without any iucrease ni [Fe/T]| from the prompt value |Fe/TI]p=3., Data for the U-star clearly show an extremely large enhancement of heavy $r$ -elements without any increase in [Fe/H] from the prompt value $_P\approx -3$ .
 The observed Os abundance of loge(Os)=0.19 is higher than those πι CS 22892-052. ΠΟ 115111 (Fe‘Tl =2.99). and ID 122563 (|Fo/II| 2.2.7E: Sneden et al.," The observed Os abundance of $\log\epsilon({\rm Os})=0.49$ is higher than those in CS 22892-052, HD 115444 ([Fe/H] $=-2.99$ ), and HD 122563 ([Fe/H] $=-2.74$; Sneden et al."
" 1998) by 0.5L 1.0L. and z1.79 dex. respectively,"," 1998) by 0.54, 1.04, and $>1.79$ dex, respectively."
 Thus observations of the U-star clearly confirm the existence of a type of r-process eveut that produces heavy. r-nuclei but no Fe., Thus observations of the U-star clearly confirm the existence of a type of $r$ -process event that produces heavy $r$ -nuclei but no Fe.
 This is in support of the hivpothesis of the above threc-comiponenut model that there mast be two types of SNII sources for maiiclei. one of which docs not produce Fe.," This is in support of the hypothesis of the above three-component model that there must be two types of SNII sources for $r$ -nuclei, one of which does not produce Fe."
" Using logey(Os)=1.66 we obtain from the observed Os abundance in the U-star that it had received coutributious from iy,7111 JI eveuts.", Using $\log\epsilon_H({\rm Os})=-1.66$ we obtain from the observed Os abundance in the U-star that it had received contributions from $n_H \approx 141$ $H$ events.
 The abundances of all other stable ;-eleiieuts can be calculated from. vy and the Ff-vields aud the P-uveutorv iu Table 1., The abundances of all other stable $r$ -elements can be calculated from $n_H$ and the $H$ -yields and the $P$ -inventory in Table 1.
 These calculated abundances are given in Table 1 an shown in Figure 1l., These calculated abundances are given in Table 1 and shown in Figure 1.
 While Sr. Y. and Zr have substaitia coutributious from the P-iuveutorv. these are xal conrpared with the coutributious from zLl 77 eveuts for CS 22892-052 or those from z111 Z7 eveuts for the U-stax.," While Sr, Y, and Zr have substantial contributions from the $P$ -inventory, these are small compared with the contributions from $\approx 41$ $H$ events for CS 22892-052 or those from $\approx 141$ $H$ events for the U-star."
 Figure 1l also shows the solar r-patteru translated to fi the observed Os abundance in the U-star., Figure 1 also shows the solar $r$ -pattern translated to fit the observed Os abundance in the U-star.
 The caleulated abuudances for the U-star show that it should be deficieu in the light +-clemeuts frou Sr to below Ba (particularly Y) relative to the solar i-patteru., The calculated abundances for the U-star show that it should be deficient in the light $r$ -elements from Sr to below Ba (particularly Y) relative to the solar $r$ -pattern.
 Asstuning the validity of the model. we cousicer the abundances predicted here for the U-star to be quantitative aud reasonably reliable subject to uncertainties in the observational data from which the ZI-vields aud the P-iuveutory ire derived.," Assuming the validity of the model, we consider the abundances predicted here for the U-star to be quantitative and reasonably reliable subject to uncertainties in the observational data from which the $H$ -yields and the $P$ -inventory are derived."
 Absolute abuudances relative to livdrogen im this star willLB provide a direct and rigorous test of the approach laid out here., Absolute abundances relative to hydrogen in this star will provide a direct and rigorous test of the approach laid out here.
 We were informed by the referee that these are uuder active study (Ifill et al., We were informed by the referee that these are under active study (Hill et al.
 2001)., 2001).
 The esseutial conclusion from our results is that abundances in the U-star should reflect the relative vield pattern of an JI event im addition to simply exhibitiug high r-process enrichments., The essential conclusion from our results is that abundances in the U-star should reflect the relative yield pattern of an $H$ event in addition to simply exhibiting high $r$ -process enrichments.
 The high muubers of ZF events for CS 22892-052 and the U-star require discussion., The high numbers of $H$ events for CS 22892-052 and the U-star require discussion.
" These two UMP, stars have essentially the same [Fe/U] as the prompt value |Fe/II|p= 3.", These two UMP stars have essentially the same [Fe/H] as the prompt value $_P\approx -3$ .
 So theycannot have received coutributions from any Fe-producing £L eveuts., So theycannot have received contributions from any Fe-producing $L$ events.
 From the frequencies of 7/7 aud L events in au average ISAL the average fraction of Lf events among all SNII is 4~0.9.," From the frequencies of $H$ and $L$ events in an average ISM, the average fraction of $H$ events among all SNII is $q\approx 0.9$."
" The probability for a standard reference mass of ISM. to have a inuuber ny; of II events im a series is q""4.", The probability for a standard reference mass of ISM to have a number $n_H$ of $H$ events in a series is $q^{n_H}$.
 The νο sj;544 oy CS 22892-0452 corresponds to a small probability of z1.3«10? and the number ay2111 for the U-star to an extremely low probability of z3.5«10. 7., The number $n_H\approx 41$ for CS 22892-052 corresponds to a small probability of $\approx 1.3\times 10^{-2}$ and the number $n_H\approx 141$ for the U-star to an extremely low probability of $\approx 3.5\times 10^{-7}$ .
 It follows hat the observed bhieh eurichiment of i;-clemoeuts in the U- and possibly also CS 22892-052 caunot be plausibly associated with many 1 eveuts raucdomly coutaminating he ISM but requires a special source., It follows that the observed high enrichment of $r$ -elements in the U-star and possibly also CS 22892-052 cannot be plausibly associated with many $H$ events randomly contaminating the ISM but requires a special source.
 It takes z10° ZI events over=10 Cyr to produce the solar r-process ratio (ΟΠ) in a standard reference uass of ISAL.," It takes $\approx 10^3$ $H$ events over$\approx 10$ Gyr to produce the solar $r$ -process ratio $_{\odot,r}$ in a standard reference mass of ISM."
 For the preseut Galactic SNII rate of zm corresponding to a total gas mass of zz1019 AL... he staudard reference mass is m3&1051 M.," For the present Galactic SNII rate of $\approx (30\ {\rm yr})^{-1}$ corresponding to a total gas mass of $\approx 10^{10}\,M_\odot$ , the standard reference mass is $\approx 3\times10^4\,M_\odot$ ."
 This is in accord with the typical mass of ISAD swept by au SNII vemnant (e.g... Thorutou et al.," This is in accord with the typical mass of ISM swept by an SNII remnant (e.g., Thornton et al."
 1998)., 1998).
 To explain the, To explain the
maximum in J? (>99%)) with respect to themodels.,maximum in $P$ $>$ ) with respect to the.
 More relevant.models with an abundance variation ALN/17]>40.2dex lie at 1.50 from the best-fit solution. whilemodels with ΔΑ>40.3 dex lie at o>2 from the best-fit solution.," More relevant, with an abundance variation $\Delta[X/H]\ge\pm 0.2$dex lie at $\simeq 1.5\sigma$ from the best-fit solution, while with $\Delta[X/H]\ge\pm 0.3$ dex lie at $\sigma \ge 2$ from the best-fit solution."
 The analvsis of the line equivalent widths provide fully consistent results., The analysis of the line equivalent widths provide fully consistent results.
 The right panel of Fig., The right panel of Fig.
 2 shows the average dillerence between the model andthe observed equivalent width measurements., \ref{IRtest} shows the average difference between the model andthe observed equivalent width measurements.
 Models with 0.2 dex abundance variations [rom the best-fit solution are still acceptable αἱ a ~1.50 significauce level. while those with +£0.38 dex variations are only mareinally acceptable al a 2—36 level.," Models with $\pm 0.2$ dex abundance variations from the best-fit solution are still acceptable at a $\simeq 1.5\sigma$ significance level, while those with $\pm 0.3$ dex variations are only marginally acceptable at a $2-3 \sigma$ level."
 Models with stellar parameters varving by .NTrz200 Ix. Aog g—250.5 and AS0.5 kms and abundances varving accordingly by 0.1-0.2 dex. in order to still reproduce (he deepness of the observed features. are also less statistical significant (on average only at >26 level) with respect to the best-fit solution.," Models with stellar parameters varying by $\Delta $ $_{\rm eff}$$\pm$ 200 K, $\Delta $ log $\pm$ 0.5 and $\Delta \xi$$\mp$ 0.5 km $^{-1}$ and abundances varying accordingly by 0.1-0.2 dex, in order to still reproduce the deepness of the observed features, are also less statistical significant (on average only at $\ge2 \sigma$ level) with respect to the best-fit solution."
 Hence. as a conservative estimate of the svstematic error in the derived best-fit’ abundances. due to the residual uncertainty in the adopted. stellar parameters. one can assume a value of <—0.1 dex.," Hence, as a conservative estimate of the systematic error in the derived best-fit abundances, due to the residual uncertainty in the adopted stellar parameters, one can assume a value of $\le \pm 0.1$ dex."
 By taking into account the overall uncertainty in the definition of the average population and (he statisticalsignificance of our spectral synthesis procedure. we can salely conclude that the stellar abundances can be constrained well within 0.3 dex and their abundance ratios down to 70.2 dex. since some (if not all) of the stellar parameter degeneracy is removed.," By taking into account the overall uncertainty in the definition of the average population and the statisticalsignificance of our spectral synthesis procedure, we can safely conclude that the stellar abundances can be constrained well within $\pm$ 0.3 dex and their abundance ratios down to $\simeq$ 0.2 dex, since some (if not all) of the stellar parameter degeneracy is removed."
 The determination of the abundances of the hot X-ray emitting gas in SD galaxies has traditionally suffered from laree uncertainties., The determination of the abundances of the hot X-ray emitting gas in SB galaxies has traditionally suffered from large uncertainties.
 Indeed. the low angular and spectral resolution of the various X-raw telescopes in the eva did not allow to disentangle between point sources and hot gas emission. makine abundance determinations severely model-dependent (Dahlemetal.2000).," Indeed, the low angular and spectral resolution of the various X-ray telescopes in the era did not allow to disentangle between point sources and hot gas emission, making abundance determinations severely model-dependent \citep{dah00}."
. The problem lies in the fact that the Xorav specirum of SB galaxies contains (wo major components: the emission [rom hot diffuse gas and the integrated. contribution of point sources., The problem lies in the fact that the X–ray spectrum of SB galaxies contains two major components: the emission from hot diffuse gas and the integrated contribution of point sources.
 The first is described bv an oplically thin thermal spectrumplus emission lines. the latter by a power-law.," The first is described by an optically thin thermal spectrum emission lines, the latter by a power-law."
 If (he angular resolution is not good enough. it is not possible to reliably subtract the point sources from (he total spectrum. so that the equivalent widtlis of the emission lines (ancl thus the element abundances) are not unambiguously defined.," If the angular resolution is not good enough, it is not possible to reliably subtract the point sources from the total spectrum, so that the equivalent widths of the emission lines (and thus the element abundances) are not unambiguously defined."
 On the other hand. high angular resolution alone is not enough: recent studies (Stricklandetal. 2002: Martin.Nobulnicky&Ileckman 2002)) demonstrated. that the relatively low spectral resolution of the detector makes individual element abundance," On the other hand, high angular resolution alone is not enough: recent studies \citealt{stric02}; ; \citealt{mart02}) ) demonstrated that the relatively low spectral resolution of the detector makes individual element abundance"
In figure 6((a) we show the contour of f;. while in (0). 6((0) ancl Gel) are plotted the contours of fs for figuresdillerent values of a.,"In figure \ref{fig:DFm3A}( (a) we show the contour of $f_{3}$, while in figures \ref{fig:DFm3A}( (b), \ref{fig:DFm3A}( (c) and \ref{fig:DFm3A}( (d) are plotted the contours of $\tilde{f}_{3}$ for different values of $\alpha$."
 We can see that the behavior of these DES is opposite to the previous cases., We can see that the behavior of these DFs is opposite to the previous cases.
 As the Jacobi's integral icreases. the DE. also increases.," As the Jacobi's integral icreases, the DF also increases."
" As we saw in section ??.. in order to find a DE using the Ixalnajs method. we must find yas a function of the relative potential in order to obtain X(W,)."," As we saw in section \ref{sec:dfm3}, in order to find a DF using the Kalnajs method, we must find $\eta$ as a function of the relative potential in order to obtain $\Sigma(\Psi_{r})$."
 For the m=4 disc. the relative potential can be expressed as Now. although we have to deal with a quartic equation. it is possible to rewrite (57)) as where and must to be chosen as Finally. by using (42)) and (48)). we find the expression which. by means of eq. (191).," For the $m = 4$ disc, the relative potential can be expressed as Now, although we have to deal with a quartic equation, it is possible to rewrite \ref{psir4}) ) as where and $\Omega$ must to be chosen as Finally, by using \ref{denseta}) ) and \ref{psi32}) ), we find the expression which, by means of eq. \ref{metkal2}) ),"
 can be used to derive the even part of the DE in the rotating frame. Therefore. the corresponding DIF in the original frame is given by where and the respective DE with maximum entropy is given by In figure 7((a) weshow the contour of fj. while in figures TC). πο) ancl Y((d) are. plotted.the contours. of fi for cillerent values ofa.," can be used to derive the even part of the DF in the rotating frame, Therefore, the corresponding DF in the original frame is given by where and the respective DF with maximum entropy is given by In figure \ref{fig:DFm4A}( (a) weshow the contour of $f_{4}$, while in figures \ref{fig:DFm4A}( (b), \ref{fig:DFm4A}( (c) and \ref{fig:DFm4A}( (d) are plottedthe contours of $\tilde{f}_{4}$ for different values of $\alpha$ ."
 As we can see. the behavior is analogous to the showed at figure 6..," As we can see, the behavior is analogous to the showed at figure \ref{fig:DFm3A}. ."
"subtracted and converted to fluxes, after an extended aperture correction was ","subtracted and converted to fluxes, after an extended aperture correction was applied."
Columns 2-3 of Table 3 list the flux in each aperture., Columns 2-3 of Table \ref{dustTable} list the flux in each aperture.
 The applied.next two columns give the total fluxes and their uncertainties with and without the nuclear point source (nuclear fluxes given in Table 1))., The next two columns give the total fluxes and their uncertainties with and without the nuclear point source (nuclear fluxes given in Table \ref{fitTable}) ).
" The uncertainties have two the in the model and the uncertainty in the components:photometric uncertaintyaccuracy of images (Reachetal.2005,Engelbracht2007)."," The uncertainties have two components: the uncertainty in the model and the uncertainty in the photometric accuracy of images \citep{rea05, eng07}."
". Draineetal.(2007) modeled the integrated IRAC, MIPS, and IRAS fluxes of the SINGS galaxy sample with a two-component dust model and determined dust masses."," \citet{dra07} modeled the integrated IRAC, MIPS, and IRAS fluxes of the SINGS galaxy sample with a two-component dust model and determined dust masses."
 They estimate their models are accurate to10%., They estimate their models are accurate to.
". To test whether the dust mass determined for NGC 1316 by Draineetal.(2007) is located within the regions visible in Figure 8,, we compared our photometry from the two regions of dust emission and the nucleus to their dust model predictions."," To test whether the dust mass determined for NGC 1316 by \citet{dra07} is located within the regions visible in Figure \ref{phot}, we compared our photometry from the two regions of dust emission and the nucleus to their dust model predictions."
 We convolved the predicted Draineetal.(2007) dust flux SED for NGC 1316 (their Figure 14) through the appropriate response functions to calculate the expected fluxes in the band passes., We convolved the predicted \citet{dra07} dust flux SED for NGC 1316 (their Figure 14) through the appropriate response functions to calculate the expected fluxes in the band passes.
" Our and total fluxes for the dust regions and nucleus of 17.4+0.9 mJy and 49.2+0.9 mJy are consistent with the Draineetal.(2007) model values of 13.0€1.3 mJy and 45.4--4.5 mJy, which are the emission for the entire galaxy."," Our and total fluxes for the dust regions and nucleus of $17.4\pm0.9$ mJy and $49.2\pm0.9$ mJy are consistent with the \citet{dra07} model values of $13.0\pm1.3$ mJy and $45.4\pm4.5$ mJy, which are the emission for the entire galaxy."
 The agreement leads us to conclude that the dust mass estimated by Draineetal.(2007) is contained in the non-stellar IR emission regions described in $33.1 and in the nuclear region., The agreement leads us to conclude that the dust mass estimated by \citet{dra07} is contained in the non-stellar IR emission regions described in 3.1 and in the nuclear region.
" In the following, we show that the dust observed in NGC 1316 is not native to the galaxy and use the dust mass to estimate the mass of the merger galaxy."," In the following, we show that the dust observed in NGC 1316 is not native to the galaxy and use the dust mass to estimate the mass of the merger galaxy."
" The clumpy morphology of the dust is significantly different from the smooth elliptical distribution of the stars, so the NGC 1316 stars could not have expelled the dust."," The clumpy morphology of the dust is significantly different from the smooth elliptical distribution of the stars, so the NGC 1316 stars could not have expelled the dust."
" In addition, Tangetal.(2009) found for nearby ellipticals that most of the non- emission is confined to the nuclear region."," In addition, \citet{tra09}
 found for nearby ellipticals that most of the non-stellar emission is confined to the nuclear region."
 This also demonstrates that the morphology of the dust emission in NGC 1316 is unusual., This also demonstrates that the morphology of the dust emission in NGC 1316 is unusual.
 Temietal.(2009) found a correlation between the K-band and luminosities of elliptical galaxies., \citet{tem09} found a correlation between the K-band and luminosities of elliptical galaxies.
" NGC 1316 has a particularlyµπι large luminosity for its K-band luminosity, about an order of magnitude greater than predicted by the Temietal. correlation."," NGC 1316 has a particularly large luminosity for its K-band luminosity, about an order of magnitude greater than predicted by the \citet{tem09} correlation."
" While Temietal.(2009) did not find a correlation between K-band luminosity and either or luminosity, NGC 1316’s integrated luminosities at these wavelengths of 1.4x109 and 1.5x109 (Daleetal.2007) are also more than an order of magnitude greater than found for the galaxies in the Temietal.(2009) sample."," While \citet{tem09} did not find a correlation between K-band luminosity and either or luminosity, NGC 1316's integrated luminosities at these wavelengths of $1.4\times 10^{43}$ and $1.5\times 10^{43}$ \citep{dal07} are also more than an order of magnitude greater than found for the galaxies in the \citet{tem09} sample."
 The large infrared luminosities of NGC 1316 demonstrate an external origin for the dusty emission., The large infrared luminosities of NGC 1316 demonstrate an external origin for the dusty emission.
" In the following, we estimate the mass of dust in NGC 1316 as well as the dust mass expected to be in an elliptical galaxy the size of NGC 1316."," In the following, we estimate the mass of dust in NGC 1316 as well as the dust mass expected to be in an elliptical galaxy the size of NGC 1316."
" Mufioz-Mateosetal.(2009) a formula (A8) for the dust mass of a galaxy providedfrom itsµπι,,µπι,,calculating and fluxes and its distance."," \citet{mun09} provided a formula (A8) for calculating the dust mass of a galaxy from its, and fluxes and its distance."
" We calculated that NGC 1316 has a total dust mass of 2.4--0.9x107Mo,, using the integrated MIPS fluxes from Daleetal. (2007).."," We calculated that NGC 1316 has a total dust mass of $2.4 \pm 0.9 \times 10^{7}$, using the integrated MIPS fluxes from \citet{dal07}. ."
" While emission from the dust is clearly observed, the large uncertainty on the dust mass results from the uncertainties in the distance to NGC 1316 (22.7€:1.8 Mpc) and in the integrated MIPS fluxes (0.43+0.02 Jy atµπι,, 5.443:0.40 Jy atµπι,, and 12.61X:1.78 Jy at μπι)."," While emission from the dust is clearly observed, the large uncertainty on the dust mass results from the uncertainties in the distance to NGC 1316 $22.7\pm1.8$ Mpc) and in the integrated MIPS fluxes $0.43\pm0.02$ Jy at, $5.44\pm0.40$ Jy at, and $12.61\pm1.78$ Jy at )."
" We revised the Draineetal.(2007) dust mass for NGC 1316, which was found on the basis of SED for our assumed distance of 22.7 Mpc to be 3.2x107Mo,, fitting,which is consistent with our dust mass."," We revised the \citet{dra07} dust mass for NGC 1316, which was found on the basis of SED fitting, for our assumed distance of 22.7 Mpc to be $3.2 \times 10^{7}$, which is consistent with our dust mass."
" We used the fluxes for the sample of elliptical galaxies in etal. (2009),, along with their B-V colors (deVaucouleursal.1991) and the mass-to-light ratios of Belletal. (2003),, to calculate the color-dependentstellar and dust massesof the sample."," We used the fluxes for the sample of elliptical galaxies in \citet{tem09}, along with their B-V colors \citep{dev91} and the color-dependent mass-to-light ratios of \citet{bel03}, to calculate the stellar and dust massesof the sample."
 We found that elliptical galaxies typically have dust-to-stellar mass ratios between 0.7—5.3x1077., We found that elliptical galaxies typically have dust-to-stellar mass ratios between $0.7-5.3\times10^{-7}$.
" Using these ratios, we estimate that NGC 1316 with its stellar mass of 5.3x10!! (based on B-V=0.87 (deVaucouleursetal. 1991), K = 5.587 (Jarrettetal.2003),, and the relations of Belletal. (2003))) had an intrinsic dust mass of 0.4—3x10? Mo,, €1% of the measured dust mass."," Using these ratios, we estimate that NGC 1316 with its stellar mass of $5.3\times10^{11}$ (based on B-V=0.87 \citep{dev91}, K = 5.587 \citep{jar03}, and the relations of \citet{bel03}) ) had an intrinsic dust mass of $0.4-3\times10^{5}$ , $\lesssim 1$ of the measured dust mass."
 We conclude that nearly all of the dust currently present in NGC1316 was contributed by a merger galaxy., We conclude that nearly all of the dust currently present in NGC1316 was contributed by a merger galaxy.
 We can constrain the galaxy type and the stellar and gas mass of the merger galaxy from its estimated dust mass of 2.420.9x107 Mo., We can constrain the galaxy type and the stellar and gas mass of the merger galaxy from its estimated dust mass of $2.4 \pm 0.9 \times 10^{7}$ .
". The merger galaxy had to be late type galaxy as its stellar mass, were it a typical elliptical,"," The merger galaxy had to be a late type galaxy as its stellar mass, were it a typical elliptical,"
". The merger galaxy had to be late type galaxy as its stellar mass, were it a typical elliptical,a"," The merger galaxy had to be a late type galaxy as its stellar mass, were it a typical elliptical,"
projection at 208+ kpe are plivsically close based ou morphological disturbances of the pairs.,projection at $20 h^{-1}$ kpc are physically close based on morphological disturbances of the pairs.
 The umber of pairs detected is close to what is expected frou the two-poimt correlation function., The number of pairs detected is close to what is expected from the two-point correlation function.
 Because the total uunuber of pairs in their sample at this separation is small. they determine the overall fraction at this separation by extrapolating the two-point correlation fiction of galaxies from measurcuents out to 1007.! kpc.," Because the total number of pairs in their sample at this separation is small, they determine the overall fraction at this separation by extrapolating the two-point correlation function of galaxies from measurements out to $100 h^{-1}$ kpc."
" Using dynamical arguments aud results of παΊος, they find that the average time for a merger starting at this separation of 205.+ kpc is P—0.3 Cyr. and that a fraction F~0.3 of such pairs ο in+ this+ time."," Using dynamical arguments and results of simulations, they find that the average time for a merger starting at this separation of $20 h^{-1}$ kpc is $T=0.3$ Gyr, and that a fraction ${\cal F}\sim0.3$ of such pairs will merge in this time."
+ Approximately.+ then. F/T~41Carl1 givesB the BHfractional+ merecr. rate forBH these e“close pairs..ο. which should hold roughly constant as loug as the galaxy population is similar to that of the low-vedshift uuverse.," Approximately, then, ${\cal F}/T\sim 1 \;{\rm Gyr}^{-1}$ gives the fractional merger rate for these “close pairs,” which should hold roughly constant as long as the galaxy population is similar to that of the low-redshift universe."
 Using these argumneuts aloug with observatious of the ummber of close pairs from the CNOC2 and ΟΕΠο survers over 0<2€1. ? fiud where Π is the merger rate for a single object aud ων) is the comoving volue deusity of iiergiug objects which for us is spheroids coutaiuniug MDIIS.," Using these arguments along with observations of the number of close pairs from the CNOC2 and CFGRS surveys over $0\le z\le 1$, \citet{Carlberg00} find where $R_g$ is the merger rate for a single object and $\phi_\BH(z)$ is the comoving volume density of merging objects which for us is spheroids containing MBHs."
 We will from here ou assume the merger-rate parameters to be equal to these canonical values given iu equation (16))., We will from here on assume the merger-rate parameters to be equal to these canonical values given in equation \ref{eq:Rzcarlberg}) ).
 Crucially. we also assune that the measured mereer rate per galaxy is equal to the desired merger rate.," Crucially, we also assume that the measured merger rate per galaxy is equal to the desired merger rate."
 Inserting this merger rate into equation (15)). we fiud Wo have taken o=1.0«10.753Mpc5 as one value for the umuber density of iuecreime objects: see retsee:BIIpop..," Inserting this merger rate into equation \ref{eq:zrate}) ), we find We have taken $\phi_\BH=1.0\times10^{-3} h_0^3 {\rm~Mpc}^{-3}$ as our value for the number density of merging objects; see \\ref{sec:BHpop}. ."
" We have left the evolution of the merecr rate. 22,06)/P [vith nonualization RyΠΟΠ. uuspecified."," We have left the evolution of the merger rate, $R_g(z)/R_0$ [with normalization $R_0=R_g(0)$ ], unspecified."
 Whereas ? find Πιτ) approsimately coustautf. ?.. à very similar group of authors using somewhat different data. fud Προ)x(1|DQQo29," Whereas \citet{Carlberg00} find $R_g(z)$ approximately constant, \citet{Patton02}, a very similar group of authors using somewhat different data, find $R_g(z)\propto(1+z)^{1.3\mbox{--}2.3}$."
" Το parameterize this difference (as well as other substantial observational disagreement ou the merecr rate as a function of time). we consider several other uodels. geuerically paraueterizius the merger rate per unit tine. 77,(:). as a power-law in the expansion actor. Πρ)=Rofl|i)."," To parameterize this difference (as well as other substantial observational disagreement on the merger rate as a function of time), we consider several other models, generically parameterizing the merger rate per unit time, $R_g(z)$, as a power-law in the expansion factor, $R_g(z)=R_0 (1+z)^\gamma$."
" We will also allow the merger rate por unit redshift to be a power-law. which neaus that 2,02)—RyL(y↽|01tye⋅∣↣⋅≻777. where we use ~!5/2E since: that has +=5 when ©,,=,1 and 94=0."," We will also allow the merger rate per unit redshift to be a power-law, which means that $R_g(z)=R_0
E(z)(1+z)(1+z)^{\gamma'-5/2}$, where we use $\gamma'-5/2$ since that has $\gamma'=\gamma$ when $\Omega_m=1$ and $\Omega_\Lambda=0$."
 In Fieure 1 we show the merecr rate with 5=0: increasing this exponent would increase he merger rate at higher redshift., In Figure \ref{fig:mergerates} we show the merger rate with $\gamma=0$; increasing this exponent would increase the merger rate at higher redshift.
 Below. we will find that our limited knowledge of the merger rate is a nain contributor to the uncertaiutv in the final GW spectra.," Below, we will find that our limited knowledge of the merger rate is a main contributor to the uncertainty in the final GW spectrum."
 ? consider merger rates with both higher xeseut-day. norlalizations aud stronger redshift evolution(sce Figure 1))., \citetalias{Rajagopal95} consider merger rates with both higher present-day normalizations and stronger redshift evolution(see Figure \ref{fig:mergerates}) ).
 > 0 <0 « 0 > 0, > 0 < 0 < 0 > 0.
" For Ravleigh uustable flows (where. 0,072.<0 aud therefore OQ< 0).eqs. (06)). (017))"," For Rayleigh unstable flows (where $\partial_{r} {\Omega r^{2}} < 0$ and therefore $\partial \Omega <0$ ),eqs. \ref{ur3}) ), \ref{uphi3}) )"
 aud (21)) show that the linear coupling teziis with the mean flow are always a source for turbulent fluctuations. a property that reflects the elobal linear instability of this class of flows.," and \ref{signeuruphi}) ) show that the linear coupling terms with the mean flow are always a source for turbulent fluctuations, a property that reflects the global linear instability of this class of flows."
 The non-lnearities are needed there oulv for the saturation of amplitudes of the radial aud azimuthal velocities along with the redistribution of euergv towards axial motions of the new bifurcated flow., The non-linearities are needed there only for the saturation of amplitudes of the radial and azimuthal velocities along with the redistribution of energy towards axial motions of the new bifurcated flow.
 Iu the caseof stable aneular p+ ⋯∪∐∐∖∐⊓∐⊔↴∖↴⊓⋅⋜↧↑↕∐↸⊳⋜↧⊓∪∐≺≪↗∣⋅≤≥∣⋮−∣⋟∙⋅⋅≽ the first order coupling terms lave opposite sigus iu Eqs (11)) aud (12)). ⊺↕∐↴∖↴⋯↸∖⋜⋯↴∖↴↑∐⋜↧↑∪∐," In the caseof stable angular momentum stratification $\partial_{r} {\Omega r^{2}} > 0$ ), the first order coupling terms have opposite signs in Eqs \ref{ur2}) ) and \ref{uphi2}) )."
↸∖∪↕⋟↑∐↸∖⋯↕↴∖↴⋜⊔⊔∖∐↸∖↥⋅∶↴∙⊾⋅↖↽↴∖↴↕↕∐↘↽↕≯∪↥⋅∪∐↸∖ ∪↕≯↕∐∖↸⊳∪∐∏≻∪↕∐∖∐↑∪↕⋟↑↕∐∖↖↽↸∖↕⋯⊳↕↑⋅↖↽∏⋯⊳⊓⋜↧↑↕∪∐↴∖↴≺∎∙↗⋝∙∙↕↑↑∐↸∖∐ ↕∪∪↘↽↴∖↴↕↕⊔↻, This means that one of them is an energy sink for one of the component of the velocity fluctuations \citep{bhs}.
∪↴∖∷∖↴∏⋝↕↸∖↑∪⋜↧∐∪↖↖⇁↕⋟∪↥⋅↑∐↸∖∶↴∙⊾↥⋅∪↖↖⇁↑∐∪↥⋅↑∪⋯⋜↧↕∐↑⋜↕↕∐ C» C» ⊓∐∎⋝∏↕↸∖∐∏∖⋜↧↴∖↴↕∪∐∩⋜↕↴∖↴↑∐↸∖⋜↧∐∩∏↕⋜∐∎↕∐∪∐∐∖∐⊓∐∐↕∖↕∐↸⊳↥∎↸∖⋜↧↴∖↴↕∐∩ C» outward., It then looks impossible to allow for the growth or to maintain turbulence as long as the angular momentum is increasing outward.
 This actually reflects the linear stability of such flows., This actually reflects the linear stability of such flows.
" E 20 un"" | Oe = uc⋅≻| = Thesexoperties for all introduced coefficients are sumnuuarized in Table (1)).", = 2 u^2 + _r = - u^2+ = _z _t k = - r _r u^2 + Theseproperties for all introduced coefficients are summarized in Table \ref{table1}) ).
 From Eq. (28)), From Eq. \ref{k4}) )
 we derive the amplitude of he fluctuations vorticity: = V.radio. This relation express that the vorticity extracted fron the background flow by the fluctuations is proportional to the local shear. , we derive the amplitude of the fluctuations vorticity: = r _r. This relation express that the vorticity extracted from the background flow by the fluctuations is proportional to the local shear. _
o0 U Crus» 2001uF oo aga),"r > 0: _r - 2 u^2, _r < 0: u^2, Which reduces to, _r > 0: - 2 _r < 0 :"
"motion its expansion velocity can be described by the vacuum Hubble constant 1,=VOLl.","motion its expansion velocity can be described by the vacuum Hubble constant $H_{v}=
\sqrt{\Omega_{\Lambda}}H_{o}$."
 Maccio et al.(2005) found from N-body simulations that the observed coldness of the local IIubble flow around the local eroup is consistent with the dark energy interpretation., Maccio et al.(2005) found from N-body simulations that the observed coldness of the local Hubble flow around the local group is consistent with the dark energy interpretation.
 llowever recently Ποια et al. (, However recently Hoffman et al. (
2008) ancl Martinez-Vaquero et al. (,2008) and Martinez-Vaquero et al. (
2009) using sophisticated cosmological simulations claim that dark energy should have no effect on the local dynamics.,2009) using sophisticated cosmological simulations claim that dark energy should have no effect on the local dynamics.
 In particular. these authors showed that a similar local Hubble flow was also found in an open cosmological model making the need for a A model unnecessary locally.," In particular, these authors showed that a similar local Hubble flow was also found in an open cosmological model making the need for a $\Lambda$ model unnecessary locally."
 Further. Sandage (1986) has shown analyGcally that sub-IIubble flows can exist around groups in cosmologies without a A term though of a different form from that found by TOs.," Further, Sandage (1986) has shown analytically that sub-Hubble flows can exist around groups in cosmologies without a $\Lambda$ term though of a different form from that found by T08."
 It is clearly of interest to confirm and extend the TOS result., It is clearly of interest to confirm and extend the T08 result.
 In order to do so a new method for finding the velocity Ποια is required since with increasing distances the only observational data available are positions aud redshilts both for the groups and the field galaxies., In order to do so a new method for finding the velocity field is required since with increasing distances the only observational data available are positions and redshifts both for the groups and the field galaxies.
 The goal here is to devise such a method. and to apply it to an existing group catalog in order to determine il the perturbations to the Hubble expansion law found by TO8 apply to groups in a Larger ancl more representative volume of space., The goal here is to devise such a method and to apply it to an existing group catalog in order to determine if the perturbations to the Hubble expansion law found by T08 apply to groups in a larger and more representative volume of space.
" Determining the expansion velocity in terms of Hubble-Hlike law (V.—77, H) requires knowledge of the velocity wilh respect to the group center in the direction of expansion V. and the clistance Irom the group center A2."," Determining the expansion velocity in terms of Hubble-like law $V=H_{exp}R$ ) requires knowledge of the velocity with respect to the group center in the direction of expansion $V$, and the distance from the group center $R$."
 To demonstrate the essence of (he method. assume for the moment that two projections of this expansion law are available (i.e. AV=Veos(8) and AR=Rsin(@) in Fig 1).," To demonstrate the essence of the method, assume for the moment that two projections of this expansion law are available (i.e. $\Delta V=Vcos(\theta)$ and $\Delta R=Rsin(\theta)$ in Fig 1 )."
" Let y=Vcos(@) andr!=1),sin(@).", Let $y^{\prime}=V~cos(\theta)$ and $x^{\prime}=H_{exp}R~sin(\theta)$.
" Then Now lake (he average of both sides of this equation assuming Chat the number of groups is large and that the surrounding field galaxies are randomly distributed about these groups and denote the mean of the angular term as alter rearranging terms /7,,, is varied until the ratio", Then Now take the average of both sides of this equation assuming that the number of groups is large and that the surrounding field galaxies are randomly distributed about these groups and denote the mean of the angular term as after rearranging terms $H_{exp}$ is varied until the ratio
1n the carly 1990s. measurements of the barvonic mass fraction in. N-rav luminous οιUaxy| Clusters| .provictec“loc compelling evidence that we in Ia low density .later Universe.,"In the early 1990s, measurements of the baryonic mass fraction in X-ray luminous galaxy clusters provided compelling evidence that we live in a low density Universe."
 Under the assumption that large clusters provide approximately fair samples of the matter content of. the Universe. X-ray. observations require that the mean matter density. Qu. is significantly less than the critical value. with a best-Lit value Qu(20.3," Under the assumption that large clusters provide approximately fair samples of the matter content of the Universe, X-ray observations require that the mean matter density, $\Omega_{\rm m}$, is significantly less than the critical value, with a best-fit value $\Omega_{\rm m}\sim 0.2-0.3$."
 When combined with the expectation from inflation models. confirmed. by⋅ Cosmic .Microwave Background. (CM) liveMn studies29therein). that the Universe should be close to spatially fat. X-ray results on the eluster ⋅⊀ ⊀ ∣⋡⋜⊔⋅∙∖⇁∩⊔⊔↓⋜↧⊳∖⊳∖⇂↓⋅⋯⇍⊔∪⊔⊏↥⋯≼∼⊔∙∖⇁↓∢⋅⋯⇂↿∪↿↓↕⋖⋅⊳∖⊔⋏∙≟⋏∙≟⋖⋅⊳∖↿↓∪⊔⇂↓⋯∣↿↓↥⋖⋅ ⊀ ⊔↓⋜↧⊳∖⊳∖⊣⋅⊔∢⊾↓⋅⋏∙≟∙∖⇁∠⇂∢⊾⊔⊳∖⊲↓↿∙∖⇁∪⇂⋅↿↓⊔⋅⇂⊽⊔⊲↓∖⇁∢⊾↓⋅⊳∖∢⊾⊔⋯∙∖⇁∣⋡⋖⋅∠⇂⋖⋟↓↕↓↕↓↕⋜↧↿⋖⊾∠⇂∣⋡∙∖⇁ a cosmological constant2).," When combined with the expectation from inflation models, later confirmed by Cosmic Microwave Background (CMB) studies, that the Universe should be close to spatially flat, X-ray results on the cluster baryon mass fraction quickly lead to the suggestion that the mass-energy density of the Universe may be dominated by a cosmological constant."
. 'lhe first direct evidence for late-time cosmic, The first direct evidence for late-time cosmic
We confirmed. the deficiency of rest-UV. luminous (Απ<—21.5) LDGs with large rest-lrame EW (2»20A)) of Ίωνα emission (Andoetal.2006).,We confirmed the deficiency of rest-UV luminous $M_{1600}<-21.5$ ) LBGs with large rest-frame EW $>20$ ) of $\alpha$ emission \citep{and06}.
.. We discussed possible causes for the deficiency and prefer (he interpretation of dust absorption rather (han gas outflow. age difference. and IME difference.," We discussed possible causes for the deficiency and prefer the interpretation of dust absorption rather than gas outflow, age difference, and IMF difference."
 We would like to thank stall members at Gemini observatory for carrying out our observations., We would like to thank staff members at Gemini observatory for carrying out our observations.
 Especially. we are grateful to support scientists Atsuko Nitta and Dryan Miller for their helpful comments during preparation.," Especially, we are grateful to support scientists Atsuko Nitta and Bryan Miller for their helpful comments during preparation."
 This work was partly made based on machine time exchange program., This work was partly made based on Gemini-Subaru machine time exchange program.
" This work is supported by Grant-in-Aid lor Scientific Research on Priority Area (19047003) from Ministry of Education. Culture. Sports. Science. and Technology of Japan. and in part supported by Παπας from the Natural Sciences and Engineering Research Council of Canada and bv the Canadian Space Agency,"," This work is supported by Grant-in-Aid for Scientific Research on Priority Area (19047003) from Ministry of Education, Culture, Sports, Science, and Technology of Japan, and in part supported by funding from the Natural Sciences and Engineering Research Council of Canada and by the Canadian Space Agency."
higher temperatures are due to O-atoms detected by the mass spectrometer when other molecules dissociate.,higher temperatures are due to O-atoms detected by the mass spectrometer when other molecules dissociate.
" The desorption temperatures for 16 and 31 amu are similar to those of pure CH, and CH:OH ice confirms their RAIR detection.", The desorption temperatures for 16 and 31 amu are similar to those of pure $_4$ and $_3$ OH ice confirms their RAIR detection.
 The TPD spectra and desorption temperatures of 29 amu are consistent with the desorption temperatures for H:CO found by Watanabeetal. (2004)., The TPD spectra and desorption temperatures of 29 amu are consistent with the desorption temperatures for $_2$ CO found by \citet{watanabe2004}.
. In addition. a TPD desorption peak 1s located at ~160 K for masses 45 and 46 amu (see Fig. 8)).," In addition, a TPD desorption peak is located at $\sim$ 160 K for masses 45 and 46 amu (see Fig. \ref{tpd}) )."
 This is assigned to C4H&OH desorption based on a comparison with the TPD of pure non-bombarded C» HsOH ices., This is assigned to $_2$ $_5$ OH desorption based on a comparison with the TPD of pure non-bombarded $_2$ $_5$ OH ices.
" In summary. a fraction of CHsCHO.below the infrared detection limit of the 1050 em! band. is converted to C:HsOH and a larger fraction forms CH,. H»CO and CH:;OH."," In summary, a fraction of $_3$ CHO,below the infrared detection limit of the 1050 $^{-1}$ band, is converted to $_2$ $_5$ OH and a larger fraction forms $_4$, $_2$ CO and $_3$ OH."
 So even though the conversion of acetaldehyde to ethanol is not complete. it is important to note that a pathway in the proposed hydrogenation scheme by Tielens&Charnley(1997) is experimentally confirmed.," So even though the conversion of acetaldehyde to ethanol is not complete, it is important to note that a pathway in the proposed hydrogenation scheme by \citet{tielens1997} is experimentally confirmed."
 The value for N(CH3;CHO) as derived from the vp(umbrella) spectral feature at 1348 em! is shown in Fig.," The value for $N$ $_3$ CHO) as derived from the $\nu_{\rm
 D}$ (umbrella) spectral feature at 1345 $^{-1}$ is shown in Fig."
 9. as a function of time for different ice thicknesses at 14.5 K. Also shown are the fits to the data., \ref{ch3chofit} as a function of time for different ice thicknesses at 14.5 K. Also shown are the fits to the data.
 The vp(umbrella) mode ischosen for analysis rather than the 1728 em! band. because the latter overlaps with the vs(C=O) of H»CO at 1720 em.," The $\nu_{\rm D}$ (umbrella) mode ischosen for analysis rather than the 1728 $^{-1}$ band, because the latter overlaps with the $\nu_{\rm
 S}$ (C=O) of $_2$ CO at 1720 $^{-1}$ ."
 Clearly. the absolute amount of CH3CHO that can react increases with ice thickness. whereas A/Ao decreases.," Clearly, the absolute amount of $_3$ CHO that can react increases with ice thickness, whereas $A/A_0$ decreases."
 The temperature behavior is more complex and is shown in Fig. 10.., The temperature behavior is more complex and is shown in Fig. \ref{ch3chofit2}.
 The «o and Bo values derived from the fits as function of the thickness and temperature are shown in Fig. 11.., The $\alpha_0$ and $\beta_0$ values derived from the fits as function of the thickness and temperature are shown in Fig. \ref{params}.
 The values for ag decrease with increasing thickness. but do not depend on ice temperature within the measured regime.," The values for $\alpha_0$ decrease with increasing thickness, but do not depend on ice temperature within the measured regime."
 The latter is not surprising as the CH3CHO ice structure does not change between 15 and 75 K. The value for fo ts independent of ice thickness. but does depend on ice temperature.," The latter is not surprising as the $_3$ CHO ice structure does not change between 15 and 75 K. The value for $\beta_0$ is independent of ice thickness, but does depend on ice temperature."
 It is largest for ice temperatures between 15-16 K. similar to the case of CO (Fuchsetal..2007).," It is largest for ice temperatures between 15–16 K, similar to the case of CO \citep{fuchs2007}."
. This is expected as the maximum reactivity is mostly determined by the mobility of H-atoms at the surface., This is expected as the maximum reactivity is mostly determined by the mobility of H-atoms at the surface.
 At low temperatures H-atoms move more slowly resulting in à lower reaction rate., At low temperatures H-atoms move more slowly resulting in a lower reaction rate.
 At higher temperatures the diffusion rate is higher but has to compete with an increased evaporation rate., At higher temperatures the diffusion rate is higher but has to compete with an increased evaporation rate.
 For the C4H3OH formation. only yields can be calculated from the TPD data because the RAIR feature at 1050 em! overlaps with the vs(CO) band of CH:;OH.," For the $_2$ $_5$ OH formation, only yields can be calculated from the TPD data because the RAIR feature at 1050 $^{-1}$ overlaps with the $\nu_{\rm S}$ (CO) band of $_3$ OH."
" The yields for CH,. CH;OH and C>HsOH are given in Table 5.."," The yields for $_4$, $_3$ OH and $_2$ $_5$ OH are given in Table \ref{ch3chorate}."
 Even when considering that there is a general quantitative uncertainty of ~10%.. it is clear that the summed yield of the different products is not 100%., Even when considering that there is a general quantitative uncertainty of $\sim$ it is clear that the summed yield of the different products is not .
. This ismost likely due to missing H2CO yields. because these are not reliably calibrated.," This ismost likely due to missing $_2$ CO yields, because these are not reliably calibrated."
" Furthermore Y(CH,j) is expected to be equal to Y(H:CO-CH;OH). because"," Furthermore $Y$ $_4$ ) is expected to be equal to $Y$ $_2$ $+$ $_3$ OH), because"
UBVRI tnages of 16 dwarf elliptical galaxies in the Virgo Cluster were obtained with the VATT Lsin on 2003 March 29-31.,UBVRI images of 16 dwarf elliptical galaxies in the Virgo Cluster were obtained with the VATT 1.8m on 2003 March 29-31.
 The telescope was equipped with CCD26. a thinned Loral 3 3015 x 3015 CCD with pixels.," The telescope was equipped with CCD26, a thinned Loral 3 2048 $\times$ 2048 CCD with pixels."
 CCD26 has a read noise of 5.7 and a gain of 1.0 ῥροι ADU was used., CCD26 has a read noise of 5.7 $^-$ and a gain of 1.9 $^-$ per ADU was used.
 On-chip binning of 2 x 2 resulted in per pixel and a field of view of 6.1 x 6.1 arcmin., On-chip binning of 2 $\times$ 2 resulted in per pixel and a field of view of 6.4 $\times$ 6.4 arcmin.
 The galaxies were centered iu the field. but dithers of approximately 1 arcmin were taken between each exposure to assist with the flat fielding process.," The galaxies were centered in the field, but dithers of approximately 1 arcmin were taken between each exposure to assist with the flat fielding process."
 Table 1 lists the basic parameters of the dE sample and sumauarizes the observations., Table \ref{tab:obs} lists the basic parameters of the dE sample and summarizes the observations.
 Unless otherwise noted in Table 1.. the VATT L-Sin observations consisted of 2 exposures of 510 sec. 120 sec. 300 sec. 210 sec. aud 300 sec with the U. B. V. B. aud I filters. respectively.," Unless otherwise noted in Table \ref{tab:obs}, the VATT 1.8m observations consisted of 2 exposures of 540 sec, 420 sec, 300 sec, 240 sec, and 300 sec with the U, B, V, R, and I filters, respectively."
 Complete UBVRI ünages were obtained for 9 galaxies in the sample: BVRI images were obtained for au additional 1 ealaxies aud 3 galaxies were iiuaged in ouly B aud BR. The observations were structured so that tLT Band R images were obtained ou the same night uuder similar observing conditions: similarly. the V aud IL images were taken sequentially.," Complete UBVRI images were obtained for 9 galaxies in the sample; BVRI images were obtained for an additional 4 galaxies and 3 galaxies were imaged in only B and R. The observations were structured so that the B and R images were obtained on the same night under similar observing conditions; similarly, the V and I images were taken sequentially."
 Thus. tle (B-R) aud (V-I) colors for these observations are quite secure. while (B-V) and (U-B) colors have additional error propagation terms since the colorW. are based ou the calibrated maguituces rather than calibration of the instrumental colors.," Thus, the (B-R) and (V-I) colors for these observations are quite secure, while (B-V) and (U-B) colors have additional error propagation terms since the colors are based on the calibrated magnitudes rather than calibration of the instrumental colors."
 The fina combined images were sulliciently deep to permit accurate photometry of the outer regions of the ealaxies., The final combined images were sufficiently deep to permit accurate photometry of the outer regions of the galaxies.
 Typical surface briglitness limits lor the combined images are 25.8. 26.8. 26.0. 25.6. sux ox25.0 imag 7. 32.in -U. B. V.T BR. aud L respectively.," Typical surface brightness limits for the combined images are 25.8, 26.8, 26.0, 25.6, and 25.0 mag $^{-2}$, in U, B, V, R, and I, respectively."
. All 3 nights were photometric., All 3 nights were photometric.
 Calibration coellicients were derived from observatious of standard stars [rom Γαμοσ(1992) iuterspersed with the galaxy observations., Calibration coefficients were derived from observations of standard stars from \citet{L92} interspersed with the galaxy observations.
 Based ou the derive photometric coellicients. the BVBI images have accuracy while the U-band images are accurate toBY.," Based on the derived photometric coefficients, the BVRI images have accuracy while the U-band images are accurate to."
 The same sample of galaxies was imaged with the 3.5m telescope on 2002 May , The same sample of galaxies was imaged with the 3.5m telescope on 2002 May 12-16.
Poor weather haumpered the usefuluess of these observations. but the WIYN üinages provide confirmation for the structural parameters derived from the VATT 1δι data.," Poor weather hampered the usefulness of these observations, but the WIYN images provide confirmation for the structural parameters derived from the VATT 1.8m data."
 In particular. the WIYN images have slightly better seeing characteristics than the VATT 1.8: images.," In particular, the WIYN images have slightly better seeing characteristics than the VATT 1.8m images."
 The WIYN 3.51n telescope was equipped with the Mini-Mosaic camera. which cousists of two SITe 1006 x 32015 CCDs with pixels.," The WIYN 3.5m telescope was equipped with the Mini-Mosaic camera, which consists of two SITe 4096 $\times$ 2048 CCDs with pixels."
 The two CCDs are read-out by f£ amplifiers (2 per CCD). with typical read noises of 5.5 e and gains of 1.Le per ADU.," The two CCDs are read-out by 4 amplifiers (2 per CCD), with typical read noises of 5.5 $^-$ and gains of 1.4 $^-$ per ADU."
 The pixel scale of Mini-Mo is per pixel. which results in a fiekl of view of 9.6 o 9.6 arcmin with a gaygap between," The pixel scale of Mini-Mo is per pixel, which results in a field of view of 9.6 $\times$ 9.6 arcmin with a gap between"
Magnetic fields in the Universe are found in almost all studied environments.,Magnetic fields in the Universe are found in almost all studied environments.
 In particular. their presence in the inter-galactic medium (IGM:see?.forarecentreview) and in the intra-cluster medium (ICM) is confirmed by difuse radio emission as well as by observations of Faraday Rotation Measures (RM) towards polarized radio sources within or behind the magnetized medium (e.g.2).," In particular, their presence in the inter-galactic medium \citep[IGM; see][ for a recent 
review]{2009ASTRA...5...43B} and in the intra-cluster medium (ICM) is confirmed by diffuse radio emission as well as by observations of Faraday Rotation Measures (RM) towards polarized radio sources within or behind the magnetized medium \citep[e.g.][]{2006AN....327..539G}."
 On the largest scales. like those of filaments. magnetic fields are notoriously difficult to measure and available data is still incomplete.," On the largest scales, like those of filaments, magnetic fields are notoriously difficult to measure and available data is still incomplete."
 This is especially difficult because these measurements require either a high thermal density (for RMs) or the presence of relativistic particles (for the synchrotron emission)., This is especially difficult because these measurements require either a high thermal density (for RMs) or the presence of relativistic particles (for the synchrotron emission).
 Therefore. measurements of the magnetic field strength have been successfull for high density regions of collapsed objects (e.g. galaxies and galaxy clusters). and thus. tields signiticantly below the 7G level can hardly be detected.," Therefore, measurements of the magnetic field strength have been successfull for high density regions of collapsed objects (e.g. galaxies and galaxy clusters), and thus, fields significantly below the $\mu$ G level can hardly be detected."
 Recently an interesting attempt to constrain the value of large scale cosmic magnetic fields was done by ?.., Recently an interesting attempt to constrain the value of large scale cosmic magnetic fields was done by \citet{2009arXiv0906.1631L}.
 These authors detected a positive cross-correlation signal between the galaxy distribution in the SDSS Sixth Data Release (2). and the RM values extracted from the ?. catalog., These authors detected a positive cross-correlation signal between the galaxy distribution in the SDSS Sixth Data Release \citep{2008ApJS..175..297A} and the RM values extracted from the \citet{2009ApJ...702.1230T} catalog.
 Using the amplitude of this signal. together with a simplified model for the magnetic fields configuration in the Universe (estimated from its mean electron density). and computing the RM typical values expected from this coherent field in a given length scale. they were able to derive limits for the corresponding cosmic magnetic fields.," Using the amplitude of this signal, together with a simplified model for the magnetic fields configuration in the Universe (estimated from its mean electron density), and computing the RM typical values expected from this coherent field in a given length scale, they were able to derive limits for the corresponding cosmic magnetic fields."
 In his work. we want to investigate: (4) to what extent a self-consistent treatment of the cosmological RM signal based on magneto-hydrodynamical (MHD) simulations. of structure formation changes the expected shape and amplitude of such a correlation signal. and @ how such an approach is affected by the presence of the Galactic foreground (GF) and noise in the tinal RM signal.," In this work, we want to investigate: ) to what extent a self-consistent treatment of the cosmological RM signal based on magneto-hydrodynamical (MHD) simulations of structure formation changes the expected shape and amplitude of such a correlation signal, and ) how such an approach is affected by the presence of the Galactic foreground (GF) and noise in the final RM signal."
 Both points are of extreme importance. if robust field properties are to be derived from any observed signal.," Both points are of extreme importance, if robust field properties are to be derived from any observed signal."
 Furthermore. the appearance of magnetic field reversals (as observed in galaxy clusters at various length scales) will alter the cosmological signal magnitude and shape. whereas the residuals of any foreground and measurement errors will bias the relation between the amplitude of the correlation function and the underlying cosmological field.," Furthermore, the appearance of magnetic field reversals (as observed in galaxy clusters at various length scales) will alter the cosmological signal magnitude and shape, whereas the residuals of any foreground and measurement errors will bias the relation between the amplitude of the correlation function and the underlying cosmological field."
 In, In
2010).,.
. Since fie first generation of galaxies is predicted to fori in high-density regions that have been pre-euriched by pop EHI stars iu münilalos. these galaxies are not expected » be inetal-free. aud are most likely dominated by chemically euriclied stars (0.8.Greifetal.2010).," Since the first generation of galaxies is predicted to form in high-density regions that have been pre-enriched by pop III stars in minihalos, these galaxies are not expected to be metal-free, and are most likely dominated by chemically enriched stars \citep[e.g.][]{Greif et al. c}."
. True populatioi HI ealaxies avy. however. form at slightly later epochs. in low-density euvironinents which have retained chemically pristine (6.8.Scannuapiecoctal.2003:Treitietal.2009:Stiavelli&Treuti 2010).," True population III galaxies may, however, form at slightly later epochs, in low-density environments which have remained chemically pristine \citep[e.g.][]{Scannapieco et al.,Trenti et al.,Stiavelli & Trenti}."
. Due to the excecclinely lig1 temperatures of massive »opulatio1 III stars photoionizationj such objects may contribute substautlally to the of the iuterstellar medi aud alter the ovcrall spectra of their ost ealaxies.," Due to the exceedingly high temperatures of massive population III stars $T_\mathrm{eff}\sim 10^5$ K), such objects may contribute substantially to the photoionization of the interstellar medium and alter the overall spectra of their host galaxies."
 A nunaber of authors have pointed out hat x»pulatiou IIL-douinated σαaNICS could be ideuti&ed sed ou the streugths of the Ίνα liuc. the HoII A1610. ALGS6 lies. or the Lyman ‘bump {e.et'Tuiuliusou& amc several searches have since tried to ayply these echuiques{e.itheDawsonctal.2001:Nagao2005:2008:Caietal. 2011)..," A number of authors have pointed out that population III-dominated galaxies could be identified based on the strengths of the $\alpha$ line, the HeII $\lambda1640$, $\lambda4686$ lines, or the Lyman `bump' \citep[e.g.][]{Tumlinson & Shull,Tumlinson et al. a,Oh et al.,Malhotra & Rhoads,Schaerer a,Schaerer b,Inoue} and several searches have since tried to apply these techniques \citep[e.g.][]{Dawson et al.,Nagao et al. a,Dijkstra & Wyithe,Ouchi et al.,Nagao et al. c,Cai et al.}."
 While a few potential population QT candidates have indeed 1ο. reported (Fosburyet2008:Thoueetal. 2011a).. their «act iatire yea unclear.," While a few potential population III candidates have indeed been reported \citep{Fosbury et al.,Raiter et al. a,di Serego Alighieri,Inoue et al.}, their exact nature remain unclear."
 So far. essentially all searches for »opulatiou III ealaxies have relied on spectroscopy or narrowbaud iotonmetry.," So far, essentially all searches for population III galaxies have relied on spectroscopy or narrowband photometry."
 Ef population III galaxy candidates could instead be singled out from large sampCS Dasec just 6ji their broadband colours (asrecentlvattemptedbyDomwveusetal.2016 Y.. this would allow for substantial eains in terms of observing time.," If population III galaxy candidates could instead be singled out from large samples based just on their broadband colours \citep[as recently attempted by][]{Bouwens et al.}, this would allow for substantial gains in terms of observing time."
" Ilere. we preseutVyydrasil a new spectral svuthesis Moccl for the first ecnerations of galaxies. and use it o explore the spectral signatures of pure population III ealaxics in (JIWST) photometric «νους,"," Here, we present, a new spectral synthesis model for the first generations of galaxies, and use it to explore the spectral signatures of pure population III galaxies in (JWST) photometric surveys."
 The technical details of the model are cleseribed in S¢ct. 2., The technical details of the model are described in Sect. \ref{Yggdrasil}.
 I1 Sect. 3..," In Sect. \ref{scenarios},"
 we define three ciffereut classes of first eaaNICS. which differ bv the relaive amount that nebular ciission is expected to contribute to their integrated spcοἶτα," we define three different classes of first galaxies, which differ by the relative amount that nebular emission is expected to contribute to their integrated spectra."
ι The resulting (JWST) amass detection Duis for both population II αιxl amore chemically evolved galaxies iu xiotoimeric survoevs are presented iu Sect. L., The resulting (JWST) mass detection limits for both population III and more chemically evolved galaxies in photometric surveys are presented in Sect. \ref{masslimits}.
 Poteutial srTateeglos for scarching for population III ealaxics (clominated either bv jiebular enission or direct star light) in deep JWST nuages are presented in Sect., Potential strategies for searching for population III galaxies (dominated either by nebular emission or direct star light) in deep JWST images are presented in Sect.
 5. aud Sec OG., \ref{typeA} and Sect. \ref{typeC}.
 A iuiuber of poteutial caveats with the proposed :ypproac109 ALC (iscussed iu Sect. 7, A number of potential caveats with the proposed approaches are discussed in Sect. \ref{discussion}.
 Sect., Sect.
 8 sunuuarizes our finelues., \ref{summary} summarizes our findings.
 While the properties of galaxies at 2ZLO remain auo uncharted teryitorv observatoually. theory and simulations provide a number of cues as to what one nuelit expect frou sich oljects," While the properties of galaxies at $z\gtrsim 10$ remain an uncharted territory observationally, theory and simulations provide a number of clues as to what one might expect from such objects."
 In1ο models of Stiavelli&Treuti (2010).. the very first ealatxies are predicted to form in ligh-densityv regions that have been pre-euriched by population III stars that exploed as superuovae in minibhalos at even higher redshifts.," In the models of \citet{Stiavelli & Trenti}, the very first galaxies are predicted to form in high-density regions that have been pre-enriched by population III stars that exploded as supernovae in minihalos at even higher redshifts."
 True population III ealaxies start to form somewhat ater. iu low-deusity environments which have remained chemically pristine.," True population III galaxies start to form somewhat later, in low-density environments which have remained chemically pristine."
 Since pockets of primordial gas may survive in galaxies hat have already experienced some chenucal enrichment. whrid salaxies in which populatiou ΠΠ. population II (representative of the metallicity in the Milky. Wav halo: ZZ.jfl10) aud population 1 (representative of the netallicity in the Milla Way disk: ZZ.f10) stars continue to form in parallel cau also be expected {e.g.àYSalvaterra.Ferrara&Daval2010).. and signatures of Us may already have been detected (Jimenez&TaianWw006).," Since pockets of primordial gas may survive in galaxies that have already experienced some chemical enrichment, hybrid galaxies in which population III, population II (representative of the metallicity in the Milky Way halo; $Z<Z_\odot/10$ ) and population I (representative of the metallicity in the Milky Way disk; $Z\gtrsim Z_\odot/10$ ) stars continue to form in parallel can also be expected \citep[e.g.][]{Salvaterra et al.}, and signatures of this may already have been detected \citep{Jimenez & Haiman}."
".. Even more exotic ealaxies nav be envisioued if the dark matter of the Universe has the properties required for the formation of longlived population III stars. fucled by WIAIP anuililations im niüuihalos (c.g,Spolvaretal.2008).", Even more exotic galaxies may be envisioned if the dark matter of the Universe has the properties required for the formation of long-lived population III stars fueled by WIMP annihilations in minihalos \citep[e.g.][]{Spolyar et al.}.
. Many such “dark stars” lay then end up within the first ealaxies duriic their hierarchical assemble and possibly imzpriut detectable signatures m their spectra (Zackrissonctal.2010).," Many such “dark stars” may then end up within the first galaxies during their hierarchical assembly, and possibly imprint detectable signatures in their spectra \citep{Zackrisson et al. c}."
. Iu this paper. however. we focus on pure population IIT galaxies.," In this paper, however, we focus on pure population III galaxies."
 Ire. wwe present a new population svuthesis codeo custom-designed or anodelling the spectral energwv distributions (SEDs) of high-redslüft ealaxies.," Here, we present, a new population synthesis code custom-designed for modelling the spectral energy distributions (SEDs) of high-redshift galaxies."
 To reflect the significaiito variance in ternis of stellar content that these oljects may display. Yeedrasil is equipped to handle mixtures of couventional population I. II aud III stars (hereafter pop 1. II aud III) as well as dark stars.," To reflect the significant variance in terms of stellar content that these objects may display, Yggdrasil is equipped to handle mixtures of conventional population I, II and III stars (hereafter pop I, II and III) as well as dark stars."
 This code also allows the treatment of nebular cussion frou t16 photoiouized gas and extinction due to dust., This code also allows the treatment of nebular emission from the photoionized gas and extinction due to dust.
 A umber of Ysedrasil moclel erids are publicly available from the ead author's, A number of Yggdrasil model grids are publicly available from the lead author's.
" The SEDs of Single Stellar Populztions (σος), from various other population svutLOSS nodels can be used as input to Yeedrasil. which will heu reweight the SSP nne steps to acconmnodate arbitrary stew formation histories."," The SEDs of Single Stellar Populations ), from various other population synthesis models can be used as input to Yggdrasil, which will then reweight the SSP time steps to accommodate arbitrary star formation histories."
 Currently. the SSP models of Zacadssonctal.(2001).. Starburst99 (Leithereretal.1999:Vazquez&Leitherer2005) aud Maraston(2005) are iuyplemeuted as options for pop I aud ID stars.," Currently, the SSP models of \citet{Zackrisson et al. a}, Starburst99 \citep{Leitherer et al.,Vazquez & Leitherer} and \citet{Maraston} are implemented as options for pop I and II stars."
 For the diration of this paper. we will adopt Starburst909 SSPs eejicrated with Padova-AGB stellar evolutionary tracks (Vázquez&Leitherer2005) and the EKroupa(2001) τι(jiversal stellar initial mass function (IME) throughout tljo nuass range 0.1100 M. for population II ((assmnnued metallicity Z= LOQQL) and pop I (assumed ictallicity Z=0.020) eaaNICS.," For the duration of this paper, we will adopt Starburst99 SSPs generated with Padova-AGB stellar evolutionary tracks \citep{Vazquez & Leitherer} and the \citet{Kroupa} universal stellar initial mass function (IMF) throughout the mass range 0.1–100 $M_\odot$ for population II (assumed metallicity $Z=0.0004$ ) and pop I (assumed metallicity $Z=0.020$ ) galaxies."
 While both theoretical aremueuts aud merical simulations give strong support to the notiou that pop III stars nist have been more massive thaw he pop II and I stars forming later on (forareview.seeBroun&Larson 2001).. the exact IME of pop IT stars remains nuknown.," While both theoretical arguments and numerical simulations give strong support to the notion that pop III stars must have been more massive than the pop II and I stars forming later on \citep[for a review, see][]{Bromm & Larson}, the exact IMF of pop III stars remains unknown."
 It has been argued that the Universe may have xoduced. two classes o: pop III stars pop ILI stars which formed first. wit1 characteristic masses of about ~100AL... and pop IIT:2 stars which formed somewhat ater aud had lower characteristic uiasses of ~LOAL. due o IID cooling promoted by he Lyiman-Werner feedback xovided by the pop IILI stars(c.g.Mackeyetal.2003: 2006).," It has been argued that the Universe may have produced two classes of pop III stars – pop III.1 stars which formed first, with characteristic masses of about $\sim 100\ M_\odot$, and pop III.2 stars which formed somewhat later and had lower characteristic masses of $\sim 10\ M_\odot$ due to HD cooling promoted by the Lyman-Werner feedback provided by the pop III.1 stars \citep[e.g.][]{Mackey et al.,Greif & Bromm}."
".Naively. «mie would expect the oop OE TIF to !© approlate for the stars forming in isolation (or i πια] nuübers) within ~lo’AY, "," .Naively, one would expect the pop III.1 IMF to be appropriate for the stars forming in isolation (or in small numbers) within $\sim 10^{5-6}\ M_\odot$ "
that part of the change of the orbital energy is used {ο eject the envelope. as described by Webbink(1984).. then where acq is the efficienev of converting the orbital energv to kinetic energy to eject the CE. Ms the mass of the secondary. and a; and e reler to the initial and. final orbital separation of the CE phase. respectively.,"that part of the change of the orbital energy is used to eject the envelope, as described by \citet{web84}, then where $\alpha_{\rm CE}$ is the efficiency of converting the orbital energy to kinetic energy to eject the CE, $M_2$ the mass of the secondary, and $a_{\rm i}$ and $a_{\rm f}$ refer to the initial and final orbital separation of the CE phase, respectively."
 Combine Eqs. (, Combine Eqs. (
2) and (3). the final orbital separation is related (o the pre-CE separation by the following formula. Equation (4) indicates that the orbital separation alter CE is sensitively dependent on the product of acy: and A. and (he convenient way is to treat both αο auc A as constants of the order of unity.,"2) and (3), the final orbital separation is related to the pre-CE separation by the following formula, Equation (4) indicates that the orbital separation after CE is sensitively dependent on the product of $\alpha_{\rm CE}$ and $\lambda$, and the convenient way is to treat both $\alpha_{\rm
CE}$ and $\lambda$ as constants of the order of unity."
 In most of the population svnthesis investigations concerning (he evolution of close binaries in the literature. A was usually taken to be a constant. normally around 0.5 throughout the evolution of the svstem.," In most of the population synthesis investigations concerning the evolution of close binaries in the literature, $\lambda$ was usually taken to be a constant, normally around $0.5$ throughout the evolution of the system."
 Ilowever. (here have lots of works (e.g.Tauris2000.2001:Poclsiadlowskietal.2003:Webbink2007) suggesting that A is a variable.," However, there have lots of works \citep[e.g.][]{han94,dew00,dew01, pod03,web07} suggesting that $\lambda$ is a variable."
 Dewi&Tauris(2000) ancl Dewi&Tauris(2001) [ound that the value of A changes as the star evolves. ancl reaches far more than 0.5 in late evolutionary stages for stars wilh mass between 3 and GAL...," \citet{dew00} and \citet{dew01} found that the value of $\lambda$ changes as the star evolves, and reaches far more than $0.5$ in late evolutionary stages for stars with mass between $3$ and $6 M_{\odot}$."
 In recent population svuthesis on post-CE binaries. Davisetal.(2010) used linear interpolations of the tabular data in Dewi&Tauris(2000). to calculate A.," In recent population synthesis on post-CE binaries, \citet{dav10} used linear interpolations of the tabular data in \citet{dew00} to calculate $\lambda$."
 We notice that Dewi&Tauris(2000) and Tauris (2001)s calculations did not cover Pop., We notice that \citet{dew00} and \citet{dew01}' 's calculations did not cover Pop.
 I stars less massive (han 34. and Pop., I stars less massive than $3 M_{\odot}$ and Pop.
 II stars. and their results in tabular form may not be easily used.," II stars, and their results in tabular form may not be easily used."
 Obviously more advanced population svnthesis requires a simple description of the parameter A for better constraints on the initial stellar population., Obviously more advanced population synthesis requires a simple description of the parameter $\lambda$ for better constraints on the initial stellar population.
 In (his work we are attempting to investigate the binding, In this work we are attempting to investigate the binding
"semi major axis, óc, which is different from planet to planet.","semi major axis, $\delta a$, which is different from planet to planet."
" Numerical simulations of the Centaur show that said population decays roughly exponentially with a certain e-folding time, rc (e.g. DiSisto Brunini, 2007)."," Numerical simulations of the Centaur show that said population decays roughly exponentially with a certain e-folding time, $\tau_C$ (e.g. DiSisto Brunini, 2007)."
" Thus the radial displacement of the planets must also decay exponentially. with the same r: Here a(1) is the semi major axis of cach planet as a function of time, dpoy the semi major axis of the planet at the end of migration (1.c. the current semi major axis) and Aq the total radial distance that the planet migrates."," Thus the radial displacement of the planets must also decay exponentially, with the same $\tau$: Here $a(t)$ is the semi major axis of each planet as a function of time, $a_{\rm now}$ the semi major axis of the planet at the end of migration (i.e. the current semi major axis) and $\Delta a$ the total radial distance that the planet migrates."
" Strictly speaking, the identity between the planet migration timescale r and the planetesimals lifetime το 1s valid only in case of (Gomes et al.,"," Strictly speaking, the identity between the planet migration timescale $\tau$ and the planetesimals lifetime $\tau_C$ is valid only in case of (Gomes et al.,"
 2004)., 2004).
" In damped migration, the loss of planetesimals is not compensated by the acquisition of new planetesimals into the planet-scattering region that is due to the displacement of the planet itself."," In damped migration, the loss of planetesimals is not compensated by the acquisition of new planetesimals into the planet-scattering region that is due to the displacement of the planet itself."
" Thus, planet migration slows down progressively as planetesimals are depleted."," Thus, planet migration slows down progressively as planetesimals are depleted."
" In massive planetesimals disks, planet migration can bese/f-susteined (da et al.,"," In massive planetesimals disks, planet migration can be (Ida et al.,"
" 2000; Gomes et al.,"," 2000; Gomes et al.,"
 2004)., 2004).
" In this case a planet can migrate through the disk by scattering planetesimals and leaving them ""behind"" relative to its migration direction.", In this case a planet can migrate through the disk by scattering planetesimals and leaving them “behind” relative to its migration direction.
" In this case, the migration speed does not slow down with time: it actually"," In this case, the migration speed does not slow down with time: it actually"
"the figure, it is not very large.","the figure, it is not very large."
 It is impossible to trace the outer lobes of B11834+620 all the way back to the core in our radio maps., It is impossible to trace the outer lobes of 1834+620 all the way back to the core in our radio maps.
 Hence our possible overestimate of the aspect ratio of one of the lobes discussed in section 5 may cause this problem., Hence our possible overestimate of the aspect ratio of one of the lobes discussed in section \ref{KDA} may cause this problem.
 An important constraint arising from the model of the outer lobes is the very short time available for the inner lobes to expand., An important constraint arising from the model of the outer lobes is the very short time available for the inner lobes to expand.
 They can only be inflated after the jet flow to the outer lobes ceases at tj., They can only be inflated after the jet flow to the outer lobes ceases at $t_{\rm j}$.
 Hence the age of the inner lobes must be less than t—t;» 2MMyr., Hence the age of the inner lobes must be less than $t-t_{\rm j} \sim 2$ Myr.
" Given the large size of the inner lobes of 11834--620, this implies a very fast expansion."," Given the large size of the inner lobes of 1834+620, this implies a very fast expansion."
 We will see in the next section that this tight constraint makes the case for the bow shock model for the inner lobes even stronger than in the case of 114504-333., We will see in the next section that this tight constraint makes the case for the bow shock model for the inner lobes even stronger than in the case of 1450+333.
 The observed spectra of the inner lobes of 118344-620 are steeper than any of the other spectra discussed in this paper., The observed spectra of the inner lobes of 1834+620 are steeper than any of the other spectra discussed in this paper.
" The spectrum of the north inner lobe is well fitted by while the spectrum of the south inner lobe is close to Because of its flatter spectral slope, the southern lobe is brighter in the observed range."," The spectrum of the north inner lobe is well fitted by while the spectrum of the south inner lobe is close to Because of its flatter spectral slope, the southern lobe is brighter in the observed range."
 This can be seen in Fig., This can be seen in Fig.
 where the fits are compared to the data in the source restframe., \ref{1834spec} where the fits are compared to the data in the source restframe.
 Note that the luminosities of the inner lobes are scaled by a factor 3 in this figure for clarity., Note that the luminosities of the inner lobes are scaled by a factor 3 in this figure for clarity.
 We apply the standard FRII model to the inner lobes of 11834--620 in the same way as in the case of 11450--333 with one important difference., We apply the standard FRII model to the inner lobes of 1834+620 in the same way as in the case of 1450+333 with one important difference.
 From the power-laws fitted to the spectra we find that we need to set m=3.18 for the north inner lobe and m=3.04 for the south inner lobe., From the power-laws fitted to the spectra we find that we need to set $m=3.18$ for the north inner lobe and $m=3.04$ for the south inner lobe.
 Hence the bulk of the energy in electrons in the model is stored in those electrons with the lowest Lorentz factors around ymin., Hence the bulk of the energy in electrons in the model is stored in those electrons with the lowest Lorentz factors around $\gamma_{\rm min}$.
 So far we have used ymin=1 and so those electrons storing the bulk of the energy do not contribute to the radio emission., So far we have used $\gamma _{\rm min} = 1$ and so those electrons storing the bulk of the energy do not contribute to the radio emission.
" As a consequence the standard FRII model predicts ages in excess of 10? yyears for the inner lobes, because the jets need to deliver a vast amount of energy to the inner lobes."," As a consequence the standard FRII model predicts ages in excess of $10^8$ years for the inner lobes, because the jets need to deliver a vast amount of energy to the inner lobes."
 The problem is solved by increasing the low energy cut-off of the electron energy distribution such that ymin=1000., The problem is solved by increasing the low energy cut-off of the electron energy distribution such that $\gamma _{\rm min} =1000$.
 The introduction of such a high cut-off leads to the truncation of the model radio spectrum., The introduction of such a high cut-off leads to the truncation of the model radio spectrum.
" In fact, we cannot set a value for ymin much larger than the 1000 used here or this cut-off will start affecting the model spectrum in the observed range."," In fact, we cannot set a value for $\gamma _{\rm min}$ much larger than the 1000 used here or this cut-off will start affecting the model spectrum in the observed range."
 We did not introduce an equivalent high cut-off in the models for B11450--333 as for the flatter spectra of this source such a change makes little difference to the modelling results., We did not introduce an equivalent high cut-off in the models for 1450+333 as for the flatter spectra of this source such a change makes little difference to the modelling results.
" Also, a further decrease in the age of the inner lobes of 11450--333 exacerbates the problems noted above."," Also, a further decrease in the age of the inner lobes of 1450+333 exacerbates the problems noted above."
 The results of the modelling are given in Table 6.., The results of the modelling are given in Table \ref{1834mod}.
" For this object the ages predicted for the inner lobes are too old for k—0 to be consistent with the properties of the outer lobes, despite the introduction of a large value for ymin."," For this object the ages predicted for the inner lobes are too old for $k=0$ to be consistent with the properties of the outer lobes, despite the introduction of a large value for $\gamma _{\rm min}$."
 In all cases 4;>t—tj and so for k=0 we cannot build a self-consistent model combining standard FRII models for both the outer and the inner lobes., In all cases $t_{\rm i} > t - t_{\rm j}$ and so for $k=0$ we cannot build a self-consistent model combining standard FRII models for both the outer and the inner lobes.
" For k—10 the ages predicted for the inner lobes are smaller than t—t,.", For $k=10$ the ages predicted for the inner lobes are smaller than $t-t_{\rm j}$.
" However, in this case the average expansion speed of the inner lobes approaches significant fractions of the speed of light."," However, in this case the average expansion speed of the inner lobes approaches significant fractions of the speed of light."
 It is therefore unlikely that the jets inflating the inner lobes will terminate in strong shocks as required by the standard FRII model., It is therefore unlikely that the jets inflating the inner lobes will terminate in strong shocks as required by the standard FRII model.
 As in the case of B11450+333 the densities required inside the outer lobes to explain the inner lobes are at least an order of magnitude higher than the model for the outer lobes predicts., As in the case of 1450+333 the densities required inside the outer lobes to explain the inner lobes are at least an order of magnitude higher than the model for the outer lobes predicts.
" Unless there is significant contamination of the outer lobe with dense gas from the source environment, equation (19)) then implies that the bulk speed of the jet must be very low."," Unless there is significant contamination of the outer lobe with dense gas from the source environment, equation \ref{gamj}) ) then implies that the bulk speed of the jet must be very low."
" We conclude that the standard FRII model for the inner lobes of 118344-620 can only work, if extensive mixing of gas across the lobe surface has occurred."," We conclude that the standard FRII model for the inner lobes of 1834+620 can only work, if extensive mixing of gas across the lobe surface has occurred."
 This is consistent with our findings for 11450--333 and ?.., This is consistent with our findings for 1450+333 and \citet{ksr00}.
" Next, we apply the bow shock model to the inner lobes of B118344-620 in the same way as in the case of"," Next, we apply the bow shock model to the inner lobes of 1834+620 in the same way as in the case of"
higher than the absorbed flux above | TeV with the maximum proton kinetic energy. 45.3 TeV and 512 TeV. respectively.,"higher than the absorbed flux above 1 TeV with the maximum proton kinetic energy, 45.3 TeV and 512 TeV, respectively."
 Even when we use the deCeadelPozoetal.(2009) interstellar SED model for M82 and the Domingo-Santamaría&Torres(2005). interstellar SED model for NGC 253. the effect of cascade emission is not significantly changed.," Even when we use the \citet{dcdp09} interstellar SED model for M82 and the \citet{ds05} interstellar SED model for NGC 253, the effect of cascade emission is not significantly changed."
 These differences would be a new indirect investigator of the highest cosmic-ray energy. although it would be difficult to see the direct >-ray signature because of the attenuation.," These differences would be a new indirect investigator of the highest cosmic-ray energy, although it would be difficult to see the direct $\gamma$ -ray signature because of the attenuation."
 It might be possible to investigate this cascade signature through a detailed differential spectrum observation with future high signal-to-noise ratio 2-ray observations such as CTA by comparing with the theoretical >-ray emission models including this cascade effect., It might be possible to investigate this cascade signature through a detailed differential spectrum observation with future high signal-to-noise ratio $\gamma$ -ray observations such as CTA by comparing with the theoretical $\gamma$ -ray emission models including this cascade effect.
 The author would like to thank M. Hayashida. K. Matsubayashi. M. Sawada. and T. Totani for useful discussions; L. Herman and T. Kamae for providing their numerical code: and A. R. Jenner for his careful reading of the draft.," The author would like to thank M. Hayashida, K. Matsubayashi, M. Sawada, and T. Totani for useful discussions; L. Herman and T. Kamae for providing their numerical code; and A. R. Jenner for his careful reading of the draft."
 The author also thanks the anonymous referee comments that improved this paper., The author also thanks the anonymous referee comments that improved this paper.
" This work was supported by the Grant-in-Aid for the Global COE Program ""The Next Generation of Physics. Spun from Universality and Emergence” from the Ministry of Education. Culture. Sports. Science and Technology (MEXT) of Japan."," This work was supported by the Grant-in-Aid for the Global COE Program ""The Next Generation of Physics, Spun from Universality and Emergence"" from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan."
 The author acknowledges support by the Research Fellowship of the Japan Society for the Promotion of Science (JSPS)., The author acknowledges support by the Research Fellowship of the Japan Society for the Promotion of Science (JSPS).
achieved again varies [rom one metal line to (he next.,achieved again varies from one metal line to the next.
 Note that the model prediction forVJ is also too blue compared to the observations: for an age of 11 Gvrs. the model predicts Vj-0.19. which is 0.07 mag bluer than the observed value (see Table 3 of Paper 1).," Note that the model prediction for is also too blue compared to the observations: for an age of 11 Gyrs, the model predicts =0.79, which is 0.07 mag bluer than the observed value (see Table 3 of Paper I)."
 This again implies (hal an older age is needed {ο reconcile wilh the observed color., This again implies that an older age is needed to reconcile with the observed color.
 On balance. these spectroscopic ages are consistent wilh the ones obtained by Vazdekis et al. (," On balance, these spectroscopic ages are consistent with the ones obtained by Vazdekis et al. ("
2001) on the basis of the same set of isochrones aud spectral library but using a different set of stellar parameters and calibrations.,2001) on the basis of the same set of isochrones and spectral library but using a different set of stellar parameters and calibrations.
 Figures 16. and 17 reproduce the data of Figures 43. and 15. but now using mocel predictions based on the Padova isochrones., Figures \ref{fig7} and \ref{fig8} reproduce the data of Figures \ref{fig5} and \ref{fig6} but now using model predictions based on the Padova isochrones.
 In order to bring all isochrones to the sime footing. we first compare results based on Padova isochrones after removing their AGB components.," In order to bring all isochrones to the same footing, we first compare results based on Padova isochrones after removing their AGB components."
 The basic conclusion from Figures 16 ancl 17 is (hat spectroscopic ages inferred from Padova isochrones are larger than (hose based on Salaris isochrones by a little more than 2 Gvis., The basic conclusion from Figures \ref{fig7} and \ref{fig8} is that spectroscopic ages inferred from Padova isochrones are larger than those based on Salaris isochrones by a little more than 2 Gyrs.
 Such a difference is significantly. higher than expected based on fits (o the position of the cluster Gurn-olf (Figures 1. and 2)). which vieldecl an age difference (due to heavy element diffusion) of ~ 1 Gyr.," Such a difference is significantly higher than expected based on fits to the position of the cluster turn-off (Figures \ref{fig1} and \ref{fig2}) ), which yielded an age difference (due to heavy element diffusion) of $\sim$ 1 Gyr."
 The small discrepancy is plausibly explained by the svstematically too warm giant branch in the Padova models. which forees an older overall spectroscopic age.," The small discrepancy is plausibly explained by the systematically too warm giant branch in the Padova models, which forces an older overall spectroscopic age."
 The temperature difference at the level of the Horizontal Branch is of the order of 50 IX and increases up to the tip of the Giant Branch. where il reaches ~ 100 Ex. This difference in (he temperature of the red eiut. branch is also responsible for another feature worthy of notice in Figures 21. and 22: that the metal lines are all weaker when Padova isochrones are used (compare will Figures 19. and 20)).," The temperature difference at the level of the Horizontal Branch is of the order of 50 K and increases up to the tip of the Giant Branch, where it reaches $\sim$ 100 K. This difference in the temperature of the red giant branch is also responsible for another feature worthy of notice in Figures \ref{fig12} and \ref{fig13}: that the metal lines are all weaker when Padova isochrones are used (compare with Figures \ref{fig10}
 and \ref{fig11}) )."
 As discussed in Section 2.. both sets of isochrones emploved in this work underestimate ihe number of giant stars brighter than the horizontal branch.," As discussed in Section \ref{isocmd}, both sets of isochrones employed in this work underestimate the number of giant stars brighter than the horizontal branch."
 In the case of the Salaris isochrones. which do not take into account AGB stars. the mismateh is of the order of 0.4 dex. while in the ease of the Padova isochrones. which do include AGBs. it is slightly lower. of the order of 0.20.3 dex.," In the case of the Salaris isochrones, which do not take into account AGB stars, the mismatch is of the order of 0.4 dex, while in the case of the Padova isochrones, which do include AGBs, it is slightly lower, of the order of 0.2–0.3 dex."
 To evaluate (he impact of these underestimates on our computations. we apply empvrical corrections to both theoretical LFs to bring them into agreement with the observations.," To evaluate the impact of these underestimates on our computations, we apply empyrical corrections to both theoretical LFs to bring them into agreement with the observations."
 We first correct the Salaris isochrones in order to bring their predicted LE into agreement, We first correct the Salaris isochrones in order to bring their predicted LF into agreement
5-!=Br.,$\hat{B}^{-1}=\hat{B}^{t}$.
 This greatly simplifies the calculations because no numerical matrix inversion is needed., This greatly simplifies the calculations because no numerical matrix inversion is needed.
 In the following. we explain the procedure that we propose for denoising the experimental Stokes profiles of magnetic stars.," In the following, we explain the procedure that we propose for denoising the experimental Stokes profiles of magnetic stars."
 The method is general. it should be used not only to retrieve Stokes | and V but to obtain Stokes Q and U given the important information encoded in it (see.e.g..thepaperstartingwithLandolfietal.. 1993).," The method is general, it should be used not only to retrieve Stokes I and V but to obtain Stokes $Q$ and $U$ given the important information encoded in it \citep[see, e.g., the series of paper starting with][]{landolfiI93}."
. In order to demonstrate the capabilities of the PCA denoising technique. we use a synthetic polarised spectrum. including Stokes Q. U and V.," In order to demonstrate the capabilities of the PCA denoising technique, we use a synthetic polarised spectrum, including Stokes $Q$, $U$ and $V$."
 We cover the wavelength range between 400 and 900 nm. with a spectral resolution of 50mÁ.," We cover the wavelength range between 400 and 900 nm, with a spectral resolution of 50."
. The synthetic spectrum has been obtained under the assumption of local thermodynamical equilibrium (LTE) using a standard solar model atmosphere (Fontenlaetal..1993). with a star-filing magnetic field of 1000 G. The inclination of the magnetic field with respect to the line of sight is 45° and its inclination is 20°.," The synthetic spectrum has been obtained under the assumption of local thermodynamical equilibrium (LTE) using a standard solar model atmosphere \citep{fontenla_falc93}, with a star-filling magnetic field of 1000 G. The inclination of the magnetic field with respect to the line of sight is $^\circ$ and its inclination is $^\circ$."
 This produces polarization signals that are much larger than those observed in real cases., This produces polarization signals that are much larger than those observed in real cases.
" For this reason. we apply a filling factor f£ to our simulated spectra in order to end up with Stokes V amplitudes that are similar to the ones expected in some cool stars observations (~10777... being J, the continuum intensity)."," For this reason, we apply a filling factor $f$ to our simulated spectra in order to end up with Stokes $V$ amplitudes that are similar to the ones expected in some cool stars observations $\sim 10^{-4} I_\mathrm{c}$, being $I_\mathrm{c}$ the continuum intensity)."
 We quantify the quality of the data (amount of information about the physical conditions m the regions of line formation available in the data) with the signal to noise ratio. S/N.," We quantify the quality of the data (amount of information about the physical conditions in the regions of line formation available in the data) with the signal to noise ratio, $S/N$."
 Consequently. the filling factor turns out to be unimportant and it is only chosen so as to end up with amplitudes comparable to the observed ones.," Consequently, the filling factor turns out to be unimportant and it is only chosen so as to end up with amplitudes comparable to the observed ones."
 The influence of realistic surface magnetic field distributions on the capabilities of the denoising technique will be addressed by Carroll et al. (, The influence of realistic surface magnetic field distributions on the capabilities of the denoising technique will be addressed by Carroll et al. (
2008: in preparation).,2008; in preparation).
 The spectral range that we use in our denoising technique ts very large (500 nm). so that there is a large difference between the Doppler width of lines in the red and in the blue part of the spectrum.," The spectral range that we use in our denoising technique is very large (500 nm), so that there is a large difference between the Doppler width of lines in the red and in the blue part of the spectrum."
 This is because the Doppler width is proportional to the wavelength., This is because the Doppler width is proportional to the wavelength.
 In order to make the Doppler widths compatible for all wavelengths. we transform the wavelength axis into the following velocity axis: where c is the speed of light. the symbol οἱ represents the wavelength and /lj;; is a reference wavelength. which we choose to be 400 nm.," In order to make the Doppler widths compatible for all wavelengths, we transform the wavelength axis into the following velocity axis: where $c$ is the speed of light, the symbol $\lambda$ represents the wavelength and $\lambda_\mathrm{ref}$ is a reference wavelength, which we choose to be 400 nm."
 This change of variables induces that all the lines have. to first order. the same Doppler width in the new axis.," This change of variables induces that all the lines have, to first order, the same Doppler width in the new axis."
 Differences may exist because the Doppler width depends on the atomic mass of each species and because it also depends on the temperature in the line formation region., Differences may exist because the Doppler width depends on the atomic mass of each species and because it also depends on the temperature in the line formation region.
 However. we assume that these differences are of second order with respect to the wavelength dependence.," However, we assume that these differences are of second order with respect to the wavelength dependence."
 Since this new axis has an irregular step size because the spectrum has been sampled regularly in a wavelength scale. we re-interpolate it to a velocity axis with a regular step using a standard linear interpolation. procedure.," Since this new axis has an irregular step size because the spectrum has been sampled regularly in a wavelength scale, we re-interpolate it to a velocity axis with a regular step using a standard linear interpolation procedure."
 We set the spectral resolution. equal to 0.2 km/s. This is equivalent to assume that the spectral resolution is the same regardless of the wavelength., We set the spectral resolution equal to 0.2 km/s. This is equivalent to assume that the spectral resolution is the same regardless of the wavelength.
 The individual spectral lines that will be used for building the matrix O will be extracted using fixed positions for the central wavelength., The individual spectral lines that will be used for building the matrix $\hat{O}$ will be extracted using fixed positions for the central wavelength.
 In this experiment. we have computed the positions. of the spectral lines às the positions. where the minimum of the intensity profile is found.," In this experiment, we have computed the positions of the spectral lines as the positions where the minimum of the intensity profile is found."
 In any case. standardized linelists have been developed for different stars depending on the spectral type (Donatietal..1997).," In any case, standardized linelists have been developed for different stars depending on the spectral type \citep{donati97}."
. The results that we show in this paper have been obtained using a database with ~6300 lines., The results that we show in this paper have been obtained using a database with $\sim$ 6300 lines.
 In principle. the capabilities of the method might be improved by using databases with more spectral lines. provided that the added lines carry sufficient information.," In principle, the capabilities of the method might be improved by using databases with more spectral lines, provided that the added lines carry sufficient information."
" We set V,=40. choosing 20 points to the red and 20 points to the blue."," We set $N_\lambda=40$, choosing 20 points to the red and 20 points to the blue."
 This translates into a velocity range ofkm/s.. which is sufficient for our experiment since we are not including the effects of rotation.," This translates into a velocity range of, which is sufficient for our experiment since we are not including the effects of rotation."
 In any case. in the analysis of a rapid rotator. a larger number of points have to be chosen.," In any case, in the analysis of a rapid rotator, a larger number of points have to be chosen."
 With each individual profile. we construct the matrix of observations (O) having one spectral line in each one of the rows.," With each individual profile, we construct the matrix of observations $\hat{O}$ ) having one spectral line in each one of the rows."
" We refer to a ""correlated"" data set when some correlation between the observables exist.", We refer to a “correlated” data set when some correlation between the observables exist.
 In our particular case. this means that the physical mechanisms of line formation in stellar atmospheres introduce correlations between different wavelenght points of each spectral line.," In our particular case, this means that the physical mechanisms of line formation in stellar atmospheres introduce correlations between different wavelenght points of each spectral line."
 The. principal components of a correlated data set have some peculiarities that allow us to reduce the dimensionality of the data set., The principal components of a correlated data set have some peculiarities that allow us to reduce the dimensionality of the data set.
 The principal components associated with the largest eigenvalues are representative of the directions of highest correlation and Eq. (3)), The principal components associated with the largest eigenvalues are representative of the directions of highest correlation and Eq. \ref{eq:cumulative_var}) )
 can be used to estimate the relative amount of variance explained by them., can be used to estimate the relative amount of variance explained by them.
 Top panels of Fig., Top panels of Fig.
 1. show the first two eigenvectors of the matrix of observations of the Stokes V parameter without any noise added., \ref{autovect} show the first two eigenvectors of the matrix of observations of the Stokes V parameter without any noise added.
 The first eigenvector has the typical antisymmetric shape representative of the Stokes V profile induced by the Zeeman effect., The first eigenvector has the typical antisymmetric shape representative of the Stokes $V$ profile induced by the Zeeman effect.
 This means that the most important common pattern to all of our spectral lines ressembles a Zeeman profile., This means that the most important common pattern to all of our spectral lines ressembles a Zeeman profile.
 Note also that the first eigenvalue is much larger than the following ones (right panel of Fig. 1::, Note also that the first eigenvalue is much larger than the following ones (right panel of Fig. \ref{autovect};
 note the logarithmic scale)., note the logarithmic scale).
 Although this is an expected result. note that we have not assumed in the analysis any systematic pattern in our data.," Although this is an expected result, note that we have not assumed in the analysis any systematic pattern in our data."
 On the contrary. it is a natural result of PCA.," On the contrary, it is a natural result of PCA."
 The rest of eigenvectors present other characteristics of the profiles whose importance decreases as the associated eigenvalue decreases., The rest of eigenvectors present other characteristics of the profiles whose importance decreases as the associated eigenvalue decreases.
 The right panel of Fig., The right panel of Fig.
 1. shows that the first eigenvalues is the most representative one and that they drop dramatically., \ref{autovect} shows that the first eigenvalues is the most representative one and that they drop dramatically.
 This 15 the key property of the PCA that allows us to reduce the dimensionality of the data set., This is the key property of the PCA that allows us to reduce the dimensionality of the data set.
 This means that our observations can be efficiently reproduced using only a few eigenvectors., This means that our observations can be efficiently reproduced using only a few eigenvectors.
" The observations were represented in a space of N, dimensions", The observations were represented in a space of $N_\lambda$ dimensions
complex magnification map. such as we have here. we expect events to be seen on timescales smaller than this.,"complex magnification map, such as we have here, we expect events to be seen on timescales smaller than this."
 In what follows we have usec horizontal light. curves relative to all the magnifications maps., In what follows we have used horizontal light curves relative to all the magnifications maps.
 Lhe variability is at its greatest. Le. highest. frequency ancl shortest. period. in that direction. because the shear operates in the vertical direction on the magnification maps. and the caustics are extended in that direction.," The variability is at its greatest, i.e. highest frequency and shortest period, in that direction, because the shear operates in the vertical direction on the magnification maps, and the caustics are extended in that direction."
 Sources moving diagonally across the causties will show a longer time period for nanolensing variations. compared to a horizontally moving source.," Sources moving diagonally across the caustics will show a longer time period for nanolensing variations, compared to a horizontally moving source."
 We now turn to an analysis of the nanolensing variations., We now turn to an analysis of the nanolensing variations.
 Figures 5 and 6 show light curves taken from the image M and image S maps in Figure 1. in the horizontal direction. over a time period of LOO vears.," Figures \ref{wiggles_by_mass} and \ref{wiggles_by_size} show light curves taken from the image M and image S maps in Figure \ref{maps strip}
 in the horizontal direction, over a time period of 100 years."
 Figure 5 uses a fixed source size of 0.02 ER and varies the mass of the small objects. so that cach panel represents a dillerent mass. indicated in the top of cach panel.," Figure \ref{wiggles_by_mass} uses a fixed source size of 0.02 ER and varies the mass of the small objects, so that each panel represents a different mass, indicated in the top of each panel."
 The top row represents the largest mass. 2.02510 M.. the next row is 6.75-10 Πλ... and so on in the same order reading down the page as in Figure 1..," The top row represents the largest mass, $2.025\times 10^{-3}$ $_\odot$, the next row is $6.75\times 10^{-4}$ $_\odot$, and so on in the same order reading down the page as in Figure \ref{maps strip}."
 The bottom row is the smooth matter map with a source size of 0.02 ER., The bottom row is the smooth matter map with a source size of 0.02 ER.
 Figure 6 uses the maps that have small objects of 2.5.10 7M... but varies the source size. indicated in the top of each panel.," Figure \ref{wiggles_by_size} uses the maps that have small objects of $2.5\times10^{-5}$ $_\odot$, but varies the source size, indicated in the top of each panel."
 The top row represents a source of size of 0.05 ER. and the next row is 0.01 ER. with the bottom row being the smooth matter map at the pixel resolution of the maps — 0.002 ER.," The top row represents a source of size of 0.05 ER, and the next row is 0.01 ER, with the bottom row being the smooth matter map at the pixel resolution of the maps – 0.002 ER."
 In both, In both
from the unpublished VLBA archive data.,from the unpublished VLBA archive data.
 The observations and data reduction is shown in section 2. and the results is given in Section 3.," The observations and data reduction is shown in Section 2, and the results is given in Section 3."
 The last section is dedicated to discussions., The last section is dedicated to discussions.
 Throughout the paper. we assume a cosmology with //;=71kms!Mpe|. Q4=027. and O4=0.73 (Spergeletal. 2003).," Throughout the paper, we assume a cosmology with $H_{0}=71~\rm km~s^{-1}~Mpc^{-1}$ $\Omega_{\rm M}=0.27$ , and $\Omega_{\Lambda}=0.73$ \citep{spe03}. ."
". The spectral indices α is defined as /,cx»"". in which |, is the [lux density at frequency. v."," The spectral indices $\alpha$ is defined as $f_{\nu}\propto\nu^{-\alpha}$, in which $f_{\nu}$ is the flux density at frequency $\nu$."
 We searched VLBA archive for the unpublished data of the sources claimed as NLS1s in various literatures., We searched VLBA archive for the unpublished data of the sources claimed as NLS1s in various literatures.
 The data of three sources were finally archived. whieh covers three radio bands 2.3. 5 and 8.4 Gllz.," The data of three sources were finally archived, which covers three radio bands 2.3, 5 and 8.4 GHz."
 All these three sources have been imaged in 8.4 GllIz with Japanese VLBI Network (JVN) (Doietal.2007).. and 1.6 Giz VLBA observations have been recently shown in Doietal.(2009).," All these three sources have been imaged in 8.4 GHz with Japanese VLBI Network (JVN) \citep{doi07}, and 1.6 GHz VLBA observations have been recently shown in \cite{doi09}."
. The source list is shown in Table 1.. in which the JVN 8.4 GIIz flux density. FIRST 1.4 GIIz. GD6 5 GIIz flux density and the conventional radio loudness are given.," The source list is shown in Table \ref{tab1}, in which the JVN 8.4 GHz flux density, FIRST 1.4 GHz, GB6 5 GHz flux density and the conventional radio loudness are given."
 All the observations were made in phase referencing mode., All the observations were made in phase referencing mode.
" The targets. their corresponding phase relerencing calibrator ancl (he angular clistances between target ancl phase referencing calibrator are listed in Table 2.. most of which lies within a range of 2.37 around the targets except for the observations of D3 11024451 at two epochs with angular distance of 3.98""."," The targets, their corresponding phase referencing calibrator and the angular distances between target and phase referencing calibrator are listed in Table \ref{tab2}, most of which lies within a range of $2.3^\circ$ around the targets except for the observations of B3 1702+457 at two epochs with angular distance of $3.98^\circ$."
 The average on-source observational time is about TO minutes., The average on-source observational time is about 70 minutes.
 Data reductions are made in AIPS., Data reductions are made in AIPS.
 Atmosphere ancl parallactic angle elfects on data are calibrated before fringe fitting of phase referencing calibrator are made. ancl ils solutions ave applied to the corresponding target.," Atmosphere and parallactic angle effects on data are calibrated before fringe fitting of phase referencing calibrator are made, and its solutions are applied to the corresponding target."
 Bandpass corrections and self-calibrations are made before data are averaged in 30 seconds so (that we can obtain the results of as high as possible signal (to noise ratio., Bandpass corrections and self-calibrations are made before data are averaged in 30 seconds so that we can obtain the results of as high as possible signal to noise ratio.
 The imaging and mocel fitting process is performed in DIFMADP with all the base contour levels given below 3o in the final residual images., The imaging and model fitting process is performed in DIFMAP with all the base contour levels given below $3\sigma$ in the final residual images.
 The model fitting results are given in Table 3.., The model fitting results are given in Table \ref{tab3}.
 From the high-resolution VLBA images.the brightnesstemperature of radio core 7j in the rest frame can beestimated with (Ghisellinietal.1993) ," From the high-resolution VLBA images,the brightnesstemperature of radio core $T_{\rm B}$ in the rest frame can beestimated with \citep{ghi93}
 "
"safely marginalize over Ho, defining a L(A,B,K,2)=[Exp|-utenP(Ho)dHo where P(Ho) represents a prior distribution function.","safely marginalize over $H_0$, defining a $
\nonumber L(A,B,K,z)= \int{Exp\left[-\frac{\chi ^{2}(H_0,A,B,K,z)}{2} \right]P(H_0) dH_0 }$ where $P(H_0)$ represents a prior distribution function."
 Here we consider a Gaussian Prior with Ho=72+8., Here we consider a Gaussian Prior with $H_0 = 72 \pm 8$.
" In the theoretical model it is demanded that the model parameters should satisfy the inequalities (i) B>0,(ii) K»0."," In the theoretical model it is demanded that the model parameters should satisfy the inequalities (i) $B>0$ ,(ii) $K>0$."
" Therefore, the model parameters obtained from the best fit analysis with observational data are determined in the theoretical parameter space."," Therefore, the model parameters obtained from the best fit analysis with observational data are determined in the theoretical parameter space."
" The best fit values obtained for the parameters here are: B=0.2615 and K=0.4742 together with x2,;,=1.02593 ( per degree of freedom).", The best fit values obtained for the parameters here are: $B=0.2615$ and $K=0.4742$ together with $\chi_{min}^2=1.02593$ ( per degree of freedom).
" The plots of 68.396, 95% and 99.7% confidence level contours are shown in fig. 2.."," The plots of $68.3 \%$, $95 \%$ and $99.7 \%$ confidence level contours are shown in fig. \ref{stern}."
 The following range of values are permitted: 0.003«B0.5996 and 0.303«K0.63 within 68.396 confidence level., The following range of values are permitted: $0.003<B<0.5996$ and $0.303<K<0.63$ within $68.3 \%$ confidence level.
" For a flat universe BAO peak parameter may be defined as in a low redshift region such as 0«z0.35 (Eisenstein 2005):: where 2, is the total density parameter for matter content of universe.", For a flat universe BAO peak parameter may be defined as in a low redshift region such as $0<z<0.35$ \citep{b6}: where $\Omega_{m}$ is the total density parameter for matter content of universe.
 One has to consider a constant w (EOS parameter)., One has to consider a constant $\omega$ (EOS parameter).
" Even if w is not strictly constant, it is quite reasonable to take a constant w value over a small redshift interval."," Even if $\omega$ is not strictly constant, it is quite reasonable to take a constant $\omega$ value over a small redshift interval."
 It would not be strictly the value of w at z=0 but rather some average value in the region 0.35., It would not be strictly the value of $\omega$ at $z=0$ but rather some average value in the region $0<z<0.35$ .
 Here we use a technique adopted by Eisensteinetal.(2005) to explore the parameter A which is independent of dark energy model., Here we use a technique adopted by \citet{b6} to explore the parameter $\mathcal {A}$ which is independent of dark energy model.
 The value of A for a flat universe is A=0.469+0.017 as measured in Eisensteinetal.(2005) using SDSS data., The value of $\mathcal {A}$ for a flat universe is $\mathcal {A} =0.469 \pm 0.017$ as measured in \citet{b6} using SDSS data.
 We define X546=E., We define $\chi ^2_{BAO} = \frac{(\mathcal {A} - 0.469)^2}{(0.017)^2}$.
 Fora joint analysis scheme we consider X20=Xtern+x}Ao-, For a joint analysis scheme we consider $\chi_{tot}^2= \chi_{stern}^2+\chi_{BAO}^2$.
" The best fit values found in the joint analysis are : B—0.2599 and K=0.4751 along with a x2,;,=1.1681 (per degree of freedom).", The best fit values found in the joint analysis are : $B=0.2599$ and $K=0.4751$ along with a $\chi_{min}^2=1.1681$ (per degree of freedom).
" Contours of 68.396, 95% and 99.7% confidence level are shown in fig."," Contours of $68.3 \%$, $95 \%$ and $99.7 \%$ confidence level are shown in fig."
 2., 2.
 Here we found that the range of values permitted within 68.396 confidence is a bit elevated: 0.009«B0.606 and 0.3126«K0.6268., Here we found that the range of values permitted within $68.3 \%$ confidence is a bit elevated: $0.009<B<0.606$ and $0.3126<K<0.6268$.
 The range of permitted values of model paramters B and K are determined above., The range of permitted values of model paramters $B$ and $K$ are determined above.
 In this section we determine the variation of both the density parameter and the effective equation of state., In this section we determine the variation of both the density parameter and the effective equation of state.
" Note that the model is an asymptotically de Sitter model and a late time phase of acceleration is assured. 68.396,"," Note that the model is an asymptotically de Sitter model and a late time phase of acceleration is assured. $68.3 \%$,"
 9596 and 99.796 confidence level contours in O4—Q plane are shown in fig., $95 \%$ and $99.7 \%$ confidence level contours in $\Omega_d - \Omega_e$ plane are shown in fig.
 3., 3.
 It is found that the best fit value (Q4+Qe= 0.3374) permits Qa=0.6626., It is found that the best fit value $\Omega_d + \Omega_e =0.3374$ ) permits $\Omega_{\Lambda}=0.6626$.
 It is also noted that the generally predicted values Q4zz0.72 and Ωςz0.04 are permitted here within 68.396 confidence level., It is also noted that the generally predicted values $\Omega_{\Lambda} \approx 0.72$ and $\Omega_d \approx 0.04$ are permitted here within $68.3 \%$ confidence level.
 We also plot the evolution of the effective EOS in fig., We also plot the evolution of the effective EOS in fig.
 4., 4.
 As expected it remains negative throughout., As expected it remains negative throughout.
" EU, as we have noted, is an asymptotically de Sitter universe and it is evident from fig."," EU, as we have noted, is an asymptotically de Sitter universe and it is evident from fig."
 5 that p decreases to a very small value at late universe., 5 that $\rho$ decreases to a very small value at late universe.
" In this paper considering a very specific model of flat EU, we determine the observational constraints on the model parameters."," In this paper considering a very specific model of flat EU, we determine the observational constraints on the model parameters."
" For this recent observational data namely, Stern data, measurement of BAO peak parameter are used."," For this recent observational data namely, Stern data, measurement of BAO peak parameter are used."
 The specific form of EOS given by eq. (, The specific form of EOS given by eq. (
1) to obtain EU scenario in a flat universe is employed here forthe purpose.,1) to obtain EU scenario in a flat universe is employed here forthe purpose.
 We set A=0 in the eq. (, We set $A=0$ in the eq. (
1) tobegin with.,1) tobegin with.
 A equal to zero represents a universe with a composition of exotic matter only., $A$ equal to zero represents a universe with a composition of exotic matter only.
 This kind of EOS has been considered in, This kind of EOS has been considered in
reveal whether the ejection angle of jet component varies in this No jet component can be reliably identified and traced in this source.,reveal whether the ejection angle of jet component varies in this No jet component can be reliably identified and traced in this source.
 This source reveals a point-like structure in. our observations. as supported by FC97.," This source reveals a point-like structure in our observations, as supported by FC97."
 The flux-density changes in this source are drastic., The flux-density changes in this source are drastic.
 We therefore do not include this source in our analysis of the The position angles of the individual jet components are too different between the epochs and prevent any reliable jet component identification., We therefore do not include this source in our analysis of the The position angles of the individual jet components are too different between the epochs and prevent any reliable jet component identification.
 In other words. any jet component identification would lead to large position angle changes between the epochs.," In other words, any jet component identification would lead to large position angle changes between the epochs."
 We therefore do not include any features in this source in the kinematic analysis in Paper Choosing the proper reference point is difficult in. this source., We therefore do not include any features in this source in the kinematic analysis in Paper Choosing the proper reference point is difficult in this source.
 In addition. the chosen reference component (r) shows significantly different flux-densities in. the. four different epochs.," In addition, the chosen reference component (r) shows significantly different flux-densities in the four different epochs."
 Thus. variability — supposing we labeled the same component m every epoch — further complicates the identification of components.," Thus, variability — supposing we labeled the same component in every epoch — further complicates the identification of components."
 Although this IDV-source (Wagner Witzel 1995. and references therein) reveals a simple structure. significantly different identification scenarios. for the jet components for this IDV source have been published in the literature. (e.g.. Bach et al.," Although this IDV-source (Wagner Witzel 1995, and references therein) reveals a simple structure, significantly different identification scenarios for the jet components for this IDV source have been published in the literature (e.g., Bach et al."
 2005. Jorstad et al.," 2005, Jorstad et al."
 2001. Britzen et al.," 2001, Britzen et al."
 2006)., 2006).
 Our identification scenario is supported by the assignment of Bach et al. (, Our identification scenario is supported by the assignment of Bach et al. (
2005). where four of the five epochs presented in this paper here are incorporated into an identification scenario based on a larger number of observations obtained at different We do not find any convincing identification scenario for Jet components in this The jet straightens out in the last epoch. the wiggling is significantly more prominent in the first and second The jet component in the third epoch cannot reliably be identified with either of the two components from the other We do not include the jet components from the first epoch in our identification since no component can reliably be traced.,"2005), where four of the five epochs presented in this paper here are incorporated into an identification scenario based on a larger number of observations obtained at different We do not find any convincing identification scenario for jet components in this The jet straightens out in the last epoch, the wiggling is significantly more prominent in the first and second The jet component in the third epoch cannot reliably be identified with either of the two components from the other We do not include the jet components from the first epoch in our identification since no component can reliably be traced."
 We find another component at a core separation of 294.5 mas and position angle of -49.7° (not listed in the table)., We find another component at a core separation of 294.5 mas and position angle of $^{\circ}$ (not listed in the table).
 This component and position is exactly supported by F2000., This component and position is exactly supported by F2000.
 Although clearly a second jet component is visible in the table. we do not label this component since the position in core separation would vary un-physically across the The (u. v) coverage of the first epoch is less dense than in the other two epochs.," Although clearly a second jet component is visible in the table, we do not label this component since the position in core separation would vary un-physically across the The (u, v) coverage of the first epoch is less dense than in the other two epochs."
" We thus ignore this epoch in this For this source the position of the ""true"" core is unknown.", We thus ignore this epoch in this For this source the position of the “true” core is unknown.
 If our identification of the core position is correct. then the core shows significant flux-density The third epoch for this source reveals a significantly different position for component C2 than expected from the other epochs.," If our identification of the core position is correct, then the core shows significant flux-density The third epoch for this source reveals a significantly different position for component C2 than expected from the other epochs."
 We thus do not label this component in. this epoch., We thus do not label this component in this epoch.
 Future monitoring of this source might clarify possible reasons for this The source was very faint in two of the observed four epochs., Future monitoring of this source might clarify possible reasons for this The source was very faint in two of the observed four epochs.
 We therefore list only the parameters of two observations., We therefore list only the parameters of two observations.
 These data are clearly not sufficient to identify jet components confidently especially since the sum over the flux densities of the (unlabeled) components ts Two identification scenarios resulting in either fast or slow jet component motion seem to be possible for this source., These data are clearly not sufficient to identify jet components confidently especially since the sum over the flux densities of the (unlabeled) components is Two identification scenarios resulting in either fast or slow jet component motion seem to be possible for this source.
 We consider the “slow’-motion scenario to be more This source is a compact double., We consider the “slow”-motion scenario to be more This source is a compact double.
 The core is in the middle of the source (see also Taylor et al., The core is in the middle of the source (see also Taylor et al.
 Although the source structure looks simple. the component identification in this source is complicated since the position angles of the individual components change and several unmatchable components appear in the second and third epoch.," Although the source structure looks simple, the component identification in this source is complicated since the position angles of the individual components change and several unmatchable components appear in the second and third epoch."
 This nearby giant radio galaxy has been studied in detail by Giovannini et al., This nearby giant radio galaxy has been studied in detail by Giovannini et al.
 The exponential scale length of a galaxy disk is. one of the most fundamental parameters to. determine. its morphological structure as well as to mocel its dynamics. and the fact that the light. distributions are. exponential makes it possible to constrain the formation mechanisms (Freeman1970).,"$^5$ The exponential scale length of a galaxy disk is one of the most fundamental parameters to determine its morphological structure as well as to model its dynamics, and the fact that the light distributions are exponential makes it possible to constrain the formation mechanisms \citep{Freeman70}."
. The scale length. determines how the stars are distributed throughout a disk. and can be used to derive its mass distribution. assuming a specific M/L ratio.," The scale length determines how the stars are distributed throughout a disk, and can be used to derive its mass distribution, assuming a specific M/L ratio."
 Ultimately. this mass clistribution is the primary constraint for determining the formation scenariotherein).. which dictates the galaxys evolution.," Ultimately, this mass distribution is the primary constraint for determining the formation scenario, which dictates the galaxy's evolution."
 As the galaxy evolves. substructures such as bulges. pseudo-bulges. bars. rings. and spiral arms may build up. and this will then considerably change the morphology of the host disks (Combes&Elmcereen|1993:Elmeereenetal.2005:Journaud 2007).," As the galaxy evolves, substructures such as bulges, pseudo-bulges, bars, rings, and spiral arms may build up, and this will then considerably change the morphology of the host disks \citep{CE93,Eetal05,Bournaud07}."
 The scale length value is intimately connected: to the circular velocity of the galaxy halo. which in turn relates. closely to the angular momentum of the halo in which the disk is formed (Dalcantonοἱal.1997:Moet1998).," The scale length value is intimately connected to the circular velocity of the galaxy halo, which in turn relates closely to the angular momentum of the halo in which the disk is formed \citep{DSS97,
Mo98}."
. Up to the last [ον vears. cosmological simulations were limited to rather low resolution. were disks and spheroids were barely resolved. and generally limited to high redshifts. so reproducing realistic disk scale lengths for modern galaxies," Up to the last few years, cosmological simulations were limited to rather low resolution, were disks and spheroids were barely resolved, and generally limited to high redshifts, so reproducing realistic disk scale lengths for modern galaxies"
ihe temperature along y axis. against (he position for selected evolution times.,"the temperature along $y$ axis, against the $x$ position for selected evolution times."
 Since the anisotropic heat conduction is initially faster than (he pressure equilibration rate. the enerev distribution around the temperature interlace change rapidly until about /=(0.4.," Since the anisotropic heat conduction is initially faster than the pressure equilibration rate, the energy distribution around the temperature interface change rapidly until about $t = 0.4$."
 This energy transfer is mostly confined to the interaction region for the low A runs. since in these cases only a lew fiekl lines can penetrate into the entire interaction reeion.," This energy transfer is mostly confined to the interaction region for the low $R_0$ runs, since in these cases only a few field lines can penetrate into the entire interaction region."
 During the initial heal exchanee phase. the thermal energy. ancl density. (quickly recistiibute in the interaction region.," During the initial heat exchange phase, the thermal energy and density quickly redistribute in the interaction region."
 As seen in Figure 2((b). islands ai. =0.48 are formecl by material bouuded by the magnetic field lines. since the field orientation blocks heat exchange with the surroundings.," As seen in Figure \ref{fig02}( (b), islands at $x=0.48$ are formed by material bounded by the magnetic field lines, since the field orientation blocks heat exchange with the surroundings."
 Around «=0.4. (here are also cavities formed where (he thermal energy is inhibitted Irom flowing.," Around $x=0.4$, there are also cavities formed where the thermal energy is inhibitted from flowing."
 The magnetic field lines. which form complete sets of loops in the 4?=0.0 case. begin (o distort.," The magnetic field lines, which form complete sets of loops in the $R=0.0$ case, begin to distort."
 It can be observed that the field lines are more strongly distorted in the low density part of the interaction region than in the hieh density part., It can be observed that the field lines are more strongly distorted in the low density part of the interaction region than in the high density part.
 This occurs because velocity gradients are driven bv the early rapid recistribution of heat (pressure) by conduction., This occurs because velocity gradients are driven by the early rapid redistribution of heat (pressure) by conduction.
 Al (ime /=0.4 (see Figure 2((b)). the field lines surrounding the cavities al +=0.4 reconnect. making thermal exchange possible.," At time $t=0.4$ (see Figure \ref{fig02}( (b)), the field lines surrounding the cavities at $x=0.4$ reconnect, making thermal exchange possible."
 During the evolution. field lines begin to link (he interaction region to the hot material on the left.," During the evolution, field lines begin to link the interaction region to the hot material on the left."
 This phenomenon is most apparent in Figure 2((d). which marks the final state of the thermal energv exchange.," This phenomenon is most apparent in Figure \ref{fig02}( (d), which marks the final state of the thermal energy exchange."
 We also see, We also see
"center, the heating source seems to be closely linked to that center.","center, the heating source seems to be closely linked to that center."
" Furthermore the unique absence of CO filamentary flow structures or ""fingers"" from the area behind the Orion KL Hot Core (behind relative to the outflow center) indicates that a dense zone of the Extended Ridge might there have impeded the expansion of such filaments.", Furthermore the unique absence of CO filamentary flow structures or “fingers” from the area behind the Orion KL Hot Core (behind relative to the outflow center) indicates that a dense zone of the Extended Ridge might there have impeded the expansion of such filaments.
" Notably, the structures revealed by our HC3N(37-36)(v7=1) and CH30H(743-64,3) A (v,=1) maps of the gas kinematics within the Hot Core show trajectories emerging from the dynamical center."," Notably, the structures revealed by our $_3$ $\nu_7$ =1) and $_3$ $_{4,3}$ $_{4,3}$ ) $^-$ $\nu_t$ =1) maps of the gas kinematics within the Hot Core show trajectories emerging from the dynamical center."
" It is important to realize that each individual CO filament obeyed a Hubble-type velocity, its velocity increases linearly with distance from the explosive origin(?),, in other words, during the explosive event some 500 years ago material of vastly different velocities was ejected simultaneously and has been traveled out to different correspondingly distances."," It is important to realize that each individual CO filament obeyed a Hubble-type velocity, its velocity increases linearly with distance from the explosive origin, in other words, during the explosive event some 500 years ago material of vastly different velocities was ejected simultaneously and has been traveled out to different correspondingly distances."
 The material that is just now arriving at the Hot Core condensation is the one that now excites the energetic vibrations observed., The material that is just now arriving at the Hot Core condensation is the one that now excites the energetic vibrations observed.
" We do not, therefore, require decay times of this shock excitation to be on the order of hundreds of years; rather, the emission we observe now is caused by streams of matter impingingat present, not in the ""distant"" past ( 500 years), such that relevant decay times may be very much shorter indeed."," We do not, therefore, require decay times of this shock excitation to be on the order of hundreds of years; rather, the emission we observe now is caused by streams of matter impingingat present, not in the “distant” past $\sim$ 500 years), such that relevant decay times may be very much shorter indeed."
" argued the Orion KL Hot Core to more likely be heated by stars embedded within the core rather than powered from outside because of the core's large column densities, and warm temperatures."," argued the Orion KL Hot Core to more likely be heated by stars embedded within the core rather than powered from outside because of the core's large column densities, and warm temperatures."
" However, such a larger column densities and warm temperatures could be generated by fast and energetic shocks arriving now to the core as discussed above."," However, such a larger column densities and warm temperatures could be generated by fast and energetic shocks arriving now to the core as discussed above."
 It is thus not necessity of having an internal warm stellar source to heat the Orion-KL Hot Core as proposed in ?.., It is thus not necessity of having an internal warm stellar source to heat the Orion-KL Hot Core as proposed in .
colmparison shows that the classifications in the two studies are consistent. but that our sample was selected more strictly.,"comparison shows that the classifications in the two studies are consistent, but that our sample was selected more strictly."
 The simall disagreement is partially due to the different criterion or the UV nuages at he rest-frame wavceleusth., The small disagreement is partially due to the different criterion for the UV images at the rest-frame wavelength.
 Because we selected. earbv-tvpe galaxies m a saluple οςubiued from: various redshift survevs. our sauple is heterogeneous.," Because we selected early-type galaxies in a sample combined from various redshift surveys, our sample is heterogeneous."
 The uuuber of redshift surveys referred here ds fifteen. and a niajor yaction of redshift data at i:<2 were retrieved youn five surveys (Cohenetal.2000:al.200:Vanzellae 2005).," The number of redshift surveys referred here is fifteen, and a major fraction of redshift data at $z<2$ were retrieved from five surveys \citep{coh00,cow04,lef04,szo04,van05}."
. These five surveys have slightly cüffereut flux lLiuits iu selectiug spectroscopic targets: /—21 in Cohenetal. (2000). R=21.5 in Cowieetal.(2001).. 7=21 in LeFevrectal.(2001).. R26 in Szokolvetal. (2000).. and 2=21.5 in Vauzellaetal.(2005).," These five surveys have slightly different flux limits in selecting spectroscopic targets: $R=24$ in \citet{coh00}, , $R=24.5$ in \citet{cow04}, $I=24$ in \citet{lef04}, $R=26$ in \citet{szo04}, and $z=24.5$ in \citet{van05}."
. Tn four redshift survevs except Vauzellctal. (2005).. targets were selected wit rucarly unbiased methods (basicallv magniude huited).," In four redshift surveys except \citet{van05}, targets were selected with nearly unbiased methods (basically magnitude limited)."
 Iu the siuuple of Vauzellaetal.(2005M nal targets were selected among the galaxies wit ld21)>0.15. which nav be somewhat jdasec to red galaxies (possibly carly-type galaxies).," In the sample of \citet{van05}, main targets were selected among the galaxies with $(i-z)>0.45$, which may be somewhat biased to red galaxies (possibly early-type galaxies)."
 Nevertheless. our BHuple is still useful iun probing the nature of blue earlv-tvpe galaxies.," Nevertheless, our sample is still useful in probing the nature of blue early-type galaxies."
 We discuss a possible bias in using oulv-spectroscopic sample., We discuss a possible bias in using only-spectroscopic sample.
 Even if a target selection itsclf im a spectroscopic SHurvev ds not biased. it is plausible that the success rate iu securing spectra is higher in objects with strong lines than iu objects with weak lines.," Even if a target selection itself in a spectroscopic survey is not biased, it is plausible that the success rate in securing spectra is higher in objects with strong lines than in objects with weak lines."
 This can result iu the excess of the late-type ratio in the whole saluple. or in the case of our study. the excess of the bhie-carly-type ratio in the earb-tvpe saluple Gf we suppose that the blue early-type ealaxies have typically stroreer nes than the red earlv-tvpe salaxies).," This can result in the excess of the late-type ratio in the whole sample, or in the case of our study, the excess of the blue-early-type ratio in the early-type sample (if we suppose that the blue early-type galaxies have typically stronger lines than the red early-type galaxies)."
 This is an unavoidable effect as Olg as We use specroscopic πας, This is an unavoidable effect as long as we use spectroscopic sample.
 Photometric redshifts could IC used as well. but current estimates of the plooletric redshifts of 1e galaxies in the GOODS fieks are not perfect.," Photometric redshifts could be used as well, but current estimates of the photometric redshifts of the galaxies in the GOODS fields are not perfect."
 Tn particular it is not casy to derive a reliable tinate of the redshift for bh Cearly-type galaxies lat are nian tarects in this sudy., In particular it is not easy to derive a reliable estimate of the redshift for blue early-type galaxies that are main targets in this study.
 We decided ο. use oulv the spectroscopic redshifts because we needed accurate values of the redshifts for the arect ealaxies., We decided to use only the spectroscopic redshifts because we needed accurate values of the redshifts for the target galaxies.
 The fraction of the carly-type galaxies iun our sample is 9% (=171/1919)., The fraction of the early-type galaxies in our sample is $9\%$ (=171/1949).
 This i9 somewhat sunaller than the result of Duudwetal.(2005) who classified the galaxies visually usine the παλιο Πασος of the GOODS field. obtainius LL% (E. E/SO iu their sample).," This is somewhat smaller than the result of \citet{bun05} who classified the galaxies visually using the same images of the GOODS field, obtaining $14\%$ (E, E/S0 in their sample)."
 Our result is similar to the results of Ehucereenctal.(20055) who classified the galaxies visually usineo the HST/ACS inmages of the UDF. obtaining ," Our result is similar to the results of \citet{elm05b} who classified the galaxies visually using the HST/ACS images of the UDF, obtaining $11\%$."
However. it 1s stnaller than those used ou the automatic classification: Couseliceetal.(2005) obtained 20SOC at τν0.5 in the GOODS fields.," However, it is smaller than those based on the automatic classification: \citet{con05} obtained $20-30\%$ at $z\sim0.5$ in the GOODS fields."
 Iu the cases of Conseleeetal.(2005).. however. carly-type galaxies were selected using a quantitative methods. (conceutration-asviuuetry-chuupiness correlations). which possibly regard bulec-donunaut late-type galaxies as carly-type.," In the cases of \citet{con05}, however, early-type galaxies were selected using a quantitative methods (concentration-asymmetry-clumpiness correlations), which possibly regard bulge-dominant late-type galaxies as early-type."
 We ivideL the sample of earlv-tvpe galaxies iuto two eroups: red eurl-tvpe galaxies (RECs) and blue early-type galaxies (BEC). using the (fFi)jap color variation as a fiction of redshift.," We divided the sample of early-type galaxies into two groups: red early-type galaxies (REGs) and blue early-type galaxies (BEGs), using the $(i-z)_{\rm AB}$ color variation as a function of redshift."
 REGs comes]ond to typical carly-type galaxies seen 111 he local universe., REGs correspond to typical early-type galaxies seen in the local universe.
 The color of carl-type ealaxies varies sjenificautlv as redshift increases mt the color evolution of typical RECs are approximately reproduced with the simple stellar x»pulatiou (SSP) model., The color of early-type galaxies varies significantly as redshift increases but the color evolution of typical REGs are approximately reproduced with the simple stellar population (SSP) model.
 Therefore. it is cfiicicut o use the coor difference between the observed color aud the SSP expectation valuefor sclecting l," Therefore, it is efficient to use the color difference between the observed color and the SSP expectation valuefor selecting BEGs."
 , Fig.
disavs the (62) color difference (ACjjmÉPOihuaoda=(Ft aha} Ws. redshift or the sampe of early-type galaxies.," 1 displays the $(i-z)$ color difference $\Delta (i-z)
\equiv (i-z)_{\rm model} - (i-z)_{\rm obs}$ ) vs. redshift for the sample of early-type galaxies."
 To derive (fFlhuoda. We used the SSP model with formation redshift ΤΕ=4 (sinele-burst 12.1 Gar ago) aud metalliciv |Fe/H| 2.0.1 dex. caleulate with the GALANEV code (Bruzual&Charlot 2003).. |," To derive $(i-z)_{\rm model}$, we used the SSP model with formation redshift $z_{\rm F}= 5$ (single-burst 12.4 Gyr ago) and metallicity [Fe/H] $= -0.4$ dex, calculated with the GALAXEV code \citep{bru03}. ["
Fe/TII =0.1 dex was chosen because it matches well he observed colors of RECs.,Fe/H] $= -0.4$ dex was chosen because it matches well the observed colors of REGs.
 Severa features are noted in Fig., Several features are noted in Fig.
 1., 1.
 First. most galaxies at 5«1.2 are concentrated around the zero color differeik0. showine that their colors are wel reproduced by the SSP model.," First, most galaxies at $z<1.2$ are concentrated around the zero color difference, showing that their colors are well reproduced by the SSP model."
 Secoud. there are a siguificant umber of ealaxies with large positive color differences at 2 1.3. and all galaxies at D2012 show even larger color differences.," Second, there are a significant number of galaxies with large positive color differences at $z<1.2$ , and all galaxies at $z>1.2$ show even larger color differences."
 Third. oue galaxv at izc15 shows a large negativecolor ciüffereuco. indicating that it may be a highly reddened ealaxy.," Third, one galaxy at $z\approx 0.75$ shows a large negativecolor difference, indicating that it may be a highly reddened galaxy."
Fie.,Fig.
" L shows the relationship between τας and Thuninosities,", \ref{CorrelationFig} shows the relationship between X-ray and luminosities.
 There is no evidence for an uncorrelated N-ray component: the correlation extends to almost zero N-rav flux aud the liehteurves show no N-rav features which are not reproduced by ((except possibly at the very eud of the lighteumνο)., There is no evidence for an uncorrelated X-ray component; the correlation extends to almost zero X-ray flux and the lightcurves show no X-ray features which are not reproduced by (except possibly at the very end of the lightcurve).
 There is. however. au approximately coustaut component to the echussion. which varies oulv slowly.," There is, however, an approximately constant component to the emission, which varies only slowly."
 From the linear fts shown in Fie. l1.," From the linear fits shown in Fig. \ref{CorrelationFig},"
 the variahle component of ]uninositv corresponds to Iuminositv iu the first seement aud of the quantities compared are bolometric Iuninosities., the variable component of luminosity corresponds to luminosity in the first segment and of the quantities compared are bolometric luminosities.
 The observed X-ray huaimosity (assinued to be isotropic) is à lower limit ou the bolometric nradiating Iuninositv. which also iucbludes EUV aud οταν emission.," The observed X-ray luminosity (assumed to be isotropic) is a lower limit on the bolometric irradiating luminosity, which also includes EUV and $\gamma$ -ray emission."
 pprovides a lower limit on the reprocessed huuinosity., provides a lower limit on the reprocessed luminosity.
 More detailed modeling will be needed to estimate these boloimetrie corrections., More detailed modeling will be needed to estimate these bolometric corrections.
 If we consider oulv radiation that cau ionize neutral hydrogen aabove eeV). aud below 100keeV then this is uulikelv to exceed the A-ravs by more than a factor of a few: for example. it is about a factor of three for a pure power-law προσ (photon iudex D=1.8) aud a factor of five for model l of Navavan.Barret.&MeCliutock.(1997)..," If we consider only irradiation that can ionize neutral hydrogen above eV), and below 100k̇eeV then this is unlikely to exceed the X-rays by more than a factor of a few; for example, it is about a factor of three for a pure power-law spectrum (photon index $\Gamma=1.8$ ) and a factor of five for model 1 of \citet{Narayan:1997a}."
. Such a low-enerev cut-off is somewhat arbitrary. but is also motivated bv the large uncertainty concerning optical svuchrotron emission in the models of Naravan.Barret.&MeCliutock(1997)..," Such a low-energy cut-off is somewhat arbitrary, but is also motivated by the large uncertainty concerning optical synchrotron emission in the models of \citet{Narayan:1997a}."
" This contributes most of the truly bolometric πιοντν, but is umch weaker n more recent models citealtQuatacrt:1099a:; 20013)."," This contributes most of the truly bolometric luminosity, but is much weaker in more recent models \\citealt{Quataert:1999a}; \citealt{Ball:2001a}) )."
 wwill uot exceed corresponds to Case B recombination (Osterbrock1989): it is likely to be substautiallv less than this., will not exceed corresponds to Case B recombination \citep{Osterbrock:1989a}; it is likely to be substantially less than this.
 Thus the reprocessed. fraction is likely to be at least a few per cout. although this is is not a solid. inodel-iudepeudeut constraint.," Thus the reprocessed fraction is likely to be at least a few per cent, although this is is not a solid, model-independent constraint."
" For a thin disk aud isotropic nradiation. the fraction intercepted is approximately ΠΠ, so the lower limit is plausible for a central compact X-ray source radiating a thin disk (T/R20.02)."," For a thin disk and isotropic irradiation, the fraction intercepted is approximately $H/R$, so the lower limit is plausible for a central compact X-ray source irradiating a thin disk $H/R\ga0.02$ )."
 However. there is also a significant component of the optical coutimmiun which is correlated with X-rays (Figs.," However, there is also a significant component of the optical continuum which is correlated with X-rays (Figs."
 P 91)., \ref{MWLCFig}~ \ref{ProfileFig}) ).
 Tf this also originates in reprocessed X-rays then the reprocessed. fraction would be larger. as the optical coutimaiu fiux exceeds that in bby a factor much larger than plausible bolometric corrections to the irradiating flix.," If this also originates in reprocessed X-rays then the reprocessed fraction would be larger, as the optical continuum flux exceeds that in by a factor much larger than plausible bolometric corrections to the irradiating flux."
 This case would then favor an elevated or vertically extended X-ray. cussion ecolmetry which allows more efficient illuniuation of the disk., This case would then favor an elevated or vertically extended X-ray emission geometry which allows more efficient illumination of the disk.
" The variable optical coutimaun component could alternatively be dominated by svuchrotron emission (ο,ο, Ixaubachetal.2001: IEvnesetal. 2003))."," The variable optical continuum component could alternatively be dominated by synchrotron emission (e.g., \citealt{Kanbach:2001a}; \citealt{Hynes:2003a}) )."
 We have established that optical aud Nay. variations in lin quiescence are fairly well correlated., We have established that optical and X-ray variations in in quiescence are fairly well correlated.
 All N-ray variability (accounting for csscutially all of the observed N-rav flix) is uurrored well byΠα. and to a lesser extent by the optical coutimuun.," All X-ray variability (accounting for essentially all of the observed X-ray flux) is mirrored well by, and to a lesser extent by the optical continuum."
 There is clearly another component of conussion. which exhibits rarer. or less pronounced various. but is not completely constant.," There is clearly another component of emission, which exhibits rarer, or less pronounced variations, but is not completely constant."
 The correlated cconiponent exhibits double-peaked Lue profiles indicating enussiou from a disk., The correlated component exhibits double-peaked line profiles indicating emission from a disk.
 The peak separation iuples that the outer edge of the cutting region is at or outside the circularization radius., The peak separation implies that the outer edge of the emitting region is at or outside the circularization radius.
 The timescales of the fares. significantly less than the dynamical timescale at the circularization radius. suggest that the cconuection is mediated by mediation of the accretion disk.," The timescales of the flares, significantly less than the dynamical timescale at the circularization radius, suggest that the connection is mediated by irradiation of the accretion disk."
 The correlated, The correlated
The first is that the rotation rate is sufficiently. moderate to allow the centrifugal force to be considered as a perturbation. compared to the gravitational field.,"The first is that the rotation rate is sufficiently moderate to allow the centrifugal force to be considered as a perturbation, compared to the gravitational field."
" The second reason rests on the conjecture that the differential rotation induced by the meridional circulation gives rise to turbulent motions which are strongly anisotropic. dte to the stable stratification. with much stronger transport in the horizontal directions than in the vertical: Le. v,« and D,«Dy respectively for the turbulent viscosity and diffusivity."," The second reason rests on the conjecture that the differential rotation induced by the meridional circulation gives rise to turbulent motions which are strongly anisotropic due to the stable stratification, with much stronger transport in the horizontal directions than in the vertical: i.e. $ \nu_{v} \ll \nu_{h}$ and $D_{v} \ll D_{h}$ respectively for the turbulent viscosity and diffusivity."
 Such anisotropic turbulence is observed in the Earth's atmosphere and oceans; in a star we expect it to smooth the horizontal variations of angular velocity and of chemical composition. a property we shall invoke to discard certain non-linear terms.," Such anisotropic turbulence is observed in the Earth's atmosphere and oceans; in a star we expect it to smooth the horizontal variations of angular velocity and of chemical composition, a property we shall invoke to discard certain non-linear terms."
 The prescriptions to be used for these turbulent diffusivities are discussed and updated in a companion paper (Mathis et al., The prescriptions to be used for these turbulent diffusivities are discussed and updated in a companion paper (Mathis et al.
 2004)., 2004).
 We thus consider an axisymmetric star. and assume that the horizontal variations of all quantities are small and smooth enough to allow their linearization and their expansion in a modest number of spherical harmonies Pj(cos89).," We thus consider an axisymmetric star, and assume that the horizontal variations of all quantities are small and smooth enough to allow their linearization and their expansion in a modest number of spherical harmonics $P_{l}(\cos\theta)$."
 As reference surface. we chose either the sphere or the isobar. and write all sealar quantities either as Or establish the relation. between those two modal directions.," As reference surface, we chose either the sphere or the isobar, and write all scalar quantities either as or Let us establish the relation between those two modal expansions."
" As expandae. the. pressure""M around the⊲⋅⋅ tosphere as: . reduceN the radial coordinate of the isobar the respective the mean value of the radius of an isobar.", We expand the pressure around the sphere as: and introduce the radial coordinate of the isobar where $r$ is the mean value of the radius of an isobar.
" Taking — turbulence. expansion of P to first order. we have: becomes non-uniform. by definition the pressure is constant on the. ""radius of conclude that mass M,. apply the same _procedure to any other variable X. we — QG-.@) AX Iu sin’ will serve zlbelow in $55.1 toorthogonality calculatecondition the fa B J"," Taking the Taylor expansion of $P$ to first order, we have: and since by definition the pressure is constant on the isobar, we conclude that If we apply the same procedure to any other variable $X$, we get and therefore This relation will serve below in 5.1 to calculate the effective gravity."
oQi ——À0) from. the momentum. equation OA) =IN where p is the density. ὁ the gravitational potential. and [τί represents the turbulent stresses.," We start from the momentum equation where $\rho$ is the density, $\phi$ the gravitational potential, and $||\tau||$ represents the turbulent stresses."
" The macroscopic velocity field V is the sum of a zonal flow with angular velocity QU.0) and a meridional flow fr.0): The latter can be split into à spherically symmetric. part. which represents the contraction or dilation of the star during its evolution. plus the meridional circulation which we expand in spherical functions Using the continuity equation in. the anelastic approximation. Le. V-(pta)=0. we obtain the following relation between Lr)and Vi(r): Making again use of the continuity equation. the azimuthal component of (9)) can be written as an. advection/diffusion equation for the angular momentum: Where as in Zahn (1992) we assume that the effect of the turbulent stresses on the large scale flow are adequately described by an anisotropic eddy viscosity. whose components are v, and v, respectively. in. the vertical: and horizontal."," The macroscopic velocity field $\vec V$ is the sum of a zonal flow with angular velocity $\Omega(r,\theta)$ and a meridional flow $\vec{\mathcal{U}}(r, \theta)$: The latter can be split into a spherically symmetric part, which represents the contraction or dilation of the star during its evolution, plus the meridional circulation which we expand in spherical functions Using the continuity equation in the anelastic approximation, i.e. $\vec{\nabla} \cdot (\rho\,\vec {\mathcal{U}}_{M})=0$, we obtain the following relation between $U_{l}(r)$ and $V_{l}(r)$: Making again use of the continuity equation, the azimuthal component of \ref{NV-vec}) ) can be written as an advection/diffusion equation for the angular momentum: where as in Zahn (1992) we assume that the effect of the turbulent stresses on the large scale flow are adequately described by an anisotropic eddy viscosity, whose components are $\nu_{v}$ and $\nu_{h}$ respectively in the vertical and horizontal directions."
" discussed""M in. Mathis.. etM al. (", As discussed in Mathis et al. (
2004). theyLet act ∣↽∙↼us bn the cause of turbulence. as observed in laboratory expansions. We rotating. flows.. namely— here the vertical anc P(r.8). = of- angular- velocity.,"2004), they act to reduce the cause of turbulence, as observed in laboratory experiments of rotating flows, namely here the vertical and horizontal gradients of angular velocity."
. This explains. why= andhorizontal introduce fluxes of angular momentum contain only Αμ.) = in contrast with the treatment of Kippenhahi I0 (1963). considered the effect of an imposed anisotropic where ris to thermal convection; in that case the rotatior the Taylor as is actually observed in the solar . A ARzn," This explains why the respective fluxes of angular momentum contain only these gradients, in contrast with the treatment of Kippenhahn (1963), who considered the effect of an imposed anisotropic turbulence, due to thermal convection; in that case the rotation becomes non-uniform, as is actually observed in the solar convection zone."
"that . introduction of the lagrangian time- Pyrt Note3) the. radial coordinate r. isa the meata Zu ) the layer (either sphere or. isobar) which enclosesand thesince isobar. we with dM, = taprdr,P"," Note the introduction of the lagrangian time-derivative ${{\rm d} / {\rm d}t}$ meaning that the radial coordinate $r$ is the mean radius of the layer (either sphere or isobar) which encloses the mass $M_{r}$, with ${\rm d}M_{r}=4\pi\rho r^{2}{\rm d}r$."
AP)The of eq. (14)), The form of eq. \ref{AM-diff-adv}) )
" incites to expand the angular velocity τμ (6) .dPs/dr horizontal average being defined as X|r- 3 the horizontal functions OQ,. #)lopXi) satisfythe MD= 20 Thispigs relation functions are readily identified: . . except for /= 2.these functions Q, reduce to the Legendre polynomials."," incites to expand the angular velocity as with the horizontal average being defined as and where the horizontal functions $Q_l(\theta)$ satisfy the orthogonality condition These horizontal functions are readily identified: except for $l=2$ ,these functions $Q_l$ reduce to the Legendre polynomials."
for the explosion site.,for the explosion site.
 We determine a vouug stellar population age of τις + 0.9 Myr for the nucleus of the GRB 020819 host galaxy. based ou a relation with the equivalent width of the IL? ciission line from Levesque et ((2010a. equ.," We determine a young stellar population age of 7.8 $\pm$ 0.9 Myr for the nucleus of the GRB 020819 host galaxy, based on a relation with the equivalent width of the $\beta$ emission line from Levesque et (2010a, eqn."
 2): however. we are unable to apply this age deteriüuation to the explosion site due to our lack of au IJ ciission line detection.," 2); however, we are unable to apply this age determination to the explosion site due to our lack of an $\beta$ emission line detection."
 For the nucleus we find au extinctiou-corrected star formation rate of 23.6 AL. /yr based on the flux of the Πα line (I&eunicutt 1998): for the explosion site we find 10.2 i/i., For the nucleus we find an extinction-corrected star formation rate of 23.6 $_{\odot}$ /yr based on the flux of the $\alpha$ line (Kennicutt 1998); for the explosion site we find 10.2 $_{\odot}$ /yr.
 The ISM. properties of the GRB 020819 host ealaxy uucleus aud explosion site are sununarized in Table 1., The ISM properties of the GRB 020819 host galaxy nucleus and explosion site are summarized in Table 1.
 Iu Figure 2 we compare CRB 020819 to six other :«1 LCRD host galaxies fro1à. Levesque et ((2010a) on a plot of voune stellar population age vs. metallicity., In Figure 2 we compare GRB 020819 to six other $z < 1$ LGRB host galaxies from Levesque et (2010a) on a plot of young stellar population age vs. metallicity.
" For comparison we also iuclude a sample of 7 2«0.1 metal-poor galaxies frou, Brown ct ((2008) and a saluple of blue compact galaxies from None Cheug (2002: for further discussion of these comparison samples see Levesque et 220108).", For comparison we also include a sample of 7 $z < 0.1$ metal-poor galaxies from Brown et (2008) and a sample of blue compact galaxies from Kong Cheng (2002; for further discussion of these comparison samples see Levesque et 2010a).
 It is evident that both the metallicity and age of the GRB 020819 host galaxy. set it apart from the current sample of LORB host galaxies., It is evident that both the metallicity and age of the GRB 020819 host galaxy set it apart from the current sample of LGRB host galaxies.
 Adoptingthe Pettini Pagel (2001) /Tle metallicity diagnostic. the explosion site metallicity[NTI of lostO/II). | 12 = 87 + 0.1 is considerably higher than the mean LORB host metallicity of los(O/II) | 12 2 81 + 02 derived using the same diagnostic.," Adopting the Pettini Pagel (2004) $\alpha$ metallicity diagnostic, the explosion site metallicity of log(O/H) + 12 = 8.7 $\pm$ 0.1 is considerably higher than the mean LGRB host metallicity of log(O/H) + 12 = 8.1 $\pm$ 0.2 derived using the same diagnostic."
 Similarly. the voune stellar population age of 7.8 + 0.9 Myr determined for the GRB 020819 host ealaxy nucleus is older than the mean age of 5.2 +4 0.15 Myr calculated for the voune stellar populations of LGRD host galaxies.," Similarly, the young stellar population age of 7.8 $\pm$ 0.9 Myr determined for the GRB 020819 host galaxy nucleus is older than the mean age of 5.2 $\pm$ 0.15 Myr calculated for the young stellar populations of LGRB host galaxies."
 Both of these disparitics sugeest that the progenitor of GRB 020819 formed iu a imnarkedlv differeut environment than that seen iu other LGRB host galaxies., Both of these disparities suggest that the progenitor of GRB 020819 formed in a markedly different environment than that seen in other LGRB host galaxies.
 Iu Figure 3 we place our GRB 020819 host observations on the Πα vs. cinission line ratio diagnostic diagram of Baldwin ct ((1981: top) and the [NTΟΠ vs. [OMTΟΠ diagnostic diagram of Dopita et ((2000: bottom). comparing its placement to the six LGRD hosts from Levesque ct ((2010a).," In Figure 3 we place our GRB 020819 host observations on the $\alpha$ vs. $\beta$ emission line ratio diagnostic diagram of Baldwin et (1981; top) and the [NII]/[OII] vs. [OIII]/[OII] diagnostic diagram of Dopita et (2000; bottom), comparing its placement to the six LGRB hosts from Levesque et (2010a)."
 Also included on these diagrams for comparison is a saluple of 60920 -O.L star-forming ealaxics from Ikewlev et ((2006). as well as the sample of metalpoor galaxies frou Brown et ((2008).," Also included on these diagrams for comparison is a sample of 60920 $z < 0.1$ star-forming galaxies from Kewley et (2006), as well as the sample of metal-poor galaxies from Brown et (2008)."
 Finally. we include the new eril of stellar population svuthesis and photoionization models published iu Levesque et ((2010b). to provide an independent comparison of metallicity and ionization paraiucter.," Finally, we include the new grid of stellar population synthesis and photoionization models published in Levesque et (2010b), to provide an independent comparison of metallicity and ionization parameter."
 We can sec that cluission line diagnostic ratios determined for both the GRB 020819 host ealaxy nucleus aud explosion site are distinct from the LORB host galaxies of Levesque et ((2010a)., We can see that emission line diagnostic ratios determined for both the GRB 020819 host galaxy nucleus and explosion site are distinct from the LGRB host galaxies of Levesque et (2010a).
 In Figure 3 (bottoni) we do see one LCRD host galaxy that appears to have a similarly. high metallicity: however. this data point represents the host ealaxv of GRD 031203. which has shown evidence of AGN activity that may coutaminate emission-IHuce-based determinations of its ISAD properties (Levesque et 22010a).," In Figure 3 (bottom) we do see one LGRB host galaxy that appears to have a similarly high metallicity; however, this data point represents the host galaxy of GRB 031203, which has shown evidence of AGN activity that may contaminate emission-line-based determinations of its ISM properties (Levesque et 2010a)."
 The CRB 020819 host galaxy shows no similar siens of such activity: in both diagnostic diagrams the GRB 020819 host appears to be very similar to a typical star-forming SDSS ealaxy. m inarked contrast to the other LGRD host ealaxies.," The GRB 020819 host galaxy shows no similar signs of such activity; in both diagnostic diagrams the GRB 020819 host appears to be very similar to a typical star-forming SDSS galaxy, in marked contrast to the other LGRB host galaxies."
 Our spectroscopic observations aud metallicity diagnostics have demonstrated that CRB 020819. did occur in a lowanetalliity region of the spiral host. but rather that the progenitor formed aud evolved in a host euvironnieut with a super-solar metallicity.," Our spectroscopic observations and metallicity diagnostics have demonstrated that GRB 020819 did occur in a low-metallicity region of the spiral host, but rather that the progenitor formed and evolved in a host environment with a super-solar metallicity."
 This is further supported by examining the position of the CRB 020819 nucleus and explosion site ou the emüssion line diagnostic diagrams of Figure 3., This is further supported by examining the position of the GRB 020819 nucleus and explosion site on the emission line diagnostic diagrams of Figure 3.
 This high metallicity sets CRB 020819. apart from all other LORB lost ealaxies examined to date - while some hosts appear to have solar or ucar-solar moetallicities based on afterglow spectra. the relationship between afterglow absorption metallicities aud cuiission-line iuetallieities las not been exanuned and these values may not be directly comparable.," This high metallicity sets GRB 020819 apart from all other LGRB host galaxies examined to date - while some hosts appear to have solar or near-solar metallicities based on afterglow spectra, the relationship between afterglow absorption metallicities and emission-line metallicities has not been examined and these values may not be directly comparable."
 It is also possible that hieher-metallicity host galaxies müght be missing from the current sample due to selection effects: the size and nature of this bias is addressed in detail in Graham et iin prep., It is also possible that higher-metallicity host galaxies might be missing from the current sample due to selection effects; the size and nature of this bias is addressed in detail in Graham et in prep.
 Due to the voune lifetimes (€ LO Myr. Woosley et 22002) associated with the asstuecl massive star progenitors of LORBs. we can take the metallicitics of their host cuviromments to be represcutative of the progenitor star metallicities.," Due to the young lifetimes $\le$ 10 Myr, Woosley et 2002) associated with the assumed massive star progenitors of LGRBs, we can take the metallicities of their host environments to be representative of the progenitor star metallicities."
 The ligh-netallicity ISM environnient that produced GRB 020819 is therefore particularly surprising in the context of our curent nuderstanuding of progenitor scenarios aud evolution for LORBs., The high-metallicity ISM environment that produced GRB 020819 is therefore particularly surprising in the context of our current understanding of progenitor scenarios and evolution for LGRBs.
 It has been suggested that low metallicities are required to produce the rapidly-rotating progenitors aud relativistic explosions associated with LGRDs (e.g. Vink et 22001. Mesiet Maeder 2005. Woosley Ποσο 2006) and the eeueral low metallicity treud secu in LORB host galaxies supports this claim (e.g. Modjaz et 22008. Locevski et 22009. Levesque et 22010a).," It has been suggested that low metallicities are required to produce the rapidly-rotating progenitors and relativistic explosions associated with LGRBs (e.g. Vink et 2001, Meynet Maeder 2005, Woosley Heger 2006) and the general low metallicity trend seen in LGRB host galaxies supports this claim (e.g. Modjaz et 2008, Kocevski et 2009, Levesque et 2010a)."
 However. the exact nature of this correlation between metallicity aud GRB progenitors remains unclear.," However, the exact nature of this correlation between metallicity and GRB progenitors remains unclear."
 The recent Type Ic supernova SN 2009bb was found to have a central-cueine-driven relativistic component similar to that associated with LCGRDs. although. no accompany σαΜααν ποσο. was associated with the event (Soderberg et 22009).," The recent Type Ic supernova SN 2009bb was found to have a central-engine-driven relativistic component similar to that associated with LGRBs, although no accompany gamma-ray trigger was associated with the event (Soderberg et 2009)."
 The host cuviromment of this supernova was found to lave a ναν lieh metallicity (Levesque et 220100). coutracicting the suppositiou that cueine-drvivenran relativistic supernovae could ouly be produced in low-1uetallicity. cuvirouments.," The host environment of this supernova was found to have a very high metallicity (Levesque et 2010c), contradicting the supposition that engine-driven relativistic supernovae could only be produced in low-metallicity environments."
 Wile its metallicity is not as high by comparison. the oulv other LGRD host ealaxy with a Z.. metallicity is CRB 051022.," While its metallicity is not as high by comparison, the only other LGRB host galaxy with a $\sim Z_{\odot}$ metallicity is GRB 051022."
" Craham et ((2009) point out that GRB 051022 is. like CRB 020819. a ""dark burst. aud postulate that the higher metallicity secu iu CRD 051022 mav be shared by the CRB 020819 host environment. a speculation that has been coufirmed by these results."," Graham et (2009) point out that GRB 051022 is, like GRB 020819, a “dark"" burst, and postulate that the higher metallicity seen in GRB 051022 may be shared by the GRB 020819 host environment, a speculation that has been confirmed by these results."
 The question of what role high metallicity wight play in the production of “dark” bursts is an intriguing one. aud requires a detailed comparison of the host euvironimenuts and energetic properties of these two bursts (see απαλά et al.," The question of what role high metallicity might play in the production of “dark"" bursts is an intriguing one, and requires a detailed comparison of the host environments and energetic properties of these two bursts (see Graham et al.,"
 in prep. for a comparison of CRB 020819 aud GRB 051022 as well as new UST observatious of the GRD 051022 host ealaxv).," in prep, for a comparison of GRB 020819 and GRB 051022 as well as new HST observations of the GRB 051022 host galaxy)."
 While both host salaxies include a inoderate amount of extinctiou (ely = 1.55 for CRB 051022. Ay = 1.98 for GRB 020819). we cannot rule out the possibility that direct effects of hiel metallicity cuviromments on progenitor evolution might," While both host galaxies include a moderate amount of extinction $A_V$ = 1.55 for GRB 051022, $A_V$ = 1.98 for GRB 020819), we cannot rule out the possibility that direct effects of high metallicity environments on progenitor evolution might"
where the Τόlr) coefficient results from the normalization of the spherical harmonics.,where the $1/(4\pi)$ coefficient results from the normalization of the spherical harmonics.
" An alternative approach of obtaining the harmonic cocticicuts f,,, 1s to employ a (least-squares) fitting procedure in equation (93).", An alternative approach of obtaining the harmonic coefficients $f_{nm}$ is to employ a (least-squares) fitting procedure in equation \ref{eq:M}) ).
 This is 1ichli more expensive than evaluating the integral iu (10)). but it cau be more robust if the maguetoegram does not cover (well) the whole surface of the Sun.," This is much more expensive than evaluating the integral in \ref{eq:integral}) ), but it can be more robust if the magnetogram does not cover (well) the whole surface of the Sun."
 Using the spherical harmonic cocficicuts the potential can be determined ou au arbitrary grid using (8)) and the magnetic field can be obtained with finite differences., Using the spherical harmonic coefficients the potential can be determined on an arbitrary grid using \ref{eq:Phi}) ) and the magnetic field can be obtained with finite differences.
" Alternatively, oue cau calculate the eradieut of the base functions analytically aud obtain the magnetic field as for 1lxr€R."," Alternatively, one can calculate the gradient of the base functions analytically and obtain the magnetic field as for $1\le r \le R$."
 Spherical harmonics provide a computationally efficient aud very elegaut wav of solving the Laplace equation on a spherical shell., Spherical harmonics provide a computationally efficient and very elegant way of solving the Laplace equation on a spherical shell.
 However. one needs to be cautious of how the iutegral in equation (103) as evaluated. especially when a large number of Larmonics are used in the seres expausionu.," However, one needs to be cautious of how the integral in equation \ref{eq:integral}) ) is evaluated, especially when a large number of harmonics are used in the series expansion."
 We will use the CONC synoptic magnetoeram for Carrington Rotation 2077 (CR2077. frou November 20 to December 17. 2008) as ai example to demonstrate the problem.," We will use the GONG synoptic magnetogram for Carrington Rotation 2077 (CR2077, from November 20 to December 17, 2008) as an example to demonstrate the problem."
 The maecuctoegram contains the radial field on a LSO2600 latitude-loueitude erid on the solar surface., The magnetogram contains the radial field on a $180\times 360$ latitude-longitude grid on the solar surface.
 The erid spacing is uniformi iu cos0 (or sine of the latitude) aud in longitude o., The grid spacing is uniform in $\cos\theta$ (or sine of the latitude) and in longitude $\phi$.
 Figure 1. shows the radial field., Figure \ref{fig:magnetogram} shows the radial field.
 Section 2 discusses the naive aud more sophisticated wavs of obtaining the potential field solution witli spherical harmonics., Section 2 discusses the naive and more sophisticated ways of obtaining the potential field solution with spherical harmonics.
 Section 3 describes au alternative approach using au iterative fuite difference., Section 3 describes an alternative approach using an iterative finite difference.
 The various mncthods are compared in the final Section 1. where we also demonstrate the ringiug effect that can arise iu the spherical harmonics solution. aud we draw our conclusions.," The various methods are compared in the final Section 4, where we also demonstrate the ringing effect that can arise in the spherical harmonics solution, and we draw our conclusions."
 To turn the analytic prescription eiven in the introduction iuto a scheme that works witl real maguctograus. oue has to pick the ανά deerce NV. aud evaluate the iutegrals i equation (10)) for cach pair of à» aud m up to the highest order.," To turn the analytic prescription given in the introduction into a scheme that works with real magnetograms, one has to pick the maximum degree $N$ , and evaluate the integrals in equation \ref{eq:integral}) ) for each pair of $n$ and $m$ up to the highest order."
" The resulting f,,, coctiicicuts can be used to coustruct the 3D potential maguetic fielcl solution at any NSeiven point using8S equationeq (11)).", The resulting $f_{nm}$ coefficients can be used to construct the 3D potential magnetic field solution at any given point using equation \ref{eq:Bpot}) ).
" The simplest approximation ο equation (10)) is a discrete inteeral using the original maguetoeram data: where the Mij is the racial field iu a pixel of the Ny by IN, sized maguctoeram."," The simplest approximation to equation \ref{eq:integral}) ) is a discrete integral using the original magnetogram data: where the $M_{i,j}$ is the radial field in a pixel of the $N_{\theta}$ by $N_{\phi}$ sized magnetogram."
 The pixel is centered at the (0ο) coordinates. aud the irea of the pixel is given by (CAcos0);(A0)j.," The pixel is centered at the $(\theta_i,\phi_j)$ coordinates, and the area of the pixel is given by $(\Delta\cos\theta)_i(\Delta\phi)_j$."
 Unfortunately. the wuiform cos mesh used by most ofthe magnetograms is not at all optimal to evaluate the iutegral in equation (10)).," Unfortunately, the uniform $\cos\theta$ mesh used by most ofthe magnetograms is not at all optimal to evaluate the integral in equation \ref{eq:integral}) )."
 Iu fact this procedure will only work with maximaorder NV that is much less than Ng., In fact this procedure will only work with maximumorder $N$ that is much less than $N_{\theta}$ .
" Figure 2. shows the 259,4 associated Legendre polvionial discretized in different waves."," Figure \ref{fig:legendre} shows the $P_{90,0}$ associated Legendre polynomial discretized in different ways."
Sun.,Sun.
 This ratio provides kev information on the CCR origin., This ratio provides key information on the GCR origin.
As a sanity cheek to assess the robustness of the average A(Li) value we repeated the analysis of the target. stars with other Z;rr scales. the temperature being the most crucial parameter in the derivation of A(Li).,"As a sanity check to assess the robustness of the average A(Li) value we repeated the analysis of the target stars with other $T_{eff}$ scales, the temperature being the most crucial parameter in the derivation of A(Li)."
 We infer T;rr in our targets by means of suitable transformations between clerecldened broad-band: colors and elfective temperatures obtained through the classical Infrared Flux Method (AREAL:Blackwell.Petford&Shallis 1980)., We infer $T_{eff}$ in our targets by means of suitable transformations between dereddened broad-band colors and effective temperatures obtained through the classical Infrared Flux Method \citep[IRFM;][]{blackwell}.
". Several Tory, scales sed on this technique are available in literature (c.g.Mon-)09:C'asagrandeetal. 2010).. that make use of dilferent model atmospheres. photometric svstems and. recipes for 1¢ absolute calibrations and zero-points."," Several $T_{eff}$ scales based on this technique are available in literature \citep[e.g.][]{monte98,alonso99,ramirez05,ghb09,casa10}, that make use of different model atmospheres, photometric systems and recipes for the absolute calibrations and zero-points."
 The comparison oetween the various LREAL seales is bevond the purpose of us work and we locus our attention only on the widely isecl in literature calibration by Alonso.Arribas&Martinez-toger(1999.hereafterA99) and the recent one by Gonzálezllernández&Bonifacio(2009.hereafter GO9).. based on the Two Micron. All Sky Survey 2ALASS photometric data to compute the infrared monochromatic [ux of the targets.," The comparison between the various IRFM scales is beyond the purpose of this work and we focus our attention only on the widely used in literature calibration by \citet[][hereafter A99]{alonso99} and the recent one by \citet[][hereafter G09]{ghb09}, based on the Two Micron All Sky Survey 2MASS photometric data to compute the infrared monochromatic flux of the targets."
" In order to have a homogeneous set of magnitudes. we adopted for all the field. stars the J ancl A, magnitudes available in the final release of the 2ALASS catalogue (Skrutskicetal."," In order to have a homogeneous set of magnitudes, we adopted for all the field stars the J and $K_s$ magnitudes available in the final release of the 2MASS catalogue \citep{skrut}."
2006).. Note that the 2ALASS magnitudes of the targets were transformed to the photometric system of the Telescope Carlos Sanchez (where the calibration by A99 is defined) by means of the relations by Carpenter(2001) ancl Alonso.Arribas&Alartinez-Roeer(1998)., Note that the 2MASS magnitudes of the targets were transformed to the photometric system of the Telescope Carlos Sanchez (where the calibration by A99 is defined) by means of the relations by \citet{carpenter} and \citet{alonso98}.
. The (/Ao colors were obtained. by adopting the extinction cocllicients by MeCall(2004) and the color excess E(B-¥) from the infrared dust maps by Schlegel.Finkbeiner&Davis (1998).. corrected. following the prescriptions by onifacio.Monai&Beers(2000).," The $(J-K)_0$ colors were obtained by adopting the extinction coefficients by \citet{mccall04} and the color excess E(B-V) from the infrared dust maps by \citet{schlegel}, , corrected following the prescriptions by \citet{boni_monai}."
. For some stars. E(D-V) is larger than 0.4 mag and the erived νε is incompatible with the evolutionary stage of 10 targets and with the spectroscopic λεει," For some stars, E(B-V) is larger than 0.4 mag and the derived $T_{eff}$ is incompatible with the evolutionary stage of the targets and with the spectroscopic $T_{eff}$."
 For these stars we computed the color excess E(B-V) from the LEW of the interstellar doublet Na Llines (at 5890 and 5896 24). through w calibration by Munari&Zwitter(1997).," For these stars we computed the color excess E(B-V) from the EW of the interstellar doublet Na I lines (at 5890 and 5896 $\mathring{A}$ ), through the calibration by \citet{munari97}."
 Cravities. anc microturbulent velocities have been derived. spectroscopicallv. as. described. in the previous Section.," Gravities and microturbulent velocities have been derived spectroscopically, as described in the previous Section."
 The differences between the photometric and spectroscopic scales are equal to TUUS - [102— I (7= 55 W) and ο”... |4 d (σξ 57 ΑΝ)., The differences between the photometric and spectroscopic scales are equal to $T_{eff}^{GB}$ $T_{eff}^{spec}$ = +102 K $\sigma$ = 55 K) and $T_{eff}^{A99}$ $T_{eff}^{spec}$ = +4 K $\sigma$ = 57 K).
 This dillerence is fully consistent with the intrinsic. dillerence vctwween the (wo scales. (see. the. discussion. in. C09)., This difference is fully consistent with the intrinsic difference between the two scales (see the discussion in G09).
 Consequently. we derived. an average AX(Li) of 0.97. dex (c— 0.07 dex) and 1.07 dex (σξ 0.07 dex) when {ει by A909 and C09 are adopted. respectively.," Consequently, we derived an average A(Li) of 0.97 dex $\sigma$ = 0.07 dex) and 1.07 dex $\sigma$ = 0.07 dex) when $T_{eff}$ by A99 and G09 are adopted, respectively."
" Thus. the spectroscopic Zor, and those obtained with he A99 calibration can be considered on the same scale. while the scale by C09 is. slightly. hotter. providing Li abundances —0.1 dex higher."," Thus, the spectroscopic $T_{eff}$ and those obtained with the A99 calibration can be considered on the same scale, while the scale by G09 is slightly hotter, providing Li abundances $\sim$ 0.1 dex higher."
 Finally. we note that the general agreement between spectroscopic and photometric 7;rr (apart from the cillerent zero-points) seems to indicate that no relevant. departures [rom the LEE condition occurs. at least when the low-X lines are excluded for the most metal-poor stars.," Finally, we note that the general agreement between spectroscopic and photometric $T_{eff}$ (apart from the different zero-points) seems to indicate that no relevant departures from the LTE condition occurs, at least when the $\chi$ lines are excluded for the most metal-poor stars."
 To date. there is no general consensus about the magnitude of non-LTI corrections for iron. due to the incompleteness of the Fe model atom and the uncertaintyabout the rate of collision with the hvdrogen: atomis.," To date, there is no general consensus about the magnitude of non-LTE corrections for iron, due to the incompleteness of the Fe model atom and the uncertaintyabout the rate of collision with the hydrogen atoms."
 Adopting several recipes for the calibration of theSg parameter. the scaling-factor to correct. the LL LE collision rate provided by the Steeenbock Llolweger generalisation (Stecnbock&Lolweeer1984) of the Drawin formula (Drawin1968. 1969).. dillerent authors provide dilferent non LTE corrections for iron (seeforinstanceCirattonetal. results).," Adopting several recipes for the calibration of the$S_H$ parameter, the scaling-factor to correct the H I collision rate provided by the Steeenbock Holweger generalisation \citep{SH84} of the Drawin formula \citep{D68,D69}, , different authors provide different non LTE corrections for iron \citep[see for instance][providing very diferent results]{gratton99,gehren04}. ."
 10M.. (e.g..2)..," $10^{13}~{\rm M_\odot}$ \citep[e.g.,][]{bro08}. \citep[e.g.,][]{whi78}."
 ~10Gyr (e.g..22).. (e.g..?).. (AGNfeedback:e.g..??).. (e.g..2).. (e.g..??).. (?).. (?)..," $\simeq 10~{\rm Gyr}$ \citep[e.g.,][]{tin68,tra00}. \citep[e.g.,][]{can87}. \citep[AGN feedback; e.g.,][]{tab93,cro06}. \citep[e.g.,][]{hop06}, \citep[e.g.,][]{fab03a,mcn00}. \citep{fab03a}. \citep{con92}."
 (e.g..1) that brief bursts of AGN activity are sufficient to truncate star formation (e.g..?)..," \citep[e.g.,][]{bal09} that brief bursts of AGN activity are sufficient to truncate star formation \citep[e.g.,][]{hop06}."
 Alternatively. a mechanism other than AGN feedback may be heating the plasma surrounding galaxies (e.g..2)..," Alternatively, a mechanism other than AGN feedback may be heating the plasma surrounding galaxies \citep[e.g.,][]{bir03}."
 Previous studies show that ~30% of the most massive galaxies are radio continuum sources (e.g..2222?)..," Previous studies show that $\sim 30\%$ of the most massive galaxies are radio continuum sources \citep[e.g.,][]{fab89,sad89,wro91,bes05,sha08}."
 These studies matched optical and radio source catalogs. which limits the sample to radio sources that meet conservative signal-to-noise criteria. so catalogs are not swamped by noise. (," These studies matched optical and radio source catalogs, which limits the sample to radio sources that meet conservative signal-to-noise criteria, so catalogs are not swamped by noise. ("
Even when conservative criteria are applied. the tail of the noise distribution may produce spurious sources.),"Even when conservative criteria are applied, the tail of the noise distribution may produce spurious sources.)"
 Recent studies have generally utilized large redshift surveys that exclude the nearest galaxies. and thus miss radio sources fainter than 10WHz!.," Recent studies have generally utilized large redshift surveys that exclude the nearest galaxies, and thus miss radio sources fainter than $10^{22}~{\rm W~{Hz}^{-1}}$."
 Consequently. the faint radio emission from nearby early-type galaxies has not been completely characterized by the prior literature.," Consequently, the faint radio emission from nearby early-type galaxies has not been completely characterized by the prior literature."
 In this letter we present a study of the 1.4 GHz radio emission from K<9 early-type galaxies., In this letter we present a study of the 1.4 GHz radio emission from $K<9$ early-type galaxies.
 The choice of 1.4 GHz is pragmatic. as it allows us to utilize existing NRAO VLA Sky Survey (NVSS:?) and single-dish imagery.," The choice of 1.4 GHz is pragmatic, as it allows us to utilize existing NRAO VLA Sky Survey \citep[NVSS;][]{con98} and single-dish imagery."
 We assume the radio emission is the consequence of either recent star formation or an AGN., We assume the radio emission is the consequence of either recent star formation or an AGN.
 If this assumption holds. our conclusions do not depend on which emission process is dominant in these galaxies (1.e.. synchrotron. free-free).," If this assumption holds, our conclusions do not depend on which emission process is dominant in these galaxies (i.e., synchrotron, free-free)."
 Rather than match our early-type galaxies to radio source catalogs alone. we also measure flux densities from radio images.," Rather than match our early-type galaxies to radio source catalogs alone, we also measure flux densities from radio images."
 We can thus include significant (albeit noisy) information on the radio flux densities of early-type galaxies that would have otherwise been excluded from our study., We can thus include significant (albeit noisy) information on the radio flux densities of early-type galaxies that would have otherwise been excluded from our study.
 This allows us to characterize the very faint radio emission from the most massive early-type galaxies., This allows us to characterize the very faint radio emission from the most massive early-type galaxies.
 Our parent sample is the 2MASS Extended Source Catalog (2).. from which we select objects with apparent magnitude K«9 (dustcorrected:?).. declination 6>—40° and galactic latitude of |b|>15°.," Our parent sample is the 2MASS Extended Source Catalog \citep{jar00}, from which we select objects with apparent magnitude $K<9$ \citep[dust corrected;][]{sch98}, declination $\delta>-40^{\circ}$ and galactic latitude of $|b|>15^{\circ}$."
 Of the 1107 objects selected with these criteria. 979 have morphologies available from the Third Reference Catalog of Bright Galaxies (?) while virtually all of the remaining objects are Galactic.," Of the 1107 objects selected with these criteria, 979 have morphologies available from the Third Reference Catalog of Bright Galaxies \citep{rc3} while virtually all of the remaining objects are Galactic."
 Our principal sample is the 400 galaxies that are classified as elliptical or lenticular galaxies in the RC3 (with Ttype classifications of -1orless).Manyof thesegalaxies have redshifts in the RC3 catalog. while the remainder," Our principal sample is the 400 galaxies that are classified as elliptical or lenticular galaxies in the RC3 (with Ttype classifications of -1orless).Manyof thesegalaxies have redshifts in the RC3 catalog, while the remainder"
"is estimated by taking the derivative of the residuals that result after fitting pulse arrival times to a model for the pulsar’s spin properties and astrometric coordinates, and binary parameters if relevant.","is estimated by taking the derivative of the residuals that result after fitting pulse arrival times to a model for the pulsar's spin properties and astrometric coordinates, and binary parameters if relevant."
" For a single plane wave the observable may be written as where (0.4.5) are the direction cosines of the pulsar with respect to the GW. Εν}. are the polarization compoucuts of the CW. and (f.f,) ave the times of emission. (0) and reception (r) of the pulses frou the pulsar which is at a distance 7."," For a single plane wave the observable may be written as where $(\alpha,\beta,\gamma)$ are the direction cosines of the pulsar with respect to the GW, $(h_+,h_\times)$ are the polarization components of the GW, and $(t_{\rm e},t_{\rm r})$ are the times of emission (e) and reception (r) of the pulses from the pulsar which is at a distance $l$."
" The f, termsin equation (1901) will be correlated between differeut pulsars.", The $t_{\rm r}$ terms in equation \ref{eq:Z}) ) will be correlated between different pulsars.
 Therefore timing measurements of au array of pulsars across the sky. the Pulsar Timine Array. creates a eravitational wave telescope that is sensitive to a spectrm of waves with periods less than the duration of the measurements which is vears. or ~ 10 ullz (c.g. ?)..," Therefore timing measurements of an array of pulsars across the sky, the Pulsar Timing Array, creates a gravitational wave telescope that is sensitive to a spectrum of waves with periods less than the duration of the measurements which is years, or $\sim$ 10 nHz \citep[\eg][]{Backer93}. ."
 The five degrees of freedom in equation (19)) correspond to the five degrees of freedom in the trace-free space-time metric., The five degrees of freedom in equation \ref{eq:Z}) ) correspond to the five degrees of freedom in the trace-free space-time metric.
 The f. terms in equation {191} will be mncorrelated between differeut pulsus. aud vet will have comparable amplitude.," The $t_{\rm e}$ terms in equation \ref{eq:Z}) ) will be uncorrelated between different pulsars, and yet will have comparable amplitude."
 These terms create an mreducible noise backerouncd iu addition to any limnitatious from the measurement errors and propertics of the pulsars themselves or the intervene turbulent plasma through which the signals propagate., These terms create an irreducible noise background in addition to any limitations from the measurement errors and properties of the pulsars themselves or the intervening turbulent plasma through which the signals propagate.
 ? apply these ideas to a search for plane waves from both our Galactic Ceuter aud nearby galaxies which lost AIBUs based ou the hypothesis that the central objects are binary., \citet{Lommen01} apply these ideas to a search for plane waves from both our Galactic Center and nearby galaxies which host MBHs based on the hypothesis that the central objects are binary.
 Iu the preceding sectious we considered the production of a stochastic background of gravitational radiation from coalesceuces of MDBII binaries., In the preceding sections we considered the production of a stochastic background of gravitational radiation from coalescences of MBH binaries.
 This is smuniurized in the form of a characteristic strain spectrum. 5.(f£). Figure &..," This is summarized in the form of a characteristic strain spectrum, $h_c(f)$, Figure \ref{fig:strainspec}."
 For the purposes of analysis of timing data froua spatial array of pulsars we need to cousider the full tensor perturbation field fj;(x.f).," For the purposes of analysis of timing data froma spatial array of pulsars we need to consider the full tensor perturbation field $h_{ij}({\bf x},t)$."
 All elements are statistically independent owing to the random superposition of παν sources from many directions., All elements are statistically independent owing to the random superposition of many sources from many directions.
 This superposition destrovs the simple aneular plane wave pattern described iu equation (19))., This superposition destroys the simple angular plane wave pattern described in equation \ref{eq:Z}) ).
 However. ? has shown that 5/8 of the variance in the stochastic fluctuations cau be extracted using the 5 quadiupole spherical harvionic Y functions as the augular basis.," However, \citet{Burke75} has shown that 5/8 of the variance in the stochastic fluctuations can be extracted using the 5 quadrupole spherical harmonic $Y^l_m$ functions as the angular basis."
 Temporal modulations of cach splierical hariuonic terii cau be described using either Fourier frequency cocficicnts as the basis. or polvuonials (2)... or orthogonal polvnomials (2)...," Temporal modulations of each spherical harmonic term can be described using either Fourier frequency coefficients as the basis, or polynomials \citep{Foster90}, or orthogonal polynomials \citep{Stinebring}."
 The polvnomial approaches are particularly suited to this analysis owing to both the steep spectrum expected for the MDBII-MBII CAV cinission (eq. 2211), The polynomial approaches are particularly suited to this analysis owing to both the steep spectrum expected for the MBH-MBH GW emission (eq. \ref{eq:fullsimple}] ])
 aud the need to fit for the spin parameters of the stars., and the need to fit for the spin parameters of the stars.
 Given any choice of the temporal basis function. the amplitude ως} for any temporal teria is formed by the square root of the stu of the squares of the 5 spherical harmonic cocficicuts.," Given any choice of the temporal basis function, the amplitude $h_{\rm rms}(f)$ for any temporal term is formed by the square root of the sum of the squares of the 5 spherical harmonic coefficients."
 Couversion to ὃςf) requires consideration of tle spectral window function which will be addressed iu a later work., Conversion to $h_c(f)$ requires consideration of the spectral window function which will be addressed in a later work.
 A second approach to the aueular basis has been suggested by ?.., A second approach to the angular basis has been suggested by \citet{Hellings90}.
 The tensor field stated above can be transformed into a spectrum of waves πια. f).," The tensor field stated above can be transformed into a spectrum of waves $\tilde h_{ij}({\bf q},f)$ ."
 These can be decomposed into wavestraveling along the three cardinal directions. cach with independent polarizatious:," These can be decomposed into wavestraveling along the three cardinal directions, each with independent polarizations:"
observed indices the contribution by blue stragglers. which are not inelucled in the theoretical isochrones.,"observed indices the contribution by blue stragglers, which are not included in the theoretical isochrones."
" It was shown in Paper 1 that such corrections are important only lor 7/05 and. to a lesser degree. Ls,yay."," It was shown in Paper I that such corrections are important only for $H\delta_F$ and, to a lesser degree, $H\gamma_{\sigma<130}$."
 The effect of blue stragglers on all indices stuclied in Chis paper is shown in Table 2.., The effect of blue stragglers on all indices studied in this paper is shown in Table \ref{tbl-4}.
 The index values adopted in this paper are those listed in the second row of Table 3 of Paper I. The resultant model spectra computed Irom the theoretical isochrones are used to deduce the clusters age., The index values adopted in this paper are those listed in the second row of Table 3 of Paper I. The resultant model spectra computed from the theoretical isochrones are used to deduce the cluster's age.
 Such a test is of fundamental importance for stellar population models., Such a test is of fundamental importance for stellar population models.
 A key requirement is that the same age has to be obtained [rom the fit of the theoretical isochrone to the clusters CAID. ancl from (he fit of theoretical spectra to the integrated spectrum of the cluster (the so-called spectroscopic age).," A key requirement is that the same age has to be obtained from the fit of the theoretical isochrone to the cluster's CMD, and from the fit of theoretical spectra to the integrated spectrum of the cluster (the so-called spectroscopic age)."
 This is especially interesting in view of the exceedingly high spectroscopic age (2 20 Gyrs) that. was obtained for 47 Tuc [rom the equivalent width of 7/5 by Gibson οἱ al. (, This is especially interesting in view of the exceedingly high spectroscopic age $>$ 20 Gyrs) that was obtained for 47 Tuc from the equivalent width of $H\gamma$ by Gibson et al. (
1999).,1999).
 The mismatch between spectroscopic and CAID-based ages may even be more general. because Cohen. Blakeslee Rhvzov (1998) have found very high spectroscopic ages for a sample of Galactic GCs. on the basis of the equivalent width of ff.," The mismatch between spectroscopic and CMD-based ages may even be more general, because Cohen, Blakeslee Rhyzov (1998) have found very high spectroscopic ages for a sample of Galactic GCs, on the basis of the equivalent width of $H\beta$."
 More recently. Vazdekis et al. (," More recently, Vazdekis et al. ("
2001) showed that a lower spectroscopic age (c 13 Gvrs) is obtained when isochrones that take into consideration effects such as a- ancl diffusion of heavy elements are used.,2001) showed that a lower spectroscopic age $\sim$ 13 Gyrs) is obtained when isochrones that take into consideration effects such as $\alpha$ -enhancement and diffusion of heavy elements are used.
 However. Vazclekis οἱ al.," However, Vazdekis et al."
 still obtained a residual difference of ~ 4 Gyrs between (heir spectroscopic and CMD-based ages. in the sense (hat the spectroscopic age was higher.," still obtained a residual difference of $\sim$ 4 Gyrs between their spectroscopic and CMD-based ages, in the sense that the spectroscopic age was higher."
 In the present paper. we approach this problem as follows.," In the present paper, we approach this problem as follows."
 We first infer an age for the cluster by fitting theoretical isochrones (ο its CMD., We first infer an age for the cluster by fitting theoretical isochrones to its CMD.
 We adopt the isochrones by Salaris and collaborators. which are (he same as those employed by Vazdekis οἱ al. (," We adopt the isochrones by Salaris and collaborators, which are the same as those employed by Vazdekis et al. ("
2001).,2001).
 For comparison purposes. we perlorm (le same exercise adopting a-enhanced isochrones by Salasnich et al. (," For comparison purposes, we perform the same exercise adopting $\alpha$ -enhanced isochrones by Salasnich et al. ("
2000. herealter. Padova isochrones).,"2000, hereafter, Padova isochrones)."
 The isochrones are compared to cluster data in both the CAID and Iuminositv function (LF) domains., The isochrones are compared to cluster data in both the CMD and luminosity function (LF) domains.
 A major conclusion is that the raw isochrones adopted do not reproduce the cluster’s LF correctly., A major conclusion is that the raw isochrones adopted do not reproduce the cluster's LF correctly.
 They underestimate the number counts of giants brighter (han the horizontal branch. by roughly a [actor of 2.5. in part because the theoretical isochrones do not include AGB stars.," They underestimate the number counts of giants brighter than the horizontal branch by roughly a factor of 2.5, in part because the theoretical isochrones do not include AGB stars."
 When we adopt the Padova isochrones. which do include AGB stars. the mismatch is reduced by ~ 0.1 dex.," When we adopt the Padova isochrones, which do include AGB stars, the mismatch is reduced by $\sim$ 0.1 dex."
 We then infer corrections to the model predictions by forcing the theoretical LF to mateh the observed one., We then infer corrections to the model predictions by forcing the theoretical LF to match the observed one.
 Such corrections are shown to be very important. implying a decrease of the order of 34 Gvis in the spectroscopic age inferred from Balmer lines.," Such corrections are shown to be very important, implying a decrease of the order of 3–4 Gyrs in the spectroscopic age inferred from Balmer lines."
 The LF of giant stars is (hus a kev input in deriving accurate spectroscopic ages of old stellar populations., The LF of giant stars is thus a key input in deriving accurate spectroscopic ages of old stellar populations.
" The revised spectroscopic ages inferred when adopting the ""LE-corrected"" isochrones are in excellent agreement. wilh those obtained from the fits to the CMD.", The revised spectroscopic ages inferred when adopting the “LF-corrected” isochrones are in excellent agreement with those obtained from the fits to the CMD.
 Via this careful (vo-step procedure in Papers | and 1. we now feel that the mysterious spectroscopic age discrepancy. [ον 47 Tuc has been resolved.," Via this careful two-step procedure in Papers I and II, we now feel that the mysterious spectroscopic age discrepancy for 47 Tuc has been resolved."
Our uext theorem coucerus a similar type inequality of (1.9)). but with functious g αμα f. defined over Qy (given by (1.2))).,"Our next theorem concerns a similar type inequality of \ref{I_inq}) ), but with functions $g$ and $f$ defined over $\O_T$ (given by \ref{omega_T}) ))."
 Before stating this result. we first remark that iu the case of functions [—Vg delined on a bounced domain. weformally have (by Poiucaré inequality): where C'>0 is a coustaut depending on the measure of the domain.," Before stating this result, we first remark that in the case of functions $f=\nabla g$ defined on a bounded domain, weformally have (by Poincaré inequality): where $C>0$ is a constant depending on the measure of the domain."
 Moreover. since the above two estimates imply that the term [[g||j« should be dropped from inequality (1.9)) when dealing with functions defiued over bounded clomatus.," Moreover, since the above two estimates imply that the term $\|g\|_{L^{\infty}}$ should be dropped from inequality \ref{I_inq}) ) when dealing with functions defined over bounded domains."
 Indeed. we have: Iu the same spirit of Remark 1.6.. our last theorem gives a comparison between inequality (1.1)) auc (1.9)) for a certain class of functious g. aud lor particular space climenusious.," Indeed, we have: In the same spirit of Remark \ref{rem_sh}, our last theorem gives a comparison between inequality \ref{eq1:IM}) ) and \ref{I_inq}) ) for a certain class of functions $g$, and for particular space dimensions."
 This paper is organized as follows., This paper is organized as follows.
 Iu Section ??.. we present some clelinitious and the main tools used in our analysis.," In Section \ref{sec2}, we present some definitions and the main tools used in our analysis."
 This includes parabolic Littlewood-Paley decomposition and various Sobolev embecddines., This includes parabolic Littlewood-Paley decomposition and various Sobolev embeddings.
" Section ?? is devoted to the proof of Theorem 1.1. (estimate on the entire space IE"". 1) uxing mainly the equivalence (1.5)) that we also show in Lemuna 3.1..", Section \ref{sec3} is devoted to the proof of Theorem \ref{theorem} (estimate on the entire space $\R^{n+1}$ ) using mainly the equivalence \ref{eq4:equiv}) ) that we also show in Lemma \ref{lem1}. .
 Iu Section ??.. we give the proof of Theorem 1.5 (estimate ou the bouuded domain 7).," In Section \ref{sec4}, we give the proof of Theorem \ref{theorem-bdd} (estimate on the bounded domain $\O_T$ )."
 Finally. in Section ??.. we give the proof of Theorem 1.7..," Finally, in Section \ref{sec5}, we give the proof of Theorem \ref{theorem3}. ."
 In this section. we define the fundamental funetiou spaces used in tliis paper.," In this section, we define the fundamental function spaces used in this paper."
 We also recall some importantembecclines., We also recall some importantembeddings.
"The functions dy. di. do. ds. and Y are given by The functions £1, and D are related cach other through equation (48)).","The functions $d_0$ , $d_1$ , $d_2$ , $d_3$, and $Y$ are given by The functions $P_0$ and $D_0$ are related each other through equation \ref{sol1:D0}) )."
 The virial theorem in non-relativistic MIID was derived by Chandrasekhar&Fermi(1953)., The virial theorem in non-relativistic MHD was derived by \citet{1953ApJ...118..116C}.
. Low(1982). applied it to the expanding magnetic loops bv evaluating the surface term., \citet{1982ApJ...261..351L} applied it to the expanding magnetic loops by evaluating the surface term.
 Landau&Lifshitz(1975) derived the theorem for a relativistic case in elegant wav by integrating the energy momentum tensor., \cite{1975ctf..book.....L} derived the theorem for a relativistic case in elegant way by integrating the energy momentum tensor.
 In this appendix. we derive the virial theorem for a relativistic self-similar MILD.," In this appendix, we derive the virial theorem for a relativistic self-similar MHD."
 We start from the equations of motion in sel-similar stage given by (36))., We start from the equations of motion in self-similar stage given by \ref{eq:reducedeom}) ).
" Taking the inner product with 7 and integrating it within a volume V. we obtain The first term is the thermal inertial term Cy, and the forth term is the gravitational potential energy VW."," Taking the inner product with $\bmath r$ and integrating it within a volume $V$, we obtain The first term is the thermal inertial term $U_\mathrm{in}$ and the forth term is the gravitational potential energy $W$."
 Integrating the second term by parts. we obtain where A is a closed surface of the volume V.," Integrating the second term by parts, we obtain where $\bmath{\mathcal{A}}$ is a closed surface of the volume $V$."
 The third term can be rewritten by using the Maxwell equations as follows. where S and σ are the Povnting Dux and the \laxwell’s stress tensor. respectively.," The third term can be rewritten by using the Maxwell equations as follows, where $\bmath S$ and $\bmath \sigma$ are the Poynting flux and the Maxwell's stress tensor, respectively."
 Note that the time derivative cannot be exchanged with the integration with volume in the first term since the volume V. changes with time., Note that the time derivative cannot be exchanged with the integration with volume in the first term since the volume $V$ changes with time.
 The second term on the right hand side of equation (€3)) has a form where Cg and C are the electric and magnetic energies givenby equations(75)) and (76)). respectively.," The second term on the right hand side of equation \ref{ap:emint}) ) has a form where $U_\mathrm{E}$ and $U_\mathrm{M}$ are the electric and magnetic energies givenby equations\ref{en:ele})) and \ref{en:mag}) ), respectively."
 By using these results. we obtain the virial theorem for the relativistic self-similar MILD: where," By using these results, we obtain the virial theorem for the relativistic self-similar MHD; where and"
not been fully understood yet.,not been fully understood yet.
" discussed the suitability of the lline ratio as a proxy of the Fe/Mg abundance ratio, as the regions in which the two ions are produced and the radiative transfer of the two lines are both very different."," discussed the suitability of the line ratio as a proxy of the Fe/Mg abundance ratio, as the regions in which the two ions are produced and the radiative transfer of the two lines are both very different."
" Computing the aand lline strength for a gas with cosmic abundances and using a wide range of hydrogen densities and ionization parameters, they predicted typical line ratios between 1.5 and 4.0 (this is indicated in Fig."," Computing the and line strength for a gas with cosmic abundances and using a wide range of hydrogen densities and ionization parameters, they predicted typical line ratios between 1.5 and 4.0 (this is indicated in Fig."
" 4.8 as a grey-shaded area), and attributed higher values to an overabundance of Fe with respect to Mg."," \ref{fig_met} as a grey-shaded area), and attributed higher values to an overabundance of Fe with respect to Mg."
 However these computations were based on a limited 70-level model of the Fe atom., However these computations were based on a limited 70-level model of the Fe atom.
 used a 371-level Fe* model to reproduce the observed emission properties in AGNs considering a large set of models of broad emission line region clouds., used a 371-level $^+$ model to reproduce the observed emission properties in AGNs considering a large set of models of broad emission line region clouds.
" From their results, all the observed ffeatures can be reproduced only if: (1) the BLR is characterized by the presence of significant microturbolence; (ii) the eemitting gas has different properties (density and/or temperature) with respect to the gas emitting other broad lines."," From their results, all the observed features can be reproduced only if: (i) the BLR is characterized by the presence of significant microturbolence; (ii) the emitting gas has different properties (density and/or temperature) with respect to the gas emitting other broad lines."
" In any case the strength of the eemission relative to the emission line of other ions (e.g the lline ratio) depends as much on the Fe abundance Ἐα//ΜΡas it does on other physical parameters of the BLR (e.g. turbulence velocity), making it difficult to convert the observed line ratios in abundance ratios."," In any case the strength of the emission relative to the emission line of other ions (e.g the line ratio) depends as much on the Fe abundance as it does on other physical parameters of the BLR (e.g. turbulence velocity), making it difficult to convert the observed line ratios in abundance ratios."
" Nevertheless, the study of the lline ratio as a function of look-back time can be used to give constraints on the BLR chemical enrichment history, under the assumption that physical conditions of the BLR that determine the eemission are not evolving."," Nevertheless, the study of the line ratio as a function of look-back time can be used to give constraints on the BLR chemical enrichment history, under the assumption that physical conditions of the BLR that determine the emission are not evolving."
 The observed lack of evolution in the measured line ratio can then be explained with an early chemical Feit//Mgenrichment of the QSO host., The observed lack of evolution in the measured line ratio can then be explained with an early chemical enrichment of the QSO host.
 Le. the QSOs in our sample must have undergone a major episode of Fe enrichment in a few hundreds Myr before the cosmic age at which they have been observed (~0.9 Gyr)., I.e. the QSOs in our sample must have undergone a major episode of Fe enrichment in a few hundreds Myr before the cosmic age at which they have been observed $\sim0.9$ Gyr).
" showed that for a massive elliptical galaxy characterized by a very intense but short star-formation history, the typical timescale for the maximum SN Ia rate can be as short as 0.3 Gyr."," showed that for a massive elliptical galaxy characterized by a very intense but short star-formation history, the typical timescale for the maximum SN Ia rate can be as short as 0.3 Gyr."
" This implies that if the Fe in high-z QSO hosts is mainly produced via SN Ia explosions, it would be possible to observe fully enriched BLR at z~6."," This implies that if the Fe in high-z QSO hosts is mainly produced via SN Ia explosions, it would be possible to observe fully enriched BLR at $z\sim6$."
" On the other hand, pointed out that SNe Ia are not necessarily the main (2004)contributors to the Fe enrichment, and that stars with a present-day initial mass function are sufficient to produce the observed lline ratios at z~6."," On the other hand, pointed out that SNe Ia are not necessarily the main contributors to the Fe enrichment, and that stars with a present-day initial mass function are sufficient to produce the observed line ratios at $z\sim6$."
 Fe could also be generated by Pop Fert//MgIIIstars: these very metal poor stars with typical masses M> 100 mmight be able to produce large amounts of Fe within a few Myr2002)., Fe could also be generated by Pop IIIstars: these very metal poor stars with typical masses $M\gtrsim$ 100 might be able to produce large amounts of Fe within a few Myr.
. We presented NIR-spectroscopic observations of three z~6 SDSS QSOs., We presented NIR-spectroscopic observations of three $z\sim6$ SDSS QSOs.
" Our NIR spectra cover the aand eemission features, which are powerful probes of and of the chemical enrichment of the BLR."," Our NIR spectra cover the and emission features, which are powerful probes of and of the chemical enrichment of the BLR."
 The new data extend the existing SDSS sample towards the faint end of the QSO luminosity function., The new data extend the existing SDSS sample towards the faint end of the QSO luminosity function.
 We have collected 22 literature spectra different sources) of high-redshift (z> 4) QSOs (19covering the rest-frame wavelength range 2700A<«3200A., We have collected 22 literature spectra (19 different sources) of high-redshift $z>4$ ) QSOs covering the rest-frame wavelength range $2700 \ \rm \AA <\lambda<3200$.
". The final sample is composed of 22 sources: our three new sources at z~6, 10 spectra from the literature of QSOs with 4«z5.7 and 9 spectra of QSOs with z(Iwamuro~6 2009).."," The final sample is composed of 22 sources: our three new sources at $z\sim6$, 10 spectra from the literature of QSOs with $4<z<5.7$ and 9 spectra of QSOs with $z\sim6$ ."
 In order to see how the derivation of physical parameters depend, In order to see how the derivation of physical parameters depend
We hope that anappropiate treatinent of this circuustance will lead to accurate predictions for all radii. so that the mie:ui spherically averaged profiles may he tuuiddlerst¢xd iu terms of the spherical collapse.,"We hope that an appropiate treatment of this circunstance will lead to accurate predictions for all radii, so that the mean spherically averaged profiles may be understood in terms of the spherical collapse."
 We find the results preseuted here very encouragingC» m this respect and we are currently working [m]along this linc., We find the results presented here very encouraging in this respect and we are currently working along this line.
 We thank Yehuda UWoffinan aud Simon White for stimulating discussions., We thank Yehuda Hoffman and Simon White for stimulating discussions.
 F.D. is a Ramoun v Cajal Fellow at the IAA (CISC)., F.P. is a Ramónn y Cajal Fellow at the IAA (CISC).
 ΕΕ. want to thank the hospitality aud financial support of the Iustituto de Astrofixica de Canarias aud the New pdexico State Universitv wrere part of this work was dono., F.P. want to thank the hospitality and financial support of the Instituto de Astrofisica de Canarias and the New Mexico State University where part of this work was done.
 F.P.. S.P. aud S.CG. would Bike to thauls Acciones DInuteeradas for suyporting the Cornuan-Spanish collaboration.," F.P., S.P. and S.G. would like to thank Acciones Integradas for supporting the German-Spanish collaboration."
 S.Ct. ackuowledges support w DAAD., S.G. acknowledges support by DAAD.
 ALIS. acknowleeees support of NASA and NSF erauts to NMSU., A.K. acknowledges support of NASA and NSF grants to NMSU.
" Computer simulations inve been done at the LRZ Munich. NIC Jiillich aud the NASA Ames,"," Computer simulations have been done at the LRZ Munich, NIC Jüllich and the NASA Ames."
 Par of the data analysis rave been carry out at CESCA., Part of the data analysis have been carry out at CESGA.
out to the resolution limit A.=ο for pixel size Ar (O is the Heaviside function).,out to the resolution limit $k_c=2\sqrt{\pi}/\Delta x$ for pixel size $\Delta x$ $\Theta$ is the Heaviside function).
 Using (his in (2.1)) gives the variance due to spatial white noise alone Are MI | , Using this in \ref{eq:sig}) ) gives the variance due to spatial white noise alone ^2_z(z) = x ) ].
"This functional form. plotted as a dotted line for each component of the field in re[fig:sig.. [alls off much faster than either a) or σι),"," This functional form, plotted as a dotted line for each component of the field in \\ref{fig:sig}, falls off much faster than either $\sigma^{(g)}$ or $\sigma^{(m)}$."
 We therefore conclude that the Gaussian component consists of contributions will spatial correlations longer (han a single pixel: it is not white noise., We therefore conclude that the Gaussian component consists of contributions with spatial correlations longer than a single pixel: it is not white noise.
 It is common practice to assess the degree to which a variable deparis from. Gaussian by its kurtosis statistic. A.," It is common practice to assess the degree to which a variable departs from Gaussian by its kurtosis statistic, $K$."
" The kurtosis is the fourth moment divided by the square of the variance. less (three: when the variable is perfectly. Gaussian A.=0,"," The kurtosis is the fourth moment divided by the square of the variance, less three; when the variable is perfectly Gaussian $K=0$."
 Excesses. relative to a Gaussian. in (he tails of the distribution will elevate (he fourth moment and lead (ο a positive kurtosis.," Excesses, relative to a Gaussian, in the tails of the distribution will elevate the fourth moment and lead to a positive kurtosis."
 Figure 4 shows that even when the excess tails account lor of the distribution. thev lead to a large kurtosis.," Figure \ref{fig:kurt} shows that even when the excess tails account for of the distribution, they lead to a large kurtosis."
 For comparison. a distribution of » point sources per unit surface area has a flat power spectrum with no cut-off (.— 2€) whose variance is (LDD03)) where (4:7) is the variance in the source fluxes.," For comparison, a distribution of $n$ point sources per unit surface area has a flat power spectrum with no cut-off $k_c\to\infty$ ) whose variance is ) _z^2(z) =, where $\avg{\varphi^2}$ is the variance in the source fluxes."
 The kurtosis of this same photospheric Ποιά is, The kurtosis of this same photospheric field is
"disappeared, the rms is considerably smaller, but the mean is also lower.","disappeared, the rms is considerably smaller, but the mean is also lower."
 These parameters are also given in Table 1., These parameters are also given in Table 1.
 The weighted mean has decreased to of the true value., The weighted mean has decreased to of the true value.
" The rms has decreased by a factor of three, but the error bars are still far below the rms."," The rms has decreased by a factor of three, but the error bars are still far below the rms."
 The same fits shown in Figure 4 are displayed in the frequency domain in Figure 6., The same fits shown in Figure 4 are displayed in the frequency domain in Figure 6.
" One can see that there is a low frequency excess in the top panels, which gave rise to spikes when fit in the time domain, but these do not significantly distort the fit in the frequency domain because the optimal weighting favors the higher frequencies."," One can see that there is a low frequency excess in the top panels, which gave rise to spikes when fit in the time domain, but these do not significantly distort the fit in the frequency domain because the optimal weighting favors the higher frequencies."
 Thus fitting the power spectrum is strongly recommended., Thus fitting the power spectrum is strongly recommended.
" It provides a much better estimator of the spatial (temporal) scale, although users will have to correct for a downwards bias of the order of and the error bars will not be more reliable."," It provides a much better estimator of the spatial (temporal) scale, although users will have to correct for a downwards bias of the order of and the error bars will not be more reliable."
" Fitting in the spectral domain would be particularly valuable when one is analyzing the effect of orbital motion on scintillation of a binary pulsar, or when one is attempting to measure the annual modulation in time scale due to the Earth's velocity."," Fitting in the spectral domain would be particularly valuable when one is analyzing the effect of orbital motion on scintillation of a binary pulsar, or when one is attempting to measure the annual modulation in time scale due to the Earth's velocity."
 It is clear that in all cases observers should be extremely cautious about the errors estimated from data blocks whose length is less than the refractive scale., It is clear that in all cases observers should be extremely cautious about the errors estimated from data blocks whose length is less than the refractive scale.
" We have not attempted to fit the frequency scale ὃν in the Fourier domain, but we expect that it would also be better fit in this way."," We have not attempted to fit the frequency scale $\delta\nu$ in the Fourier domain, but we expect that it would also be better fit in this way."
 The theoretical model for T'z(Af) is demonstrably inadequate because the value of ὃν measured from the simulation shown is only of that expected theoretically., The theoretical model for $\Gamma_{\cal I} (\Delta \text{f})$ is demonstrably inadequate because the value of $\delta\nu$ measured from the simulation shown is only of that expected theoretically.
" The theory applicable to moderately strong scattering has been worked out (Codona et al.,"," The theory applicable to moderately strong scattering has been worked out (Codona et al.,"
" 1986), but it has not been applied to interstellar scintillation."," 1986), but it has not been applied to interstellar scintillation."
" This should be done, but is beyond the scope of this paper."," This should be done, but is beyond the scope of this paper."
 Observers have also noted this effect and Gupta et al. (, Observers have also noted this effect and Gupta et al. (
"1994) have given a heuristic model which explains the reduction in ὃν in terms of refractive modulation of the diffractive scintillation, combined with the plasma dispersion.","1994) have given a heuristic model which explains the reduction in $\delta\nu$ in terms of refractive modulation of the diffractive scintillation, combined with the plasma dispersion."
 This model agrees approximately with the simulations., This model agrees approximately with the simulations.
 The bias changes slowly with increasing strength of scattering as will be shown later., The bias changes slowly with increasing strength of scattering as will be shown later.
 We do not understand why the fluctuations in spatial scale are not correlated with those in bandwidth., We do not understand why the fluctuations in spatial scale are not correlated with those in bandwidth.
" This effect has been considered by Gupta et al, (1994) who suggested that refractive variations that tilt the spatial structure should change the bandwidth but not the scale."," This effect has been considered by Gupta et al, (1994) who suggested that refractive variations that tilt the spatial structure should change the bandwidth but not the scale."
" This is clearly not true of our simulations, both the bandwidth and the spatial scale are highly variable."," This is clearly not true of our simulations, both the bandwidth and the spatial scale are highly variable."
 'These variations have also been observed in an extensive monitoring of ISS from a set of 18 pulsars by Bhat et al. (, These variations have also been observed in an extensive monitoring of ISS from a set of 18 pulsars by Bhat et al. (
1999).,1999).
" They estimated the frequency and time scales fitting the covariance functions as we have done, but with a Gaussian model."," They estimated the frequency and time scales fitting the covariance functions as we have done, but with a Gaussian model."
" We believe that the variability is due to the fact that some of the variance is caused by refractive effects which are ignored, but which significantly modulate the diffractive effects."," We believe that the variability is due to the fact that some of the variance is caused by refractive effects which are ignored, but which significantly modulate the diffractive effects."
" T'he various heuristic models employed by observers are useful, but this problem would benefit from further theoretical work based on Codona et al. ("," The various heuristic models employed by observers are useful, but this problem would benefit from further theoretical work based on Codona et al. ("
1986) and further simulations.,1986) and further simulations.
 In particular it would be very useful to extrapolate our results to stronger scintillation where the bias should decrease., In particular it would be very useful to extrapolate our results to stronger scintillation where the bias should decrease.
 It has been noticed for decades et al., It has been noticed for decades (Ewing et al.
" 1970; Roberts Ables 1982), that dynamic (Ewingspectra often show “criss-cross” structures."," 1970; Roberts Ables 1982), that dynamic spectra often show “criss-cross” structures."
" These structures, which are easily visible in Figure 1(b), are responsible for the “parabolic arcs"" discovered by Stinebring et al. ("," These structures, which are easily visible in Figure 1(b), are responsible for the “parabolic arcs” discovered by Stinebring et al. ("
2001) and discussed by Cordes et al. (,2001) and discussed by Cordes et al. (
"2006), which are seen in the “secondary spectrum.""","2006), which are seen in the “secondary spectrum.”"
" The secondary spectrum, which is the two-dimensional power spectrum of the dynamic spectrum and has been called the delay-Doppler spectrum, is shown in Figure 7."," The secondary spectrum, which is the two-dimensional power spectrum of the dynamic spectrum and has been called the delay-Doppler spectrum, is shown in Figure 7."
 Here the delay axis has been scaled to ns assuming the center frequency is 1.4, Here the delay axis has been scaled to ns assuming the center frequency is 1.4
"with no guide field (case I, a= 0) and models with a weak guide field (case II, a= ","with no guide field (case I, $\alpha=0$ ) and models with a weak guide field (case II, $\alpha=1/(2\sqrt{\sigma_1})$ )."
"The inflow into the reconnection region is not relativistic, thus 1/(2,/o1)).the relation between density and magnetic field is pic?~B2/(4no1)."," The inflow into the reconnection region is not relativistic, thus the relation between density and magnetic field is $\rho_1c^2\sim B_1^2/(4\pi\sigma_1)$."
" (2005) estimated the parameters of the reconnection outflow: bulk Lorentz factor Ὦ2~ density p»~ 2,/o1pi.The reconnected magnetic field is Byνσι,~Βιθι/νσι, where 6; is the angle between the magnetic field lines and the oblique shock surface in the inflow region."," \cite{2005MNRAS.358..113L} estimated the parameters of the reconnection outflow: bulk Lorentz factor $\Gamma_2\sim\sqrt{\sigma_1}$, density $\rho_2\sim 2\sqrt{\sigma_1}\rho_1$ .The reconnected magnetic field is $B_2\sim B_1\theta_1/\sqrt{\sigma_1}$, where $\theta_1$ is the angle between the magnetic field lines and the oblique shock surface in the inflow region."
" However, if a guide field is present, it will be compressed to the value Bog~2,/o1B1,c."," However, if a guide field is present, it will be compressed to the value $B_{2,\rm G}\sim 2\sqrt{\sigma_1}B_{1,\rm G}$."
" In case II this yields ΡοςΒι, greatly exceeding the reconnected component."," In case II this yields $B_{2,\rm G}\sim B_1$, greatly exceeding the reconnected component."
" Pressure in the minijet region is given by P»=Bi/(8m) in case I. As demonstrated in numerical simulations by this parameter is very sensitive to the strength of the guide (2009),field."," Pressure in the minijet region is given by $P_2=B_1^2/(8\pi)$ in case I. As demonstrated in numerical simulations by \cite{2009ApJ...705..907Z}, this parameter is very sensitive to the strength of the guide field."
" We adopt the following scaling: P»~(1—B2/2010?)(Απ). thus in case II the minijet pressure is roughly half of the value in case I. The ratio of thermal to rest energy densities is P2/(p2c?)=01/8, thus minijet matter is relativistically hot for σι260."," We adopt the following scaling: $P_2\sim (1-2\sigma_1\alpha^2)B_1^2/(8\pi)$, thus in case II the minijet pressure is roughly half of the value in case I. The ratio of thermal to rest energy densities is $P_2/(\rho_2c^2)\gtrsim\sqrt{\sigma_1}/8$, thus minijet matter is relativistically hot for $\sigma_1\gtrsim 60$."
 The magnetization of the minijet is O2~63/(201) in case I and c1 in caseII., The magnetization of the minijet is $\sigma_2\sim\theta_1^2/(2\sigma_1)$ in case I and $\sigma_2\sim 1$ in caseII.
" The minijet has an opening angle v?~θι/(2σι) and volume V2~1/3i3, assuming that its width Ay is similar to its length l5."," The minijet has an opening angle $\psi_2\sim \theta_1/(2\sigma_1)$ and volume $V_2\sim\psi_2l_2^3$, assuming that its width $\Delta y$ is similar to its length $l_2$."
" The propagation of the minijet flow is affected by radiative processes described in Section E.2.T]: radiative losses of the electrons tend to reduce their pressure, while Compton drag by photons emitted from the island region causes deceleration of the bulk flow."," The propagation of the minijet flow is affected by radiative processes described in Section \ref{sec_est_rad_min}: radiative losses of the electrons tend to reduce their pressure, while Compton drag by photons emitted from the island region causes deceleration of the bulk flow."
" Thus, we introduce correction factors that describe the final values of evolving parameters: P»;=npP2 and Do;=tjr L2."," Thus, we introduce correction factors that describe the final values of evolving parameters: $P_{\rm 2,f}=\eta_PP_2$ and $\Gamma_{\rm 2,f}=\eta_\Gamma\Gamma_2$ ."
 We will calculate these factors using the numerical scheme described in Section I3]., We will calculate these factors using the numerical scheme described in Section \ref{sec_num_sch}.
 Initial parameters of the island region can be found by solving the shock-jump conditions., Initial parameters of the island region can be found by solving the shock-jump conditions.
" Under the assumption of negligible matter rest energy density on both sides of the shock and highly relativistic upstream flow, one can reduce the problem to a quadratic equation for I5, giving the following solution (see Eq."," Under the assumption of negligible matter rest energy density on both sides of the shock and highly relativistic upstream flow, one can reduce the problem to a quadratic equation for $\Gamma_3$, giving the following solution (see Eq."
" 4.11 & in|KennelCoroniüjI984)): Τ2$ right]],, where 02,5=B3/(167P»,2)."," 4.11 in \citealt{1984ApJ...283..694K}) ): _3^2 , where $\sigma_{\rm 2,f} = B_2^2/(16\pi P_{\rm 2,f})$."
 Then we find: 37 Ba p3~ Ps «, Then we find: _3 B_3 _3 P_3 .
"( Since [316703<Lo, radiation from the island region is strongly boosted in the minijet co-moving frame."," Since $\Gamma_3\ll\Gamma_2$, radiation from the island region is strongly boosted in the minijet co-moving frame."
 And we expect that due to plasma compression both the magnetic field and average particle energy may be significantly higher than in the minijet region., And we expect that due to plasma compression both the magnetic field and average particle energy may be significantly higher than in the minijet region.
" We assume that the length of the island region is of the order of its height /3~2v»l5, hence its volume is V3~l;i2."," We assume that the length of the island region is of the order of its height $l_3\sim 2\psi_2l_2$, hence its volume is $V_3\sim l_2l_3^2$."
 Non-thermal particle acceleration in relativistic plasmas is an open field of research., Non-thermal particle acceleration in relativistic plasmas is an open field of research.
" There are numerous studies of thisprocess in relativistic Poorshocks (e.g.,[Bednarz&Ostrowski]1998;po03 D009)., leading to a E003,self-consistentpitkovsky| (atD008, leastSironi_& in weaklySpitkovsky| magnetized pair plasmas) scenario in which the first order Fermi process is initiated by the Weibel instability, producing power-law particle spectra NcxΥ? of index p~2—3."," There are numerous studies of thisprocess in relativistic shocks \citep[\eg,][]{1998PhRvL..80.3911B,2001MNRAS.328..393A,2003ApJ...589L..73L,2003ApJ...595..555N,2008ApJ...682L...5S,2009ApJ...698.1523S}, leading to a self-consistent (at least in weakly magnetized pair plasmas) scenario in which the first order Fermi process is initiated by the Weibel instability, producing power-law particle spectra $N\propto \gamma^{-p}$ of index $p\sim 2-3$."
" Particle acceleration in current sheets undergoing relativistic magnetic reconnection is in principle a more straightforward process, since strong electric fields eiareal] present."," Particle acceleration in current sheets undergoing relativistic magnetic reconnection is in principle a more straightforward process, since strong electric fields are present."
"2004} Numerical studies Daroschek have shown that a relativelyP007, hard particle spectrum (p008)~1) can be produced, if the current sheet can be stabilized against relativistic drift-kink instabilities (RDKI) by introduction of the guide component of magnetic field."," Numerical studies \citep{2003ApJ...586...72L,2004PhPl...11.1151J,2007ApJ...670..702Z,2008ApJ...677..530Z,2008ApJ...682.1436L} have shown that a relatively hard particle spectrum $p\sim 1$ ) can be produced, if the current sheet can be stabilized against relativistic drift-kink instabilities (RDKI) by introduction of the guide component of magnetic field."
" Particles energized to the point that they are able to leave the current sheet can be further accelerated by the Fermi process, as they bounce between the two regions of reconnecting inflow (Giannios|2010).."," Particles energized to the point that they are able to leave the current sheet can be further accelerated by the Fermi process, as they bounce between the two regions of reconnecting inflow \citep{2010arXiv1007.1522G}."
" We are not investigating details of the particle acceleration process here, but consider the injection of relativistic electrons of fixed energy distribution."," We are not investigating details of the particle acceleration process here, but consider the injection of relativistic electrons of fixed energy distribution."
" In the case of PKS 2155-304, the electron distribution cannot be constrained by multiwavelength observations if we accept the argument that X-ray emission is not produced co-spatially with the TeV emission."," In the case of PKS 2155-304, the electron distribution cannot be constrained by multiwavelength observations if we accept the argument that X-ray emission is not produced co-spatially with the TeV emission."
" However, the results imply the existence of a soft high-energy tail that in the flaring state shows a harder-when-brighter behaviour Do10).."," However, the results imply the existence of a soft high-energy tail that in the flaring state shows a harder-when-brighter behaviour \citep{2010arXiv1005.3702H}."
 The dynamical model of relativistic reconnection and the shock jump conditions provide us with the values of density p and pressure P in both the minijet and post-shock region., The dynamical model of relativistic reconnection and the shock jump conditions provide us with the values of density $\rho$ and pressure $P$ in both the minijet and post-shock region.
 We assume that internal energy is equally divided between protons and electrons., We assume that internal energy is equally divided between protons and electrons.
 The average energy of an electron depends on plasma composition and is highest when no electron-positron pairs are present., The average energy of an electron depends on plasma composition and is highest when no electron-positron pairs are present.
" The electron number density is then given by Nec p/Mp. The equation of state for both particle species is Pp)= Ge(p)€e(p)/3, Where e is the internal energy density and g is a parameter equal to 1 for relativistic particles and 2 for non- particles."," The electron number density is then given by $n_e\sim\rho/m_p$ The equation of state for both particle species is $P_{e(p)}=g_{e(p)}e_{e(p)}/3$ , where $e$ is the internal energy density and $g$ is a parameter equal to 1 for relativistic particles and 2 for non-relativistic particles."
" From equipartition we have ee= ey, hence the pressure of electrons (protons) is"," From equipartition we have $e_e = e_p$ , hence the pressure of electrons (protons) is"
Without loss of generality we assume that is transformed into given by Equation ?? and00.,Without loss of generality we assume that is transformed into given by Equation \ref{secT} and.
". By Equation (??)), we havePrrerrom2r+l Furthermore, the condition implies thatd*°*°™?""*"" 2 Theorem implies that there exist transformations such that can be transformed into as desired."," By Equation \ref{2rl}) ), we have Furthermore, the condition implies that 2 Theorem \ref{LNF} implies that there exist transformations such that can be transformed into as desired."
 Since does not have any term of grade higher than we have The uniqueness of together with an argument similar to the proof of Theorem9) complete the proof., Since does not have any term of grade higher than we have The uniqueness of together with an argument similar to the proof of Theorem \ref{inftThmONF} complete the proof.
 A linear change of state variables creates the linear part back into the infinite level normal form system., A linear change of state variables creates the linear part back into the infinite level normal form system.
 This together with Lemma proves the following theorem., This together with Lemma \ref{SPNF} proves the following theorem.
 The following theorem sheds light to the dynamics of the infinite level parametric normal form system., The following theorem sheds light to the dynamics of the infinite level parametric normal form system.
" By Equation (2.1)) we have = Jandthus, is an invariant set for the system."," By Equation \ref{Eul}) ) we have = and thus, is an invariant set for the system."
 The rest of the proof follows from Theorem, The rest of the proof follows from Theorem \ref{PNF}.
 Now we present an example and find its parametric normal form., Now we present an example and find its parametric normal form.
A yariety of different methods have been used to determine the age of elobular clusters in ow galaxy.,A variety of different methods have been used to determine the age of globular clusters in our galaxy.
 The Monte Carlo analvsis referred (o above involves dating (hese clusters using main-sequence (urnoll luminosity. and vields an age estimate lor the oldest clusters αἱ the 95% confidence level of 12.643:À Gyr.," The Monte Carlo analysis referred to above involves dating these clusters using main-sequence turnoff luminosity, and yields an age estimate for the oldest clusters at the $\%$ confidence level of $12.6\pm ^{3.4}_{2.2}$ Gyr."
 The most likely age for these globular clusters is thus x 800 Myr vounger than the WMAP lower limit on the age of the Universe., The most likely age for these globular clusters is thus $\approx$ 800 Myr younger than the WMAP lower limit on the age of the Universe.
 However. because the distribution is broad. (he possibility (hat globular clusters formed before the period of cosmic reionization determined by WMAP to occur zz 200 Myr after the Dig Dang is certainly sill viable (Jimenezetal (2003))).," However, because the distribution is broad, the possibility that globular clusters formed before the period of cosmic reionization determined by WMAP to occur $\approx$ 200 Myr after the Big Bang is certainly still viable \cite{jimenez}) )."
 Nevertheless. examining (he probability distribution in IxraussandChabover(2003).. as fit analvtically in Jimenezetal(2003).. one finds a 75% likelihood that the oldest globular clusters are in fact less (han 13.5 Gyr old.," Nevertheless, examining the probability distribution in \cite{krausschab}, as fit analytically in \cite{jimenez}, one finds a $\%$ likelihood that the oldest globular clusters are in fact less than 13.5 Gyr old."
 While not compelling. the possibility (hat globular clusters in our galaxy may have Iormed well after reionization could shed light on a number of issues. including whether reionizalion is due (ο a very early generation of massive stars and whether such svstems formecl before (ancl if so. how much before) larger structures such as globular clusters.," While not compelling, the possibility that globular clusters in our galaxy may have formed well after reionization could shed light on a number of issues, including whether reionization is due to a very early generation of massive stars and whether such systems formed before (and if so, how much before) larger structures such as globular clusters."
 This could probe the nature of possible hierarchical clustering., This could probe the nature of possible hierarchical clustering.
 The likelihood of this possibility is increased. when one recognizes that several other methods for determining the age οἱ elobular clusters. including using DIuminositv [unctions (JimenezanclPacloan/ (1998))). white dwarl cooling (Ilansenetal (2002))) aud eclipsing binaries (2002))) favor globular cluster ages in (he range of 11-13 Gyr.," The likelihood of this possibility is increased when one recognizes that several other methods for determining the age of globular clusters, including using luminosity functions \cite{jimenez2}) ), white dwarf cooling \cite{hansen}) ) and eclipsing binaries \cite{krausschab2}) ) favor globular cluster ages in the range of 11-13 Gyr."
 The existing uncertainty in globular cluster dating techniques is al present (oo large {ο do more than hint that there max be a gap in (ime between reionization in (he Universe and the formation of larger scale structures., The existing uncertainty in globular cluster dating techniques is at present too large to do more than hint that there may be a gap in time between reionization in the Universe and the formation of larger scale structures.
 However. this hint strongly motivates efforts to further reduce the absolute uncertainty in globular dating techniques.," However, this hint strongly motivates efforts to further reduce the absolute uncertainty in globular dating techniques."
 In. particular. the possible use of (he age-mass relation suggested by Paczvnski (Paczviski (1996)))," In particular, the possible use of the age-mass relation suggested by Paczynski \cite{pacz}) )"
The Burst aud Transient Source Experiment (BATSE) on board theObservatory las been very effective in recording eanuna-rav bursts (CRB).,The Burst and Transient Source Experiment (BATSE) on board the has been very effective in recording gamma-ray bursts (GRB).
 Soon after the observatory’s launch ou April 19. 1991. the results obtained with BATSE showed convincinely that the skv distribution of GRBs was isotropic (Alecean et al," Soon after the observatory's launch on April 19, 1991, the results obtained with BATSE showed convincingly that the sky distribution of GRBs was isotropic (Meegan et al."
 1992a) and that the lue-ofsight distribution Was incompatible with a homogeneous distribution iu euclidean space (Alecean et al., 1992a) and that the line-of-sight distribution was incompatible with a homogeneous distribution in euclidean space (Meegan et al.
 19925)., 1992b).
 The proposition based on these fiudiugs that the distance scale of GRBs is cosinological (Paczvuski 1992) was eventually confined by the observation of a large redshitt (Aletzecr 1997)., The proposition based on these findings that the distance scale of GRBs is cosmological (Paczynski 1992) was eventually confirmed by the observation of a large redshift (Metzger 1997).
 The GRB data frou BATSE have been published primarily in a succession of catalogs (cf, The GRB data from BATSE have been published primarily in a succession of catalogs (cf.
 Meegan et al., Meegan et al.
 1997)., 1997).
 These data are based on an ou-board trigger. which acts when certain conditions are fulfilled.," These data are based on an on-board trigger, which acts when certain conditions are fulfilled."
 Usually these require that the counts in the energy range ος300 keV exceed. the background. by 5.50 on a time scale of 61. 256 or 1021 msec in at least two of the eight detectors.," Usually these require that the counts in the energy range $50-300$ keV exceed the background by $5.5 \sigma$ on a time scale of 64, 256 or 1024 msec in at least two of the eight detectors."
 Variations of these criteria. in the clhamnels aud the signalo-hoise linits used. have been in effect at various tines (c£.," Variations of these criteria, in the channels and the signal-to-noise limits used, have been in effect at various times (cf."
 Moegan et al., Meegan et al.
 1997)., 1997).
 BATSE produces data in various modes in archival onu., BATSE produces data in various modes in archival form.
 The DISCLA data provide a continuous record of he counts in channels 1. 2. 3. and £ for the eight detectors on a time scale of 102 Linsec.," The DISCLA data provide a continuous record of the counts in channels 1, 2, 3, and 4 for the eight detectors on a time scale of 1024 msec."
 The DISCLA data allow the detection of CRBsposteriori in a way similar to the on-voard trieeer (except for the availability of only one time scale)., The DISCLA data allow the detection of GRBs in a way similar to the on-board trigger (except for the availability of only one time scale).
 There are distinct advantages to searching for CRBs in archival data: the detection paramcters cau be set independeutlv of those that are hard-wired iu the on-board σος. mechaunisii the search cau be repeated with a different detection algorithi: each search can be carried out on the full data set. etc.," There are distinct advantages to searching for GRBs in archival data: the detection parameters can be set independently of those that are hard-wired in the on-board trigger mechanism; the search can be repeated with a different detection algorithm; each search can be carried out on the full data set, etc."
 A search for CRBs uot detected bv the on-board BATSE ποσοao las been couducted by Nonuners et al. (, A search for GRBs not detected by the on-board BATSE trigger has been conducted by Kommers et al. (
1997).,1997).
 We have used the DISCLA data to search for GREy. in the time period TJD 836510528., We have used the DISCLA data to search for GRBs in the time period TJD $8365-10528$.
" Iu the ollowiug sections we describe the search. the classification of the trigeers. and the derivation of <V/V,2 of the resulting sample."," In the following sections we describe the search, the classification of the triggers, and the derivation of $<V/V_{max}>$ of the resulting sample."
 We have tried to automate the search procedure as much as possible. for the sake of both speed and consistency.," We have tried to automate the search procedure as much as possible, for the sake of both speed and consistency."
 This will allow simulations to be carried out to investigate various scicutific problems., This will allow simulations to be carried out to investigate various scientific problems.
 Our search las sole siularities to that carried out bv the ou-hoard BATSE trigeer: using the counts in chanucls 2|3 covering the energv range 50300 keV: averaging backeromud 'ounts over 17.108 s and requiring that two nodules see Qinininmun excess over backeround., Our search has some similarities to that carried out by the on-board BATSE trigger: using the counts in channels $2+3$ covering the energy range $50-300$ keV; averaging background counts over 17.408 s; and requiring that two modules see a minimum excess over background.
 We differ. however. oe1 the evaluation of the background as explained below.," We differ, however, in the evaluation of the background as explained below."
 Tn the search conducted by the on-board BATSE trigecr on the 1021 msec time scale. the backeround is crived over a given stretch of 17.108 sec iux the trigeer test is carried out for the 1021 msec biu following that," In the search conducted by the on-board BATSE trigger on the 1024 msec time scale, the background is derived over a given stretch of 17.408 sec and the trigger test is carried out for the 1024 msec bin following that"
"across a wide range of wavelengths, particularly in the submillimeter (see,e.g.","across a wide range of wavelengths, particularly in the submillimeter \citep[see, e.g.,][]{cal02,cal05,and09a}."
" However, each class of models has limitations."," However, each class of models has limitations."
" The ???)..similarity solution models have a large number of free parameters, some with significant degeneracies (seediscussioninΤ).."," The similarity solution models have a large number of free parameters, some with significant degeneracies \citep[see discussion in][]{
and09a}."
" By fitting only the emission, these models also neglect potential CO(3-2)information provided by dust emission, including stronger constraints on the disk density."," By fitting only the CO(3-2) emission, these models also neglect potential information provided by dust emission, including stronger constraints on the disk density."
" However, the neglect of dust emission avoids complications due to heating processes and chemistry that affect gas differently than dust."," However, the neglect of dust emission avoids complications due to heating processes and chemistry that affect gas differently than dust."
 The D’Alessio et al., The D'Alessio et al.
" models of dust emission include only stellar irradiation and viscous dissipation as heating sources, and do not take into account the additional heating processes that may affect molecular line strengths in the upper layers of circumstellar disks (?).."," models of dust emission include only stellar irradiation and viscous dissipation as heating sources, and do not take into account the additional heating processes that may affect molecular line strengths in the upper layers of circumstellar disks \citep{qi06}."
" While the constraints from the dust continuum reduce the number of free parameters in this class of models, they also have the disadvantage of an unrealistic treatment of the density structure at the disk outer edge: since they are simply truncated at a particular outer radius, they are not capable of simultaneously reproducing the extent of gas and dust emission in these systems (?).."," While the constraints from the dust continuum reduce the number of free parameters in this class of models, they also have the disadvantage of an unrealistic treatment of the density structure at the disk outer edge: since they are simply truncated at a particular outer radius, they are not capable of simultaneously reproducing the extent of gas and dust emission in these systems \citep{hug08}."
" The similarity solution models are vertically isothermal, which is an unrealistic assumption."," The similarity solution models are vertically isothermal, which is an unrealistic assumption."
" With only one molecular line included in the model, this limitation will not affect the results of the study presented here, although caution should be exercised when applying the best-fit model parameters to other lines."," With only one molecular line included in the model, this limitation will not affect the results of the study presented here, although caution should be exercised when applying the best-fit model parameters to other lines."
" The primary reason for using the two types of models, however, is that they differ substantially in their treatment of the disk temperature structures."," The primary reason for using the two types of models, however, is that they differ substantially in their treatment of the disk temperature structures."
 For the D'Alessio et al., For the D'Alessio et al.
" models, the temperature structure is fixed by the dust continuum."," models, the temperature structure is fixed by the dust continuum."
" The similarity solution models, by contrast, allow the temperature to vary to best match the data."," The similarity solution models, by contrast, allow the temperature to vary to best match the data."
" There are a few independent constraints on temperature: it should increase with height above the midplane, due to surface heating by the star and low viscous heating in the midplane, and the dust will generally not be hotter than the gas, since the gas is subject to additional heating processes beyond the stellar irradiation that determines dust temperature."," There are a few independent constraints on temperature: it should increase with height above the midplane, due to surface heating by the star and low viscous heating in the midplane, and the dust will generally not be hotter than the gas, since the gas is subject to additional heating processes beyond the stellar irradiation that determines dust temperature."
" The temperature structure in the disk is the single factor most closely tied to the derived value of the turbulent linewidth (see discussion in Section 4.4)), which will be model-dependent."," The temperature structure in the disk is the single factor most closely tied to the derived value of the turbulent linewidth (see discussion in Section \ref{sec:degen}) ), which will be model-dependent."
" We therefore fit both classes of models to the data, in order to compare the model-dependent conclusions about turbulent linewidth for two distinct types of models with very different treatments of gas temperature."," We therefore fit both classes of models to the data, in order to compare the model-dependent conclusions about turbulent linewidth for two distinct types of models with very different treatments of gas temperature."
 The spatial dynamic range of the data is insufficient to investigate radial variations in turbulent linewidth., The spatial dynamic range of the data is insufficient to investigate radial variations in turbulent linewidth.
" We therefore assume a global value, £, that will apply to size scales commensurate with the spatial resolution of the data."," We therefore assume a global value, $\xi$, that will apply to size scales commensurate with the spatial resolution of the data."
 'The D'Alessio et al., The D'Alessio et al.
 models are described in detail in 7???7?..," models are described in detail in \citet{dal98,dal99,dal01,dal06}."
 Here we provide a general outline of the model properties and discuss the particular models used in this paper., Here we provide a general outline of the model properties and discuss the particular models used in this paper.
 The D'Alessio et al., The D'Alessio et al.
" models were developed to reproduce the unresolved SEDs arising from warm dust orbiting young stars, although they have also been demonstrated to be successful at reproducing spatially resolved dust continuum emission at millimeter wavelengths (see,e.g.,??7) as well as spatially-resolved molecular line emission (see,e.g.,??).."," models were developed to reproduce the unresolved SEDs arising from warm dust orbiting young stars, although they have also been demonstrated to be successful at reproducing spatially resolved dust continuum emission at millimeter wavelengths \citep[see, e.g.,][]{cal02,hug07,
hug09} as well as spatially-resolved molecular line emission \citep[see,
e.g.,][]{qi04,qi06}."
" The models include heating from the central star and viscous dissipation within the disk, although they tend to be dominated by stellar irradiation."," The models include heating from the central star and viscous dissipation within the disk, although they tend to be dominated by stellar irradiation."
 The structure is solved iteratively to provide consistency between the irradiation, The structure is solved iteratively to provide consistency between the irradiation
to the lees of the triangle.,to the legs of the triangle.
 The phase of the measured bispecirum is known as (he closure phase (Lawson2001)., The phase of the measured bispectrum is known as the closure phase \citep{lawson}.
. The closure phase is immune to many forms of atmospheric corruption. which can be illustrated as follows: above each aperture there is a column of aimosphere with time-variable parcels of differing inclices of refraction and hence optical pathleneth.," The closure phase is immune to many forms of atmospheric corruption, which can be illustrated as follows: above each aperture there is a column of atmosphere with time-variable parcels of differing indices of refraction and hence optical pathlength."
" Thus the almosphere above each aperture contributes a time-variable phase error. eiving where ©, and © are (he phase errors associated wilh apertures 1 and 2 respectively. and ©ys is an intrinsic phase associated with the source as measured by the 1-2 baseline."," Thus the atmosphere above each aperture contributes a time-variable phase error, giving where $\phi_1$ and $\phi_2$ are the phase errors associated with apertures 1 and 2 respectively, and $\phi_{12}$ is an intrinsic phase associated with the source as measured by the 1-2 baseline."
 The bispectrum is (hus We see (hal the atmospheric phase errors (as well as many other aperture-dependent phase errors) cancel., The bispectrum is thus We see that the atmospheric phase errors (as well as many other aperture-dependent phase errors) cancel.
 This is a well-known result. first applied in radio interferometry 1953)..," This is a well-known result, first applied in radio interferometry \citep{jennison}."
 Llowever. it is not immediately obvious what the closure phase represents.," However, it is not immediately obvious what the closure phase represents."
 Below we derive an expression relating the observed closure phase to the binary point source representing a microlensineg event., Below we derive an expression relating the observed closure phase to the binary point source representing a microlensing event.
 Assume 3 apertures. resulting in 3 baselines D4.D» and By.," Assume 3 apertures, resulting in 3 baselines $\vec{B}_1, \vec{B}_2$ and $\vec{B}_3$."
 Note that As before. we are looking at (wo point sources with intensity ratio A and separation As.," Note that As before, we are looking at two point sources with intensity ratio $R$ and separation $\Delta\vec{s}$."
" On each baseline we measure a visibility V, given bv Equation (9)).", On each baseline we measure a visibility $\hat{V}_n$ given by Equation \ref{vCZ}) ).
 the closure phase is thus, the closure phase is thus
Iu the analvsis of the reception of polarized radiation. the following couventious are used.,"In the analysis of the reception of polarized radiation, the following conventions are used."
 The respouse of a single receptor is defined by the Jones vector. r. such that the voltage induced in the receptor by the mcideut electric field is given by the scalar product. e=rte.," The response of a single receptor is defined by the Jones vector, $\mbf{r}$, such that the voltage induced in the receptor by the incident electric field is given by the scalar product, $v=\mbf{r}^\dagger\mbf{e}$."
 A duabreceptor feed is represcuted by the Wermitian transpose of a Jones matrix with cohunus equal to the Jones vector of cach receptor. The receptors in au ideal feed respond to orthogonal senses of polarization (ic.," A dual-receptor feed is represented by the Hermitian transpose of a Jones matrix with columns equal to the Jones vector of each receptor, The receptors in an ideal feed respond to orthogonal senses of polarization (ie."
 the scalar product. aud have identical gains (ic.," the scalar product, $\mbf{r}_0^\dagger\mbf{r}_1=0$ ) and have identical gains (ie."
 rir=riri |., $\mbf{r}_0^\dagger\mbf{r}_0=\mbf{r}_1^\dagger\mbf{r}_1$ ).
" A amore incanineful eeoinetrie interpretation of Jones vectors ds. provided by the correspondius Stokes parameters, ο=tro.@ri."," A more meaningful geometric interpretation of Jones vectors is provided by the corresponding Stokes parameters, $S_k=\trace[\pauli{k}\mbf{r \otimes r}^\dagger]$."
 The state of polarization to which a receptor maxiually responds is completely described bv the three components of its associated Stokes polarization vector. S.," The state of polarization to which a receptor maximally responds is completely described by the three components of its associated Stokes polarization vector, $\mbf{S}$."
 Therefore. it is como to define a receptor using the spherical coordinates of S$ (Chandrasekhar1960): in the linear basis. these include the gain. y=|r|9n|$]2. the orientation. and the ellipticity. such that impact of nou-icdeal feed receptors on pulsar timine is analyzed by exploiting a powerful classification of Jones matrices motivated by the polar decomposition.," Therefore, it is common to define a receptor using the spherical coordinates of $\mbf{S}$ \citep{cha60}; in the linear basis, these include the gain, $g=|\mbf{r}|=|\mbf{S}|^{1\over2}$, the orientation, and the ellipticity, such that The impact of non-ideal feed receptors on pulsar timing is analyzed by exploiting a powerful classification of Jones matrices motivated by the polar decomposition."
 Àuy nou- siugularmatrix can be decomposed iuto the product of a uuitary matrix and a positive-definite Hermnitian matrix., Any non-singular matrix can be decomposed into the product of a unitary matrix and a positive-definite Hermitian matrix.
" Using the axis-augle paraiucterization (Britton 2000).. the polar decomposition of a Jones matrix (Ibuuaker2000) is expressed as where J=(det J)2.li positive-definite Ποια, aud is unitary: both aand aare uuinodulu."," Using the axis-angle parameterization \citep{bri00}, the polar decomposition of a Jones matrix \citep{ham00} is expressed as where $J=(\det{\bf J})^{1\over2}$ is positive-definite Hermitian, and is unitary; both and are unimodular."
 The iuit 3-vectors. re and 7%. correspoud to axes of svnuuetry in the three-diniensional space of the Stokes polarization vector.," The unit 3-vectors, $\mbf{\hat m}$ and $\mbf{\hat n}$, correspond to axes of symmetry in the three-dimensional space of the Stokes polarization vector."
 Under the congrueuce transformation of the cohereucyv matrix. the Ποια lnatrices. effect a Lorentz boost of the Stokes. l-vector along the We axis by au inpact paraiueter 22. such that the resulting total intensity. 55=Sycosh23|S+rhsiuh2).," Under the congruence transformation of the coherency matrix, the Hermitian matrices, effect a Lorentz boost of the Stokes 4-vector along the $\mbf{\hat m}$ axis by an impact parameter $2\beta$, such that the resulting total intensity, $S^\prime_0 = S_0 \cosh 2\beta +
\mbf{S\cdot\hat{m}} \sinh 2\beta$."
 Similarly. the unitary matrices. rotate the Stokes polarization vector about the f$ axis bv au augle δω. leaving the total intensity unchauged.," Similarly, the unitary matrices, rotate the Stokes polarization vector about the $\mbf{\hat n}$ axis by an angle $2\phi$, leaving the total intensity unchanged."
 This paraicterization enables the important distinction between polarimetric trausformatious that mix the total and polarized intensities (boosts) and those that effect a change of basis (rotations)., This parameterization enables the important distinction between polarimetric transformations that mix the total and polarized intensities (boosts) and those that effect a change of basis (rotations).
 The primary purpose of this paper is the formal description of the matrix template matching technique and the quantitative comparison of its effectiveness with that of conventional scalar methods., The primary purpose of this paper is the formal description of the matrix template matching technique and the quantitative comparison of its effectiveness with that of conventional scalar methods.
 The performance of a method of TOÀ measurement may be evaluated iu terms of the precision and accuracy of the arrival time estimates that it produces., The performance of a method of TOA measurement may be evaluated in terms of the precision and accuracy of the arrival time estimates that it produces.
 The analvsis of TOA precision requires careful attention to the propagation of experimental error. as described in 23.2...," The analysis of TOA precision requires careful attention to the propagation of experimental error, as described in \ref{sec:precision}."
 TOA accuracy depends upon the susceptibility. of the technique to sources of systematic error., TOA accuracy depends upon the susceptibility of the technique to sources of systematic error.
 To quautitatively compare different methods. a «απο that spaus the full range of potential artifacts is devised iu 3.3.," To quantitatively compare different methods, a simulation that spans the full range of potential artifacts is devised in \ref{sec:accuracy}."
 A pulsus mean pulse profile is measured by integrating the observed flux deusitv as a function of pulse phase., A pulsar's mean pulse profile is measured by integrating the observed flux density as a function of pulse phase.
 By averaging many pulse profiles. one with hieh S/N iav be formed and used as a template against which the individual observations are matched.," By averaging many pulse profiles, one with high S/N may be formed and used as a template against which the individual observations are matched."
 The best-fit phase shift derived by the template matching procedure is then used to compute the pulse TOA., The best-fit phase shift derived by the template matching procedure is then used to compute the pulse TOA.
 Tavlor(1992) prescuts a method for modeling the phase shift between the teiiplate and observed total iutensitv xofiles in the Fourier domain., \cite{tay92} presents a method for modeling the phase shift between the template and observed total intensity profiles in the Fourier domain.
 Iu the cuneit treatment. he scalar equation that relates two total intesusity profiles is replaced * anu analogous matrix equation. which is expressed using the Jones caleulus.," In the current treatment, the scalar equation that relates two total intensity profiles is replaced by an analogous matrix equation, which is expressed using the Jones calculus."
" Let the colercucy uatrices. p/(o,). represent the observed polarization as a function of discrete pulse phase. ορ where 0x09N and Vis the munuber of intervals iuto which the pulse xeriod is evenly divided."," Let the coherency matrices, $\mbf{\rho}^\prime (\phi_n)$, represent the observed polarization as a function of discrete pulse phase, $\phi_n$, where $0\le n< N$ and $N$ is the number of intervals into which the pulse period is evenly divided."
" Each observed polarization profile is related to the template. py(o,,). by the iiatrix equation. where J is the polarimetric transformation. y is the phase slift. ppg. is the DC offset between the two profiles. aud px represcuts the svsteii noise."," Each observed polarization profile is related to the template, $\mbf{\rho}_0(\phi_n)$, by the matrix equation, where ${\bf J}$ is the polarimetric transformation, $\varphi$ is the phase shift, $\mbf{\rho}_{\mathrm DC}$ is the DC offset between the two profiles, and $\mbf{\rho}_{\mathrm N}$ represents the system noise."
" The discrete Fourier transtorma (DET) of is where p, is the discrete frequency.", The discrete Fourier transform (DFT) of is where $\nu_m$ is the discrete frequency.
" Given the observed Stokes pirzuneters. 57(0,). aud their DFTs. 57(17,,). the best-fit model parameters will müunuize the objective ierit function. whereqq ds equal to the rius of the noise in cach DFT and tr is the matrix trace operator."," Given the observed Stokes parameters, $S_k^\prime(\phi_n)$ , and their DFTs, $S_k^\prime(\nu_m)$, the best-fit model parameters will minimize the objective merit function, where$\varsigma_k$ is equal to the rms of the noise in each DFT and $\trace$ is the matrix trace operator."
 As in (200L).. the partial derivatives of are computed with respect to both y and the seven parameters that determine J.," As in \cite{van04}, the partial derivatives of are computed with respect to both $\varphi$ and the seven non-degenerate parameters that determine ${\bf
J}$ ."
 The Leveubere- method is then applied to find the parameters that nuninize u (Pressetal.1992).., The Levenberg-Marquardt method is then applied to find the parameters that minimize $\chi^2$ \citep{ptvf92}..
significant peak in the U band is due to the observing window.,significant peak in the U band is due to the observing window.
 We estimated. the error on the periods. found. by employing a Monte-Carlo technique: we generated: ~ 10.000 data sets with the same variance. amplitude ancl period as the observed. data.," We estimated the error on the periods found by employing a Monte-Carlo technique; we generated $\sim$ 10,000 data sets with the same variance, amplitude and period as the observed data."
 We then subjected the faked data sets to the Lomb-Scargle algorithm: the distribution of the most significant peaks then leads to le error estimates., We then subjected the faked data sets to the Lomb-Scargle algorithm; the distribution of the most significant peaks then leads to $\sigma$ error estimates.
 We also fitted a sine wave to the cata near the found periods. where the errors in the magnituce measurements were scaled so that the fit had a reduced 7 of —1: the Le uncertainty in the period. was determined. using 47=1.," We also fitted a sine wave to the data near the found periods, where the errors in the magnitude measurements were scaled so that the fit had a reduced $\chi^2$ of $\sim$ 1; the $\sigma$ uncertainty in the period was determined using $\Delta\chi^2=1$."
 This resulted in similar error estimates., This resulted in similar error estimates.
 We derived 44:=4.92002:0.0008 clays. and Pe=4.92183+0.0009 clays.," We derived $P_{V} = 4.9200 \pm 0.0008$ days, and $P_{B} = 4.9213 \pm 0.0009$ days."
 Clearly the period. found. in the D and V. band. cata is half the (spectroscopic) orbital period., Clearly the period found in the $B$ and $V$ band data is half the (spectroscopic) orbital period.
 Our analysis therefore gives the first independent. proof of (hall) the orbital period., Our analysis therefore gives the first independent proof of (half) the orbital period.
 No clear peak can be found. near the 78 clay X-ray period (Wijnanes. Ixuulkers SSmale 1996: see also Ixong. Charles IxIxuulkers 1998).," No clear peak can be found near the $\sim 78$ day X-ray period (Wijnands, Kuulkers Smale 1996; see also Kong, Charles Kuulkers 1998)."
 However. other significant peaks are found alee. ~12.1] and ~35.3 davs in V. —10.1 and ~39 clays in D. —10.1. 12.1. 35.3 and ~125 days in C. and ab aliases between the different periods tthe peak at ~0.82 days in V is the alias of half the orbital period and the ~35.3 days period).," However, other significant peaks are found at $\sim 12.1$ and $\sim 35.3$ days in $V$, $\sim 10.1$ and $\sim 39$ days in $B$, $\sim 10.1$, $\sim 12.1$, $\sim 35.3$ and $\sim 125$ days in $U$ , and at aliases between the different periods the peak at $\sim 0.82$ days in $V$ is the alias of half the orbital period and the $\sim 35.3$ days period)."
 We note that the ~35 day period is close to the second significant peak in X-rays reported by Wijnands et ((1996)., We note that the $\sim 35$ day period is close to the second significant peak in X-rays reported by Wijnands et (1996).
 Since only the D and V. band data shows significant orbital variations. we will concentrate only on mean light. curves from these two bands.," Since only the $B$ and $V$ band data shows significant orbital variations, we will concentrate only on mean light curves from these two bands."
 As noted by CGoranskii LLvutvi (1988). XNN-2 shows à strong. concentration of data points towards the lowest magnitudes. which they called the “quiet state” (see Figure 1 of Goranskii LLwutvi 1988 and Figure 2))," As noted by Goranskii Lyutyi (1988), X-2 shows a strong concentration of data points towards the lowest magnitudes, which they called the “quiet state” (see Figure 1 of Goranskii Lyutyi 1988 and Figure \ref{foldall}) )."
 On top of that Cyve N-2 displays increases in brightness on time-scales ranging from x5 days to 710 davs. Lares lasting less than a day. ancl drops inbrightness for a few days (Coranskii LLvutyi LOSS).," On top of that Cyg X-2 displays increases in brightness on time-scales ranging from $\approx 5$ days to $\approx 10$ days, flares lasting less than a day, and drops inbrightness for a few days (Goranskii Lyutyi 1988)."
Alternatively one could consider kinetic instabilities which are known to produce magnetic turbulence at the shock Ivont Ge~0).,Alternatively one could consider kinetic instabilities which are known to produce magnetic turbulence at the shock front $x\simeq 0$ ).
 The instabilities should not operate in the downstream region and hence the growth rate would vanish there., The instabilities should not operate in the downstream region and hence the growth rate would vanish there.
 Equation 2 must be separately solved on either side of the shock., Equation \ref{2} must be separately solved on either side of the shock.
 As boundary condition we may assume absence of turbulence lar ahead of the shock. VW(A.=σκι)0. whereas the MIID jump condiüons applied to the upstream solution at c=0 provide the boundary condition for the downstream solution al 7—0 (Vainio&Schlickeiser1999).," As boundary condition we may assume absence of turbulence far ahead of the shock, $W(k,x=-\infty)=0$, whereas the MHD jump conditions applied to the upstream solution at $x=0$ provide the boundary condition for the downstream solution at $x\rightarrow 0$ \citep{vs99}."
. Earlier studies found that the streaming instability curing the early stages of SNR evolution can be so strong that the amplified turbulent. magnetic field 0B>100μα far exceed the undisturbed magnetic field B2(3—10)iG. upstream of the SNR. blast wave (Lucek&Bell2000:DellLucek2001).," Earlier studies found that the streaming instability during the early stages of SNR evolution can be so strong that the amplified turbulent magnetic field $\delta B\gtrsim 100 \ {\rm \mu G}$ far exceed the undisturbed magnetic field $B\approx (3-10)\,{\rm \mu G}$ upstream of the SNR blast wave \citep{lb00,bl01}."
". The cosmic-ray diffiision coefficient & should then be close to the Bolu limit. and consequently both the cosmic ravs with energy. ἐς ancl the amplified magnetic field would in the upstream region be confined to a shock precursor zone of thickness where UL, is the SNR shock velocity."," The cosmic-ray diffusion coefficient $\kappa$ should then be close to the Bohm limit, and consequently both the cosmic rays with energy $E$ and the amplified magnetic field would in the upstream region be confined to a shock precursor zone of thickness where $U_s$ is the SNR shock velocity."
 Let us in the following assume that the streaming instability has efficiently produced strong magnetic fields in the precursor zone., Let us in the following assume that the streaming instability has efficiently produced strong magnetic fields in the precursor zone.
 The magnitude of the amplified magnetic field upstream of the shock depends on the efficiency of (he various possible damping mechanisms., The magnitude of the amplified magnetic field upstream of the shock depends on the efficiency of the various possible damping mechanisms.
 In anv case a fraction of the magnetic turbulence will propagate through the shock to the downstream region. where it will convect away [rom the shock.," In any case a fraction of the magnetic turbulence will propagate through the shock to the downstream region, where it will convect away from the shock."
 We are interested in the spatial scale. on which the amplilied magnetic energv is damped downstream of the shock.," We are interested in the spatial scale, on which the amplified magnetic energy is damped downstream of the shock."
 If (his length scale is small compared with the dimensions of a supernova rennant. then the streaming instability essentially produces a magnetic filament at the location of the forwad shock. that should be observable as a non-thermal X-ray. filament on account of enhanced," If this length scale is small compared with the dimensions of a supernova remnant, then the streaming instability essentially produces a magnetic filament at the location of the forward shock, that should be observable as a non-thermal X-ray filament on account of enhanced"
are more homogeneous or more diverse than the general population of elliptical galaxies.,are more homogeneous or more diverse than the general population of elliptical galaxies.
 In this paper. we look at the stellar populations of BCCGs. by measuring the strength. of the 2.203/ m. CO absorption feature for 21 BCGs. and. comparing the distribution of values with similar measurements for a large sample of field. group ancl cluster ellipticals (Mobasher James 1996: James Mobasher 1999: Mobasher James 2000).," In this paper, we look at the stellar populations of BCGs, by measuring the strength of the $\mu$ m CO absorption feature for 21 BCGs, and comparing the distribution of values with similar measurements for a large sample of field, group and cluster ellipticals (Mobasher James 1996; James Mobasher 1999; Mobasher James 2000)."
" CO strength contains information on receney of star formation. since it is very strong in supergiants (present 10° 107? vears after a burst of star formation). strong in the cool AGB stars which contribute significantly to the near-I light after 107 10"" vears (Renzini Buzzoni 1986: Oliva et al."," CO strength contains information on recency of star formation, since it is very strong in supergiants (present $^7$ $^8$ years after a burst of star formation), strong in the cool AGB stars which contribute significantly to the near-IR light after $^8$ $^9$ years (Renzini Buzzoni 1986; Oliva et al."
 1995). and somewhat weaker in older populations.," 1995), and somewhat weaker in older populations."
 I also displavs some metallicity dependence. being weak in very low metallicity elobular clusters (Origliaetal.1997).," It also displays some metallicity dependence, being weak in very low metallicity globular clusters \cite{or:97}."
. This dependence was quantified by Dovon. Joseph Wrieh (1994).. and further studied in Mobasher James (1999).," This dependence was quantified by Doyon, Joseph Wright \shortcite{do:94}, and further studied in Mobasher James \shortcite{mo:99}."
. Such studies of BCGs are particularly significan considering the apparent large-scale velocity Low founc by Lauer Postman (1994)., Such studies of BCGs are particularly significant considering the apparent large-scale velocity flow found by Lauer Postman \shortcite{la:94}.
". Using a sample of 119 3XC6s out to a redshift, of 15000 +. they found. the restframe defined by the galaxies to diller from that of the Cosmic Microwave Background by almost 700 +."," Using a sample of 119 BCGs out to a redshift of 15000 $^{-1}$, they found the restframe defined by the galaxies to differ from that of the Cosmic Microwave Background by almost 700 $^{-1}$."
 This result has been interpreted as evidence for a cosmological streaming Blow. but an alternative explanation would. be that BCC properties vary systematically around: the sky. for example due to stellar population changes from galaxy to galaxy.," This result has been interpreted as evidence for a cosmological streaming flow, but an alternative explanation would be that BCG properties vary systematically around the sky, for example due to stellar population changes from galaxy to galaxy."
 This provides a further motivation for the present stucly., This provides a further motivation for the present study.
 The organisation of this paper is as follows., The organisation of this paper is as follows.
 Section 2 cleseribes the selection of target. galaxies. the observations. and the data reduction.," Section 2 describes the selection of target galaxies, the observations, and the data reduction."
 Section 3 contains the main results. including a comparison of CO absorption. strengths of DBCCGs and other elliptical galaxies. and correlations of CO strengths with other galaxy parameters.," Section 3 contains the main results, including a comparison of CO absorption strengths of BCGs and other elliptical galaxies, and correlations of CO strengths with other galaxy parameters."
 Section 4 suminarises the main conclusions., Section 4 summarises the main conclusions.
 The galaxy sample was selected from the BCG list of Lauer Postman (1994)., The galaxy sample was selected from the BCG list of Lauer Postman \shortcite{la:94}.
. All have measured recession velocities less than 15.000 ἐν with Ro band photometry presented in Lauer Postman (1994).," All have measured recession velocities less than 15,000 $^{-1}$, with R band photometry presented in Lauer Postman \shortcite{la:94}."
". The observations presented here were carried. out using the United. Ixingdom Infrared. ""Telescope (UIXIICE) during the 4 nights of 2124 February 1999.", The observations presented here were carried out using the United Kingdom Infrared Telescope (UKIRT) during the 4 nights of 21–24 February 1999.
 The instrument used was the long-slit near-L1t spectrometer COSA. with the 40 lino mm erating and the long-focal-length (300 mm) camera.," The instrument used was the long-slit near-IR spectrometer CGS4, with the 40 line $^{-1}$ grating and the long-focal-length (300 mm) camera."
 The 4-pixel-wide slit was chosen. corresponding to a projected width on the sky of 2.4 aresec.," The 4-pixel-wide slit was chosen, corresponding to a projected width on the sky of 2.4 arcsec."
 Working in Ist order at a central wavelength of 2.2 pin. this gave coverage of the entire Ix window.," Working in 1st order at a central wavelength of 2.2 $\mu m$ , this gave coverage of the entire K window."
 Phe CO absorption [eature. required for this study. extends from 2.293 µη (rest frame) into the Ix-band atmospheric eut-olf.," The CO absorption feature, required for this study, extends from 2.293 $\mu m$ (rest frame) into the K-band atmospheric cut-off."
 The principal uncertainty in determining the absorption depth comes from estimating the level and slope of the continuum shortward of this absorption which requires wavelength coverage down to at least 2.2 yen anc preferably to shorter wavelengths., The principal uncertainty in determining the absorption depth comes from estimating the level and slope of the continuum shortward of this absorption which requires wavelength coverage down to at least 2.2 $\mu m$ and preferably to shorter wavelengths.
 ‘There are many regions of the continuum free from lines even at this relatively low resolution., There are many regions of the continuum free from lines even at this relatively low resolution.
 The cllective resolution. including the degradation caused by the wide slit. is about 230.," The effective resolution, including the degradation caused by the wide slit, is about 230."
 For cach observation. the galaxy was centred. on the slit by maximising the LR signal. using an automatic peak-up facility.," For each observation, the galaxy was centred on the slit by maximising the IR signal, using an automatic peak-up facility."
 Total on-chip integration times of 12 minutes were used for the brightest and most centrallv-concentrated ellipticals while an integration time of 24 minutes was more typically: required., Total on-chip integration times of 12 minutes were used for the brightest and most centrally-concentrated ellipticals while an integration time of 24 minutes was more typically required.
 During this time. the galaxy was slicl up and down the slit at one minute intervals by 22 aresec. giving two olfset spectra which were subtracted to remove most of the sky emission.," During this time, the galaxy was slid up and down the slit at one minute intervals by 22 arcsec, giving two offset spectra which were subtracted to remove most of the sky emission."
 Moreover. the array was moved bv L1 pixel in the spectral direction. between integrations to enable bad. pixel replacement in the final spectra.," Moreover, the array was moved by 1 pixel in the spectral direction between integrations to enable bad pixel replacement in the final spectra."
 Stars of spectral types AQAG. suitable for monitoring telluric absorption. were observed in the same wav before and alter cach galaxy. with airmasses matching those of the galaxy observations as closely as possible.," Stars of spectral types A0–A6, suitable for monitoring telluric absorption, were observed in the same way before and after each galaxy, with airmasses matching those of the galaxy observations as closely as possible."
 Flat fields and argon are spectra were taken using the CGS+4 calibration lamps., Flat fields and argon arc spectra were taken using the CGS4 calibration lamps.
 A otal of 21 brightest cluster galaxies was observed., A total of 21 brightest cluster galaxies was observed.
 The data reduction was performed. using the FIGARO xickage in the STARLININ environment., The data reduction was performed using the FIGARO package in the STARLINK environment.
 The spectra were latfieldecl and polynomials fitted to estimate and. remove he sky background., The spectra were flatfielded and polynomials fitted to estimate and remove the sky background.
 These spectra were then shifted. to he rest frame of the galaxy. using redshifts [from Lauer Postman (1994).," These spectra were then shifted to the rest frame of the galaxy, using redshifts from Lauer Postman \shortcite{la:94}."
. The atmospheric transmissions were corrected by dividing cach spectrum with the spectrum of he star observed. closely in time to the galaxy. ancl at a similar airmass.," The atmospheric transmissions were corrected by dividing each spectrum with the spectrum of the star observed closely in time to the galaxy, and at a similar airmass."
 The resulting spectrum was converted into a normalised. rectified spectrum by. fitting a power-aw to featureless sections of the continuum and. dividing he whole spectrum by this power-law. extrapolated over he full wavelength range.," The resulting spectrum was converted into a normalised, rectified spectrum by fitting a power-law to featureless sections of the continuum and dividing the whole spectrum by this power-law, extrapolated over the full wavelength range."
 Two rectified spectra are shown in Fig., Two rectified spectra are shown in Fig.
 1., 1.
 Phe apparent emission features at 2.14 fam ancl 2.10 yam are artefacts caused by absorptions in the A stars used for atmospheric transmission correction. and appear in dillerent. positions because of the restframe corrections.," The apparent emission features at 2.14 $\mu$ m and 2.10 $\mu$ m are artefacts caused by absorptions in the A stars used for atmospheric transmission correction, and appear in different positions because of the restframe corrections."
 To measure the depth ofthe CO absorption feature. the procedure outlined in James Mobasher (1999). is. used.," To measure the depth of the CO absorption feature, the procedure outlined in James Mobasher \shortcite{ja:99} is used."
 The restframe. rectified spectra were rebinned to à common wavelength range and number of pixels. to avoid rounding errors in the effective wavelength range sampled by a given number of pixels.," The restframe, rectified spectra were rebinned to a common wavelength range and number of pixels, to avoid rounding errors in the effective wavelength range sampled by a given number of pixels."
 The CO strength for each spectrum was determined. using the method. of Puxles. Dovon Ward (1997).," The CO strength for each spectrum was determined using the method of Puxley, Doyon Ward \shortcite{pu:97}."
. Thev advocate the use of an equivalent width. COrw. which is determined within the CO. absorption feature between rest-frame wavelengths of 2.293. ja and 2.320 pm. This wavelength range was found by Pusxley et al.," They advocate the use of an equivalent width, $_{EW}$, which is determined within the CO absorption feature between rest-frame wavelengths of 2.293 $\mu$ m and 2.320 $\mu$ m. This wavelength range was found by Puxley et al."
 (1907) to give maximum sensitivity to stellar population variations. and can be used forgalaxies with recession velocities of up to 718000 1 before the spectral region of interest. shifts out of the usable Ix. window.," \shortcite{pu:97} to give maximum sensitivity to stellar population variations, and can be used forgalaxies with recession velocities of up to $\sim$ 18000 $^{-1}$ before the spectral region of interest shifts out of the usable K window."
 This is not, This is not
are better suited to the physics of RT-driven turbulence in thermonuclear supernovae.,are better suited to the physics of RT-driven turbulence in thermonuclear supernovae.
 Our proposition is corroborated by the the scaling properties of the structure functions that will be presented in the following Section., Our proposition is corroborated by the the scaling properties of the structure functions that will be presented in the following Section.
 The radial and angular structure functions of order p are defined by the averages of the radial and angular velocity increments to the power p. respectively: where the length scale (:=|r»—r;|.," The radial and angular structure functions of order $p$ are defined by the averages of the radial and angular velocity increments to the power $p$, respectively: where the length scale $\ell:=|\mathbf{r}_{2}-\mathbf{r}_{1}|$."
 There is a large range of length scales which encompasses the turbulent interior of the exploding WD., There is a large range of length scales which encompasses the turbulent interior of the exploding WD.
" For fully developed turbulence the structure functions are given by power laws $5,440)X(5o and ρω)XCorre. where Cprad and Έρως are Characteristic scaling exponents."," For fully developed turbulence the structure functions are given by power laws $S_{p,\mathrm{rad}}(\ell)\propto\ell^{\zeta_{p,\mathrm{rad}}}$ and $S_{p,\mathrm{ang}}(\ell)\propto\ell^{\zeta_{p,\mathrm{ang}}}$, where $\zeta_{p,\mathrm{rad}}$ and $\zeta_{p,\mathrm{ang}}$ are characteristic scaling exponents."
" If we further assume isotropy. Gp;7 ANd 6,=p/3 according to the theoretical analysis by Cpang-Kolmogorov(194)."," If we further assume isotropy, $\zeta_{p,\mathrm{rad}}\simeq\zeta_{p,\mathrm{ang}}$, and $\zeta_p=p/3$ according to the theoretical analysis by \citet{Kolmogorov41}."
. In particular. it follows that the turbulent velocity fluctuation v/(£)X(47.," In particular, it follows that the turbulent velocity fluctuation $v'(\ell)\propto\ell^{1/3}$."
" Forthe turbulent flow driven by the RT instability. on the other hand. v/(£)~(> &Taylor1950) corresponding to ¢,=p/2."," Forthe turbulent flow driven by the RT instability, on the other hand, $v'(\ell)\propto\ell^{1/2}$ \citep{DavTay50} corresponding to $\zeta_p=p/2$."
 For the numerical computation of the structure functions. one has to take a sufficient. large number of sample points that are distributed with uniform probability within à spherical region of prescribed radius in order to achieve converged statistics.," For the numerical computation of the structure functions, one has to take a sufficient large number of sample points that are distributed with uniform probability within a spherical region of prescribed radius in order to achieve converged statistics."
 This was achieved by à Monte-Carlo-type algorithm. where the total number of sample points was varied and. thereby. convergence was established.," This was achieved by a Monte-Carlo-type algorithm, where the total number of sample points was varied and, thereby, convergence was established."
 In order to analyze the isotropy of the velocity field elose to the flame. we performed calculations in small boxes intersected by the flame.," In order to analyze the isotropy of the velocity field close to the flame, we performed calculations in small boxes intersected by the flame."
 The algorithm is based on the analysis performed by Zingaleetal.(2005)., The algorithm is based on the analysis performed by \citet{Zingale05}.
.. To simplify the calculation. the box is placed along a coordinate axis. in our case the z-axis. which defines the local direction of gravity.," To simplify the calculation, the box is placed along a coordinate axis, in our case the $z$ -axis, which defines the local direction of gravity."
 For each cell within the box. the velocity difference ὃν between the local velocity and the velocity at the center of the box is calculated.," For each cell within the box, the velocity difference $\delta\mathbf{v}$ between the local velocity and the velocity at the center of the box is calculated."
" Then projected contours of the velocity differences in Fourier space can be constructed. by integrating àv(K) over circles of radius k,,=tK in planes perpendicular to the z-component of k."," Then projected contours of the velocity differences in Fourier space can be constructed, by integrating $\delta\hat{\mathbf{v}}(\mathbf{k})$ over circles of radius $k_\rho= \sqrt{k^2_x + k^2_y}$ in planes perpendicular to the $z$ -component of $\mathbf{k}$."
 This MSprocedure was applied for several positions of the box center corresponding to different fractions of burned matter in the box., This procedure was applied for several positions of the box center corresponding to different fractions of burned matter in the box.
" We plot the energy spectra as functions of the normalized wave number &,=512Ao(f)k/a for 16<Ky512. where Aj(r) is the size of the cells in the uniform part of the grid at time r."," We plot the energy spectra as functions of the normalized wave number $k_{\mathrm{n}} = 512\Delta_0(t)k/\pi$ for $16\le k_{\mathrm{n}}\le
512$, where $\Delta_0(t)$ is the size of the cells in the uniform part of the grid at time $t$."
 We have Ao(r)=2.93 and 14.69km at times ¢20.5 and 1.0 seconds. respectively.," We have $\Delta_0(t)=2.93$ and $14.69\,\mathrm{km}$ at times $t=0.5$ and $1.0$ seconds, respectively."
" Note that wave numbers &,<32 are obscured by data windowing (see Section 2)).", Note that wave numbers $k_{\mathrm{n}}<32$ are obscured by data windowing (see Section \ref{Analysis}) ).
 The computed energy spectrum functions at 0.5 seconds are shown as black curves in Fig., The computed energy spectrum functions at 0.5 seconds are shown as black curves in Fig.
 | (a)., \ref{Fig:1} (a).
 The thin gray lines corresponds to power- fits and the dashed line indicates the expected spectrum according to the Kolmogorov theory with an exponent .= 5/3., The thin gray lines corresponds to power-law fits and the dashed line indicates the expected spectrum according to the Kolmogorov theory with an exponent $\beta = 5/3$ .
 For the longitudinal spectrum function. we find .}z1.64 for high wave numbers. which is in good agreement with the Kolmogorov theory.," For the longitudinal spectrum function, we find $\beta \approx 1.64$ for high wave numbers, which is in good agreement with the Kolmogorov theory."
 The longitudinal spectrum possibly stiffens toward lower wave numbers. but the accuracy of the computed spectra does not allow for a conclusive result.," The longitudinal spectrum possibly stiffens toward lower wave numbers, but the accuracy of the computed spectra does not allow for a conclusive result."
 We exclude the lower part of wavenumbers from the fit. because the slope becomes steeper than a Kolmogorov spectrum for ky<64.," We exclude the lower part of wavenumbers from the fit, because the slope becomes steeper than a Kolmogorov spectrum for $k_\mathrm{n}\lesssim 64$."
 The transversal spectrum is slightly steeper (.7~1.71). but close to a Kolmogorov spectrum for the whole range of wave numbers.," The transversal spectrum is slightly steeper $\beta \approx 1.71$ ), but close to a Kolmogorov spectrum for the whole range of wave numbers."
 These results were corroborated by the computation of second-order structure funetions with much higher accuracy (see section 3.2))., These results were corroborated by the computation of second-order structure functions with much higher accuracy (see section \ref{ResultsII}) ).
 We also note that the Kolmogorov scaling for higher wave numbers agrees with the findings of Répkeetal.(2007).. where turbulence energy spectra were computed without splitting the velocity. field.," We also note that the Kolmogorov scaling for higher wave numbers agrees with the findings of \citet{RoepHille07}, where turbulence energy spectra were computed without splitting the velocity field."
 This is m accordance with the expectation that the radial expansion will mostly affect low wave numbers modes., This is in accordance with the expectation that the radial expansion will mostly affect low wave numbers modes.
 At t=1.0 seconds. on the other hand. the longitudinal spectrum has an exponent 3}z1.97 over the entire range of wave numbers.," At $t=1.0$ seconds, on the other hand, the longitudinal spectrum has an exponent $\beta \approx 1.97$ over the entire range of wave numbers."
 In contrast. the transverse spectrum is much shallower.," In contrast, the transverse spectrum is much shallower."
 The exponent ./=2 corresponds to RT scaling. because E(k)&K7 implies à)x(7.," The exponent $\beta= 2$ corresponds to RT scaling, because $E(k)\propto k^{-2}$ implies $\delta v(\ell)\propto \ell^{1/2}$."
 Consequently. it appears that the velocity component in the direction of gravity 1s dominated by the RT instability even at the smallest numerically resolved scales in the late phase of the explosion. while Kolmogorov sealing is found for the velocity component perpendicular to gravity.," Consequently, it appears that the velocity component in the direction of gravity is dominated by the RT instability even at the smallest numerically resolved scales in the late phase of the explosion, while Kolmogorov scaling is found for the velocity component perpendicular to gravity."
 For the computation of the structure functions following equation (4a)) and (4b)) we chose a spherical region in which of the material was burned.," For the computation of the structure functions following equation \ref{Eq:5a}) ) and \ref{Eq:5b}) ), we chose a spherical region in which of the material was burned."
 This choice of the region resulted from the requirement of encompassing the bulk of turbulence at a given time. while excluding the outer. non-turbulent regions of the white dwarf.," This choice of the region resulted from the requirement of encompassing the bulk of turbulence at a given time, while excluding the outer, non-turbulent regions of the white dwarf."
 Fig., Fig.
 2 shows double-logarithmie plots of the radial (solid curve) and angular (dashed curve) structure functions of second order at different times., \ref{Fig:2} shows double-logarithmic plots of the radial (solid curve) and angular (dashed curve) structure functions of second order at different times.
 In all cases up to ¢=0.7 seconds. a scaling exponent c» close to 2/3 1s found for the range of length scales (X10km.," In all cases up to $t=0.7$ seconds, a scaling exponent $\zeta_{2}$ close to $2/3$ is found for the range of length scales $\ell\lesssim 10\,\mathrm{km}$."
 Moreover. ρω)© which indicates isotropy at small length scales.," Moreover, $S_{p,\mathrm{rad}}(\ell)\approx S_{p,\mathrm{ang}}(\ell)$, which indicates isotropy at small length scales."
 ForSpass). larger length scales. on the other hand. the radial structure functions μας) obey à scaling law with an exponent ὅτι7:1. whereas $5450) still follows Kolmogorov scaling.," For larger length scales, on the other hand, the radial structure functions $S_{p,\mathrm{rad}}(\ell)$ obey a scaling law with an exponent $\zeta_{2,\mathrm{rad}}\approx 1$, whereas $S_{p,\mathrm{ang}}(\ell)$ still follows Kolmogorov scaling."
 From Cs:71. it follows that v/()x(7.," From $\zeta_{2,\mathrm{rad}}\approx 1$, it follows that $v'(\ell)\propto\ell^{1/2}$."
 As outlined in section 2.. this corresponds to RT scaling.," As outlined in section \ref{Analysis}, this corresponds to RT scaling."
 For this reason. the change of slope of the radial structure function indicates a transition from the inertial-range turbulence cascade to the regime of RT instabilities at a length scale (κε approaching ~I4km in the course of the explosion.," For this reason, the change of slope of the radial structure function indicates a transition from the inertial-range turbulence cascade to the regime of RT instabilities at a length scale $\ell_{\mathrm{K/RT}}$ approaching $\approx 14\,\mathrm{km}$ in the course of the explosion."
 Thus. our analysis confirms the estimate by Niemeyer&Woosley(1997).," Thus, our analysis confirms the estimate by \citet{NieWoos97}."
. As a result of the overall expansion of the co-moving grid. the transition length drops below the numerical resolution of the simulation after ~ 0.7 to 1.0 seconds.," As a result of the overall expansion of the co-moving grid, the transition length drops below the numerical resolution of the simulation after $\sim$ $0.7$ to $1.0$ seconds."
 The time evolution of ἐκ 18 further illustrated in Fig. 3..," The time evolution of $\ell_{\mathrm{K/RT}}$ is further illustrated in Fig. \ref{Fig:3},"
 where the second order structure functions are plotted for all data sets. for which (xy; is numerically resolved.," where the second order structure functions are plotted for all data sets, for which $\ell_{\mathrm{K/RT}}$ is numerically resolved."
 While in Fig., While in Fig.
 2 the range of length scales is adjusted to the size of the co-moving grid. a fixed range of length scales is used in. Fig. 3..," \ref{Fig:2} the range of length scales is adjusted to the size of the co-moving grid, a fixed range of length scales is used in Fig. \ref{Fig:3}. ."
 Additionally. the typical mass density in the vicinity of the flame front is specified for each instant of time.," Additionally, the typical mass density in the vicinity of the flame front is specified for each instant of time."
 In agreement with Fig., In agreement with Fig.
 | of Niemeyer&Woosley (1997).. Fig.," 1 of \citet{NieWoos97}, , Fig."
 2 and 3 show that (x-y; becomes smaller with decreasing density (and advancing time)., 2 and 3 show that $\ell_{\mathrm{K/RT}}$ becomes smaller with decreasing density (and advancing time).
 Remarkably. it appears that (cj; approaches an asymptotic value. but we cannot investigate this behavior forf>0.8 seconds.," Remarkably, it appears that $\ell_{\mathrm{K/RT}}$ approaches an asymptotic value, but we cannot investigate this behavior for $t > 0.8$ seconds."
 To obtain more properties of (yqe additional high-resolved numerical simulations are needed. in which (κ. can be tracked for a longer time.," To obtain more properties of $\ell_{\mathrm{K/RT}}$ additional high-resolved numerical simulations are needed, in which $\ell_{\mathrm{K/RT}}$ can be tracked for a longer time."
 In Figure 4.. the structure functions up to the sixth order are plotted for ¢2 0.5. 0.6 and 0.7 seconds.," In Figure \ref{Fig:4},, the structure functions up to the sixth order are plotted for $t=0.5$ , $0.6$ and $0.7$ seconds."
 As one can see, As one can see
a separation D Ξ AU between the stars (so that the WCR is radiative; see $ 3).,a separation $D=$ 4 AU between the stars (so that the WCR is radiative; see $\S$ 3).
 The result is shown in Figure 3.., The result is shown in Figure \ref{f3}.
 It shows the contribution to the total radio emission of the unshocked stellar winds and the WCR., It shows the contribution to the total radio emission of the unshocked stellar winds and the WCR.
 As expected for tonized stellar envelopes (see $ 1). the flux densities from the stellar winds increases ds ~5.," As expected for ionized stellar envelopes (see $\S$ 1), the flux densities from the stellar winds increases as $\sim \nu^{0.6}$."
 However. deviation from the expected 0.6 value of the spectral index at high frequencies 1s observed from the emission of the wind source |.," However, deviation from the expected 0.6 value of the spectral index at high frequencies is observed from the emission of the wind source 1."
 This is probably due to the presence of the WCR inside the optically thick region of the wind., This is probably due to the presence of the WCR inside the optically thick region of the wind.
 We note that as v increases the emission from the WCR becomes more important., We note that as $\nu$ increases the emission from the WCR becomes more important.
 The intrinsic flux density from the WCR shows a spectral index of ~l.l. consistent with the numerical models (in massive O«O type binary stars) developed by Pittard (2010).," The intrinsic flux density from the WCR shows a spectral index of $\sim 1.1$, consistent with the numerical models (in massive O+O type binary stars) developed by Pittard (2010)."
" At low frequencies. the total flux density grows as S,~v? approaching the emission from the stronger wind."," At low frequencies, the total flux density grows as $S_{\nu}\sim \nu^{0.6}$ approaching the emission from the stronger wind."
" On the other hand. at higher frequencies. the radio spectrum from the system approaches the flux density from the WCR (S,~v! "," On the other hand, at higher frequencies, the radio spectrum from the system approaches the flux density from the WCR $S_{\nu}\sim \nu^{1.1}$ )."
As mentioned in § l. radio observations (e.g. Moran et al.," As mentioned in $\S$ 1, radio observations (e.g. Moran et al."
 1989: Dougherty. Williams & Pollaco 2000: Montes et al.," 1989; Dougherty, Williams $\&$ Pollaco 2000; Montes et al."
 2009) and theoretical models (see. for instance. Dougherty et al.," 2009) and theoretical models (see, for instance, Dougherty et al."
 2003; Pittard et al., 2003; Pittard et al.
 2006: Pittard 2000) of massive binary stars have revealed strong shocks formed in the wind-wind interaction zone., 2006; Pittard 2000) of massive binary stars have revealed strong shocks formed in the wind-wind interaction zone.
 These shocks emit radio-continuum radiation consistent with thermal emission thàt may produce variations in the expected flux densities and spectral indices from ionized stellar winds., These shocks emit radio-continuum radiation consistent with thermal emission that may produce variations in the expected flux densities and spectral indices from ionized stellar winds.
 In this section. we apply the model of colliding-wind binary systems developed in § 2 by adopting different wind parameters of the components.," In this section, we apply the model of colliding-wind binary systems developed in $\S$ 2 by adopting different wind parameters of the components."
 Our model assumes strong radiative shocks which collapse onto a thin shell. so that the width of the WCR can be neglected.," Our model assumes strong radiative shocks which collapse onto a thin shell, so that the width of the WCR can be neglected."
 We investigate the contribution of the WCR to the thermal radiation from colliding-wind binaries. and the effect of the binary separation on the radio spectrum.," We investigate the contribution of the WCR to the thermal radiation from colliding-wind binaries, and the effect of the binary separation on the radio spectrum."
 Stevens. Blondin & Pollock (1992) investigated the collision of stellar winds in early-type binary systems.," Stevens, Blondin $\&$ Pollock (1992) investigated the collision of stellar winds in early-type binary systems."
 They studied the role of radiative cooling in the structure and dynamics of colliding wind binaries., They studied the role of radiative cooling in the structure and dynamics of colliding wind binaries.
 In this work. the importance of cooling in a particular system is quantified using the cooling parameter y (=0.15ENdau/Ms. where vi the wind velocity in units of 10kms!. dau the distance to the contact discontinuity in units of AU. and Ms is the mass loss rate in units of 107?M.yr! ). defined as the ratio of the cooling time of the shocked gas to the escape time from the intershock region.," In this work, the importance of cooling in a particular system is quantified using the cooling parameter $\chi$ $\approx 0.15 \, v_3^4\,d_{\rm{AU}}/\dot{M}_5$, where $v_3$ the wind velocity in units of $10^3\,\rm{km}\,s^{-1}$, $d_{\rm{AU}}$ the distance to the contact discontinuity in units of AU, and $\dot{M}_5$ is the mass loss rate in units of $10^{-5}\,\rm{M_\odot \, yr^{-1}}$ ), defined as the ratio of the cooling time of the shocked gas to the escape time from the intershock region."
 For models with y> I. the postshock flow can be assumed to be adiabatic. while it is roughly isothermal for models with y< I.," For models with $\chi \ge$ 1, the postshock flow can be assumed to be adiabatic, while it is roughly isothermal for models with $\chi \ll$ 1."
 Numerical simulations by these authors show that the cooling result in the formation of a thin dense shell. confined by isothermal shocks. as y drops below unity.," Numerical simulations by these authors show that the cooling result in the formation of a thin dense shell, confined by isothermal shocks, as $\chi$ drops below unity."
 Antokhin. Owocki. & Brown (2004) have also investigated the narrowness of the cooling layer using the ratio /o/R (where {0 Is the cooling length and R the radius from the star source). which is closely related to the above parameter y.," Antokhin, Owocki, $\&$ Brown (2004) have also investigated the narrowness of the cooling layer using the ratio $l_0/ R$ (where $l_0$ is the cooling length and $R$ the radius from the star source), which is closely related to the above parameter $\chi$."
 These authors show that the ratio /)/R can serve as well to distinguish between adiabatic and radiative shocks. with /o/R.>| implying an adiabatic shock and /o/R<| a radiative one.," These authors show that the ratio $l_0/ R$ can serve as well to distinguish between adiabatic and radiative shocks, with $l_0/ R>1$ implying an adiabatic shock and $l_0/ R < 1$ a radiative one."
 Nonetheless. radiative pressure that moderates the windwind collisior may be important in close hot-star binaries.," Nonetheless, radiative pressure that moderates the wind-wind collision may be important in close hot-star binaries."
 An initial analysis was developed by Stevens & Pollock (1994). who investigated the dynamics of colliding winds in massive binary systems.," An initial analysis was developed by Stevens $\&$ Pollock (1994), who investigated the dynamics of colliding winds in massive binary systems."
 They show that. in close binaries. the radiation of a luminous star inhibits the initial. acceleration of the companion’s wind towards the stagnation point.," They show that, in close binaries, the radiation of a luminous star inhibits the initial acceleration of the companion's wind towards the stagnation point."
 These radiative forces result in lower velocities than those expected in single-star nodels moderating the wind collision., These radiative forces result in lower velocities than those expected in single-star models moderating the wind collision.
 In other work. Gayley. Owocki & Cranmer (1997) investigated the potential role of the radiative braking effect. whereby the primary winc is decelerated by radiation pressure às. it approaches the surface of the companion star.," In other work, Gayley, Owocki $\&$ Cranmer (1997) investigated the potential role of the radiative braking effect, whereby the primary wind is decelerated by radiation pressure as it approaches the surface of the companion star."
 These authors conclud that radiative braking must have a significant effect for wind-wind collision in. WR+O_ binaries with medium separations (D.< 0.5 AU)., These authors conclud that radiative braking must have a significant effect for wind-wind collision in WR+O binaries with medium separations $D<$ 0.5 AU).
 Furthermore. Parkin and Pittard (2008) carried out 3D hydrodynamical simulations of colliding winds in binary systems.," Furthermore, Parkin and Pittard (2008) carried out 3D hydrodynamical simulations of colliding winds in binary systems."
 They shows that the shape of the WCR ts deformed by Coriolis forces into spiral structures by the motion of the stars., They shows that the shape of the WCR is deformed by Coriolis forces into spiral structures by the motion of the stars.
 The shape of the shock layer is more deformed in systems with eccentric orbits., The shape of the shock layer is more deformed in systems with eccentric orbits.
 In addition. Pittard (2010) developed 3D hydrodynamical models of massive O-O star binaries for computing the thermal radio to submillimeter emission.," In addition, Pittard (2010) developed 3D hydrodynamical models of massive O+O star binaries for computing the thermal radio to submillimeter emission."
 In this work. flux and spectral index variations with orbital phase and orientation of the observer (from radiative and adiabatic systems) are investigated.," In this work, flux and spectral index variations with orbital phase and orientation of the observer (from radiative and adiabatic systems) are investigated."
 These authors found strong, These authors found strong
We computed the monochromatic flux at the central frequency of each band. normalizing the fluxes by taking into account the spectral shape of the afterglow (using published spectral indexes or a value of 1.0 in the case of an unknown value).,"We computed the monochromatic flux at the central frequency of each band, normalizing the fluxes by taking into account the spectral shape of the afterglow (using published spectral indexes or a value of 1.0 in the case of an unknown value)."
 The corrected light curves are presented in Fig. 2.., The corrected light curves are presented in Fig. \ref{Fig_traite}.
 As one can clearly see inFig. 2..," As one can clearly see inFig. \ref{Fig_traite},"
 we observe a hint of clustering of luminosity into two groups., we observe a hint of clustering of luminosity into two groups.
 From the sample of 19 events. 14 belong to a group of bright events. 3 to a group of dim events. and 2 are isolated.," From the sample of 19 events, 14 belong to a group of bright events, 3 to a group of dim events, and 2 are isolated."
 In the following. we will use the notation of Gendreetal.(2008): bright events in X-ray (0) or optical (ο) are labeled with a7. and dim events are labeled with a7/7. A burst bright in the optical and dim in X-rays may thus be labeled asv//-of.," In the following, we will use the notation of \citet{gen08} : bright events in X-ray ) or optical ) are labeled with a, and dim events are labeled with a. A burst bright in the optical and dim in X-rays may thus be labeled as."
 Outliers are labeled with a7/7. We note that the infrared groups are identical to the ones observed by Kannetal.(2006);Liang&Zhang(2006):Nardini(2006) : we will thus not introduce the labeli7 but use the label to discuss the infrared luminosity clustering.," Outliers are labeled with a. We note that the infrared groups are identical to the ones observed by \citet{kan06, lia06, nar06} : we will thus not introduce the label but use the label to discuss the infrared luminosity clustering."
 This reinforce the hypothesis that the clustering of infrared luminosity 15 not spurious., This reinforce the hypothesis that the clustering of infrared luminosity is not spurious.
 The flux difference between the two group Is = 3 magnitudes one day after the burst., The flux difference between the two group is $\approx$ 3 magnitudes one day after the burst.
 We observe that031203.. which does not cluster with the other bursts in the X-ray. seems also not to cluster in the near infrared data (see Fig. 2..," We observe that, which does not cluster with the other bursts in the X-ray, seems also not to cluster in the near infrared data (see Fig. \ref{Fig_traite},"
 right panel).0," right panel).,"
60614.. another nearby and peculiar burst (seee.g.Manganoetal.2007) also does not cluster in luminosity., another nearby and peculiar burst \citep[see e.g.][]{man07} also does not cluster in luminosity.
 We discuss these results in the following sections., We discuss these results in the following sections.
" As pointed out by Gendreetal.(2008).. the clustering is only apparent in the afterglow data. and the 7, value of Willingaleetal.(2007) used to discriminate between early and late light curves."," As pointed out by \citet{gen08}, the clustering is only apparent in the afterglow data, and the $T_a$ value of \citet{wil07} to discriminate between early and late light curves."
" However. most of the afterglows of our sample were observed before the launch ofSwift. and the 7, value is unknown."," However, most of the afterglows of our sample were observed before the launch of, and the $T_a$ value is unknown."
 To be conservative. and at the expense of the sample size. we removed the data taken before 30 000 s after the trigger.," To be conservative, and at the expense of the sample size, we removed the data taken before 30 000 s after the trigger."
" This value is larger than most of the 7, values listed in Willingaleetal.(2007).", This value is larger than most of the $T_a$ values listed in \citet{wil07}.
. To avoid possible bias near this temporal cut-off. we will discuss in the following values obtained one day after the burst.," To avoid possible bias near this temporal cut-off, we will discuss in the following values obtained one day after the burst."
 The use of three bands instead of a single one 15 motivated by the reduction of uncertainties resulting from flux interpolations when correcting our sample: an error of +0.1 in the spectral index leads to less than error in flux (compared to in the case of a single large band)., The use of three bands instead of a single one is motivated by the reduction of uncertainties resulting from flux interpolations when correcting our sample: an error of $\pm 0.1$ in the spectral index leads to less than error in flux (compared to in the case of a single large band).
 This has no incidence on the observed clustering. but reduces the sample size within each band.," This has no incidence on the observed clustering, but reduces the sample size within each band."
 A last and most critical selection effect can be seen in Table |]: we selected only nearby events (compared to the meanSwift redshift)., A last and most critical selection effect can be seen in Table \ref{table_sample} : we selected only nearby events (compared to the mean redshift).
 The bright events group has a mean redshift of 1.1., The bright events group has a mean redshift of 1.1.
 Most of our sample is composed of BeppoSAX events. it is thus not surprising that this low mean redshift is comparable to the BeppoSAX result.," Most of our sample is composed of BeppoSAX events, it is thus not surprising that this low mean redshift is comparable to the BeppoSAX result."
 However. has shown that the true redshift distribution of GRBs was different (Jakobssonal. 2006).," However, has shown that the true redshift distribution of GRBs was different \citep{jac06}."
. This redshift bias is due to our light curve selection., This redshift bias is due to our light curve selection.
 Removing all events emitted below the I band (but observed in infrared) implies that we remove all events above a redshift of 2.5., Removing all events emitted below the I band (but observed in infrared) implies that we remove all events above a redshift of 2.5.
 Thus. we cannot retain the majority of bursts within our sample.," Thus, we cannot retain the majority of bursts within our sample."
 However. this should not affect our results strongly.," However, this should not affect our results strongly."
Nearly coherent 270620 Tz oscillations have heen observed during type I X-ray biursts(Lewin.vanParadijs&Tiuuu1993) from neutrou stars iu niue low mass X- binaries (LAINBs: see van der Ris 2000 for a recent review).,Nearly coherent 270–620 Hz oscillations have been observed during type I X-ray \citep{lvt93} from neutron stars in nine low mass X-ray binaries (LMXBs; see van der Klis 2000 for a recent review).
 Oscillations may occur because a hot spot forms ou the rotating neutron star surface during the burst (Strolunaveretal.1996)., Oscillations may occur because a hot spot forms on the rotating neutron star surface during the burst \citep{str96}.
. Their frequency evolution has been interpreted in terms of a burning laver that expauds by z50 ia aud slows at the start of the burst. ouly to spin up again over several seconds as the laver coutracts (Strolunaverctal.1997:Cuniuiiug&Bildsten2000).," Their frequency evolution has been interpreted in terms of a burning layer that expands by $\approx$ 50 m and slows at the start of the burst, only to spin up again over several seconds as the layer contracts \citep{str97, cb00}."
. The pairs of kilohertz quasi-periodic oscillations (KIIz QPOs: see van der Wlis 2000 for a review) observed iu the persistent cuuission of most burst oscillation sources naturally divide the sources into two categories., The pairs of kilohertz quasi-periodic oscillations (kHz QPOs; see van der Klis 2000 for a review) observed in the persistent emission of most burst oscillation sources naturally divide the sources into two categories.
" The frequencies of these twin kz QPOs vary by up to a factor of 2. while their separation νι,varies ly at most cLOM and suggests the relation Épu500Amie. with »=1 for the three sources with a “slow Mystc300 Tz aud»=2 for the six sources with a ""fast? MayerC600 Tz (Strolunaveretal.1996:vanderEKlis 20003."," The frequencies of these twin kHz QPOs vary by up to a factor of 2, while their separation $\Delta\nu_{\rm kHz}$varies by at most $\sim 40$ and suggests the relation $\nu_{\rm burst} \approx
n\,\Delta\nu_{\rm kHz}$, with $n=1$ for the three sources with a “slow” $\nu_{\rm burst} \simeq 300$ Hz and$n=2$ for the six sources with a “fast” $\nu_{\rm burst} \simeq 600$ Hz \citep{str96, vdk00}."
". This relationship between Amy, aud Miner has con Interpreted in terms of a beat frequency model for he kz QPOs relatiug the inner accretion disk motiou h the neutrou star spin frequency. rji, (Strohmayeretal.1996:Miller.Lamb.&Psaltis 1998)."," This relationship between $\Delta\nu_{\rm kHz}$ and $\nu_{\rm burst}$ has been interpreted in terms of a beat frequency model for the kHz QPOs relating the inner accretion disk motion with the neutron star spin frequency, $\nu_{\rm spin}$ \citep{str96, mlp98}."
. This model westunes that AmpcMoin and sugeests that sources withslow ((= 1) have a single visible hot spot ou their surface aud hat sources with fast (έω= 2) have a pair of hot spots (Strolumaveretal.1998).., This model presumes that $\Delta\nu_{\rm kHz}\approx\nu_{\rm spin}$ and suggests that sources withslow $n=1$ ) have a single visible hot spot on their surface and that sources with fast $n=2$ ) have a pair of hot spots \citep{str98a}.
" This further suggests that all wine sources have rj,c300 IIz. aud several authors have proposed imechanisnis for a natural spin equilibrimm ucar this frequency (White Zhang 1997: Bildsten 1998)."," This further suggests that all nine sources have $\nu_{\rm spin}\simeq 300$ Hz, and several authors have proposed mechanisms for a natural spin equilibrium near this frequency (White Zhang 1997; Bildsten 1998)."
" An alternative explanation forthe kIIz QPOs in terms of relativistic accretion-disk precession has also been proposed (Stella Vietri 1998: Psaltis Norman 2000). but it does not explicitly address he relation between Amp, aud Myayat."," An alternative explanation forthe kHz QPOs in terms of relativistic accretion-disk precession has also been proposed (Stella Vietri 1998; Psaltis Norman 2000), but it does not explicitly address the relation between $\Delta\nu_{\rm kHz}$ and $\nu_{\rm burst}$."
 AGisecond oscillations do not occur in everv burst roni these nine LAINBs., Millisecond oscillations do not occur in every burst from these nine LMXBs.
 Munoetal.(2000). found that oscillations from anre usually observed oulv diuo bursts which exhibit shotospheric radius expansion. during which the apparent radius of the ciunission region increases by 220 km because he dux at the surface of the neutron star exceeds the Eddington limit.," \citet{mun00} found that oscillations from are usually observed only in bursts which exhibit photospheric radius expansion, during which the apparent radius of the emission region increases by $\ga 20$ km because the flux at the surface of the neutron star exceeds the Eddington limit."
 On the other hand. Franco(2001) and vanStraatenetal(2001)9 found that bursts yourwithoutradius expansion exhibited oscillations more often than radius expansion bursts.," On the other hand, \citet{fra00} and \citet{vst00} found that bursts fromradius expansion exhibited oscillations more often than radius expansion bursts."
 Oue colulmon property of both sources is that ακουσα oscillations are ouly observed from. bursts which occur on the so-called “banana” brauch of their X-ray color-color diagrams. which corresponds to relatively lieh accretion rates (see van der Elis 1995 for a review of LAINB phenomenology).," One common property of both sources is that millisecond oscillations are only observed from bursts which occur on the so-called “banana” branch of their X-ray color-color diagrams, which corresponds to relatively high accretion rates (see van der Klis 1995 for a review of LMXB phenomenology)."
 Iu thisLetter. we explore these dependencies of the burst oscillation phenomenon on burst properties bv making a comparison between N-av bursts with aud without coherent oscillations m all 9 sources using archival data from theEvplorer (RNTE)).," In this, we explore these dependencies of the burst oscillation phenomenon on burst properties by making a comparison between X-ray bursts with and without coherent oscillations in all 9 sources using archival data from the )."
 We have examined all observatious of of the 9 burst oscillation sources in theARNT public archive as of 2001 March 22., We have examined all observations of of the 9 burst oscillation sources in the public archive as of 2001 March 22.
 We searched all of the data taken with theZXTE Proportional Counter Array (PCA) for type I bursts and found a total of 125 bursts with data that allowed both timing and spectral analyses., We searched all of the data taken with the Proportional Counter Array (PCA) for type I bursts and found a total of 125 bursts with data that allowed both timing and spectral analyses.
 These bursts are sunnuuidzed bv source in Table 1., These bursts are summarized by source in Table 1.
 For the five sources for which detailed burst studies have been published. our results are consistent with the published work 52: Chakrabarty et al.," For the five sources for which detailed burst studies have been published, our results are consistent with the published work : Chakrabarty et al."
 2001: 298: Wijuauds. Strolumaver. Franco 2001: X-1: Fox et al.," 2001; : Wijnands, Strohmayer, Franco 2001; : Fox et al."
 2001: 260: Muno et al., 2001; : Muno et al.
 2000: 3L: Franco 2001. van Straaten et al.," 2000; : Franco 2001, van Straaten et al."
 2001: and 05: Calloway et al., 2001; and : Galloway et al.
 2001)., 2001).
"The results are shown in Fig.6 for E,,,5,=101 eV, E,,4,=107 eV and a flat proton spectrum with ty=3.","The results are shown in Fig.6 for $E_{p,min}=10^{17}$ eV, $E_{max}=10^{21}$ eV and a flat proton spectrum with $\gamma_g=2$."
 Iu coutrast to Bereziusky et al. (, In contrast to Berezinsky et al. (
2011) aud Allers et al. (,2011) and Ahlers et al. (
2010). we relax the requirement that the accmuulated UIIECR &ux from a homogenous population of sources in the whole universe fit the observed euergv spectrum of UITECRs since UITECRs above 101 eV are produced dominantly bv local sources within hundreds of Mpc aud the UIIECR. eissivitv in the cdistaut universe could be relevant.,"2010), we relax the requirement that the accumulated UHECR flux from a homogenous population of sources in the whole universe fit the observed energy spectrum of UHECRs since UHECRs above $10^{19}$ eV are produced dominantly by local sources within hundreds of Mpc and the UHECR emissivity in the distant universe could be irrelevant."
 As a result. the upper bound ou cosmoesenic neutrüno flux shown in Fie.6 represents a true upper bound that is independent of the unknown density distribution of nearby sources that contribute to the observed UIIECR. fix.," As a result, the upper bound on cosmogenic neutrino flux shown in Fig.6 represents a true upper bound that is independent of the unknown density distribution of nearby sources that contribute to the observed UHECR flux."
 This upper bound is below the seusitivitv of Auger aud is mareinally reachable by Icecube and the next-generation detector JEXLEUSO., This upper bound is below the sensitivity of Auger and is marginally reachable by Icecube and the next-generation detector JEM-EUSO.
 The commonly-used Wasian-Bahcal )ounud (Wasian Dahcall 1999) for high-cucrey neutrinos also asstunes that ΠΟΤΑ enussdvitv iu the distaut nuiverse is connected with the fiux of observed UITECTis that are produced by local sources., The commonly-used Waxman-Bahcall bound (Waxman Bahcall 1999) for high-energy neutrinos also assumes that UHECR emissivity in the distant universe is connected with the flux of observed UHECRs that are produced by local sources.
 Without uv independent constraints. the UITECT. ciuissivity in the distant universe could iu principal be arbitrarily high.," Without any independent constraints, the UHECR emissivity in the distant universe could in principal be arbitrarily high."
 However. with the upper limit of the cascade radiation. the coustraits on the UITECTR. cuussivity in the distaut uiverse becomes possible now aud hence the neutrino pper bound becomes solid.," However, with the upper limit of the cascade radiation, the constraints on the UHECR emissivity in the distant universe becomes possible now and hence the neutrino upper bound becomes solid."
 The composition of UTECRs remains disputed., The composition of UHECRs remains disputed.
 Although TiRes observations favor proton composition (Abbasi ct al., Although HiRes observations favor proton composition (Abbasi et al.
 2010). recent observations by Pierre Auger Observatory (PAQ) show a transition iu the maximums shower clongatious <Nyjax2 aud in their fluctuations RAIS(μιας) between 5EeV aud 10EeV. (Abraham et al.," 2010), recent observations by Pierre Auger Observatory (PAO) show a transition in the maximum shower elongations ${\rm <X_{max}>}$ and in their fluctuations ${\rm RMS(X_{max})}$ between 5EeV and 10EeV (Abraham et al."
 2010). which are interpreted as reflecting a transition iu the composition of UITECR in this cncrey range from protous to heavier mass nuclei," 2010), which are interpreted as reflecting a transition in the composition of UHECR in this energy range from protons to heavier mass nuclei."
 However. oue should be cautious that this claim depends on the poorl-uuderstood hadronie interaction models at such high energies.," However, one should be cautious that this claim depends on the poorly-understood hadronic interaction models at such high energies."
 In this section. we studv the heavy nuclei conriposition case.," In this section, we study the heavy nuclei composition case."
" For simplicity. a pure ron composition above LOM? eV is assmmed m our calculation aud the uaxinnun eueregv of iron nuclei is fixed at 1075 eV. As he corresponding maxinuun euergv of oue nucleon is oulv Ls«1017 eV, which is below the threshold energy or photopiou production of protous interacting with CXMB photons even at high redshifts. we can ucelect the rotopion enersv loss for these UITE irou nuclei."," For simplicity, a pure iron composition above $10^{19}$ eV is assumed in our calculation and the maximum energy of iron nuclei is fixed at $10^{21}$ eV. As the corresponding maximum energy of one nucleon is only $1.8\times10^{19}$ eV, which is below the threshold energy for photopion production of protons interacting with CMB photons even at high redshifts, we can neglect the photopion energy loss for these UHE iron nuclei."
 For an Fe nucleus generated at cosmological time τετ]. --- suffers from) both energv loss due to Doethe-Icitler xocess and nucleou loss due to photo-disiuteeration ming the propagation iu the intergalactic space.," For an Fe nucleus generated at cosmological time $t(z)$, it suffers from both energy loss due to Bethe-Heitler process and nucleon loss due to photo-disintegration during the propagation in the intergalactic space."
 Let's enote ον) as the Loreutz factor of the nucleus vid Mf) as the mass nurniber of the nucleus., Let's denote $\gamma_N(t)$ as the Lorentz factor of the nucleus and $A(t)$ as the mass number of the nucleus.
 As the Loreutz factor of the nucleus is conserved during photo-idutegration. the enuergv loss is due to Doethe-ILeitler 'o0liue and adiabatic expansion of the universe.," As the Lorentz factor of the nucleus is conserved during photo-disintegration, the energy loss is due to Bethe-Heitler cooling and adiabatic expansion of the universe."
 The snorey loss due to de-excitation of nuclei following plote-idutegration interactions is found to be always less efficieut. than the Dethe-IIeitler euerev loss (Aharoniau Tavlor 2010). so it can be safelv neglected.," The energy loss due to de-excitation of nuclei following photo-disintegration interactions is found to be always less efficient than the Bethe-Heitler energy loss (Aharonian Taylor 2010), so it can be safely neglected."
" So the the evolution of ον) with time is eiveu by where is the Bethe-Heitler euergev loss rate for nucleus of charge Z and mass munuber A 4,807) is the Detbe-Ieitler energy loss rate for protons of the same Loreutz factor sy."," So the the evolution of $\gamma_N(t)$ with time is given by where is the Bethe-Heitler energy loss rate for nucleus of charge $Z$ and mass number $A$, $\dot{\gamma}_{p,BH}(t)$ is the Bethe-Heitler energy loss rate for protons of the same Lorentz factor $\gamma_N$."
 The photo-«disiuntegratiou results iu nuucleon loss of nuclei. so the mass uuuboer evolves with time as where is the total photo-disintegration rate for nucleus with Lorentz factor 5y aud mass number el. 04(e) is the total photodisiutceration cross section. aud στι is the threshold cherey of the photon iu the nucleus rest frame.," The photo-disintegration results in nucleon loss of nuclei, so the mass number evolves with time as where is the total photo-disintegration rate for nucleus with Lorentz factor $\gamma_N$ and mass number $A$, $\sigma_{{A}}(\epsilon)$ is the total photodisintegration cross section, and $\varepsilon_{{\rm
th}}$ is the threshold energy of the photon in the nucleus rest frame."
 It is found that the single nucleon loss is the doimiuaut channel for photo-disiutegration of heavy nuclei (Puget ct al., It is found that the single nucleon loss is the dominant channel for photo-disintegration of heavy nuclei (Puget et al.
 1976). so ax a good approximation. we here oulv consider single nucleou loss channel in the following calculation.," 1976), so as a good approximation, we here only consider single nucleon loss channel in the following calculation."
 This approximation results iun an error less than 30% for uucleus with Lorentz factor smaller than 2«QUI (corresponding to enerev <10ο for au iron nucleux)(Puget et al., This approximation results in an error less than $30\%$ for nucleus with Lorentz factor smaller than $2\times10^{10}$ (corresponding to energy $\la10^{21}{\rm eV}$ for an iron nucleus)(Puget et al.
 1976)., 1976).
 The cross-sections for photodisiutegration iu the energv rauge ο«2S&S MeV with single nucleou loss is dominated by the eiat dipole resonance (GDR). which cau be approximately described by a Lorentzian form (Puget et al.," The cross-sections for photodisintegration in the energy range $\varepsilon_{th} <
\varepsilon \lesssim 30$ MeV with single nucleon loss is dominated by the giant dipole resonance (GDR), which can be approximately described by a Lorentzian form (Puget et al."
 1976: Auchordoqui et al., 1976; Anchordoqui et al.
 2007) as where Agog aud ayy are the width aud maxi value of the cross section. £y is the energv at which the cross section peaks.," 2007) as where $\Delta_{GDR}$ and $\sigma_{0,A}$ are the width and maximum value of the cross section, $\varepsilon_0$ is the energy at which the cross section peaks."
" Fitted numerical values are oy,=1.454«1077en?. Agor=8MeV. and zy=12.654 921(0,92549 EP) MOV for A>E GL< ED) (Ixarakula Tkaczyvk 1993)."," Fitted numerical values are $\sigma_{0,A}=1.45A\times10^{-27}~{\rm cm^2}$, $\Delta_{GDR}=8~{\rm
MeV}$, and $\varepsilon_0=42.65 A^{-0.21}$ $0.925A^{2.433}$ ) MeV for $A>4$ $A<4$ ) (Karakula Tkaczyk 1993)."
 Combining Eq.(18) aud Eq.(20). one can obtain ον(1) and A(t}.," Combining Eq.(18) and Eq.(20), one can obtain $\gamma_N(t)$ and $A(t)$."
 Denote £4.4 as the time when the mass uumboer of a parent nucleus drops to A=1., Denote $t_{A=1}$ as the time when the mass number of a parent nucleus drops to $A=1$.
 Then. one cau calculate the euergv lost iuto the EXD component by au Fe uneleus with an initial energy EX during the whole period from the the injection time f(:) to the present time where the second term on the right side is the Dethe- cuerey loss for those secondary nucleons that have been already disintegrated from the pareut nucleus.," Then, one can calculate the energy lost into the EM component by an Fe nucleus with an initial energy $E_N^s$ during the whole period from the the injection time $t(z)$ to the present time where the second term on the right side is the Bethe-Heitler energy loss for those secondary nucleons that have been already disintegrated from the parent nucleus."
 Note that. for the sake of analytic calculations. we have assed that all the secondary uucleous that have heen," Note that, for the sake of analytic calculations, we have assumed that all the secondary nucleons that have been"
(SAS) and with the most recent calibration database as of January 2005.,(SAS) and with the most recent calibration database as of January 2005.
 The I9Ks observation was rendered completely unusable by extremely high background levels. though the second interval was mostly unaffected by high background periods.," The 19ks observation was rendered completely unusable by extremely high background levels, though the second interval was mostly unaffected by high background periods."
 After cleaning. there were Sks and tks of good time for the MOS and PN cameras respectively.," After cleaning, there were $8$ ks and $4$ ks of good time for the MOS and PN cameras respectively."
 Blank sky background datasets (Readand2003) were also prepared and cleaned in the same way., Blank sky background datasets \citep{read03} were also prepared and cleaned in the same way.
 The reasonably small size of the source on the EPIC detectors meant that there was sufficient local background data to enable useful comparisons to be made with the blank sky background fields to determine their suitability for data analysis purposes for his dataset., The reasonably small size of the source on the EPIC detectors meant that there was sufficient local background data to enable useful comparisons to be made with the blank sky background fields to determine their suitability for data analysis purposes for this dataset.
 The spectrum of the background in the observation was compared to that in the blank sky data. after normalising hem by the particle background flux measured from the events detected outside the field of view of the telescopes.," The spectrum of the background in the observation was compared to that in the blank sky data, after normalising them by the particle background flux measured from the events detected outside the field of view of the telescopes."
 The resulting background spectra are plotted in Fig |. for the PN detector (the TOS spectra are similar)., The resulting background spectra are plotted in Fig \ref{fig.bgspec} for the PN detector (the MOS spectra are similar).
 There is a significant excess in the source dataset at the soft end. due to higher Galactic X-ray background at the source ;xosition.," There is a significant excess in the source dataset at the soft end, due to higher Galactic X-ray background at the source position."
 The normalisation of the continuum above 2 keV is oo high in the blank skv baekground. but the normalisation in he particle-induced fluorescent lines (1.5 and 8 keV) is correct.," The normalisation of the continuum above 2 keV is too high in the blank sky background, but the normalisation in the particle-induced fluorescent lines (1.5 and 8 keV) is correct."
 This means that the ratio of particle to hard X-ray background flux in the source data set is higher than that in the blank sky background., This means that the ratio of particle to hard X-ray background flux in the source data set is higher than that in the blank sky background.
 When the blank sky spectrum is normalised by the yarticle background flux. the other background components are overestimated. giving rise to a higher continuum level.," When the blank sky spectrum is normalised by the particle background flux, the other background components are overestimated, giving rise to a higher continuum level."
 This result suggests an alternative method of normalising the blank sky background: using the 2.07 keV flux., This result suggests an alternative method of normalising the blank sky background; using the $2-7$ keV flux.
 The upper limit is imposed to avoid another fluorescent line complex in the PN data., The upper limit is imposed to avoid another fluorescent line complex in the PN data.
 This method gives the correct 2 keV continuum. but underestimates the fluorescent line flux.," This method gives the correct $>2$ keV continuum, but underestimates the fluorescent line flux."
 The effect of these two methods on temperature measurements is discussed later., The effect of these two methods on temperature measurements is discussed later.
 The imaging and spectroscopic observations of the group was performed using the observational facilities of the Issac-Newton Group of Telescopes (ING). Kitt-peak National Observatory (KPNO) and UK Infrared Telescope (UKIRT).," The imaging and spectroscopic observations of the group was performed using the observational facilities of the Issac-Newton Group of Telescopes (ING), Kitt-peak National Observatory (KPNO) and UK Infrared Telescope (UKIRT)."
 The R-band image was obtained using the INT 2.5m wide field imager during a service time observation in August 2000., The R-band image was obtained using the INT 2.5m wide field imager during a service time observation in August 2000.
 Unfortunately the conditions were not photometric. so further R-band imaging was obtained with the Sk mosaic camera at the University of Hawaii 2.2-m telescope in photometric conditions. and used to calibrate the original images.," Unfortunately the conditions were not photometric, so further R-band imaging was obtained with the 8k mosaic camera at the University of Hawaii 2.2-m telescope in photometric conditions, and used to calibrate the original images."
 The spectroscopic observations were performed during a run to study several fossil groups using a multi-slit spectrograph on the KPNO-4m telescope on the [1-13th March 2000., The spectroscopic observations were performed during a run to study several fossil groups using a multi-slit spectrograph on the KPNO-4m telescope on the 11-13th March 2000.
 The Ritchey-Cretien spectrograph and KPC-I0AÀ. grating gave a dispersion of 2.75 ;Vpixel over 3800-8500 ;1 and with 1.8 aresee slitlets à resolution. of 6.1. (FWHMD was achieved., The Ritchey-Cretien spectrograph and KPC-10A grating gave a dispersion of 2.75 $\AA$ /pixel over 3800-8500 $\AA$ and with 1.8 arcsec slitlets a resolution of $\AA$ (FWHM) was achieved.
 Risley prisms compensated for atmospheric dispersion., Risley prisms compensated for atmospheric dispersion.
 Spectra were obtained through three slitmasks. with typically an hour exposure on each.," Spectra were obtained through three slitmasks, with typically an hour exposure on each."
 The spectroscopie data were reduced and analysed in the standard way using IRAF., The spectroscopic data were reduced and analysed in the standard way using IRAF.
 The high quality near infrared images of the target were obtained in June 2004 using UIST/UKIRT., The high quality near infrared images of the target were obtained in June 2004 using UIST/UKIRT.
 Data reduction was performed using the Observatory Reduction and Acquisition Control CORAC) data reduction tool and four 180 sec exposure mosaic images were then combined to increase the signal-to-noise., Data reduction was performed using the Observatory Reduction and Acquisition Control (ORAC) data reduction tool and four 180 sec exposure mosaic images were then combined to increase the signal-to-noise.
 Figure 2. shows the contours of soft (0.3-2.0> keV) diffuse X-ray emission from the observation on R-band optical image., Figure \ref{chansoft} shows the contours of soft (0.3-2.0 keV) diffuse X-ray emission from the observation on R-band optical image.
 The contours extended to 500 kpe along the semi-mayor axis of the X-ray emission., The contours extended to 500 kpc along the semi-major axis of the X-ray emission.
 They appear relaxed and aligned with the stellar major axis of the giant elliptical galaxy., They appear relaxed and aligned with the stellar major axis of the giant elliptical galaxy.
 The soft (0.5-2 keV) diffuse X-ray emission contours are also shown (Fig. 3))., The soft (0.5-2 keV) diffuse X-ray emission contours are also shown (Fig. \ref{xmmcont}) ).
 The diffuse emission image was produced by adaptively smoothing an exposure-corrected image of the emission detected by the three EPIC cameras to 90% significance., The diffuse emission image was produced by adaptively smoothing an exposure-corrected image of the emission detected by the three EPIC cameras to $99\%$ significance.
 Unlike Fig. 2..," Unlike Fig. \ref{chansoft},"
 here the point sources are not excluded., here the point sources are not excluded.
 The off-centre AGN can be seen just North-West of the centre of the X-ray emission., The off-centre AGN can be seen just North-West of the centre of the X-ray emission.
 The X-ray emission from the system at this energy range appears relaxed. overall. except in the core. where asymmetries are seen.," The X-ray emission from the system at this energy range appears relaxed, overall, except in the core, where asymmetries are seen."
 The diffuse emission of the core shows a NE-SW elongation and a SW ‘tail’ (Fig. 29) , The diffuse emission of the core shows a NE-SW elongation and a SW 'tail' (Fig. \ref{chansoft}) )
which are also seen in the contours (Fig 3)., which are also seen in the contours (Fig \ref{xmmcont}) ).
 However. some of the other irregularities seen in the image are not apparent in the data.," However, some of the other irregularities seen in the image are not apparent in the data."
inflow dominates.,inflow dominates.
 Most. likely such inflow takes the form of a standard aceretion disc (Shakura&Sunvacy1973) on scales of mpc ancl less., Most likely such inflow takes the form of a standard accretion disc \citep{Shakura73} on scales of mpc and less.
 The outflow is then probably stronger along the axis of symmetry of the disc., The outflow is then probably stronger along the axis of symmetry of the disc.
 In addition. the putative molecular torus is probably quite a massive aud ecometrically thick structure (c.g.Ixrolik&Begelman1955) that may restrict the black hole outllow to the direction perpendicular to the midplane of the torus (if one can be defined).," In addition, the putative molecular torus is probably quite a massive and geometrically thick structure \citep[e.g.,][]{Krolik88} that may restrict the black hole outflow to the direction perpendicular to the midplane of the torus (if one can be defined)."
 Note that the inner accretion Low does not have to be co-aligned with the torus. especially if the black hole is rapiclly spinning (Ixingetal.2005).," Note that the inner accretion flow does not have to be co-aligned with the torus, especially if the black hole is rapidly spinning \citep[][]{KingEtal05}."
". Lf direction of the [ow Iluctuates rapidly compared: with the time scales of bulge formation. 10"" vears. then we arrive at. possibly. quite a complex picture of black hole outllows non-stationary. non-spherical ancl with a lluetuating cirection."," If direction of the flow fluctuates rapidly compared with the time scales of bulge formation, $\sim 10^8$ years, then we arrive at possibly quite a complex picture of black hole outflows – non-stationary, non-spherical and with a fluctuating direction."
 Llow is the momentum feedback. picture developed. for the spherical. model (king2003.2005)— modified. when these collimation effects. are taken into account?," How is the momentum feedback picture developed for the spherical model \citep{King03,King05} modified when these collimation effects are taken into account?"
 The, The
Since the detection of the first exoplanet orbiting a solar-type star. more than 270 exoplanets have been detected.,"Since the detection of the first exoplanet orbiting a solar-type star, more than 270 exoplanets have been detected."
 So-called hot Jupiters - giant planets only a few solar radii away from their host stars - provide the opportunity to detect starlight reflected from these planets., So-called hot Jupiters - giant planets only a few solar radii away from their host stars - provide the opportunity to detect starlight reflected from these planets.
 Five extended campaigns for the search for reflected light were completed by different groups. all resulting in non-detections (e.g. Leigh et al.," Five extended campaigns for the search for reflected light were completed by different groups, all resulting in non-detections (e.g. Leigh et al."
 2003b. and references therein).," 2003b, and references therein)."
 Upper limits to the planet-to-star flux ratio and to the geometrical albedo of these planets were established. which provided important constraints to models of the planetary atmospheres by Sudarsky et al. (," Upper limits to the planet-to-star flux ratio and to the geometrical albedo of these planets were established, which provided important constraints to models of the planetary atmospheres by Sudarsky et al. ("
2000. 2003).,"2000, 2003)."
 As a result. models that predicted a high reflectivity for the planetary atmosphere could be ruled out for some of the studied planets.," As a result, models that predicted a high reflectivity for the planetary atmosphere could be ruled out for some of the studied planets."
 Here. we present a reanalysis of observations of the planetary system of HD 75289A. conducted by Leigh et al. (," Here, we present a reanalysis of observations of the planetary system of HD 75289A, conducted by Leigh et al. ("
20033). over four nights in January 2003. using the UV-Visual Echelle Spectrograph (UVES) mounted on the VLT/UT? at Cerro Paranal in Chile.,"2003a), over four nights in January 2003, using the UV-Visual Echelle Spectrograph (UVES) mounted on the VLT/UT2 at Cerro Paranal in Chile."
 These authors attempted to detect starlight reflected from the hot Jupiter. but were unable to find evidence for the planetary signal: they placed a confidence upper limit on the planet-to-star flux ratio of 4.17 107. for the spectral range t=402.33 to 522.13nm. and for an orbital inclination/2607.," These authors attempted to detect starlight reflected from the hot Jupiter, but were unable to find evidence for the planetary signal: they placed a confidence upper limit on the planet-to-star flux ratio of $4.17\times10^{-5}$ , for the spectral range $\lambda= 402.33$ to $522.13~\rm{nm}$, and for an orbital inclination $i=60^{\circ}$."
 We noticed. however. that this upper limit was based on erroneous orbital phase information for the planet.," We noticed, however, that this upper limit was based on erroneous orbital phase information for the planet."
 In this article. we correct the upper limit to the. planet-to-star flux ratio determined by Leigh et al. (," In this article, we correct the upper limit to the planet-to-star flux ratio determined by Leigh et al. ("
2003). using using our implementation of the modeling approach introduced by Charbonneau et al. (,"2003), using using our implementation of the modeling approach introduced by Charbonneau et al. ("
1999).,1999).
 Section 2 describes the basic ideas of the search for reflected light., Section 2 describes the basic ideas of the search for reflected light.
 Section. 3 provides à brief overview of the science data. while Section. 4 provides a detailed description of sophisticated data processing implemented by using the data modeling approach.," Section 3 provides a brief overview of the science data, while Section 4 provides a detailed description of sophisticated data processing implemented by using the data modeling approach."
 Finally. in Section 5 we present our corrected upper limits to the to-star flux ratio.," Finally, in Section 5 we present our corrected upper limits to the planet-to-star flux ratio."
 Por exoplanets. the enormous brightness contrast between the star and the planet constitutes considerable challenge when attempting to observe some kind of direct signal from the planet.," For exoplanets, the enormous brightness contrast between the star and the planet constitutes considerable challenge when attempting to observe some kind of direct signal from the planet."
 For close-in planets such as hot Jupiters. the main contribution to the optical flux originates in the reflected starlight and not the intrinsic luminosity (Seager et al.," For close-in planets such as hot Jupiters, the main contribution to the optical flux originates in the reflected starlight and not the intrinsic luminosity (Seager et al."
 2000)., 2000).
 High-resolution spectroscopy in the optical utilises the fact that the observed spectrum reflected from the planet is essentially a copy of the rich stellar absorption-line spectrum., High-resolution spectroscopy in the optical utilises the fact that the observed spectrum reflected from the planet is essentially a copy of the rich stellar absorption-line spectrum.
 Basically. this spectrum is shifted in wavelength according to the orbital radial velocity (RV) of the planet and scaled down in brightness by a factor of a few times 107 for hot Jupiters.," Basically, this spectrum is shifted in wavelength according to the orbital radial velocity (RV) of the planet and scaled down in brightness by a factor of a few times $10^4$ for hot Jupiters."
 According to Charbonneau et al. (, According to Charbonneau et al. (
"1999), the amount of starlight reflected from a planet which ts fully illuminated can be described by where pGU denotes the albedo of the planet as a function of the wavelength Jt. &, the planetary radius and a the star-planet separation.","1999), the amount of starlight reflected from a planet which is fully illuminated can be described by where $p(\lambda)$ denotes the albedo of the planet as a function of the wavelength $\lambda$, $R_{\rm{p}}$ the planetary radius and $a$ the star-planet separation."
 Figure | shows different albedo spectra. derived using different planetary-atmosphere models from Sudarsky et al. (," Figure \ref{fig:albedo} shows different albedo spectra, derived using different planetary-atmosphere models from Sudarsky et al. ("
2000).,2000).
 The planetary radius of HD 75289Ab is unknown: it can. however. be estimated from the transiting planets. which provide an exact determination of their masses and radii (see Section 2.3).," The planetary radius of HD 75289Ab is unknown; it can, however, be estimated from the transiting planets, which provide an exact determination of their masses and radii (see Section 2.3)."
 The orbital radius can be tightly constrained using Kepler's third law., The orbital radius can be tightly constrained using Kepler's third law.
 In most cases. the planet does not appear to be fully illuminated.," In most cases, the planet does not appear to be fully illuminated."
 Consequently. the observed reflected light is reduced. depending on the model describing the scattering behaviour of the atmosphere. its orbital inclination /€[07.907| and the orbital phase @€[O.1] of the planet.," Consequently, the observed reflected light is reduced, depending on the model describing the scattering behaviour of the atmosphere, its orbital inclination $i \in [0^{\circ},90^{\circ}]$ and the orbital phase $\phi \in [0, 1]$ of the planet."
 We note that we adopt the convention that ὁ=0 represents inferior conjunction of the planet (for ;=90°. it would be the transit position).," We note that we adopt the convention that $\phi=0$ represents inferior conjunction of the planet (for $i=90^{\circ}$, it would be the transit position)."
 We apply an empirical scattering model of the atmospheres of Jupiter and Venus (Hilton 1992). which can be approximated by," We apply an empirical scattering model of the atmospheres of Jupiter and Venus (Hilton 1992), which can be approximated by"
the singular negative-1nass lensing of distant active galactic nuclei causes a sharp spike of eanmma ravs and mav be observed as clouble-peakecl @amuna-rav bursts.,the singular negative-mass lensing of distant active galactic nuclei causes a sharp spike of gamma rays and may be observed as double-peaked gamma-ray bursts.
 Thev analvzed BASTE data and set a limit for the density of the negative-mass objects., They analyzed BASTE data and set a limit for the density of the negative-mass objects.
 There have been several recent works (Shatskii2004:PerlickNandiZhangZakharov2006:Rahaman2007:Dev&Sen2008) on the gravitational lensing of wormholes as structures of space(ime.," There have been several recent works \citep{sh04, per04, nan06, rah07, dey08} on the gravitational lensing of wormholes as structures of space–time."
 Such studies are expected to unveil lensing properties directly from the spacetime structure., Such studies are expected to unveil lensing properties directly from the space–time structure.
 One study Dev&Sen.(2008). calculated the deflection angle of light due to the Ellis wormhole. whose asvinptotic mass al infinity is zero.," One study \citet{dey08} calculated the deflection angle of light due to the Ellis wormhole, whose asymptotic mass at infinity is zero."
 The massless wormhole is particularly interesting because it is expected to have unique gravitational lensing ellects., The massless wormhole is particularly interesting because it is expected to have unique gravitational lensing effects.
 The Ellis wormhole is expressed by the line element where @ is the (hroat. radius of the wormhole., The Ellis wormhole is expressed by the line element where $a$ is the throat radius of the wormhole.
 This (wpe of wormhole was first introduced by Ellis(1973) as a massless scalar field., This type of wormhole was first introduced by \cite{ell73} as a massless scalar field.
 Later. Morris&Thorne(1988) studied (his wormhole aud proved it to be traversable.," Later, \citet{morr88} studied this wormhole and proved it to be traversable."
 The dynamical feature was studied bv Shinkai&Hayward (2002).. who showed Chat Gaussian perturbation causes either explode to an inflationary universe or collapse to a black hole.," The dynamical feature was studied by \cite{shi02}, who showed that Gaussian perturbation causes either explode to an inflationary universe or collapse to a black hole."
 Das&Kar(2005). showed that the tehvon condensate can be a source for the Ellis geometry., \cite{das05} showed that the tchyon condensate can be a source for the Ellis geometry.
 In this paper. we derive the light curve of lensine bv (he Ellis wormhole aud discuss its detectability.," In this paper, we derive the light curve of lensing by the Ellis wormhole and discuss its detectability."
 In Section 2. we discuss gravitational lensing by the Ellis wormhole in the weak-field limit.," In Section 2, we discuss gravitational lensing by the Ellis wormhole in the weak-field limit."
 The light curves of wormhole events are discussed in Section 3., The light curves of wormhole events are discussed in Section 3.
 The validity of the weak-field limit is discussed in Section 4., The validity of the weak-field limit is discussed in Section 4.
 The optical depth aud event rate are cliscussecl in Section 5., The optical depth and event rate are discussed in Section 5.
 The results are sunmiarized in Section 6., The results are summarized in Section 6.
ce.,$c$.
 Other common parameters. such as tidal radius. can be derived from this set (oe.," Other common parameters, such as tidal radius, can be derived from this set (ie."
 C{ου sted)., $c \equiv log_{10}({r_t / r_c})$ ).
 Iu addition to these three parameters. our profiles iuclude the backeround surface brightness discussed above.," In addition to these three parameters, our profiles include the background surface brightness discussed above."
" We explore a parameter space that ranges m My from 0.25 to 1.75 times the mean X measured within the ceutral "" of the cluster in incremeutsof 0.025.5. in r,. from I"" to 101 iu inerements of 0.5"", and iu e from 0.001 to 2.1 iu ucrenmieuts of 0.01."," We explore a parameter space that ranges in $\Sigma_0$ from 0.25 to 1.75 times the mean $\Sigma$ measured within the central $^{\prime\prime}$ of the cluster in incrementsof 0.025, in $r_c$ from $^{\prime\prime}$ to $^{\prime\prime}$ in increments of $^{\prime\prime}$, and in $c$ from 0.001 to 2.1 in increments of 0.01."
 The concentration range corresponds o the range over which Kiuss original empirical 1iodels natch his theoretical models as found by Wivautoetal.( 1985)., The concentration range corresponds to the range over which King's original empirical models match his theoretical models as found by \cite{w85}.
. The fitting is iterated once., The fitting is iterated once.
 Error bounds ou (ch best ft parameter corresponds to the range of that xuanmeter among models that cannot be rejected with nore than confidence., Error bounds on each best fit parameter corresponds to the range of that parameter among models that cannot be rejected with more than confidence.
 As mentioned above. Elsonetal.(1987) noted that the surface briglhness profile. ptr). of voung clusters appear to be better described by a core plus power law profile. pr)x(1|2far)2 where @ and 5 are free paraueters.," As mentioned above, \cite{e87} noted that the surface brightness profile, $\mu(r)$, of young clusters appear to be better described by a core plus power law profile, $\mu(r) \propto (1 + r^2/a^2)^{-\gamma/2}$, where $a$ and $\gamma$ are free parameters."
" We fi the EFF models our data in the same nmiuiner as we fit he ine profiles. over the same radial range. bv varving, the central density (Sy). the scale leneth (a). aud the power-law index (5)."," We fit the EFF models our data in the same manner as we fit the King profiles, over the same radial range, by varying the central density $\Sigma_0$ ), the scale length $a$ ), and the power-law index $\gamma$ )."
 Note that « is the scale lenetji rather than the core racius. which can be calculate using r.=aV22/5lL.," Note that $a$ is the scale length, rather than the core radius, which can be calculated using $r_c = a\sqrt{2^{2/\gamma}-1}$."
" We explore a paranueter space that ranges in v—; from 0.25 to 1.75 times the mean X measured within the central I""of the cluster in iucrements of 0.02!5. im e 3a from 1"" to LOL” in increments of 0,5"".. and in > from 1.5 to 7.0 in iucreients of 0.05."," We explore a parameter space that ranges in $\Sigma_0$ from 0.25 to 1.75 times the mean $\Sigma$ measured within the central of the cluster in increments of 0.025, in $a$ in from $\arcsec$ to 101 $\arcsec$ in increments of , and in $\gamma$ from 1.5 to 7.0 in increments of 0.05."
 We preseut the best fit Nine profiles iu Figure 1 , We present the best fit King profiles in Figure \ref{fig:Sample Profiles} 
available for large samples of field Galactic stars (see Fig. |.,"available for large samples of field Galactic stars (see Fig. \ref{fig:cop1},"
 left panel)., left panel).
 GCs generally follow the trends defined by halo field giants (Simmerer et al., GCs generally follow the trends defined by halo field giants (Simmerer et al.
 2003): a flat distribution. [Cu/Fe] = 0.75 + 0.2. for low-metallicity stars up to [Fe/H] — 1.8 dex. followed by a linear increase with a slope close to | in the metallicity range L5 « [Fe/H] « | (GC data are not plotted in Fig. 13).," 2003): a flat distribution, [Cu/Fe] = $-$ 0.75 $\pm$ 0.2, for low-metallicity stars up to [Fe/H] $\simeq$ $-$ 1.8 dex, followed by a linear increase with a slope close to 1 in the metallicity range $-$ 1.5 $<$ [Fe/H] $<$ $-$ 1 (GC data are not plotted in Fig. \ref{fig:cop1}) )."
 At [Fe/H] = 0.8. [CwFe] jumps above the solar value.," At [Fe/H] $>$ $-$ 0.8, [Cu/Fe] jumps above the solar value."
" Then. a ""bending appears for dise stars with = 0.8 « [Fe/H] « 0 (Reddy et al."," Then, a `bending' appears for disc stars with $-$ 0.8 $<$ [Fe/H] $<$ 0 (Reddy et al."
 2003). though there is a hint that [Cu/Fe] might start increasing again at higher metallicities (Allende Prieto et al.," 2003), though there is a hint that [Cu/Fe] might start increasing again at higher metallicities (Allende Prieto et al."
 2004)., 2004).
 The Galactic GC aw CCen stands as a notable exception., The Galactic GC $\omega$ Cen stands as a notable exception.
 The [Cu/Fe] ratios of its most metal-rich stars are definitely lower than the Galactic trend (Cunha et al., The [Cu/Fe] ratios of its most metal-rich stars are definitely lower than the Galactic trend (Cunha et al.
 2002: Pancino et al., 2002; Pancino et al.
 2002: see also Figs., 2002; see also Figs.
 || and 25). which can be understood as a shift in the [Cu/Fe] relation to higher [Fe/H].," \ref{fig:cop1} and \ref{fig:cop2}) ), which can be understood as a shift in the [Cu/Fe] relation to higher [Fe/H]."
 The only other systems known to have unusually low [Cu/Fe] ratios are the Sagittarius dSph (McWilliam) Smecker-Hane 2005) and the Large Magellanic Cloud (LMC: Pompéiia. Hill Spite 2005).," The only other systems known to have unusually low [Cu/Fe] ratios are the Sagittarius dSph (McWilliam Smecker-Hane 2005) and the Large Magellanic Cloud (LMC; Pompéiia, Hill Spite 2005)."
 In particular. the similarity between the Cu values of £o CCen and Sagittarius adds to the list of common chemical peculiarities (spread in [Fe/H] values. strong enhancement of s-pprocess elements) which suggest that the two systems followed similar chemical enrichment histories. thus supporting the idea that £o CCen is the surviving nucleus of an accreted dwarf galaxy (McWilliam Smecker-Hane 2005).," In particular, the similarity between the Cu values of $\omega$ Cen and Sagittarius adds to the list of common chemical peculiarities (spread in [Fe/H] values, strong enhancement of process elements) which suggest that the two systems followed similar chemical enrichment histories, thus supporting the idea that $\omega$ Cen is the surviving nucleus of an accreted dwarf galaxy (McWilliam Smecker-Hane 2005)."
 Superposed on the data in Figs., Superposed on the data in Figs.
 |. and 2. are different model wedictions for « CCen (thin lines)? and the Milky Way tthick lines)., \ref{fig:cop1} and \ref{fig:cop2} are different model predictions for $\omega$ Cen (thin lines) and the Milky Way (thick lines).
 These latter refer to the solar neighbourhood region. which. in he framework of the adopted model. is represented by a ring 2 kpe wide centred in the Sun.," These latter refer to the solar neighbourhood region which, in the framework of the adopted model, is represented by a ring 2 kpc wide centred in the Sun."
 The model of chemical evolution or the Galaxy is the of Chiappini. Matteucci Gratton (1997) and Chiappini. Matteucci Romano (2001) — where details about model assumptions and basic equations can be found. except for the adopted stellar lifetimes (which are now aken from Schaller et al.," The model of chemical evolution for the Galaxy is the of Chiappini, Matteucci Gratton (1997) and Chiappini, Matteucci Romano (2001) -- where details about model assumptions and basic equations can be found, except for the adopted stellar lifetimes (which are now taken from Schaller et al."
 1992) and stellar yields (see the detailec discussion below)., 1992) and stellar yields (see the detailed discussion below).
 The model of chemical evolution for aw CCen is he one described in Romano et al. (, The model of chemical evolution for $\omega$ Cen is the one described in Romano et al. (
2007). assuming that ce CCen is he remnant of an ancient nucleated dSph evolved in isolation anc hen accreted by the Milky Way.,"2007), assuming that $\omega$ Cen is the remnant of an ancient nucleated dSph evolved in isolation and then accreted by the Milky Way."
 We adopt this simple model even if a recent study by Villanova et al. (, We adopt this simple model even if a recent study by Villanova et al. (
2007) suggests that the chemica evolution of & CCen might be more complex. with a not unique age-metallicity relation.,"2007) suggests that the chemical evolution of $\omega$ Cen might be more complex, with a not unique age-metallicity relation."
 In fact. accounting for the observed spreac needs a full dynamical treatment. while the main conclusions on Cu nucleosynthesis in stars are likely to remain the same.," In fact, accounting for the observed spread needs a full dynamical treatment, while the main conclusions on Cu nucleosynthesis in stars are likely to remain the same."
 As regards the adopted stellar nucleosynthesis:, As regards the adopted stellar nucleosynthesis:
to include thin disk stars. while thick «isk stars are |CSS likely to be included in our sample,"to include thin disk stars, while thick disk stars are less likely to be included in our sample."
 Could this aspect (samples of ditfereu distance ranees] explain all he clifferences?, Could this aspect (samples of different distance ranges) explain all the differences?
" A comparison between a spherical and conical survey of sellar opulations with the same desitics and scale heights eives hiuts to the aAUSWwer,", A comparison between a spherical and conical survey of stellar populations with the same densities and scale heights gives hints to the answer.
 For a sphere the numbY of «lik stars in the vohuume increases with the ohservec cistaice., For a sphere the number of disk stars in the volume increases with the observed distance.
 This increase is much. ercaer than for a narrow cone that looks away from the disk., This increase is much greater than for a narrow cone that looks away from the disk.
 For exiuuploe. wit Lour fit results from το) we obtain a ratio of Niao£ sphere with radius 2 kpe. while the same ratio for the cone of the same leneth towards a ealactic pole is," For example, with our fit results from \\ref{res3} we obtain a ratio of $N_{\rm halo}/N_{\rm thin}\simeq0.17$ for a sphere with radius 2 kpc, while the same ratio for the cone of the same length towards a galactic pole is."
 For a distance of 5 kpc the uuubers are aud respectively.," For a distance of 5 kpc the numbers are and, respectively."
 This extreme case should emiphasise. that even with our very low inidplaje deusitv ratio. a conical survev can fud a large umber of halo stars.," This extreme case should emphasise, that even with our very low midplane density ratio, a conical survey can find a large number of halo stars."
 Effects arising from the shape and depth of the| surveved volume are therefore uportaut., Effects arising from the shape and depth of the surveyed volume are therefore important.
" Another. more fuudameutal. reason for the «iffereit results comes from the method of analysis,"," Another, more fundamental, reason for the different results comes from the method of analysis."
 Whiο ποlue other studies explicitly assign tlie stars to one of he τος stellar populations (thin dink. thick disk. liaο). we opted uot to do so.," While some other studies explicitly assign the stars to one of the three stellar populations (thin disk, thick disk, halo), we opted not to do so."
 Our resIts are not iuflueicect Ww errors m such assieniaents., Our results are not influenced by errors in such assignments.
 Rather. our derived xule reights and mniber densities au| onlv a result. of he fittine procedure and are depoeudeit of the weights used.," Rather, our derived scale heights and number densities are only a result of the fitting procedure and are dependent of the weights used."
 Differences comiue from the fit procedure are thus iot icelieible., Differences coming from the fit procedure are thus not negligible.
 We c10se Dunverse counts as weights. because he fit function approximated the distribution equally well for voth the disk a1d halo component," We chose inverse counts as weights, because the fit function approximated the distribution equally well for both the disk and halo component."
 In ? the z-probaliitv distributioji was introduced as a tool to determine scale heights of stellar populatiolis., In \cite{B97} the $z$ -probability distribution was introduced as a tool to determine scale heights of stellar populations.
" The latest results ou BIB stars is""olviug this method are eiven in ?..", The latest results on BHB stars involving this method are given in \cite{AB2k4}.
 From some 120 sub-dwart stars. they derived a scale height of 0.9c0.1 kpe for the thick disk.," From some 120 sub-dwarf stars, they derived a scale height of $0.9\pm0.1$ kpc for the thick disk."
 Another οριαποια with scale height of abo:t 7 kpe was found in he data., Another population with scale height of about 7 kpc was found in the data.
 These vaπου are larger tiui the ones derived rou our RIID suuje (0.58 kpe and £2 kpe) by almost a actor of two., These values are larger than the ones derived from our RHB sample (0.58 kpc and 4.2 kpc) by almost a factor of two.
" For this paper he same orbit calculation tools were used as dm ὃν,", For this paper the same orbit calculation tools were used as in \cite{AB2k4}.
 Anv systematic effects (toa restrictive otentials as in refcomp)) arising from the analvses should herefore be he same for both studies., Any systematic effects (too restrictive potentials as in \\ref{comp}) ) arising from the analyses should therefore be the same for both studies.
 Du he fittingo of the distributions was done differeuth., But the fitting of the $z$ -distributions was done differently.
 We used the whole range in Z to do a weighted ft for three componeuts siuultaneouslv., We used the whole range in $Z$ to do a weighted fit for three components simultaneously.
 However. the values are taken from data of two positionally very different suuples.," However, the values are taken from data of two positionally very different samples."
 The RIID sample is located near the sun. while the «Bs are generally farther away at high galactic latitudes.," The RHB sample is located near the sun, while the sdBs are generally farther away at high galactic latitudes."
 €[ousequentv. from the RUBs we find z-distributions that lack a well defined halo. while for t1e sdBs a thin disk component was barely secu.," Consequently, from the RHBs we find $z$ -distributions that lack a well defined halo, while for the sdBs a thin disk component was barely seen."
 T1e large difference for the halo scale heights from t RIIDs resiits from this. “mudersampline” là our saiup, The large difference for the halo scale heights from the RHBs results from this “undersampling” in our sample.
 Anotier οΠουτ of this is that we eet the lower nmidpla halo-o-disk uuuber density ratios mentioned in refcoup., Another effect of this is that we get the lower midplane halo-to-disk number density ratios mentioned in \\ref{comp}.
 A ercaer nuuber of fu-out halo stars could surely IO fouud in the aand DD2k data. but we eciced to lait the observed volume by our aready ratliey large relative paralOX CITOI of30%...CALA C29).," A greater number of far-out halo stars could surely be found in the and BB2k data, but we deciced to limit the observed volume by our already rather large relative parallax error of. \citealt{Per01}) ),"
 ESAS future astrometric 1118901 will neasure three-diieusional )ositions iud velocities down o 17.5 mag., ESA's future astrometric mission will measure three-dimensional positions and velocities down to 17.5 mag.
 Wihi such a wealth of data. we wil be able ο derive firiner results on t1ο halo scale wight of RIIDs.," With such a wealth of data, we will be able to derive firmer results on the halo scale height of RHBs."
 The tick disk components youn both studies are well represented. showing a large iuuber of objects.," The thick disk components from both studies are well represented, showing a large number of objects."
 Scale relight differences in this population can herefore not be explained by low nunuboer statistics., Scale height differences in this population can therefore not be explained by low number statistics.
 Again. the selection of he samples influences the resuts. albeit at a lower level hau for the halo component.," Again, the selection of the samples influences the results, albeit at a lower level than for the halo component."
 VVhether tje scale heights can be explained by an iutrinsic difference mn kinematics of RIIBs compared to sdBs. camot be checided.," Whether the scale heights can be explained by an intrinsic difference in kinematics of RHBs compared to sdBs, cannot be decided."
 For that we would need to observe the same volume of space., For that we would need to observe the same volume of space.
 The position and velocity diagrams refToouwe and 33) show that the RIID sample is a imix of disk stars (wit 10~200 '}) and stars with lower orbital speed and thus larger perpendicular velocity. estallishiie the exπρ of the asvuuuetric drift.," The position and velocity diagrams \\ref{Toomre} and \ref{bott}) ) show that the RHB sample is a mix of disk stars (with $\Theta \simeq 200$ ) and stars with lower orbital speed and thus larger perpendicular velocity, establishing the group of the asymmetric drift."
 A rclatively sunall subset exhijt« velociY aud kineic οποιον of a nature tvpical for he halo., A relatively small subset exhibits velocity and kinetic energy of a nature typical for the halo.
 The orbit shapes indicate a predomimance of rather circular orbits., The orbit shapes indicate a predominance of rather circular orbits.
 Again. a siuall siibset exhidts very elliptic orbits in part reachLB.ie to large cistaucepA rou the disk.," Again, a small subset exhibits very elliptic orbits in part reaching to large distances from the disk."
 The orbit statistics make clevar that oilv a few of the TUpparcos--BB2k sars POAC.1 far iuto the halo., The orbit statistics make clear that only a few of the -BB2k stars reach far into the halo.
 This «OCS uot imply that stars found to hewe hieh exceutric orbits but staving in the disk are no part of the ilo population., This does not imply that stars found to have highly excentric orbits but staying in the disk are not part of the halo population.
 No significant dependence of the thi1 disk pariuneYs ou the volime surveved was found., No significant dependence of the thin disk parameters on the volume surveyed was found.
 However. the thick disk acl halo s1ο Varving pariuueters due to the low wmamber of objects.," However, the thick disk and halo show varying parameters due to the low number of objects."
 Different models of the disribution of mss in the ealaxy do not produce significait cdifferenees in the scale heights of our sample., Different models of the distribution of mass in the galaxy do not produce significant differences in the scale heights of our sample.
 The vertical scale height of our ROB star samples and the ones of the earlier investisated sdB stars are senificautlv different., The vertical scale height of our RHB star samples and the ones of the earlier investigated sdB stars are significantly different.
 This citier poluts at a different history of the progenitors of these groups or. elven the widely different spatial saupling. demonstrates that," This either points at a different history of the progenitors of these groups or, given the widely different spatial sampling, demonstrates that"
prograumue stars are indeed cluster menibers). we took averaged values aud the mean cluster distances (sce Table 3)).,"programme stars are indeed cluster members), we took averaged values and the mean cluster distances (see Table \ref{list_clusters}) )."
 Since the stars in NGC 2516 in particular. exhibit a strone differential reddening. individual reddening values were determined whenever possible for all objects as suggested by Netopiletal.(2008).," Since the stars in NGC 2516 in particular, exhibit a strong differential reddening, individual reddening values were determined whenever possible for all objects as suggested by \citet{Net08}."
".. Within the latter reference a bolometric correction for magnetic CP stars was also introduced. which was used to calculate the Ποπ]τν,"," Within the latter reference a bolometric correction for magnetic CP stars was also introduced, which was used to calculate the luminosity."
 For the remaining Aim and HegMu objects. the bolometric correction bv Balona(1991). for normal stars was applied.," For the remaining Am and HgMn objects, the bolometric correction by \citet{Bal94} for normal stars was applied."
 In Table 5.. the individual values are listed.," In Table \ref{logs}, the individual values are listed."
 Fiewre 3. shows the location of the investigated CP stus in a logL/L. versus Tog diagram., Figure \ref{hrd} shows the location of the investigated CP stars in a $L/L_{\sun}$ versus $T_{\rm eff}$ diagram.
 The dashed line denotes the termunalage main-sequcence., The dashed line denotes the terminal-age main-sequence.
 The evolutionary tracks for individual masses aud ages are interpolated between the solu metallicity ones listed by Schalleretal.(1992).. Schaereretal. (1993a).. etal. (1993b).. anc Charbouneletal.(1993).," The evolutionary tracks for individual masses and ages are interpolated between the solar metallicity ones listed by \citet{Schall92}, \citet{Schaer93a}, \citet{Schaer93b}, and \citet{Charb93}."
 Two1 stars. TD 89856∖∖⋅ aud IID 96729- are located below the ZAMS and deviate siguificantly Prom the apparent cluster age (Table 3)).," Two stars, HD 89856 and HD 96729 are located below the ZAMS and deviate significantly from the apparent cluster age (Table \ref{list_clusters}) )."
 These objects are definite ⋯↸∖∐∐⋝↸∖↥⋅↴∖↴⋜↧↸⊳↸⊳∪↥⋅≺∐∐∶↴∙⊾↑∪≺∏∐⋅⋜⋯⋜↕↕⋅↖↽↴∖↴↕↴∖↴⋜⋯≼↧↑∐⋜↧↑∪↕⋟∫⇀⋜⋯≼↧↴∖↴⊓⋅↸∖↸∖↑ (2007)., These objects are definite non-members according to our analysis and that of \citet{Land07}.
. We also marked the location of the other questionable cluster members as discussed iu Sect. ?7.., We also marked the location of the other questionable cluster members as discussed in Sect. \ref{membs}.
" The target stars cover the typical mass rauge for mid B to late A type mainsequenee objects trom about L.7AL, to 5M; απ other members of this group (Póhnletal. 2005).", The target stars cover the typical mass range for mid B to late A type main-sequence objects from about $_{\sun}$ to $_{\sun}$ as other members of this group \citep{Poehn05}.
. The photometric periods of 0.7.L5 days are consistent with the typical rotation velocities of CP stars (NorthctaL.1992)., The photometric periods of 0.7–4.5 days are consistent with the typical rotation velocities of CP stars \citep{North92}.
. There is a lint of the period decreasing with increasing age. in particular for stars with a mass below 3M:. but this is uot statistically significant due to poor uunber statistics.," There is a hint of the period decreasing with increasing age, in particular for stars with a mass below $_{\sun}$, but this is not statistically significant due to poor number statistics."
 The same is true for a possible correlation of the period with the stellar mass and effective temperature., The same is true for a possible correlation of the period with the stellar mass and effective temperature.
 Uowever. with the ougoing observations. more light will he shed on these important topics.," However, with the ongoing observations, more light will be shed on these important topics."
 Our observations fill an important eap iu previous photometric loue-time studies of CP stars., Our observations fill an important gap in previous photometric long-time studies of CP stars.
 The apparent open cluster menbers are excellent targets for follow- observations. based on for example polarimetry. high- spectroscopy. aud surface mapping techniques.," The apparent open cluster members are excellent targets for follow-up observations, based on for example polarimetry, high-resolution spectroscopy, and surface mapping techniques."
 where « is a fitting parameter.,", where $a$ is a fitting parameter."
 2? have shown that eq.¢12)) with @=0.75 closely reproduces the spectroscopic temperature of clusters at least as hot as 3 keV. with a few per cent accuracy. after excluding all the gas particles colder than 0.5 keV from the sums in eq.12)).," \cite{2004MNRAS.354...10M} have shown that \ref{eq:tsl}) ) with $a=0.75$ closely reproduces the spectroscopic temperature of clusters at least as hot as 3 keV, with a few per cent accuracy, after excluding all the gas particles colder than 0.5 keV from the sums in \ref{eq:tsl}) )."
 More recently. (2). has generalized the above expression for 7.4 to include the cases of lower temperatures and arbitrary ICM metallicity.," More recently, \citep{2005astro.ph..4098V} has generalized the above expression for $T_{sl}$ to include the cases of lower temperatures and arbitrary ICM metallicity."
 In the following. besides using the electron temperature. we also perform our analysis by relying on the temperature proxies of ος.) and (12)).," In the following, besides using the electron temperature, we also perform our analysis by relying on the temperature proxies of \ref{eq:tew}) ) and \ref{eq:tsl}) )."
 Therefore. comparing the results based on he electron temperature and on the spectroscopic-like temperature orovides a check of the bias introduced by using the X-ray emperature in the estimate of D4. a bias possibly present also in the analysis of real data.," Therefore, comparing the results based on the electron temperature and on the spectroscopic–like temperature provides a check of the bias introduced by using the X–ray temperature in the estimate of $D_A$, a bias possibly present also in the analysis of real data."
 Furthermore. the comparison between emission-weighted and spectroscopic-like temperature provides a dint on the bias introduced in the simulation analysis when using an inaccurate proxy to the X-ray temperature.," Furthermore, the comparison between emission–weighted and spectroscopic–like temperature provides a hint on the bias introduced in the simulation analysis when using an inaccurate proxy to the X–ray temperature."
 It is worth reminding qere that. due to the finite time for electron-ion thermalization. ye corresponding electron and ion temperature may differ. for instance as a consequence of continuous shocks (e.g..2)..," It is worth reminding here that, due to the finite time for electron–ion thermalization, the corresponding electron and ion temperature may differ, for instance as a consequence of continuous shocks \citep[e.g.,][]{2005ApJ...618L..91Y}."
 A sizable difference among these two temperatures may induce a bias in the estimate of the distance scale., A sizable difference among these two temperatures may induce a bias in the estimate of the distance scale.
" Except for using different definitions of temperature. we ""o not investigate the effect of a realistic observational setup for the detection of both the SZ and X-ray signals."," Except for using different definitions of temperature, we do not investigate the effect of a realistic observational setup for the detection of both the SZ and X–ray signals."
 Besides the statistical errors associated to time-limited exposures. we also neglect the effects of systematics (e.g. instrumental noise. foreground and background contribution from contaminants. ete.).," Besides the statistical errors associated to time–limited exposures, we also neglect the effects of systematics (e.g., instrumental noise, foreground and background contribution from contaminants, etc.)."
 A detailed analysis of the contaminations in the SZ signal has been provided by ? and by ?.., A detailed analysis of the contaminations in the SZ signal has been provided by \cite{2004ApJ...612...96K} and by \cite{2004astro.ph..2571A}.
 A comprehensive description of the instrumental effects on the recovery of X-ray. observables. calibrated on hydrodynamical simulations. has been provided by ? (seealso2).," A comprehensive description of the instrumental effects on the recovery of X–ray observables, calibrated on hydrodynamical simulations, has been provided by \cite{2004MNRAS.351..505G} \citep[see also][] 
{2006astro.ph..2434R}."
 In this sense. our analysis will be based on ideal maps. which are free of any noise.," In this sense, our analysis will be based on ideal maps, which are free of any noise."
 We defer to a future analysis the inclusion of the errors associated to realistic X-ray and SZ observational setups., We defer to a future analysis the inclusion of the errors associated to realistic X–ray and SZ observational setups.
" The sample of simulated galaxy clusters used in this paper has been extracted from the large-scale cosmological hydro-N-bodysimulation of a “concordance” ACDM model with ο=0.3 for the matter density parameter at present time. {δν=0.7 for the cosmological constant term. Q1,=0.019? for the baryons density parameter. 7=0.7 for the Hubble constant in units of 100 km s!Mpe | and cx=0.8 for the rms."," The sample of simulated galaxy clusters used in this paper has been extracted from the large-scale cosmological hydro-N-bodysimulation of a “concordance” $\Lambda$ CDM model with $\Omega_m=0.3$ for the matter density parameter at present time, $\Omega_\Lambda=0.7$ for the cosmological constant term, $\Omega_{\rm b}=0.019\,h^{-2}$ for the baryons density parameter, $h=0.7$ for the Hubble constant in units of 100 km $^{-1}$ $^{-1}$ and $\sigma_8=0.8$ for the r.m.s."
 density perturbation within a top-hat sphere having comoving radius of SfMpc., density perturbation within a top–hat sphere having comoving radius of $8\hm$.
 We refer to ?. (BO4 hereafter) for a detailed presentation of this simulation. while we give here only a short description.," We refer to \cite{2004MNRAS.348.1078B} (B04 hereafter) for a detailed presentation of this simulation, while we give here only a short description."
 The run. performed with the massively parallel Tree+SPH code (??).. follows the evolution of 480° dark matter particles and an equal number of gas particles in a periodic cube of size 192h+ Mpc.," The run, performed with the massively parallel Tree+SPH code \citep{SP01.1,2005astro.ph..5010S}, follows the evolution of $480^3$ dark matter particles and an equal number of gas particles in a periodic cube of size $192 h^{-1}$ Mpc."
 The mass of the gas particles is mea.6.9.1075. *AL.. while the Plummer-equivalent force softening is 7.5h* Κρο at z=0.," The mass of the gas particles is $m_{\rm gas}=6.9 \times 10^8 h^{-1} M_\odot$ , while the Plummer-equivalent force softening is $7.5 h^{-1}$ kpc at $z=0$."
 Besides gravity and hydrodynamics. the simulation includes the treatment of radiative cooling. the effect of a uniform time-dependent UV background. a sub-resolution model for star formation from a multiphase interstellar medium. as well as galactic winds powered by SN explosions (2)..," Besides gravity and hydrodynamics, the simulation includes the treatment of radiative cooling, the effect of a uniform time–dependent UV background, a sub–resolution model for star formation from a multiphase interstellar medium, as well as galactic winds powered by SN explosions \citep{2003MNRAS.339..289S}."
 At >=0 we extract ü set of 117 clusters. whose mass.as computed from a friends-of-friends algorithm with linking length b=0.15 (in units of the mean interparticle distance) is larger than 103ATAL.," At $z=0$ we extract a set of 117 clusters, whose mass,as computed from a friends-of-friends algorithm with linking length $b=0.15$ (in units of the mean interparticle distance) is larger than $10^{14}\msun$."
" Due to the finite box size. the largest cluster found in the cosmological simulation has ἐν75 KeV. In order to extend our analysis to more massive and hotter systems. which are mostly relevant for current SZ observations. we include four more galaxy clusters having Aci,>10thiij? and belonging to a different set of hydro-N-body simulations (2).."," Due to the finite box size, the largest cluster found in the cosmological simulation has $T_{\rm e}\approx 5$ keV. In order to extend our analysis to more massive and hotter systems, which are mostly relevant for current SZ observations, we include four more galaxy clusters having $M_{\rm vir}>10^{15} \msun$ and belonging to a different set of hydro-N-body simulations \citep{2006MNRAS.tmp..270B}."
" Since these objects have been obtained by re-simulating. at high resolution. a patch of a pre-existing cosmological simulation. they havea better mass resolution. with mi,=169.LohΣΑΕ,"," Since these objects have been obtained by re-simulating, at high resolution, a patch of a pre-existing cosmological simulation, they havea better mass resolution, with $m_{\rm gas}= 1.69 \times 10^{8}
h^{-1}M_\odot$."
 These simulations iive been performed by using the same code with the same choice of the parameters defining starformation and feedback., These simulations have been performed by using the same code with the same choice of the parameters defining star–formation and feedback.
 The cosmological parameters also are the same. except for a larger yower Spectrum normalization. ex=0.9.," The cosmological parameters also are the same, except for a larger power spectrum normalization, $\sigma_8=0.9$."
" Therefore. our total sample comprises 121 objects. spanning 1e range of Spectroscopic temperatures 75;219 keV. out of which 25 have 7,=2.5 keV and only four have 7475 keV. The corresponding temperature distribution is reported in Figure ."," Therefore, our total sample comprises 121 objects, spanning the range of spectroscopic temperatures $T_{sl}\simeq 1 - 9 $ keV, out of which 25 have $T_{sl} > 2.5$ keV and only four have $T_{sl} > 5$ keV. The corresponding temperature distribution is reported in Figure \ref{fi:tmp_distr}."
 Quite apparently. our set of clusters on average samples a lower temperature range with respect to that covered by current SZ observations.," Quite apparently, our set of clusters on average samples a lower temperature range with respect to that covered by current SZ observations."
 For this reason. we will discuss in the following the stability of our results when selecting only the high end of the temperature distribution.," For this reason, we will discuss in the following the stability of our results when selecting only the high end of the temperature distribution."
 Since our set of simulated clusters covers a relatively low temperature range. we can safely ignore any relativistic corrections to the SZ signal (e.g.. 2).. ," Since our set of simulated clusters covers a relatively low temperature range, we can safely ignore any relativistic corrections to the SZ signal \citep[e.g.,][]{1998ApJ...502....7I}. ."
"Around each cluster we extract a spherical region extending out to 6 /?.;,.", Around each cluster we extract a spherical region extending out to 6 $R_{vir}$ .
" Following ?.. we create maps of the relevant quantities along three orthogonal directions. extending out to about 2 Rj, from the cluster center."," Following \cite{2005MNRAS.356.1477D}, , we create maps of the relevant quantities along three orthogonal directions, extending out to about 2 $R_{vir}$ from the cluster center."
 Each map is a regular 2565 grid., Each map is a regular $256\times 256$ grid.
Cousider a blazar enütting gamuna rays at distance L.,	Consider a blazar emitting gamma rays at distance $L$.
" Cama ravs enütted at an angle 0. velative to the ine of sight mayproduce an c*| pair via absorption ou i6 photon backeround(Could&Sclaéder1967) at v distance £"" from the source. not uecessarily equal/ to je 110211 free path."," 	Gamma rays emitted at an angle $\theta_s$ relative to the line of sight mayproduce an $e^\pm$ pair via absorption on the photon 	background \citep{Gould1967} at a distance $L'$ from the source, not necessarily equal to the mean free path."
 After being deflected by the ECAIF wough the angle 064. the pairs could scatter background xiotons to σαλάτα energies. redirecting them toward 1e observer.," After being deflected by the EGMF 	through the angle $\theta_d$, the pairs could scatter background photons to gamma-ray energies, redirecting them toward the observer."
" These secondary ezunia rays would arrive oan incidence angle 0, (see Fig. 1))5", These secondary gamma rays would 	arrive at an incidence angle $\theta_c$ (see Fig. \ref{fig:geometry}) ).
" Tn this picture. 1ο Influence of the ECGME cuters solely through 0,."," In this picture, the influence of the EGMF enters solely through $\theta_d$ ."
" The aneles 0, aud 0, are uniquely specified in terms of 04. LE. aud 1. provided 0.—7/2."," The angles $\theta_c$ and $\theta_s$ are uniquely specified in terms of $\theta_d$, $L$, and $L'$, provided $\theta_c<\pi/2$."
" Because the energv density of CAIB photous far exceeds that of the extragalactic backerouud light (EBL). we asstme that inverse Compton scattering proceeds in the Thomson reeime via c interactious with the CXMB exclusively,"," 	Because the energy density of CMB photons far exceeds that of the extragalactic background light (EBL), we assume that inverse Compton scattering proceeds in 	the Thomson regime via $e^\pm$ interactions with the CMB exclusively."
" An electron. with Loreutz factor >, will on average scatter secondary plotous to oenergv [r2ey/3. €y7OGL meV is the average CMD photon cncrev where(Bhuneuthal&Could19703."," An electron with Lorentz factor $\gamma_e$ will on average scatter secondary photons to 	energy $4\gamma_e^2\epsilon_0/3$, where $\epsilon_0\approx0.64$ meV is the average CMB photon energy \citep{Blumenthal1970}."
. The cuerey loss rate of the electronis where ¢ is the speed of light. Nevip7ULcm3 is the CMB photon density. aud oT2EGME6.65ς107?cm? is the Thomson cross section.," The energy loss rate of the 	electron is 	where $c$ is the speed of light, $n_\textnormal{CMB}\approx411\text{ cm}^{-3}$ is the CMB photon density, and $\sigma_T\approx6.65\times10^{-25}\text{ cm}^2$ 	is the Thomson cross section."
" For an B perpeudicular to the clectron inomieutum p,. the de‘flection rate in terms of the Larmor radius rj=smiοςis Thus. when au electrou's Loreutz factor has changed from 249 to 2,. the electron will have heen deflected by Iowever. if the angle 0; between B aud p, is other than 7/2. Eq."," For an EGMF $\textbf{\textit{B}}$ perpendicular to the electron momentum $\textbf{\textit{p}}_e$, the deflection rate in terms of 	the Larmor radius $r_l=\gamma_em_ec^2/eB$is 	Thus, when an electron's Lorentz factor has changed from $\gamma_{e0}$ to $\gamma_e$, the electron will have been deflected by 	However, if the angle $\theta_f$ between $\textbf{\textit{B}}$ and $\textbf{\textit{p}}_e$ is other than $\pi/2$, Eq."
 3. should be eeneralized. to We use the full CMB black-body. spectrmu to deteriuue the observed cascade spectrum., \ref{eq:defangle} should be generalized 	to 	 	We use the full CMB black-body spectrum to determine the observed cascade spectrum.
" The number of secondary plotous between cucrgics £L aud E|4E produced by an electron that chanecs Lorentz factor from ,|ds, to >, is the ummber deusitv of CAIB photons between 3£/((157) and3E|dE)(157) times the Thomson cross section and the distance travelled by the electron: where 5 is the Planck constant. & the Boltzimaun constant. and 7—2.73 Ik the CMD temperature."," The number of secondary photons between energies $E$ and $E+dE$ produced 	by an electron that changes Lorentz factor from $\gamma_e+d\gamma_e$ to $\gamma_e$ is the number density of CMB photons between $3E/(4\gamma_e^2)$ and $3(E+dE)/
	(4\gamma_e^2)$ times the Thomson cross section and the distance travelled by the electron: 	where $h$ is the Planck constant, $k$ the Boltzmann constant, and $T=2.73$ K the CMB temperature."
 Iu terms of the mean free path A(e)=τε] interred from the optical depth τε) of the EBL. the probability for a photon ofeuergv € to be absorbed between £/ and L| οMe).," 	In terms of the mean free path $\lambda(\epsilon)=L/\tau(\epsilon)$ inferred from the optical depth $\tau(\epsilon)$ of the EBL, the probability for a photon ofenergy $\epsilon$ to be absorbed between $L'$ and $L'+dL'$ is $e^{-L'/\lambda(\epsilon)}dL'/\lambda(\epsilon)$ ."
" Approximating both particles in the resulting pair to have initial energv Ημ=6/2. we calculate the differential flux of observed secondary photous by inteerating over L'. and >,.. and averaging over (y: Tere. (0) is the probability distribution of Oy. equal to sind, for an ECMP uuiforily distributed in direction. auc fle.@.) is the intrinsic flux of the source. with Ó.—0;0. trom Fig. 1.."," Approximating both particles in the resulting pair to have initial energy $m_e\gamma_{e0}c^2=\epsilon/2$, we calculate the differential flux 	of observed secondary photons by integrating over $L'$, $\epsilon$, and $\gamma_e$, and averaging over $\theta_f$: 	Here, $g(\theta_f)$ is the probability distribution of $\theta_f$, equal to $\sin\theta_f$ for an EGMF uniformly distributed in direction, and $f(\epsilon,\theta_s)$ is the intrinsic flux of the source, with $\theta_s=\theta_d-\theta_c$ from Fig. \ref{fig:geometry}."
" The 1/27 factor from the et being deflected into the surface of a cone with opening anele 0, caucels the 27 cuhancement from a simular effect at the source.", The $1/2\pi$ factor from the $e^{\pm}$ being deflected into the surface of a cone with opening angle $\theta_d$ cancels the $2\pi$ enhancement from a similar effect at the source.
 We take the integral over 0 from 0 to 2., We take the integral over $\theta_f$ from $0$ to $\pi/2$.
 The physical lower bound. for the Over he primary euecrgv e iS ἐμμμσημ.integratio, The physical lower bound 	for the integration over the primary energy $\epsilon$ is $\epsilon_\textnormal{min}=2\gamma_em_ec^2$.
nNearly all of he photons above 200 TeV will iο absorbed within 1 Mpe of the source. and the &* pairs will be isotropized w the strong field of the surrounding galaxy. resulting iu negligible cascade contribution.," Nearly all of the photons above 200 TeV will be absorbed within 	1 Mpc of the source, and the $e^\pm$ pairs will be isotropized by the strong field of the surrounding galaxy, resulting in negligible cascade contribution."
" We therefore adopt an upper ΠΕ of ἐμως=200 TeV. sugeesting au upper iut of ἕως)ο ou the ~, iutegratiou."," We 	therefore adopt an upper limit of $\epsilon_\textnormal{max}=200$ TeV, suggesting an upper limit of $\epsilon_\textnormal{max}/2m_ec^2$ on the $\gamma_e$ 	integration."
" As a practical hatter. we enforce a lower limit of >,=10° on the >, integration. motivated by the CAIB density becoming at energies above 3 meV aud our disinterest iu he cascade spectrum below 100 MeV. Observational effects cuter Eq."," As a practical matter, we enforce a lower limit of $\gamma_e=10^5$ on the $\gamma_e$ integration, motivated by the CMB density becoming 	negligible at energies above 3 meV and our disinterest in the cascade spectrum below 100 MeV. 	Observational effects enter Eq."
" 6 through limits on he £"" integration.", \ref{eq:model} through limits on the $L'$ integration.
 As ποσα in Fie. L..," As seen in Fig. \ref{fig:geometry},"
" we can express 0, as so that à cut ou 7. translates directly into à cut on L’.", we can express $\theta_c$ as 	so that a cut on $\theta_c$ translates directly into a cut on $L'$ .
 Siniluh. the time delav AT of cascade pliotousmay be written as exchanging a lanit ou the source livetime AT for another constraiut on £7.," Similarly, the time delay $\Delta T$ of cascade photonsmay be written as 	exchanging a limit on the source livetime $\Delta T$ for another constraint on $L'$ ."
 We adopt the intersection of the E'/ cuts from Eqs., We adopt the intersection of the $L'$ cuts from Eqs.
 7 and 8. in evaluatiug the cascade flux via Eq. 6 , \ref{eq:angle} and \ref{eq:time} in evaluating the cascade flux via Eq. \ref{eq:model}. .
We nowbriefly exanuüne several assunuptious mace in the coustruction of this cascade model., 	We nowbriefly examine several assumptions made in the construction of this cascade model.
 (4) Exact enerev distrbutious of pair production products are approximated as each having half the energv of the primary photon. as the cascade spectrum only weakly," 	(i) Exact energy distributions of pair production products are approximated as each having half the energy of the primary photon, as the cascade spectrum only 	weakly"
thermal time scales are lone in the low-clensity IGM tha is responsible for the forest.,thermal time scales are long in the low-density IGM that is responsible for the forest.
 Since the temperature of the photo-ionised IGM. is determined. by the evolution. of the ionising background. unravelling the thermal history wil have the added benefit of putting strong limits on the sources of UN light at high redshifts.," Since the temperature of the photo-ionised IGM is determined by the evolution of the ionising background, unravelling the thermal history will have the added benefit of putting strong limits on the sources of UV light at high redshifts."
 We have presented a new wav of analysing the smal scale structure of the forest. based. on the unique decomposition of a spectrum in discrete wavelets.," We have presented a new way of analysing the small scale structure of the forest, based on the unique decomposition of a spectrum in discrete wavelets."
 We have shown that the rms amplitude C473 of narrow wavelets (18.3 km. +) correlates stronely with the temperature of the ICM. and also depends on the slope of the equation. of state.," We have shown that the rms amplitude $\langle
A^2\rangle$ of narrow wavelets (18.3 km $^{-1}$ ) correlates strongly with the temperature of the IGM, and also depends on the slope of the equation of state."
 We have quantified to what extent different models can he distinguished. using statistics of Cl Our mock spectra have oen designed. to. mimick. an observed. spectrum of QSO 11O7|485 as much as possible.," We have quantified to what extent different models can be distinguished, using statistics of $\langle A^2\rangle$ Our mock spectra have been designed to mimick an observed spectrum of QSO 1107+485 as much as possible."
 In particular. we have impose on our simulated spectra the same large scale optical depth luctuations as are observed in QSO 1107. making our mock s»ectra quite realistic.," In particular, we have imposed on our simulated spectra the same large scale optical depth fluctuations as are observed in QSO 1107, making our mock spectra quite realistic."
 Leven so. we can still easily distinguish »etween models that eller in temperature by less than 30 ner cent.," Even so, we can still easily distinguish between models that differ in temperature by less than 30 per cent."
 We have quantified the dependence. of these staistics on numerical artifacts (missing long wavelength perturbations due to the smallness of our simulation box) and on the amplitude of the dark matter [Ductuations (as)., We have quantified the dependence of these statistics on numerical artifacts (missing long wavelength perturbations due to the smallness of our simulation box) and on the amplitude of the dark matter fluctuations $\sigma_8$ ).
 Wavelets are also localised in space. making it possible to study Zo and 5 as a function. of position along the spectrum.," Wavelets are also localised in space, making it possible to study $T_0$ and $\gamma$ as a function of position along the spectrum."
 We characterised. the extent to which we can distinguish models with a single value of Z5 from a model with temperature Huctuations. as might result. from. late reionization or local effects.," We characterised the extent to which we can distinguish models with a single value of $T_0$ from a model with temperature fluctuations, as might result from late reionization or local effects."
" We acknowledge simulating discussion with Martin ]laehnelt. Michael Hauch. Joop Schave and Simon White. This work has been supported by the “Formation anc Evolution of network set up by the European Commission under contract ERB EMIUN-C""E96086.— οἱ its TMER programme."," We acknowledge simulating discussion with Martin Haehnelt, Michael Rauch, Joop Schaye and Simon White, This work has been supported by the Formation and Evolution of network set up by the European Commission under contract ERB FMRX-CT96086 of its TMR programme."
 This research. was conducted. in cooperation with Silicon Ciraphies/Cray. Research utilising the Origin 2000 super computer at DAA. Cambridge.," This research was conducted in cooperation with Silicon Graphics/Cray Research utilising the Origin 2000 super computer at DAMTP, Cambridge."
hieher than f=60 because the deeree-dependence of the signal becomes difficult to model aud fit.,higher than $\ell=60$ because the degree-dependence of the signal becomes difficult to model and fit.
 The quantity we are most interested in is the amplitude of the oscillatory signal [rom Ie ll ionization zone as a function of the magnetic activity level of the Sun when the data were obtained., The quantity we are most interested in is the amplitude of the oscillatory signal from He II ionization zone as a function of the magnetic activity level of the Sun when the data were obtained.
 Since the amplitude is both degree-dependent as well as Irequency-dependent. we use the averaged amplitude in the frequency range 2 (o0 3.5imillIz alter the degree dependence is removed.," Since the amplitude is both degree-dependent as well as frequency-dependent, we use the averaged amplitude in the frequency range 2 to 3.5mHz after the degree dependence is removed."
 This is the same as what was done by Basu et al. (, This is the same as what was done by Basu et al. (
1994). Basu Antia (1994) and Basu (1997).,"1994), Basu Antia (1994) and Basu (1997)."
 The error on the result is determined by Monte-Carlo simulations., The error on the result is determined by Monte-Carlo simulations.
 The fit to the signal from the Ile II ionization zone. alter removal of the degree dependence. is shown in Fig.," The fit to the signal from the He II ionization zone, after removal of the degree dependence, is shown in Fig."
 2 lor one set of low-degree GONG data., \ref{fig:fit4} for one set of low-degree GONG data.
 The amplitudes of the oscillatory signal (hat arises from the 11ο II ionization zone are plotted as a [function of the solar activity index in Fig. 3.., The amplitudes of the oscillatory signal that arises from the He II ionization zone are plotted as a function of the solar activity index in Fig. \ref{fig:sepa}.
 The 10.7 cm flux is in units of the Solar Flux Unit (SFU). ie.. 10.72 Js ! 2 !.," The 10.7 cm flux is in units of the Solar Flux Unit (SFU), i.e., $10^{-22}$ J $^{-1}$ $^{-2}$ $^{-1}$."
" We have plotted the four sets of data separately,", We have plotted the four sets of data separately.
 We find that in all cases. the amplitude decreases wilh increasing solar activity. a result that is expected if the active-region results can be applied to the elobal Sun.," We find that in all cases, the amplitude decreases with increasing solar activity, a result that is expected if the active-region results can be applied to the global Sun."
 We can fit straight lines to (he data «quite easily the large errors do not justly fitting more complicated trends., We can fit straight lines to the data quite easily — the large errors do not justify fitting more complicated trends.
 We can see that for all 4 sets. the straight line has a finite slope. however. the slope is not always statistically significant.," We can see that for all 4 sets, the straight line has a finite slope, however, the slope is not always statistically significant."
 This is particularly (rue for the GONG data., This is particularly true for the GONG low-degree data.
 The MDI low-degree sets show only a marginally significant decrease., The MDI low-degree sets show only a marginally significant decrease.
 However. the intermediate-degree sets for both GONG ancl MDI show a reasonably significant. trend (zz 4o).," However, the intermediate-degree sets for both GONG and MDI show a reasonably significant trend $\approx 4\sigma$ )."
 The scatter in the plots is somewhat less than what the errors on (he points should suggest. so itis likely (hat the errors have been overestimatecl and significance of the slope uncerestimated.," The scatter in the plots is somewhat less than what the errors on the points should suggest, so it is likely that the errors have been overestimated and significance of the slope underestimated."
 It is not completely surprising that the low- aud intermecdiate-degree sets give us somewhat different. results., It is not completely surprising that the low- and intermediate-degree sets give us somewhat different results.
 For the low-degree sets. we need to correctly remove the signal from the CZ base to get the correct aaplitude from the Ie IL ionization zone.," For the low-degree sets, we need to correctly remove the signal from the CZ base to get the correct amplitude from the He II ionization zone."
 Simulations performed with different solar models show that this process leads (o substantial svstematic errors in the results., Simulations performed with different solar models show that this process leads to substantial systematic errors in the results.
 The intermediate-degree modes are not affected by the CZ base at all. ancl hence the signal due to the Ile II zone is cleaner ancl easier to measure.," The intermediate-degree modes are not affected by the CZ base at all, and hence the signal due to the He II zone is cleaner and easier to measure."
 Thus we put more weight on (he results obtained [rom the intermediate degree modes., Thus we put more weight on the results obtained from the intermediate degree modes.
 Figure 4 shows both GONG and MDI intermecdiate-deeree resulüs plotted as a function, Figure \ref{fig:high} shows both GONG and MDI intermediate-degree results plotted as a function
I. (Thomson1,$_3^+$ \citep{Thomson11}.
911).. HL] (Nealeaud. (Lystrupefad.2008:Ioskinen2004))..," $\Delta E\approx -1.7$ $_3^+$ \citep{Neale95ApJ}, \citep{Miller08ApJ,Koskinen09ApJ}."
 IL; (Nealectal.IKoskineu.e£a£," $_3^+$ \citep{Neale96ApJ,Tennyson04ApJ,Koskinen07ApJ}."
2007).. I. (NealeaudTeuuysou1995).. (Neale (Dinellie£αἱ.1995).., $_3^+$ \citep{Neale95ApJ}. \citep{Neale95ApJ}. \citep{Tennyson95jcp}.
 HL] (Nealectαἱ.1996).., $_3^+$ \citep{Neale96ApJ}.
 dissociate to its fragments. and in fact. the equilibrium needs to be considered above about 1000 TS. the balance depending strouglv ou both the temperature aud the clensity.," dissociate to its fragments, and in fact, the equilibrium needs to be considered above about $4000$ K, the balance depending strongly on both the temperature and the density."
 This brings forth two questions. at the least.," This brings forth two questions, at the least."
 First. how relevant if is to cosider the molecular cuerectics and related partition fiuction at temperatures where the molecule has dissocqated and appears in form of fraciments of the equililniin reaction. Eq.(," First, how relevant it is to consider the molecular energetics and related partition function at temperatures where the molecule has dissociated and appears in form of fragments of the equilibrium reaction, Eq.,"
2). Oonly., only.
 Secondly. the balance ο: the equilibrium reaction may be strougly affected. no ouly bv the deusitv. but also by the enviromuent including the ucutralizing negative counterparts of the positive IL.," Secondly, the balance of the equilibrium reaction may be strongly affected, not only by the density, but also by the environment including the neutralizing negative counterparts of the positive $_3^+$."
 Thus. the thermal dissociationrecombination balance above about £000 Iv eives rise to prollenis. which have uot been taken iuto account im this «o»text. vet.," Thus, the thermal dissociation–recombination balance above about $4000$ K gives rise to problems, which have not been taken into account in this context, yet."
 Iu this study. using the path inteeral quantum Moute Carlo (CPINMC) method we have carried out the first μπαΊος of the full quantum statistics of the IL) ion. described by Eq.(," In this study, using the path integral quantum Monte Carlo (PIMC) method we have carried out the first simulations of the full quantum statistics of the $_3^+$ ion, described by Eq.,"
2). at low densities aud high temperatures raneine from 160 I& up to about 15000 I. PIMC is the method to mect the above challenges: we need not make auy approximations or restrictions iu the sununidue over states. ecoletiics or quanti description of dvnamics.," at low densities and high temperatures ranging from $160$ K up to about $15000$ K. PIMC is the method to meet the above challenges: we need not make any approximations or restrictions in the summing over states, geometries or quantum description of dynamics."
 The finite temperature is inherent in the PIMC approach aud the Coulomb miauv-body treatineut of the particle interactions is exact., The finite temperature is inherent in the PIMC approach and the Coulomb many-body treatment of the particle interactions is exact.
 The PIMC method is coluputationally expensive. butfeasiblefor zinall enough systems. (Ceperley1995:PierceaudMauousalkis1999: 2009).," The PIMC method is computationally expensive, butfeasiblefor small enough systems. \citep{Ceperley95,Pierce99,Kwon99,Knoll00,Cuervo06,Kylanpaa09pra}."
.The couveutionalquantumchemical description of the TL! ion emerges as the zero. Kelvin, .Theconventionalquantumchemical description of the $_3^+$ ion emerges as the zero Kelvin
" Á from which we have that 60,>0.","_l=- _n=- , from which we have that $\theta_l\theta_n~>~0$."
 Fromequation (28)) we see that the space-time is always singular when (¢)»0., Fromequation \ref{Ip}) ) we see that the space-time is always singular when $(-t)\rightarrow0$.
 On the other laud. the following expression. is always nonzero.," On the other hand, the following expression, - is always nonzero."
 Iu this solution we do uot have an appareut horizon but a simguluitw at f=0., In this solution we do not have an apparent horizon but a singularity at $t=0$.
 Thus. it may be interpreted as representiug à cosinological model.," Thus, it may be interpreted as representing a cosmological model."
 Iuthe case of equation (29)). the metric reads |>," Inthe case of equation \ref{IIIp}) ), the metric reads ]^2dr^2."
" The outgoing[m] aud iugomg[m] null [m]ecodesics expausious 0"" are such that 00,>ο.", The outgoing and ingoing null geodesics expansions_l=- _n=- are such that $\theta_l\theta_n~>~0$.
 Thus. there is no apparent horizon.," Thus, there is no apparent horizon."
 The eeoumetrical radius is giveu by ...HS f). where it is assuied that Sy>0.," The geometrical radius is given by =lS_0(-t) , where it is assumed that $S_0>0$."
 Ou the other haud. we see that the right haud side of the expression 20.," On the other hand, we see that the right hand side of the expression - ,"
 Ou the other haud. we see that the right haud side of the expression 20.4," On the other hand, we see that the right hand side of the expression - ,"
 Ou the other haud. we see that the right haud side of the expression 20.4.," On the other hand, we see that the right hand side of the expression - ,"
can be predicted.,can be predicted.
 The Compton cooling scenario rough equiparliGon conditions in SN 2002ap., The Compton cooling scenario rough equipartition conditions in SN 2002ap.
 Furthermore. the actual value deduced for ej (~e.g) is close to the one derived by BIC [rom the observed. values of the svnchrotron sell-absorption frequency. ancl Παςassuming equipartition.," Furthermore, the actual value deduced for $\epsilon_{\rm B}$ $\sim \epsilon_{\rm rel}$ ) is close to the one derived by BKC from the observed values of the synchrotron self-absorption frequency and flux equipartition."
 This shows that the model sell-consistentlv. predicts the Irequency of the svuehrotvon sell-absorption. as was illustrated in 33..," This shows that the model self-consistently predicts the frequency of the synchrotron self-absorption, as was illustrated in \ref{sec_3}."
 There is. however. one underlying assumption: namely. a spherically svimmetric source.," There is, however, one underlying assumption; namely, a spherically symmetric source."
 It is seen in 82.2 (hat (he only place where the assumption of a spherically svimimetric source geometry enters is in the derivation of the energy density of relativistic electrons [rom the observed X-ray. luminosity (cl, It is seen in \ref{sec_2.2} that the only place where the assumption of a spherically symmetric source geometry enters is in the derivation of the energy density of relativistic electrons from the observed X-ray luminosity (cf.
 eq. 191)., eq. \ref{eq:1.18}] ]).
 Deviations from spherical symmetry. for example a jet structure. would (hen have to be compensated [or by an increasecl energy. density of relativistic electrons.," Deviations from spherical symmetry, for example a jet structure, would then have to be compensated for by an increased energy density of relativistic electrons."
" Since the deduced. values of B and ry, ave not affected. (οἱ."," Since the deduced values of $B$ and $v_{\rm
sh}$ are not affected (cf."
 eqs. ο and[18]]).," eqs. \ref{eq:1.16}] ] \ref{eq:1.17}] ]),"
 this results in an increased synchrotron self-absorption frequency., this results in an increased synchrotron self-absorption frequency.
" Due to the short term flux variations. which are likely caused by interstellar scattering and scintillation. (he limits of the allowed variations of the predicted sell-absorption frequency are hard (o evaluate precisely,"," Due to the short term flux variations, which are likely caused by interstellar scattering and scintillation, the limits of the allowed variations of the predicted self-absorption frequency are hard to evaluate precisely."
" From the early observations at the lowest frequency (1.43. GIIz). when the radiation at this frequency was optically thick. it seems unlikely (hat the observed frequency has been underestimated by more (han a factor (vo,"," From the early observations at the lowest frequency (1.43 GHz), when the radiation at this frequency was optically thick, it seems unlikely that the observed self-absorption frequency has been underestimated by more than a factor two."
" Since svnchrotron sell-absorption frequency scales with energy. density of relativistic electrons as 20""the value of ενω can be increased at most by a factor ten."," Since synchrotron self-absorption frequency scales with energy density of relativistic electrons as $\epsilon_{\rm rel}^{2/(p+4)}$, the value of $\epsilon_{\rm rel}$ can be increased at most by a factor ten."
 Hence. the solid angle of a jet has to cover al least LO of the sky.," Hence, the solid angle of a jet has to cover at least 10 of the sky."
 This conclusion is similar to the one reached by (2003).. using a different line of reasoning.," This conclusion is similar to the one reached by \citet{Tot03}, using a different line of reasoning."
 BKC :wgue that the observed XMM πας can be described as an extrapolation of the svichrotro1 flux., BKC argue that the observed XMM flux can be described as an extrapolation of the synchrotron flux.
 This is apparently based on the assumption that the radio spectral index is close to 3c-0.5. which is needed to explain (he lisht curves in (he absence of cooling.," This is apparently based on the assumption that the radio spectral index is close to $\beta\sim 0.5$, which is needed to explain the light curves in the absence of cooling."
 The resulting spectral break in the optical frequency range due to svnehrotron cooling In an equipartütion magnetic field would give rise to an X-ray flux ancl spectral index in approximate agreement with those observed., The resulting spectral break in the optical frequency range due to synchrotron cooling in an equipartition magnetic field would give rise to an X-ray flux and spectral index in approximate agreement with those observed.
 However. as discussed in 82.2.. the observed spectral index in the radio is ;20.9. which is similar (ο that in the X-ray range. makine ihis scenario untenable.," However, as discussed in \ref{sec_2.2}, the observed spectral index in the radio is $\beta\sim 0.9$, which is similar to that in the X-ray range, making this scenario untenable."
 eSutaria.Chandra.Bhatnagar.5&Rav(2003) explain the X-ray [ιν as a resu (olfthermal inverse Compton scattering bv the thermal electrons behind the shock (seeFransson19382)., \citet{SCB03} explain the X-ray flux as a result of inverse Compton scattering by the thermal electrons behind the shock \citep[see][]{F82}.
. In order to have sufficient electron optical depth. (μον need to have the X-ray emitling region moving with a velocity 16.000kms+.," In order to have sufficient electron optical depth, they need to have the X-ray emitting region moving with a velocity $\sim 16,000\kms$."
 A similar low velocity of the forward shock is needed in the model by Soria.Pian.&Mazzali(2004)., A similar low velocity of the forward shock is needed in the model by \citet{SPM03}.
. They argue that the X-ray. emission is emission [rom the reverse shock., They argue that the X-ray emission is free-free emission from the reverse shock.
 There are several features of these models which make (hem less attractive., There are several features of these models which make them less attractive.
 In the thermal inverse Compton scattering model. the spectral index," In the thermal inverse Compton scattering model, the spectral index"
The three-point correlation [ποιοι (3PCTE). or its Fourier trauslorim. the bispectrum. is a valuable complement to two-point statistics in characterizing galaxy clustering.,"The three-point correlation function (3PCF), or its Fourier transform, the bispectrum, is a valuable complement to two-point statistics in characterizing galaxy clustering."
 The behavior of the 3PCF of the matter is well uuderstood in perturbation theory (e.g. Fry1984:Corolletal.Scoccimnarro&Frieman1999:Bernardeauetal. 2002)).," The behavior of the 3PCF of the matter is well understood in perturbation theory (e.g., \citealt{Fry84,Goroff86,Bernardeau92,Jain94,Scoccimarro96,
Scoccimarro98,Scoccimarro99,Bernardeau02}) )."
 For Gaussian initial couditious. perturbation theory predicts that the amplitude of the 3PCF £7 scales like the square of the amplitude of the two-point correlation Dunctiou (2PCF) € (Peebles 19501). and this scaling is one of," For Gaussian initial conditions, second-order perturbation theory predicts that the amplitude of the 3PCF $\xithree$ scales like the square of the amplitude of the two-point correlation function (2PCF) $\xi$ \citealt{Peebles80}) ), and this scaling is one of"
similar to the original test proposed by Nake Piran. except that agreement with the Amati relation corresponds to about violators.),"similar to the original test proposed by Nakar Piran, except that agreement with the Amati relation corresponds to about violators.)"
 We apply this test to many burst samples., We apply this test to many burst samples.
 The samples of early bursts with spectroscopic redshifts (as originally used to calibrate the Amati relation) pass our test. as does the sample of WETE bursts (even though the scatter about the Amati relation is nnusably large).," The samples of early bursts with spectroscopic redshifts (as originally used to calibrate the Amati relation) pass our test, as does the sample of HETE bursts (even though the scatter about the Amati relation is unusably large)."
 All other satellites have a large fraction of violators far below the Amati limit line., All other satellites have a large fraction of violators far below the Amati limit line.
 This is (ame whether we look at bursts with or without measured spectroscopic redshifts., This is true whether we look at bursts with or without measured spectroscopic redshifts.
 This constitutes a proof that the Amati relation could possibly appl. ab best. to only a small and unrecognizable fraction of GRBs.," This constitutes a proof that the Amati relation could possibly apply, at best, to only a small and unrecognizable fraction of GRBs."
 Indeed. the wide variations in distribution from detector to detector constitute a proof that selection ellects must dominate ihe Amati relation.," Indeed, the wide variations in distribution from detector to detector constitute a proof that selection effects must dominate the Amati relation."
 We find [our selection effects restrict. the distribution on all sides., We find four selection effects restrict the distribution on all sides.
 The best. known detector selection effect is (he trigger threshokl. which produces a roughly horizontal and [uzzv cutoll," The best known detector selection effect is the trigger threshold, which produces a roughly horizontal and fuzzy cutoff."
" A more subtle and more restrictive selection effect is that for an. E,44, value to be reported. the burst must be brighter than some threshold. with this (hreshold rising fast with increasing £,,5,5'."," A more subtle and more restrictive selection effect is that for an $E_{peak,obs}$ value to be reported, the burst must be brighter than some threshold, with this threshold rising fast with increasing $E_{peak,obs}$."
 These two detector selection ellects will cut out. bursts that are some combination of faint and hard. with these ellects changing greatly [rom detector to detector.," These two detector selection effects will cut out bursts that are some combination of faint and hard, with these effects changing greatly from detector to detector."
 The third aud fourth selection effects operate to restrict the burst population as il appears in the sky., The third and fourth selection effects operate to restrict the burst population as it appears in the sky.
 The third selection elfect is that bursts have a loe-normal distribution Of E. With the mean value shifting to lower values for faint bursis.," The third selection effect is that bursts have a log-normal distribution of $E_{peak,obs}$ with the mean value shifting to lower values for faint bursts."
 This effect will also reduce the number of detectable bursts that are faint and hard., This effect will also reduce the number of detectable bursts that are faint and hard.
 The fourth selection ellect is (hat bright bursts are much rarer than faint bursts. as quantified by the usual power-law log)N(>P)]—log|P?] curve.," The fourth selection effect is that bright bursts are much rarer than faint bursts, as quantified by the usual power-law $\log [N(>P)]-\log[P]$ curve."
 The combination of the third and fourth effects means (hat the bright and soft bursts are doublv-rare. so that the upper-left side of the Shots—E0455. diagram will be empty.," The combination of the third and fourth effects means that the bright and soft bursts are doubly-rare, so that the upper-left side of the $S_{bolo} - E_{peak,obs}$ diagram will be empty."
" For a detector with a range5 of spectral sensitivity and a low detection threshold. the distribution in the Spor—E,"" diagram will extend relatively low. with a large fraction of violators below the Amati limit (like for BATSE)."," For a detector with a range of spectral sensitivity and a low detection threshold, the distribution in the $S_{bolo} - E_{peak,obs}$ diagram will extend relatively low, with a large fraction of violators below the Amati limit (like for BATSE)."
 For a detector with a low energv range of sensilivily and a low detection threshold. the cutoff will be a diagonal line just below the Amati limit.," For a detector with a low energy range of sensitivity and a low detection threshold, the cutoff will be a diagonal line just below the Amati limit."
 When combined with the paucity of bright-soft bursts in the GRB population (i.e.. those above the Amati limit line). we have a combined selection effect that picks out bursts near the Amati limit.," When combined with the paucity of bright-soft bursts in the GRB population (i.e., those above the Amati limit line), we have a combined selection effect that picks out bursts near the Amati limit."
 Such a burst sample would then appear to follow the Amati relation., Such a burst sample would then appear to follow the Amati relation.
 Thus. the very strong selection effects [or the early bursts with spectroscopic redshifts will create the Amati relation without anv need for a physical connection between the {ουςpecak.ol and bolο.," Thus, the very strong selection effects for the early bursts with spectroscopic redshifts will create the Amati relation without any need for a physical connection between the $E_{peak,obs}$ and $S_{bolo}$."
 That is. the Amati relation is not real. but its appearance in some data sets is simply a result of various selection elfects by the detectors and within the GRD population.," That is, the Amati relation is not real, but its appearance in some data sets is simply a result of various selection effects by the detectors and within the GRB population."
The ssystem stands out of the plethora of known exoplanet systems both for its exceptionally active host star and its unusually inflated planet.,The system stands out of the plethora of known exoplanet systems both for its exceptionally active host star and its unusually inflated planet.
 The hot Jupiter us the second transiting planet discovered by the space-based CoRoT mission (?):: its planetary nature was confirmec by spectroscopic follow-up observations with SOPHIE anc HARPS (?).., The hot Jupiter is the second transiting planet discovered by the space-based CoRoT mission \citep{Alonso2008}; its planetary nature was confirmed by spectroscopic follow-up observations with SOPHIE and HARPS \citep{Bouchy2008}.
 The planet orbits its host star every 1.74 days., The planet orbits its host star every $1.74$ days.
" Given its mass of 3.31 M, and large radius of 1.465 Ry, (?).. aappears to be anomalously inflated in comparisor to current evolutionary models (?).."," Given its mass of $3.31$ $M_\mathrm{J}$ and large radius of $1.465$ $R_\mathrm{J}$ \citep{Alonso2008}, appears to be anomalously inflated in comparison to current evolutionary models \citep{GuillotHavel2011}."
 A’ spectral analysis showed that its host star.CoRoT-2A.. is a G7 dwarf with solar composition.," A spectral analysis showed that its host star, is a G7 dwarf with solar composition."
 Its spectrum shows strong Li I absorptior and emission-line cores inK.. indicating- that tis a young and active star (?)..," Its spectrum shows strong Li I absorption and emission-line cores in, indicating that is a young and active star \citep{Bouchy2008}."
" hhas a close visual companion.J19270636+0122577.. separated by about 4""."," has a close visual companion, separated by about $4\arcsec$."
 Photometric magnitudes from. the optical to the infrared concordantly suggest that this object is a late-K or early-M type star located at the same distance as citepAlonso2008.Gillon2010..," Photometric magnitudes from the optical to the infrared concordantly suggest that this object is a late-K or early-M type star located at the same distance as \\citep{Alonso2008,Gillon2010}."
 Thus. aand its visual companion possibly form a physical pair.," Thus, and its visual companion possibly form a physical pair."
 The continuous photometric data of pprovided by the CoRoT telescope span 152 days., The continuous photometric data of provided by the CoRoT telescope span $152$ days.
 CoRoT-2A’ss light curve shows a distinct pattern of variability caused by starspots., s light curve shows a distinct pattern of variability caused by starspots.
 In several studies. the light curve was used to reconstruct the surface brightness distribution ofCoRoT-2A:: ? applied a light-curve inversion technique and found that most spots are concentrated in two active longitudes of alternating strength located on opposite hemispheres.," In several studies, the light curve was used to reconstruct the surface brightness distribution of: \citet{Lanza2009} applied a light-curve inversion technique and found that most spots are concentrated in two active longitudes of alternating strength located on opposite hemispheres."
 Moreover. it was demonstrated that starspots influence the profiles of transit light-curves and that this effect cannot be neglected in transit modeling (??)..," Moreover, it was demonstrated that starspots influence the profiles of transit light-curves and that this effect cannot be neglected in transit modeling \citep{Wolter2009, Czesla2009}."
 Because the latitudinal band eclipsed by the planet is accurately known (?).. it is even feasible to study the spot coverage on the surface section recurrently eclipsed by the planet (???)..," Because the latitudinal band eclipsed by the planet is accurately known \citep{Bouchy2008}, , it is even feasible to study the spot coverage on the surface section recurrently eclipsed by the planet \citep{Huber2009, Silva-Valio2010, Huber2010}."
 Secondary eclipses of wwere observed in the optical with CoRoT (??).. in the infrared with Spitzer (??).. and from the ground (?). ," Secondary eclipses of were observed in the optical with CoRoT \citep{Alonso2009, Snellen2010}, in the infrared with Spitzer \citep{Gillon2010, Deming2011}, and from the ground \citep{Alonso2010}. ."
While atmospheric models (?) suggest the presence of a stratospheric thermal-inversion layer in. ecaused by the strong irradiation. the observational situation remains inconclusive (e.g..?)..," While atmospheric models \citep{Fortney2008} suggest the presence of a stratospheric thermal-inversion layer in caused by the strong irradiation, the observational situation remains inconclusive \citep[e.g.,][]{Deming2011}."
 The observed emissiol of the planet is currently incompatible with any kind of standard atmosphere model. and more sophisticated approaches including. for example. substantial carbon monoxide nass loss or additional substructure in the atmosphere may be needed to explain the observations (see?.foradiscussion): the substantial activity of the host star adds another complicating factor to the picture (e.g..?)..," The observed emission of the planet is currently incompatible with any kind of standard atmosphere model, and more sophisticated approaches including, for example, substantial carbon monoxide mass loss or additional substructure in the atmosphere may be needed to explain the observations \citep[see][for a discussion]{Deming2011}; the substantial activity of the host star adds another complicating factor to the picture \citep[e.g.,][]{Knutson2010}."
 Using KECK/HIRES data. ? searched for a relation between stellar activity as manifested by chromospheric emission in the lline cores and the emission spectra of hot Jovians.," Using KECK/HIRES data, \citet{Knutson2010} searched for a relation between stellar activity as manifested by chromospheric emission in the line cores and the emission spectra of hot Jovians."
" Among their sample of planet host-stars. sstands out as being the most active as measured by its logA, index."," Among their sample of planet host-stars, stands out as being the most active as measured by its $\log{R'_{\mathrm{HK}}}$ index."
 ? reanalyzed the archival UVES data presented in ? (program 080.C-0661D) and determined precise estimates of CoRoT-2A’ss spectral properties such as effective temperature and iron abundance., \citet{AmmlervonEiff2009} reanalyzed the archival UVES data presented in \citet{Bouchy2008} (program 080.C-0661D) and determined precise estimates of s spectral properties such as effective temperature and iron abundance.
 In August 2009. ? obtained and analyzed a new UVES spectrum (program 083.C-0174C).," In August 2009, \citet{Gillon2010} obtained and analyzed a new UVES spectrum (program 083.C-0174C)."
 The authors provide a more detailed discussion of the Li absorption line and derive an age between 30 and 316 Ma forCoRoT-2A., The authors provide a more detailed discussion of the Li absorption line and derive an age between 30 and 316 Ma for.
". Additionally. they find evidence for a slight eccentricity of 0.014+0.008 for the planetary orbit. which they attribute to the youth of the system. if not caused by CoRoT-2A’ss potential stellar companion,"," Additionally, they find evidence for a slight eccentricity of $0.014 \pm 0.008$ for the planetary orbit, which they attribute to the youth of the system, if not caused by s potential stellar companion."
 ? investigated the matter of CoRoT-2A’ss anomalously inflated planet on theoretical grounds by. simultaneously modeling the planetary and stellar evolution including stellar activity., \citet{GuillotHavel2011} investigated the matter of s anomalously inflated planet on theoretical grounds by simultaneously modeling the planetary and stellar evolution including stellar activity.
 The authors? models favor two classes of solutions: Either a young system with a star on the pre-main sequence (30—40 Ma) or a much older system (>100 Ma) with a main- star., The authors' models favor two classes of solutions: Either a young system with a star on the pre-main sequence $30-40$ Ma) or a much older system $>100$ Ma) with a main-sequence star.
 The authors discuss several effects that could have led to the anomalously large radius ofCoRoT-2b., The authors discuss several effects that could have led to the anomalously large radius of.
. While they argue that the influence of starspots is minor. either the presence of additional infrared opacity sources in the planetary atmosphere that reduces the rate of heat loss during the planet's evolution or a recent interaction with athird body in thesystem that leaves the planet in an eccentric orbit could account for the observed radius anomaly.," While they argue that the influence of starspots is minor, either the presence of additional infrared opacity sources in the planetary atmosphere that reduces the rate of heat loss during the planet's evolution or a recent interaction with athird body in thesystem that leaves the planet in an eccentric orbit could account for the observed radius anomaly."
with respect to the Sun and r = |r|.,with respect to the Sun and $r$ $=$ $\vert \vec{r} \vert$.
 The acceleration caused by the flow of interstellar gas will be considered as a perturbation acceleration to the central acceleration caused by the solar gravity., The acceleration caused by the flow of interstellar gas will be considered as a perturbation acceleration to the central acceleration caused by the solar gravity.
" In order to compute secular time derivatives of Keplerian orbital elements (a - semi-major axis, e - eccentricity, w - argument of perihelion, Q - longitude of ascending node, { - inclination) we want to use Gauss perturbation equations of celestial mechanics."," In order to compute secular time derivatives of Keplerian orbital elements $a$ - semi-major axis, $e$ - eccentricity, $\omega$ - argument of perihelion, $\Omega$ - longitude of ascending node, $i$ - inclination) we want to use Gauss perturbation equations of celestial mechanics."
" To do this, we need to know radial, transversal and normal components of acceleration given by Eq. ("," To do this, we need to know radial, transversal and normal components of acceleration given by Eq. ("
1).,1).
" Orthogonal radial, transversal and normal unit vectors of the dust particle on the Keplerian orbit are (see Fig."," Orthogonal radial, transversal and normal unit vectors of the dust particle on the Keplerian orbit are (see Fig."
 1 and e.g. Passtor 2009) where f is true anomaly., 1 and e.g. Pásstor 2009) where $f$ is true anomaly.
" Thus, we need to calculate the values of ag = dv/dt-eg, ar = dv/dt-ey and ay = dv/dtΣΕΝ."," Thus, we need to calculate the values of $a_{R}$ $=$ $d \vec{v}/dt \cdot \vec{e}_{R}$, $a_{T}$ $=$ $d \vec{v}/dt \cdot \vec{e}_{T}$ and $a_{N}$ $=$ $d \vec{v}/dt \cdot \vec{e}_{N}$."
 Velocity of the particle in an elliptical orbit can be calculated from where and p = a(1—e?)., Velocity of the particle in an elliptical orbit can be calculated from where and $p$ $=$ $a (1 - e^{2})$.
 In this calculation also the second Kepler’s law df/dt = J/up/r? must be used., In this calculation also the second Kepler's law $df/dt$ $=$ $\sqrt{\mu p}/r^{2}$ must be used.
" Now, one can easily verify that where and vg = |vg|."," Now, one can easily verify that where and $v_H$ $=$ $\vert \vec{v}_{H} \vert$."
 Hence where the identity vA?+B?C? = vg was used., Hence where the identity $\sqrt{A^{2}+B^{2}+C^{2}}$ $=$ $v_{H}$ was used.
" If we denote components of the velocity vector of hydrogen gas in the stationary Cartesian frame associated with the Sun as vg = (vax,υην,ΌΗ2), then we obtain Now we consider only such orbits for which or, more precisely, the value σ΄2 is negligible in comparison with c."," If we denote components of the velocity vector of hydrogen gas in the stationary Cartesian frame associated with the Sun as $\vec{v}_{H}$ $=$ $(v_{HX},v_{HY},v_{HZ})$, then we obtain Now we consider only such orbits for which or, more precisely, the value $\sigma^{2}$ is negligible in comparison with $\sigma$."
" This is reasonable for orbits with not very large eccentricities, since v « vy."," This is reasonable for orbits with not very large eccentricities, since $v$ $\ll$ $v_H$."
" Using this approximation, Eqs. ("," Using this approximation, Eqs. ("
"13)-(14) yield For radial, transversal and normal components of acceleration we obtain from Eq. (","13)-(14) yield For radial, transversal and normal components of acceleration we obtain from Eq. ("
"1), Eqs. (","1), Eqs. ("
9)-(11) and Eq. (,9)-(11) and Eq. (
16) Now we can use Gauss perturbation equations of celestial mechanics to compute time derivatives of orbital,16) Now we can use Gauss perturbation equations of celestial mechanics to compute time derivatives of orbital
Finally. pou is estimated from (he sell-similar settling flow solution (Aledvedey2001) by setting the transition radius approximately equal (ο the radius of the star: ((as?r1).,"Finally, $p_{\rm out}$ is estimated from the self-similar settling flow solution \citep{MN01} by setting the transition radius approximately equal to the radius of the star: s^2."
" The transition from the boundary laver to the hot settling flow occurs at some distance d,,. Which can be estimated by matching the boundary laver density or sound speed (which is equivalent. because the pressure also matches) to that of the hot settling flow."," The transition from the boundary layer to the hot settling flow occurs at some distance $d_{tr}$, which can be estimated by matching the boundary layer density or sound speed (which is equivalent, because the pressure also matches) to that of the hot settling flow."
" Assuming that d;«1. the hot settling flow has the proton sound speed squared is equal to (ο/η,1."," Assuming that $d_{tr}\ll 1$, the hot settling flow has the proton sound speed squared is equal to $(c^2/6)r_*^{-1}$."
" Therefore. from cà,e(/6)r,!. we obtain: (Ομ) 0.044 for typical parameters. a=01. ο=0.01. s=0.3. m= LAr,=3."," Therefore, from $c_{s0}^2\sim (c^2/6)r_*^{-1}$, we obtain: (6 0.044 for typical parameters, $\alpha=0.1$, $\dot m=0.01$, $s=0.3$, $m=1.4$, $r_*=3$."
" In the one-temperature regime. (he temperatures of (he protons and electrons are nearly equal. C=(m, /my)c2,. and the both species contribute equally to the pressure."," In the one-temperature regime, the temperatures of the protons and electrons are nearly equal, $c_{sp}^2\approx (m_e/m_p)c_{se}^2$ , and the both species contribute equally to the pressure."
 The energy equations (26)) ancl (27)) reduce to the single energy equation for (he accreting eas (2))., The energy equations \ref{4r}) ) and \ref{5r}) ) reduce to the single energy equation for the accreting gas \ref{45}) ).
 Since dO/dD—0. the heating rate in equation (2)) vanishes.," Since $d\Omega/dD=0$, the heating rate in equation \ref{45}) ) vanishes."
 Together with the continuity equation (2)). (he energy equation reads.," Together with the continuity equation\ref{1}) ), the energy equation reads,"
detection and classification in X-rays. the subsequent optical identification and spectroscopic target selection demonstrate the efficiency of the programme and the associated follow-up.,"detection and classification in X-rays, the subsequent optical identification and spectroscopic target selection demonstrate the efficiency of the programme and the associated follow-up."
 In the near future. our goal will be to confirm. via spectroscopic identifications. all XMM-LSS clusters down to ~8xLO7P oover 8 sq.deg.," In the near future, our goal will be to confirm, via spectroscopic identifications, all XMM-LSS clusters down to $\sim 8\times 10^{-15}$ over $\sim 8$ sq.deg."
 of the AO-1 and AO-2 observations., of the AO-1 and AO-2 observations.
 This will form a complete sample of about 100 X-ray selected clusters at O«z«Il., This will form a complete sample of about 100 X-ray selected clusters at $0<z<1$.
A follow-up of the most interesting objects at z~| is also previewed with integral-field spectroscopy and possibly deeper targeted X-ray observations with XMM or Chandra for better insight into the cluster physics., A follow-up of the most interesting objects at $z\sim 1$ is also previewed with integral-field spectroscopy and possibly deeper targeted X-ray observations with XMM or Chandra for better insight into the cluster physics.
separated (wins are. in principle. easy to identify: just think about the Double Cluster in Perseus (see caption in Figure 5)).,"Separated twins are, in principle, easy to identify; just think about the Double Cluster in Perseus (see caption in Figure \ref{separatedtwins}) )."
 But. what about merger remnants?," But, what about merger remnants?"
 One easy to implement test is based on star counts., One easy to implement test is based on star counts.
 Figure 13. shows the surface number density. profile for models with q = lat 210 Myr., Figure \ref{radialprofile} shows the surface number density profile for models with $q$ = 1 at 210 Myr.
 Two single models with .N = 8192 ancl 4096 evolved in a similar tidal field and a Ning profile (Ning 1962) are also included as reference., Two single models with $N$ = 8192 and 4096 evolved in a similar tidal field and a King profile (King 1962) are also included as reference.
 The outer regions of merger remnants are similar to (hose of an equivalent single cluster having twice the population of the individual clusters but the number density of the inner regions is rather different., The outer regions of merger remnants are similar to those of an equivalent single cluster having twice the population of the individual clusters but the number density of the inner regions is rather different.
 In. general. merger remnants are expected to be fanter.," In general, merger remnants are expected to be fainter."
 However. some models ending in merger show clear central cusps which are absent from single models.," However, some models ending in merger show clear central cusps which are absent from single models."
 Merger models characterized by higher central concentration are preferentially associated {ο pairs with high initial eccentricitv ancl. (herefore. shorter merger timescale.," Merger models characterized by higher central concentration are preferentially associated to pairs with high initial eccentricity and, therefore, shorter merger timescale."
 They are also the pairs in which the mutual Gdal disruption has been the weakest as thev have been interacting for a shorter period of time., They are also the pairs in which the mutual tidal disruption has been the weakest as they have been interacting for a shorter period of time.
 This explains why their cores are nearly denser than that of an equivalent Ning model., This explains why their cores are nearly denser than that of an equivalent King model.
 In contrast. mergers of low eccentricity pairs have lower central densities.," In contrast, mergers of low eccentricity pairs have lower central densities."
 This is the result of longer merger timescale and enhanced mutual tidal disruption., This is the result of longer merger timescale and enhanced mutual tidal disruption.
 This lower densitv (rauslates into higher production of hierarchical svstems in the Form of temporarily stable triple and quadruple stellar svstems will respect to single models., This lower density translates into higher production of hierarchical systems in the form of temporarily stable triple and quadruple stellar systems with respect to single models.
 This is to be expected as higher stellar densitv increases the probability of relatively close-range gravitational interactions (hat quickly destroy multiple svstems., This is to be expected as higher stellar density increases the probability of relatively close-range gravitational interactions that quickly destroy multiple systems.
 In general. the central regions of merger remnants are clistinelively different [rom those of clusters evolving without companions but haloes look very. similar.," In general, the central regions of merger remnants are distinctively different from those of clusters evolving without companions but haloes look very similar."
 Regarcing the kinematic signature of merging. it is also obvious in the central regions.," Regarding the kinematic signature of merging, it is also obvious in the central regions."
 Data in the figures discussed here are referred to the center of masses of the merged/single cluster., Data in the figures discussed here are referred to the center of masses of the merged/single cluster.
 In (his analvsis we use the root mean square velocity defined as the square root of the average velocily-squared of the stars in (he cluster. (heir radial velocity and. (transverse velocity.," In this analysis we use the root mean square velocity defined as the square root of the average velocity-squared of the stars in the cluster, their radial velocity and transverse velocity."
" The V,,,; is always greater (han or equal to the average as il includes (he stancard deviation (VZ,.=<V2? +07).", The $V_{rms}$ is always greater than or equal to the average as it includes the standard deviation $V^{2}_{rms} = <V>^{2} + \sigma^2$ ).
 The radial velocity is given by where Fis the position of the star and (its velocity., The radial velocity is given by where $\vec{r}$ is the position of the star and $\vec{v}$ its velocity.
 Finally. (ae (ransverse velocity. is defined by The transverse velocity is also the product of the angular speed w and the magnitude of the position vector.," Finally, the transverse velocity is defined by The transverse velocity is also the product of the angular speed $\omega$ and the magnitude of the position vector."
 Therelore anc [or a given star cluster region. transverse velocity," Therefore and for a given star cluster region, transverse velocity"
dominated by t16 supercluster-void network.,dominated by the supercluster-void network.
 Thus. in order to investigate he character of the mass distribution ou ]arge scales. rich superclusters must be present in sufficient quautities (E9το).," Thus, in order to investigate the character of the mass distribution on large scales, rich superclusters must be present in sufficient quantities (E97c)."
 Figure 3 shows that the Abell cluster salple is conrete enough to trace the network of rich superclusters τα otorga =375Mype., Figure 3 shows that the Abell cluster sample is complete enough to trace the network of rich superclusters up to $r_{lim} = 375$.
 The APM sample with measured redshifts contains only two rich supercluster colmplexes within a distance of r=325Mpc.," The APM sample with measured redshifts contains only two rich supercluster complexes within a distance of $r
= 325$."
. The uutual separajon of these two supercluster coniplexes determines thie| shape of the correlation fiction aud. the )oWOor spectrun of the whole APM sample of clusters with neasured redslifts., The mutual separation of these two supercluster complexes determines the shape of the correlation function and the power spectrum of the whole APM sample of clusters with measured redshifts.
 But this is not sufficient to trace the whole superchster-void network., But this is not sufficient to trace the whole supercluster-void network.
 Tle sample is diluted aud rot all rich suerclusters actually present can be traced iu lis distance range (see Figure 6)., The sample is diluted and not all rich superclusters actually present can be traced in this distance range (see Figure 6).
 This examle shows that the use of the weights does lot conupoensae for the lack of data., This example shows that the use of the weights does not compensate for the lack of data.
 The APM sample of all clusters contains a sufficieutlv laree number of rich aud very rich superclusters. but most of the clusters iu hese superchsters do not vet have measured redshifts.," The APM sample of all clusters contains a sufficiently large number of rich and very rich superclusters, but most of the clusters in these superclusters do not yet have measured redshifts."
 The anavais of the sampe of all APM clusters has shown hat usiic this larger sample will probably vield a more represenative picture ofthe supercluster-void network., The analysis of the sample of all APM clusters has shown that using this larger sample will probably yield a more representative picture of the supercluster-void network.
 T98 lS WC the APM chster suuple D for which a huit of estimated redslüfts 54;μα was applied. corresponding o the apparetif inagnitude hnuüt of myx19.1.," T98 has used the APM cluster sample B for which a limit of estimated redshifts $z_{est} \le 0.118$ was applied, corresponding to the apparent magnitude limit of $m_X \le 19.4$."
 This lait is implied by the limiting magnitude of the APM. ealaxy survey. 5;=οί 15. and the maeuitude range funyOD.aay|1.0] to deernune the custer richness A.," This limit is implied by the limiting magnitude of the APM galaxy survey, $b_J= 20.5$ , and the magnitude range $[m_X - 0.5, m_X + 1.0]$ to determine the cluster richness ${\cal R}$."
 Croft (1997) have formed a deeper APM cluster sample C. using a fainter Πτιπιο magnitude of he ealaxy catalog. by= 21.0. aud a Warrowcr uaenitude ra wey05mx|OT]. which vields lim—SbIh ffor the sunge C. This sample coutains several rich superclusCrs at a distance of =G00Mpes these superclusOYS Ocwe also seen in the Abell catalog as clusters of distauce class 6 (Croft 1997).," Croft (1997) have formed a deeper APM cluster sample C, using a fainter limiting magnitude of the galaxy catalog, $b_J = 21.0$ , and a narrower magnitude range $m_X - 0.5,
m_X + 0.7]$, which yields $r_{lim} = 850$ for the sample C. This sample contains several rich superclusters at a distance of $\approx 600$; these superclusters are also seen in the Abell catalog as clusters of distance class 6 (Croft 1997)."
 Uufortunatelv. this much deexx APM cluster siuuple has not vet been studied to determune the power spectrum.," Unfortunately, this much deeper APM cluster sample has not yet been studied to determine the power spectrum."
 To conclud| the discussion we can sav that preseutlv the Abell cluster sample vields more accurate data on the structure of tl10 supereuster-void network than the APM saluple with measured redshitts — the effective vole of the last sample is too sniall., To conclude the discussion we can say that presently the Abell cluster sample yields more accurate data on the structure of the supercluster-void network than the APM sample with measured redshifts – the effective volume of the last sample is too small.
 We have conpared the spatial distribution of Abell aud APAL clusters and cluster-defined superclusters im order to understaud the similarities and differences between the correlation fuicfions and power spectra of these clusters., We have compared the spatial distribution of Abell and APM clusters and cluster-defined superclusters in order to understand the similarities and differences between the correlation functions and power spectra of these clusters.
 Qur main restIts can be sunimuuized as follows., Our main results can be summarized as follows.
 1) We have compiled a catalog of superclusters on the basis of APA clusters: the catalog contaius data on 55 superchusters with at least 1 members. it is given in Appendix: niost clusters have ouly estimated redshifts.," 1) We have compiled a catalog of superclusters on the basis of APM clusters; the catalog contains data on 55 superclusters with at least 4 members, it is given in Appendix; most clusters have only estimated redshifts."
 2) Abell axb APM. cblusters of galaxies show aliuost identical high-density regions rich aud very rich superclusters) in the space where samples overlap. if all clusters are used to trace the structure.," 2) Abell and APM clusters of galaxies show almost identical high-density regions rich and very rich superclusters) in the space where samples overlap, if all clusters are used to trace the structure."
 3) The sample of APM clusters with measured redshifts covers a nmchn stualler vohune in space than that of the Abell clusters., 3) The sample of APM clusters with measured redshifts covers a much smaller volume in space than that of the Abell clusters.
 Statistical properties of the APAL sample with measured redshifts reflect the distribution of clusters in this particular voluue which is dominated bv two very rich supercluster complexes., Statistical properties of the APM sample with measured redshifts reflect the distribution of clusters in this particular volume which is dominated by two very rich supercluster complexes.
 The Abell saaple of clusters contains 31 very rich superclusters aud can be considered as a candidate of a fair (representative) sample of the Universe., The Abell sample of clusters contains 31 very rich superclusters and can be considered as a candidate of a fair (representative) sample of the Universe.
 1) The location of the secondary maxinuun of the correlation function for APM clusters with measured redshifts at a separation of r=1855Mpc.. and the position of the maxinuun of the power spectrum. &=0.033 H1... correspond to the mutual separation between the IlorologimurRetieuhun aud the Sculptor SIoorclusters: aud do uot characterize the structure of the whole supercluster-void network.," 4) The location of the secondary maximum of the correlation function for APM clusters with measured redshifts at a separation of $r=185$, and the position of the maximum of the power spectrum, $k =
0.033$ , correspond to the mutual separation between the Horologium-Reticulum and the Sculptor superclusters; and do not characterize the structure of the whole supercluster-void network."
 5) The analysis of the new Abell guuple of clusters COirs earlier Ποιος that the cluster power spectrum las a niaxinumn on a scale of &=0.05 which correspouds to the period of the supercluster-void vetwork. 120Mpe.," 5) The analysis of the new Abell sample of clusters confirms earlier findings that the cluster power spectrum has a maximum on a scale of $k =
0.05$ which corresponds to the period of the supercluster-void network, 120."
. 6) The use of weights in calculation of the correlation πιοΊο aud the power spectrum does not compensate for he lack of data., 6) The use of weights in calculation of the correlation function and the power spectrum does not compensate for the lack of data.
 Properties of the supercluster-void network can onlv be determined if data are available for a sufficieutlv aree tuber of rich superclusters., Properties of the supercluster-void network can only be determined if data are available for a sufficiently large number of rich superclusters.
 The catalog of superclusters of Abell clusters is based on cluster sample ACO.A2. ic. it contains all superchisters of richuess class Vy22.," The catalog of superclusters of Abell clusters is based on cluster sample ACO.A2, i.e. it contains all superclusters of richness class $N_{cl} \geq 2$."
 This catalog is published in Paper I. Tere we present a supercluster catalog based ou the APM Ciscr seunple used in this paper., This catalog is published in Paper I. Here we present a supercluster catalog based on the APM cluster sample used in this paper.
" The catalog is based on cluster sample APALAL ie. it contains all superclusters of richness class Ni,2d. the reason of the use of this luit was given above — it is due to the large number of clusters without measured redshifts in the APAL sample. thus increasing the limit of 1nemiber clusters for the catalog we hope to increase the reliability of the catalog."," The catalog is based on cluster sample APM.A4, i.e. it contains all superclusters of richness class $N_{cl}
\geq 4$, the reason of the use of this limit was given above – it is due to the large number of clusters without measured redshifts in the APM sample, thus increasing the limit of member clusters for the catalog we hope to increase the reliability of the catalog."
 Ny is the ΠΙΟ of member clusters in the supercluster: AAe aud ac are coordinates of the ceuter of the supercluster (equinox 1950.0). derived from coordinates of 1udividual clusters: is the distance of the ceuter from us: it follows the of Abell clusters which are members of the supercluster.," $N_{cl}$ is the number of member clusters in the supercluster; $RA_C$ and $\delta_C$ are coordinates of the center of the supercluster (equinox 1950.0), derived from coordinates of individual clusters; $D_C$ is the distance of the center from us; it follows the list of Abell clusters which are members of the supercluster."
 Au index ο after the Abell or APA cluster umber in the column 6 shows that this cluster has estinated velocity.," An index ""e"" after the Abell or APM cluster number in the column 6 shows that this cluster has estimated velocity."
 In the last colin we list a commonly used name of the supercluster. identifications show the uunber of corresponding supercluster iu the Table Al of Paper I. We thank Eun Saar aud Alexei Stavobiuskv for stimulating discussion.," In the last column we list a commonly used name of the supercluster, identifications show the number of corresponding supercluster in the Table A1 of Paper I. We thank Enn Saar and Alexei Starobinsky for stimulating discussion."
 This work was supported by the Estoman Science Foundation erant 2625., This work was supported by the Estonian Science Foundation grant 2625.
 JE thanks Astrophysical Institute Potsdam for hospitality where part ofthis study was performed., JE thanks Astrophysical Institute Potsdam for hospitality where part ofthis study was performed.
 ITA thanks CONACYT for financial supportπιο eraut 27602-E., HA thanks CONACyT for financial supportunder grant 27602-E.
distance [from 293 pe (strict lower limit) to 513 pe while for V751 Cveni. we obtained a range 201 pe (strict lower limit) to 352 pe.,"distance from 293 pc (strict lower limit) to 513 pc while for V751 Cygni, we obtained a range 201 pc (strict lower limit) to 352 pc."
 FUV spectroscopy of BIX Lyn. V751 Cyvegni and V380 Oph was obtained with 7751/5TIS duringUST Cyele Ll.," FUV spectroscopy of BK Lyn, V751 Cygni and V380 Oph was obtained with /STIS during Cycle 11."
" The data were obtained using the GI40L erating and the 52”x0.2"" aperture. providing a spectral resolution of Re1000 over the wavelength range 1140-1720A."," The data were obtained using the G140L grating and the $52^{\prime\prime} \times 0.2^{\prime\prime}$ aperture, providing a spectral resolution of $\sim 1000$ over the wavelength range 1140-1720."
. Since the total time involved in each snapshot observation was short (<35min). the observations were made in the ACCUAL mode in order to minimize the instrument overheacls.," Since the total time involved in each snapshot observation was short $< 35$ min), the observations were made in the ACCUM mode in order to minimize the instrument overheads."
 This resulted in exposure times of 600 to 900 seconds., This resulted in exposure times of 600 to 900 seconds.
 Each snapshot observation resulted in a single time averaged spectrum of each svstem., Each snapshot observation resulted in a single time averaged spectrum of each system.
 All of the spectral data were processed wilh IRAF using CALSTIS V2.13b., All of the spectral data were processed with IRAF using CALSTIS V2.13b.
During target acquisition./Z/5T points at the nominal target coordinates and takes a5”x5” CCD image with an exposure time of a few seconds.,"During target acquisition, points at the nominal target coordinates and takes a $5^{\prime\prime} \times 5^{\prime\prime}$ CCD image with an exposure time of a few seconds."
 Subsequently. a small slew is performed that centers the target in the acquisition box. and a second CCD image is taken.," Subsequently, a small slew is performed that centers the target in the acquisition box, and a second CCD image is taken."
 The acquisition imagesfor these observations were obtained using the FE28x50LP long-pass filter. which has a central wavelength of 7228.5 aud a full-width at half maximum (FWILIM) of 2721.6 A(Araujo-Detancoretal.2005).," The acquisition imagesfor these observations were obtained using the F28x50LP long-pass filter, which has a central wavelength of 7228.5 and a full-width at half maximum (FWHM) of 2721.6 \citep{Araujo-Betancor2005}."
. The instrumental setup ancl exposure details of the//9T STIS spectra of BIN Lan. V380 Oph and V751 Cveni are provided in the observing log given in Table 2. (he entries are by column: (1) the target. (2) Data ID. (3) Instrument Config/Mocde. (4) Grating. (5) Aperture. (6) Date of Observation (vyvv-mnme-dd). (7) Time of observation. aud (8) Exposure time (s).," The instrumental setup and exposure details of the STIS spectra of BK Lyn, V380 Oph and V751 Cygni are provided in the observing log given in Table 2, the entries are by column: (1) the target, (2) Data ID, (3) Instrument Config/Mode, (4) Grating, (5) Aperture, (6) Date of Observation (yyyy-mm-dd), (7) Time of observation, and (8) Exposure time (s)."
 Until 2003. there were no FUV spectra of DIN Lyn with which to check for P Cvgni profiles indicating wind outflow or an analvze the FUV spectral slope or FUV line profiles.," Until 2003, there were no FUV spectra of BK Lyn with which to check for P Cygni profiles indicating wind outflow or an analyze the FUV spectral slope or FUV line profiles."
 As part of an HST snapshot program (see above). the first FUV spectrum of DIX Lyn was secured.," As part of an HST snapshot program (see above), the first FUV spectrum of BK Lyn was secured."
 The spectrum is displaved in Fig.l where a steeply rising continuum toward shorter wavelengths is seen together with strong emission features at C IT (1175). NV (1240). Si III + OI (1300). C II (1335). Si IV (1400). C IV (1550) ancl weak Le II (1640) emission.," The spectrum is displayed in Fig.1 where a steeply rising continuum toward shorter wavelengths is seen together with strong emission features at C III (1175), NV (1240), Si III + OI (1300), C II (1335), Si IV (1400), C IV (1550) and weak He II (1640) emission."
 The enission lines suggest i( is probable (hat an accretion disk is present in the svstem at the lime of our LST spectrum., The emission lines suggest it is probable that an accretion disk is present in the system at the time of our HST spectrum.
 The continuum fIux level ranges from ~ 2 x !! ergs/em? al the short end to 1.2 x !! ergs/cn? , The continuum flux level ranges from $\sim$ 2 x $^{-14}$ $^{2}$ at the short end to $\sim$ 1.2 $\times$ $^{-14}$ $^{2}$ 
 of v; (CiamaiuieL996. Matstunuraetal.2X00).. 1998:Aikawa," $x_i$ \citep{Gammie96}. \citep{Ciesla07, Matsumura09}. \citep[e.g.][]{Willacy98,Aikawa99}."
&Herbst1999).. 1 Co., \ref{fig0} $^+$ $^+$ \citep[e.g.][]{Aikawa06}.
 No Lin (Obereetal.2005εν Hy. H4 H5D DoH (AsensioRa10sοἱ," $_2$ \citep{Oberg05}, $_2$ $_3^+$ $_2$ $^+$ $_2$ $^+$ \citep{AsensioRamos07}."
al.2007).. τοι No H5D (e.g.Qietal.2011).., $_2$ $_2$ $^+$ \citep[e.g.][]{Qi11}.
The models for M33 produce results in good agreement with the observational data in the outer region of the galaxy but fail to reproduce the present day gas content in the inner region of M33 disk.,The models for M33 produce results in good agreement with the observational data in the outer region of the galaxy but fail to reproduce the present day gas content in the inner region of M33 disk.
 Magrint et al. (, Magrini et al. (
2007) also. predicted an overestimated gas content in the inner kpes of M33 disk.,2007) also predicted an overestimated gas content in the inner kpcs of M33 disk.
 Perhaps the lower than predicted gas content could be attributed to some bulge-disk interaction effect., Perhaps the lower than predicted gas content could be attributed to some bulge-disk interaction effect.
 The present-day stellar surface mass density of the Milky Way is in good agreement with observational data and the threshold effect can be clearly seen in the outer disk of the Galaxy. where model MWA-1 (with the highest threshold value) shows a steeper behavior demonstrating that the star formation has been suppressed.," The present-day stellar surface mass density of the Milky Way is in good agreement with observational data and the threshold effect can be clearly seen in the outer disk of the Galaxy, where model MWA-1 (with the highest threshold value) shows a steeper behavior demonstrating that the star formation has been suppressed."
 Comparing the distributions of the stellar density in all galaxies we note that it gets flatter going from M33 to M3l. thus indicating a possible relation between the galaxy total surface mass density and the slope of the stellar distribution.," Comparing the distributions of the stellar density in all galaxies we note that it gets flatter going from M33 to M31, thus indicating a possible relation between the galaxy total surface mass density and the slope of the stellar distribution."
 We found that the oxygen gradient along the disk of the Milky Way is well reproduced if an inside-out disk formation ts assumed together with a threshold in the star formation of 7M.pc7 or 4Mapc. in agreement with previous works (CMR2001. Colavitti et al.," We found that the oxygen gradient along the disk of the Milky Way is well reproduced if an inside-out disk formation is assumed together with a threshold in the star formation of $7M_{\odot}pc^{-2}$ or $4M_{\odot}pc^{-2}$, in agreement with previous works (CMR2001, Colavitti et al."
 2008)., 2008).
 The present time radial oxygen gradient is very dependent on the threshold in the star formation while it seems not to be so sensitive to the efficiency (v) of the SER., The present time radial oxygen gradient is very dependent on the threshold in the star formation while it seems not to be so sensitive to the efficiency $\nu$ ) of the SFR.
 The oxygen gradient can either flatten or steepen in time according to the assumption made on the star formation efficiency as a function of galactocentrie distance., The oxygen gradient can either flatten or steepen in time according to the assumption made on the star formation efficiency as a function of galactocentric distance.
 Models with a constant v tend to predict a steepening of the gradients in time. whereas those with a v decreasing with the radius tend to flatten (in agreement with some recent observations of Maciel et al.," Models with a constant $\nu$ tend to predict a steepening of the gradients in time, whereas those with a $\nu$ decreasing with the radius tend to flatten (in agreement with some recent observations of Maciel et al."
 2003) Clearly the gradient evolution with time is strongly related to the assumed history of star formation in the disk., 2003) Clearly the gradient evolution with time is strongly related to the assumed history of star formation in the disk.
 The present-day gas profile in the MW ts better reproduced by the model with a threshold of 4M.pc- and v(R)., The present-day gas profile in the MW is better reproduced by the model with a threshold of $4M_{\odot}pc^{-2}$ and $\nu(R)$.
 All models predict a lower SFR for the inner disk of the Galaxy, All models predict a lower SFR for the inner disk of the Galaxy
(Εν) as in the hard state provided the power supplied to the corona is a constant fraction of the accretion power.,$F_{\rm hot}$ ) as in the hard state provided the power supplied to the corona is a constant fraction of the accretion power.
" reff:hot,olshowsthatthisisindeedthecase. withatmostaweakde pendence. cükllre Ma xx-Nésy "," \\ref{f:hot_bol} shows that this is indeed the case, with at most a weak dependence, and the fraction equals $\sim$ 1/4."
Both the constancy and the fractional value are consistent with theoretical expectations. for the gas-pressure dominated disc (Merloni2003:Merlonietal.20091.," Both the constancy and the fractional value are consistent with theoretical expectations for the gas-pressure dominated disc \citep{merloni03,mhd03}."
 This is also in agreement with the finding that the dise in Cyg X-I is in the gas-pressure dominance regime (Gierlinskietal.1999)., This is also in agreement with the finding that the disc in Cyg X-1 is in the gas-pressure dominance regime \citep{gierlinski99}.
.. Then. the fact that the radio/X-ray correlation extends. with about the same p. from the hard state to the soft one (for Fj.) represents then another argument for the high accretion ethciency in the hard state Cyg X-l.," Then, the fact that the radio/X-ray correlation extends, with about the same $p$, from the hard state to the soft one (for $F_{\rm hot}$ ), represents then another argument for the high accretion efficiency in the hard state Cyg X-1."
 An alternative to the accretion flow model as an explanation of the radio/X-ray correlation is that both radio and X-rays are emitted by the jet., An alternative to the accretion flow model as an explanation of the radio/X-ray correlation is that both radio and X-rays are emitted by the jet.
 In particular. both could be emitted by the synchrotron emission of the same population of non-thermal electrons. with the radio and X-rays from the optically thick and thin parts. respectively.," In particular, both could be emitted by the synchrotron emission of the same population of non-thermal electrons, with the radio and X-rays from the optically thick and thin parts, respectively."
" For this ease. Heinz&Sunyaev(2003) have derived. which yields €= ϱ.5-0.7 for p,= 2-3."," For this case, \citet{hs03} have derived, which yields $\zeta\simeq 0.8$ –0.7 for $p_{\rm e}=2$ –3."
" Thus. this model would have required pa,=€ 0.7-0.8. and a large correction to p due to free-free absorption. which is in conflict with our results "," Thus, this model would have required $p_{\rm intr}=\zeta\simeq 0.7$ –0.8, and a large correction to $p$ due to free-free absorption, which is in conflict with our results in Section \ref{free-free}."
Moreover. reffisprx shows that the normalization of the X-ray emission in the hard state is too high by a factor of ~30 for the X-rays to be due to optically thin non-thermal synchrotron emission above the turnover frequency. which is 20.1 eV in Cyg X-1 (Rahouie 2011).," Moreover, \\ref{f:sprx} shows that the normalization of the X-ray emission in the hard state is too high by a factor of $\sim$ 30 for the X-rays to be due to optically thin non-thermal synchrotron emission above the turnover frequency, which is $\simeq$ 0.1 eV in Cyg X-1 \citep{rahoui11}."
 The situation becomes even worse for the intermediate state Gin which the radio emission peaks). where the disagreemen in the normalization at 0.1 eV is by three orders of magnitude.," The situation becomes even worse for the intermediate state (in which the radio emission peaks), where the disagreement in the normalization at 0.1 eV is by three orders of magnitude."
 As discussed in Section 4.2.2. the etfect of free-free absorption on the average 2-220 GHz spectrum can be at most a factor of -2. which cannot explain this diserepaney.," As discussed in Section \ref{free-free}, the effect of free-free absorption on the average 2–220 GHz spectrum can be at most a factor of $\sim$ 2, which cannot explain this discrepancy."
 This rules out non-hermal synchrotron as the origin of the X-rays., This rules out non-thermal synchrotron as the origin of the X-rays.
 This has also been independently found by Rahouietal.2011)., This has also been independently found by \citet{rahoui11}.
. We note tha another ground for ruling out this model for luminous hard state of black-hole binaries is that it does not reproduce the shape of the ligh-energy cut-off and it has problems reproducing the narrow distribution of the observed cut-off energies (Zdziarskietal. 2003).," We note that another ground for ruling out this model for luminous hard state of black-hole binaries is that it does not reproduce the shape of the high-energy cut-off, and it has problems reproducing the narrow distribution of the observed cut-off energies \citep{z03}. ."
 We note that Russelletal.(2010) found the X-ray spectra of he black-hole binary XTE 11550—564 to be dominated by thermal Comptonization in its luminous hard states. at L2x10κ.," We note that \citet{russell10} found the X-ray spectra of the black-hole binary XTE J1550–564 to be dominated by thermal Comptonization in its luminous hard states, at $L\ga 2\times 10^{-3} L_{\rm E}$."
 Cyg X-I in the hard state is relatively luminous. typically with ἐς0.01Li (Z02). where Ly is the Eddington luminosity.," Cyg X-1 in the hard state is relatively luminous, typically with $L\ga 0.01 L_{\rm E}$ (Z02), where $L_{\rm E}$ is the Eddington luminosity."
 Thus. our findings above are consistent with those of Russelletal. (2010).," Thus, our findings above are consistent with those of \citet{russell10}. ."
 On the other hand. the spectra of XTE J71550-564 were found to be dominated by jet non-thermal synchrotron emission at lower luminosities.," On the other hand, the spectra of XTE J1550–564 were found to be dominated by jet non-thermal synchrotron emission at lower luminosities."
 A weak jet contribution. not detectable in our X-ray data. remains also possible in Cyg ΧΙ. given the relative normalization of the radio power law and that of the X-rays. see reff:sprx..," A weak jet contribution, not detectable in our X-ray data, remains also possible in Cyg X-1, given the relative normalization of the radio power law and that of the X-rays, see \\ref{f:sprx}."
 X-ray jet models for luminous states of black-hole binaries. and for Cyg X-I in particular. have been also ruled out on several other grounds by Malzaeetal.(2009).," X-ray jet models for luminous states of black-hole binaries, and for Cyg X-1 in particular, have been also ruled out on several other grounds by \citet{mbf09}."
 In particular. they discuss the model of Markotf.Nowak&Wilms(2005).. in which the in the hard state of Cyg X-1 (and other black-hole binaries) are due to synchrotron-self-Compton by thermal electrons with {Fae uofl low Thomson optical depth at the jet base.," In particular, they discuss the model of \citet*{mnw05}, in which the in the hard state of Cyg X-1 (and other black-hole binaries) are due to synchrotron-self-Compton by thermal electrons with $kT_{\rm e}\sim 3$ –5 MeV of a very low Thomson optical depth at the jet base."
 Malzaeetal.(2009) find that the parameters fitted by Markotfetal.(2005). strongly violate the e pair equilibrium. with the self-consistent optical depth being two orders of magnitude higher than the fitted one due to the produced pairs.," \citet{mbf09} find that the parameters fitted by \citet{mnw05} strongly violate the $^\pm$ pair equilibrium, with the self-consistent optical depth being two orders of magnitude higher than the fitted one due to the produced pairs."
 Furthermore. that model relies on first-order Compton scattering to fit the X-ravs. and thus it requiresstrong fine-tuning (as noted by Yuan2007) to reproduce the observed spectral cut-off which is at ~ 100 keV in both Cyg X-I and in most of the black-hole binaries in the qard state.," Furthermore, that model relies on first-order Compton scattering to fit the X-rays, and thus it requiresstrong fine-tuning (as noted by \citealt{y07}) ) to reproduce the observed spectral cut-off, which is at $\sim$ 100 keV in both Cyg X-1 and in most of the black-hole binaries in the hard state."
 Other problems with the X-ray jet models are discussed by Heinz(2004) tetfeet of electron energy loss on optically-thin synchrotron spectra) and by Maccarone(2005). (comparison of black-hole and neutron-star sources)., Other problems with the X-ray jet models are discussed by \citet{heinz04} (effect of electron energy loss on optically-thin synchrotron spectra) and by \citet{maccarone05} (comparison of black-hole and neutron-star sources).
 A number of papers have also attributed the high-energy tail observed in the soft state of X-ray binaries to optically thin non- synchrotron or self-Compton emission from the jet. e.g.. Vadawaleetal.001)... Fiocchietal.(2006).," A number of papers have also attributed the high-energy tail observed in the soft state of X-ray binaries to optically thin non-thermal synchrotron or self-Compton emission from the jet, e.g., \citet{vadawale01}, \citet{fiocchi06}."
.. We note that for he soft state in Cyg X-1. the extrapolation of the high-energy tail down to | eV is a few orders of magnitude above any possible extrapolation of the radio emission in that state.," We note that for the soft state in Cyg X-1, the extrapolation of the high-energy tail down to 1 eV is a few orders of magnitude above any possible extrapolation of the radio emission in that state."
 This rules out this model., This rules out this model.
 In addition. it requires that the actual bolometric luminosity of the modelled sources is a few orders of magnitude above the ones determined based on the X-rays. as well as that the emission is unbeamed. which appear highly unlikely.," In addition, it requires that the actual bolometric luminosity of the modelled sources is a few orders of magnitude above the ones determined based on the X-rays, as well as that the emission is unbeamed, which appear highly unlikely."
 Instead. these high-energy fails appear compatible with Compton scattering of disc blackbody photons by a hybrid electron distribution. e.g.. Gierlinskietal. (1999).," Instead, these high-energy tails appear compatible with Compton scattering of disc blackbody photons by a hybrid electron distribution, e.g., \citet{gierlinski99}."
 We have obtained broad-band X-ray spectra of Cyg ΧΙ as a unction of time using the broad-band monitoring by RXTE/ASM ogether with either CGRO//BATSE or Swif//BAT., We have obtained broad-band X-ray spectra of Cyg X-1 as a function of time using the broad-band monitoring by /ASM together with either /BATSE or /BAT.
 Based on these spectra. we have calculated both the bolometric fluxes (δη). and approximate values of the Comptonization flux εως not including he blackbody component).," Based on these spectra, we have calculated both the bolometric fluxes $F_{\rm bol}$ ), and approximate values of the Comptonization flux $F_{\rm hot}$; not including the blackbody component)."
 We have classified the spectra into hree spectral states based on their 3-12 keV photon index., We have classified the spectra into three spectral states based on their 3–12 keV photon index.
 We wesent light curves of Fi for the available periods., We present light curves of $F_{\rm bol}$ for the available periods.
 The range of variability of the bolometric flux using |-day averages is by a uctor of =10., The range of variability of the bolometric flux using 1-day averages is by a factor of $\simeq 10$.
 We tind the fluxes in ditferent states overlap. e.g. some fluxes in the hard state are higher than some in the soft state.," We find the fluxes in different states overlap, e.g., some fluxes in the hard state are higher than some in the soft state."
 This indicates the presence of some X-ray hysteresis in Cyg X-I. 10ugh weaker than that in low-mass X-ray binaries.," This indicates the presence of some X-ray hysteresis in Cyg X-1, though weaker than that in low-mass X-ray binaries."
 We have studied X-ray variability patterns of Cyg ΧΙ., We have studied X-ray variability patterns of Cyg X-1.
 In the ward state. the dominant pattern in the — 10-150 keV range is of 1ο intrinsic. spectrum changing its normalization only. but with apparently more absorption at soft X-rays. causing their flux to respond to changes of the bolometric luminosity more strongly jan. the hard X-ray flux.," In the hard state, the dominant pattern in the $\sim$ 10–150 keV range is of the intrinsic spectrum changing its normalization only, but with apparently more absorption at soft X-rays, causing their flux to respond to changes of the bolometric luminosity more strongly than the hard X-ray flux."
 In the intermediate state. there is strong spectral variability with the overall spectra changing their slopewith a pivot around 20 keV. In the soft state. there is an approximate ooportionality of the flux in a given energy band to Fi. but with the scatter strongly increasingwith the photon energy.," In the intermediate state, there is strong spectral variability with the overall spectra changing their slopewith a pivot around 20 keV. In the soft state, there is an approximate proportionality of the flux in a given energy band to $F_{\rm bol}$ , but with the scatter strongly increasingwith the photon energy."
 Still. PoofPoo Was found approximately constant on average in this state. 51/4. see reff:hotpol..," Still, $F_{\rm hot}/F_{\rm bol}$ was found approximately constant on average in this state, $\simeq 1/4$ , see \\ref{f:hot_bol}. ."
The source of the energy needed to heat the Sun's corona is a long-standing enigma.,The source of the energy needed to heat the Sun's corona is a long-standing enigma.
 The two main competing theories proposed to explain the energy excess in the outer atmosphere of the Sun are Joule heating through resistive dissipation by magnetic field reconnection and mechanical heating by waves (see?.forareviewofthemechanismsproposed).., The two main competing theories proposed to explain the energy excess in the outer atmosphere of the Sun are Joule heating through resistive dissipation by magnetic field reconnection and mechanical heating by waves \citep[see][for a review of the mechanisms proposed]{2001ApJ...560.1035A}.
 However. both Joule heating and mechanical heating by high-frequency acoustic waves (v.>5.2 mHz) have recently been ruled out as major contributors to the energy budget of the corona (??)..," However, both Joule heating and mechanical heating by high-frequency acoustic waves $\nu_{c}>5.2$ mHz) have recently been ruled out as major contributors to the energy budget of the corona \citep{2006ApJ...646..579F,npg-16-443-2009}."
 Low-frequency MHD waves (v<5 mHz). on the other hand. may represent a significant source of energy (?)..," Low-frequency MHD waves $\nu < 5$ mHz), on the other hand, may represent a significant source of energy \citep{2006ApJ...648L.151J}."
" Though they are generally not allowed to propagate into the atmosphere. as their frequency does not exceed the expected photospheric cutoff frequency (v,=5.2 mHz). in regions where the magnetic field is largely inclined with respect to the gravity vector the cutoff frequency can be substantially lowered through the ramp effect: where ὡς is the effective cutoff frequency and 8 is the angle of the magnetic field to the local gravity vector."," Though they are generally not allowed to propagate into the atmosphere, as their frequency does not exceed the expected photospheric cutoff frequency $\nu_{c}=5.2$ mHz), in regions where the magnetic field is largely inclined with respect to the gravity vector the cutoff frequency can be substantially lowered through the ramp effect: where $\omega_{eff}$ is the effective cutoff frequency and $\theta$ is the angle of the magnetic field to the local gravity vector."
" This effect 1s behind the so-called magneto-acoustic portals. (2)) which allow waves with frequencies far below 5.2 mHz to be channeled into the strongly inclined magnetic It has been demonstrated. both theoretically (2?)— and through numerical simulations (22).. that at locations where the sound speed c, and Alfvénn speed « nearly coincide. part of the energy contained in the acoustic-like component (fast MHD mode in the6>| regime) can be converted to two types of waves: field aligned acoustic waves (slow MHD mode in P<l| plasma). or magnetic-like waves (fast mode in B<| regions),"," This effect is behind the so-called magneto-acoustic portals \cite{2006ApJ...648L.151J}) ) which allow waves with frequencies far below $5.2$ mHz to be channeled into the strongly inclined magnetic It has been demonstrated, both theoretically \citep{2006MNRAS.372..551S,2008SoPh..251..251C} and through numerical simulations \citep{2006ApJ...653..739K, 2010ApJ...719..357F}, that at locations where the sound speed $c_{s}$ and Alfvénn speed $a$ nearly coincide, part of the energy contained in the acoustic-like component (fast MHD mode in the $\beta>1$ regime) can be converted to two types of waves: field aligned acoustic waves (slow MHD mode in $\beta<1$ plasma), or magnetic-like waves (fast mode in $\beta<1$ regions)."
" These two processes are commonly referred to as “fast to slow"" and ""fast to fast” conversion."," These two processes are commonly referred to as ""fast to slow"" and ""fast to fast"" conversion."
 In the first case. the acoustic nature of the wave is preserved while. in the fast to fast conversion. the wave changes from acoustic-like to magnetic-," In the first case, the acoustic nature of the wave is preserved while, in the fast to fast conversion, the wave changes from acoustic-like to magnetic-like."
 We note that since ez/«.=(7/2). the layer where the gas pressure is equal to the magnetic pressure (the 5=| or equipartition layer) is in. practice very close to the layer where the phase speed of the fast and slow modes coincide. even If they are conceptually different.," We note that since $c^{2}_{s}/a^{2}=(\gamma/2) \beta$, the layer where the gas pressure is equal to the magnetic pressure (the $\beta=1$ or equipartition layer) is in practice very close to the layer where the phase speed of the fast and slow modes coincide, even if they are conceptually different."
" The amount of energy transferred to the acoustic-like mode or converted into the magnetic-like mode. as the wave crosses the equipartition layer. depends on the angle between the wavevector and the magnetic field (the attack angle a): where /1 is the thickness of the equipartition layer as measured along the direction of propagation. in. which the process of mode conversion is taking place. & the wavenumber and 7 the ""fast-to-slow"" transmission coefficient."," The amount of energy transferred to the acoustic-like mode or converted into the magnetic-like mode, as the wave crosses the equipartition layer, depends on the angle between the wavevector and the magnetic field (the attack angle $\alpha$ ): where $h_{s}$ is the thickness of the equipartition layer as measured along the direction of propagation, in which the process of mode conversion is taking place, $k$ the wavenumber and $T$ the ""fast-to-slow"" transmission coefficient."
 It is important to note that this relation is strictly valid only for small attack angles. a comparison with the exact solution can be found in ?..," It is important to note that this relation is strictly valid only for small attack angles, a comparison with the exact solution can be found in \cite{2009SoPh..255..193H}."
" The ""fast-to-fast transmission coefficient C is obtated by invoking conservation of energy. Le. and C is complex (as we need to take into account possible phase changes during conversion)."," The ""fast-to-fast"" transmission coefficient $C$ is obtained by invoking conservation of energy, i.e. and $C$ is complex (as we need to take into account possible phase changes during conversion)."
 ? demonstrated that the ramp and mode conversion effects together result in à strong depe=ence of the acoustic energy flux on both the magnetic field inclination and the attack angle., \citet{2006MNRAS.372..551S} demonstrated that the ramp and mode conversion effects together result in a strong dependence of the acoustic energy flux on both the magnetic field inclination and the attack angle.
 In particular. the acoustic flux should have à maximum for magnetic field inclination angles between 20 and 30 degrees.," In particular, the acoustic flux should have a maximum for magnetic field inclination angles between $20$ and $30$ degrees."
 This 15 a result of the transmission coefficient being large at smaller attack. angles and the ramp effect allowing the propagation of low frequency waves once cos«Ωω... that is at large inclination angles.," This is a result of the transmission coefficient being large at smaller attack angles and the ramp effect allowing the propagation of low frequency waves once $cos~\theta < \omega_{eff}/ \omega_{c}$, that is at large inclination angles."
 Here we investigate this claim and show how the velocity field fluctuations of a solar active region observed by the Interferometric BIdimensional Spectrometer (IBIS) based on a dual Fabry-Perot system. depend on the inclination angle of the magnetic field. as inferred from the speectropolarimetric inversions of the same region observed by Hinode SOT/SP (?)..," Here we investigate this claim and show how the velocity field fluctuations of a solar active region observed by the Interferometric BIdimensional Spectrometer (IBIS) based on a dual Fabry-Perot system, depend on the inclination angle of the magnetic field, as inferred from the spectropolarimetric inversions of the same region observed by Hinode SOT/SP \citep{springerlink:10.1007/s11207-008-9174-z}."
 Among other things. we find that the power of the velocity oscillations is dependent on both the frequency and on the magnetic field inclination: this is in accord with the above theoretical picture.," Among other things, we find that the power of the velocity oscillations is dependent on both the frequency and on the magnetic field inclination: this is in accord with the above theoretical picture."
 This scenario is also supported by the analysis of the spatial distribution of the power in the chromosphere. which shows that there is a substantial lack of power at the locations where the magnetic field is bent horizontally.," This scenario is also supported by the analysis of the spatial distribution of the power in the chromosphere, which shows that there is a substantial lack of power at the locations where the magnetic field is bent horizontally."
 This 1s consistent with longitudinal waves moving, This is consistent with longitudinal waves moving
particular. R aud (r7) play similar roles for determining M.aud(/ <j) aud |M/II| for determining Z.,"particular, $R$ and $(r-i)$ play similar roles for determining $M$, and $(i-z)$ and [M/H] for determining $Z$."
 The distauce d ds mniquely determined by π when no photometric information is iucluded. while the colors aud magnitude contribute to determing d when these are included. primarily due to the eror on the parallax.," The distance $d$ is uniquely determined by $\pi$ when no photometric information is included, while the colors and magnitude contribute to determining $d$ when these are included, primarily due to the error on the parallax."
 When 1cFY oscillation mode is included. then all of the observable: aro duportaunt for constraining the parameters eve— poorly. and the inclusion of a correctly identified mock replaces the role of A for determing AL.," When no oscillation mode is included, then all of the observables are important for constraining the parameters even poorly, and the inclusion of a correctly identified mode replaces the role of $R$ for determining $M$."
 For the binary svstem the photometric information does not have as unich inpact as it does for the sinel star. partially because these observations are bleuded values resulting from the two components.," For the binary system the photometric information does not have as much impact as it does for the single star, partially because these observations are blended values resulting from the two components."
 However o- reaching precisions of ~0.003 mae. then the photometric observables beein to dominate the roles of Roy. μι. ΑΙ aud ffor ‘TI.determing the stellar parameters.," However on reaching precisions of $\sim 0.003$ mag, then the photometric observables begin to dominate the roles of $R_A$, $_{A}$, [M/H], and for determining the stellar parameters."
 Iu particular. (roArp vields simular information to Tig4.," In particular, $(r-i)_{EB}$ yields similar information to $_A$."
 For a single star system correctly ideutifving an oscillation mode is necessary to reduce the parameter uncertainties to values that are useful., For a single star system correctly identifying an oscillation mode is necessary to reduce the parameter uncertainties to values that are useful.
 Ou the other haud. a binary svsteni contains chough information. without having to use the identified mode to constrain the stellar parameters well.," On the other hand, a binary system contains enough information, without having to use the identified mode to constrain the stellar parameters well."
 Iu fact. including the identified mode docs not improve the parameter nucertainties. cuiphasizing its utilitv for learning soimethiug else about the star.," In fact, including the identified mode does not improve the parameter uncertainties, emphasizing its utility for learning something else about the star."
 This same trend can be seen for the error box iu the IT-R. diagram: it does nof shrink for the binary system when the mode is included or the errors in A74 are improved., This same trend can be seen for the error box in the H-R diagram: it does not shrink for the binary system when the mode is included or the errors in $R_A$ are improved.
 For the suele stax. however. duaprovinge [4 leads directly to shrinking the error box in the huuünositv axis ouly when a correctly labeled modo is included.," For the single star, however, improving $R$ leads directly to shrinking the error box in the luminosity axis only when a correctly labeled mode is included."
 Other parameter values were also considered in this study: we varied the primary mass of the star (1.80 aand 2.50 NL..)). the mass ratio of primary to secondary (1.10 and 1.60). the evolutionary stage of the primary star (central hydrogen mass fraction of 0.50 [AIS] aud 0.15. of and the metallicity of both stars (0.020 lendaud 0.035).," Other parameter values were also considered in this study; we varied the primary mass of the star (1.80 and 2.50 ), the mass ratio of primary to secondary (1.10 and 1.60), the evolutionary stage of the primary star (central hydrogen mass fraction of 0.50 [MS] and 0.15 [end of MS]), and the metallicity of both stars (0.020 and 0.035)."
 MS[).For a single star ideutifving a mode has more impact ou the reference model than the more evolved iiodel aud for both the sinele star aud the binary system the ligher metallicity iiodel benefited more from the photometric information., For a single star identifying a mode has more impact on the reference model than the more evolved model and for both the single star and the binary system the higher metallicity model benefited more from the photometric information.
 However. changing the size of the primary mass did not change the uucertaiutyv dependencies (Creevey2008).," However, changing the size of the primary mass did not change the uncertainty dependencies \citep{cre08}."
. Because mode-identification in 6 Seuti (and other) stars is a complicated task. we addressed whether au iucorrecth-labeled mode could be correctly diagnosed using the observational constraints provided bv the suele star and the detached eclipsing binary svsteni.," Because mode-identification in $\delta$ Scuti (and other) stars is a complicated task, we addressed whether an incorrectly-labeled mode could be correctly diagnosed using the observational constraints provided by the single star and the detached eclipsing binary system."
 We used siaüulatious to test the effects of recovering stellar parameters with arbitrarilyideutified oscillation modes., We used simulations to test the effects of recovering stellar parameters with arbitrarily-identified oscillation modes.
 We found that for the simele star. dt ds necessary to identify the mode unanmbieuouslv. because the recovered solutions using an iucorrect or a correct mode identification are not distinguishable.," We found that for the single star, it is necessary to identify the mode unambiguously, because the recovered solutions using an incorrect or a correct mode identification are not distinguishable."
 Moeaiivhile for the binary system. an ducorrecth-ideutifiod mode can be diagnosed by simply comparing the paramctcr solutions when the mode is iuclided aud not.," Meanwhile for the binary system, an incorrectly-identified mode can be diagnosed by simply comparing the parameter solutions when the mode is included and not."
 If the mode is correctly identified. the solutions are in agreement.," If the mode is correctly identified, the solutions are in agreement."
 Taking this discussion sliehtlv. further. in the binary system we also showed that we could iu fact tightly constrain (and even identify correctly) the pulsation mode parameters by comparing the distribution of model solutions with and without a mode.," Taking this discussion slightly further, in the binary system we also showed that we could in fact tightly constrain (and even identify correctly) the pulsation mode parameters by comparing the distribution of model solutions with and without a mode."
 The model solutions are In agreement when the mode is correctly identified even if the assumptions on the interior plysics are slightly incorrect., The model solutions are in agreement when the mode is correctly identified even if the assumptions on the interior physics are slightly incorrect.
 This type of test and this method. of mode-ideutification has not vet been done with available observational data., This type of test and this method of mode-identification has not yet been done with available observational data.
 It is clear that studving pulsatious iu binary svstenis has its coniplexities observationallv. however. the extra effort is definitely worth it.," It is clear that studying pulsations in binary systems has its complexities observationally, however, the extra effort is definitely worth it."
 Apart from the advantage of using the screeuing effect of the pulsatious duriug eclipse to help ideutifv the mode. this study curplasizes the power that the binary imeasuremenuts have for deteriuuius fundamental parameters aud subsequently constraiing aud even ideutifiviug the modo.," Apart from the advantage of using the screening effect of the pulsations during eclipse to help identify the mode, this study emphasizes the power that the binary measurements have for determining fundamental parameters and subsequently constraining and even identifiying the mode."
 Tn this paper we use the SVD technique to compare the constraints for sinele stars and binary systems., In this paper we use the SVD technique to compare the constraints for single stars and binary systems.
 We uote. however. that with the flood of data from space-based missions. this type of study can be subsequently extended to investigate which detached eclipsing binary systenuis provide the best astrophysical laboratories.," We note, however, that with the flood of data from space-based missions, this type of study can be subsequently extended to investigate which detached eclipsing binary systems provide the best astrophysical laboratories."
 Dart of this work was supported by a graduate studentFellowship at the Tigh Altitude Observatory/National Center for Atmospheric Research. Boulder. CO. USA.," Part of this work was supported by a graduate student at the High Altitude Observatory/National Center for Atmospheric Research, Boulder, CO, USA."
 This work was also supported by he European WUWelio- and Asteroscisincloey Network (UELAS). a major international collaboration funded » the European Commissions Sixth Framework Progranunuc.," This work was also supported by the European Helio- and Asteroseismology Network (HELAS), a major international collaboration funded by the European Commission's Sixth Framework Programme."
 We thauk the referees for comments and sugecstious that ercatly improved the preseutation aud he scientific content of the mauuscript., We thank the referees for comments and suggestions that greatly improved the presentation and the scientific content of the manuscript.
the cluster.,the cluster.
 The most important result of this. process is that the higher-mass cluster members. gradually sink towards the cluster center and in the process transfer their kinetic energv to the more numerous lower-mass stellar component. thus leading to mass segregation.," The most important result of this process is that the higher-mass cluster members gradually sink towards the cluster center and in the process transfer their kinetic energy to the more numerous lower-mass stellar component, thus leading to mass segregation."
 The time scale on which a cluster will have lost all traces of its initial conditions is well represented by its relaxation time Zi., The time scale on which a cluster will have lost all traces of its initial conditions is well represented by its relaxation time $T_{E}$.
 lt is given where AN is the number of cluster members. A is the radius containing half of the cluster mass ancl «m2 is the njean mass of the cluster stars (cf.," It is given where $N$ is the number of cluster members, $R$$_{h}$ is the radius containing half of the cluster mass and $<m>$ is the mean mass of the cluster stars (cf."
 Spitzer Llart 1971)., Spitzer Hart 1971).
" 1""he number of probable MS stars is estimated using the CAL iagrams of the clusters after subtracting the contribution ue to field stars ancl applying the necessary corrections for 1¢ data incompleteness.", The number of probable MS stars is estimated using the CM diagrams of the clusters after subtracting the contribution due to field stars and applying the necessary corrections for the data incompleteness.
 For determining the I. we assume wt the Ry is equal to of halfthe cluster racius estimated by Uus.," For determining the $_{h}$ , we assume that the $_{h}$ is equal to half of the cluster radius estimated by us."
 The angular values are converted to linear values using je cluster distances which are derived: here., The angular values are converted to linear values using the cluster distances which are derived here.
 Inclusion. of Custer members fainter than the limiting V magnitude will decrease the value of «mmo> and increase the value of NV’., Inclusion of cluster members fainter than the limiting $V$ magnitude will decrease the value of $<m>$ and increase the value of $N$.
" ""nhis will result in higher values of 7.", This will result in higher values of $T_{E}$.
 Hence the Ze values QXained here may be considered as the lower Limit., Hence the $T_{E}$ values obtained here may be considered as the lower limit.
 A comparison of cluster age with its relaxation time nidicates that the relaxation time issmaller than the age of, A comparison of cluster age with its relaxation time indicates that the relaxation time issmaller than the age of
We use the same method as we have done for the quadrupole.,We use the same method as we have done for the quadrupole.
" The octopole has three multipole vectors. ej. 0» and es. from ἐξοἱ—Ay(aae|64geiz)eoebeJydcaza3gess ) which. gives. a 6,i order of⋅ equations in a: in which the coellicients are. Each multipole has 24 roots of a which οives the Cf.fF?) pairs. however only ( components are used to find the multipoles since their conjugatorsgive the sameresults. as we mentioned earlier."," The octopole has three multipole vectors, $\upsilon_1$ , $\upsilon_2$ and $\upsilon_3$, from $F=L_1L_2L_3=\lambda_1(a_1x+b_1y+c_1z)(a_2x+b_2y+c_2z)(a_3x+b_3y+c_3z)$ , which gives a $6^{th}$ order of equation in $\alpha$: in which the coefficients are, Each multipole has $\l$ roots of $\alpha$ which gives the $(f_i,
f^*_i)$ pairs, however only $\l$ components are used to find the multipoles since their conjugatorsgive the sameresults, as we mentioned earlier."
predictions alreacv given in the literature on the basis of of tιο Frascati or Padua evolutionary codes before the last updating of he input physics.,predictions already given in the literature on the basis of of the Frascati or Padua evolutionary codes before the last updating of the input physics.
 The figure gives the comforting evidence that luninositics from Castellani ct al. (, The figure gives the comforting evidence that luminosities from Castellani et al. (
1992) appear in rather good agreement with similar data w Bressan ο al. (,1992) appear in rather good agreement with similar data by Bressan et al. (
1993).,1993).
 As we will further discuss in the jext section. the sheht underhuninosity aud the little difference in the RGD-pt mass of Bressan et al.," As we will further discuss in the next section, the slight underluminosity and the little difference in the RGB-pt mass of Bressan et al."
 inodels is ouly the expeced consequence of their adoption of a moderate core overshooting sceuario., models is only the expected consequence of their adoption of a moderate core overshooting scenario.
 The same figure shows that the updated iuput plysics adopted in C99 has the effect of increasing the Iuninosity of the models with a degenerate progenitors. according to the discussion already given iu Cassis ο al. (," The same figure shows that the updated input physics adopted in C99 has the effect of increasing the luminosity of the models with a degenerate progenitors, according to the discussion already given in Cassisi et al. ("
1998) and in reasonable agreement with stellar uocels recently presented by Pols et al. (,1998) and in reasonable agreement with stellar models recently presented by Pols et al. (
1998).,1998).
 However. one also &uds that the new input physics in the Padua models (Carardi Bertelli 1998. Carardi et al.," However, one also finds that the new input physics in the Padua models (Girardi Bertelli 1998, Girardi et al."
 1999) has ti6 opposite effect. sensitivelv decreasing the predicted. huninosities.," 1999) has the opposite effect, sensitively decreasing the predicted luminosities."
 As a whole. one finds that uncertainties on predicted Duuinosities can |© even larecr than AloeL~0.1. leaving al ouyalatable uncertainty iu the curent evolutionary SCCLIALIO.," As a whole, one finds that uncertainties on predicted luminosities can be even larger than $\Delta$ $\sim$ 0.1, leaving an unpalatable uncertainty in the current evolutionary scenario."
 Ou eeneoral grounds. oue expects that he quoted differeices are the results of differences either iu the iuput plhlwsies or in the assunptious about the effüciencev of macroscopic imechanisnis. like core overshooine. which can affect the eveution of stellar structures.," On general grounds, one expects that the quoted differences are the results of differences either in the input physics or in the assumptions about the efficiency of macroscopic mechanisms, like core overshooting, which can affect the evolution of stellar structures."
 To discuss this poiut. in the next sections we will iuvestieate the range of variability in current theoretical xedietions. as produced by the various assuniptious governing the evolutionary behaviour.," To discuss this point, in the next sections we will investigate the range of variability in current theoretical predictions, as produced by the various assumptions governing the evolutionary behaviour."
" Masing reference to the set of models preseuted iu C99. in this section we will explore the ifence on central Ie burning models of several assuiptiois concerning these snσος, namely. 1) the efficiency ¢| core overshooting mechamisius. aud. i) the effect o[aguas loss."," Making reference to the set of models presented in C99, in this section we will explore the influence on central He burning models of several assumptions concerning these structures, namely, i) the efficiency of core overshooting mechanisms, and, ii) the effect of mass loss."
 In this way we alm to reach a clear insight on fje solidity” of the result one is dealing with in the literalure.," In this way we aim to reach a clear insight on the ""solidity"" of the result one is dealing with in the literature."
 Fig., Fig.
 3 (upper panel) shows he effect on the model uuuuosiv of selected choices aout tjoe ficiency of core overshooting when the original «telar lass ds varied vetween Land 33 . while the ower panel i the same fieure acopts the GOs represenation to show the ruu of he same models iu the IIR diagram.," \ref{over} (upper panel) shows the effect on the model luminosity of selected choices about the efficiency of core overshooting when the original stellar mass is varied between 1 and 3 $_{\odot}$, while the lower panel in the same figure adopts the G98 representation to show the run of the same models in the HR diagram."
 Labels iu hese figure eive the adoted auount of extrimixius (in unity of the ocal pressure scale height) aroiud the convective cores., Labels in these figure give the adopted amount of extramixing (in unity of the local pressure scale height) around the convective cores.
" Iu passing. note that comparison between this figure aud Fig.l gives the already known evidence tha the RGB xhase transition shifts to lower nasses as the metallicity decreases,"," In passing, note that comparison between this figure and Fig.1 gives the already known evidence that the RGB phase transition shifts to lower masses as the metallicity decreases."
 As already kuown. One fiuds lat overshooting decreases the mass of the ROB-p (although it then occurs at a larger age) aud. correspoucdinely. at the πια DIuunositv reached by the models before the transition decreases.," As already known, one finds that overshooting decreases the mass of the RGB-pt (although it then occurs at a larger age) and, correspondingly, that the maximum luminosity reached by the models before the transition decreases."
 However. one finds that for moderate amounts of overshooting such a decrease is rarer snall aud. iu any case. models with masses of the order o(1.2 M. Or lower are little affected by such a mechauisin.," However, one finds that for moderate amounts of overshooting such a decrease is rather small and, in any case, models with masses of the order of 1.2 $_{\odot}$ or lower are little affected by such a mechanism."
 Iu addition the nmüuimunn huuinositv attained at je RGD-pt. varies by only AlogL/L..©0.03 between a «αμαας model aud a 1uodoel with 7.20.25., In addition the minimum luminosity attained at the RGB-pt varies by only $\Delta$ $_{\odot} \approx 0.03$ between a standard model and a model with $l_{ov}$ =0.25.
 Tlis the differences im the assumuptions about the eficicncey of overshooine can hardly be at ie origin of the differences in Fig., Thus the differences in the assumptions about the efficiency of overshooting can hardly be at the origin of the differences in Fig.
 2 ancl. in turn. they cannot ο used to recowile Pols et a. (," \ref{girardi} and, in turn, they cannot be used to reconcile Pols et al. ("
1998) or C99 conttations with AfGT or IHipparcos coustraiuts.,1998) or C99 computations with M67 or Hipparcos constraints.
 The effect of nass oss deserves a bit more discussion., The effect of mass loss deserves a bit more discussion.
 Tere we will assunie tlat mass loss occurs in the acvaucec xiase of IT shell buruiug. so that the interna structure of he We burning star is iot affeced by such a loccnurmencee. which ouly decreases the amouit of envelope stromlue he ceutral He core.," Here we will assume that mass loss occurs in the advanced phase of H shell burning, so that the internal structure of the He burning star is not affected by such an occurrence, which only decreases the amount of envelope surrounding the central He core."
 Uider this assuniptiou. the effect of nass loss ou Ile buruiie inodoels cau be casily comptec w stuuply decreasing the euveope of the coustaπμπο uodel.," Under this assumption, the effect of mass loss on He burning models can be easily computed by simply decreasing the envelope of the constant-mass model."
 Fie., Fig.
 1 maps the effect in the IIR diagram o iferent amount of mass loss roni the selected uodels., \ref{massloss} maps the effect in the HR diagram of different amount of mass loss from the selected models.
" The behavior depicted by data in this figre cau be easilv ""understood as follows: i) As long as models develop strong electron degeneracy (1.¢.. for masses lower or of he order of 1.5 AI.) the mass of the He core at the Πο ignition is the result of RGB evolution."," The behavior depicted by data in this figure can be easily understood as follows: i) As long as models develop strong electron degeneracy (i.e., for masses lower or of the order of 1.5 $_{\odot}$ ) the mass of the He core at the He ignition is the result of RGB evolution."
" As a consequeice it is hugely independent of the evolving mass and. i1 adcditiou. it is little affected by miass loss (see. ο,οBS. the cliscussion iu"," As a consequence it is largely independent of the evolving mass and, in addition, it is little affected by mass loss (see, e.g., the discussion in"
wwith [Fe/H].,with [Fe/H].
" In the literature, the slope of the MDF can be reproduced by different models of chemical enrichment, from galactic models to hierarchical analytic models including merger trees, as shown in Fig."," In the literature, the slope of the MDF can be reproduced by different models of chemical enrichment, from galactic models to hierarchical analytic models including merger trees, as shown in Fig."
 12 of ? (see also ?))., 12 of \citet{2008arXiv0809.1172S} (see also \citealt{2006ApJ...641....1T}) ).
 This indicates that the slope of the MDF does not discriminate between the methods used and the associated level of heterogeneity., This indicates that the slope of the MDF does not discriminate between the methods used and the associated level of heterogeneity.
" In contrast, the pattern at [Fe/H]<—3.5 is more difficult to reproduce."," In contrast, the pattern at $<-3.5$ is more difficult to reproduce."
 ? claim that no model considered in their paper can reproduce the MDF at very low iron abundances., \citet{2008arXiv0809.1172S} claim that no model considered in their paper can reproduce the MDF at very low iron abundances.
 We find that the modification of the tail at low values of [Fe/H] may be related to the presence of ΡΟΡΠΙ stars., We find that the modification of the tail at low values of [Fe/H] may be related to the presence of PopIII stars.
" In our study, we have tested the impact of the massive mode by varying the typical PopIII minimal mass from 8 to 40Mo."," In our study, we have tested the impact of the massive mode by varying the typical PopIII minimal mass from 8 to 40."
. This appears to be an important parameter as found in the study of ?.., This appears to be an important parameter as found in the study of \citet{2007MNRAS.381..647S}.
 They used a mass range from 140 to 200 wwhich we consider disfavoured by the very specific yields of the stars within this mass range (?).., They used a mass range from 140 to 200 which we consider disfavoured by the very specific yields of the stars within this mass range \citep{2006ApJ...647..773D}.
" In this paper, we demonstrate that the minimum mass must be larger than about 30 iin order to reproduce the observed part of the MDF."," In this paper, we demonstrate that the minimum mass must be larger than about 30 in order to reproduce the observed part of the MDF."
 We have shown that the existence of PoplII stars at high redshift is required to explain the abundance pattern observed in the CEMP stars., We have shown that the existence of PopIII stars at high redshift is required to explain the abundance pattern observed in the CEMP stars.
" In addition, we have shown that a massive mode with a typical mass of 40 rreproduces the evolution of observedDtrans."," In addition, we have shown that a massive mode with a typical mass of 40 reproduces the evolution of observed."
". In contrast, it is known that PISN with masses 140-200 ddo not provide the correct chemical pattern and cannot reach high values of ffor low values of [Fe/H] (the ratio C/Fe in their yields, ?,, is not high enough)."," In contrast, it is known that PISN with masses 140-200 do not provide the correct chemical pattern and cannot reach high values of for low values of [Fe/H] (the ratio C/Fe in their yields, \citealt{2003ApJ...591..288H}, is not high enough)."
" However, if it could be established that the CEMP stars were particular cases, such as belonging to binaries (??) or due to the preferential depletion of iron in grains (?),, the SFR related to PopIII stars would be diminished, at least as far as chemical evolution is concerned."," However, if it could be established that the CEMP stars were particular cases, such as belonging to binaries \citep{2005ApJ...635..349R,2007ApJ...665.1361T} or due to the preferential depletion of iron in grains \citep{2008ApJ...677..572V}, the SFR related to PopIII stars would be diminished, at least as far as chemical evolution is concerned."
" In conclusion, our analysis hints at a massive mode at zc20—30,"," In conclusion, our analysis hints at a massive mode at $z\simeq 20-30$ \citep{2003Natur.425..812B,2006MNRAS.373..128G,2006MNRAS.366..247J,2007MNRAS.374.1557J,2007ApJ...665...85J,2007ApJ...663..687Y,2008MNRAS.387.1021G,2009ApJ...691..441S}."
 (????????).. (?) ??)) (e.g.?)..," \citep{2007MNRAS.381..647S} \citealt{2007MNRAS.381..647S,2006ApJ...641....1T}) \citep[e.g.][]{2008arXiv0812.1227F}."
 (?2?) ?)). (?).. (222?).. ?;; ?)) ?))," \citep{2003AJ....125.1649F,2004ApJ...607..697K,2006Natur.443..186I} \citealt{2009AAS...21342603S}) \citep{2007AAS...211.9114A}. \citep{2003ApJ...591..288H,2004ApJ...604L...1B,2006ApJ...642..382B,2006MNRAS.372.1034D}. \citealt{2006Natur.440..184K}; \citealt{2009ApJ...693.1610G}) \citealt{2009arXiv0906.1577T})"
 (2???) (??).. (???)..," \citep{2001ApJ...561L.153S,2002ApJ...576....1A,2004A&A...419..811A} \citep{2003MNRAS.346..209L,2003ApJ...595L...9P}. \citep{2001ApJ...555...92M,2002ApJ...571...40M,2003ApJ...591...38W}."
"Ti~(0.1—1). we obtain e;S0.01e. and M,~(20—50).","$T_6 \sim (0.1- 1)$, we obtain $v_{\ell} \lesssim 0.01\,c$ , and ${\cal M}_{\ell} \sim (20 - 50)$."
 Hence. regardless on the details ol the jet duty evele in the considerecl source. we conclude that the giant lobes in the svstem are expected to modcdily substantially the surrounding matter bv driving strong shocks and heating WILIIM at the outskirts of the filamentary galactic distribution.," Hence, regardless on the details of the jet duty cycle in the considered source, we conclude that the giant lobes in the system are expected to modify substantially the surrounding matter by driving strong shocks and heating WHIM at the outskirts of the filamentary galactic distribution."
 Delativistic jets in luminous radio galaxies and radio-loud. quasars are widely believed to be powered via the Dlandford&Znajek(LOTT) mechanism by a rotational energy. οἱ supermassive black holes (SMIBIIs) residing in the centers of their host galaxies (see.e.g.andreferences therein)..," Relativistic jets in luminous radio galaxies and radio-loud quasars are widely believed to be powered via the \citet{bla77} mechanism by a rotational energy of supermassive black holes (SMBHs) residing in the centers of their host galaxies \citep[see, e.g.,][and references therein]{sik07}."
 The maximum energy that can be extracted in (his wav is equal to the ‘reducible mass’ of a maximallv-spinning SAIBIL. namely where μμ=Adex10M. is the black hole mass.," The maximum energy that can be extracted in this way is equal to the `reducible mass' of a maximally-spinning SMBH, namely where $M_{\rm BH} \equiv M_8 \times 10^8 M_{\odot}$ is the black hole mass."
 The total power of a relativistic oulllows formed in the DlandfordZuajek process is (wpically approximated as where ο)μι is the black hole spin normalized to the maximum value Snax=GAR)/¢ the intensity of the magnetic field threading the black hole horizon isBy. and re=GAlyy/ is the gravitational radius of a SMDII (lorthemostrecentdiscussionTchekhovskovetal. 2010).," The total power of a relativistic outflows formed in the BlandfordZnajek process is typically approximated as where $J/J_{\rm max}$ is the black hole spin normalized to the maximum value $J_{\rm max} = G M_{\rm BH}^2/c$, the intensity of the magnetic field threading the black hole horizon is$B_{\rm g}$, and $r_{\rm g} = G M_{\rm BH} / c^2$ is the gravitational radius of a SMBH \citep[for the most recent discussion on this issue see][]{tch10}."
". The exact value of D, is not known. but it is often. assumed that (he maximum magnetic field intensity close to the black hole horizon corresponds (o the case when the magnetic field energy density is equal to the radiation energv density of a avatem accreting at the Eddington rate."," The exact value of $B_{\rm g}$ is not known, but it is often assumed that the maximum magnetic field intensity close to the black hole horizon corresponds to the case when the magnetic field energy density is equal to the radiation energy density of a system accreting at the Eddington rate."
" This gives D,2(2Lyr;n260425GxLOL"" OG. where Lyπο&10/9M L| is the Eddington luminosity."," This gives $B_{\rm g} \simeq (2 \, L_{\rm Edd} / r_{\rm g}^2 \, c)^{1/2} \simeq 6 \times 10^4 M_8^{-1/2}$ G, where $L_{\rm Edd} = 4 \pi G M_{\rm BH} m_{\rm p} c / \sigma_{\rm T} \simeq 10^{46} M_8$ $^{-1}$ is the Eddington luminosity."
 Combining all the above formulae together. and assuming further J=μας. we obtain finally Mieergss. !.," Combining all the above formulae together, and assuming further $J = J_{\rm max}$, we obtain finally $Q_{\rm BZ} \sim 2 \times 10^{45} \, M_8$ $^{-1}$."
 In the case of an estimate of the mass of the central SMDII can be derived from the velocity dispersion in optical spectrum of the host galaxy., In the case of an estimate of the mass of the central SMBH can be derived from the velocity dispersion in optical spectrum of the host galaxy.
 Such a spectrum. obtained with the ISIS double-beam spectrograph al the WIIT 4.21m telescope. was published previously inMachalskiοἱal. (2003)..," Such a spectrum, obtained with the ISIS double-beam spectrograph at the WHT m telescope, was published previously in\citet{mach08}. ."
 Based on the spectrum. the stellar velocity dispersion is determined using the svnthesis code of CidFernandesetal. (2005)..," Based on the spectrum, the stellar velocity dispersion is determined using the synthesis code of \citet{cid05}. ."
 The, The
described by a burst with a continuous duration zo100 Myr on top of the pre-existing stellar population.,described by a burst with a continuous duration $\gtrsim 100$ Myr on top of the pre-existing stellar population.
 The siuuulatious of DiMatteoetal.(2008) sinUlarly sugeestOO a mereer-diriven starburst duration of up to a few hundred Myr. cousisteut with our measured duration.," The simulations of \citet{dimatteo08} similarly suggest a merger-driven starburst duration of up to a few hundred Myr, consistent with our measured duration."
 We examine spectroscopic xoperties of pair and feld galaxies to quantifv effects of eravitational interactions at imuteriuediate recshift., We examine spectroscopic properties of pair and field galaxies to quantify effects of gravitational interactions at intermediate redshift.
 Our sample derives frou the Sinithsoman Hectosve Leusine survey (SITELS:Celleretal.205.2010).," Our sample derives from the Smithsonian Hectospec Lensing Survey \citep[SHELS;][]{geller05,geller10}."
. SIIELS includes 9.825 ealaxies aud is 97.( spectroscopically complete to Y=>20.3 over aji area of: { deer.," SHELS includes 9,825 galaxies and is $97.7\%$ spectroscopically complete to $R=20.3$ over an area of 4 $^2$."
> Wo select for galaxies in the τοςshift range 2=0.08)0.376., We select for galaxies in the redshift range $z=0.080-0.376$.
 This survey represeuts the nost conu]ete spectroscopic saniple im its redshift lange., This survey represents the most complete spectroscopic sample in its redshift range.
 We foa son the systems that have the poteutial o exhibit musts of star formation as a result of the interaction., We focus on the systems that have the potential to exhibit bursts of star formation as a result of the interaction.
 Substautial evidence slows that major udrs are nijore stronglv affected by the interaction., Substantial evidence shows that major pairs are more strongly affected by the interaction.
 We identi voa full set of major (AAg 1.75) urs Inchding 622 ealaxics iu the redshitt ranec Do0.0800.376. and a vobluuc-nuited subset of najor pair sin the redshift rauge +=0.0800.310. including 327 galaxies to My=20.8.," We identify a full set of major $\left | \Delta M_R \right | < 1.75$ ) pairs including 622 galaxies in the redshift range $z = 0.080-0.376$, and a volume-limited subset of major pairs in the redshift range $z = 0.080-0.310$, including 327 galaxies to $M_R = -20.8$."
" Witiu our iuajor pair suüuple. we further τον our selection using the spectroscopic iudex D,A00l.Hi as the divide between svsteuis with oder stellar populations. and systems with vouug stellay populations that likelv coutain gas."," Within our major pair sample, we further narrow our selection using the spectroscopic index $D_n4000 = 1.44$ as the divide between systems with older stellar populations, and systems with young stellar populations that likely contain gas."
 We rthe vovestrict our sample to svstenus with low sturounding density. which we measure with a count of neighbors wihin a volume of comoving radius 985 kpc.," We further restrict our sample to systems with low surrounding density, which we measure with a count of neighbors within a volume of comoving radius 985 kpc."
" The spectroscopic clagnostics of Πα specific star formation rate 55,3...D,1000. alxd a set of stellar. popuation 1uodcls enable t1ο investigation of the streneth. frequency. alxd timescale of trigecredao sar formation."," The spectroscopic diagnostics of $\alpha$ specific star formation rate $_{H\alpha}$ ), $D_n4000$, and a set of stellar population models enable the investigation of the strength, frequency, and timescale of triggered star formation."
" We show: The most effective way ο lncrease our abilitv to lueastre differeuces between pair auc fiek ealaxies as à function of redshift. or to determine he ACN fraction in pairs would (0 to observe a larger populatio1 of very close pairs (AD<15 kpe) at redshift +o»0.3 ""usine Sit] aperture spectroscopy."," We show: The most effective way to increase our ability to measure differences between pair and field galaxies as a function of redshift, or to determine the AGN fraction in pairs would be to observe a larger population of very close pairs $\Delta D < 15$ kpc) at redshift $z\sim 0.3$ using small aperture spectroscopy."
 It is iuiportaut to have hie1resolutiou photometric datadu combination with good seciug to distinguish close pairs., It is important to have high resolution photometric data in combination with good seeing to distinguish close pairs.
 This work benefited C»ereatlv frou. discussions with Elizabcth Barton. Nelson Calchwell. Scott Ikeuvon. aud Lisa Iexley.," This work benefited greatly from discussions with Elizabeth Barton, Nelson Caldwell, Scott Kenyon, and Lisa Kewley."
 We thank the 1iemibers ot DFWes PhD thesis conuuittee for their conmucuts that improved this work: Lars Heoruquish. Robert Kirshner. and Audrew Szeutevorgvi.," We thank the members of DFW's PhD thesis committee for their comments that improved this work: Lars Hernquish, Robert Kirshner, and Andrew Szentgyorgyi."
 We thauk tle anonviuous referee for a helpful aud kuowlegeable report., We thank the anonymous referee for a helpful and knowledgeable report.
 We eratefully acknowledge the coutribulon of the CfAs Telescope Data Center team. especiallv Doug Mink. Susan Tokarz. and William Watt for their work with the IHectospec data reuction pipeline.," We gratefully acknowledge the contribution of the CfA's Telescope Data Center team, especially Doug Mink, Susan Tokarz, and William Wyatt for their work with the Hectospec data reduction pipeline."
 We thauk the lIhectospec cuginecri18o team. iachding Robert Fata. Tom Caurou. Edward Ilertz. Mark Mueller. aud Mark Lacasse. aud t1ο iustruinent specialists Perry Berlind aud Alichael Calkins. aloug with the rest of the staff at the MAIT Observatory.," We thank the Hectospec engineering team, including Robert Fata, Tom Gauron, Edward Hertz, Mark Mueller, and Mark Lacasse, and the instrument specialists Perry Berlind and Michael Calkins, along with the rest of the staff at the MMT Observatory."
 Funding for the SDSS and SDSS-II has been provided bv the Alfred P. Sloan Fouudatin. the," Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the"
It is important (o stress that in a lime dependent model of a turbulent cloud with eravily. (he statistical properties of the cores formed in the cloud may. vary. wilh time (e.g.. Jappsen klessen 2004: Dib et al.,"It is important to stress that in a time dependent model of a turbulent cloud with gravity, the statistical properties of the cores formed in the cloud may vary with time (e.g., Jappsen Klessen 2004; Dib et al."
 2007a)., 2007a).
 In addition to angular momentum loss (hat mav be due to the cores secular evolution (i.e.. magnetic braking). the angular momentum of a core might be modified if the core enters a soft gravitational encounter with another/other core(s) and/or a plivsical merger (e.g.. Larson 2010).," In addition to angular momentum loss that may be due to the cores secular evolution (i.e., magnetic braking), the angular momentum of a core might be modified if the core enters a soft gravitational encounter with another/other core(s) and/or a physical merger (e.g., Larson 2010)."
 Following a collision. (he remnant merger may inherit a reduced or enhanced specific angular momentum.," Following a collision, the remnant merger may inherit a reduced or enhanced specific angular momentum."
 In our simulations. Fig.," In our simulations, Fig."
 1. shows (hat the number of cores detected at the lowest thresholds declines as a function of time while the number of cores identified al the highest thresholds increases., \ref{fig1} shows that the number of cores detected at the lowest thresholds declines as a function of time while the number of cores identified at the highest thresholds increases.
 As some of the cores evolve into a stage of gravitational contraction. (heir average clensitv will increase and they will be detected at higher density thresholds.," As some of the cores evolve into a stage of gravitational contraction, their average density will increase and they will be detected at higher density thresholds."
" ILlowever. as most of the cores identified at the thresholds of 10—80Πο, are eravitationally unbound. and have generally long dispersion timescales (i.e.. Vazzquez-Semadeni οἱ al."," However, as most of the cores identified at the thresholds of $10-80~n_{aver}$ are gravitationally unbound, and have generally long dispersion timescales (i.e., Vázzquez-Semadeni et al."
 2005). it is likely Chat (he rapid decline in (heir nunbers is due to merger events.," 2005), it is likely that the rapid decline in their numbers is due to merger events."
 Thus. in a cvnemically evolving cloud. it is important to keep in mind that the overall angular momentum of the dense cores that form in the cloud will be re-distributed among the cores and the inter-core medium.," Thus, in a dynamically evolving cloud, it is important to keep in mind that the overall angular momentum of the dense cores that form in the cloud will be re-distributed among the cores and the inter-core medium."
 Fies., Figs.
 5 and 6 display the time evolution of the normalized distributions of the intrinsic specific angular momentum js and of the rotational parameter 244; for the C20 and C160 cores identified in the (wo simulations., \ref{fig5} and \ref{fig6} display the time evolution of the normalized distributions of the intrinsic specific angular momentum $j_{3D}$ and of the rotational parameter $\beta_{rot}$ for the C20 and C160 cores identified in the two simulations.
" Albeit our models were not necessarily tailored to mimick any particular star forming region. it is temptative (o over-plot to the numerical results the observationally derived NIL; ancl Noll distributions of j and 3,4 (dashed-line histograms)."," Albeit our models were not necessarily tailored to mimick any particular star forming region, it is temptative to over-plot to the numerical results the observationally derived $_{3}$ and $_{2}$ $^{+}$ distributions of $j$ and $\beta_{rot}$ (dashed-line histograms)."
 The NIL; cores are those observed by Goodman et al. (, The $_{3}$ cores are those observed by Goodman et al. (
1993) ancl Barranco Goodman (1998). whereas the Noll cores are those observed by Caselli et al.,"1993) and Barranco Goodman (1998), whereas the $_{2}$ $^{+}$ cores are those observed by Caselli et al."
(2002a)°.. The median value of j45 for the C20 and C160 cores fluctuates in time but remains close (o fpped ," The median value of $j_{3D}$ for the C20 and C160 cores fluctuates in time but remains close to $j_{3D,med}$ "
ed was also remarked recently à a sample of mdividual IST FOS spectra (Zheng. Kriss Davidsen 1995).,"and was also remarked recently in a sample of individual HST FOS spectra (Zheng, Kriss Davidsen 1995)."
 Among weaker chiission lines. OIAI302 aud SiTV/OTV] show a mareinal (< 26) trend in the opposite direction. with sunaller in the NB composite.," Among weaker emission lines, $\,\lambda 1302$ and SiIV/OIV] show a marginal $<2\sigma$ ) trend in the opposite direction, with smaller in the XB composite."
 There is also a sueecstion that in the NF composite. NV is weal or nonexistent.," There is also a suggestion that in the XF composite, NV is weak or nonexistent."
 These should be investigated at higher S/N. 3) There is mareinal evidence for a coutimaiun flies deficit blueward of of the ΝΕ οὐπια., These should be investigated at higher S/N. 3) There is marginal evidence for a continuum flux deficit blueward of of the XF continuum.
" It proved dificult to ft the AF spectra with a convincing PL continu. because of a dip blueward of the cluission line, which we tentatively interpret as absorption."," It proved difficult to fit the XF spectrum with a convincing PL continuum, because of a dip blueward of the emission line, which we tentatively interpret as absorption."
 We fit a simple Gaussian component to the absorption. which is sufficient to characterize the absorbed flux. and velocity width.," We fit a simple Gaussian component to the absorption, which is sufficient to characterize the absorbed flux and velocity width."
 The result is that the CTV cinission line fits remain unchanged. while the overall fit improves. but oulv for the NF spectrum. (," The result is that the CIV emission line fits remain unchanged, while the overall fit improves, but only for the XF spectrum. ("
The formal improvemeut in 4 would appear marginal because the absorbed region covers only a few percent of the spectrum),The formal improvement in $\chi^2$ would appear marginal because the absorbed region covers only a few percent of the spectrum.)
 The equivalent width (43) of the absorption is NS+LA. centered at 1180+LOA. with FWIIM of 12500E2500104 ενος Table 1).," The equivalent width ) of the absorption is $8.8\pm1.4$, centered at $1480\pm10$, with FWHM of $12500\pm2800$ (see Table 4)."
 Some evidence for a similar dip cau be secu even in the NB spectrum. but it is smaller. aud its 13 not siguificaut in the fit in comparison to the formal errors (<< 1.50).," Some evidence for a similar dip can be seen even in the XB spectrum, but it is smaller, and its is not significant in the fit in comparison to the formal errors $<1.5\sigma$ )."
 Tf individual absorbers coutribute to the dip iu the NF composite. they are likely to be narrow. weak. aud undetected iu the noise of the individual spectra.," If individual absorbers contribute to the dip in the XF composite, they are likely to be narrow, weak, and undetected in the noise of the individual spectra."
 When the spectra of NF QSOs are combined. however. the enlarged width aud higher S/N of the composite absorber could enable detection of a broad feature.," When the spectra of XF QSOs are combined, however, the enlarged width and higher S/N of the composite absorber could enable detection of a broad feature."
 Wiel velocity intrinsic narrow line absorption in QSOs is just now being recognized iu individual QSOs (IL:unauu ct al., High velocity intrinsic narrow line absorption in QSOs is just now being recognized in individual QSOs (Hamann et al.
 1997): the challenge is to properly distinguish it from intervening absorption., 1997); the challenge is to properly distinguish it from intervening absorption.
 Iu suuunuarxy. there is evidence for a dip blueward of the enüssion line in the ΝΕ conrposite. independent of any reasonable continui οvoice.," In summary, there is evidence for a dip blueward of the emission line in the XF composite, independent of any reasonable continuum choice."
 If the dip iu the NF composite is due to absorption. the absorber is Helly ionized. aud probably situated near the iouiziug source.," If the dip in the XF composite is due to absorption, the absorber is highly ionized, and probably situated near the ionizing source."
 The large velocity width also suggests proximity to the broad line region (DLR)., The large velocity width also suggests proximity to the broad line region (BLR).
 The weak X-ray emission combined with evidence for high velocity ionized absorbers is reniüulsceut of recent results associating soft N-rav and. UV absorption (Alathur 1991. Alathur. Elvis Wilkes 1995. Caeen Mathur 1996. Creen 1997).," The weak X-ray emission combined with evidence for high velocity ionized absorbers is reminiscent of recent results associating soft X-ray and UV absorption (Mathur 1994, Mathur, Elvis Wilkes 1995, Green Mathur 1996, Green 1997)."
 We now consider a variety of possibilities to account for the optical and UV spectral difference between N-rav bright and X-ray faint QSOs: 1) huuinositv effects; 2) radio loudness. 3) absorption. aud 1) changes in theénfrinsic spectral energy. distribution (SED).," We now consider a variety of possibilities to account for the optical and UV spectral difference between X-ray bright and X-ray faint QSOs; 1) luminosity effects, 2) radio loudness, 3) absorption, and 4) changes in the spectral energy distribution (SED)."
 The streugth of some of these effects is directly testable using the samples at haul., The strength of some of these effects is directly testable using the samples at hand.
 Both selection effects aud scecoudary correlatious iust be considered when evaluating the siguificauce of observed correlations such as these., Both selection effects and secondary correlations must be considered when evaluating the significance of observed correlations such as these.
" Two well-known effects could conspire to produce an overall weakening of euission lines with increasing0,4.", Two well-known effects could conspire to produce an overall weakening of emission lines with increasing.
 First. Is known to increase with optical huuinositv (Wilkes et al.," First, is known to increase with optical luminosity (Wilkes et al."
 1991. Cacen et al.," 1994, Green et al."
 1995). at least for opticallv-selected samples (LaFranca 1995).," 1995), at least for optically-selected samples (LaFranca 1995)."
" Secoudly. as Iunuinositv increases, line equivalent width decreases (.c.. the Baldwin Effect: Baldwin 1977)."," Secondly, as luminosity increases, line equivalent width decreases (i.e., the Baldwin Effect; Baldwin 1977)."
 Could these effects combine to produce the auti-correlation of aud line strength observed. here?, Could these effects combine to produce the anti-correlation of and line strength observed here?
 As can be seen from Table 1. the LBQS subsamples are welbiunatehed i optical bIpuuinositv. so that uo Daldwiu effect is expected.," As can be seen from Table 1, the LBQS subsamples are well-matched in optical luminosity, so that no Baldwin effect is expected."
 Furthermore. the strength of the Baldwin effect iu the optical is known to be weak.," Furthermore, the strength of the Baldwin effect in the optical is known to be weak."
 Our results from the subsamples are less muuuuue to a Baldwin οπουἳ/SED conspiracy for the following reasons: 1) our subsamples are not as wellimatched im ΠΕ aud 2) the Daldwiu effect is much stronger in the UV.," Our results from the subsamples are less immune to a Baldwin effect/SED conspiracy for the following reasons: 1) our subsamples are not as well-matched in luminosity, and 2) the Baldwin effect is much stronger in the UV."
 We therefore perform a striugeut check. by applying the same spectral averaging techniques now to new subsamples defined by UV DIuuinosity.," We therefore perform a stringent check, by applying the same spectral averaging techniques now to new subsamples defined by UV luminosity."
 We divided the suuple at the mean UV οςαν value of 30.6., We divided the sample at the mean UV luminosity value of 30.6.
 The resulting low UV huninosityv (UVLO: 27 QSO) aud high UV luminosity (UVIIE 22 QSO) subsamples both had nien αρ=Liltοι , The resulting low UV luminosity (UVLO; 27 QSO) and high UV luminosity (UVHI; 22 QSO) subsamples both had mean $\aox=1.4\pm .04$.
SPECFEIT procedures identical to those of the NB and ΝΕ samples were applied., SPECFIT procedures identical to those of the XB and XF samples were applied.
 Virtually all spectral differences were siguificant in the UV huninosity subsamples than in the subsamples., Virtually all spectral differences were significant in the UV luminosity subsamples than in the subsamples.
 Oulv narrow enission Changes more stronely between UV. subsamples than between the subsamples., Only narrow emission changes more strongly between UV subsamples than between the subsamples.
 Indeed. the Baldwin Effect appears to be stronecst iu the narrow Lue components of both andCIV.," Indeed, the Baldwin Effect appears to be strongest in the narrow line components of both and."
. The bulk of the effect could be due to differences in narrow line region (NLR) enuüssiou. as also sugeested by Osimer. Porter. Creen (1991).," The bulk of the effect could be due to differences in narrow line region (NLR) emission, as also suggested by Osmer, Porter, Green (1994)."
" Since cussion liue correlations are stronger with ethan with πιοςνο, we conclude that either 1) depends primarily on the of the ionizing coutimua. crudely characterized here by or 2) both ed are related to some third parameter characterizing the QSO physics."," Since emission line correlations are stronger with than with luminosity, we conclude that either 1) depends primarily on the of the ionizing continuum, crudely characterized here by or 2) both and are related to some third parameter characterizing the QSO physics."
 One such possibility is absorption., One such possibility is absorption.
 Could the correlation of to luminosity the Baldwin effect?, Could the correlation of to luminosity the Baldwin effect?
 Although by design we have selected. stbsamples of similar huninositv for our NF and NB composites. we may suppose that the primary relationship between aud," Although by design we have selected subsamples of similar luminosity for our XF and XB composites, we may suppose that the primary relationship between and"
for a quantitative analysis.,for a quantitative analysis.
" Thus we consider only X-ray data taken with the EPIC (European Photon Imaging Camera). consisting of two MOS and one PN detector: all detectors operated in the ""Full Frame’ mode with the medium filter."," Thus we consider only X-ray data taken with the EPIC (European Photon Imaging Camera), consisting of two MOS and one PN detector; all detectors operated in the 'Full Frame' mode with the medium filter."
 The PN is the most sensitive instrument and primarily used for our analysis., The PN is the most sensitive instrument and primarily used for our analysis.
 The EPIC detectors are temporally affected by high background levels. thus to minimize contamination we extract photons from a circular region around the source position and restrict the analysis to the 22.0 keV band. where most of the source photons were detected.," The EPIC detectors are temporally affected by high background levels, thus to minimize contamination we extract photons from a circular region around the source position and restrict the analysis to the 2.0 keV band, where most of the source photons were detected."
 Only during a large flare occurring i our observation. photons of higher energies are present and a harder band 33.0 keV) is used for its study.," Only during a large flare occurring in our observation, photons of higher energies are present and a harder band 3.0 keV) is used for its study."
 The background was taken from close-by regions on the same CCD that contains SCR 1845., The background was taken from close-by regions on the same CCD that contains SCR 1845.
 We additionally verified our findings by applying standard selection criteria. which exclude the respective high-background time intervals.," We additionally verified our findings by applying standard selection criteria, which exclude the respective high-background time intervals."
 Since we are dealing with a high proper motion object. we further derive the exact X-ray positior with the source detection algorithm “edetect_cchain’.," Since we are dealing with a high proper motion object, we further derive the exact X-ray position with the source detection algorithm chain'."
 Spectral analysis was performed with XSPEC V12.3 (?).. and we use multi-temperature plasma models (APEC) with elemental abundances relative to solar values as given by ?..," Spectral analysis was performed with XSPEC V12.3 \citep{xspec}, and we use multi-temperature plasma models (APEC) with elemental abundances relative to solar values as given by \cite{grsa}."
 We note that the applied metallicity is interdependent with the emission neasure. and different combinations of both parameters lead to very similar results.," We note that the applied metallicity is interdependent with the emission measure, and different combinations of both parameters lead to very similar results."
 Due to the proximity of the target. interstellar absorption is negligible and not required in the modelling of our X-ray data.," Due to the proximity of the target, interstellar absorption is negligible and not required in the modelling of our X-ray data."
 The OM (Optical Monitor). an onboard optical/UV telescope. was operated in the imaging mode in the U-band 4400 nm. la=344 nm) and took five images with exposure times of 3.3 ks each. hence no detailed optical light curve is available.," The OM (Optical Monitor), an onboard optical/UV telescope, was operated in the imaging mode in the U-band 400 nm, $\lambda_{\rm eff}=344$ nm) and took five images with exposure times of 3.3 ks each, hence no detailed optical light curve is available."
 Nevertheless. the X-ray flare is clearly accompanied by a significant UV/optical brightening as can be seen in Fig. |...," Nevertheless, the X-ray flare is clearly accompanied by a significant UV/optical brightening as can be seen in Fig. \ref{opt},"
 where we show the pre-flare. flare and post-flare phase of SCR 1845 (center).," where we show the pre-flare, flare and post-flare phase of SCR 1845 (center)."
 In the exposure that covers the flare. SCR 1845 is about 2.6 mag brighter than in the pre-flare exposure.," In the exposure that covers the flare, SCR 1845 is about 2.6 mag brighter than in the pre-flare exposure."
 The other two objects visible in the images. DENIS J184507.7-635740 (upper right) and USNO-B 0260-0695925 (lower left). are not in common proper motion with SCR 1845.," The other two objects visible in the images, DENIS J184507.7-635740 (upper right) and USNO-B 0260-0695925 (lower left), are not in common proper motion with SCR 1845."
 An X-ray source is clearly detected at the expected position of SCR 1845., An X-ray source is clearly detected at the expected position of SCR 1845.
 The X-ray position coincides very well with the expected position for epoch 2008.7 coordinates as calculated from the known proper motion and the 2MASS position., The X-ray position coincides very well with the expected position for epoch 2008.7 coordinates as calculated from the known proper motion and the 2MASS position.
 Both the positional error and the offset are about and no other X-ray source is located at distances of around the position of SCR 1845: thus the identification is unambiguous., Both the positional error and the offset are about and no other X-ray source is located at distances of around the position of SCR 1845; thus the identification is unambiguous.
 Additionally the soft X-ray spectra and the observed flare make an unknown extra-galactic source very unlikely., Additionally the soft X-ray spectra and the observed flare make an unknown extra-galactic source very unlikely.
" The source ""Setection parameters are summarized in reflog..", The source detection parameters are summarized in \\ref{log}.
 The system is not resolved and appears like a point-source n the XMM data., The system is not resolved and appears like a point-source in the XMM data.
 While a small contribution from the brown aowarf to the overall X-ray emission cannot be excluded. it is “‘ery likely dominated by the late-type star.," While a small contribution from the brown dwarf to the overall X-ray emission cannot be excluded, it is very likely dominated by the late-type star."
 We thus assume in the following that the detected X-rays originate exclusively from the 88.5 dwarf., We thus assume in the following that the detected X-rays originate exclusively from the 8.5 dwarf.
 In reflec) we show the X-ray light curve of SCR 1845. which reveals a strong flare in the second half of the observation and quasi-quiescent emission over the total exposure time.," In \\ref{lc} we show the X-ray light curve of SCR 1845, which reveals a strong flare in the second half of the observation and quasi-quiescent emission over the total exposure time."
 Light curves were obtained from the PN data in the 22.0 keV band and binned to 100 s and are plotted separately for the source region and for the background., Light curves were obtained from the PN data in the 2.0 keV band and binned to 100 s and are plotted separately for the source region and for the background.
 The black histogram in the upper panel is the count rate from the source with c errors. the blue curve is the corresponding background level.," The black histogram in the upper panel is the count rate from the source with $\sigma$ errors, the blue curve is the corresponding background level."
 As can be seen. the remaining background is negligible.," As can be seen, the remaining background is negligible."
 For comparison we further show in the bottom panel of refle the U-band brightness averaged over the respective OM exposure., For comparison we further show in the bottom panel of \\ref{lc} the U-band brightness averaged over the respective OM exposure.
 The X-ray brightness of SCR 1845 is never constant. thus we call this level quasi-quiescent.," The X-ray brightness of SCR 1845 is never constant, thus we call this level quasi-quiescent."
 During the quasi-quiescent phase the average count rate ts 0.05 cts/s. Variability of up to a factor of about two in count rate on timescales of several minutes is observed throughout the whole exposure., During the quasi-quiescent phase the average count rate is 0.05 cts/s. Variability of up to a factor of about two in count rate on timescales of several minutes is observed throughout the whole exposure.
 This behavior points to persistent minor activity on SCR 1845., This behavior points to persistent minor activity on SCR 1845.
 An even stronger deviation of the quasi-quiescent level is seen towards the end of the observation. where the average," An even stronger deviation of the quasi-quiescent level is seen towards the end of the observation, where the average"
again as TIT ealaxies depeuds on their ability to retain eas during the observed burst of star formation. our observations are unable to provide any useful iutormation on the ultimate fate of these galaxies.,"again as HII galaxies depends on their ability to retain gas during the observed burst of star formation, our observations are unable to provide any useful information on the ultimate fate of these galaxies."
 The spectroscopic observations were carried out on the welts 1997 July 3-5 aud L998 July 25-27 usine the EMMI multi-purpose iustrmucut at the NTT (New Technology Telescope) in La Silla Observatory (ESO-Chile).,	 The spectroscopic observations were carried out on the nights 1997 July 3-5 and 1998 July 25-27 using the EMMI multi-purpose instrument at the NTT (New Technology Telescope) in La Silla Observatory (ESO-Chile).
 The observations are described iu detail iu VAIBF99., The observations are described in detail in VMBF99.
 The data reduction was done using standard nethods in IRAF., 	 	The data reduction was done using standard methods in IRAF.
 The spectra were bias subtracted aud civided by a normalized flat-fieldl frame (dome flat-Beld)., The spectra were bias subtracted and divided by a normalized flat-field frame (dome flat-field).
 Uhuuination corrections along the slit were found to be iegelieible., Illumination corrections along the slit were found to be gligible.
 The spectra were calibrated ia wavelcneth une Colmparison spectra of HeAÀr., The spectra were calibrated in wavelength using comparison spectra of HeAr.
 Cosmic rays were removed automaticcally (ve obtaimed at least three similar renes for cach object)., Cosmic rays were removed cally (we obtained at least three similar frames for each object).
 Skv lines were subtracted aud he spectra correctted for atimospheric extinction with he aid of mean extinction coeffücieuts for La Silla., Sky lines were subtracted and the spectra ted for atmospheric extinction with the aid of mean extinction coefficients for La Silla.
 For cach might we built a cal response curve frou the standard stars observed tha weht with a wide slit (5 arc sec), For each night we built a mean response curve from the standard stars observed that night with a wide slit (5 arc sec).
 Each object frame was fux calibrated. with the corresponding respouse curve., Each object frame was flux calibrated with the corresponding response curve.
 The spectra were also corrected for galactic reddening., The spectra were also corrected for galactic reddening.
 The reddening values were based on Burstein aud Teiles (1981)) maps. using enipirical selective function of Cardelli. Clayton Mathis (19893).," The reddening values were based on Burstein and Heiles \cite{burs84}) ) maps, using empirical selective function of Cardelli, Clayton Mathis \cite{card89}) )."
 The recdshitted CTITAL909 for SMM. J02399-0136 is contanuuated by the atmospheric absorption baud at ~7250Α., The redshifted $\lambda$ 1909 for SMM J02399-0136 is contaminated by the atmospheric absorption band at $\sim$ 7250.
. We created the spectrum of the atmospheric band from the 1-D spectrum of a standard star taken with the same slit width as the one used for the radio galaxy (1.5 are sec)., We created the spectrum of the atmospheric band from the 1-D spectrum of a standard star taken with the same slit width as the one used for the radio galaxy (1.5 arc sec).
 We fitted the coutimmun aud divided the original spectrin by the fit., We fitted the continuum and divided the original spectrum by the fit.
 By removing the absorption features intrinsic to the star. we obtained the spectrum of the atinospheric baud.," By removing the absorption features intrinsic to the star, we obtained the spectrum of the atmospheric band."
 We divided the spectrum of SMM J02399-0136 bv it trviug differeut factors., We divided the spectrum of SMM J02399-0136 by it trying different factors.
 Our conclusion is that the remaining effect of the atmospheric absorption is negligible after correction., Our conclusion is that the remaining effect of the atmospheric absorption is negligible after correction.
 Both IRAF aud STARLINK (DIPSO) routines were used to ueasure the emission line fluxes. EWIIMSs aud waveleugths.," 	Both IRAF and STARLINK (DIPSO) routines were used to measure the emission line fluxes, FWHMs and wavelengths."
 1-D spectra were extracted for all objects from apertures described below., 1-D spectra were extracted for all objects from apertures described below.
 We then fitted Gaussiau profiles to the lines., We then fitted Gaussian profiles to the lines.
 The measured fux aud FWOAL of the spectral ine are the values measured from the fit of the Gaussian., The measured flux and FWHM of the spectral line are the values measured from the fit of the Gaussian.
 The mstruineutal profile was subtracted frou the observed PWHAL in quadrature., The instrumental profile was subtracted from the observed FWHM in quadrature.
 The spatially integrated spectra of our objects are shown in Fie. l.., The spatially integrated spectra of our objects are shown in Fig. \ref{Fig1}.
 We extracted cach spectrum from an aperture inside which the weakest lines were detected with higher S/N: MBC2025-218 (1.9 arc sec. centered at the spatial contimmun ceutroid): MRC2101-212 (5.9 are sec centered at the intersection between the two bright clumps): AIRC'1558-003 (2.7 are sec centered at the spatial positiou of ceutroid of the brightest Lya component).," We extracted each spectrum from an aperture inside which the weakest lines were detected with higher S/N: MRC2025-218 (1.9 arc sec, centered at the spatial continuum centroid); MRC2104-242 (5.9 arc sec centered at the intersection between the two bright clumps); MRC1558-003 (2.7 arc sec centered at the spatial position of centroid of the brightest $\alpha$ component)."
 The two spectra of SAINT J02399-0136 correspond to a) the whole system (L1L2) (the spectrum was extracted form a. 1 arc sec aperture covering the brightest cussion of the Li|L2 components) aud b) he AGN component. L1. (," The two spectra of SMM J02399-0136 correspond to a) the whole system (L1+L2) (the spectrum was extracted form a 5.4 arc sec aperture covering the brightest emission of the L1+L2 components) and b) he AGN component, L1. ("
2.2 arc sec aperture centered at the ceutroid of Lya emission in L1) The spectra (except for SAINE 02399-0136) are typical of ΠΠ.,2.2 arc sec aperture centered at the centroid of $\alpha$ emission in L1) The spectra (except for SMM J02399-0136) are typical of HzRG.
 Lye is the strongest Lue and weaker CIVALDSSO. TeTTA1610 and CTHJAT909 are also detected.," $\alpha$ is the strongest line and weaker $\lambda$ 1550, $\lambda$ 1640 and $\lambda$ 1909 are also detected."
 NVAL2 LO is detected only in AIRC2025-218 aud SMM. J02399-0136., $\lambda$ 1240 is detected only in MRC2025-218 and SMM J02399-0136.
 This line is often not detected in ITZRG. (Róttteerius et al., This line is often not detected in HzRG (Rötttgering et al.
 1996)., 1996).
 We compare iu Fig., We compare in Fig.
 2. the spectrum of LI with an average spectrin of ITZRC. (Veruct et al. 1999)), \ref{Fig2} the spectrum of L1 with an average spectrum of HzRG (Vernet et al. \cite{ver99}) )
 aud the lyperhuninous (also gravitational lensed) Sevfert 2 galaxy FSCIO0211]|1721 (Ctoodrich et al. 1998))., and the hyperluminous (also gravitational lensed) Seyfert 2 galaxy FSC10214+4724 (Goodrich et al. \cite{goo96}) ).
 The differences are striking., The differences are striking.
 Ll presents very weak ΠΟΠ. stroug NV aud weak Lyra compared to typical ΠΠ spectra.," L1 presents very weak HeII, strong NV and weak $\alpha$ compared to typical HzRG spectra."
 It is similar to FSCLO2LL|L72 bin the sense that Lyo is weak aud NV strong. but Well is relatively much weaker in L1.," It is similar to FSC10214+4724 in the sense that $\alpha$ is weak and NV strong, but HeII is relatively much weaker in L1."
 We present in Table 1 some parameters characterizing the main UV cmission lines. resulting from 1-D Cassia fits to the line profiles.," 	We present in Table 1 some parameters characterizing the main UV emission lines, resulting from 1-D Gaussian fits to the line profiles."
 We described in VAIFB99 the spatial properties of the Ίνα cimitting eas derived from the 2-D spectra., 	 We described in VMFB99 the spatial properties of the $\alpha$ emitting gas derived from the 2-D spectra.
 Here we present 1-D spatial profiles for Lvo. the coutimmin and the strongest UV lines.," Here we present 1-D spatial profiles for $\alpha$, the continuum and the strongest UV lines."
 We created the cussion line spatial profiles by adding those pixels Gu the dispersion, We created the emission line spatial profiles by adding those pixels (in the dispersion
Tt is well known that another mixing phenomenon occurs on the AGL. for intermediate nass stars (IMS: A>4.5—54M. ).,"It is well known that another mixing phenomenon occurs on the AGB, for intermediate mass stars (IMS: $M \ge 4.5 - 5 M_{\odot}$ )."
 HU ds driven by the convective envelope extension down to the II-burning lavers. in a process called Hot Bottom Burning (IIBB).," It is driven by the convective envelope extension down to the H-burning layers, in a process called Hot Bottom Burning (HBB)."
 The isotopic mix of presolar oxide grains cannot however be explained by this mechanism: (is was made clear in the works by Boothrovd&Sackmann (1999).. Lugaroetal.(2007) and al. (2008)..," The isotopic mix of presolar oxide grains cannot however be explained by this mechanism; this was made clear in the works by \citet{sb99}, , \citet{lug} and \citet{ili}. ."
" In particular. Hiadisοἱal.(2008) revised the !O(p.5 ) reaction rate. essentially conlirming the NACRE value but reducing the uncertainty,"," In particular, \citet{ili} revised the $^{16}$ $\gamma$ ) reaction rate, essentially confirming the NACRE value but reducing the uncertainty."
 On this basis. Chev found an equilibrium FO/!O ratio in their IMS model of 525x10.7. incompatible with presolar erain data.," On this basis, they found an equilibrium $^{17}$ $^{16}$ O ratio in their IMS model of $^{+0.88}_ {-0.76}\times10^{-3}$, incompatible with presolar grain data."
" Thev concluded that ""there is not clear evidence to date for anv stellar grain origin from massive AGB stars” (seealsoBoothrovd&Sackmann1999.Figure7).", They concluded that “there is not clear evidence to date for any stellar grain origin from AGB stars” \citep[see also][Figure 7]{sb99}.
. The measurements of Figure 2. cluster around an P O//9O0 ratio of 0.0012. as tvpical of the shell II-burning temperatures in AGB stars of masses up to about 2 M..," The measurements of Figure \ref{two} cluster around an $^{17}$ $^{16}$ O ratio of 0.0012, as typical of the shell H-burning temperatures in AGB stars of masses up to about 2 $M_{\odot}$."
 Both lower and higher temperatures (as found in RGB and HDD conditions. respectively) would bring the moclel tracks outside the area of (he measured data.," Both lower and higher temperatures (as found in RGB and HBB conditions, respectively) would bring the model tracks outside the area of the measured data."
 This fact. when coupled with the abundances of Al in the grains. offers compelling evidence in favor of deep mixing in the AGB phases of low mass stars.," This fact, when coupled with the abundances of $^{26}$ Al in the grains, offers compelling evidence in favor of deep mixing in the AGB phases of low mass stars."
" Our results would not change significantly by adopting the reaction rate for ""O+p from Chalaetal.(2007)... as done by IKCS10: the differences in the equilibrium 110/190 values between this choice and the NACRE oneamount (at maximum) to 20."," Our results would not change significantly by adopting the reaction rate for $^{17}$ O+p from \citet{chafa}, as done by KCS10: the differences in the equilibrium $^{17}$ $^{16}$ O values between this choice and the NACRE oneamount (at maximum) to ."
".. One may further notice that. among the eight opticallv-visible. moderatelv-evolved MS and S stars observed by Harrisetal.(1985).. four (50%)) have !O/!*O ratios below 5x10. 1, and two (254%.)) around 2x10 +."," One may further notice that, among the eight optically-visible, moderately-evolved MS and S stars observed by \citet{har}, four ) have $^{18}$ $^{16}$ O ratios below $\times$ $^{-4}$, and two ) around $\times$ $^{-4}$."
 Despite the low statistics and large error bars of stellar observations. (his compares well with the family of oxide grains requiring extira-mixing.," Despite the low statistics and large error bars of stellar observations, this compares well with the family of oxide grains requiring extra-mixing."
 As an example. in the Saint Louis database (http://presolar.wustledu/~ped/) onefinds 16 erains of group L and 79 grains of eroup 2 with “O/1°O ratios lower than permitted byFDU.," As an example, in the Saint Louis database $\sim$ pgd/) onefinds 76 grains of group 1 and 79 grains of group 2 with $^{18}$ $^{16}$ O ratios lower than permitted byFDU."
 For of the wholesample this ratio is below 5x10. and for it is below 2x10 ' , For of the wholesample this ratio is below $\times$ $^{-4}$and for it is below $\times$ $^{-4}$ .
Among group 2 grains alone these numbers become ancl 33%... respectively.," Among group 2 grains alone these numbers become and , respectively."
A,A
outflow rate in a stellar wind to be comparable to the augular momentum deposited onto the star from accretion of disk material (andseeMatt&Pudyritz2005b).,outflow rate in a stellar wind to be comparable to the angular momentum deposited onto the star from accretion of disk material \citep[and see][]{mattpudritz05}.
". Observations of large-scale outflows from T Tauri stars and (presumably younger] Class I sources indicate mass outflow rates of ~0.1 times the accretion rates, with about an order of magnitude of scatter aud/or nucertaityin this value (e.g..seereviewbyCabrit 2007)."," Observations of large-scale outflows from T Tauri stars and (presumably younger) Class I sources indicate mass outflow rates of $\sim 0.1$ times the accretion rates, with about an order of magnitude of scatter and/or uncertaintyin this value \citep[e.g., see review
by][]{cabrit07}."
. It is still not clear what fraction of the mass outflow rates observed ou larec-scales may be due to flows that are magnetically counected to the star (as required in the present work). απ opposed to flows from the accretion disk (o...Ferreiraetal.2006:Iurosawaot2006:Iwvauetal.2007:I&urosawact 2011).," It is still not clear what fraction of the mass outflow rates observed on large-scales may be due to flows that are magnetically connected to the star (as required in the present work), as opposed to flows from the accretion disk \citep[e.g.,][]{ferreira3ea06, kurosawa3ea06, kwan3ea07,
 kurosawa3ea11}."
. Recent models of accretion-powered stellar winds by Crammer(2008.2009). exhibit outflows from the star itself with \~0.0L.," Recent models of accretion-powered stellar winds by \cite{Cranmer:2008p1657, Cranmer:2009p1647} exhibit outflows from the star itself with $\chi\sim0.01$."
 Thus. in the preseut work. we consider cases with both 4=0.1 and 0.01. to explore a possible rauge of this value.," Thus, in the present work, we consider cases with both $\chi=0.1$ and 0.01, to explore a possible range of this value."
 The evolution of the stellar structure follows simple Welvin-Uechuholz contraction of a polvtrope (with index 3/2)., The evolution of the stellar structure follows simple Kelvin-Helmholz contraction of a polytrope (with index 3/2).
 This treatiuent results in an evolution of stellar radius that follows where ΠΠ. and Af. are the stella radius aud mass. JT. i the effective temperature of the star. aud σ and G are the Stefan-Boltzimanu constant aud Newton's eravitational constant.," This treatment results in an evolution of stellar radius that follows where $R_*$ and $M_*$ are the stellar radius and mass, $T_e$ is the effective temperature of the star, and $\sigma$ and $G$ are the Stefan-Boltzmann constant and Newton's gravitational constant."
 As in Paper L we adopt au initial stellar radius of SAR. aud constant photospheric temperature 7.=1280 Is for all calculations. so that the evolution of the stars structure resembles that from the model of Siessetal.(2000).. as the star descends aloug the Tavashi track in the ΠΠ ciaegram (sec 33 iu Paper D.," As in Paper I, we adopt an initial stellar radius of $8 R_\odot$ and constant photospheric temperature $T_e = 4280$ K for all calculations, so that the evolution of the star's structure resembles that from the model of \citet{siess3ea00}, as the star descends along the Hayashi track in the H-R diagram (see 3 in Paper I)."
 The oulx difference between this equation aud the correspouding equation of Paper Lis the addition of the factor (1.A). which takes mass loss into account.," The only difference between this equation and the corresponding equation of Paper I is the addition of the factor $(1-\chi)$, which takes mass loss into account."
 The evolution of the aneular spin rate of the star follows where ©. is the (solid body) angular rotation rate of he star. T. is the net torque on the star. and 7. is he stellar moment of inertia. Z.=ΑΠΕ. where hds the normalized radius of evration (we adopt κ = 12).," The evolution of the angular spin rate of the star follows where $\Omega_*$ is the (solid body) angular rotation rate of the star, $T_*$ is the net torque on the star, and $I_*$ is the stellar moment of inertia, $I_*\equiv~k^2M_*R_*^2$, where $k$ is the normalized radius of gyration (we adopt $k^2$ = 0.2)."
 The only difference between this equation aud the correspouding equation of Paper Tis the addition of the actor (1X). which takes mass loss into account.," The only difference between this equation and the corresponding equation of Paper I is the addition of the factor $(1-\chi)$, which takes mass loss into account."
 It is often iustructive to express the spin rate as a raction of the breakup speed. defined as the I&epleriau velocity at the stars equator.," It is often instructive to express the spin rate as a fraction of the breakup speed, defined as the Keplerian velocity at the star's equator."
 This normalized spin rate is defined Following Paper L we consider two cases with differcut initial spin rates.," This normalized spin rate is defined Following Paper I, we consider two cases with different initial spin rates."
 The two cases have initial fractional spin rates of fy=0.3 and 0.06. represcuting the two extremes of rapid aud slow initial rotation.," The two cases have initial fractional spin rates of $f_0 = 0.3$ and 0.06, representing the two extremes of rapid and slow initial rotation."
 The preseut work considers the simultaueous effects of torques arising iu the magnetic star-disk interaction and anenlar momentum loss from stellar winds., The present work considers the simultaneous effects of torques arising in the magnetic star-disk interaction and angular momentum loss from stellar winds.
 Iu both cases. the angular ποιοται eaim and loss of the star is primarily transnütted bv a magnetic field.," In both cases, the angular momentum gain and loss of the star is primarily transmitted by a magnetic field."
 The model assunes a rotatiou-axis-aliecned dipole magnetic field. with a strength of D. at the surface aud equator of the star.," The model assumes a rotation-axis-aligned dipole magnetic field, with a strength of $B_*$ at the surface and equator of the star."
 We consider two different values of the maguetic field streugth. B.=500 € aud 2000 C. iu addition to a case with D.=0 used for comparison.," We consider two different values of the magnetic field strength, $B_*=500$ G and 2000 G, in addition to a case with $B_*=0$ used for comparison."
 The model assumes that D. is coustaut in time for all cases., The model assumes that $B_*$ is constant in time for all cases.
 The torques arising from the magnetic iuteractiou between the star and accretion disk follow Matt&Pudiitz(2005b).. and the governing equations are eiven um Paper 1. It is convenicut to define the corotatiou radius which is the sineular radius in the Ieplerian disk that rotates at the same aneular speed as the star.," The torques arising from the magnetic interaction between the star and accretion disk follow \citet{mattpudritz05}, and the governing equations are given in Paper I. It is convenient to define the corotation radius which is the singular radius in the Keplerian disk that rotates at the same angular speed as the star."
 This location is plvsically meaningful iu the maguetic star-disk interaction because it is where the differentia rotation between the star and disk equals zero., This location is physically meaningful in the magnetic star-disk interaction because it is where the differential rotation between the star and disk equals zero.
 The magnetic Ποια of the star is typically strong enough to be able to truncate the disk at a distance of a few stellar radu., The magnetic field of the star is typically strong enough to be able to truncate the disk at a distance of a few stellar radii.
 The truncation radius is denoted 1., The truncation radius is denoted $R_t$.
" The torque associated with disk truucatiou aud iufall of material from A to the stellar surface is the accretion torque Z,.", The torque associated with disk truncation and infall of material from $R_t$ to the stellar surface is the accretion torque $T_a$.
 There is also a magnetic torque associate with the magnetic connection to a rauge of radii in the disk., There is also a magnetic torque associated with the magnetic connection to a range of radii in the disk.
" This magnetic torque is denoted Z7,,.", This magnetic torque is denoted $T_m$.
" The methoc and equations used forcalculating Ry. T,. aud T,, are even in Paper P aud are not modified for the present work."," The method and equations used forcalculating $R_t$, $T_a$, and $T_m$ are given in Paper I and are not modified for the present work."
" Two key paramucters involved in the calculation of the star-disk iuteraction torques capture the plivsics of the magnetic coupling streneth (parameter 3) aud the opening of magnetic field lines due to the differeutial rotation (parameter 5,: see Paper I aud Matt&Pirdvitz 200553).", Two key parameters involved in the calculation of the star-disk interaction torques capture the physics of the magnetic coupling strength (parameter $\beta$ ) and the opening of magnetic field lines due to the differential rotation (parameter $\gamma_c$; see Paper I and \citealp{mattpudritz05}) ).
" Paraicter 5. reprents the maxiuun ratio between the aziuuuthal and vertical maeuetic field conrponeuts (5,/D.) threading the disk. in order for the dipolar maguetic field lues to remain closed."," Parameter $\gamma_c$ reprents the maximum ratio between the azimuthal and vertical magnetic field components $B_\phi/B_z$ ) threading the disk, in order for the dipolar magnetic field lines to remain closed."
" In the present work. we adopt +,=1 which correspouds to realistic expecations (Uzdeuskyetal.2002)."," In the present work, we adopt $\gamma_c = 1$ which corresponds to realistic expecations \citep{uzdensky3ea02}."
.. Parameter Pais equivalent to the inverse of the magnetic Reynolds uunmber in the inner disk region., Parameter $\beta$ is equivalent to the inverse of the magnetic Reynolds number in the inner disk region.
 Tere we adopt ./=0.01. preseuted in Paper I (andMatt&Pudritz2005h) as a reasonable guess for T Tari systems.," Here we adopt $\beta=0.01$, presented in Paper I \citep[and][]{mattpudritz05}
 as a reasonable guess for T Tauri systems."
 The effect of varving these two parameters was the subject of Paper I. Tn order to caleulate the angular momentum loss via stellar winds. we use the stellar sviud torque formulation of Matt&Pucitz (2008a)..," The effect of varying these two parameters was the subject of Paper I. In order to calculate the angular momentum loss via stellar winds, we use the stellar wind torque formulation of \citet{mattpudritz08II}. ."
 This formulation is based upon analytic caleulatious goiug back to Weber&Davis (1967).. in which the torque from a one-dimcusional wind Is given by," This formulation is based upon analytic calculations going back to \citet{weberdavis67}, , in which the torque from a one-dimensional wind is given by"
is. the measurement. error.,is the measurement error.
 EThe. smaller the value of. 2στ. rw greater the effect upon the bias.," The smaller the value of $\sigma_x^2$, the greater the effect upon the bias."
 We mention this sxplicithy to underscore that analyzing samples for which 10 predictors are. e.g.. uniformlv distributed: may reduce 1e magnitude of the bias magnitude but will not eliminate un since measurement error is still present.," We mention this explicitly to underscore that analyzing samples for which the predictors are, e.g., uniformly distributed may reduce the magnitude of the bias magnitude but will not eliminate it since measurement error is still present."
 In Fig. 5..," In Fig. \ref{fig:bias_unif},"
 we show jo estimated sample bias as a function of Z for a 10.000-ealaxy sample constructed so as to be uniform in Z (though 1¢ distribution of the predictors themselvesthe dilfusion coordinatesis not necessarily uniform).," we show the estimated sample bias as a function of $Z$ for a 10,000-galaxy sample constructed so as to be uniform in $Z$ (though the distribution of the predictors themselves–the diffusion coordinates–is not necessarily uniform)."
 Comparing these results with the top panels of Vie. 2.," Comparing these results with the top panels of Fig. \ref{fig:bias},"
 we find that uniformity in Z reduces the bias slightly (while also slightly increasing seumple standard deviation)., we find that uniformity in $Z$ reduces the bias slightly (while also slightly increasing sample standard deviation).
 Vhis indicates that measurement error is the dominant. cause of the observed bias., This indicates that measurement error is the dominant cause of the observed bias.
" Nonparametric estimators such as k-nearest neighbor (KNN) ancl local polynomial regression are also allected by measurement error bias (whose mitigation is clubbed the “deconvolution problem"") and design bias. and in aclelition by boundary bias (see. e... chapter 5 of Wasserman2006 and chapter 12 of Carrolletal.2006 and references therein)."," Nonparametric estimators such as k-nearest neighbor (kNN) and local polynomial regression are also affected by measurement error bias (whose mitigation is dubbed the “deconvolution problem"") and design bias, and in addition by boundary bias (see, e.g., chapter 5 of \citealt{Wasserman2006} and chapter 12 of \citealt{Carroll06} and references therein)."
 Thus the similarity of our bivariate distribution to that of. og. Balletal. (See their lie.," Thus the similarity of our bivariate distribution to that of, e.g., \citeauthor{Ball08} (See their fig."
 6., 6.
 In this figure. we note slightly larger deviations from the 2=Z locus at the endpoints than our bivariate distribution exhibits. which max indicate boundary bias but also could be a result of the fact that Balletal. do not minimize risk and thus could be adopting a solution with relatively higher bias and lower variance than our solution.)," In this figure, we note slightly larger deviations from the $\hat{z} = Z$ locus at the endpoints than our bivariate distribution exhibits, which may indicate boundary bias but also could be a result of the fact that \citeauthor{Ball08} do not minimize risk and thus could be adopting a solution with relatively higher bias and lower variance than our solution.)"
 1n addition to estimator bias. we also examine the estimator variance. Le. the width of the observed. bivariate distribution (given as a function of Z in the right column of Fig. 2)).," In addition to estimator bias, we also examine the estimator variance, i.e., the width of the observed bivariate distribution (given as a function of $Z$ in the right column of Fig. \ref{fig:bias}) )."
 Contributing to the variance. is (a) moclel uncertainty. Le. the standard deviation of the estimates = (given by the square root of the diagonal elements of the matrix given in equation X3)): (b) uncertainty in the flux for each object: and (c) intrinsic scatter. i.e. the fact that the AISG sample does not necessarily contain a homogencega set of objects.," Contributing to the variance is (a) model uncertainty, i.e., the standard deviation of the estimates $\zhat$ (given by the square root of the diagonal elements of the matrix given in equation \ref{eqn:vy}) ); (b) uncertainty in the flux for each object; and (c) intrinsic scatter, i.e., the fact that the MSG sample does not necessarily contain a homogeneous set of objects."
 Model uncertainty contributes little to the observed scatter: the mean. median. and standard deviation of the model uncertainties are 7.," Model uncertainty contributes little to the observed scatter; the mean, median, and standard deviation of the model uncertainties are $\la$ $^{-5}$."
 Flux uncertainty enters via attenuation bias: as [lux errors increase. the linear regression slope flattens ancl acts to. decrease. the sample variance within a redshift bin.," Flux uncertainty enters via attenuation bias; as flux errors increase, the linear regression slope flattens and acts to decrease the sample variance within a redshift bin."
 However. in our simple attenuation-bias demonstration we observe only negligible changes in the sample variance.," However, in our simple attenuation-bias demonstration we observe only negligible changes in the sample variance."
 Thus we conclude. that the observed. sample variance is primarily due to intrinsic scatter. and can only be reduced by introducing more data (ef ρουetal.2008..," Thus we conclude that the observed sample variance is primarily due to intrinsic scatter, and can only be reduced by introducing more data (cf. \citealt{Ilbert09},"
 who achieve ReyX 0.01 by utilizing data from 30 bands in the UV. optical. and LR regimes)," who achieve $\Rhat \la$ 0.01 by utilizing data from 30 bands in the UV, optical, and IR regimes)."
 From our data sample. we extract those 30.700 ealaxies for which Z0.2 andPRIMTARGET = 32(TARGETGALAXYRED: Isensteinetal. 2001)).," From our data sample, we extract those 30,700 galaxies for which $Z > 0.2$ and = 32; \citealt{Eisen01}) )."
 Vhis is our luminous red galaxy or LRG sample., This is our luminous red galaxy or LRG sample.
 As with the MS. training set. werandomly select. 10.000. &alaxies and then remove outliers.," As with the MSG training set, werandomly select 10,000 galaxies and then remove outliers."
 Because the s band. data of high-redshift LliGs lacks constraining power (as LAGs are faint in v and thus the magnitudes are noisy). we use only grit fluxes in analyses (so that p = 12).," Because the $u$ band data of high-redshift LRGs lacks constraining power (as LRGs are faint in $u$ and thus the magnitudes are noisy), we use only $griz$ fluxes in analyses (so that $p$ = 12)."
 The training set contains 9.734 objects.," The training set contains 9,734 objects."
 Application of the algorithm outlined in 882.1-2.2 vields tuning parameter estimates (c.m) = (0.012.200).," Application of the algorithm outlined in 2.1-2.2 yields tuning parameter estimates $(\epshat,\mhat)$ = (0.012,200)."
 The results of fitting are shown in Table 1 and the bottom. panel of Fig. 1l. , The results of fitting are shown in Table \ref{tab:results} and the bottom panel of Fig. \ref{fig:sdss}. .
As in the case of the MSG analysis. our value eq = 0.0195 (0.0270 without 1|Z normalization) compares favorably," As in the case of the MSG analysis, our value $\Rhat$ = 0.0195 (0.0270 without $1+Z$ normalization) compares favorably"
mass numberdependence ofpolarizations ofhvperons is low. Theenergy dependenc,hyperon polarization in $\Sigma^-A$ collisions is small due to the strangeness of the incident
mass numberdependence ofpolarizations ofhvperons is low. Theenergy dependence,hyperon polarization in $\Sigma^-A$ collisions is small due to the strangeness of the incident
mass numberdependence ofpolarizations ofhvperons is low. Theenergy dependence ,hyperon polarization in $\Sigma^-A$ collisions is small due to the strangeness of the incident
mass numberdependence ofpolarizations ofhvperons is low. Theenergy dependence o,hyperon polarization in $\Sigma^-A$ collisions is small due to the strangeness of the incident
mass numberdependence ofpolarizations ofhvperons is low. Theenergy dependence of,hyperon polarization in $\Sigma^-A$ collisions is small due to the strangeness of the incident
+je vorticity of the equilibrium flow.,the vorticity of the equilibrium flow.
 Iu an uunaegnetized +imn disk this quautity can be written as (2): where Sis the surface mass deusitv. vis the velocity of the fluid. 5 the adiabatic index. 9 the rotation frequency and #7=JO|200 the epicevelic frequency squared (κο that 52/20 is the νιticity).," In an unmagnetized thin disk this quantity can be written as \citep{RWI2}: : where $\Sigma$ is the surface mass density, $\vec v$ is the velocity of the fluid, $\gamma$ the adiabatic index, $\Omega$ the rotation frequency and $\kappa^2=4\Omega+2\Omega \Omega '$ the epicyclic frequency squared (so that $\kappa^2/2\Omega$ is the vorticity)."
 Two possibilitics that can result in an extrem in £ have been investigated: the first oue occurs near the mareinally stable orbit around a compact object. where relativistic effects create a miaximuunm of 47/20.," Two possibilities that can result in an extremum in $\mathcal{L}$ have been investigated: the first one occurs near the marginally stable orbit around a compact object, where relativistic effects create a maximum of $\kappa^2/2\Omega$."
 The erowth rate of the RWI is stronely increased bx a poloidal maeuetic field threading the disk (?).. but decreased by a toroidal one (2)...," The growth rate of the RWI is strongly increased by a poloidal magnetic field threading the disk \citep{TAV06}, but decreased by a toroidal one \citep{YU09}."
 This has been proposed as an explanation for the hieh frequency quasi-periodic oscillation (ΟΡΟ) of microquasars (2?7)..," This has been proposed as an explanation for the high frequency quasi-periodic oscillation (QPO) of microquasars \citep{TAV06, LAI09, TSA09}."
 The secoud possibility is to have au οποια of the surface deusitv., The second possibility is to have an extremum of the surface density.
 Themodel of ?. for protoplanctary disks relics ou 1ο fact that extrema of X should occur at the edees of the Dead Zone of these disks. so that the RWI should be uustable there.," Themodel of \cite{VAR06} for protoplanetary disks relies on the fact that extrema of $\Sigma$ should occur at the edges of the Dead Zone of these disks, so that the RWI should be unstable there."
 ? and? have also used the RWI in an explanation for the quasi-periodicity that may have been observed during the flares of SgrA*., \cite{TAG06} and \cite{FAL07} have also used the RWI in an explanation for the quasi-periodicity that may have been observed during the flares of SgrA*.
 The RWI has been studied both analytically (77) aud uumneneallv (2?)..," The RWI has been studied both analytically \citep{RWI1,RWI2} and numerically \citep{RWI3, VAR06}."
 Tt is formed by Rossby waves trapped iu the extyeunun of £. as shown in figure L..," It is formed by Rossby waves trapped in the extremum of $\mathcal L$, as shown in figure \ref{FigSchema}."
 differential vorticity and differential rotation couple them to spiral waves. eiitted on both sides of the extrema region.," differential vorticity and differential rotation couple them to spiral waves, emitted on both sides of the extremum region."
 Rossby waves have their corotation radius (where their phase velocity equals the rotation velocity of the eas) at that extremum., Rossby waves have their corotation radius (where their phase velocity equals the rotation velocity of the gas) at that extremum.
" The standing wave pattern they form appears as a vortex located in the region of the extrema. and grows exponentially,"," The standing wave pattern they form appears as a vortex located in the region of the extremum, and grows exponentially."
 The waves have a positive flux of enerev and aneular momentum bevond that radius. aud a neeative flux inside it. so that (as will be checked iu the simulation) the pattern can grow as it causes the eas inside corotation to lose augular momentum aud acercte. while the eas bevoud corotation gains that angular ολοται and moves outward.," The waves have a positive flux of energy and angular momentum beyond that radius, and a negative flux inside it, so that (as will be checked in the simulation) the pattern can grow as it causes the gas inside corotation to lose angular momentum and accrete, while the gas beyond corotation gains that angular momentum and moves outward."
 As a result the iustabilitv tends to destroy the οκτοι of £. as seeu for instance in 2..," As a result the instability tends to destroy the extremum of $\mathcal L$, as seen for instance in \cite{TAG06}."
 In the context of the mechanisin proposed by ? for xotoplanetary disks. we expect the mstabilitv to saturate at the amplitude where this is balanced by the continuous regeueration of the extrenmuu of deusitv bv the eas accreting from the Laval© à«ak AN ime-upt» at the edee of the Dead Zone (and oppodsitch®TNYA afXm the iuner edge of: the Dead Zone).," In the context of the mechanism proposed by \cite{VAR06} for protoplanetary disks, we expect the instability to saturate at the amplitude where this is balanced by the continuous regeneration of the extremum of density by the gas accreting from the outer disk and piling up at the edge of the Dead Zone (and oppositely at the inner edge of the Dead Zone)."
 However these studies have all been done in the approximation of au infinitely thin disk. because of the coluplesity of a full 3D :alytical study. or of the numerical resources needed or 3D simulations.," However these studies have all been done in the approximation of an infinitely thin disk, because of the complexity of a full 3D analytical study, or of the numerical resources needed for 3D simulations."
" Such a study is however highly desirable. both to consider the ""ull -τσexitv of the eas (aud eraius) flow. aud to validate thin disk approximation: this approximation was introduced (uad its Bits defined) by ??.. but this does uot apply as such to Rossby perturbations."," Such a study is however highly desirable, both to consider the full complexity of the gas (and grains) flow, and to validate the thin disk approximation: this approximation was introduced (and its limits defined) by \cite{GOL65-1,GOL65-2}, but this does not apply as such to Rossby perturbations."
 We will see farther in this paper that indeed 3D effects bring in significant aud potentially iniportaut qualitative differences., We will see farther in this paper that indeed 3D effects bring in significant and potentially important qualitative differences.
 We work m cevlindrical coordinates (7.0.:) with the 3D Euler equation: ορV. TEM where p ds the mass density of the fluid. aud w its velocity.. and p the pressure.," We work in cylindrical coordinates $(r, \phi, z)$ with the 3D Euler equation: _t. _t where $\rho$ is the mass density of the fluid, and $\vec v$ its velocity, and $p$ the pressure."
 ὃς=GAL(p5uy3 is the gravity potential of the ceutral object with € the eravitational constant and AY. the mass of the ceutral object., $\Phi_G={-GM_*}/{(r^2+z^2)^{1/2}}$ is the gravity potential of the central object with G the gravitational constant and $M_*$ the mass of the central object.
 We consider a barotropic flow. the entropy 5 Is constant in the eutire svsteni: with the adiabatic iudex 5=5/3.," We consider a barotropic flow, the entropy $S$ is constant in the entire system: with the adiabatic index $\gamma=5/3$."
 The sound speed is . ο , The sound speed is given by $c_s^2=\gamma p/\rho=S\gamma \rho^{\gamma-1}$ and the temperature by $T=p/\rho=S\rho ^{\gamma -1}$.
"We choose as initial equilibriun a density profile decreasing radially as rt? to which is added a density bun: The deusity is normalized by p,,. the midplane densityat the inner boundary of the simulation cj; aud rp is the position of the bump."," We choose as initial equilibrium a density profile decreasing radially as $r^{-1/2}$ , to which is added a density bump: The density is normalized by $\rho_m$, the midplane densityat the inner boundary of the simulation $r_{i}$, and $r_B$ is the position of the bump."
 For the paramcters y aud o. which control the amplitude aud the width of the density bunip. we take the values 4=0.1 audσ=0.1 respectively zone.," For the parameters $\chi$ and $\sigma$ , which control the amplitude and the width of the density bump, we take the values $\chi=0.4$ and$\sigma=0.1$ respectively ."
 These values allow the iustability to erow relatively fast. decreasing the ummerical load.," These values allow the instability to grow relatively fast, decreasing the numerical load,"
bbecause the velocity due to particle noise can approach the sound speed. which can wash out the physical velocity perturbation relevant for this test.,because the velocity due to particle noise can approach the sound speed which can wash out the physical velocity perturbation relevant for this test.
 For the simulations. we set up the problem in three dimensions using a periodic thin slab defined by ανC 9€[05.0.5] and z€[.1/64.1/64].," For the simulations, we set up the problem in three dimensions using a periodic thin slab defined by $x\in \{-0.5,0.5\}$ , $y\in \{-0.5,0.5\}$ and $z\in \{-1/64,1/64\}$."
" The domain satisfied: The density and temperature ratio were £2,=pifps72/7,= οί. ensuring that the whole system was pressure equilibrium."," The domain satisfied: The density and temperature ratio were $R_\rho=\rho_{\rm 1}/\rho_{\rm
 2}=T_{\rm 2}/T_{\rm 1}=c_{\rm 2}^2/c_{\rm 1}^2$ , ensuring that the whole system was pressure equilibrium."
" The two lavers were given constant and opposing shearing velocities. with the low density [aver moving at a Mach. number Mo=οzO11 and the dense laver moving at Vf,=MeVES"," The two layers were given constant and opposing shearing velocities, with the low density layer moving at a Mach number $\mathcal{M}_{\rm{2}}=-v_{\rm 2}/c_{\rm 2}
\approx 0.11$ and the dense layer moving at $\mathcal{M}_{\rm{1}}=\mathcal{M}_{\rm{2}}\sqrt{R_\rho}$."
 The density. ratios considered. in this work are small which assures a subsonic regime where the growth of instabilities can be treated using equation 56. (?).., The density ratios considered in this work are small which assures a subsonic regime where the growth of instabilities can be treated using equation \ref{eq:KHI} \citep{1997ApJ...483..262V}.
 To trigger instabilities. velocity. perturbations were imposed on the two boundaries of the form: where the perturbation velocity defer=1/8 and is the wavelength of the node.," To trigger instabilities, velocity perturbations were imposed on the two boundaries of the form: where the perturbation velocity $\delta v_{\rm y}/v=1/8$ and $\lambda=0.5$ is the wavelength of the mode."
 Equal mass particles were placed in lattice configuralions to satisfy the setup. described above., Equal mass particles were placed in lattice configurations to satisfy the setup described above.
 To satisfy pressure equilibrium everywhere. in tthe temperatures were adjusted. at boundaries {ο be coherent with the smoothecl density step measured by equation L..," To satisfy pressure equilibrium everywhere, in the temperatures were adjusted at boundaries to be coherent with the smoothed density step measured by equation \ref{eqn:sphcont}."
 This was not done for the ssimulations since these sharpen the densities using the discrete initial temperatures., This was not done for the simulations since these sharpen the densities using the discrete initial temperatures.
 The low density region po was set up using 256 particles in the .r-direction and the appropriate number of particles in the other dimensions to satis[v a fixed inter-particle distance., The low density region $\rho_2$ was set up using 256 particles in the $x$ -direction and the appropriate number of particles in the other dimensions to satisfy a fixed inter-particle distance.
 The high density region pj was created in the same wav with 320 particles in the .r-cdirection., The high density region $\rho_1$ was created in the same way with 320 particles in the $x$ -direction.
 We adopted a periodic simulation domain., We adopted a periodic simulation domain.
 ‘The simulation used the same numerical set-up as described above. but in 2D rather than in a thin slab.," The simulation used the same numerical set-up as described above, but in 2D rather than in a thin slab."
" We performed the Z4,=2 simulation using the LLP Riemann solver (7) on a 256 [ixed. Cartesian grid.", We performed the $R_\rho=2$ simulation using the LLF Riemann solver \citep{toro} on a $256\times256$ fixed Cartesian grid.
 The LLE solver is rather cilfusive and is used in order to suppress the erowth of undesirable small scale. Ws arising from. eric irregularities., The LLF solver is rather diffusive and is used in order to suppress the growth of undesirable small scale KHIs arising from grid irregularities.
 We note that all numerical schemes carry. numerical viscosit whether it is manifested through limited resolution or artificialv. shock-capturing viscosity.," We note that all numerical schemes carry numerical viscosity, whether it is manifested through limited resolution or artificial shock-capturing viscosity."
 A detailed: study. of this elfect on the KIL and the relation to physical viscosity is bevond the scope of this paper., A detailed study of this effect on the KHI and the relation to physical viscosity is beyond the scope of this paper.
" Figure 4. shows our results for the WILL test. (density ratio R,=2) at τικη=1 modelled with SPLL aandΟΡΙΟ. using three different kernels: CS. C'T and HOCTA. and dillerent. neighbour numbers as marked. on cach plot (see also Table 2))."," Figure \ref{fig:clump} shows our results for the KHI test (density ratio $R_\rho = 2$ ) at $\tau_\mathrm{KH}=1$ modelled with SPH, and, using three different kernels: CS, CT and HOCT4, and different neighbour numbers as marked on each plot (see also Table \ref{tab:sims}) )."
 From left to right. the panels show. in a slice of width £r=1 about the z-axis: density contours of the simulation box. à zoom in on the particle distribution around on of the rolls. the magnitude of the E error (equation 28)) as a function of jy. and the pressure as a function of y in a slice of width d.c—1 about the x-axis.," From left to right, the panels show, in a slice of width $dx=1$ about the z-axis: density contours of the simulation box, a zoom in on the particle distribution around on of the rolls, the magnitude of the $|\uE|$ error (equation \ref{eqn:e0int}) ) as a function of $y$, and the pressure as a function of $y$ in a slice of width $dx=1$ about the x-axis."
 Using the standard CS kernel. SPII-CS-128 (top row. Figure 4)) and TSPLI--CS-128 (second row) give poor results that improve very slowly with increasing neighbour number.," Using the standard CS kernel, SPH-CS-128 (top row, Figure \ref{fig:clump}) ) and -CS-128 (second row) give poor results that improve very slowly with increasing neighbour number."
 This can be seen both in the lack of strong evolution on the boundary. and in the large οἱ error. even for 128 neighbours.," This can be seen both in the lack of strong evolution on the boundary, and in the large $|\uE|$ error, even for 128 neighbours."
 PSPLE-CS-128 gives slightly better results than SPLI-CS-128. showing the first beginnings of a WILL roll. but both are in poor agreement with the results (bottom Low).," -CS-128 gives slightly better results than SPH-CS-128, showing the first beginnings of a KHI roll, but both are in poor agreement with the results (bottom row)."
 The reason for the poor performance in both SPLII-CS-128 and TSPILII--CS-128 is the clumping instability (827))., The reason for the poor performance in both SPH-CS-128 and -CS-128 is the clumping instability \ref{sec:clumpinginst}) ).
 Particles gather together on the kernel scale. giving poor kernel sampling. and poor associated error.," Particles gather together on the kernel scale, giving poor kernel sampling, and poor associated error."
 This can be seen in the particle distribution for SPLHI-CS-128 and TSPLI--CS-128 (second row. Figure 4)) which show visible holes and over-densities in the particle distribution.," This can be seen in the particle distribution for SPH-CS-128 and -CS-128 (second row, Figure \ref{fig:clump}) ) which show visible holes and over-densities in the particle distribution."
 Using instead the CP kernel introduced in refsec:clumpinginst.. the results improve dramatically (third row. Figure 4))," Using instead the CT kernel introduced in \\ref{sec:clumpinginst}, the results improve dramatically (third row, Figure \ref{fig:clump}) )."
 Now the errors reduce for increasing neighbour number (see Appendix ?22))., Now the errors reduce for increasing neighbour number (see Appendix \ref{sec:partnumber}) ).
 With 128 neighbours. we successfully resolve a WHE roll up to mH=1 with the correct growth time.," With 128 neighbours, we successfully resolve a KH roll up to $\tau_\mathrm{KH}=1$ with the correct growth time."
 lt has been noted. previously in the literature that putting a small core inside a cubic spline kernel suppresses the clumping instability (?2: 7 2)). though its importance [or modelling multiphase Dow was not realised.," It has been noted previously in the literature that putting a small core inside a cubic spline kernel suppresses the clumping instability \bcite{1992MNRAS.257...11T}; \bcite{1994MmSAI..65.1013H}) ), though its importance for modelling multiphase flow was not realised."
 Alternative fixes include adding an negative pressure term. (7)... which in tests we find. works also.," Alternative fixes include adding an negative pressure term \citep{2000Monaghan}, which in tests we find works also."
 However. we prefer. changing the kernel to introducing new forces since we may then still estimate our errors through [Eu|.," However, we prefer changing the kernel to introducing new forces since we may then still estimate our errors through $|\uE|$."
 In addition to the clumping instability. there is also an instability to transverse waves the banding instability refsec:bandinginst)).," In addition to the clumping instability, there is also an instability to transverse waves – the banding instability \\ref{sec:bandinginst}) )."
 For the KIL tests we present here. the bancding instability occurs only on the boundary and appears to be relatively benign.," For the KHI tests we present here, the banding instability occurs only on the boundary and appears to be relatively benign."
" Ες is shown in Figure 5.. that shows a zoom in on the boundary at τη=1 for TSPLI--C'TF-128. TSPL-HOCT4-442 and OSPLI--LLOC""E4-42."," This is shown in Figure \ref{fig:banding}, that shows a zoom in on the boundary at $\tau_\mathrm{KH}=1$ for -CT-128, -HOCT4-442 and -HOCT4-442."
 The TSPL--CUIE-128 simulation has à kernel and neighbour number combination that are unstable to transverse waves (sce Ligure 2)) and banding is clearly visible on the x»uncdarv.," The -CT-128 simulation has a kernel and neighbour number combination that are unstable to transverse waves (see Figure \ref{fig:stabct}) ), and banding is clearly visible on the boundary."
 However. TSPLF--LIOCTTE4-42 should be stable to ransverse waves. vet the banding persists.," However, -HOCT4-442 should be stable to transverse waves, yet the banding persists."
" Only in our full scheme. OSPLI--LIOC""E4-442. is the banding is gone."," Only in our full scheme, -HOCT4-442, is the banding is gone."
 Yo understand the above results. we ran an acdcditional estthat we omit. for. brevity TSPH--HOCT4-96.," To understand the above results, we ran an additional testthat we omit for brevity – -HOCT4-96."
 This simulation showed little boundary evolution. because he low neighbour number and associated large [η] significantly damped the WIL, This simulation showed little boundary evolution because the low neighbour number and associated large $|\uE|$ significantly damped the KHI.
L Llowever. interestingly. there was no banding observed. on the boundary (recall that 96 neighbours for the LOCTS kernel should be stable to both transverse and longitudinal wave perturbations).," However, interestingly, there was no banding observed on the boundary (recall that 96 neighbours for the HOCT4 kernel should be stable to both transverse and longitudinal wave perturbations)."
As secu above. both isothermal aud NEW halo provide a good fit to the observed kinematics of DDO210.,"As seen above, both isothermal and NFW halo provide a good fit to the observed kinematics of DDO210."
 Profiles steeper than NEW have also been proposed by some N-body simulations (6.8. Moore et al., Profiles steeper than NFW have also been proposed by some N-body simulations (e.g. Moore et al.
 1999)., 1999).
 lu order to check whether such steep profiles are also consistent with the data. lass models were fit using a broader famuly of density profiles. viz.," In order to check whether such steep profiles are also consistent with the data, mass models were fit using a broader family of density profiles, viz."
 The circular velocity correspouding to the above density profile (see Ixravtsov ot al., The circular velocity corresponding to the above density profile (see Kravtsov et al.
 1998) is: ↖↖↽∐∖↥⋅↸∖↥⋅⊤⋜⋯≼↧∖⊽⊤⋜⋯∖↑∐↸∖↸∖↕−↥⋅↸∖↸⊳↑↕↖↽↸∖⋅⇁⊓∐⋅∐∪↖↽↸∖↥⋅∥↥⋅⋜∥∐∏↴∖↴ and velocity.," 1998) is: where $_{\rm{t}}$ and $_{\rm{t}}$ are the effective “turnover"" radius and velocity."
" The parameter B is related to the iuner slope of the deusity xofile. a bv e=1|a/2.0. ""b is the outer logaritlinic slope of the rotation curve while ""a deteriumnes the sharpuess of turnover."," The parameter “g"" is related to the inner slope of the density profile, $\alpha$ by $= 1+ \alpha/2.0$, “b"" is the outer logarithmic slope of the rotation curve while “a"" determines the sharpness of turnover."
 Fits to the rotation curve with all three parameters left free did not converge., Fits to the rotation curve with all three parameters left free did not converge.
 Teuce. since we are primarily concerned with the slope in the immer regions. we fixed the parameters b anda to the values of 134 2nd 1.5 respectively. (which are the typical values ound for the rotation curves of chwart ealaxies: Ixravtsov et al.," Hence, since we are primarily concerned with the slope in the inner regions, we fixed the parameters b and a to the values of 0.34 and 1.5 respectively, (which are the typical values found for the rotation curves of dwarf galaxies; Kravtsov et al."
 1998). while r4 and Vi were left as free parameters.," 1998), while $_{\rm{t}}$ and $_{\rm{t}}$ were left as free parameters."
 Yp was fixed to a value of 0.5. as sugeested by he observed colours iu the galaxy: this also allows a meaningful comparison of derived mass models for a fuuilv o: deusitv profiles.," $\Upsilon_B$ was fixed to a value of 0.5, as suggested by the observed colours in the galaxy; this also allows a meaningful comparison of derived mass models for a family of density profiles."
 We found that the reduced v for the fi continuously mereases as the profile gets steeper., We found that the reduced $\chi^2$ for the fit continuously increases as the profile gets steeper.
 For comparison. fixing ο to 0.5 (correspoxding to a =L.0: NEW profile) eave reduced \? —0.1 while ο of 0.1 (corresponding to à =1.2) eave reduced 4? =0.7.," For comparison, fixing g to 0.5 (corresponding to $\alpha=$ 1.0; NFW profile) gave reduced $\chi^2=$ 0.4 while g of 0.4 (corresponding to $\alpha=$ 1.2) gave reduced $\chi^2=$ 0.7."
 At the extreme. fixing ο to 0.2 (a =1.6) ((which substantially over-predicts the observed rotation velocity at s11all radii. while the velocity at large radii) gave reduced 4? =2.5.," At the extreme, fixing g to 0.2 $\alpha=$ 1.6) (which substantially over-predicts the observed rotation velocity at small radii, while underestimates the velocity at large radii) gave reduced $\chi^2=$ 2.5."
" nuderestimatesNote that since there are heavistics ""involved in computing the error bars on Ce. 1 is nof possible to vigorously trauslate the inininmin 47 value oeito a confidence interval for the paraimecters of the fit."," Note that since there are heuristics involved in computing the error bars on $v_c$, it is not possible to rigorously translate the minimum $\chi^2$ value into a confidence interval for the parameters of the fit."
 However. a lower 4? value does iuply a betterfit (sec also ie discussion in vau deu Bosh Swaters 2001).," However, a lower $\chi^2$ value does imply a betterfit (see also the discussion in van den Bosh Swaters 2001)."
 Fig., Fig.
 11 VAlows the best fit mass model with a=1.2., \ref{fig:mond} shows the best fit mass model with $\alpha=1.2$.
 So far we have assumed that the discrepancy between je dynamical mass. estimated. from the ΠΕος drift” corrected rotation curve. and the huuinous mass oe1i DDO21IO0 can be explained by cousidering au extended dark halo around the galaxy.," So far we have assumed that the discrepancy between the dynamical mass, estimated from the “asymmetric drift” corrected rotation curve, and the luminous mass in DDO210 can be explained by considering an extended dark halo around the galaxy."
 Anaternate explanation for this discrepancy is that the dvuamiics becomes non-Newtouian in the limit of low acceleration. ic. the MOND theory (AGilerom 1983).," An alternate explanation for this discrepancy is that the dynamics becomes non-Newtonian in the limit of low acceleration, i.e. the MOND theory (Milgrom 1983)."
 We have also tried fitting the rotation curve using the MOND prescription., We have also tried fitting the rotation curve using the MOND prescription.
 Tn this fit. Yp aud ay (the critical acceleration parameter) were takeu ax free parameters.," In this fit, $\Upsilon_B$ and $_0$ (the critical acceleration parameter) were taken as free parameters."
 Fig., Fig.
 LL shows the best fit MOND rotation curve., \ref{fig:mond} shows the best fit MOND rotation curve.
 As can be seen. the MOND rotation curve agrees well with the observed curve in the inner regions of the galaxy. while it underestimate the observed curve (bv up to 2.0 lj np the outer regions.," As can be seen, the MOND rotation curve agrees well with the observed curve in the inner regions of the galaxy, while it underestimate the observed curve (by up to 2.0 $^{-1}$ ) in the outer regions."
 The best fit model eave Lp oEO. {02 auc ay of 1.74023 (in. units of N 2 7) with: reduced 472 —0.7., The best fit model gave $\Upsilon_B$ of $\pm$ 0.2 and $_0$ of $\pm$ 0.3 (in units of $^{-8}$ $^{-2}$ ) with reduced $\chi^2=$ 0.7.
EN The best fit value of Yp agrees with the value expected from the observed colours in DDO210., The best fit value of $\Upsilon_B$ agrees with the value expected from the observed colours in DDO210.
" Also. the best fit value of ay is cousistent with the mean value of ay found for other. xiehter galaxies (IxXeut (L987): sce also Mileroui. 1955),"," Also, the best fit value of $_0$ is consistent with the mean value of $_0$ found for other, brighter galaxies (Kent (1987); see also Milgrom 1988)."
 DDO210 is the faintest shown dwart ireeular galaxw for which the MOND prescription provides a reasonably eood fit to the observed kinematics., DDO210 is the faintest known dwarf irregular galaxy for which the MOND prescription provides a reasonably good fit to the observed kinematics.
 Recall that all the above imass imodels have Όσοι derive by assieuimg au inclination of 30 deerees (obtained roni the outer III contours. as discuss πι Soect.3.1)).," Recall that all the above mass models have been derived by assigning an inclination of 30 degrees (obtained from the outer HI contours, as discuss in \ref{ssec:HI_dis}) )."
 Iuorder to estimate the effect of using an CIYOLCOUs inclination on he derived halo parameters. mass modoelimg was also tried with two other values of inclination viz.," Inorder to estimate the effect of using an erroneous inclination on the derived halo parameters, mass modeling was also tried with two other values of inclination viz."
 GU cerees (L0. tha estimated from the optical isoplotes) aud 15 CETCOS (a value between the optical aud III inclination)., 60 degrees (i.e. that estimated from the optical isophotes) and 45 degrees (a value between the optical and HI inclination).
 The best fit mass model for à coustaut density halo. using an inclination of 60 degrees. eave Y5of 1550.2 and py21240«10OAL. with reduced 4?=tL3.," The best fit mass model for a constant density halo, using an inclination of 60 degrees, gave $\Upsilon_B$of $\pm$ 0.2 and $\rho_0=27\pm2.0~\times10^{-3} M_\odot$ $^{-3}$ with reduced $\chi^2=0.3$."
" On the other haud. au inclination of 15 deerees gave the best fit model with Yp of LS+0.2 and py=3142.40«1041, 5 with reduced 47= 0.2."," On the other hand, an inclination of 45 degrees gave the best fit model with $\Upsilon_B$ of $\pm$ 0.2 and $\rho_0=31\pm2.0~\times10^{-3} M_\odot$ $^{-3}$ with reduced $\chi^2=0.2$ ."
 Recall that au inclination of 30 deerees gave the best fit with Tp of 1220.5 aud py= ? with reduced 4?= 0.1., Recall that an inclination of 30 degrees gave the best fit with $\Upsilon_B$ of $\pm$ 0.5 and $\rho_0=29\pm5.0~\times10^{-3} M_\odot$ $^{-3}$ with reduced $\chi^2=0.4$ .
 As can be seen. the ceutral halo deusitv is relatively imseusitive to," As can be seen, the central halo density is relatively insensitive to"
The passbands have been implemented on the two web sites of Padova (http://stev.oapd.inaf.it/) and BASTI (http://albione.oa-teramo.inaf.it/).,The passbands have been implemented on the two web sites of Padova (http://stev.oapd.inaf.it/) and BASTI (http://albione.oa-teramo.inaf.it/).
 This way stellar tracks and isochrones can be computed and downloaded., This way stellar tracks and isochrones can be computed and downloaded.
 Figure 18 shows the Padova isochrones (Marigo et al., Figure \ref{fig:iso} shows the Padova isochrones (Marigo et al.
" 2008) in the passbands for solar metallicity and for different ages, just as an example."," 2008) in the passbands for solar metallicity and for different ages, just as an example."
 As explained in Sect., As explained in Sect.
" 6.2 of ?,, during the observational process only the pixels in the area immediately surrounding the target source are sent to the ground in the form of a’ window’."," 6.2 of \cite{2006MNRAS.367..290J}, during the observational process only the pixels in the area immediately surrounding the target source are sent to the ground in the form of a 'window'."
 In most cases the pixels in the window are binned in the across-scan direction so that the resulting data consist of a one-dimensional set of number counts per sample (a set of pixels)., In most cases the pixels in the window are binned in the across-scan direction so that the resulting data consist of a one-dimensional set of number counts per sample (a set of pixels).
 The images in the one- or two- dimensional windows will be fitted with line-spread or point-spread functions to estimate the fluxes of the objects., The images in the one- or two- dimensional windows will be fitted with line-spread or point-spread functions to estimate the fluxes of the objects.
 The estimated associated error of the derived flux is related to the signal within the window as in the case of an aperture photometry’ approach., The estimated associated error of the derived flux is related to the signal within the window as in the case of an 'aperture photometry' approach.
 It is assumed that the object flux fx within a given passband X is measured in a rectangular 'aperture' of ns samples within the window., It is assumed that the object flux $f_X$ within a given passband $X$ is measured in a rectangular 'aperture' of $n_s$ samples within the window.
 Some light loss is produced because of the finite extent of the 'aperture'., Some light loss is produced because of the finite extent of the 'aperture'.
" Hence the actual flux in the window will be gaper-fx, where gaper<1."," Hence the actual flux in the window will be $g_{\rm aper} \cdot f_X$, where $g_\mathrm{aper} \le 1$."
" While scanning the sky, will observe the sources transiting the focal plane."," While scanning the sky, will observe the sources transiting the focal plane."
" In each transit, the same source will be observed nine times in and one time in BP and RP CCDs (see Fig. 1))."," In each transit, the same source will be observed nine times in and one time in BP and RP CCDs (see Fig. \ref{fig:focalplane}) )."
" The magnitude error for a transit (ox) is computed taking into account (1) the photon noise, (2) the total detection noise per sample r, which includes the detector read- noise, (3) the sky background contribution by assumed to be derived from n; background samples, (4) the contribution of the calibration error per observation oa, and (5) the averaged total number of columns in each band Nstrips"," The magnitude error for a transit $\sigma _{X}$ ) is computed taking into account (1) the photon noise, (2) the total detection noise per sample $r$, which includes the detector read-out noise, (3) the sky background contribution $b_X$ assumed to be derived from $n_b$ background samples, (4) the contribution of the calibration error per observation $\sigma_{\rm cal}$, and (5) the averaged total number of columns in each band $n_{\rm strips}$."
 The magnitude errors are artificially increased by 20 per cent (m= 1.2)., The magnitude errors are artificially increased by 20 per cent $m=1.2$ ).
" This safety margin accounts for sources of error not considered here such as the dependence of the calibration error on the sky density, complex background, etc."," This safety margin accounts for sources of error not considered here such as the dependence of the calibration error on the sky density, complex background, etc."
" For the calculations here we have assumed o2.=0, ie. negligible compared to the poissonian and read-out noise."," For the calculations here we have assumed $\sigma^{2}_{\rm cal}=0$, i.e. negligible compared to the poissonian and read-out noise."
 In reality this might not be the case because the complexity of the instrumental effects is rather challenging., In reality this might not be the case because the complexity of the instrumental effects is rather challenging.
" At present it is not completely understood to which level of perfectness effects like saturation, non-linearity, radiation damage, and charge transfer inefficiencies on the data can be calibrated."," At present it is not completely understood to which level of perfectness effects like saturation, non-linearity, radiation damage, and charge transfer inefficiencies on the data can be calibrated."
 Therefore a general, Therefore a general
"Although the jets of microquasars present a complex phenomenology of their own (Fenderetal.2004,2009),, on top of that it is expected additional phenomena linked to the jet-wind interaction in HMMQ, as this and previous works (PB08, PBK10) show.","Although the jets of microquasars present a complex phenomenology of their own \citep{fen04,fen09}, on top of that it is expected additional phenomena linked to the jet-wind interaction in HMMQ, as this and previous works (PB08, PBK10) show."
" Since the jet power is strongly linked to the mass-loss rate, HMMQ jets detectable in X-rays or gamma-rays will be probably found in systems with moderate-to-strong winds."," Since the jet power is strongly linked to the mass-loss rate, HMMQ jets detectable in X-rays or gamma-rays will be probably found in systems with moderate-to-strong winds."
" Therefore, unless particle acceleration is negligible in clump bow shocks, HMMQ phenomenology at energies must be strongly affected by them, showing wind-related strong variability at high energies unless the wind is quite homogeneous or clumps with R,>10!° cm are completely missing."," Therefore, unless particle acceleration is negligible in clump bow shocks, HMMQ phenomenology at high-energies must be strongly affected by them, showing wind-related strong variability at high energies unless the wind is quite homogeneous or clumps with $R_{\rm c}>10^{10}$ cm are completely missing."
" Concerning (powerful) transient ejections, usually associated to X-ray state transitions, we note that such an ejections will require some time to form."," Concerning (powerful) transient ejections, usually associated to X-ray state transitions, we note that such an ejections will require some time to form."
" If this takes hours, the wind will have time to surround the transient jet."," If this takes hours, the wind will have time to surround the transient jet."
" Then, the clump impact will be as described here unless the jet is too powerful."," Then, the clump impact will be as described here unless the jet is too powerful."
" If powerful blobs would appear as discrete even at the scales of the binary, they may have too much inertia to be significantly affected by the wind."," If powerful blobs would appear as discrete even at the scales of the binary, they may have too much inertia to be significantly affected by the wind."
" The dynamical impact of the stellar wind on the jet, enhanced by clumpiness, should not be neglected when interpreting radio emission from HMMQ."," The dynamical impact of the stellar wind on the jet, enhanced by clumpiness, should not be neglected when interpreting radio emission from HMMQ."
" Even if jets escape from disruption, the enhanced jet entropy"," Even if jets escape from disruption, the enhanced jet entropy"
linc-of-ieht. to the observed velocity dispersion estimates by ininimizineg the 47. This procedure implicitly assumes that the svsteni is at equilibrimu.E,"line-of-sight, to the observed velocity dispersion estimates by minimizing the $\chi^2$ This procedure implicitly assumes that the system is at equilibrium.:"
. We cousider the complete sample of 37 PNe plus the GCs data from Iissler-Patig et al. (19993)., We consider the complete sample of 37 PNe plus the GCs data from Kissler-Patig et al. \cite{kisl99}) ).
 The fit to the velocity dispersion profile is shown in Fie., The fit to the velocity dispersion profile is shown in Fig.
 | with the confidence regions for the best-fit paramcters (σας 130 laus [| ατα].," \ref{dismod} with the confidence regions for the best-fit parameters $\sigma_\mathrm{d}$ =430 km $^{-1}$, $r_\mathrm{d}$ $''$ )."
 lass distribution is shown iu Fig. Si, The mass distribution is shown in Fig. \ref{mod}:
" it ewes ALp""=The6d2ML. within 100"". where the quoted errors are to the extreme values of o4 and ra in confidence reeion and produce the dot-dashed dispersion models in Fig. IT:"," it gives $M/L_\mathrm{B}=56^{+15}_{-13}M_{\odot}/L_{\odot}$ within $''$, where the quoted errors are related to the extreme values of $\sigma_\mathrm{d}$ and $r_\mathrm{d}$ in confidence region and produce the dot-dashed dispersion models in Fig. \ref{dismod}.:"
 Tere only 31 PNe (the three PNe (ID = ]. 13. 36) were excluded) are cousidered to be at equilibrium.," Here only 34 PNe (the three PNe (ID = 1, 13, 36) were excluded) are considered to be at equilibrium."
 Fig., Fig.
 El. shows the ft to the velocity dispersion estimates with the related couficence regious in paranueter space., \ref{dismod} shows the fit to the velocity dispersion estimates with the related confidence regions in parameter space.
" The best-fit parameter are 6,2280 hin to and ιτ.", The best-fit parameter are $\sigma_\mathrm{d}$ =280 km $^{-1}$ and $r_\mathrm{d}$ $''$.
" Du this case, we introduced a tidal radius. R,=360"". where the stellar distribution is truncated. which has improved the ft to the data."," In this case, we introduced a tidal radius, $R_\mathrm{t}$ $''$, where the stellar distribution is truncated, which has improved the fit to the data."
 This possibly indicates the most external radius of NGC 1399. while the cluster potential dominates at larger radi.," This possibly indicates the most external radius of NGC 1399, while the cluster potential dominates at larger radii."
 The derived mass distributiou is also shown in Fig. 5:, The derived mass distribution is also shown in Fig. \ref{mod}:
" Despiten ⋯↑↕∐∖⋯∖↸↖↖↸∪↴⋝↑≺⊔∐∐∠↳∶⋅≱⋅∪⇂∐∠↖∏↑↕∐∐∩∩⊔∙ the oversimplified approximation for the rotation curve. the above analysis provides the mass distribution needed to match the velocity dispersion profile in the πο extreme rotation regimes (i.e. rigid rotation within σι ή, null rotation outside]."," in this case we obtain $M/L_\mathrm{B}=33^{+16}_{-14}M_{\odot}/L_{\odot}$ within $''$ Despite the oversimplified approximation for the rotation curve, the above analysis provides the mass distribution needed to match the velocity dispersion profile in the two extreme rotation regimes (i.e. rigid rotation within $\approx$ $''$, null rotation outside)."
 The link between the two regions calls for a more detailed Kinematics at the intermediate radi., The link between the two regions calls for a more detailed kinematics at the intermediate radii.
 The mass distribution from our analysis is in perfect agreement with estimates from Saelia ct al. (20003) , The mass distribution from our analysis is in perfect agreement with estimates from Saglia et al. \cite{sagl00}) )
who found 10AL. within 100., who found $\times$ $^{12} M_{\odot}$ within $''$ .
 The peculiar kinematics aud the temperature profile of hot gas from he X-rav observations niv suggestOO vat NGC. 1399 is nof a relaxed svsteni, The peculiar kinematics and the temperature profile of the hot gas from the X-ray observations may suggest that NGC 1399 is not a relaxed system.
; Miuniti et (1998)), Minniti et al. \cite{minn98}) )
 and [isler-Patis et al. (19993) , and Kissler-Patig et al. \cite{kisl99}) )
lise the -jetallicitv distribution and specific density of GCs to clau evidence for a recent interaction with the nearby companion NGC 1101., use the metallicity distribution and specific density of GCs to claim evidence for a recent interaction with the nearby companion NGC 1404.
 If such interaction occurred. the uost spectacular effect might be the strong heating of je intergalactic eas.," If such interaction occurred, the most spectacular effect might be the strong heating of the intergalactic gas."
 The hot eas In NGC 1399 has teiiperature which. OCC converted info a velocity aispersion. scclus systematically larger dw ~30 lan 1 iu that of the stellar population (see the long-dashed curve in Fie. tL).," The hot gas in NGC 1399 has a temperature which, once converted into a velocity dispersion, seems systematically larger by $\sim$ 30 km $^{-1}$ than that of the stellar population (see the long-dashed curve in Fig. \ref{dismod}) )."
 Moreover. the decline of the rotation curve of NGC 1399 is similar to those observed iu spiral svstenis and reproduced by single aud/or multiple galaxy eucouater (I&auffinanu 1999:: Salo Laurilkainen 2000)). We shal then explore a model where NGC 1399 is outof equilibrium. and the stars in the outer halo are re-arraneing theniselves after a fivby encounter with NGC 1ος," Moreover, the decline of the rotation curve of NGC 1399 is similar to those observed in spiral systems and reproduced by single and/or multiple galaxy encounter (Kauffmann \cite{kauf99}; Salo Laurikainen \cite{salau00}) We shall then explore a model where NGC 1399 is outof equilibrium, and the stars in the outer halo are re-arranging themselves after a flyby encounter with NGC 1404."
 NGC. 1399 and NOC Llol have a simal projected distance. b=9%. aud a large relative radia velocity. V.—522 kin (Viggo=1125#5. Craham et al. 1998..," NGC 1399 and NGC 1404 have a small projected distance, $b=9'$, and a large relative radial velocity, $V=522$ km $^{-1}$ $V_{1399}=1425\pm 5$, Graham et al. \cite{grah98},"
. ἔτι1917EH. Ὁοποίο et al. 1995)).," $V_{1404}=1947\pm 5$ , D'Onofrio et al. \cite{dono95}) )."
 The simplest approach is to use the general scheme of he (Binney Tremaine 1987)). where NGC 1399 is the perturbed svstem aud NGC 110 is the perturber.," The simplest approach is to use the general scheme of the (Binney Tremaine \cite{bintr}) ), where NGC 1399 is the perturbed system and NGC 1404 is the perturber."
" Iu. this approach. the cneounter does rot inodifv the votential of the perturbed system. auk ie kinetic energv in the iuner regions. while the outer reeions (2 110"") experienced 1) au energy injection. 2) ie disruption of the streaming motions. 1.0. of the angular ποιοι (Suecrinan et al. 2000))."," In this approach, the encounter does not modify the potential of the perturbed system, and the kinetic energy in the inner regions, while the outer regions $R \ge 140''$ ) experienced 1) an energy injection, 2) the disruption of the streaming motions, i.e. of the angular momentum (Sugerman et al. \cite{suka00}) ),"
 both redistributed m ie rancdon motions. aud 3) no mass loss (awe will discuss Us assunrptionu ator}.," both re-distributed in the random motions, and 3) no mass loss (we will discuss this assumption later)."
 Following this scheme. the post-counter kinetic enerev of the perturbed system. Eg. can be written as where {αμis the kinetic encres before the encounter. that is at equilibrium. aud AF is the variation in the kinetic enerev iuduced by the encounter.," Following this scheme, the post-encounter kinetic energy of the perturbed system, $E_\mathrm{fin}$, can be written as where $E_\mathrm{in}$ is the kinetic energy before the encounter, that is at equilibrium, and $\Delta E$ is the variation in the kinetic energy induced by the encounter."
 Iu Eq. (5)).," In Eq. \ref{efin}) ),"
" Eg, is associated to the observed random motious oulv. which are the result of the cnerev injection and the disruption of the streaming motions: it can be computed as £g,3/2M.EP 72..."," $E_\mathrm{fin}$ is associated to the observed random motions only, which are the result of the energy injection and the disruption of the streaming motions; it can be computed as $E_\mathrm{fin}=3/2 M \sigma_\mathrm{obs}^2$ ."
" Let us estimate. £y, aud AE. Ey, writes as where Vor aud 64 are derived from the kiuematical data of both the inteerated light aud PNe in the range of radii where the system is assumed to be still at equilibrium GR 110"").", Let us estimate $E_\mathrm{in}$ and $\Delta E$ $E_\mathrm{in}$ writes as where $V_\mathrm{rot}$ and $\sigma_\mathrm{eq}$ are derived from the kinematical data of both the integrated light and PNe in the range of radii where the system is assumed to be still at equilibrium $R < 140''$ ).
" Tn particular. for the PNe system we obtain Ta.=1165473 kin Py,=Bleτετ grady” kins 1 arcsec ! (BF)."," In particular, for the PNe system we obtain $V_\mathrm{sys}=1465\pm73$ km $^{-1}$ , $\Phi_\mathrm{Z1}=131^\circ \pm 7^\circ$, $gradV= 2.1\pm0.3$ km $^{-1}$ arcsec $^{-1}$ (BF)."
 Hee we cluphasize that the VL4 estimate. from the inner PNe subsample. is iu eood agrecinent with the stellar light data.," Here we emphasize that the $V_\mathrm{sys}$ estimate, from the inner PNe subsample, is in good agreement with the stellar light data."
 Theestimates in Table 1 show a positive residual in the outer regions. 1.6.," Theestimates in Table \ref{glqu} show a positive residual in the outer regions, i.e."
of nearby galaxies with masses >10!! aare descendants of quiescent z=2.5 galaxies in this model: we will return to this point below.,of nearby galaxies with masses $>10^{11}$ are descendants of quiescent $z=2.5$ galaxies in this model; we will return to this point below.
 Remarkably. we can rule out the equal-mass merger model as the main mode of growth based on reffig:numdens.. as it implies a mass growth of a factor of ~5.," Remarkably, we can rule out the equal-mass merger model as the main mode of growth based on \\ref{fig:numdens}, as it implies a mass growth of a factor of $\sim 5$."
 The number density of nearby galaxies with M>5«10! iis lower by more than an order of magnitude than the number density of compact galaxies with M>10!! aat >=2.5., The number density of nearby galaxies with $M>5\times 10^{11}$ is lower by more than an order of magnitude than the number density of compact galaxies with $M>10^{11}$ at $z=2.5$.
 In the equal-mass merger model. compact galaxies can obviously merge with each other. which will lower their number density.," In the equal-mass merger model, compact galaxies can obviously merge with each other, which will lower their number density."
 However. a factor of ~5 mass growth is not allowed even when compact galaxies are permitted to nerge with each other: the stellar mass density in galaxies with M>5«1011 aat>=0.1 is δες10° MMpe™. a factor of 6 lower than the mass density in compact galaxies with M>10!! aat z=2.5.," However, a factor of $\sim 5$ mass growth is not allowed even when compact galaxies are permitted to merge with each other: the stellar mass density in galaxies with $M>5\times 10^{11}$ at $z=0.1$ is $8.1^{+2.1}_{-1.6}\times 10^5$ $^{-3}$, a factor of 6 lower than the mass density in compact galaxies with $M>10^{11}$ at $z=2.5$."
 Also remarkably. the growth in the minor merger model is close to the cross-over point. where each compact galaxy has one descendant.," Also remarkably, the growth in the minor merger model is close to the cross-over point, where each compact galaxy has one descendant."
 A plausible explanation is that the central parts of many elliptical galaxies formed at z>2.5. after which they grew through minor. mostly dry mergers.," A plausible explanation is that the central parts of many elliptical galaxies formed at $z>2.5$, after which they grew through minor, mostly dry mergers."
 More generally. we can combine panelα of reffig:allprop with reffig:numdens to derive an empirical constraint on. the amount of size —growth for a given amount of mass growth.," More generally, we can combine panel of \\ref{fig:allprop}
 with \\ref{fig:numdens} to derive an empirical constraint on the amount of size growth for a given amount of mass growth."
 Parameterizing the relation between size growth and mass growth as we find that o.=2 to simultaneously satisfy the constraints from the evolution of the size — mass relation reffig:allpropa; van der Wel et 22008). and from the evolution of the mass function.," Parameterizing the relation between size growth and mass growth as we find that $\alpha \gtrsim 2$ to simultaneously satisfy the constraints from the evolution of the size – mass relation \\ref{fig:allprop}{ ; van der Wel et 2008), and from the evolution of the mass function."
 This limit for à is similar to naive expectations from minor mergers. which is. why we obtain a good correspondence between progenitors and descendants for this class of models.," This limit for $\alpha$ is similar to naive expectations from minor mergers, which is why we obtain a good correspondence between progenitors and descendants for this class of models."
" The equal-mass merger model has a~| (or even <I; see 2006): for the expansion model M,,/M,=1 (or even < I1) and refeq:sizemass is not well defined."," The equal-mass merger model has $\alpha \sim 1$ (or even $<1$; see 2006); for the expansion model $M_{1,f}/M_{1} = 1$ (or even $<1$ ) and \\ref{eq:sizemass} is not well defined."
 We expect that each of these toy models is responsible at some level for the growth and evolution of galaxies from zo2.5 until today., We expect that each of these toy models is responsible at some level for the growth and evolution of galaxies from $z \sim 2.5$ until today.
 Observational evidence of merging events. both equal-mass and minor. exists at intermediate redshifts and can definitely produce growth in galaxy mass and size.," Observational evidence of merging events, both equal-mass and minor, exists at intermediate redshifts and can definitely produce growth in galaxy mass and size."
 Mass loss from the central regions of galaxies should also occur and would therefore cause increases in galaxy sizes., Mass loss from the central regions of galaxies should also occur and would therefore cause increases in galaxy sizes.
 Given this complexity. we hope to identify which of our simple models best describes the mechanism responsible for the majority of the growth of the compact galaxies at high redshifts into descendant galaxies in the nearby universe.," Given this complexity, we hope to identify which of our simple models best describes the mechanism responsible for the majority of the growth of the compact galaxies at high redshifts into descendant galaxies in the nearby universe."
 Ins 55.1 we found that the equal-mass merger model is inconsistent with the number density of massive galaxies today., In 5.1 we found that the equal-mass merger model is inconsistent with the number density of massive galaxies today.
 We are therefore left with two feasible models. growth via “in-situ” expansion or via minor mergers.," We are therefore left with two feasible models, growth via “in-situ” expansion or via minor mergers."
 Both of these modes of galaxy growth have the effect of puffing up the galaxies without extreme mass growth., Both of these modes of galaxy growth have the effect of puffing up the galaxies without extreme mass growth.
 Number densities of the implied descendants of galaxies that have grown via either mode correspond to sufficiently common galaxies in the local universe., Number densities of the implied descendants of galaxies that have grown via either mode correspond to sufficiently common galaxies in the local universe.
 Although number density arguments do not immediately discredit the expansion model of galaxy evolution. they dolead to uncomfortable questions.," Although number density arguments do not immediately discredit the expansion model of galaxy evolution, they dolead to uncomfortable questions."
 The implication of no mass growth is that only a very small number of nearby galaxies with mass >10! wwas already formed at z=2.5: approximately are considered. and ~14 M>1011 aare considered.," The implication of no mass growth is that only a very small number of nearby galaxies with mass $>10^{11}$ was already formed at $z=2.5$: approximately are considered, and $\sim 14$ $M>10^{11}$ are considered."
 This. raises the question where. the progenitors of the remaining ~90 galaxies are at z=2.5., This raises the question where the progenitors of the remaining $\sim 90$ galaxies are at $z=2.5$.
 In a hierarchical growth scenario. one expects that the most massive galaxies today have always been the most massive galaxies.," In a hierarchical growth scenario, one expects that the most massive galaxies today have always been the most massive galaxies."
 Instead. the expansion model implies that the most massive galaxies at z~2.5 evolve into a small fraction of average-mass elliptical galaxies today.," Instead, the expansion model implies that the most massive galaxies at $z \sim 2.5$ evolve into a small fraction of average-mass elliptical galaxies today."
 Furthermore. the most massive galaxies in the local universe. with masses M>3«I0M. must then have formed rapidly in the later universe. implying an extremely active merging history of smaller objects.," Furthermore, the most massive galaxies in the local universe, with masses $M \gtrsim 3\times10^{11}M_{\odot}$ must then have formed rapidly in the later universe, implying an extremely active merging history of smaller objects."
 One might conclude that they formed through star formation at lower redshift. but this would be inconsistent with the stellar ages of massive ellipticals (e.g.. 2005; 2008).," One might conclude that they formed through star formation at lower redshift, but this would be inconsistent with the stellar ages of massive ellipticals (e.g., 2005; 2008)."
 There are other potential problems with the physical model proposed by (2008)., There are other potential problems with the physical model proposed by (2008).
 The growth relies on strong heating of the inner regions of the galaxy. such as that produced by a central active galactic nucleus (AGN).," The growth relies on strong heating of the inner regions of the galaxy, such as that produced by a central active galactic nucleus (AGN)."
 However. the high redshift galaxies in our sample are already shown to be quiescent. with old stellar populations.," However, the high redshift galaxies in our sample are already shown to be quiescent, with old stellar populations."
 If there was an active central engine at one point in the galaxies? histories. it would have already blown out gas and led to expansion of the galaxy.," If there was an active central engine at one point in the galaxies' histories, it would have already blown out gas and led to expansion of the galaxy."
 While growth through mass loss may have played a role m the evolution of such galaxies. it is unlikely to do so again between z=2.5 and z=0. except possibly through stellar winds and supernovae.," While growth through mass loss may have played a role in the evolution of such galaxies, it is unlikely to do so again between $z=2.5$ and $z=0$, except possibly through stellar winds and supernovae."
 Based on simulations of open clusters. (2008) argue that there could be a long delay between the expulsion of gas and the response of the stellar distribution to the new potential. but it is not clear whether these simulations can easily be appliec to massive galaxies.," Based on simulations of open clusters, (2008) argue that there could be a long delay between the expulsion of gas and the response of the stellar distribution to the new potential, but it is not clear whether these simulations can easily be applied to massive galaxies."
 Finally. the expansion model requires significant fine-tuning of the amount of mass that is removed from the galaxies: removing a small fraction of the mass does not have an appreciable effect. and removing too much would destroy the galaxies.," Finally, the expansion model requires significant fine-tuning of the amount of mass that is removed from the galaxies: removing a small fraction of the mass does not have an appreciable effect, and removing too much would destroy the galaxies."
" Minor mergers (or rather. ""un-equal mass mergers"") are expected in galaxy formation models. and are predicted. to dominate the mass growth of massive galaxies at late times (e.g.. 2007; 2008)."," Minor mergers (or rather, ""un-equal mass mergers"") are expected in galaxy formation models, and are predicted to dominate the mass growth of massive galaxies at late times (e.g., 2007; 2008)."
 Simulations have shown that the central regions of a galaxy can be minimally affected by dry mergers but that an envelope of newly accreted material is formed that grows with time 2007)., Simulations have shown that the central regions of a galaxy can be minimally affected by dry mergers but that an envelope of newly accreted material is formed that grows with time 2007).
 They have also been observed (e.g.. Schweizer 1992). (," They have also been observed (e.g., 1992). ("
2005) infers that visible tidal features,2005) infers that visible tidal features
As shown in Figure 15.. the dependence of the halo spin-spin correlations on the velocity magnitude turns out not to be so strong.,"As shown in Figure \ref{fig:v}, the dependence of the halo spin-spin correlations on the velocity magnitude turns out not to be so strong."
 The significant nonlinear effect on the halo-halo correlation is found only in the first bin of low-e halos (top-left. panel). For this bin. the linear model fails in fitting the numerical data while the nonlinear model gives a better fit. predicting the large-scale correlations.," The significant nonlinear effect on the halo-halo correlation is found only in the first bin of $v$ halos (top-left panel), For this bin, the linear model fails in fitting the numerical data while the nonlinear model gives a better fit, predicting the large-scale correlations."
 As shown in (he top-left panel of Fig.16.. the value of ey for the ease of lowest-e halos deviates [rom zero at 95% confidence level.," As shown in the top-left panel of \ref{fig:cv}, the value of $\varepsilon_{\rm nl}$ for the case of $v$ halos deviates from zero at $95\%$ confidence level."
 We summarize our results in the following:, We summarize our results in the following:
"low column densities, whereas recombination following photoionization dominates at high column densities.","low column densities, whereas recombination following photoionization dominates at high column densities."
" Following their prescription, the RRC intensity will increase compared to He-like triplet line when column density increases, which would imply a value of Ny larger for NW than for SE."," Following their prescription, the RRC intensity will increase compared to He-like triplet line when column density increases, which would imply a value of $\mathrm{N_H}$ larger for NW than for SE."
" Alternatively, the RRC line could be produced by hot collisionally ionized plasma, although the line widths reported by Guainazzi&Bianchi(2007) do not support this scenario."," Alternatively, the RRC line could be produced by hot collisionally ionized plasma, although the line widths reported by \citet{Guainazzi07} do not support this scenario."
 It is very unlikely that a broad feature contributes only in a few percentage of the total flux of source., It is very unlikely that a broad feature contributes only in a few percentage of the total flux of source.
" Moreover, the radio maps of 5573 are not sensitive enough to show great detail concerning radio emission although two faint blobs are observed in the NW cone (Falckeetal.1998)."," Moreover, the radio maps of 573 are not sensitive enough to show great detail concerning radio emission although two faint blobs are observed in the NW cone \citep{Falcke98}."
. The low signal-to-noise ratio of the spectra from the cones prevents us from a more detailed study of the line transitions in the extended emission., The low signal-to-noise ratio of the spectra from the cones prevents us from a more detailed study of the line transitions in the extended emission.
" Using version c08.00 of the Cloudy package (lastde-scribedbyFerlandetal. 1998), we attempted to reproduce the observed spectra of the nuclear region and NE and SW cones seen in data."," Using version c08.00 of the Cloudy package \citep[last described by ][]{Ferland98}, we attempted to reproduce the observed spectra of the nuclear region and NE and SW cones seen in data."
" In these Cloudy simulations we assumed the source of ionization to emit as a typical AGN continuum (we used the model AGN available in Cloudy) defined by a “big bump” of temperature T=10°K, an X-ray to UV ratio Qox=—1.15, plus a X-ray power-law of spectral index of a=—1.0."," In these Cloudy simulations we assumed the source of ionization to emit as a typical AGN continuum (we used the model AGN available in Cloudy) defined by a “big bump” of temperature $\mathrm{T} = 10^6 \rm{K}$, an X-ray to UV ratio $\rm{\alpha_{OX}=-1.15}$, plus a X-ray power-law of spectral index of $\rm{\alpha = -1.0}$."
" A plane-parallel geometry is assumed, with the slab depth controlled by the hydrogen column density parameter "," A plane–parallel geometry is assumed, with the slab depth controlled by the hydrogen column density parameter $\rm{N_H}$ )."
Two grids of (Ny).parameters were constructed to simulate the expected BLR and NLR conditions., Two grids of parameters were constructed to simulate the expected BLR and NLR conditions.
" For each of them, a grid of models was simulated by varying the ionization parameter the density of the material (ng), and the hydrogen column(U), density (Ng)."," For each of them, a grid of models was simulated by varying the ionization parameter (U), the density of the material $\mathrm{n_H}$ ), and the hydrogen column density $\rm{N_H}$ )."
" U ranges from 1073 to 10°, Ng ranges from 1020cm? to 1074cm? and ny from 109?cm-? to 1011cm-? for BLR conditions, and from 10?cm? to 104cm-? for NLR conditions."," U ranges from $\rm{10^{-3}}$ to $\rm{10^{3}}$, $\rm{N_H}$ ranges from $\rm{10^{20}\, cm^{-2}}$ to $\rm{10^{24}\, cm^{-2}}$ and $\mathrm{n_H}$ from $\rm{10^{9}\, cm^{-3}}$ to $\rm{10^{11}\, cm^{-3}}$ for BLR conditions, and from $\rm{10^{2}\, cm^{-3}}$ to $\rm{10^{4}\, cm^{-3}}$ for NLR conditions."
 In both BLR or NLR models the outputs of each Cloudy simulation include a transmitted and reflected emission line spectra., In both BLR or NLR models the outputs of each Cloudy simulation include a transmitted and a reflected emission line spectra.
" Under the Cloudy terminologya ""reflected"" spectrum refers to the emission escaping into the 27 sr subtended by the illuminated face towards the ionizing source and by “transmitted” the emission", Under the Cloudy terminology “reflected” spectrum refers to the emission escaping into the $2\pi$ sr subtended by the illuminated face towards the ionizing source and by “transmitted” the emission
hieher Lyman series lines: while (heir values are smaller. (hev are also effectively quenched through decays to levels a>1 and then eventually through Lyà as soon as scattering depths become significant.,"higher Lyman series lines; while their f-values are smaller, they are also effectively quenched through decays to levels $n> 1$ and then eventually through $\alpha$ as soon as scattering depths become significant."
 O VIII 16.01 LLvw2. for example. is lost to resonant scattering in decavs through the 5»=3-2 Balmer line at. 102.43. A. and then through Lya.," O VIII 16.01 $\beta$, for example, is lost to resonant scattering in decays through the $n=3$ -2 Balmer line at 102.43 , and then through $\alpha$."
 Unfortunately. the I9M. absorbing column to iis (oo large for the Balmer lines to be visible. though a future detection of O VIII Baa in other similar objects to wwould provide a useful test of this model.," Unfortunately, the ISM absorbing column to is too large for the Balmer lines to be visible, though a future detection of O VIII $\alpha$ in other similar objects to would provide a useful test of this model."
 Ifthe ~1 keV emission found by O'Dwyeretal.(2003). is indeed due (o a wind or outflow. then an oplically-thin plasma model with a temperature of 2xIt)° IX accounting for the observed ROSAT counts at this energv has a total luminosity of ~5x107 ere 4. or 10.1 times the stellar bolometric Iuminositv.," If the $\sim 1$ keV emission found by \citet{O'Dwyer.etal:03} is indeed due to a wind or outflow, then an optically-thin plasma model with a temperature of $2\times 10^6$ K accounting for the observed ROSAT counts at this energy has a total luminosity of $\sim 5\times
10^{31}$ erg $^{-1}$, or $10^{-4}$ times the stellar bolometric luminosity."
 The 0.1-2.5 keV X-ray to bolometric luminosity ralio is ~2xLO? a somewhat higher value than observed for OD stars. whose X-rays are believed (o originate in shocked winds ancl lor which the X-ray to bolometrie luminosity ratio Ly/Lig~LO °-10? (e.g.Derghoeferetal.1997).," The 0.1-2.5 keV X-ray to bolometric luminosity ratio is $\sim 2\times 10^{-5}$ —a somewhat higher value than observed for OB stars, whose X-rays are believed to originate in shocked winds and for which the X-ray to bolometric luminosity ratio $L_X/L_{bol}\sim 10^{-6}$ $10^{-8}$ \citep[e.g.][]{Berghoefer.etal:97}."
. We have shown that a coronal plasma is unable to match the LETG--I1IRC-S 20-80 sspectrum of aand (hat coronal models are energetically implausible as an origin for this observed solt X-ray lux., We have shown that a coronal plasma is unable to match the LETG+HRC-S 20-80 spectrum of and that coronal models are energetically implausible as an origin for this observed soft X-ray flux.
 This part of the soft X-ray spectrum of ccan instead be explained bv photospheric models containing (race amounts of heavier elements., This part of the soft X-ray spectrum of can instead be explained by photospheric models containing trace amounts of heavier elements.
 Photospheric models do not. however. explain the soft X-ray emission al shorter wavelengths (~12A: 1 keV) revealed recently by ODwyeretal.(2003). and discussed in more detail bv Chuetal.(2004)..," Photospheric models do not, however, explain the soft X-ray emission at shorter wavelengths $\sim 12$; 1 keV) revealed recently by \citet{O'Dwyer.etal:03} and discussed in more detail by \citet{Chu.etal:04b}."
 The origin of this emission remains mvsterious. though an outflow or wind with a temperature of ~2x105 IN is able to explain both the X-rays and the presence of high » O VIII UV-optical emission lines but an absence of significant QO VIII Lvo flux in the spectrum.," The origin of this emission remains mysterious, though an outflow or wind with a temperature of $\sim 2\times 10^6$ K is able to explain both the X-rays and the presence of high $n$ O VIII UV-optical emission lines but an absence of significant O VIII $\alpha$ flux in the spectrum."
 In this scenario. the Lvo photons are trapped by resonance scattering and destroved by photoelectric absorption.," In this scenario, the $\alpha$ photons are trapped by resonance scattering and destroyed by photoelectric absorption."
 If an outflow is responsible [or the 1 keV X-rays. the total luminosity of this plasma amounts to ~10.Πω. which is a [actor of 100 or so largerthan for winds of OD stars.," If an outflow is responsible for the 1 keV X-rays, the total luminosity of this plasma amounts to $\sim 10^{-4}L_{bol}$, which is a factor of 100 or so largerthan for winds of OB stars."
 We thank the NASA AISRP for providing financial assistance for the development of, We thank the NASA AISRP for providing financial assistance for the development of
sttars aud dust.,tars and dust.
 It is known to host a super-massive black hole., It is known to host a super-massive black hole.
The formation and evolution of galaxies rank among the big questions in astronomy and still await a complete explanation.,The formation and evolution of galaxies rank among the big questions in astronomy and still await a complete explanation.
 According to current theory. the formation of dark matter haloes by gravitational instabilities is an essential first step in the formation of galaxies (?)..," According to current theory, the formation of dark matter haloes by gravitational instabilities is an essential first step in the formation of galaxies \citep{eggen62}."
 Stars are believed to form when gas cools at the centres of these haloes (2).. and make up the part of the galaxy that we can observe.," Stars are believed to form when gas cools at the centres of these haloes \citep{white78}, and make up the part of the galaxy that we can observe."
 A number of physical processes strongly affect this baryonic mass assembly. like the hydrodynamics of the gas. feedback processes by supernovae and stellar winds. possibly magnetic fields. the role of AGN. or the effects of galaxy-galaxy interactions and mergers.," A number of physical processes strongly affect this baryonic mass assembly, like the hydrodynamics of the gas, feedback processes by supernovae and stellar winds, possibly magnetic fields, the role of AGN, or the effects of galaxy-galaxy interactions and mergers."
 For these reasons the modelling of galaxy formation depends on many free parameters and is not very well constrained., For these reasons the modelling of galaxy formation depends on many free parameters and is not very well constrained.
 Over the past decade the high redshift universe has become accessible observationally through the use of photometric techniques., Over the past decade the high redshift universe has become accessible observationally through the use of photometric techniques.
 By detection of the spectral discontinuity due to the redshifted Lyman-break 1n à multi-wavelength filter set. large and clean samples of high redshift star-forming galaxies can be selected (???).. with low amounts of contamination.," By detection of the spectral discontinuity due to the redshifted Lyman-break in a multi-wavelength filter set, large and clean samples of high redshift star-forming galaxies can be selected \citep{steidel96, steidel99, 2002ARA&A..40..579G}, with low amounts of contamination."
 These samples can be used to study several properties of the early universe., These samples can be used to study several properties of the early universe.
 For example. by measuring the correlation function of these Lyman-break Galaxies (LBGs) anc comparing it with the correlation of dark matter. the characteristic mass of their haloes can be determined (e.g.?????).. H," For example, by measuring the correlation function of these Lyman-break Galaxies (LBGs) and comparing it with the correlation of dark matter, the characteristic mass of their haloes can be determined \citep[e.g.][]{giadick01,
 ouchi04b, 2005A&A....Hildebrandt, 2007A&A...462..865H,
 hildebrandt09a}."
ubble Space Telescope observations of LBGs are used to study how certain morphological types evolve with time (2).., Hubble Space Telescope observations of LBGs are used to study how certain morphological types evolve with time \citep{pirzkal05}.
 À study of the evolution of the UV Luminosity Function (LF) (????).. which is the measure of the number of galaxies per unit volume as a function of luminosity. is another fundamental probe in galaxy formation and evolution. because of its close relation to star formation processes.," A study of the evolution of the UV Luminosity Function (LF) \citep{steidel96, steidel99, st2,
 bouwens07}, which is the measure of the number of galaxies per unit volume as a function of luminosity, is another fundamental probe in galaxy formation and evolution, because of its close relation to star formation processes."
 Several techniques can be used to estimate the star formation rate (SFR) in galaxies. mostly based on the existence of massive. young stars. indicative of recent star formation.," Several techniques can be used to estimate the star formation rate (SFR) in galaxies, mostly based on the existence of massive, young stars, indicative of recent star formation."
 A commonly used way to probe the existence of massive stars is the Ha luminosity (2).. because Ha photons originate from the gas tonized by the radiation of massive stars.," A commonly used way to probe the existence of massive stars is the $\alpha$ luminosity \citep{kennicutt83}, because $\alpha$ photons originate from the gas ionized by the radiation of massive stars."
 A second star formation indicator is the infrared (IR) luminosity originating from dust continuum emission (??)..," A second star formation indicator is the infrared (IR) luminosity originating from dust continuum emission \citep{kennicutt98,hirashita03}."
 The absorption cross section of dust is strongly peaked in the UV. and therefore the existence of UV emitting. 1e. massive. stars is probed indirectly.," The absorption cross section of dust is strongly peaked in the UV, and therefore the existence of UV emitting, i.e. massive, stars is probed indirectly."
 Thirdly. the UV continuum is used as à star formation probe. with the main advantages being that the UV-emission of the young stellar population ts directly observed. unlike in H-w and IR studies.," Thirdly, the UV continuum is used as a star formation probe, with the main advantages being that the UV-emission of the young stellar population is $directly$ observed, unlike in $\alpha$ and IR studies."
 Furthermore. this technique can be applied from the ground to star-forming galaxies over a wide range of redshifts.," Furthermore, this technique can be applied from the ground to star-forming galaxies over a wide range of redshifts."
 Hence. it is still the most powerful probe of cosmological evolution of the SFR (?)..," Hence, it is still the most powerful probe of cosmological evolution of the SFR \citep{madau96}."
 However. information about the initial mass function (IMF). and particularly the extinction by dust are required to estimate the total star formation rate.," However, information about the initial mass function (IMF), and particularly the extinction by dust are required to estimate the total star formation rate."
 In this paper we estimate the UV LF at redshifts :=3- from the Canada-France-Hawaii-Telescope Legacy Survey (CFHTLS) Deep. a survey covering 4+ square degrees in four independent fields spread across the sky.," In this paper we estimate the UV LF at redshifts $z$ =3-5 from the Canada-France-Hawaii-Telescope Legacy Survey (CFHTLS) Deep, a survey covering 4 square degrees in four independent fields spread across the sky."
 Since our samples. at different redshifts. are all extracted from. the same dataset. this gives an excellent opportunity to study a possible evolution of the LF in this redshift interval.," Since our samples, at different redshifts, are all extracted from the same dataset, this gives an excellent opportunity to study a possible evolution of the LF in this redshift interval."
 Several systematic effects that need to be considered when comparing results at different redshifts from different surveys (e.g. source extraction. masking. PSF-modelling. ete.)," Several systematic effects that need to be considered when comparing results at different redshifts from different surveys (e.g. source extraction, masking, PSF-modelling, etc.)"
 can be avoided when the different redshift samples are extracted from the same survey., can be avoided when the different redshift samples are extracted from the same survey.
 Due to the large volumes we probe with our 4 square degree survey. the influence of cosmic variance on the shape of the estimated LF ts negligible (?).. as we expect cosnic variance to affect our number counts only at the level (?)..," Due to the large volumes we probe with our 4 square degree survey, the influence of cosmic variance on the shape of the estimated LF is negligible \citep{trenti08}, as we expect cosmic variance to affect our number counts only at the level \citep{somerville04}."
 We can study the bright end of the LF with unprecedented accuracy. as these objects are rare and we are able to measure down to very low densities.," We can study the bright end of the LF with unprecedented accuracy, as these objects are rare and we are able to measure down to very low densities."
 This allows us to study the effect, This allows us to study the effect
The wav in which cooling acts in reconciling the observed and the sipiulated. AZ 2 relations implies that temperature xofiles should steepen in central cluster regions.,The way in which cooling acts in reconciling the observed and the simulated $M$ $T$ relations implies that temperature profiles should steepen in central cluster regions.
 From an observational viewpoint. the possibility of realizing spatially resolved. spectroscopy. has. recently. opened. the. possibility o determine temperature profiles for fairly large. samples of clusters.," From an observational viewpoint, the possibility of realizing spatially resolved spectroscopy has recently opened the possibility to determine temperature profiles for fairly large samples of clusters."
 Interestingly. observations based on the ASCA (c.g.. Markeviteh et al.," Interestingly, observations based on the ASCA (e.g., Markevitch et al."
" 1998) and BeppoSAX (De Cirandi Alolendi 2002) satellites showdeclining temperature oofiles in the outer regions. at. cluster-centric distances z002 0.3454, (οἱ."," 1998) and Beppo–SAX (De Grandi Molendi 2002) satellites show temperature profiles in the outer regions, at cluster-centric distances $\magcir
0.2$ $R_{\rm vir}$ (cf."
 also να Breeman 2000)., also Irwin Bregman 2000).
 This »haviour is generally reproduced. by simulations that do not include cooling (e.g... BOW).," This behaviour is generally reproduced by simulations that do not include cooling (e.g., BGW)."
 Furthermore. both BeppoSAX (De Crandi AMolendi 2002). Chandra (c.g.. Ettori ct al.," Furthermore, both Beppo--SAX (De Grandi Molendi 2002), Chandra (e.g., Ettori et al."
 2002: Allen et al., 2002; Allen et al.
 2001: Johnstone et al., 2001; Johnstone et al.
 2002) and NMM (6.8... Γαία et al.," 2002) and XMM (e.g., Tamura et al."
 2001) data for fairly hot svstems. Zxz4 keV. show temperature profiles. declining towards the very central regions of clusters. thus indicating the presence of cooling cores.," 2001) data for fairly hot systems, $T_X\magcir 4$ keV, show temperature profiles declining towards the very central regions of clusters, thus indicating the presence of cooling cores."
" This behaviour is grossly at variance with respect to that found for the ""Virgo"" runs. as reported in Figure 13: the only case where a somewhat declining profile is produced is the one with gravitational heating. while cooling always gives rise to steeply increasing profiles with no evidence for any decline. independent of the presence of extra heating."," This behaviour is grossly at variance with respect to that found for the “Virgo” runs, as reported in Figure \ref{fi:tprof}: the only case where a somewhat declining profile is produced is the one with gravitational heating, while cooling always gives rise to steeply increasing profiles with no evidence for any decline, independent of the presence of extra heating."
 Ao more comprehensive comparison with the observations would require simulations to be realized for a set of clusters with higher temperature., A more comprehensive comparison with the observations would require simulations to be realized for a set of clusters with higher temperature.
 On the other hand. our simulated Vireo cluster has been chosen. as a fairly relaxed svstem.," On the other hand, our simulated Virgo cluster has been chosen as a fairly relaxed system."
 Therefore. as long as observations sugeest. profiles to be universal for such systems (Allen et al.," Therefore, as long as observations suggest profiles to be universal for such systems (Allen et al."
 2001). such a discrepancy should be taken quite seriously.," 2001), such a discrepancy should be taken quite seriously."
 A stecpening of the temperature profiles caused by cooling has been already noticed by Lewis et al. (, A steepening of the temperature profiles caused by cooling has been already noticed by Lewis et al. (
2000). Muanwong οἱ al. (,"2000), Muanwong et al. ("
2002) ancl Valdarnini (2002).,2002) and Valdarnini (2002).
 Phe temperature profiles in Fig., The temperature profiles in Fig.
 13. generalise this result also in the presence of a varietv of extra.heating mechanisms., \ref{fi:tprof} generalise this result also in the presence of a variety of extra–heating mechanisms.
 We also note that the steep. temperature profiles predicted. by simulations are also at variance with respect to those predicted. by the semianalytical model for 1C'M heating/cooling by Voit et al. (, We also note that the steep temperature profiles predicted by simulations are also at variance with respect to those predicted by the semi–analytical model for ICM heating/cooling by Voit et al. (
2002).,2002).
 A detailed comparison between the predictions of semianalytical models. and simulations is bevond the scope of this paper., A detailed comparison between the predictions of semi–analytical models and simulations is beyond the scope of this paper.
 Llowever. a full unclerstancling of the physical processes taking place in the LOCAL will only be obtained if the reasons for such cillerences can be understood and eventually sorted out.," However, a full understanding of the physical processes taking place in the ICM will only be obtained if the reasons for such differences can be understood and eventually sorted out."
 If the discrepaney between observed. ancl simulated emperature profiles will be confirmed. it may indicate hat we are missingὃν some basic physical mechanism: which allects the thermal properties. of the eas in the high density cooling regions.," If the discrepancy between observed and simulated temperature profiles will be confirmed, it may indicate that we are missing some basic physical mechanism which affects the thermal properties of the gas in the high density cooling regions."
 For instance. thermal conduction iw been advocated by some authors as a mechanisms hat. in combination with central heating. may regulate gas cooling (e.g. Voigt et al.," For instance, thermal conduction has been advocated by some authors as a mechanisms that, in combination with central heating, may regulate gas cooling (e.g. Voigt et al."
 2002) while providing acceptable emperature profiles for a suitable choice of the conductivity xwameter (e... Zalumska Naravan 2002: Ruszkowski Degelman 2002).," 2002) while providing acceptable temperature profiles for a suitable choice of the conductivity parameter (e.g., Zakamska Narayan 2002; Ruszkowski Begelman 2002)."
 In this scenario. one expects the outer lavers to heat gas in le innermost regions. so as to increase its cooling time. dlowing it to stay in the diffuse phase at a relatively low emperature.," In this scenario, one expects the outer layers to heat gas in the innermost regions, so as to increase its cooling time, allowing it to stay in the diffuse phase at a relatively low temperature."
 However. the detection of sharp features. in 10 teniperature map of several clusters. as observed by the Chandra satellite. led some authors to suggest that thermal conduction is suppressed in the ICM (e.g.. ο Fabian 2000).," However, the detection of sharp features in the temperature map of several clusters, as observed by the Chandra satellite, led some authors to suggest that thermal conduction is suppressed in the ICM (e.g., Ettori Fabian 2000)."
 Magnetic fields are naturally expected το produce such a suppression (e.g. Sarazin LOSS)," Magnetic fields are naturally expected to produce such a suppression (e.g., Sarazin 1988)."
 Still. it ids not ‘lear whether this mechanism can act in an ubiquitous way inside clusters or whether the turbulence associated. with 1 presence of magnetic fields is actually able to maintain a relatively ellicient thermal conduction (c.g... Naravan AMecvecey 2001).," Still, it is not clear whether this mechanism can act in an ubiquitous way inside clusters or whether the turbulence associated with the presence of magnetic fields is actually able to maintain a relatively efficient thermal conduction (e.g., Narayan Medvedev 2001)."
 We presented. results from high resolution “Pree|SPLL simulations of a moderately poor “Virgo”like cluster aud of three groupsized halos. including the elfects of radiative cooling and nongravitational gas heating.," We presented results from high resolution Tree+SPH simulations of a moderately poor “Virgo”–like cluster and of three group–sized halos, including the effects of radiative cooling and non–gravitational gas heating."
 The numerical accuracy reached in these simulations was aimed at following in detail the pattern of gas cooling and its effect on the (X properties of groups and clusters of galaxies., The numerical accuracy reached in these simulations was aimed at following in detail the pattern of gas cooling and its effect on the $X$ --ray properties of groups and clusters of galaxies.
 The main results that we obtained can be summarised as follows., The main results that we obtained can be summarised as follows.
The faintest target in our sample. 770. has been reported originally as a cὉALjup IPAIO with tentative spectral (wpe T5.5 (ZapateroOsorioetal.2002b).,"The faintest target in our sample, 70, has been reported originally as a $\sim 3\,M_{\mathrm{Jup}}$ IPMO with tentative spectral type T5.5 \citep{2002ApJ...578..536Z} ."
. If confirmed. il would be the lowest mass Iree-[loating object found to date.," If confirmed, it would be the lowest mass free-floating object found to date."
 Its mass would put it close to or even bevond (he predicted opacity limit for fragmentation (seeBonnellrelerences (herein).. ancl (hus poses a challenge for star formation theory.," Its mass would put it close to or even beyond the predicted opacity limit for fragmentation \citep[see][and references therein]{2007prpl.conf..149B}, and thus poses a challenge for star formation theory."
 ILowever. Durgasser have questioned! the cluster membership (and thus the extremely low mass) of 770. and argue that ils neza-inflrared spectrum is perlectly consistent wilh a foreground cwarf with spectral type ~TG-7.," However, \citet{2004ApJ...604..827B} have questioned the cluster membership (and thus the extremely low mass) of 70, and argue that its near-infrared spectrum is perfectly consistent with a foreground dwarf with spectral type $\sim$ T6-7."
" In response. Martín(2004) reinterated the claim lor cluster menbership and vouth mainly based on the (//—K) colour of 1770. which is unusually hieh for a T ναί, and is interpreted as evidence for low surface gravity."," In response, \citet{2004astro.ph.10678M} reinterated the claim for cluster membership and youth mainly based on the $(H-K)$ colour of 70, which is unusually high for a T dwarf, and is interpreted as evidence for low surface gravity."
 To date. (he nature ol this object remains unclear.," To date, the nature of this object remains unclear."
 Our deep IRAC images now allow a re-investigation of the Issue., Our deep IRAC images now allow a re-investigation of the issue.
 770 is clearly detected in IRAC channels 1: and 2., 70 is clearly detected in IRAC channels 1 and 2.
 In addition. it is detected in IRACS. with a 1o significance (peak countrate over background noise).," In addition, it is detected in IRAC3, with a $\sim 4\sigma$ significance (peak countrate over background noise)."
 The IRACS fhix uncertainty has been derived based on the very. [nct that the object is just detected. 1 it were 225% fainter than (he estimated. mmae. we would not be able to see it.," The IRAC3 flux uncertainty has been derived based on the very fact that the object is just detected – if it were $\gtrsim 25$ fainter than the estimated mag, we would not be able to see it."
 Ii 4. we plot its IRAC colours vs. spectral type in comparison with measurements for field T dwarls. taken from Pattenοἱal.(2006)..," In \ref{f2} we plot its IRAC colours vs. spectral type in comparison with measurements for field T dwarfs, taken from \citet{2006ApJ...651..502P}."
 770 is tentativelv. plotted spectral tvpe Το (average of the (wo available literature estimates)., 70 is tentatively plotted spectral type T6 (average of the two available literature estimates).
 As can be seen in this ligure. the field T chwarfs form a clear sequence. whereas 770 stands out: In both IRAC colours. it appears to have some excess.," As can be seen in this figure, the field T dwarfs form a clear sequence, whereas 70 stands out: In both IRAC colours, it appears to have some excess."
 Compared with the mean ivend [or the field T clwarls. the significance of this excess is e26 in both IRAC? and IRAC3.," Compared with the mean trend for the field T dwarfs, the significance of this excess is $\sim 2\sigma$ in both IRAC2 and IRAC3."
 This excess cannot be accounted lor by uncertainties in the spectral type. since the 3.6—5.8pum colour saltrates in the late T dsvarf regime and reaches maximum values of ~1.2 compared with 1.6 for 710.," This excess cannot be accounted for by uncertainties in the spectral type, since the $3.6-5.8\,\mu m$ colour saturates in the late T dwarf regime and reaches maximum values of $\sim 1.2$ – compared with 1.6 for 70."
 It should also be pointed out that 770 is brighter than the more massive L5 dwarf 667 in IRAC2? and 3. again indicating an unusual SED for this object.," It should also be pointed out that 70 is brighter than the more massive L5 dwarf 67 in IRAC2 and 3, again indicating an unusual SED for this object."
 There are two possible origins5 for a mid-infrared colour excess in 770: a) As reported bv Leegettetal.(2007).. gravity. alfects the near/mid-nfrared colours of mid/late T. clwarls in the sense that it can produce a significant5 excess al 2-650. for low-eravily5 objects.," There are two possible origins for a mid-infrared colour excess in 70: a) As reported by \citet{2007ApJ...655.1079L}, gravity affects the near/mid-infrared colours of mid/late T dwarfs in the sense that it can produce a significant excess at $\mu m$ for low-gravity objects."
 b) sinilulv to the L tvpe IPMOs in og OOn. SOTTO might harbour a dusty disk. which produces the IRAC excess.," b) Similarly to the L type IPMOs in $\sigma$ Ori, 70 might harbour a dusty disk, which produces the IRAC excess."
 Both possibilities provide additional evidence for vouth. and thus the mid-inlrared excess bolsters the claim that it is the lowest mass free-Iloating object," Both possibilities provide additional evidence for youth, and thus the mid-infrared excess bolsters the claim that it is the lowest mass free-floating object"
Since we lave no backeround exposure. we estimated the backeroune contribution bv connecting the counts from the Las Campanas Redshift Survey (LCRS. Lin ct al.,"Since we have no background exposure, we estimated the background contribution by connecting the counts from the Las Campanas Redshift Survey (LCRS, Lin et al."
 1996) aud roni the ESO-Sculptor Survey (ESS. Áruouts al.," 1996) and from the ESO-Sculptor Survey (ESS, Arnouts et al."
 1997). as described in our study of Abell 85 (Diuxet al.," 1997), as described in our study of Abell 85 (Durret et al."
 1999a. Fig.," 1999a, Fig."
 10 and text). aud we subtracted this backgroun to the observed umber of galaxies.," 10 and text), and we subtracted this background to the observed number of galaxies."
 The result is shown iu Fig. Hl.., The result is shown in Fig. \ref{Rccd}.
 We have checked that the cousisteucyv of the bacseround umber counts estimated by Tyson (1988) with hose of the LORS and ESS combined as deseribed above is good., We have checked that the consistency of the background number counts estimated by Tyson (1988) with those of the LCRS and ESS combined as described above is good.
 The difference vctween the observed nuuber of ealaxies aud he backeround (Fig. 11)), The difference between the observed number of galaxies and the background (Fig. \ref{Rccd}) )
 becomes negative for magnitues BR15.1. while the CCD catalogue is complete at least up o R=21.," becomes negative for magnitudes $\geq
18.4$, while the CCD catalogue is complete at least up to R=21."
 Therefore. this backeroux cannot be «'nsÓdered. as representativo of the loca backeround i1i our CCD field of view.," Therefore, this background cannot be considered as representative of the local background in our CCD field of view."
 Note that this was already he case for he CCD photometric data of Alcl 85., Note that this was already the case for the CCD photometric data of Abell 85.
 Oue jotable feature is t1e dip in the galaxy magnitude distribution at R~19.5 o9 1T). which ds detectec at a high confidence level.," One notable feature is the dip in the galaxy magnitude distribution at $\sim 19.5$ $_{\rm R} \sim -17$ ), which is detected at a high confidence level."
 This dip corresponds to that observe by Molinari ct a. (, This dip corresponds to that observed by Molinari et al. (
1998). who found a dip at R19 (Mg1 45).,"1998), who found a dip at $\sim$ 19 $_{\rm R} \sim
-17.5$ )."
 Note that thev also fud a similar dip iu the ο banCL. and possibly in the 1 baud.," Note that they also find a similar dip in the g band, and possibly in the i band."
 Molinari ( al. (, Molinari et al. (
1998) mace a SCCOLLC determination of the CLF by selecting cluster nenibers i ra colom-magutude diagram.,1998) made a second determination of the GLF by selecting cluster members in a colour-magnitude diagram.
 Iu this case. they fik astnall dip. or at least a flattening. for R~18 (Mg 15.5).," In this case, they find a small dip, or at least a flattening, for $\sim 18$ $_{\rm R} \sim -18.5$ )."
 This value does not agree either with the xieht nor with the faim GLF that we derived., This value does not agree either with the bright nor with the faint GLF that we derived.
 It is clitticalt to understand why. since them colouranaenitudc YC‘lation appears quite well defiucd.," It is difficult to understand why, since their colour-magnitude relation appears quite well defined."
 Tn order to investigate the origin of the dip secu iu our data. we propose a tov model. which is not a fit but ouly illustrates how the dip could be accounted for.," In order to investigate the origin of the dip seen in our data, we propose a toy model, which is not a fit but only illustrates how the dip could be accounted for."
 Let us first note that the contribution of the other sructures detected along tic lue of sight is ueeligible., Let us first note that the contribution of the other structures detected along the line of sight is negligible.
 Assuimiug a Cassia | oa ScLhechter fiuction to model he CLF (sec section 1.5.]) we rescaled the παο of ealaxies xoduced by this conrposite ftnction o fit the dimension of the CCD fek.," Assuming a Gaussian + a Schechter function to model the GLF (see section 4.5.1), we rescaled the number of galaxies produced by this composite function to fit the dimension of the CCD field."
 We then a»plied. a iuaguituce cut-off o this GLE. as suggested by Adami et al. (," We then applied a magnitude cut-off to this GLF, as suggested by Adami et al. ("
"2WOO), for ealaxies fainter than Mg=19.75 in he inner core of the Coma cluster.","2000), for galaxies fainter than $_{\rm R}=-19.75$ in the inner core of the Coma cluster."
 This effect becoues very strong for galaxies zdnter than Mg17., This effect becomes very strong for galaxies fainter than $_{\rm R} =-17$.
 The exact shape of such a cut-off is unknown. so we ayplied a convenient apodization unctiou (the choice of tus function oeinfluences the shape aud smoothness of the dip).," The exact shape of such a cut-off is unknown, so we applied a convenient apodization function (the choice of this function influences the shape and smoothness of the dip)."
 T1ο background counts were nodeled as the backerotud contribution from the LORS aud ESS described above., The background counts were modeled as the background contribution from the LCRS and ESS described above.
 We theji mnmnnunued the cluster aud backerouud contribtions. aud the result is shown iu Fig. 12..," We then summed the cluster and background contributions, and the result is shown in Fig. \ref{fdlada}."
 Such a tov model can reprouce the elobal CLF shape. with couuts siniaw to the observed data aud a dip comparable to the observed one.," Such a toy model can reproduce the global GLF shape, with counts similar to the observed data and a dip comparable to the observed one."
 A fine-tuning of the various parameters involved could uake Figs., A fine-tuning of the various parameters involved could make Figs.
 Hl. aud muore sinilu. but lis would push the model too far.," \ref{Rccd} and more similar, but this would push the model too far."
 Tlowever. we cun stae that a cut-off iu the CLF of ssinilu to tha observed ii Coma is a solution to account for the observed dip.," However, we can state that a cut-off in the GLF of similar to that observed in Coma is a solution to account for the observed dip."
 A pixel bv pixe fit was performed on the N-rav image. as described by Diskuw et al. (," A pixel by pixel fit was performed on the X-ray image, as described by Pislar et al. ("
1997).,1997).
" The pixel size is 30 aresec,", The pixel size is 30 arcsec.
 À -nodelaxd a 3D Sésce model (Lima Neto et al., A $\beta$ -model and a 3D Sérrsic model (Lima Neto et al.
 1999) were οςynsiclered for the variatiois of the density with radius., 1999) were considered for the variations of the density with radius.
 The eloval temperature estimated from these ROSAT data. 1sine a Ravinoud-Siuith spectrum and a Galactic absorplon column density was ‘Ouxl to be 11 co ando assumed o be constant (Dislar 1998).," The global temperature estimated from these ROSAT data, using a Raymond-Smith spectrum and a Galactic absorption column density was found to be $\pm$ 1 keV and assumed to be constant (Pislar 1998)."
 This Is consistent wi ht1ο temperatures of 3.9 and L7 keV ο measured with the Eiustein and ENOSAT satellites respectively (David et al., This is consistent with the temperatures of 3.9 and 4.7 keV previously measured with the Einstein and EXOSAT satellites respectively (David et al.
 1993: Edge Stewart 1991)., 1993; Edge Stewart 1991).
 The parameters correspoxdins to the best fits for voth inodels are eiven in Tabe Dh. and the result of he model 1 fit superimpose ou the observed image is displaved in Fig. 1 3..," The parameters corresponding to the best fits for both models are given in Table \ref{tabfitx}, , and the result of the $\beta$ -model 1 fit superimposed on the observed image is displayed in Fig. \ref{fitx}. ."
 We observe that in model 2 the central density is ower than iu model | aud that the > and r. parameters aro higher., We observe that in model 2 the central density is lower than in model 1 and that the $\beta$ and $_c$ parameters are higher.
 TUs is because in model 2 we do not imclude the central region. wrere the cooling flow lies.," This is because in model 2 we do not include the central region, where the cooling flow lies."
 The effect 1s the same for modes and d., The effect is the same for models 3 and 4.
" Our values of > and τ, (in model 2) are higher than those of \larkevite1 et al. (", Our values of $\beta$ and $_c$ (in model 2) are higher than those of Markevitch et al. (
1999). who fouud >=0.7 and 1r.=219 kpc.,"1999), who found $\beta=0.7$ and $_c=249$ kpc."
 This is due to the fact tha they exclude a central region siialer thanours (3 arcnmün instead of 3.3 arcmin)., This is due to the fact that they exclude a central region smaller thanours (3 arcmin instead of 3.3 arcmin).
" Pislar (1998) has shown that i ra cooling flow cluster the bigeer the excluded central region.the higher >and z,. ancl the ower the central deusitv."," Pislar (1998) has shown that in a cooling flow cluster the bigger the excluded central region,the higher $\beta$ and $_c$ , and the lower the central density."
Moreover. at,"Moreover, at"
ratio Ry — 3.1 (Ricke Lebofski 1985).,ratio $R_V$ = 3.1 (Rieke Lebofski 1985).
 This iplies that the intrinsic magnitude of the star is Vy~ 11.0., This implies that the intrinsic magnitude of the star is $V_0 \sim$ 11.0.
 Therefore. given that a carbon star of spectral type C(6.2) has an absolute magnitude Mym 2.6 (Cohen 1979). we obtain a distance d 5.2 kpc.," Therefore, given that a carbon star of spectral type C(6,2) has an absolute magnitude $_V \approx $ $-$ 2.6 (Cohen 1979), we obtain a distance $d \sim$ 5.2 kpc."
 This would locate CGCS 5926 in the far side of the outer part of the Perseus Arvin of the Galaxy (see e.g. Fig., This would locate CGCS 5926 in the far side of the outer part of the Perseus Arm of the Galaxy (see e.g. Fig.
 1. of Leitch Vasisht 1998)., 1 of Leitch Vasisht 1998).
 The Galactic linc-ofsielt reddening iu the direction of CCGCS 5926 i E(BV) = 1.33 mae according to the naps of Schlegel et al. (, The Galactic line-of-sight reddening in the direction of CGCS 5926 is $E(B-V)$ = 1.33 mag according to the maps of Schlegel et al. (
1998).,1998).
 This value compares well with our reddening estimate for the source. lius indicating hat this star is behind that Calactic Arm and that the observed reddeniug is likely due to interstellar absorption oulv. with no substantial contribution from material local o the source.," This value compares well with our reddening estimate for the source, thus indicating that this star is behind that Galactic Arm and that the observed reddening is likely due to interstellar absorption only, with no substantial contribution from material local to the source."
 We nevertheless note that the tabulated Galactic absorption naps should be treated with some deeree of caution for objects which have the line of sight along the Calactic Plane. such as the present case (for which the Galactic latitude is b = 0796).," We nevertheless note that the tabulated Galactic absorption maps should be treated with some degree of caution for objects which have the line of sight along the Galactic Plane, such as the present case (for which the Galactic latitude is $b$ = $\fdg$ 96)."
 We remark that the above approach rules out the possibility that COCS 5926 is a red superejianut of huuinosity class I: indeed. in this case. its absolute maguitude woulc be My~ 5.6 (Lang 1992). which would place the object at au uncomfortably large distance of ~20 kpc. thus well outside the Galaxy eiven the Galactic longitude of the source (= 11575).," We remark that the above approach rules out the possibility that CGCS 5926 is a red supergiant of luminosity class I: indeed, in this case, its absolute magnitude would be $_V \sim $ $-$ 5.6 (Lang 1992), which would place the object at an uncomfortably large distance of $\sim$ 20 kpc, thus well outside the Galaxy given the Galactic longitude of the source $l$ = $\fdg$ 5)."
 No XNrav source was detected in the NRT poiutine. either at the optical position of COCS 5926 or within theROSAT error circle.," No X–ray source was detected in the XRT pointing, either at the optical position of CGCS 5926 or within the error circle."
 Using the bavesiuu approach of Άτα et al. (, Using the bayesian approach of Kraft et al. (
1991). we ect a 3-07 coufidence level upper limit count rate of 2.10 7 bin the 0.310 keV οποίον baud.,"1991), we get a $\sigma$ confidence level upper limit count rate of $\times$ $^{-3}$ $^{-1}$ in the 0.3–10 keV energy band."
 This. assuniug a Crab-like spectrum. correspouds to an observed flux linüt of 9410. H ere ? + in this energy range.," This, assuming a Crab-like spectrum, corresponds to an observed flux limit of $\sim$ $\times$ $^{-14}$ erg $^{-2}$ $^{-1}$ in this energy range."
 Likewise. no UV source was detected iu coincidence of he target down to a 3-0 liuüt of 21.5 mag in the CVA72 uid.," Likewise, no UV source was detected in coincidence of the target down to a $\sigma$ limit of 21.8 mag in the $UVM2$ band."
" The above SuvftfXRT upper lait in Xrays can therefore be compared to the detection iu the faint source catalog: here theROSAT source is reported with a 0.12.1 keV count vate of (1.9640.76)<10 7 1,", The above /XRT upper limit in X–rays can therefore be compared to the detection in the faint source catalog: here the source is reported with a 0.1–2.4 keV count rate of $\pm$ $\times$ $^{-2}$ $^{-1}$.
 This. assundue again a Crab-like spectrum. implies a flux of τν]n Dà erg )7 Ἐν," This, assuming again a Crab-like spectrum, implies a flux of $\sim$ $\times$ $^{-13}$ erg $^{-2}$ $^{-1}$."
 Tt can be secu that theROSAT spectral coverage is basically a subset of the NRT one: moreover. the contriution of the Nrav enuüssiou below 0.3 keV to the total fiux should not be relevant οἼναι the non-negligible line-of-sight absorption toward COCS 5926 apparent from the optical data. which converts into a hydrogen column deusity Aq;~ «1075 cin? if one uses the empirical ormula of Predell Schuutt (1995).," It can be seen that the spectral coverage is basically a subset of the XRT one; moreover, the contribution of the X–ray emission below 0.3 keV to the total flux should not be relevant given the non-negligible line-of-sight absorption toward CGCS 5926 apparent from the optical data, which converts into a hydrogen column density $N_{\rm H} \sim$ $\times$ $^{21}$ $^{-2}$ if one uses the empirical formula of Predehl Schmitt (1995)."
 The above figures hus sugeest that. if theROSAT detection is veal. the source should possess variability at Norays as well.," The above figures thus suggest that, if the detection is real, the source should possess variability at X–rays as well."
 We will discuss this in detail iu the next section., We will discuss this in detail in the next section.
 These fluxes. using the above distance estimate for ⊲⊀⋅ ⋅ - ≼⊲≼∶≼⊲∺⋅↱⊐≝∟≻∩∙↑⋯↴∖↴∐⊔↻↕⋅↖↽⋜⋯⊸∖↥⋅⋜↧⋅↖⇁↕⋯⊔∐⋯↴∖↴↕↑⋅↖⇁∪↕≈⋅≩∖↓∩⋟−⋅⋅ ⋟∙↽⋮↜⋅≽ ↸∖↥⋅∶↴↜∏∖↴↓↕≯∪↥⋅↑∐↸∖∏∩∣≲⊽↼−∏↴↕⊔↸∖⋜↧↴∖↴⋯⋅↸∖⋯↸∖∐↑⋜⋯≼," These fluxes, using the above distance estimate for CGCS 5926, thus imply an X–ray luminosity of $\approx$ $\times$ $^{32}$ erg $^{-1}$ for the measurement and an upper limit"
 These fluxes. using the above distance estimate for ⊲⊀⋅ ⋅ - ≼⊲≼∶≼⊲∺⋅↱⊐≝∟≻∩∙↑⋯↴∖↴∐⊔↻↕⋅↖↽⋜⋯⊸∖↥⋅⋜↧⋅↖⇁↕⋯⊔∐⋯↴∖↴↕↑⋅↖⇁∪↕≈⋅≩∖↓∩⋟−⋅⋅ ⋟∙↽⋮↜⋅≽ ↸∖↥⋅∶↴↜∏∖↴↓↕≯∪↥⋅↑∐↸∖∏∩∣≲⊽↼−∏↴↕⊔↸∖⋜↧↴∖↴⋯⋅↸∖⋯↸∖∐↑⋜⋯≼↧," These fluxes, using the above distance estimate for CGCS 5926, thus imply an X–ray luminosity of $\approx$ $\times$ $^{32}$ erg $^{-1}$ for the measurement and an upper limit"
 These fluxes. using the above distance estimate for ⊲⊀⋅ ⋅ - ≼⊲≼∶≼⊲∺⋅↱⊐≝∟≻∩∙↑⋯↴∖↴∐⊔↻↕⋅↖↽⋜⋯⊸∖↥⋅⋜↧⋅↖⇁↕⋯⊔∐⋯↴∖↴↕↑⋅↖⇁∪↕≈⋅≩∖↓∩⋟−⋅⋅ ⋟∙↽⋮↜⋅≽ ↸∖↥⋅∶↴↜∏∖↴↓↕≯∪↥⋅↑∐↸∖∏∩∣≲⊽↼−∏↴↕⊔↸∖⋜↧↴∖↴⋯⋅↸∖⋯↸∖∐↑⋜⋯≼↧⋜," These fluxes, using the above distance estimate for CGCS 5926, thus imply an X–ray luminosity of $\approx$ $\times$ $^{32}$ erg $^{-1}$ for the measurement and an upper limit"
 These fluxes. using the above distance estimate for ⊲⊀⋅ ⋅ - ≼⊲≼∶≼⊲∺⋅↱⊐≝∟≻∩∙↑⋯↴∖↴∐⊔↻↕⋅↖↽⋜⋯⊸∖↥⋅⋜↧⋅↖⇁↕⋯⊔∐⋯↴∖↴↕↑⋅↖⇁∪↕≈⋅≩∖↓∩⋟−⋅⋅ ⋟∙↽⋮↜⋅≽ ↸∖↥⋅∶↴↜∏∖↴↓↕≯∪↥⋅↑∐↸∖∏∩∣≲⊽↼−∏↴↕⊔↸∖⋜↧↴∖↴⋯⋅↸∖⋯↸∖∐↑⋜⋯≼↧⋜⋯," These fluxes, using the above distance estimate for CGCS 5926, thus imply an X–ray luminosity of $\approx$ $\times$ $^{32}$ erg $^{-1}$ for the measurement and an upper limit"
 These fluxes. using the above distance estimate for ⊲⊀⋅ ⋅ - ≼⊲≼∶≼⊲∺⋅↱⊐≝∟≻∩∙↑⋯↴∖↴∐⊔↻↕⋅↖↽⋜⋯⊸∖↥⋅⋜↧⋅↖⇁↕⋯⊔∐⋯↴∖↴↕↑⋅↖⇁∪↕≈⋅≩∖↓∩⋟−⋅⋅ ⋟∙↽⋮↜⋅≽ ↸∖↥⋅∶↴↜∏∖↴↓↕≯∪↥⋅↑∐↸∖∏∩∣≲⊽↼−∏↴↕⊔↸∖⋜↧↴∖↴⋯⋅↸∖⋯↸∖∐↑⋜⋯≼↧⋜⋯∏," These fluxes, using the above distance estimate for CGCS 5926, thus imply an X–ray luminosity of $\approx$ $\times$ $^{32}$ erg $^{-1}$ for the measurement and an upper limit"
 These fluxes. using the above distance estimate for ⊲⊀⋅ ⋅ - ≼⊲≼∶≼⊲∺⋅↱⊐≝∟≻∩∙↑⋯↴∖↴∐⊔↻↕⋅↖↽⋜⋯⊸∖↥⋅⋜↧⋅↖⇁↕⋯⊔∐⋯↴∖↴↕↑⋅↖⇁∪↕≈⋅≩∖↓∩⋟−⋅⋅ ⋟∙↽⋮↜⋅≽ ↸∖↥⋅∶↴↜∏∖↴↓↕≯∪↥⋅↑∐↸∖∏∩∣≲⊽↼−∏↴↕⊔↸∖⋜↧↴∖↴⋯⋅↸∖⋯↸∖∐↑⋜⋯≼↧⋜⋯∏⋯," These fluxes, using the above distance estimate for CGCS 5926, thus imply an X–ray luminosity of $\approx$ $\times$ $^{32}$ erg $^{-1}$ for the measurement and an upper limit"
 These fluxes. using the above distance estimate for ⊲⊀⋅ ⋅ - ≼⊲≼∶≼⊲∺⋅↱⊐≝∟≻∩∙↑⋯↴∖↴∐⊔↻↕⋅↖↽⋜⋯⊸∖↥⋅⋜↧⋅↖⇁↕⋯⊔∐⋯↴∖↴↕↑⋅↖⇁∪↕≈⋅≩∖↓∩⋟−⋅⋅ ⋟∙↽⋮↜⋅≽ ↸∖↥⋅∶↴↜∏∖↴↓↕≯∪↥⋅↑∐↸∖∏∩∣≲⊽↼−∏↴↕⊔↸∖⋜↧↴∖↴⋯⋅↸∖⋯↸∖∐↑⋜⋯≼↧⋜⋯∏⋯⋉," These fluxes, using the above distance estimate for CGCS 5926, thus imply an X–ray luminosity of $\approx$ $\times$ $^{32}$ erg $^{-1}$ for the measurement and an upper limit"
 These fluxes. using the above distance estimate for ⊲⊀⋅ ⋅ - ≼⊲≼∶≼⊲∺⋅↱⊐≝∟≻∩∙↑⋯↴∖↴∐⊔↻↕⋅↖↽⋜⋯⊸∖↥⋅⋜↧⋅↖⇁↕⋯⊔∐⋯↴∖↴↕↑⋅↖⇁∪↕≈⋅≩∖↓∩⋟−⋅⋅ ⋟∙↽⋮↜⋅≽ ↸∖↥⋅∶↴↜∏∖↴↓↕≯∪↥⋅↑∐↸∖∏∩∣≲⊽↼−∏↴↕⊔↸∖⋜↧↴∖↴⋯⋅↸∖⋯↸∖∐↑⋜⋯≼↧⋜⋯∏⋯⋉∖," These fluxes, using the above distance estimate for CGCS 5926, thus imply an X–ray luminosity of $\approx$ $\times$ $^{32}$ erg $^{-1}$ for the measurement and an upper limit"
 These fluxes. using the above distance estimate for ⊲⊀⋅ ⋅ - ≼⊲≼∶≼⊲∺⋅↱⊐≝∟≻∩∙↑⋯↴∖↴∐⊔↻↕⋅↖↽⋜⋯⊸∖↥⋅⋜↧⋅↖⇁↕⋯⊔∐⋯↴∖↴↕↑⋅↖⇁∪↕≈⋅≩∖↓∩⋟−⋅⋅ ⋟∙↽⋮↜⋅≽ ↸∖↥⋅∶↴↜∏∖↴↓↕≯∪↥⋅↑∐↸∖∏∩∣≲⊽↼−∏↴↕⊔↸∖⋜↧↴∖↴⋯⋅↸∖⋯↸∖∐↑⋜⋯≼↧⋜⋯∏⋯⋉∖↥," These fluxes, using the above distance estimate for CGCS 5926, thus imply an X–ray luminosity of $\approx$ $\times$ $^{32}$ erg $^{-1}$ for the measurement and an upper limit"
 These fluxes. using the above distance estimate for ⊲⊀⋅ ⋅ - ≼⊲≼∶≼⊲∺⋅↱⊐≝∟≻∩∙↑⋯↴∖↴∐⊔↻↕⋅↖↽⋜⋯⊸∖↥⋅⋜↧⋅↖⇁↕⋯⊔∐⋯↴∖↴↕↑⋅↖⇁∪↕≈⋅≩∖↓∩⋟−⋅⋅ ⋟∙↽⋮↜⋅≽ ↸∖↥⋅∶↴↜∏∖↴↓↕≯∪↥⋅↑∐↸∖∏∩∣≲⊽↼−∏↴↕⊔↸∖⋜↧↴∖↴⋯⋅↸∖⋯↸∖∐↑⋜⋯≼↧⋜⋯∏⋯⋉∖↥⋅," These fluxes, using the above distance estimate for CGCS 5926, thus imply an X–ray luminosity of $\approx$ $\times$ $^{32}$ erg $^{-1}$ for the measurement and an upper limit"
 These fluxes. using the above distance estimate for ⊲⊀⋅ ⋅ - ≼⊲≼∶≼⊲∺⋅↱⊐≝∟≻∩∙↑⋯↴∖↴∐⊔↻↕⋅↖↽⋜⋯⊸∖↥⋅⋜↧⋅↖⇁↕⋯⊔∐⋯↴∖↴↕↑⋅↖⇁∪↕≈⋅≩∖↓∩⋟−⋅⋅ ⋟∙↽⋮↜⋅≽ ↸∖↥⋅∶↴↜∏∖↴↓↕≯∪↥⋅↑∐↸∖∏∩∣≲⊽↼−∏↴↕⊔↸∖⋜↧↴∖↴⋯⋅↸∖⋯↸∖∐↑⋜⋯≼↧⋜⋯∏⋯⋉∖↥⋅∐," These fluxes, using the above distance estimate for CGCS 5926, thus imply an X–ray luminosity of $\approx$ $\times$ $^{32}$ erg $^{-1}$ for the measurement and an upper limit"
 These fluxes. using the above distance estimate for ⊲⊀⋅ ⋅ - ≼⊲≼∶≼⊲∺⋅↱⊐≝∟≻∩∙↑⋯↴∖↴∐⊔↻↕⋅↖↽⋜⋯⊸∖↥⋅⋜↧⋅↖⇁↕⋯⊔∐⋯↴∖↴↕↑⋅↖⇁∪↕≈⋅≩∖↓∩⋟−⋅⋅ ⋟∙↽⋮↜⋅≽ ↸∖↥⋅∶↴↜∏∖↴↓↕≯∪↥⋅↑∐↸∖∏∩∣≲⊽↼−∏↴↕⊔↸∖⋜↧↴∖↴⋯⋅↸∖⋯↸∖∐↑⋜⋯≼↧⋜⋯∏⋯⋉∖↥⋅∐⋯," These fluxes, using the above distance estimate for CGCS 5926, thus imply an X–ray luminosity of $\approx$ $\times$ $^{32}$ erg $^{-1}$ for the measurement and an upper limit"
 These fluxes. using the above distance estimate for ⊲⊀⋅ ⋅ - ≼⊲≼∶≼⊲∺⋅↱⊐≝∟≻∩∙↑⋯↴∖↴∐⊔↻↕⋅↖↽⋜⋯⊸∖↥⋅⋜↧⋅↖⇁↕⋯⊔∐⋯↴∖↴↕↑⋅↖⇁∪↕≈⋅≩∖↓∩⋟−⋅⋅ ⋟∙↽⋮↜⋅≽ ↸∖↥⋅∶↴↜∏∖↴↓↕≯∪↥⋅↑∐↸∖∏∩∣≲⊽↼−∏↴↕⊔↸∖⋜↧↴∖↴⋯⋅↸∖⋯↸∖∐↑⋜⋯≼↧⋜⋯∏⋯⋉∖↥⋅∐⋯↕," These fluxes, using the above distance estimate for CGCS 5926, thus imply an X–ray luminosity of $\approx$ $\times$ $^{32}$ erg $^{-1}$ for the measurement and an upper limit"
 These fluxes. using the above distance estimate for ⊲⊀⋅ ⋅ - ≼⊲≼∶≼⊲∺⋅↱⊐≝∟≻∩∙↑⋯↴∖↴∐⊔↻↕⋅↖↽⋜⋯⊸∖↥⋅⋜↧⋅↖⇁↕⋯⊔∐⋯↴∖↴↕↑⋅↖⇁∪↕≈⋅≩∖↓∩⋟−⋅⋅ ⋟∙↽⋮↜⋅≽ ↸∖↥⋅∶↴↜∏∖↴↓↕≯∪↥⋅↑∐↸∖∏∩∣≲⊽↼−∏↴↕⊔↸∖⋜↧↴∖↴⋯⋅↸∖⋯↸∖∐↑⋜⋯≼↧⋜⋯∏⋯⋉∖↥⋅∐⋯↕↑," These fluxes, using the above distance estimate for CGCS 5926, thus imply an X–ray luminosity of $\approx$ $\times$ $^{32}$ erg $^{-1}$ for the measurement and an upper limit"
We use p-mode frequencies. obtained from theGONG!.. for the individual (1.(0) multiplets. μμ. where » is the radial order and i is (he azimuthal order. running from —f to +f.,"We use $p$ -mode frequencies, obtained from the, for the individual $n, \ell, m$ ) multiplets, $\nu_{n \ell m}$, where $n$ is the radial order and $m$ is the azimuthal order, running from $-\ell$ to $+\ell$."
 The mode lrequencies for each multiplet were estimated [rom (he mr—7 power spectra constructed by (he time series for individual GONG Month (GM = 36 days)., The mode frequencies for each multiplet were estimated from the $m-\nu$ power spectra constructed by the time series for individual GONG Month (GM = 36 days).
 Here we used the standard GONG peak-fitGng algorithm to compute the power spectra based on the multitaper spectral analvsis coupled with a Fast Fourier transform 1999)., Here we used the standard GONG peak-fitting algorithm to compute the power spectra based on the multitaper spectral analysis coupled with a Fast Fourier transform \citep{rudi99}.
. Finally. Lorentzian profiles were used to fit the peaks in the m—» spectra using a minimization scheme guided bv an initial guess table (Anderson.1990:Ililletal. 1998).," Finally, Lorentzian profiles were used to fit the peaks in the $m-\nu$ spectra using a minimization scheme guided by an initial guess table \citep{ander90, hill98}."
". The guess table is based on fits to a special data set — a grand average of six 2-month periods at the beginning of GONG operation (1, Lowe 2011. private communication) and is consistent for all data sets."," The guess table is based on fits to a special data set – a 'grand average' of six 3-month periods at the beginning of GONG operation (R. Howe 2011, private communication) and is consistent for all data sets."
 Frequencies lor m z 0 are ealeulated by applving a Legendre rotation expansion to the m = 0 frequencies., Frequencies for m $\ne$ 0 are calculated by applying a Legendre rotation expansion to the m $ = $ 0 frequencies.
 The data analyzed here consist of 293 36-clav overlapping data sets. with a spacing of 18 days between consecutive data sets. covering the period [rom 1995 Alay 7 to 2009 October 31 (ve. GM = 1 147) in 5-minute oscillation band: 2000 << 3300 jllz and 0 «(CR 120.," The data analyzed here consist of 293 36-day overlapping data sets, with a spacing of 18 days between consecutive data sets, covering the period from 1995 May 7 to 2009 October 31 (i.e. GM = 1 – 147) in 5-minute oscillation band; 2000 $\le \nu \le$ 3300 $\mu$ Hz and 0 $\le \ell \le$ 120."
 Thus. these data sets start about à vear before the minimum of solar cvele 23 and end several months after the minimum of solar evele 24.," Thus, these data sets start about a year before the minimum of solar cycle 23 and end several months after the minimum of solar cycle 24."
 While most of earlier analysis are based on the m-averaged Irequences. our analvsis based on (i. £i) multiplets has the advantage of studying latitudinal variations in frequency shifts that allows us to investigate the changes around the activitv belt where signatures of the rise of a new solar evele first appear.," While most of earlier analysis are based on the $m$ -averaged frequencies, our analysis based on $n, \ell, m$ ) multiplets has the advantage of studying latitudinal variations in frequency shifts that allows us to investigate the changes around the activity belt where signatures of the rise of a new solar cycle first appear."
"would imply that older galaxies, which have undergone more dry mergers since their formation epoch, would end up, on average, with boxier isophotes with respect to younger galaxies (e.g., ??)).","would imply that older galaxies, which have undergone more dry mergers since their formation epoch, would end up, on average, with boxier isophotes with respect to younger galaxies (e.g., \citealt{KhochfarBurkert06,KochfarSilk06Rez}) )."
 The recent study by ? actually confirms that older galaxies appear boxier., The recent study by \citet{Kormendy08} actually confirms that older galaxies appear boxier.
" ? also discussed that several other correlations, including the velocity dispersion, size and luminosity are reproduced by the ? model with no extra tuning of the parameters."," \citet{Almeida07} also discussed that several other correlations, including the velocity dispersion, size and luminosity are reproduced by the \citet{Bower06} model with no extra tuning of the parameters."
" During the wet phase, the correlations between the central black hole mass aand their host galaxy potential wells, characterized by theirc,, might have also been settled, especially in AGN feedback-constrained galaxy evolution models (e.g., ???;; but see also, e.g., ?))."," During the wet phase, the correlations between the central black hole mass and their host galaxy potential wells, characterized by their, might have also been settled, especially in AGN feedback-constrained galaxy evolution models (e.g., \citealt{Granato04,Hopkins06,Monaco07}; but see also, e.g., \citealt{MiraldaKoll}) )."
" If most of the black hole mass was already in place at the end of the wet phase, but only about half of the host galaxy mass was assembled, the hierarchical models considered here would then naturally imply an higher black hole mass to stellar mass ratio with respect to the local one, i.e., a positive evolution in the normalization of the rrelation."," If most of the black hole mass was already in place at the end of the wet phase, but only about half of the host galaxy mass was assembled, the hierarchical models considered here would then naturally imply an higher black hole mass to stellar mass ratio with respect to the local one, i.e., a positive evolution in the normalization of the relation."
"Mstar On the other hand, given that the host halo potential well is rapidly built during the fast accretion phase, it is also reasonable to expect the rrelation to possibly already be fully established at the epoch of the wet phase (e.g.,???).."," On the other hand, given that the host halo potential well is rapidly built during the fast accretion phase, it is also reasonable to expect the relation to possibly already be fully established at the epoch of the wet phase \citep[e.g.,][]{Granato04,Marulli08,Hop08FP}."
" Some empirical works have, in fact, found only marginal evidence for evolution in the rrelation, and possibly only in the more massive systems, (e.g.,???,andreferencestherein)."," Some empirical works have, in fact, found only marginal evidence for evolution in the relation, and possibly only in the more massive systems, \citep[e.g.,][and references
therein]{Shields06,Gaskell09,ShankarMsigma}."
" However, minor dry mergers are expected to have some impact on the initial velocity dispersion ((e.g., ??))."," However, minor dry mergers are expected to have some impact on the initial velocity dispersion (e.g., \citealt{CiottiReview,Naab09}) )."
" Also, late black hole re-activations (e.g., Menci et al."," Also, late black hole re-activations (e.g., Menci et al."
" 2004, Vittorini et al."," 2004, Vittorini et al."
" 2005), and/or black hole mergers (e.g., Volonteri et al."," 2005), and/or black hole mergers (e.g., Volonteri et al."
" 2005, Malbon et al."," 2005, Malbon et al."
" 2007), might have increased the black hole masses since the wet epoch, further influencing the evolution in the scaling relations between black holes and their host galaxies."," 2007), might have increased the black hole masses since the wet epoch, further influencing the evolution in the scaling relations between black holes and their host galaxies."
" Overall, the dynamical evolution of galaxies and their central black holes, tested against the local velocity dispersion function (Sheth et al."," Overall, the dynamical evolution of galaxies and their central black holes, tested against the local velocity dispersion function (Sheth et al."
" 2003, Bernardi et al."," 2003, Bernardi et al."
" 2009) and fundamental plane of early-type galaxies, should provide valuable additional insights into our understanding of galaxy evolution."," 2009) and fundamental plane of early-type galaxies, should provide valuable additional insights into our understanding of galaxy evolution."
 In this paper we make use ofthe data sets derived from SDSS DR6 by Bernardi et al. (, In this paper we make use ofthe data sets derived from SDSS DR6 by Bernardi et al. (
"2009) and ?,, used to derive the size and stellar mass functions for a sample of early-type galaxies with concentration C,>2.86, comprised of both ellipticals and S0 galaxies, and a sample dominated by ellipticals, respectively.","2009) and \citet{Hyde09a}, , used to derive the size and stellar mass functions for a sample of early-type galaxies with concentration $C_r>2.86$, comprised of both ellipticals and S0 galaxies, and a sample dominated by ellipticals, respectively."
 We compare these statistical distributions with the hierarchical model by ?.., We compare these statistical distributions with the hierarchical model by \citet{Bower06}. .
 The aim of this exercise isto, The aim of this exercise isto
"such sources existed in Arp 220. we would expect to detect all those above ~5x LO“eres 7 in luminosity,","such sources existed in Arp 220, we would expect to detect all those above $\sim$ $\times 10^{39}$ ergs $^{-1}$ $^{-2}$ in luminosity."
 We only see one such source. X-2. which lies 77 away [rom the nucleus.," We only see one such source, X-2, which lies 7” away from the nucleus."
 The hard X-ray emission from Arp 220 thus appears to be significantly more concentrated in ihe nucleus than that of other interacting or merging galaxies observed by Chandra., The hard X-ray emission from Arp 220 thus appears to be significantly more concentrated in the nucleus than that of other interacting or merging galaxies observed by Chandra.
 Indeed. the spatial distribution of hard emission in Arp 220 would appear to be more similar to that of Mrk27T3 (Nia οἱ al.," Indeed, the spatial distribution of hard emission in Arp 220 would appear to be more similar to that of Mrk273 (Xia et al."
 2002). à ULIRG containing an AGN at its core. than NGC3256 or the Antennae. neither of which seem to have a significant AGN contribution.," 2002), a ULIRG containing an AGN at its core, than NGC3256 or the Antennae, neither of which seem to have a significant AGN contribution."
 The X-ray output [rom the nuclear regions of Arp 220 is energetically dominated by an extended hard kpe-scale component. wilh a significant point source contribution (<200pe). that has a power law spectrum with P—1.421.0. with an unabsorbed 2-lLOkeV Iuminosity οἱ 4x107 eres/s. The central question is the origin of this radiation does it arise [rom voune supernovae. X-ray binaries. or the result. of accretion onto a more massive body. possibly a weak ACN.," The X-ray output from the nuclear regions of Arp 220 is energetically dominated by an extended hard kpc-scale component, with a significant point source contribution $<200$ pc), that has a power law spectrum with $\Gamma$ $\pm$ 1.0, with an unabsorbed 2-10keV luminosity of $\times 10^{40}$ ergs/s. The central question is the origin of this radiation – does it arise from young supernovae, X-ray binaries, or the result of accretion onto a more massive body, possibly a weak AGN."
 We consider each of these possibilities in turn:, We consider each of these possibilities in turn:
 to understand their sensitivity to a variety of parameters., to understand their sensitivity to a variety of parameters.
Monte Carlo algoritlun developed by Thorstensen&Freed(1985) to assess the confidence with which the highest peak in the perioclogram cau be identified with the true orbital (requencey.,Monte Carlo algorithm developed by \citet{thfreed85} to assess the confidence with which the highest peak in the periodogram can be identified with the true orbital frequency.
 Once we were satisfied that the period was correct. we fit the time-series with sinusoids of the form uxing a hybrid linear least-squarealeorithiu’.," Once we were satisfied that the period was correct, we fit the time-series with sinusoids of the form using a hybrid linear least-square."
. This procedure is described in detail in ΤΕΤΟΙ., This procedure is described in detail in TFT04.
 For those CVs with absorption-liue radial velocity solutions. we shifted the individual spectra into the absorption-line rest frame before averaging them.," For those CVs with absorption-line radial velocity solutions, we shifted the individual spectra into the absorption-line rest frame before averaging them."
 As noted earlier. the secondary-star spectrum is often detectable in loiger-period CVs.," As noted earlier, the secondary-star spectrum is often detectable in longer-period CVs."
 The absorption-line radial velocities should track the orbital motion of tlie secoucary. though the racial velocities may be alected by irradiatiou and other ellects (Davey&Sinith1t)92).," The absorption-line radial velocities should track the orbital motion of the secondary, though the radial velocities may be affected by irradiation and other effects \citep{davey92}."
". However. a contribution ueed not arise [rou the secondary: i£ the late-type spect""unm is nearly. fixed in velocity. it may cot1ο from an unrelated field star. or the otter member of a hierarchical tripe: This appears be the case for V512 Cyg. discussed further below."," However, a late-type contribution need not arise from the secondary; if the late-type spectrum is nearly fixed in velocity, it may come from an unrelated field star, or the outer member of a hierarchical triple; This appears be the case for V542 Cyg, discussed further below."
 Peters&TLOLSensen(2005) aud TETOL discuss our specral decomposition techuique auc the inferences basec ol ie secondary star. wllch we summarize brielly here.," \citet{peters05} and TFT04 discuss our spectral decomposition technique and the inferences based on the secondary star, which we summarize briefly here."
 To estimate the secondary stars spectral type axl its contribution to the light. we scale spectra of cool spectral-type staucar| stars. subtract hem from the target specrum. aud look for the best possible caucellation of tle late-type features.," To estimate the secondary star's spectral type and its contribution to the light, we scale spectra of cool spectral-type standard stars, subtract them from the target spectrum, and look for the best possible cancellation of the late-type features."
 Tus vields estimates of the spectral type of the secondary aud its coutributiou to the total ligl., This yields estimates of the spectral type of the secondary and its contribution to the total light.
 The spectral type constalus the secondarys surface brightuess. and the orbital period (togethe “with the condition that the secoudary fills its Roche critical lobe) tightly coustraius the secoudarys radiis dio.," The spectral type constrains the secondary's surface brightness, and the orbital period (together with the condition that the secondary fills its Roche critical lobe) tightly constrains the secondary's radius $R_2$."
 The precise vaue of f» does depend weakly on the secoudarys ass. Als: to compute a realistic range for fi». we 1se the evolutionary calculatious of to guide the selectiou of a rauge fo: Ma.," The precise value of $R_2$ does depend weakly on the secondary's mass, $M_2$; to compute a realistic range for $R_2$, we use the evolutionary calculations of \citet{bk00} to guide the selection of a range for $M_2$."
 The estimates of the radius aud surface brightness together vielcl the secondarys absolute magniude. which in turn gives the distauce. without any assuiptiou that the secondary is a typica ualn-sequence star.," The estimates of the radius and surface brightness together yield the secondary's absolute magnitude, which in turn gives the distance, without any assumption that the secondary is a typical main-sequence star."
 Where applicable. we estimate the visual extiuetion using the Schlegel.Finkjener.&Davis(1098) maps: these give the extinction to the edge of the Galaxy. so we use their tabilated OB—V) as au upper limit.," Where applicable, we estimate the visual extinction using the \citet{schlegel98} maps; these give the extinction to the edge of the Galaxy, so we use their tabulated $E(B-V)$ as an upper limit."
 For most of the stars studied here. we have collected direct images using the Hiltuer 2.[m telescope and a SITe 20187 CCD detector.," For most of the stars studied here, we have collected direct images using the Hiltner 2.4m telescope and a SITe $^2$ CCD detector."
 Most of the celestial positions it Table 1 were measured," Most of the celestial positions in Table \ref{tab:star_info}
 were measured"
Dlazars are distant and powerful active ealactic nuclei (AGNs) which are oriented in such a wav that a jet expelled from the central black hole is directed at simall aneles with respect to the observers line of sight (for a recent review. see Padovani 2007).,"Blazars are distant and powerful active galactic nuclei (AGNs) which are oriented in such a way that a jet expelled from the central black hole is directed at small angles with respect to the observer's line of sight (for a recent review, see Padovani 2007)."
 Iu the widely adopted scenario of blazars. a sinele population of hieh-electrons in a. relativistic jet .radiates overdouble-hunped the ⋅↜ ° | ↸∖∐↑∐⋅↸∖↸∖↕↸∖↸⊳⊓⋅≺≻⋯⋜↧∩⊾∐↸∖↑↕↸⊳↴∖↴⋉∖↸⊳⊓⋅⋯⊔↖↽↕⋜↧↴∖↴↖⇁↕∐⊳↕∐⋅∪⊓⋅∪↕⋜⋯≼↧ inverse Compton processes. the former dominating at low enereies. the latter being relevant at high euergies (Ghisclling ct al.," In the widely adopted scenario of blazars, a single population of high-energy electrons in a relativistic jet radiates over the entire electromagnetic spectrum via synchrotron and inverse Compton processes, the former dominating at low energies, the latter being relevant at high energies (Ghisellini et al."
 1998)., 1998).
 The ambient photons that are inverse Compton scattered can be either iuternal (svuchrotron self-Conipton) aud/or external (external Compton scattering) to the jet., The ambient photons that are inverse Compton scattered can be either internal (synchrotron self-Compton) and/or external (external Compton scattering) to the jet.
 As a consequence. the spectral euergv distribution (SED) of blazars shows a shape. with the svuchrotron component enerev Dp - ↻↸∖⋜∐↘↽∐↕∶↴∙⋜⋯⋅↖↽↖↖⇁∐↸∖↥⋅↸∖↕↥⋅∪∐⊔∐↕↥⋅⋜∐⋅↸∖≼↧↑∪⊸∖↥⋅⋜↧⋅↖↽↴∖↴⋜⋯≼↧↑∐↸∖∐↕↖↽↸∖↥⋅↴∖↴↸∖. ⋅⋅ ≼⊲∪∐∏≻↑∪∐↸∖∐∐↴∖↴↴∖↴↕∪↓↸∖⊼↑↸∖∐≼∐∐∶↴∙⊾↿∏≻↑∪≼∶↸∖∖⊺↸∖∖∶↴∙⊾⋜⊔∐⊔⋜↧⋅ ⇁∣↴⇁ Fans.," As a consequence, the spectral energy distribution (SED) of blazars shows a double-humped shape, with the synchrotron component peaking anywhere from infrared to X–rays and the inverse Compton emission extending up to GeV/TeV gamma rays."
 To explain the various SED shapes observed in blazars. Fossati et al (," To explain the various SED shapes observed in blazars, Fossati et al. ("
1998) proposed the so-called “blazar sequence”. according to which a relation between peak enereies and >-dominance (the hunünosity ratio of! the second to the first peak) is present as a function of the source total power.,"1998) proposed the so-called “blazar sequence"", according to which a relation between peak energies and $\gamma$ -dominance (the luminosity ratio of the second to the first peak) is present as a function of the source total power."
 This micas that nore huuinous sources lave both svuchrotron aud iuverse Compton, This means that more luminous sources have both synchrotron and inverse Compton
Jeans equation leaves us with a Jeans equation. only involving the unperturbed velocity dispersious.,"Jeans equation leaves us with a Jeans equation, only involving the unperturbed velocity dispersions."
 The dominating terms iu Eq. (18)), The dominating terms in Eq. \ref{eq:new}) )
 are the derivative and the mass termes., are the derivative and the mass terms.
 Makine the conjecture that the rotation term. which is just a nünor perturbation of the Jeans equation. iust follow the profile of the dominating lnass term. and assunuüugs (for now) that jj=0. we ect directly from Eq. (151) ," Making the conjecture that the rotation term, which is just a minor perturbation of the Jeans equation, must follow the profile of the dominating mass term, and assuming (for now) that $\beta=0$, we get directly from Eq. \ref{eq:new}) )"
a relation between the rotational perturbation aud the dominating mass. which reads Iu principle iau other solutious. than the conjecture of the small term followine the dominant one used above. are allowed to exist. but these would all imply sole deeree of compensation or flne-tumine between he various terms.," a relation between the rotational perturbation and the dominating mass, which reads In principle many other solutions, than the conjecture of the small term following the dominant one used above, are allowed to exist, but these would all imply some degree of compensation or fine-tuning between the various terms."
 We therefore suspect that there is a nore physical. explauatiou. for+ why the ey;V75» torni is. xoportional to eM than our conjecture. but noue las oen found so far.," We therefore suspect that there is a more physical explanation for why the $v_{\textrm{rot}} \sqrt{\sigma_\phi^2}$ term is proportional to $\frac{GM}{r}$ than our conjecture, but none has been found so far."
 The different structures may have fairly cliffereut uaenitudes of the angular momentum. and Eq. (193) ," The different structures may have fairly different magnitudes of the angular momentum, and Eq. \ref{eq:vm}) )"
expresses onlv that the radial of the angular nunoimientuni is alhwavs the same. however. the absolute is unknown. aud may vary from structure to structure.," expresses only that the radial of the angular momentum is always the same, however, the absolute is unknown, and may vary from structure to structure."
 Tn a similar wav we can look at the relationship between the .jz0 aud the rotational term., In a similar way we can look at the relationship between the $\beta \neq 0$ and the rotational term.
 We fiud from Eq. (18)), We find from Eq. \ref{eq:new}) )
 that this connection is This relation miplies that if > eoes to 0. the rotation term should eo to 0 as well.," that this connection is This relation implies that if $\beta$ goes to 0, the rotation term should go to 0 as well."
 Since we are here sueecstineg a rolation between the two minor terms in Eq. (15)), Since we are here suggesting a relation between the two minor terms in Eq. \ref{eq:new}) )
 the relation (20)) müsht not be as strong as relation (19))., the relation \ref{eq:vbeta}) ) might not be as strong as relation \ref{eq:vm}) ).
 The case 3<0 does not occur iu the equilibrated part of the simulated DM halo structure aud has therefore uo relevance to the problem at haud., The case $\beta < 0$ does not occur in the equilibrated part of the simulated DM halo structure and has therefore no relevance to the problem at hand.
 We are aware that 2 is mareinally smaller than 0 iu DM»., We are aware that $\beta$ is marginally smaller than 0 in DM05.
 Tn fact some of our structures also have ος0 in some of the inner most bius., In fact some of our structures also have $\beta<0$ in some of the inner most bins.
" But since we. as well as DM, are working with simulations which are known to rave cifficultics simulating structures at the iunermost varts. such values (which are not much below 0) mast be considered iu agreement with 0 within errors aud does herefore not conflict our suggested relation between beta and "," But since we, as well as DM05, are working with simulations which are known to have difficulties simulating structures at the innermost parts, such values (which are not much below 0) must be considered in agreement with 0 within errors and does therefore not conflict our suggested relation between beta and $\vrot$."
If ou the other hand cosmological siniulatious were to ci.produce an equilibrated structure with a clear rend that a fully resolved smooth region of the structure mad οκO0 this would definitely question the validity of our work., If on the other hand cosmological simulations were to produce an equilibrated structure with a clear trend that a fully resolved smooth region of the structure had $\beta < 0$ this would definitely question the validity of our work.
 Note that including a centrifugal term into the equations will basically give a simall energy couserviug perturbation. which goes as to the new azimuthal velocity dispersion.," Note that including a centrifugal term into the equations will basically give a small energy conserving perturbation, which goes as $\vrot^2$, to the new azimuthal velocity dispersion."
 However this Cot:perturbation is so stall that it is not visible iun the nunerical simulations. and it is therefore ignored.," However this perturbation is so small that it is not visible in the numerical simulations, and it is therefore ignored."
 It is now straight forward to test these sueecsted relations with the results from numerical simulations., It is now straight forward to test these suggested relations with the results from numerical simulations.
 We have argued that there may be clear relations between the new rotational supplement to the Jeaus equation aud the mass- and auisotropy-terunis., We have argued that there may be clear relations between the new rotational supplement to the Jeans equation and the mass- and anisotropy-terms.
" To test this we used 10 intermediately resolved galaxv aud cluster sized nmuuerical sinmulatious of DM halos (Maccióetal.2007).. one high resolution cluster. Cy” 23. aud oue lich resolution galaxy. the ""Via Lactea simulation (Dicinaudotal.2007a.b).."," To test this we used 10 intermediately resolved galaxy and cluster sized numerical simulations of DM halos \citep{mac07}, one high resolution cluster, $_{HR}$ .W3, and one high resolution galaxy, the 'Via Lactea' simulation \citep{diemand,diemand2}."
 The 10 intermediately resolved simulations have been foriued using PRDGRAV. a treecode written hv Joachim Stadel iud Thomas Quinn (Stadel2001).," The 10 intermediately resolved simulations have been performed using PKDGRAV, a treecode written by Joachim Stadel and Thomas Quinn \citep{stad01}."
. The initial conditions are ecuerated with the GRAFIC2 owkage (Bertschineger2001).., The initial conditions are generated with the GRAFIC2 package \citep{bert01}. .
 The starting redshifts +; are set to the time when the standard deviation of he smallest density. fluctuations resolved within the «λαΊο. box reaches 0.2 (the smallest scale resolved witlin the initial conditions is defined as twice the mtra-varticle distance)., The starting redshifts $z_i$ are set to the time when the standard deviation of the smallest density fluctuations resolved within the simulation box reaches $0.2$ (the smallest scale resolved within the initial conditions is defined as twice the intra-particle distance).
 All the halos were ideutified using a SO (Spherical Overdeusitv) aleorithuii (Alaccioetal.2007)., All the halos were identified using a SO (Spherical Overdensity) algorithm \citep{mac07}.
". The cluster-like haloes have been extracted from a63.9 Afpe/h simulation containing 600"" particles. with à uas resolution of =8.98.LOCALfh."," The cluster-like haloes have been extracted from a 63.9 $Mpc/h$ simulation containing $600^3$ particles, with a mass resolution of $m_p=8.98 \times 10^7 M_{\odot}/h$."
" Tho masses of the clusters usedji, for this study are 2.1. L8. and 16«101!A£./h."," The masses of the clusters used for this study are 2.1, 1.8, and 1.6$\times 10^{14} M_{\odot}/h$."
 The ealaxy sized halocs have been obtained by re-sinuuating at high resolution haloes found in the previous simulation., The galaxy sized haloes have been obtained by re-simulating at high resolution haloes found in the previous simulation.
" The simulated lalocs are iu the mass range 0.92.5«1072A7./] and lave a Inass resolutiou of in,L16«10Η./h that gives a iiuiuaun umuber of particles per halo of about 2.5«10° particles.", The simulated haloes are in the mass range $0.9-2.5 \times 10^{12} M_{\odot}/h$ and have a mass resolution of $m_p=4.16 \times 10^5 M_{\odot}/h$ that gives a minimum number of particles per halo of about $2.5 \times 10^6$ particles.
" The Tiegh resolution cluster Cj;54.2. based ocere the PRDCGRAV as well. has 11 iillions particles withi its virial radius and a mass of M=dol&10ΑΕΠ, "," The High resolution cluster $_{HR}$ .W3, based on the PKDGRAV as well, has 11 millions particles within its virial radius and a mass of $ M=1.81\times 10^{14} M_{\odot}/h$."
"The ""Via Lactea (which is also based ou the PRDGRAV code) simulation iucludes 231 nüllioun. particles with force resolutiou of 90 pc. and it includes oue highly equilibrated structure of nass Afoyy=L.77«107AL... containing about SL nüllión particles (αμαoetal. 20072)."," The 'Via Lactea' (which is also based on the PKDGRAV code) simulation includes 234 million particles with force resolution of 90 pc, and it includes one highly equilibrated structure of mass $M_{200}
= 1.77 \times 10^{12} M_\odot$, containing about 84 million particles \citep{diemand}."
 Plotting the rotatiou-term against the mass for the different simulations gives Fie. 3.., Plotting the rotation-term against the mass for the different simulations gives Fig. \ref{fig:vmall}.
" Here the diamonds. triangles. crosses and squares represeut the galaxy sized halos. the cluster sized halos. the μμ simulation and the Dieniandetal.(2007a) ""Via Lactea> high resolution sinmlation respectively,"," Here the diamonds, triangles, crosses and squares represent the galaxy sized halos, the cluster sized halos, the $_{HR}$ .W3 simulation and the \cite{diemand} ""Via Lactea"" high resolution simulation respectively."
 Iu Fie., In Fig.
 5. we see a clear linear relation between the two terms., \ref{fig:vmall} we see a clear linear relation between the two terms.
 This nemus that the gencralized Jeaus equation (Eq. (18))}) , This means that the generalized Jeans equation (Eq. \ref{eq:new}) ))
determines the radial behavior of the rotation. ic. the aneular momentum (7).," determines the radial behavior of the rotation, i.e. the angular momentum $j(r)$."
" This also explains why Bullocketal.(2001) find a strong relation between the angular momentum and the mass in their simulations. since our conjecture resembles the results of Bullock:etal.(2001) ""heu on is coustant."," This also explains why \cite{bullock} find a strong relation between the angular momentum and the mass in their simulations, since our conjecture resembles the results of \cite{bullock} when $\sigma_\phi^2$ is constant."
 We have tested that this relation is not just an effect of choosing (actually deriving) a term in the Jeans equation with the rightunits., We have tested that this relation is not just an effect of choosing (actually deriving) a term in the Jeans equation with the rightunits.
 For instance the term with. Cot!U docs not have a correct relation. to the mass (as Tojseaardctal.(2007). also conchide)., For instance the term with $v_{\textrm{rot}}^2 r$ does not have a correct relation to the mass (as \cite{bach} also conclude).
 Tn a similar wav we can test our sugeested linearrelation. between op2 aud πο= /c.," In a similar way we can test our suggested linearrelation between $\sigma_r^2 \beta$ and $v_{\textrm{rot}}
\sqrt{\sigma_{\phi}^2}$ ."
 Plotting. these quantities for the intermediate resolution halos together with the μμκ and “Via Lactea’ high resolution sinulations gives Fie. L. , Plotting these quantities for the intermediate resolution halos together with the $_{HR}$ .W3 and 'Via Lactea' high resolution simulations gives Fig. \ref{fig:vbeta}. .
Tere we see a clear correlation for the majority of . values., Here we see a clear correlation for the majority of $\beta$ values.
 However. there is some," However, there is some"
Usually it is interpreted in terms of (he svnchrotron radiation.,Usually it is interpreted in terms of the synchrotron radiation.
 However. svnchrotron approximation is nol always valid. in particular when the magnetic fields are highly turbulent.," However, synchrotron approximation is not always valid, in particular when the magnetic fields are highly turbulent."
 Electrons suffer from random. accelerations and do not trace a helical (trajectory., Electrons suffer from random accelerations and do not trace a helical trajectory.
 In general. the radiation spectrum is characterized by the strengtli parameter where Ap is the typical scale of turbulent fields. |B| is the mean value of the turbulent mmagnelic fields. e is the elementary charge. mm is the mass of electron and e is the speed of light (Reville Ixirk 2010).," In general, the radiation spectrum is characterized by the strength parameter where $\lambda_{\mathrm{B}}$ is the typical scale of turbulent fields, $|B|$ is the mean value of the turbulent magnetic fields, $e$ is the elementary charge, $m$ is the mass of electron and $c$ is the speed of light (Reville Kirk 2010)."
" When α>>5. where 5 is the Lorentz [actor of radiating electron. the scale of turbulent. fields is much larger than the Larmor radius r,=5mc/e|D|. and electrons move in an approximately uniform field. so that the svuchrotron approximation is valid."," When $a\gg \gamma$, where $\gamma$ is the Lorentz factor of radiating electron, the scale of turbulent fields is much larger than the Larmor radius $r_g\equiv \gamma m c^2/e|B|$, and electrons move in an approximately uniform field, so that the synchrotron approximation is valid."
 In. contrast. when α<1. Ap is much smaller than the scale r;/5=Ap/a which corresponds (to the emission of the characteristic svnchrotron [lrequency.," In contrast, when $a\ll1$, $\lambda_{\mathrm{B}}$ is much smaller than the scale $r_g/\gamma = \lambda_{\mathrm{B}}/a$ which corresponds to the emission of the characteristic synchrotron frequency."
 In. (his regime. electrons move approximately straightly. and jitter approximation or the weak random field reeime of diffusive svnchrotron radiation (DSR) can be applied (Aledvedey 2010. Fleishman and Urtiev 2010).," In this regime, electrons move approximately straightly, and jitter approximation or the weak random field regime of diffusive synchrotron radiation (DSR) can be applied (Medvedev 2010, Fleishman and Urtiev 2010)."
 For 1a<4. no simple approximation of the radiation spectrum has been known.," For $1\lesssim a \lesssim \gamma$, no simple approximation of the radiation spectrum has been known."
 The standard model of Gamma Rav Bursts (GRD) is based on the svnchrotron radiation from accelerated electrons al the internal shocks., The standard model of Gamma Ray Bursts (GRB) is based on the synchrotron radiation from accelerated electrons at the internal shocks.
 The observational spectra of prompt enussion of GRB can be well fitted by a broken power law spectrum which is called. the Dand function., The observational spectra of prompt emission of GRB can be well fitted by a broken power law spectrum which is called the Band function.
 Around a third of GRBs show a spectrum in the low energy side harder than (he svichrotron theory. predicts., Around a third of GRBs show a spectrum in the low energy side harder than the synchrotron theory predicts.
 To explain (his. other radiation mechanisms are needed.," To explain this, other radiation mechanisms are needed."
 Aleclveclev exaanined relativistic collisionless shocks in relevance to internal shocks ol GRB. and noticed the generation of small scale turbulent magnetic fields near the shock front (Aledvedey Loeb 1999).," Medvedev examined relativistic collisionless shocks in relevance to internal shocks of GRB, and noticed the generation of small scale turbulent magnetic fields near the shock front (Medvedev Loeb 1999)."
 Then he calculated analvUically radiation spectrum from electrons moving in small scale turbulent magnetic fields. to make a harder spectrum than the svuchrotron radiation (\ledvedey 2000).," Then he calculated analytically radiation spectrum from electrons moving in small scale turbulent magnetic fields, to make a harder spectrum than the synchrotron radiation (Medvedev 2000)."
 ILowever. he assumed that (he strength parameter α 15 much smaller than 1 and (hat turbulent field is of one-dimensional structure. which mav be over simplified in general (Fleishman 2006).," However, he assumed that the strength parameter $a$ is much smaller than $1$ and that turbulent field is of one-dimensional structure, which may be over simplified in general (Fleishman 2006)."
 Medvedev also calculated 3-dimensional structure assuming that the turbulent field is highly anisotropic (Aledvedey 2006)., Medvedev also calculated 3-dimensional structure assuming that the turbulent field is highly anisotropic (Medvedev 2006).
 He conclude that the harder spectrum is achieved in head on” case. and that in edge on” case. the spectrum is softer (han svnchrotron radiation.," He conclude that the harder spectrum is achieved in ""head on"" case, and that in ""edge on"" case, the spectrum is softer than synchrotron radiation."
 The spectral index depends on (he angle ϐ between the particle velocity and shock normal with hard spectrum obtained when 9<10° (Medvedev. 2009)., The spectral index depends on the angle $\theta$ between the particle velocity and shock normal with hard spectrum obtained when $\theta \lesssim 10^{\circ}$ (Medvedev 2009).
 Recently several particle-in-cell (VIC) simulations of relativistic collisionless shocks have been performed to study (he nature of turbulent maenetic fields which are generated near, Recently several particle-in-cell (PIC) simulations of relativistic collisionless shocks have been performed to study the nature of turbulent magnetic fields which are generated near
down at hk~021)1.,"down at $k
\sim 0.31$."
" To the inside pauel. we show the BAO wigeles of both Py(k) aud linear ο]. dividing out the Eiseusteiu&IIu(1998) no-wigele"" power spectrin."," In the inside panel, we show the BAO wiggles of both $P_A(k)$ and linear $P_{\delta}(k)$, dividing out the \cite{EH98}
 `no-wiggle' power spectrum."
" The: PT: result of. P4(&) (solid. line). includes. coutributious. from"" Εν(1) as well as P4.(2)", The PT result of $P_A(k)$ (solid line) includes contributions from $\Gamma^{(1)}_A$ as well as $\Gamma^{(2)}_A$.
 SinceT the mmucrical: integration: involving.: (2) becomes extremely tiuc-consmuimes.: we ouly calculate it: up to one-loop order. while: Ἐν(li. is douc to wo-loop order.," Since the numerical integration involving $\Gamma^{(2)}_A$ becomes extremely time-consuming, we only calculate it up to one-loop order, while $\Gamma^{(1)}_A$ is done to two-loop order."
D The agreement with the data measured from simulation is good. eiven the several approximations we rave iade.," The agreement with the data measured from simulation is good, given the several approximations we have made."
" For &=1. the calculation breaks down after &>0.2hAIpeὃν,"," For $a=1$, the calculation breaks down after $k\gtrsim 0.2$."
 Also. the discrepancy with data between k—04 and hk—025 ypeaks at over1054.," Also, the discrepancy with data between $k=0.1$ and $k=0.2$ peaks at over."
. This ↴⋅⋅is where P(2)| becomes dominant.: but is: ον caleulated up to ouc-loop order.," This is where $\Gamma_A^{(2)}$ becomes dominant, but is only calculated up to one-loop order."
 The: dotted ino. prescuts the D'47(1) contribution., The dotted line presents the $\Gamma_A^{(1)}$ contribution.
: For higher: redshifts.HU tho differencesMug between data aud theory become zinaller.," For higher redshifts, the differences between data and theory become smaller."
 At a=QT. the prediction breaks down around &0.28h+.," At $a=0.7$, the prediction breaks down around $k\sim 0.28$."
. In the lower panel of cach figure. we also plot the ratio tween Py(fh) aud the linear power spectrum. after applying the pixel window function.," In the lower panel of each figure, we also plot the ratio between $P_A(k)$ and the linear power spectrum, after applying the pixel window function."
 Iu this paper. we developed the cosmological perturbation theory for the loe-deusity field 4—ας.|4).," In this paper, we developed the cosmological perturbation theory for the log-density field $A=\ln(1+\delta)$."
 In the contest of standard perturbation theory. we showed how differcut simoothing scales cau alter the amplitude of the A power spectrum at large scales.," In the context of standard perturbation theory, we showed how different smoothing scales can alter the amplitude of the $A$ power spectrum at large scales."
 With the help of amulti-point propagators developed in renormalized perturbation theory. we coustructed the building blocks for the power spectrum of the A field.," With the help of multi-point propagators developed in renormalized perturbation theory, we constructed the building blocks for the power spectrum of the $A$ field."
 Iu our formalism. each diagram effectively includes infinitely many loop contributions.," In our formalism, each diagram effectively includes infinitely many loop contributions."
 The Caussian damping of the propagator for the A field eusures that the convergence of the series is well-coutrollec., The Gaussian damping of the propagator for the $A$ field ensures that the convergence of the series is well-controlled.
 We found that except for the large-scale bias. this A propagator. which quautifies the memory of initial conditions as a function of scale. is similar to the à propagator. daumping at a similar length scale.," We found that except for the large-scale bias, this $A$ propagator, which quantifies the memory of initial conditions as a function of scale, is similar to the $\delta$ propagator, damping at a similar length scale."
 This means that the memory of iiode-byauode initial phases aud amplitudes in the A field is not much better than in the 6 field., This means that the memory of mode-by-mode initial phases and amplitudes in the $A$ field is not much better than in the $\delta$ field.
 Even with several approximations. our PT calculation for Py achieves good agrecinent with simulation measurements.," Even with several approximations, our PT calculation for $P_A$ achieves good agreement with simulation measurements."
 However. further work is necessary to obtain results with sufficient precision to resolve the question of whether the mucl-veduced nonhnearity in the shape of P4 compared to P; is understandable perturbatively.," However, further work is necessary to obtain results with sufficient precision to resolve the question of whether the much-reduced nonlinearity in the shape of $P_A$ compared to $P_\delta$ is understandable perturbatively."
 We thank WNatrin IHeitinann aud Adrian Pope for help accessing the Covote Universe simmlations., We thank Katrin Heitmann and Adrian Pope for help accessing the Coyote Universe simulations.
 NW. MN aud AS are grateful for support from the Wiseck aud the Cordon aud Betty Moore Foundations. aud IS frou NASA erauts NNCOGCETIC and NNNIOAD5S3C. and from the Polanuyvi Program of the Wnuearian National Office," XW, MN and AS are grateful for support from the Keck and the Gordon and Betty Moore Foundations, and IS from NASA grants NNG06GE71G and NNX10AD53G, and from the Polánnyi Program of the Hungarian National Office"
αἱ FP A maw result [rom a high coronal pressure which prevents most energetic electrons accelerated in the corona from precipitating deep into the chromosphere ellectively.,at FP A may result from a high coronal pressure which prevents most energetic electrons accelerated in the corona from precipitating deep into the chromosphere effectively.
 Llowever. the pprofile at. FP D is associated with a relatively low coronal pressure. which allows energetic electrons to easily penetrate into (he chromosphere.," However, the profile at FP B is associated with a relatively low coronal pressure, which allows energetic electrons to easily penetrate into the chromosphere."
" We further estimate the coronal column density. NV. in the loop as follows. where EM. vl. and £ are the emission measure. (he loop footpoint area. and the loop length. respectively, which can be derived from theGOES soft X-ray [luxes and images."," We further estimate the coronal column density, $N$, in the loop as follows, where ${\rm EM}$, $A$, and $L$ are the emission measure, the loop footpoint area, and the loop length, respectively, which can be derived from the soft X-ray fluxes and images."
" The quantity of V is estimated to be ~1.0x107"" 7 in the impulsive phase.", The quantity of $N$ is estimated to be $\sim 1.0 \times 10^{20}$ $^{-2}$ in the impulsive phase.
 Since FP A is much denser than FP DB. the coronal cohunn density al FP A may be roughly equal to the value derived above.," Since FP A is much denser than FP B, the coronal column density at FP A may be roughly equal to the value derived above."
 The corresponding enerev £. electrons of οποιον above which can penetrate to the chromosphere. follows (Brown1972:Veronig&Brown2004) where A=2ze!X (with e the electron charge and A the Coulomb logarithm) ancl Vo is the column density. measured in. 10P >7.," The corresponding energy $E$, electrons of energy above which can penetrate to the chromosphere, follows \citep{bro72,ver04} where $K=2 \pi e^4 \Lambda$ (with $e$ the electron charge and $\Lambda$ the Coulomb logarithm) and $N_{19}$ is the column density measured in $10^{19}$ $^{-2}$."
 Inserting. the quantity. VT derived. above into. Eq. (, Inserting the quantity $N$ derived above into Eq. (
3) vields E~27 keV. The consequence is that only ~30% of the beam enerey is deposited into the chromosphere at FP A and therefore the backwarming effect is not significant there.,3) yields $E \simeq 27$ keV. The consequence is that only $\sim 30$ of the beam energy is deposited into the chromosphere at FP A and therefore the backwarming effect is not significant there.
 In comparison. we believe that electron heating of the chromosphere followed by the backwarming ellect results in the continuum enhancement al FP D. Using the same method as in Dingetal.(2003b).. we perform calculations that can preclict (he continuum enhancement from a model atinosphere that is bombarded by an electron beam.," In comparison, we believe that electron heating of the chromosphere followed by the backwarming effect results in the continuum enhancement at FP B. Using the same method as in \citet{din03b}, we perform calculations that can predict the continuum enhancement from a model atmosphere that is bombarded by an electron beam."
 Figure 6 shows the continuum enhancement at A=6600 aas a [unction of the beam energy f[Iux., Figure 6 shows the continuum enhancement at $\lambda=6600$ as a function of the beam energy flux.
 It is seen that an electron beam with an energy fIux of 0.8 x cean produce a continuum enhancement of e&%.., It is seen that an electron beam with an energy flux of 0.8 $\times$ can produce a continuum enhancement of $\sim 8$.
 Thus. the energy. [Iux derived for FP D seenis enough {ο meet the energv requirement of the continuum enhancement.," Thus, the energy flux derived for FP B seems enough to meet the energy requirement of the continuum enhancement."
 However. we should mention that the deduced energy. [αν sulfers a great uncertainty that arises indeed from the uncertainty of the low-energy eutolf of the electron beam.," However, we should mention that the deduced energy flux suffers a great uncertainty that arises indeed from the uncertainty of the low-energy cutoff of the electron beam."
 As shown in Figure 2. (he nonthermal component of the INR emission in the two EPs is still visible below 20 keV: therefore. if we select a low-enerev cutoff lower than 20 keV. καν. 15 keV. the deduced beam enerev flux will be 23 times that if adopting the usually assumed low-enerev eutotff of 20 keV.," As shown in Figure 2, the nonthermal component of the HXR emission in the two FPs is still visible below 20 keV; therefore, if we select a low-energy cutoff lower than 20 keV, say, 15 keV, the deduced beam energy flux will be 2–3 times that if adopting the usually assumed low-energy cutoff of 20 keV."
does not exhibit a negative profile. characteristic of the inner galactic regions.,"does not exhibit a negative profile, characteristic of the inner galactic regions."
 The value of the slope is independent of the exact set of stellar evolutionary tracks used (although the older. more a-enhanced tsochrones result in lower overall metallicities). (," The value of the slope is independent of the exact set of stellar evolutionary tracks used (although the older, more $\alpha$ -enhanced isochrones result in lower overall metallicities). ("
v) The outer disk metallicity gradient is in disagreement with the inner disk slope.,v) The outer disk metallicity gradient is in disagreement with the inner disk slope.
 The inner and outer disk abundances in the overlap region are potentially in agreement after o/Fe] ratio. age-metallicity relationship and the use of specific abundance indicators have been taken into Results presented in refsec:mdf suggest that the abundance gradient derived from outer disk stellar [Fe/H] metallicities differs in slope from the gradient calculated using [O/H] abundances from inner disk HII regions (Figure 7)).," The inner and outer disk abundances in the overlap region are potentially in agreement after $\alpha$ /Fe] ratio, age-metallicity relationship and the use of specific abundance indicators have been taken into Results presented in \\ref{sec:mdf} suggest that the abundance gradient derived from outer disk stellar [Fe/H] metallicities differs in slope from the gradient calculated using [O/H] abundances from inner disk HII regions (Figure \ref{gradient}) )."
 However. the two cannot be directly compared as the latter dataset probes recent gas abundances. while the former refers to chemical composition in. stars that are at least a couple of Gyr old.," However, the two cannot be directly compared as the latter dataset probes recent gas abundances, while the former refers to chemical composition in stars that are at least a couple of Gyr old."
 In addition. given the results of ?.. which suggest that gas and stellar metallicities are decoupled and follow opposite trends. it is difficult to conclude whether our results point to an overall abundance gradient that gets shallower or steeper with time.," In addition, given the results of \citet{roskar08b}, which suggest that gas and stellar metallicities are decoupled and follow opposite trends, it is difficult to conclude whether our results point to an overall abundance gradient that gets shallower or steeper with time."
 (Modelsoftrends.e.g.2222?) However. our results support the scenario presented by ? in which gas abundances become steeper with time (this is consistent with relatively steep inner disk slope in NGC 7793) and the stellar abundance gradient in old stars is shallower than that in young stars.," \citep[Models of galactic chemical
evolution are successful in reproducing both trends,
e.g.][]{molla97,boissierprantzos99,portinarichiosi99,tosi88,chiappini01}
 However, our results support the scenario presented by \citet{roskar08b} in which gas abundances become steeper with time (this is consistent with relatively steep inner disk slope in NGC 7793) and the stellar abundance gradient in old stars is shallower than that in young stars."
 Although the stellar metallicity is the primary. factor influencing colors of RGB stars. age-metallicity degeneracy and the assumption of single age in calculating the metallicity distribution function introduce uncertainties in the derived MDF.," Although the stellar metallicity is the primary factor influencing colors of RGB stars, age-metallicity degeneracy and the assumption of single age in calculating the metallicity distribution function introduce uncertainties in the derived MDF."
 As shown in Figure 7.. the derived metallicity gradient is practically independent on adopted tsochrones. assuming that age gradient over the extent of the disk is close to constant; a non-zero age gradient would result in a different metallicity profile.," As shown in Figure \ref{gradient}, the derived metallicity gradient is practically independent on adopted isochrones, assuming that age gradient over the extent of the disk is close to constant; a non-zero age gradient would result in a different metallicity profile."
 Negative age gradient in the outer disk of NGC 7793 would suggest that the real abundance gradient has a higher slope than derived under a constant age assumption., Negative age gradient in the outer disk of NGC 7793 would suggest that the real abundance gradient has a higher slope than derived under a constant age assumption.
 Stellar ages which decrease with radius are indeed consistent with the inside-out scenario for galaxy formation (?2?2?)..," Stellar ages which decrease with radius are indeed consistent with the inside-out scenario for galaxy formation \citep{larson76,matteuccifrancois89,chiappini97,naabostriker06,munozmateos07}."
 In this picture. a galaxy’s inner regions are built up at earlier times than outer parts. and as a result contain on average older stars than outermost regions.," In this picture, a galaxy's inner regions are built up at earlier times than outer parts, and as a result contain on average older stars than outermost regions."
 However. recent results from resolved stars (2???) and surface photometry (?) seem to suggest that positive age gradients are frequently observed in outer disks of spirals.," However, recent results from resolved stars \citep{barker07,williams09,williams10} and surface photometry \citep{bakos08} seem to suggest that positive age gradients are frequently observed in outer disks of spirals."
 This is supported by recent simulations of disk evolution (222)... which find that radial migrations of stars within the disk are responsible for the reversed age profile at large radii.," This is supported by recent simulations of disk evolution \citep{roskar08a,roskar08b,sanchezblazquez09}, which find that radial migrations of stars within the disk are responsible for the reversed age profile at large radii."
 If the same holds in NGC 7793. the true abundance gradient would be negative. flat or mildly positive. depending on the magnitude of this effect.," If the same holds in NGC 7793, the true abundance gradient would be negative, flat or mildly positive, depending on the magnitude of this effect."
 There is a broad agreement that negative stellar abundance gradients. easily explained in the context of inside-out models for galaxy formation (??).. are a common feature of disk galaxies (???)..," There is a broad agreement that negative stellar abundance gradients, easily explained in the context of inside-out models for galaxy formation \citep{goetzkoeppen92,matteuccifrancois89}, are a common feature of disk galaxies \citep{zaritsky94,ferguson98,gogarten10}."
 Surface density. yield and star formation all decrease with radius. resulting in metallicity distribution that is More metal-rich in central parts and decreases progressively towards the outer disk.," Surface density, yield and star formation all decrease with radius, resulting in metallicity distribution that is more metal-rich in central parts and decreases progressively towards the outer disk."
 However. abundance profiles in faint outer disks are more difficult to derive and there ts no general consensus on their shape and origin.," However, abundance profiles in faint outer disks are more difficult to derive and there is no general consensus on their shape and origin."
 Growing body of evidence suggests that (most) spirals exhibit a flattening of their metallicity gradient in the outermost disk., Growing body of evidence suggests that (most) spirals exhibit a flattening of their metallicity gradient in the outermost disk.
 Observationally. the strongest case has been made for the Galaxy (222?).. M83 (2).. and M31 (?)..," Observationally, the strongest case has been made for the Galaxy \citep{andrievsky04,yong06,carraro07,pedicelli09}, M83 \citep{bresolin09}, and M31 \citep{worthey05}."
" In the models of ?.. 2. and ?. stellar radial mixing has been shown to be able to produce flat abundance profiles by ""smoothing out the underlying negative gradient."," In the models of \citet{roskar08a}, \citet{roskar08b} and \citet{sanchezblazquez09}, stellar radial mixing has been shown to be able to produce flat abundance profiles by 'smoothing out' the underlying negative gradient."
 On the other hand. a mildly positive metallicity gradient has been observed in NGC 300 (?)..," On the other hand, a mildly positive metallicity gradient has been observed in NGC 300 \citep{vlajic09}."
 As mentioned earlier. a positive age gradient in. the outer disk of NGC 7793 would bias our derivation of abundance profile and a flat underlying metallicity profile would be observed as a positive gradient mstead.," As mentioned earlier, a positive age gradient in the outer disk of NGC 7793 would bias our derivation of abundance profile and a flat underlying metallicity profile would be observed as a positive gradient instead."
 Our positive metallicity gradient in the NW field could therefore be interpreted as a combination of a flat abundance and positive age gradient., Our positive metallicity gradient in the NW field could therefore be interpreted as a combination of a flat abundance and positive age gradient.
 This particular combination of age and metallicity behavior has been found to arise as a consequence of stellar migrations (??)..," This particular combination of age and metallicity behavior has been found to arise as a consequence of stellar migrations \citep{roskar08b,sanchezblazquez09}."
 On the other hand. it is possible that the positive metallicity gradient in NGC 7793 is real and does not reflect the effects of age-metallicity degeneracy.," On the other hand, it is possible that the positive metallicity gradient in NGC 7793 is real and does not reflect the effects of age-metallicity degeneracy."
 ? find that the overlap of spiral and bar resonances in the disk triggers significant migration of stars and results in positive abundance profile in the outermost regions. similar to what we observe in NGC 7793.," \citet{minchev10b} find that the overlap of spiral and bar resonances in the disk triggers significant migration of stars and results in positive abundance profile in the outermost regions, similar to what we observe in NGC 7793."
 Alternatively. an external mechanism could be responsible for the shape of the metallicity gradient in outer disks of spirals.," Alternatively, an external mechanism could be responsible for the shape of the metallicity gradient in outer disks of spirals."
 In NGC 7793 in particular. the origin of a particular abundance profile could be explained by the fact that the galaxy harbors a surprisingly small disk.," In NGC 7793 in particular, the origin of a particular abundance profile could be explained by the fact that the galaxy harbors a surprisingly small disk."
 While a great majority of spirals have more or less extended disks. sometimes stretching out far beyond the known optical edges. neutral hydrogen in NGC 7793 is detected only out to ~11.5% (2?).. covering practically the same radial extent as our stellar photometry. (," While a great majority of spirals have more or less extended disks, sometimes stretching out far beyond the known optical edges, neutral hydrogen in NGC 7793 is detected only out to $\sim11.5'$ \citep{carignanpuche90,walter08}, covering practically the same radial extent as our stellar photometry. ("
In addition. NGC 7793 exhibits a decreasing velocity curve in its outermost parts. which is highly unusual for a galaxy of its size.),"In addition, NGC 7793 exhibits a decreasing velocity curve in its outermost parts, which is highly unusual for a galaxy of its size.)"
 The reason for a relatively modest disk in NGC 7793 is unclear. particularly given that the galaxy has no obvious interactions that could have potentially stripped the gas and truncated its distribution.," The reason for a relatively modest disk in NGC 7793 is unclear, particularly given that the galaxy has no obvious interactions that could have potentially stripped the gas and truncated its distribution."
 Evidence for stripped stars in the outer disk of NGC 7793 1s also lacking., Evidence for stripped stars in the outer disk of NGC 7793 is also lacking.
 However. it is possible to imagine that the upturn in the abundance gradient in the NW field is a consequence of a dispersed stream of stars that have long fallen below the detectability threshold 1n surface brightness. but still pollute the outer disk metallicities.," However, it is possible to imagine that the upturn in the abundance gradient in the NW field is a consequence of a dispersed stream of stars that have long fallen below the detectability threshold in surface brightness, but still pollute the outer disk metallicities."
 Similar to stellar age. positive gradient in [o/Fe] would — under the assumption of constant [a/Fe] — be disguised as a positive gradient in metallicity.," Similar to stellar age, positive gradient in $\alpha$ /Fe] would – under the assumption of constant $\alpha$ /Fe] – be disguised as a positive gradient in metallicity."
 Accounting for the [a/Fe] increase from zero to 0.3 over the range covered by our data would likely not result in a flat abundance gradient. but would certainly lower the slope of the gradient we derive for the NW field.," Accounting for the $\alpha$ /Fe] increase from zero to $0.3$ over the range covered by our data would likely not result in a flat abundance gradient, but would certainly lower the slope of the gradient we derive for the NW field."
 Finally. the shape of the metallicity gradient in the outer disk could be primordial. originating in. specific. galaxy formation processes taking place at high redshift.," Finally, the shape of the metallicity gradient in the outer disk could be primordial, originating in specific galaxy formation processes taking place at high redshift."
 ? show that rotating systems at c3 show positive abundance gradients., \citet{cresci10} show that rotating systems at $\;\approx3$ show positive abundance gradients.
 These are presumed to be generated by cold streams depositing pristine material into the centers of galaxies., These are presumed to be generated by cold streams depositing pristine material into the centers of galaxies.
 In today’s galaxies the early positive gradient in galactic center is reversed through processes of star formation and chemical evolution. while the signs of the early gradient remain in the outskirts of galaxies.," In today's galaxies the early positive gradient in galactic center is reversed through processes of star formation and chemical evolution, while the signs of the early gradient remain in the outskirts of galaxies."
 From the perspective of potential for star formation or radial migration in a given region of a spiral disk. it is interesting to examine the radial behavior of the Toomre Q parameter.," From the perspective of potential for star formation or radial migration in a given region of a spiral disk, it is interesting to examine the radial behavior of the Toomre $Q$ parameter."
 In a thin differentially rotating disk. rotation and pressure work to stabilize the disk against axisymmetric perturbations.," In a thin differentially rotating disk, rotation and pressure work to stabilize the disk against axisymmetric perturbations."
 On the, On the
eet al.,et al.
 1999: Dunham οἱ al., 1999; Dunham et al.
 2006)., 2006).
 Furthermore. the Noll emission. observed with the Plateau de Bure Interferometer (PDBI) and the IRANI 30 m telescope. shows a hole in the center of the envelope (Belloche 22004).," Furthermore, the $_2$ $^+$ emission, observed with the Plateau de Bure Interferometer (PDBI) and the IRAM 30 m telescope, shows a hole in the center of the envelope (Belloche 2004)."
 In general. Noll emission tends (ο peak towards the center of starless cores (Lee el al.," In general, $_2$ $^+$ emission tends to peak towards the center of starless cores (Lee et al."
 2003). but. be deficient. [rom the centers of Class 0/1 sources due to destruction by CO as il evaporates (Lee et al.," 2003), but be deficient from the centers of Class 0/I sources due to destruction by CO as it evaporates (Lee et al."
 2004)., 2004).
 IRAM 04191 shows moderate CO depletion (Crapsi et al., IRAM 04191 shows moderate CO depletion (Crapsi et al.
 2004): Belloche ((2004) suggest Chat Ireeze-out of No in the high-density. inner envelope might result in the observed Noll hole.," 2004); Belloche (2004) suggest that freeze-out of $_2$ in the high-density, inner envelope might result in the observed $_2$ $^+$ hole."
 ILowever. if [reeze-out of No is significant enough to explain this hole. there should be sienilicantly more deuteration and depletion of CO than observed (Crapsi et al.," However, if freeze-out of $_2$ is significant enough to explain this hole, there should be significantly more deuteration and depletion of CO than observed (Crapsi et al."
 2004). similar to (hiat seen in prestellar cores (Lee et al.," 2004), similar to that seen in prestellar cores (Lee et al."
 2003)., 2003).
 In this studs. we model the chemical evolution in the process of episoclic accretion (o provide a possible explanation of the chemical distributions of CO and Nell in gas and to preclict observable consequences in the COs ice feature in VeLLOs such as IAM 04191 that show strong evidence for undergoing such a process.," In this study, we model the chemical evolution in the process of episodic accretion to provide a possible explanation of the chemical distributions of CO and $_2$ $^+$ in gas and to predict observable consequences in the $_2$ ice feature in VeLLOs such as IRAM 04191 that show strong evidence for undergoing such a process."
 We use the chemo-dsynamical model developed by Lee et al. (, We use the chemo-dynamical model developed by Lee et al. (
2004).,2004).
 This model calculates the chemical evolution. of a model core evolving from the prestellar stage through the embedded protostellar stages., This model calculates the chemical evolution of a model core evolving from the prestellar stage through the embedded protostellar stages.
 The dynamical evolution is described by combining a sequence of Donnor-Ebert spheres (Bonnor 1956. Ebert 1955) with the inside-out collapse model (Shu 1977). where the accretion rate from the envelope onto the star+disk svstem is constant.," The dynamical evolution is described by combining a sequence of Bonnor-Ebert spheres (Bonnor 1956, Ebert 1955) with the inside-out collapse model (Shu 1977), where the accretion rate from the envelope onto the star+disk system is constant."
 The model also includes the First Hyerostatie Core (FIISC) stage. which results [rom the first erxavitational collapse of a dense molecular core and lasts until (the core temperature reaches 2000 Ix. and the dissociation of molecular hydrogen causes the second collapse (Boss 1993. Masunaga et al.," The model also includes the First Hydrostatic Core (FHSC) stage, which results from the first gravitational collapse of a dense molecular core and lasts until the core temperature reaches 2000 K and the dissociation of molecular hydrogen causes the second collapse (Boss 1993, Masunaga et al."
 1998)., 1998).
 The radius of the FIISC is about 5 AU. and the disk is not vet well developed at this stage.," The radius of the FHSC is about 5 AU, and the disk is not yet well developed at this stage."
 As a result. (he accretion luminosity arising from accretion onto the FIISC is not significant.," As a result, the accretion luminosity arising from accretion onto the FHSC is not significant."
 The evolution of the central liminosity follows that adopted bv Young Evans (2005). who incorporated the evolution of an unresolved disk and stellar photosphere into the central Iuminositv.," The evolution of the central luminosity follows that adopted by Young Evans (2005), who incorporated the evolution of an unresolved disk and stellar photosphere into the central luminosity."
 This huninositv is proportional to the accretion Iuninosity arising from envelope accretion following the inside-out collapse model (see Young Evans 2005 [or details)., This luminosity is proportional to the accretion luminosity arising from envelope accretion following the inside-out collapse model (see Young Evans 2005 for details).
 In this study. we assume that the accretion [rom the envelope to the disk is constant. but the accretion [rom the disk (to the star is episoclic.," In this study, we assume that the accretion from the envelope to the disk is constant, but the accretion from the disk to the star is episodic."
 Thus. the envelope density structure is identical to that of the inside-out collapse model. but the internal Iuninosity is changed," Thus, the envelope density structure is identical to that of the inside-out collapse model, but the internal luminosity is changed"
as the data released by the Auger collaboration in 2007 only included: 27 events. which is too sparse to make sub-samples with cifferent energies.,"as the data released by the Auger collaboration in 2007 only included 27 events, which is too sparse to make sub-samples with different energies."
 We show in Table 1. the values in the parameter space explored in our study for these three parameters c. Dive. and Alp.," We show in Table \ref{tab:scan} the values in the parameter space explored in our study for these three parameters $\psi$, $D_{max}$ and $M_{\rmn{B}}$."
 We note that the most finely scanned quantity is the angular separation c. which is related to the dellection angle by the intervening magnetic fields.," We note that the most finely scanned quantity is the angular separation $\psi$, which is related to the deflection angle by the intervening magnetic fields."
 The small number of galaxies in the catalogue of 7? do not allow to perform a fine slicing in all the three parameters simultaneously. so we choose Ae=(7.1 for comparison with Fig.," The small number of galaxies in the catalogue of \citet{2004AJ....127.2031K} do not allow to perform a fine slicing in all the three parameters simultaneously, so we choose $\Delta\psi=0^{\circ}.1$ for comparison with Fig."
 3 in ?.. and took several slices in distance ancl Luminosity.," 3 in \citet{2008APh....29..188T}, and took several slices in distance and luminosity."
 The sampled values according to ‘Table 1 extends over a grid. of only 5.325 points in this space. which is computationally inexpensive.," The sampled values according to Table \ref{tab:scan} extends over a grid of only 5,325 points in this space, which is computationally inexpensive."
 In order to have an estimation of the probability. of rejecting the null hypothesis (ie. that the UlllZClts in our sample show a distribution compatible with isotropy). we need to calculate. the probability. of correlation with a possible isotropic Εαν. following ?..," In order to have an estimation of the probability of rejecting the null hypothesis (i.e. that the UHECRs in our sample show a distribution compatible with isotropy), we need to calculate the probability of correlation with a possible isotropic flux, following \citet{2008APh....29..188T}."
 Provided that a particular combination of values for our three parameters can show a pronounced minimum in this probability. we have to explore the full parameter space so that we can study the case in which isotropy. seems to be unlikely.," Provided that a particular combination of values for our three parameters can show a pronounced minimum in this probability, we have to explore the full parameter space so that we can study the case in which isotropy seems to be unlikely."
 Therefore. for each set of values of our parameters we evaluate the probability. of isotropic Hux associated. to (at. least) Neo correlated: source.cosmicray event pairs.," Therefore, for each set of values of our parameters we evaluate the probability of isotropic flux associated to (at least) $N_{\rmn{corr}}$ correlated source–cosmicray event pairs."
 This is given as expected by the binomial distribution: where p is the probability that an event drawn from isotropy correlates with a ealaxy within c. using the sub-sample given by the other two parameters.," This is given as expected by the binomial distribution: where $p$ is the probability that an event drawn from isotropy correlates with a galaxy within $\psi$, using the sub-sample given by the other two parameters."
 To make this more clear. let us assume that the observatory has uniform exposure for the entire sky.," To make this more clear, let us assume that the observatory has uniform exposure for the entire sky."
 In this case the circles in the sky of radius c around galaxies in the catalogue which are brighter than Aj and nearer than Ds deline an area which is a fraction p of the full 4a sr sky., In this case the circles in the sky of radius $\psi$ around galaxies in the catalogue which are brighter than $M_{\rmn{B}}$ and nearer than $D_{\mathrm{max}}$ define an area which is a fraction $p$ of the full $4\pi$ sr sky.
 Phe value of p is estimated by \lonteCarlo sampling of the sphere. calculating the fraction of points whose distance to a galaxy in the catalogue is smaller than a given angle c.," The value of $p$ is estimated by MonteCarlo sampling of the sphere, calculating the fraction of points whose distance to a galaxy in the catalogue is smaller than a given angle $\psi$."
 For very small values of c. this estimation is straightforward as the areas covered by individual galaxies do not overlap. and hence the total area is equal to the number of galaxies IN times the area covered by the spherical cap subtended by the angle c. ic. OON(Lcose}," For very small values of $\psi$, this estimation is straightforward as the areas covered by individual galaxies do not overlap, and hence the total area is equal to the number of galaxies $N$ times the area covered by the spherical cap subtended by the angle $\psi$, i.e. $0.5N(1-\cos\psi)$."
 On the other hand. for large values of oor larec number of galaxies. the area around individual galaxies will overlap and this approximation is no longer valid. so a numerical estimation is needed.," On the other hand, for large values of $\psi$ or large number of galaxies, the area around individual galaxies will overlap and this approximation is no longer valid, so a numerical estimation is needed."
 In the general case. we also need to take into account the declination dependence on the exposure due to partial skv coverage by the observatory.," In the general case, we also need to take into account the declination dependence on the exposure due to partial sky coverage by the observatory."
 ‘This is done by generating events according to the relative exposure distribution «(3)., This is done by generating events according to the relative exposure distribution $\omega(\delta)$.
" The number of points we used in the MonteCarlo sampling of the sphere is 10"" so we have a 10. uncertainty on the determination of p for cach node in the grid of the parameter space.", The number of points we used in the MonteCarlo sampling of the sphere is $10^6$ so we have a $10^{-3}$ uncertainty on the determination of $p$ for each node in the grid of the parameter space.
 We now apply the method cdeseribed in the previous Section to caleulate the probability in the case of isotropic [lux of Noor correlated sourcecosmic ray event pairs. as a function of the parameters c. {δω and Ale.," We now apply the method described in the previous Section to calculate the probability in the case of isotropic flux of $N_{\mathrm{corr}}$ correlated source–cosmic ray event pairs, as a function of the parameters $\psi$ , $D_{max}$ and $M_{B}$."
 A full exploratory scan is performed over the entire parameter space. and. as a result. we find that this probability reaches its absolute minimum (hereafter. Lita) at cosmic ray event dellections below of=30 and galaxies accelerating VILECRs with distances below Dias=4Mpc and brighter than AMj-15.," A full exploratory scan is performed over the entire parameter space, and as a result we find that this probability reaches its absolute minimum (hereafter $P_{\rmn{data}}$ ) at cosmic ray event deflections below $\psi=3.0^{\circ}$ and galaxies accelerating UHECRs with distances below $D_{\rmn{max}}=4$ Mpc and brighter than $M_{\rmn{B}}$ =-15."
 ‘This implies a preference for the VLLECRs arrival directions to be correlated with the nearest and most luminous galaxies in the catalogue. while the angular distance between the cosmic rav events and their possible sources is similar to that found by ? using AGNs instead. of local. galaxies.," This implies a preference for the UHECRs arrival directions to be correlated with the nearest and most luminous galaxies in the catalogue, while the angular distance between the cosmic ray events and their possible sources is similar to that found by \citet{2008APh....29..188T} using AGNs instead of local galaxies."
 In order to visualize the dependence. of this. probability with individual parameters. we refer to Figure 2..," In order to visualize the dependence of this probability with individual parameters, we refer to Figure \ref{fig:scan}."
 Here we display the chance probability of correlation with the Auger VLECKs above £&£>55 EeV as a function of each one of the scan parameters. keeping the other two parameters. [ixed at the absolute minimum of the probability of isotropic lux.," Here we display the chance probability of correlation with the Auger UHECRs above $E>55$ EeV as a function of each one of the scan parameters, keeping the other two parameters fixed at the absolute minimum of the probability of isotropic flux."
 When the angular distance c varies. we find several local minima. although the region in which the chance correlation probability is below is in the range of 4°.," When the angular distance $\psi$ varies, we find several local minima, although the region in which the chance correlation probability is below is in the range of $^{\circ}$."
 On the other hand. the behaviour with the other two scan parameters is quite robust with a single minimum. although this is also due to the coarseness in the scanning values in this case.," On the other hand, the behaviour with the other two scan parameters is quite robust with a single minimum, although this is also due to the coarseness in the scanning values in this case."
 Nevertheless. it seems clear that including cistant ancl intrinsically faint sources decreases the correlation signal.," Nevertheless, it seems clear that including distant and intrinsically faint sources decreases the correlation signal."
 Moreover. given the value. of ce the deflection of cosmic ràv trajectories due to intervening magnetic fields is not large. suggesting that these events are light nuclei. as suggested by 2," Moreover, given the value of $\psi$ the deflection of cosmic ray trajectories due to intervening magnetic fields is not large, suggesting that these events are light nuclei, as suggested by \citet{2008APh....29..188T}."
" As shown in Figure 2.. the probability at the absolute minimun is Pu,=Ll.10+."," As shown in Figure \ref{fig:scan}, the probability at the absolute minimum is $P_{\rmn{data}}=1.1\times 10^{-4}$."
" This signal is similar to the previous result of 2... who found. Pua,=2]03, and even stronger than the revised result by 2.. who found that Pusm67107 for the correlation with AGNs up to T5Alpe."," This signal is similar to the previous result of \citet{2008APh....29..188T}, who found $P_{\rmn {data}}=2\times10^{-4}$, and even stronger than the revised result by \citet{2009arXiv0906.2347T}, who found that $P_{\rmn {data}}=6\times10^{-3}$ for the correlation with AGNs up to $75$ Mpc."
 Nevertheless. our result is not free from the negative impact of trial factors in a posteriori anisotropy searches. as i was not tested on an independent. data set with the scan parameters specified a priori.," Nevertheless, our result is not free from the negative impact of trial factors in a posteriori anisotropy searches, as it was not tested on an independent data set with the scan parameters specified a priori."
 For reference. the Auger result including all the 27 events is Zu—4.6107.," For reference, the Auger result including all the 27 events is $P_{\rmn {data}}=4.6\times10^{-9}$."
 Also. our value is very sensitive to the low number of correlating events at this minimum (five cosmic ravs associated to four sources). so removing one ULLECIU can boost Pats to 1.1010," Also, our value is very sensitive to the low number of correlating events at this minimum (five cosmic rays associated to four sources), so removing one UHECR can boost $P_{\rmn{data}}$ to $1.10\times 10^{-3}$."
 llowever. it js important to note that Eq. (1))," However, it is important to note that Eq. \ref{eqn:binom}) )"
" is not the true probability. of chance correlation due to isotropic Lux. as pointed out by ον, "," is not the true probability of chance correlation due to isotropic flux, as pointed out by \citet{2004APh....21..359F}. ."
Although this exploratory scan is useful in order to detect the location of the strongest. potential correlation signal. the fact that we havechosen our parameters in such a way to get the münimum. value of this probability has to be taken into account.," Although this exploratory scan is useful in order to detect the location of the strongest potential correlation signal, the fact that we havechosen our parameters in such a way to get the minimum value of this probability has to be taken into account."
 In order to correct the value Z4 that we have, In order to correct the value $P_{\rmn{data}}$ that we have
other elements.,other elements.
" The ο. wj, and C parameters depends on the electron temperature Τ,."," The $\alpha_{rad}$ , $\alpha_{die}$ and $C$ parameters depends on the electron temperature $_e$."
 The I coefficients were adopted from the WJ2 model (deBoereral. (1973)))., The $\Gamma$ coefficients were adopted from the WJ2 model \cite{Boer}) ).
" The recombination coefficients (oj, and aye) and the collisional ionisation rate coefficient (C) for the Ca and Fe elements were adopted from Shull&vanSteenberg (1982).", The recombination coefficients $\alpha_{rad}$ and $\alpha_{die}$ ) and the collisional ionisation rate coefficient $C$ ) for the Ca and Fe elements were adopted from \cite{Shull}. .
. For K and Na these parameters wereadopted from Landini&MonsignortFosi(1991) and) Landini&MonsignoriFost(1990)., For K and Na these parameters wereadopted from \cite{Landini1991} and \cite{Landini1990}.
". For Τί «ce, was adopted from Badnellefa£.(2006) and die comes from Mazzottaetαἱ.", For Ti $\alpha_{rad}$ was adopted from \cite{Badnell} and $\alpha_{die}$ comes from \cite{Mazzotta}.
(1998)... The collisional ionisation rate coefficient (C) for Ti was adopted from Voronov(1997)., The collisional ionisation rate coefficient $C$ ) for Ti was adopted from \cite{Voronov}.
. The CH and CN molecules are not present in. CaFe clouds (Bondarefaf. (2007)))., The CH and CN molecules are not present in CaFe clouds \cite{Bondar}) ).
 The CH column. density is directly proportional to the column density of the Ἡ» molecule (eg. Federman(19532)... Dankseta£.(1984).. Gnacifiskieral. (2007))).," The CH column density is directly proportional to the column density of the $_2$ molecule (eg. \cite{Federman}, \cite{Danks}, \cite{GnaKroKre}) )."
 Furthermore. the H+ molecule is known to be formed on dust grains.," Furthermore, the $_2$ molecule is known to be formed on dust grains."
 We infer that the of simple molecules is caused by grains completely a in CaFe clouds., We infer that the absence of simple molecules is caused by grains completely missing in CaFe clouds.
 Weingartner Drainehave MEN recombinations on polycyclie& aromatic hydrocarbons(2001) Eo and on dust grains to play an important role in ion ο... in cold neutral medium., \cite{Weingartner} have proposed recombinations on polycyclic aromatic hydrocarbons (PAHs) and on dust grains to play an important role in ion recombinations in cold neutral medium.
 Since we do not P the simplest molecules in CaFe clouds we do not 3 + recombinations on PAHs or dust grains here., Since we do not observe even the simplest molecules in CaFe clouds we do not consider the recombinations on PAHs or dust grains here.
 3 Ca equation necessary to determine Λίσα T) andook Na inour model was the conservation of thenumber of L Ti 0.0 —dq6 II) wascalculated from the ionisation Fig. 2. observed N(Ca ID., The second equation necessary to determine $N(Ca\:I)$ and $N(Ca\:II)$ in our model was the conservationof the number of Ca atoms: where $N(Ca\:III)$ was calculated from the ionisation equilibrium with observed $N(Ca\:II)$.
 Wehave used arrows shows System. Abundances (SSA) as given by Grevesse &, We have used the Solar System Abundances (SSA) as given by \cite{Grevesse}.
 Sauval(2000)...Otherelements (eg., Other elements (eg.
" Fe) have the second ionisation potential larger or close to 13.6 eV. and are present in the interstellar medium only in two tonisation stages: The hydrogen column density N(H). the electron density n; and the electron temperature T, were treated as free parameters."," Fe) have the second ionisation potential larger or close to 13.6 eV, and are present in the interstellar medium only in two ionisation stages: The hydrogen column density N(H), the electron density $_e$ and the electron temperature $_e$ were treated as free parameters."
 We have used the procedure Pressetal.(1996). to find the minimum of the y function: where XzCa I. Ca II. Na I. Fe I. K Land Ti IL.," We have used the procedure \cite{Press} to find the minimum of the $\chi$ function: where $X$ =Ca I, Ca II, Na I, Fe I, K I and Ti II."
 The model that fits the observedcolumn densities is presented in Table 2.., The model that fits the observedcolumn densities is presented in Table \ref{model}. .
 N(H) is the column density of hydrogen in a single analysed cloud., N(H) is the column density of hydrogen in a single analysed cloud.
" Physical condition are described bythe electron density n, and the electron temperature T,.", Physical condition are described bythe electron density $_e$ and the electron temperature $_e$ .
 For, For
"M<0.45Mo, (WDs).(2005) 0.4x10719 pc? yr-!, ~10% ~0.5 Mc (Hansenetal]2007), (2006) J09174-4638 |Kilicetal.|(2007alb)) Tog=11,855 g M£z0.17Mo. M«0.1Mo, uncovered variations with a period of 7.6 hr, implying that the mass of the companion is >0.28Mo (Kilic⋅⋅","$M < 0.45\ M_\odot$ \citet{liebert05} $0.4\times10^{-13}$ $^{-3}$ $^{-1}$ $\sim$ $\%$ $\sim$ $M_\odot$ \citep{hansen07}, \citet{brown06} $+$ \citet{kilic07a,kilic07b} $T_{\rm eff}= 11,855$ $g$ $M\approx0.17 M_\odot$ $M < 0.1\ M_\odot$ uncovered variations with a period of 7.6 hr, implying that the mass of the companion is $\geq 0.28\ M_\odot$ \citep{kilic07b}."
 What is the nature of this companion?, What is the nature of this companion?
" While LMWDs are found in WD/WD systems (e.g.,|Marshetal.1995),, most known LMWDs are found as companions to neutron stars (NSs), and specifically to NSs “recycled” as millisecond pulsars (MSPs;2007)."," While LMWDs are found in WD/WD systems \citep[e.g.,][]{marsh95}, most known LMWDs are found as companions to neutron stars (NSs), and specifically to NSs “recycled” as millisecond pulsars \citep[MSPs;][]{panei07}."
". Most field radio pulsars in binary systems are MSPs, where a middle-aged, radio-quiet NS has been reactivated as a pulsar via accretion from its companion."," Most field radio pulsars in binary systems are MSPs, where a middle-aged, radio-quiet NS has been reactivated as a pulsar via accretion from its companion."
" The MSP companions are generally thought to be LMWDs with M—0.10.4Mo, although they are often too faint for optical spectroscopy to confirm that they are LMWDs (seeKerkwijk[van"," The MSP companions are generally thought to be LMWDs with $M = 0.1 - 0.4\ M_\odot$, although they are often too faint for optical spectroscopy to confirm that they are LMWDs \citep[see][]{vankerkwijk05}."
" Still, a third of the ~50 MSP companions discoveredetal|/2005).. outside of globular clusters have M<0.2Mo, assuming the systems have a median inclination of 60° ⋅⋅"," Still, a third of the $\sim$ 50 MSP companions discovered outside of globular clusters have $M\ \lapprox\ 0.2\ M_\odot$, assuming the systems have a median inclination of $60^{\circ}$ \citep[][]{manchester05}."
" While simulations designed to identify the evolutionary pathways that produce LMWD/MSP systems do not generally predict many systems with P,,, much shorter than a day (e.g.[Nelson[2004)., and while the system’s mass function implieset al]that the probability that J0917+4638 has a WD companion is (Kilicetal. [2007b),, a NS (or black hole) companion to this LMWD cannot be ruled out with the current optical observations."," While simulations designed to identify the evolutionary pathways that produce LMWD/MSP systems do not generally predict many systems with $P_{\rm orb}$ much shorter than a day \citep[e.g.,][]{nelson04}, and while the system's mass function implies that the probability that $+$ 4638 has a WD companion is \citep{kilic07b}, a NS (or black hole) companion to this LMWD cannot be ruled out with the current optical observations."
" In addition, for the currently known sample of WD/WD systems where both WD masses have been measured the mass ratio is typically about unity (seeandreferences while the ratio for the J0917+4638 binary system is therein),,<0.61."," In addition, for the currently known sample of WD/WD systems where both WD masses have been measured, the mass ratio is typically about unity \citep[see][and references therein]{nelemans05}, while the ratio for the $+$ 4638 binary system is $\leq 0.61$."
" Because of the connections between LMWDs and MSPs, we used the Green Bank Telescope (GBT) to search for a putative pulsar companion to J0917--4638, and report here on these observations (Section ?7))."," Because of the connections between LMWDs and MSPs, we used the Green Bank Telescope (GBT) to search for a putative pulsar companion to $+$ 4638, and report here on these observations (Section \ref{radio}) )."
 We also report on an Observatory observation of this LMWD ??))., We also report on an observation of this LMWD (Section \ref{xray}) ).
" Blackbody emission from a putative NS companion(Section to the LMWD should be gravitationally bent, allowing us to detect the NS in X rays even if it were radio-quiet or if its pulsar"," Blackbody emission from a putative NS companion to the LMWD should be gravitationally bent, allowing us to detect the NS in X rays even if it were radio-quiet or if its pulsar"
Assuming a one-temperatre hvdrodsuanie post-shock accretion column as f1ο source for polarized radiation in models of magueic cataclvsude variables can lead to erroneous predicfous for the radiation when the cyclotron cooling efficiency. is ereater than the electron-ion cherey exchange efficiency.,Assuming a one-temperature hydrodynamic post-shock accretion column as the source for polarized radiation in models of magnetic cataclysmic variables can lead to erroneous predictions for the radiation when the cyclotron cooling efficiency is greater than the electron-ion energy exchange efficiency.
 This effect shows up at the lower mass flow rate modeled here (ip⋅=0.5 , This effect shows up at the lower mass flow rate modeled here $\dot{m} = 0.5$ 
recent work.,recent work.
 We summarise the main points here., We summarise the main points here.
 We obtained Week/LILRES spectra of 28 QSOs and analysecl 49 absorption svstems Iving along their lines of sight., We obtained Keck/HIRES spectra of 28 QSOs and analysed 49 absorption systems lying along their lines of sight.
 These systems included: those systems. considered. in W99 and also a higher redshift sample of clamped o svstems (DLAs) containing absorption lines of ions such asMgr.MeiAlu. Alii. Sin. Cru. Feu. andZnll. so that our redshift range now covers 0.5<z3.5. corresponding to look-back times from 5 to 12 billion vears (Hy=68kms!Mpe+. Oy=03. Q4.=07).," These systems included those systems considered in W99 and also a higher redshift sample of damped $\alpha$ systems (DLAs) containing absorption lines of ions such as, and, so that our redshift range now covers $0.5<z<3.5$, corresponding to look-back times from 5 to 12 billion years $H_0=68{\rm ~kms}^{-1}{\rm Mpc}^{-1}$, $\Omega_{\rm M}=0.3$, $\Omega_{\Lambda}=0.7)$."
 Our absorption systems fell conveniently into two sub-samples: thett systems comprised the low redshift. sample (2= 1.0) and theDLAs comprised the high redshift sample (2= 2.1)., Our absorption systems fell conveniently into two sub-samples: the systems comprised the low redshift sample $\bar{z}=1.0$ ) and theDLAs comprised the high redshift sample $\bar{z}=2.1$ ).
 There were. however. 2 absorbers within the sample that lav at low redshift’ but we have included. them in the sample since. the observations and data reduction. for the two sub-sanmples were carried out independently by two different groups.," There were, however, 2 absorbers within the sample that lay at low redshift but we have included them in the sample since the observations and data reduction for the two sub-samples were carried out independently by two different groups."
" The analysis is based on the following equation for the wavenumber. ως. of à given transition at a recshilt where wy is the laboratory rest wavenumber of the transition. q, and qo are relativistic coellicients. a=(αςαμ1 and y—(osoui1."," The analysis is based on the following equation for the wavenumber, $\omega_z$ , of a given transition at a redshift $z$; where $\omega_0$ is the laboratory rest wavenumber of the transition, $q_1$ and $q_2$ are relativistic coefficients, $x\equiv(\alpha_z/\alpha_0)^2-1$ and $y \equiv (\alpha_z/\alpha_0)^4-1$."
 Note that the second and third terms on the right hand side only contribute if Aajazx0., Note that the second and third terms on the right hand side only contribute if $\da\neq 0$.
 The values of q; and d» have been calculated using manv-body techniques in Dzuba et al. (, The values of $q_1$ and $q_2$ have been calculated using many-body techniques in Dzuba et al. (
19992a.b. 2001) and we tabulate those values relevant to our analysis in table 1 of MOla.,"1999a,b, 2001) and we tabulate those values relevant to our analysis in table 1 of M01a."
 The values of ws must be known to a high precision in order to place stringent constraints on «λαία., The values of $\omega_0$ must be known to a high precision in order to place stringent constraints on $\da$.
 A precision of Aafa~10 corresponds to an uncertainty on wy .1 ⋅ ⊥↽∶⊳∖⋠ ∿∪⋅∪−≻≼∼⊔↓↿∖∿≱⋅⇀∫≻↓∡⊔↓⊳∖⊐⊳⊳∐⊔⊳∖≼∼∪↓⋅↓⋅⋖⋅⊳∖↓≻∪⊔∠⇂⊳∖⇂⋜⊔↓⋅," A precision of $\da \sim 10^{-5}$ corresponds to an uncertainty on $\omega_0$ $\sim0.02{\rm \,cm}^{-1}$ $\sim 0.3 {\rm \,kms}^{-1}$ ."
↓∙∖⇁∖∖⋎∢⊾∐ ⋅⋠ ↿∪↿⇂↥⋖⋅∠⇂⋜↧⋯⊏↥⇂⋯∐↿∙∖⇁≻↕↓↕≼↛∢⊾∖∖⋎⋖⋅⋯⊔⊓⊾⊔⇂↓⋅∪⊲⊔⇂⋜↧↓↕⋜↧∣⋡≻∢≱↓⋅↓≻↿↕⋖⋟↓↕ ⇂⋅∢⋅⋜⊔⊔↓⋅⋖⋅⋯⋜↧↓≻↓≻↓⋅⋖≱⇀∖↕↓↥↓⋜↧↿⋖⋅↓∙∖⇁∪⊔⋖⊾↿⋖⋅⊔↿↓↕∪⇂⋅⇂↓↥⋖⊾↓∐↓∥⊲⇀⊲∺↓⋅⋖⋅⊳∖∪↓⊔↕∪⊔⊳ ∿⊤↓∡⊔↓⊳∖↓⊳∺⋯⇍↓↕≻↓⋅∢," This corresponds fairly well to the data quality since we can centroid an absorption feature to approximately one tenth of the HIRES resolution, $\sim 7{\rm \,kms}^{-1}$."
⋅≼⋰↓⊳∖⊲↓∪⊔↓⋯⊳∖⊔∪∣∣⋡∢⋅⋖⊾⊔↓≻↓⋅⋖⋅∖⋰↓∪⊔⊳∖↓∙∖⇁⋯⇍↓↥⊲⊓⊾∖⇁⋖⋅∠⇂ [or most resonance transitions of ionized species and so measurements of wy for all relevant species were carried out by several groups (Nave et al., Such precision has not been previously achieved for most resonance transitions of ionized species and so measurements of $\omega_0$ for all relevant species were carried out by several groups (Nave et al.
 1991: Pickering. Thorne Webb 1998: Pickering et al.," 1991; Pickering, Thorne Webb 1998; Pickering et al."
 2000: Griesmann Ixling 2000) using laboratory Fourier transform spectrometers., 2000; Griesmann Kling 2000) using laboratory Fourier transform spectrometers.
 We have sumnmarised and tabulatecd these measurements in MOla., We have summarised and tabulated these measurements in M01a.
 Ixnowinge all values of zx. qj ancl qo. we then deconvolve each absorption svstem into individual Voigt components and perform a non-linear. least. squares x7.2 minimization to find the best-fitting value of Aasa at cach absorption redshift.," Knowing all values of $\omega_0$, $q_1$ and $q_2$, we then deconvolve each absorption system into individual Voigt components and perform a non-linear least squares $\chi^2$ minimization to find the best-fitting value of $\da$ at each absorption redshift."
 For the sample we confirm the W99 result. our new results giving a weighted mean of Aafa=(0.7040.23)10 ," For the sample we confirm the W99 result, our new results giving a weighted mean of $\da = (-0.70 \pm
0.23)\times 10^{-5}$ ."
For the new. sample. we find a similar result: AajaΟτο0.28)10," For the new, sample, we find a similar result: $\da = (-0.76 \pm 0.28)\times 10^{-5}$."
 3oth results independently suggest. a smaller value. of à in the past., Both results independently suggest a smaller value of $\alpha$ in the past.
 ‘Taking the sample as whole we find Aafa=(.0.72+0.18)107. a de result.," Taking the sample as whole we find $\da = (-0.72 \pm 0.18)\times 10^{-5}$ , a $4\sigma$ result."
 These new results are also summarised in Webb et al. (, These new results are also summarised in Webb et al. (
2001. hereafter WO).,"2001, hereafter W01)."
 Given the potential importance of such a result. for fundamental physics. à thorough investigation of possible systematic problems in the data or in the analysis is essential. and this is the purpose of the present paper.," Given the potential importance of such a result for fundamental physics, a thorough investigation of possible systematic problems in the data or in the analysis is essential, and this is the purpose of the present paper."
 In Section 2 we list. all effects that one might. consider. as being able to mimic a svstematically non-zero Aa/a., In Section 2 we list all effects that one might consider as being able to mimic a systematically non-zero $\da$.
 We are able to exclude many of them with general arguments., We are able to exclude many of them with general arguments.
 Sections 37 are then given over to à more detailed analysis of five specific elfects:: wavelength mis-calibration. ionic line. blending. atmospheric dispersion. cllects. dillerential isotopic saturation and possible isotopic variation.," Sections 3–7 are then given over to a more detailed analysis of five specific effects: wavelength mis-calibration, ionic line blending, atmospheric dispersion effects, differential isotopic saturation and possible isotopic variation."
 Section i escribes another test which is sensitive to a simple monotonic wavelength distortion. specifically for the sample.," Section 8 describes another test which is sensitive to a simple monotonic wavelength distortion, specifically for the sample."
 We make our conclusions in Section 9., We make our conclusions in Section 9.
 In MOla and WOL we found that values of Aaya were systematically negative and that this trend was evident in wo different samples of data occupying cdilferent redshift regimes., In M01a and W01 we found that values of $\da$ were systematically negative and that this trend was evident in two different samples of data occupying different redshift regimes.
 We note that the sample is more susceptible ο. systematic errors than the sample., We note that the sample is more susceptible to systematic errors than the sample.
 The. ines act as anchors against which the larger shifts can x: measured., The lines act as anchors against which the larger shifts can be measured.
 All of the lines have similar magnitude shifts in the same direction (i.c. dj is large and. positive in all cases)., All of the lines have similar magnitude shifts in the same direction (i.e. $q_1$ is large and positive in all cases).
 Furthermore. all the lines lie to the Xue of the doublet.," Furthermore, all the lines lie to the blue of the doublet."
 Lf some systematic error in the wavelength scale is present. which cllectively the spectrum. this would. mimic a negative shift in the mean value of Aafa (iit were not degenerate with redshift).," If some systematic error in the wavelength scale is present, which effectively the spectrum, this would mimic a negative shift in the mean value of $\da$ (if it were not degenerate with redshift)."
 Phe sample is far more complex in this regard. since it contains tons not only with positive coellicients.but also with negative qj coellicients. (Le. all lines ancl ALT41 and A1751).," The sample is far more complex in this regard since it contains ions not only with positive coefficients,but also with negative $q_1$ coefficients (i.e. all lines and $\lambda$ 1741 and $\lambda$ 1751)."
 Also. the shifts for the various ions are of various magnitudes making it more complicated to predict the effect of a svstematic error on our measured. values of Aafa.," Also, the shifts for the various ions are of various magnitudes making it more complicated to predict the effect of a systematic error on our measured values of $\da$."
 Errors in the values of wy will lead clirectly to errors in anv single determination of Aea/ea., Errors in the values of $\omega_0$ will lead directly to errors in any single determination of $\da$.
 Lf for cxaniple. the laboratory wavelengths of the lines wereall shifted to the blue or red then this would systematically bias the valuesof Aafe for the sample.," If, for example, the laboratory wavelengths of the lines wereall shifted to the blue or red then this would systematically bias the valuesof $\da$ for the sample."
 la MOlIa we summarise the measurements of all values of wy., In M01a we summarise the measurements of all values of $\omega_0$ .
 Most measurements were repeated. independently and. σου agreement: was obtained, Most measurements were repeated independently and good agreement was obtained
significantly and in the sense of bringing it closer to the true scale- of the model disc. which increases from small values very close to the plane. where the gas dise dominates the gravitational ;xotential. through 300pe at z~300pe. where the thin disc accounts for the majority of stars. to ~|kpe at large heights. where the thick dise is dominant.,"significantly and in the sense of bringing it closer to the true scale-height of the model disc, which increases from small values very close to the plane, where the gas disc dominates the gravitational potential, through $300\pc$ at $z\sim300\pc$, where the thin disc accounts for the majority of stars, to $\sim1\kpc$ at large heights, where the thick disc is dominant."
" Note that far from the plane the dominant population's scale-height 7j is significantly smaller than the locally measured scale-height of the disc because the population is dominated by stars with A,«ΔΝ. which by equation (25)) have δω.ΔΝ)>fy."," Note that far from the plane the dominant population's scale-height $h_0$ is significantly smaller than the locally measured scale-height of the disc because the population is dominated by stars with $\Rg< R$, which by equation \ref{eq:giveshratio}) ) have $h(\Rg,R)> h_0$."
 Even so. when AE. is omitted. the fitted values of /tp are unexpectedly small.," Even so, when $\Delta E_z$ is omitted, the fitted values of $h_0$ are unexpectedly small."
" Including AE. increases 7j, at all heights. while limiting the values of E£- employed to less than (80kms!£ yields intermediate values of 75. which are not far from constant as we would wish."," Including $\Delta E_z$ increases $h_0$ at all heights, while limiting the values of $\overline{E_z}$ employed to less than $(50\kms)^2$ yields intermediate values of $h_0$, which are not far from constant as we would wish."
" The reason adding AE. to the effective potential increases {η is that ΔΕ increases the contribution to the velocity distribution at Ry of stars with small values of A, and therefore v, and thus reduces the need to suppress the contribution of the population with A,~Ay. which dominates the peak of the 1, distribution. relative to the stars that form the prominent left wing of the distribution."," The reason adding $\Delta E_z$ to the effective potential increases $h_0$ is that $\Delta E_z$ increases the contribution to the velocity distribution at $R_0$ of stars with small values of $\Rg$ and therefore $v_\phi$ and thus reduces the need to suppress the contribution of the population with $\Rg\simeq R_0$, which dominates the peak of the $v_\phi$ distribution, relative to the stars that form the prominent left wing of the distribution."
 The other improvement etfected by including AE. isto lower Q3)* slightly and thus bring it closer to its true value at high altitudes., The other improvement effected by including $\Delta E_z$ isto lower $\langle v_R^2\rangle^{1/2}$ slightly and thus bring it closer to its true value at high altitudes.
 When there is no upper limit on the values of E. used in the calculation of AE.. this lowering of Qu)!* becomes excessive above z=2kpe because at such altitudes the vertical energy becomes comparable to the radial energy.," When there is no upper limit on the values of $\overline{E_z}$ used in the calculation of $\Delta E_z$, this lowering of $\langle v_R^2\rangle^{1/2}$ becomes excessive above $z\simeq2\kpc$ because at such altitudes the vertical energy becomes comparable to the radial energy."
" Irrespective of whether AE. is used. the scale-length Α,. exhibits a continuous rise in the fits. moving away from the value Rí4/0.45 of the corresponding parameter of the torus model."," Irrespective of whether $\Delta E_z$ is used, the scale-length $R_\sigma$ exhibits a continuous rise in the fits, moving away from the value $R_\d/0.45$ of the corresponding parameter of the torus model."
 &.. comes closer to Ry/O.45 the lower a is chosen at higher altitudes., $R_{\sigma}$ comes closer to $R_\d/0.45$ the lower $\alpha$ is chosen at higher altitudes.
 As we VRremarked in Section ??.. the (373) is such that stars of given L. have a Gaussian distribution in rg.," As we remarked in Section \ref{sec:moments}, the \ref{eq:threedDF}) ) is such that stars of given $L_z$ have a Gaussian distribution in $v_R$."
 Consequently. the distribution in rp of all stars found at a given distance from the plane should in this picture be a weighted sum of Gaussian distributions with the weights implicit in equation (38)).," Consequently, the distribution in $v_R$ of all stars found at a given distance from the plane should in this picture be a weighted sum of Gaussian distributions with the weights implicit in equation \ref{eq:givessr}) )."
 Fig., Fig.
 7 compares this prediction (lines) at several altitudes z with he corresponding distributions from the torus models (data points)., \ref{fig:Udistr} compares this prediction (lines) at several altitudes $z$ with the corresponding distributions from the torus models (data points).
 The overall agreement between tqe data points and the predictions of the formula is remarkable whet none bears in mind that the curves ive not been obtained by fitting o the data points., The overall agreement between the data points and the predictions of the formula is remarkable when one bears in mind that the curves have not been obtained by fitting to the data points.
 At low altitudes (red and green) the formula precicts a distribution that is slightly oo sharply peaked and deficient i nthe wings., At low altitudes (red and green) the formula predicts a distribution that is slightly too sharply peaked and deficient in the wings.
 Around ~|kpe from he plane the tit is near perfect., Around $\sim1\kpc$ from the plane the fit is near perfect.
 The agreement between the curve or 2kpe and the data points at [vj«SOkms' is much better in he lower panel than the upper o»unel. vindicating the use of the correction provided by AE-.," The agreement between the curve for $2\kpc$ and the data points at $|v_R|<50\kms$ is much better in the lower panel than the upper panel, vindicating the use of the correction provided by $\Delta E_z$."
 We have fitted the full forimula (369) at an altitude of ς= to the velocity distribution of the Geneva-Copenhagen Survey (GCS) of F and G stars (Nordstrómetal.2004:Holmberg.Nord- 2009)..," We have fitted the full formula \ref{eq:nvRz}) ) at an altitude of $z=40 \pc$ to the velocity distribution of the Geneva-Copenhagen Survey (GCS) of F and G stars \citep[][]{Nord04, Holmberg09}. ."
 As sample we selected the full 13520 objects that have measured space velocities.," As sample we selected the full $13\,520$ objects that have measured space velocities."
" We adopted v,= and assumed that the Sun's velocity with respect to the Local Standard of Rest is I224kms! ", We adopted $\vc=220\kms$ and assumed that the Sun's velocity with respect to the Local Standard of Rest is $12.24\kms$ 
Cataclysmic Variables are accreting binary systems in which a white dwarf accretes material from. a late type main sequence star through Roche lobe overllow.,Cataclysmic Variables are accreting binary systems in which a white dwarf accretes material from a late type main sequence star through Roche lobe overflow.
 If. the white dwarf has a significant magnetic field then the formation of an accretion disk can be disrupted. or prevented., If the white dwarf has a significant magnetic field then the formation of an accretion disk can be disrupted or prevented.
 For white cdwarls with Ποια strengths &reater than 10. MC. the accretion stream gets channelled onto the magnetic poles where X-rays are emitted from the post-shock region.," For white dwarfs with field strengths greater than $\sim$ 10 MG, the accretion stream gets channelled onto the magnetic poles where X-rays are emitted from the post-shock region."
 The magnetic field also forces the spin period of the white dwarf to svnchronise with the binary orbital period., The magnetic field also forces the spin period of the white dwarf to synchronise with the binary orbital period.
 These accreting binaries are called AM Ler binaries or polars. since their optical emission is strongly polarised.," These accreting binaries are called AM Her binaries or polars, since their optical emission is strongly polarised."
 The studs of polars was transformed with the launch of the X-ray satellite in 1990., The study of polars was transformed with the launch of the X-ray satellite in 1990.
 Prior to this. around 17 systems were known.," Prior to this, around 17 systems were known."
ROSAL led directly to the discovery of around 30 new systems (eg Beuermann Burwitz 1995)., led directly to the discovery of around 30 new systems (eg Beuermann Burwitz 1995).
 It was expected. thatNALALNewtou. launched in. 1999. would lead to the discovery of many more such svstenis.," It was expected that, launched in 1999, would lead to the discovery of many more such systems."
 Surprisingly. comparatively [ον have so far been discovered.," Surprisingly, comparatively few have so far been discovered."
 The 2XMM catalogue (Watson ct al 2009) gives a description of serendipitous. X-ray sources discovered. using the EPIC wide-fick instruments on boardNewton., The 2XMM catalogue (Watson et al 2009) gives a description of serendipitous X-ray sources discovered using the EPIC wide-field instruments on board.
" ""his was followed by the release of the 2XMM incremental catalogue which has 17 percent more discrete sources than the 2NXMM catalogue.", This was followed by the release of the 2XMMi incremental catalogue which has 17 percent more discrete sources than the 2XMM catalogue.
 Moreover. each source is accompanied by source specific light curve and spectral products.," Moreover, each source is accompanied by source specific light curve and spectral products."
 In this paper we report the discovery of an eclipsing polar. 2XMMi J225036.9|573154. which was found as a result of searching the 2NAIAT catalogue for sources which showed variability in their X-ray light. curve.," In this paper we report the discovery of an eclipsing polar, 2XMMi J225036.9+573154, which was found as a result of searching the 2XMMi catalogue for sources which showed variability in their X-ray light curve."
 The 2NAMA catalogue has associated spectra ancl light curves that are automatically extracted by the Science Survey Centre pipeline processing software (Watson et al 2001) for sources with more than 500 counts in the EPIC detectors., The 2XMMi catalogue has associated spectra and light curves that are automatically extracted by the Science Survey Centre pipeline processing software (Watson et al 2001) for sources with more than 500 counts in the EPIC detectors.
 An assessment of variability in the individual light. curves is made by determining of the cata about the mean. and then computing the consequent probability of the constant (null) hypothesis.," An assessment of variability in the individual light curves is made by determining of the data about the mean, and then computing the consequent probability of the constant (null) hypothesis."
 Those light curves for which this probability is <107 are deemed. variable., Those light curves for which this probability is $< 10^{-5}$ are deemed variable.
 Sources which were possibly compromised bv further data. quality issues were removed., Sources which were possibly compromised by further data quality issues were removed.
 An initial search of the catalogue. found. around 400 sources which passed these criteria., An initial search of the catalogue found around 400 sources which passed these criteria.
 The light curves of these sources were visually inspected for periodic behaviour., The light curves of these sources were visually inspected for periodic behaviour.
 One source.," One source,"
"in Schunkeretal.(2005),, one can tell that the travel time variation trends are similar for the June 7 and 10 measurements, except that the variation magnitude in our measurement is approximately 12 sec, substantially smaller than that from the holography measurement, which is of the order of 30 sec.","in \citet{sch05}, one can tell that the travel time variation trends are similar for the June 7 and 10 measurements, except that the variation magnitude in our measurement is approximately 12 sec, substantially smaller than that from the holography measurement, which is of the order of 30 sec."
" Perhaps, the use of different measurement annulus (or pupil) sizes, phase-speed filtering and different acoustic frequencies in these techniques may have caused such differences."," Perhaps, the use of different measurement annulus (or pupil) sizes, phase-speed filtering and different acoustic frequencies in these techniques may have caused such differences."
" It is interesting to investigate how this measurement effect affects our inversion results for sound-speed structures beneath the sunspot (Kosovichev,Duvall,&Scherrer2000)..", It is interesting to investigate how this measurement effect affects our inversion results for sound-speed structures beneath the sunspot \citep{kos00}.
" Since the inversion procedure involves integration over large areas of different annuli and over a large depth range, as well as averaging and smoothing, it is not obvious how much this systematic measurement"," Since the inversion procedure involves integration over large areas of different annuli and over a large depth range, as well as averaging and smoothing, it is not obvious how much this systematic measurement"
"Once the Reynokls decomposition has been lmplemented. progress is mace by cdefinine the first three equal-time ceumulants ο, ον). and ej, of the combiued scalar fields (yj) as? where mj. nj. aud 10;;; are respectively the traditional definitions of the first. second and third moments.","Once the Reynolds decomposition has been implemented, progress is made by defining the first three equal-time cumulants $c_i$ , $c_{ij}$ , and $c_{ijk}$ of the combined scalar fields $q_i$ ) as: where $m_i$, $m_{ij}$, and $m_{ijk}$ are respectively the traditional definitions of the first, second and third moments."
 We stress here that the second aud higher cumulants contain information about correlatious that are uou-local in space aud therefore include interactions that are uot included iu the simple local moment hierarchies discussed in the introduction., We stress here that the second and higher cumulants contain information about correlations that are non-local in space and therefore include interactions that are not included in the simple local moment hierarchies discussed in the introduction.
 For this reason this approach is more tailored to inhomogeneous problems., For this reason this approach is more tailored to inhomogeneous problems.
 The hierarchy. of equations of motions for the evolution of the cumulauts can be obtaiued directly be differentiating Eqs., The hierarchy of equations of motions for the evolution of the cumulants can be obtained directly be differentiating Eqs.
 ὁ with respect to time aud using Eqs. 1..," \ref{cumulants} with respect to time and using Eqs. \ref{algebraicEOMs},"
 together with repeated back substitution., together with repeated back substitution.
 A more elegant method is to introduce variables p; that are. in analogy to quantum mechanics. conjugate to the q; in the seuse that gy=—70/Op; as in Eq.," A more elegant method is to introduce variables $p_i$ that are, in analogy to quantum mechanics, conjugate to the $q_i$ in the sense that $q_i = -i \partial / \partial p_i$ as in Eq."
 T below 2005).., \ref{Hopf-moments} below \citep{ma:2005p108}.
 Then oue may define the Hopf geueratiug functional (Frisch1995):: recalling the sunumnatiou overrepeatedindices., Then one may define the Hopf generating functional \citep{frisch95}: recalling the summation overrepeatedindices.
 The Hopf functional obeys a Scliróddiuger-like equation: with liuear operator H eiven by:, The Hopf functional obeys a Schröddinger-like equation: with linear operator $\hat{H}$ given by:
enission are presented.,emission are presented.
 The first set of light curves show radio observations of flaring activity tliat, The first set of light curves show radio observations of flaring activity that
(to II8 line profiles.,to H8 line profiles.
 Our best Lit is clisplavecl in Figure 3.., Our best fit is displayed in Figure \ref{fg:f3}.
 Remarkably. our spectroscopic solution Tuy=10.7604150 Ix and logy=9.46+0.04. which (rauslates into AM=1.33540.011 and 2=0.00358+0.00019 uusing the ELamacda-Salpeter mass-racdius relation for carbon-core configurations. is in excellent agreement with the solution obtained with the photometry aud trigonometric parallax method.," Remarkably, our spectroscopic solution $\Te=10,760\pm150$ K and $\logg=9.46\pm0.04$, which translates into $M=1.335\pm0.011$ and $R=0.00358\pm0.00019$ using the Hamada-Salpeter mass-radius relation for carbon-core configurations, is in excellent agreement with the solution obtained with the photometry and trigonometric parallax method."
 This is arguably (he most massive white dwarl subjected to a rigorous mass determination (see.e.g...Table3ofDupuisetal.2002).," This is arguably the most massive white dwarf subjected to a rigorous mass determination \citep[see, e.g., Table 3
of][]{dupuis02}."
. Note that despite (he extreme surface eravily of LIIS 4033. the IIunumner-Milalas formalism. used in the line profile calculations remains perfectly valid. since the density at the photosphere remains low (p~10? @ 7) as a result of the high opacity of hydrogen at these temperatures.," Note that despite the extreme surface gravity of LHS 4033, the Hummer-Mihalas formalism used in the line profile calculations remains perfectly valid, since the density at the photosphere remains low $\rho\sim10^{-5}$ g $^{-3}$ ) as a result of the high opacity of hydrogen at these temperatures."
 In a venerable paper. Hamada&Salpeter(1961). [ist emplovecl an equation-ol-state (EOS) including coulomb “corrections” to the pressure ancl energy of a degenerate Fermi gas (Salpeter1961). to caleulate the mass-radius-central density relations for models composed ol helium through iron.," In a venerable paper, \citet{hamada} first employed an equation-of-state (EOS) including coulomb “corrections” to the pressure and energy of a degenerate Fermi gas \citep{salpeter61} to calculate the mass-radius-central density relations for models composed of helium through iron."
 These corrections to the classic Chandrasekhar EOS lor degenerate malter are more important at high mass., These corrections to the classic Chandrasekhar EOS for degenerate matter are more important at high mass.
 It mary also be noted (hat. especially at (he relatively low elfeclive temperature of LIIS. 4033. neglect of the internal enerev of the ions modelling) is likelv to be a reasonable assumption.," It may also be noted that, especially at the relatively low effective temperature of LHS 4033, neglect of the internal energy of the ions (``zero-temperature'' modelling) is likely to be a reasonable assumption."
 since LIIS 4033 may have a core composed of material much heavier than carbon. we must explore the effects of core composition on the results of our analysis.," Since LHS 4033 may have a core composed of material much heavier than carbon, we must explore the effects of core composition on the results of our analysis."
 We compare in Figure + the mass-radius relation obtained [rom the detailed evolutionary carbou- and carbon/oxvgen-core models of Fontaineetal.(2001.seealsoDergeron2001) with the Tamada-Salpeter zero-temperature configurations lor carbon and magnesium al a mass of 1.8M... the highest mass of the Fontaine et al.," We compare in Figure \ref{fg:f4} the mass-radius relation obtained from the detailed evolutionary carbon- and carbon/oxygen-core models of \citet[][see also Bergeron et
al. 2001]{fon01} with the Hamada-Salpeter zero-temperature configurations for carbon and magnesium at a mass of 1.3, the highest mass of the Fontaine et al."
 models., models.
 At the effective temperature and mass of LIIS 4033. the carbon- or carbon/oxvgen-core models of Fontaine et al.," At the effective temperature and mass of LHS 4033, the carbon- or carbon/oxygen-core models of Fontaine et al."
 reveal (hat finile temperature effects are extremely small. and account lor an increase in radius of only ~0.5 (i.e. bv comparing the radius at 10.000 IX. with the value at 3500 IX where it becomes constant).," reveal that finite temperature effects are extremely small, and account for an increase in radius of only $\sim 0.5$ (i.e. by comparing the radius at 10,000 K with the value at 3500 K where it becomes constant)."
 Moreover. al the temperature of LIIS 4033. the carbon-core models of Fontaine et al.," Moreover, at the temperature of LHS 4033, the carbon-core models of Fontaine et al."
 and Hoamacda-Salpeter differ bv only 2.7 in radius. or 0.007. iin mass.," and Hamada-Salpeter differ by only 2.7 in radius, or 0.007 in mass."
 Details of the equation-of-state are (hus also negligible in the present context., Details of the equation-of-state are thus also negligible in the present context.
 Finally. the Mg and C configurations of Haamada-Salpeter differ by 7.4% in radius. or 0.02 ii mass.," Finally, the Mg and C configurations of Hamada-Salpeter differ by 7.4 in radius, or 0.02 in mass."
 Indeed.| the parallax method with the Mg configurations vields a mass of 1.310 ((instead of 1.330 when C configurations are used). while the spectroscopic method vields a," Indeed, the parallax method with the Mg configurations yields a mass of 1.310 (instead of 1.330 when C configurations are used), while the spectroscopic method yields a"
used no aperture correction Lor these measurements. as our apertures extend. well bevond (he visible portions of the knots.,"used no aperture correction for these measurements, as our apertures extend well beyond the visible portions of the knots."
 The final [Iuxes. along with the distance Irom the core for each knot are listed in Table1..," The final fluxes, along with the distance from the core for each knot are listed in Table\ref{tab:data}. ."
to explain the large-scale eas kinematics observed iu MIRC 1138-262.,to explain the large-scale gas kinematics observed in MRC 1138-262.
 Direct coupling between the jet aud the ealactic gas should result in the outflow bee coufiued within a narrow cone around the jet axis. contrary to observations.," Direct coupling between the jet and the galactic gas should result in the outflow being confined within a narrow cone around the jet axis, contrary to observations."
 Reearding the effect of radiation pressure roni the quasar photon output on iuterstellar dust eraius 2).. 3t is hard to understand how this could remove a significant fraction of the galactic gas. since the UW xiotous will be degraded to IR frequencies after a few scatterings. within a parsec from the black hole.," Regarding the effect of radiation pressure from the quasar photon output on interstellar dust grains , it is hard to understand how this could remove a significant fraction of the galactic gas, since the UV photons will be degraded to IR frequencies after a few scatterings, within a parsec from the black hole."
 Also. he optical depth for the resulting far IR photons will rot exceed unity bevond a few teus of parsecs.," Also, the optical depth for the resulting far IR photons will not exceed unity beyond a few tens of parsecs."
 The jet-powered cosmüc ταν feedback scenario xeseuted here does not suffer any othese deficiencies., The jet-powered cosmic ray feedback scenario presented here does not suffer any of these deficiencies.
 The cosmic rav hinunosity injected iito the host galaxy is naller than the black hole photoji power bv roughly wo orders of magnitude. but cosnic ravs exchange noimentun with he ealactic gas ~FagLO? more efficiently.," The cosmic ray luminosity injected into the host galaxy is smaller than the black hole photon power by roughly two orders of magnitude, but cosmic rays exchange momentum with the galactic gas $\sim\tau_g/\tau_\ditto{UV}\sim10^3$ more efficiently."
 Tere. Ty.~ Lis the opical faudepth for UV photons on dust erains.," Here, $\tau_{\ditto{UV}}\sim1$ is the optical depth for UV photons on dust grains."
" Moreover. since the cosmic rav optical depth im the ealaxws 1iterstella medium is very large ~ 107) auy inemory of the cosudc rav momentum (n,distribution at injection is quickly lost and their effect on the galactic eas should resemble a sphervically-svuuuetric outward pressure force. so that he resulting eas outflow is nearly spherical."," Moreover, since the cosmic ray optical depth in the galaxy's interstellar medium is very large $\tau_g\sim10^3$ ), any memory of the cosmic ray momentum distribution at injection is quickly lost and their effect on the galactic gas should resemble a spherically-symmetric outward pressure force, so that the resulting gas outflow is nearly spherical."
" Also. the raction of cosmic rav energy lost at each imteraction with the interstellar gas ix minimal (~ 7,7). meaning hat they can propagate up to the large scales where uost of the eas resides without suffering siguificaut OSSCS,"," Also, the fraction of cosmic ray energy lost at each interaction with the interstellar gas is minimal $\sim\tau_g^{-2}$ ), meaning that they can propagate up to the large scales where most of the gas resides without suffering significant losses."
" Au interesting result of our study ds that. per nuit of black hole cnereyv release. the cosmic rax cedback cfficicncy €.,. Which gives the fraction of jet o»wer available to uubind the galactic gas. is roughly a constaut with black hole mass"," An interesting result of our study is that, per unit of black hole energy release, the cosmic ray feedback efficiency $\epsilon_\ditto{CR}$, which gives the fraction of jet power available to unbind the galactic gas, is roughly a constant with black hole mass."
" Lustead. for selfreeulation models relying on the black hole photon output dunues radiativelv-effücieut quasar phasesανν the feedback efficiency is coustrained to scale as ~EQ/AE.xol in order for the system to lie ou the M,— relation."," Instead, for self-regulation models relying on the black hole photon output during radiatively-efficient quasar phases, the feedback efficiency is constrained to scale as $\sim E_g/\Delta E_\bullet\propto\sigma_\star^2$ in order for the system to lie on the $M_\bullet-M_\star$ relation."
" Were. E,~ is the biudiug enerev of the galactic gas and AL, is the [,M.otime-inteerated energy output resulting from black hole accretion."," Here, $E_g\simeq f_g M_\star\sigma_\star^2$ is the binding energy of the galactic gas and $\Delta E_\bullet$ is the time-integrated energy output resulting from black hole accretion."
" It would be a surprising coincidence if an iutrinsically sel-regulatiou mechanism were to result in the Al,M, rolation. which holds for nearly four decades iu mass."," It would be a surprising coincidence if an intrinsically self-regulation mechanism were to result in the $M_\bullet-M_{\star}$ relation, which holds for nearly four decades in mass."
 The explosive radio-loud phase does not suffer from such severe constraints., The explosive radio-loud phase does not suffer from such severe constraints.
" Rather. since the coupling efficiency ειν for our cosmic rav-driven feedback scenario is scale-independeut. the euergy balance εί,~ required for black hole. sclfreeulation iuplies that LE,the time-inteerated jet kinetic output should scale as AE,xMio? for a constant eas fraction f,."," Rather, since the coupling efficiency $\epsilon_\ditto{CR}$ for our cosmic ray-driven feedback scenario is scale-independent, the energy balance $\epsilon_{\ditto{CR}}\Delta E_{\ditto{J}}\sim E_g$ required for black hole self-regulation implies that the time-integrated jet kinetic output should scale as $\Delta E_{\ditto{J}}\propto M_\star \sigma_\star^2$ for a constant gas fraction $f_g$."
" By inferring the black hole mass function AL,ofAL.) (dotted line in 1)) from the velocity cispersion function of carly- galaxies bv via the AZ,o, relation. we can predict the dependence ou black hole mass of the kinetic energv output of radio jets mtegrated over cosmic time GNE, solid line in 13). for systems Iving on the M,Af,ωςαν): aud AL,6, relations."," By inferring the black hole mass function $M_\bullet\,\phi(M_\bullet)$ (dotted line in ) from the velocity dispersion function of early-type galaxies by via the $M_\bullet-\sigma_\star$ relation, we can predict the dependence on black hole mass of the kinetic energy output of radio jets integrated over cosmic time $\Delta E_\ditto{J}M_\bullet\,\phi(M_\bullet)$ ; solid line in ), for systems lying on the $M_\bullet-M_\star$ and $M_\bullet-\sigma_\star$ relations."
" We find that its slope at the low-mass eud is 2.5 and it peaks at Af,c3«105AZ..."," We find that its slope at the low-mass end is $\sim2.5$ and it peaks at $M_\bullet\simeq3\times10^8\,M_\sun$."
 With amore reliable measurements of jet kinetic power aud black hole mass. this could oxovide a stringeut observatioual test for our proposed sel£regulatioun scenario.," With more reliable measurements of jet kinetic power and black hole mass, this could provide a stringent observational test for our proposed self-regulation scenario."
" For example. finding a slope close to 2.5 at the low-mass end would nuplv that je ratio between the timc-iutegrated jet kinetic output ""ESοad the binding euergv of the galactic gas should be πιiudepenudeut of black hole mass. thus strongly inuplicatiug wat black hole selfreeulation occurs iu the radio-loud inse. Irrespective of the actual coupling mechanism itself."," For example, finding a slope close to 2.5 at the low-mass end would imply that the ratio between the time-integrated jet kinetic output and the binding energy of the galactic gas should be independent of black hole mass, thus strongly implicating that black hole self-regulation occurs in the radio-loud phase, irrespective of the actual coupling mechanism itself."
" For a generic feedback mechanism acting during radio-ond epochs. the scaling AE,xM.o2 can he recast as At,μ.μ.Ax62, for a black hole galaxy system which ‘ollows the Af,Ad. relation."," For a generic feedback mechanism acting during radio-loud epochs, the scaling $\Delta E_{\ditto{J}}\propto M_\star \sigma_\star^2$ can be recast as $\Delta t_{\ditto{RP}}\Lambda_\ditto{Edd}\propto \sigma_\star^2$, for a black hole – galaxy system which follows the $M_\bullet-M_\star$ relation."
" Here. μ.μ.A is the ratio of the jet kinetic power to the black hole Thomson Eddiugtou iit and Af, is the duration of the radio-loud plase."," Here, $\Lambda_\ditto{Edd}$ is the ratio of the jet kinetic power to the black hole Thomson Eddington limit and $\Delta t_{\ditto{RP}}$ is the duration of the radio-loud phase."
 This implies that. for svstenis where a significant amount of mass is beime built up. radio-loud signatures will niost ikelv be observed in galaxies with large black holes and bulges. in Hine with the basic phenomenology of radio-loud AGN and quasars?2?).," This implies that, for systems where a significant amount of mass is being built up, radio-loud signatures will most likely be observed in galaxies with large black holes and bulges, in line with the basic phenomenology of radio-loud AGN and quasars."
". The AL,M, relation perhaps is then connected to the fact that raclio-loud actively-accyeting objects are relatively absent im relatively small svstenis(2): black hole sclfreeulation takes place during the radio-loud phase aud. due to the abundance of total energy available. this pliase isshort- in relatively stall svsteius because the amount of enerev required to unbiud the galaxy is relatively low."," The $M_\bullet-M_{\star}$ relation perhaps is then connected to the fact that radio-loud actively-accreting objects are relatively absent in relatively small systems: black hole self-regulation takes place during the radio-loud phase and, due to the abundance of total energy available, this phase isshort-lived in relatively small systems because the amount of energy required to unbind the galaxy is relatively low."
of the ligh-temperature peak compared to the low-temperature one for ((compare Table 9 here auc Table 2 in 2005)),of the high-temperature peak compared to the low-temperature one for (compare Table \ref{tabglobal} here and Table 2 in ).
 Indeed. a 2T fit of 01 CC vields values of 0.7 and kkeV. with the hottest conrponeut having an eniüssion neasure [ tines lavecr than that of the coolest one. whereas the enission lncasures are similar for the “hot” model of1185937.. which has temperatures simula to those of the 2T fit of 01 CC. This suggests that most of the overluuinosity of cconmes from relatively soft plasma.," Indeed, a 2T fit of $\theta^1$ C yields values of 0.7 and keV with the hottest component having an emission measure 4 times larger than that of the coolest one, whereas the emission measures are similar for the “hot” model of, which has temperatures similar to those of the 2T fit of $\theta^1$ C. This suggests that most of the overluminosity of comes from relatively soft plasma."
 Iu general. the absorption docs not seen to exceed the ISAL value by auch.," In general, the absorption does not seem to exceed the ISM value by much."
 The derived abundance values are in general consistent with solar abundances. except for ion (but the solar abundance of won has been revised since L989)): the elobal fits confirm the 3/1 solar abundance of Meg/8i fou from the line ratios.," The derived abundance values are in general consistent with solar abundances, except for iron (but the solar abundance of iron has been revised since ): the global fits confirm the 3/4 solar abundance of Mg/Si found from the line ratios."
 Finally. the flux observed by Chaudra is consistent with that derived from he NAIANewton low-resolution spectra2008a).. confirmune the lack of large variations iu the X-ray domain.," Finally, the flux observed by Chandra is consistent with that derived from the XMM-Newton low-resolution spectra, confirming the lack of large variations in the X-ray domain."
 Hs a peculiar object belonging to the iutriguiug category of Of?p stars., is a peculiar object belonging to the intriguing category of Of?p stars.
 The presence of a maguetic field in these stars. together with thei optical various are eecnerally explained within the framework of the Magnetic Oblique Rotator model.," The presence of a magnetic field in these stars, together with their optical variations are generally explained within the framework of the Magnetic Oblique Rotator model."
 In 2008. a first X-ray investigation of musing NMM-Neswtou had revealed peculiarities in its X-rav spectrum too.," In 2008, a first X-ray investigation of using XMM-Newton had revealed peculiarities in its X-ray spectrum too."
 Uufortunately. no detailed. high-resolution data of good quality was available until we obtained new data with Chandra-HETCS.," Unfortunately, no detailed, high-resolution data of good quality was available until we obtained new data with Chandra-HETGS."
 These new data enable us to study Hn more detail, These new data enable us to study in more detail.
 The X-rav lines detected hy Chiaudra display an average shift of 19t52 gus. and an average EWIIM of 82790aus.," The X-ray lines detected by Chandra display an average shift of $49\pm32$ , and an average FWHM of $827\pm90$."
 The lines from bieh-Z clemeuts. whose Cluissivity peaks at high temperatures. thus appear rather narrow. sugecsting tha they could ο linked. to magnetically confined winds.," The lines from high-Z elements, whose emissivity peaks at high temperatures, thus appear rather narrow, suggesting that they could be linked to magnetically confined winds."
 If the areer width of the line found from the roinicr ROS data is real it means that there is no unique source or location for the hot plasma.," If the larger width of the line found from the noisier RGS data is real, it means that there is no unique source or location for the hot plasma."
 This is a similar situation to what was found for 0: CC though the FWIIM of the high-Z lines was even narrower for this star. aboutlaus.," This is a similar situation to what was found for $\theta^1$ C - though the FWHM of the high-Z lines was even narrower for this star, about."
 While RCS data already. provided hints of a suppressed. forbidden line for the triplet2008a).. the good quality TETC spectra confriià these hints and provide solid evidence for suppressed forbidden lines iu two other He-like triplets. those of andNIL.," While RGS data already provided hints of a suppressed forbidden line for the triplet, the good quality HETG spectra confirm these hints and provide solid evidence for suppressed forbidden lines in two other He-like triplets, those of and."
" These He-like triplets of Me aud Si incicate a formation radius of about one stellar radius from the photosphere. which is rather close to the stars surface. but not uncoumiou iu. ""normal or Inaenetic O-stars2009)."," These He-like triplets of Mg and Si indicate a formation radius of about one stellar radius from the photosphere, which is rather close to the star's surface, but not uncommon in “normal” or magnetic O-stars."
. The temperatures derived frou ILto-Ie like ratios are higher than for “normal” O-stars. but still mot as extreme as those of 01 OOriCC2008).. This indicates the preseuce of hot plasina. which is coufirmed iu elobal fits.," The temperatures derived from H-to-He like ratios are higher than for “normal” O-stars, but still not as extreme as those of $\theta^1$ C. This indicates the presence of hot plasma, which is confirmed in global fits."
" Global fits further show that this very hot commponcut is much stronger than for ""normal"" QO-stars but still πιο] less dominant thau iu the extreme case of 064 CC2005).. The comparison of IT-like aud IIc-like line pairs supports this view. as ddisplavs a higher ionization than “normal” ο stars. albeit not quite as extreme asin 04 CC2009).. The fitting also shows that here is no large additional absorption over the ISM value. aud that the overall flux agrees within with that recorded 8.5 vears before by NADIAENewtou."," Global fits further show that this very hot component is much stronger than for “normal” O-stars but still much less dominant than in the extreme case of $\theta^1$ C. The comparison of H-like and He-like line pairs supports this view, as displays a higher ionization than “normal” O stars, albeit not quite as extreme as in $\theta^1$ C. The fitting also shows that there is no large additional absorption over the ISM value, and that the overall flux agrees within with that recorded 8.5 years before by XMM-Newton."
" Regarding abunud:aces of Ne. Me. Si, and ο, the elobal fits favor close-to-solar aluucdauces (with a slight excess iu sulpliur aud a deficit iu iron)."," Regarding abundances of Ne, Mg, Si, and S, the global fits favor close-to-solar abundances (with a slight excess in sulphur and a deficit in iron)."
 Iun conclusion. the new. οσους quality ligh-resolution data obtained by Chandra vielded additional clues in favor of the ALOR τους]: relatively narrow N-ray lines (FWIDM~s00kins 1)) andl a similar ‘cloudiness’ for the radiative shock model of(2007).. plus a confirmation of the presence of ναν hot plasima.," In conclusion, the new, good quality high-resolution data obtained by Chandra yielded additional clues in favor of the MOR model: relatively narrow X-ray lines $\sim$ ) and a similar 'cloudiness' for the radiative shock model of, plus a confirmation of the presence of very hot plasma."
" Ποπονα, abundant soft plasma is also present. iu contrast with the MOR-prototype 01 OO1CC: in every respect (e.g. Lue widths ofhieh-Z clements or temperature distributious). tthus appears less extreme than 01 CC"," However, abundant soft plasma is also present, in contrast with the MOR-prototype $\theta^1$ C: in every respect (e.g. line widths ofhigh-Z elements or temperature distributions), thus appears less extreme than $\theta^1$ C,"
" Ποπονα, abundant soft plasma is also present. iu contrast with the MOR-prototype 01 OO1CC: in every respect (e.g. Lue widths ofhieh-Z clements or temperature distributious). tthus appears less extreme than 01 CC."," However, abundant soft plasma is also present, in contrast with the MOR-prototype $\theta^1$ C: in every respect (e.g. line widths ofhigh-Z elements or temperature distributions), thus appears less extreme than $\theta^1$ C,"
The same procedure in relslse leads (o equations governing a self-similar flow in the shocked ambient mediunm as limit.,The same procedure in \\ref{sfse} leads to equations governing a self-similar flow in the shocked ambient medium as in the relativistic limit.
 The boundary conditions are [(1) 9 g(1) These are exactly (hie same equations as presented in Blandlord&Melee(1976)., The boundary conditions are These are exactly the same equations as presented in \citet{Blandford76}.
". The density distribution has a discontinuity at the contact surface defined as £=€ and \=\. where G(£.)£.=L/q and g(x,.)X,=2. while the velocitv ancl pressure are continuous."," The density distribution has a discontinuity at the contact surface defined as $\xi=\xi_{\rm c}$ and $\chi=\chi_{\rm c}$ where $G(\xi_{\rm c})\xi_{\rm c} = 1/q$ and $g(\chi_{\rm c})\chi_{\rm c} = 2$, while the velocity and pressure are continuous."
 The same velocity of the two flows at the contact surface indicates that the ratio of Lorentz factors of the two shock fronts should become according to equations (191) and (31))., The same velocity of the two flows at the contact surface indicates that the ratio of Lorentz factors of the two shock fronts should become according to equations \ref{ge}) ) and \ref{ga}) ).
 The continuous pressure at the contact surface requires that the pressures at both sides of the contact surface evolve with time in the same manner., The continuous pressure at the contact surface requires that the pressures at both sides of the contact surface evolve with time in the same manner.
 Thus we obtain from equations (18)) ancl (30)), Thus we obtain from equations \ref{pe}) ) and \ref{pa}) )
"Several mechanisms can brake the spin-up of an accreting neutron star: the magnetospheric centrifugal barrier (??),, GW emission (??) and the magnetic-dipole torque (?)..","Several mechanisms can brake the spin-up of an accreting neutron star: the magnetospheric centrifugal barrier \citep{illarionov1975, ghosh1979}, GW emission \citep{wagoner1984, bildsten1998} and the magnetic-dipole torque \citep{ostriker1969}."
" Every one of these mechanisms eventually balances the accretion torque and stalls the spin-up process, when the spin frequency v, is large enough."," Every one of these mechanisms eventually balances the accretion torque and stalls the spin-up process, when the spin frequency $\nu_{\mathrm{s}}$ is large enough."
 We use equation (21)) for spin balance which assumes the usual thin-disc accretion model (?).., We use equation \ref{spin_equilibrium}) ) for spin balance which assumes the usual thin-disc accretion model \citep{bildsten1998}.
" It should be noted that this is not necessarily valid, as more refined accretion models weaken the spin-up torque or strengthen the propeller effect, thus obviating the need for a strong GW torque."," It should be noted that this is not necessarily valid, as more refined accretion models weaken the spin-up torque or strengthen the propeller effect, thus obviating the need for a strong GW torque."
" The feedback provided by radiation pressure in rapidly accreting systems could lead to a thick and sub-Keplerian inner accretion disc, which modulates the accretion torque of the standard thin-disc model (?).."," The feedback provided by radiation pressure in rapidly accreting systems could lead to a thick and sub-Keplerian inner accretion disc, which modulates the accretion torque of the standard thin-disc model \citep{andersson2005}."
" Also, for weak accretors, if the magnetospheric radius becomes larger than the corotation radius, the star can exist in either a strong or weak 'propeller' phase (see ? and references therein), with the transition between these phases being strongly dependent on the kinematic viscosity and magnetic diffusivity of the accreting matter (??).."," Also, for weak accretors, if the magnetospheric radius becomes larger than the corotation radius, the star can exist in either a strong or weak `propeller' phase (see \citet{romanova2008} and references therein), with the transition between these phases being strongly dependent on the kinematic viscosity and magnetic diffusivity of the accreting matter \citep{romanova2004, romanova2005}."
" Nevertheless, these improved accretion models do not invalidate any of the proposed GW-generating mechanisms."," Nevertheless, these improved accretion models do not invalidate any of the proposed GW-generating mechanisms."
" In this section, we investigate how the stalling frequency depends on the EOS, if all the braking comes from gravitational radiation reaction."," In this section, we investigate how the stalling frequency depends on the EOS, if all the braking comes from gravitational radiation reaction."
" In this work, we do not consider radiation-pressure feedback on the accretion disc since we are interested in modelling moderately accreting LMXBs where this effect is small."," In this work, we do not consider radiation-pressure feedback on the accretion disc since we are interested in modelling moderately accreting LMXBs where this effect is small."
" Also, in the vicinity of the bottom magnetic field [107—10°G; see ? and ?]], where the magnetosphere touches the stellar surface and the propeller effect can be neglected, the GW torque dominates the magneto-centrifugal and magnetic-dipole torques."," Also, in the vicinity of the bottom magnetic field $10^{7} - 10^{8} \ \mathrm{G}$; see \citet{van_den_Heuvel1995} and \citet{zhang2006}] ], where the magnetosphere touches the stellar surface and the propeller effect can be neglected, the GW torque dominates the magneto-centrifugal and magnetic-dipole torques."
" Clearly, this approach yields an upper bound on νο; the other mechanisms can lower 14 further."," Clearly, this approach yields an upper bound on $\nu_{\mathrm{s}}$ ; the other mechanisms can lower $\nu_{\mathrm{s}}$ further."
ORPs.,ORPs.
" An ORP is defined as the initial rotation period, about 180 yr, at radial zone 200 (zz 33 AU)."," An ORP is defined as the initial rotation period, about 180 yr, at radial zone 200 $\approx~$ 33 AU)."
" The cylindrical grid in (w,¢,z) is initially 256x128x32.", The cylindrical grid in $\varpi$ $\phi$ $z$ ) is initially 256x128x32.
 An additional 256 radial zones are added at about 5 ORPs to extend the grid to about co= 85 AU once GIs cause the disk to expand radially off the initial computational grid., An additional 256 radial zones are added at about 5 ORPs to extend the grid to about $\varpi =$ 85 AU once GIs cause the disk to expand radially off the initial computational grid.
" The initial Q-distribution has a minimum of about 1.5 at czοὐ 34 AU, and so the disk is only marginally stable at time t=0."," The initial $Q$ -distribution has a minimum of about 1.5 at $\varpi \approx$ 34 AU, and so the disk is only marginally stable at time $t = 0$."
" The indirect potential simulation is run for a total of about 19.6 ORPS or 3,500 yr."," The indirect potential simulation is run for a total of about 19.6 ORPS or 3,500 yr."
" In the ? simulation, the fixed initial central ""star"" is a radially extended oblate mass distribution inside the central disk hole."," In the \citet{mejia2005} simulation, the fixed initial central “star” is a radially extended oblate mass distribution inside the central disk hole."
" When fitting the Mejíaa star by a point mass for the indirect case, an error of is made in the star's mass."," When fitting the Mejíaa star by a point mass for the indirect case, an error of is made in the star's mass."
 An additional error in the central force due to the nonsphericity of the Mejíaa star is about at 11 AU and falls off quickly outside that radius., An additional error in the central force due to the nonsphericity of the Mejíaa star is about at 11 AU and falls off quickly outside that radius.
 These discrepancies are two orders of magnitude less than the tens of percent differences reported for the GI behavior outside 10 AU and should be unimportant., These discrepancies are two orders of magnitude less than the tens of percent differences reported for the GI behavior outside 10 AU and should be unimportant.
" Qualitatively, the overall outcomes are fairly similar."," Qualitatively, the overall outcomes are fairly similar."
" The disk simulated with the indirect potential goes through the same four phases as the disk in the fixed star case (?),, namely cooling, the onset of Gls in aburst, and a to a final quasi- asymptotic phase."," The disk simulated with the indirect potential goes through the same four phases as the disk in the fixed star case \citep{mejia2005}, namely , the onset of GIs in a, and a to a final quasi-steady phase."
 The dividing times between these phases are also roughly the same., The dividing times between these phases are also roughly the same.
 The onset of the burst phase occurs around 4.5 ORPs with the initial burst being predominately in discrete four to six-armed modes., The onset of the burst phase occurs around 4.5 ORPs with the initial burst being predominately in discrete four to six-armed modes.
" The transition phase begins near 7 ORPs and continues until the start of the quasi-steady asymptotic phase around 11 to 12 ORPs, after which heating by GI activity balances cooling on average throughout the Gl-active region and instability of a large number of interacting spiral waves is sustained in an approximate steady state (seealso?).."," The transition phase begins near 7 ORPs and continues until the start of the quasi-steady asymptotic phase around 11 to 12 ORPs, after which heating by GI activity balances cooling on average throughout the GI-active region and instability of a large number of interacting spiral waves is sustained in an approximate steady state \citep[see also][]{gammie2001}."
 The right-hand panels in Figure offer a comparison of the final midplane densities for the disks., The right-hand panels in Figure \ref{SMfinalcomp} offer a comparison of the final midplane densities for the disks.
"[I] The structures in the indirect potential simulation appear to be a bit less sharply defined, probably owing to somewhat weaker GI amplitudes, as discussed in refresults:asymptotic.."," The structures in the indirect potential simulation appear to be a bit less sharply defined, probably owing to somewhat weaker GI amplitudes, as discussed in \\ref{results:asymptotic}. ."
" One can also see that the system COM, indicated by the white x in Figure [I]; has remained within the central hole of the grid."," One can also see that the system COM, indicated by the white x in Figure \ref{SMfinalcomp}, has remained within the central hole of the grid."
" Although this motion is not large from the disk's perspective, it may be of observational interest (see refdiscussion:star))."," Although this motion is not large from the disk's perspective, it may be of observational interest (see \\ref{discussion:star}) )."
" Additionally, as can be seen in Figure D], the final azimuthally-averaged surface density profiles show very little difference, except that the indirect potential disk is slightly less extended radially."," Additionally, as can be seen in Figure \ref{SMsurfcomp}, the final azimuthally-averaged surface density profiles show very little difference, except that the indirect potential disk is slightly less extended radially."
" Assuming the surface density profile is a power law ©cr?, a least squares fit for q between 15 and 40 AU gives 2.33 and 2.31 for the indirect potential and fixed star cases, respectively."," Assuming the surface density profile is a power law $\Sigma \propto r^{-q}$, a least squares fit for $q$ between 15 and 40 AU gives 2.33 and 2.31 for the indirect potential and fixed star cases, respectively."
" Also, the Toomre Q-values are similar in the asymptotic phase and average to about 1.2 to 1.3 over the 15 to 40 AU region."," Also, the Toomre $Q$ -values are similar in the asymptotic phase and average to about 1.2 to 1.3 over the 15 to 40 AU region."
" Despite the overall similarities, the GI structure for the indirect case exhibits some interesting differences."," Despite the overall similarities, the GI structure for the indirect case exhibits some interesting differences."
" These can best be illustrated quantitatively by examining the overall amplitudes A,, of sin(m@) and cos(m@) terms in a Fourier decomposition of the density in the azimuthal direction.", These can best be illustrated quantitatively by examining the overall amplitudes $A_m$ of $\sin(m\phi)$ and $\cos(m\phi)$ terms in a Fourier decomposition of the density in the azimuthal direction.
" We compute the Fourier components as in ? such that where and Here po is the axisymmetric component of the density, and the integrals extend over the computational grid."," We compute the Fourier components as in \citet{imamura2000} such that where and Here $\rho_0$ is the axisymmetric component of the density, and the integrals extend over the computational grid."
" We typically sample the value of the components 100 times per ORP and, for some purposes, average them over a time interval, which is typically several ORPs in the asymptotic phase."," We typically sample the value of the components 100 times per ORP and, for some purposes, average them over a time interval, which is typically several ORPs in the asymptotic phase."
" As shown in Figure [I], there is a qualitative difference in dominant mode during the burst."," As shown in Figure \ref{SMfinalcomp}, , there is a qualitative difference in dominant mode during the burst."
" For both cases, analyses of A,»(t) plots reveal exponential growth in the linear regime at similar rates for m—3 to 6 spiral waves centered near 30 AU, the region where Q is initially minimum."," For both cases, analyses of $A_m(t)$ plots reveal exponential growth in the linear regime at similar rates for $m = 3$ to 6 spiral waves centered near 30 AU, the region where $Q$ is initially minimum."
" On the other hand, the m—4 and 5 waves play very different roles in the two cases."," On the other hand, the $m = 4$ and 5 waves play very different roles in the two cases."
 Aa grows first and is dominant for the fixed case; growth in As is substantially delayed., $A_4$ grows first and is dominant for the fixed case; growth in $A_5$ is substantially delayed.
" On the other hand, As and Ag dominate growth for the indirect case, with m—4 remaining unimportant until amplitudes become nonlinear."," On the other hand, $A_5$ and $A_6$ dominate growth for the indirect case, with $m = 4$ remaining unimportant until amplitudes become nonlinear."
 All spiral waves grow from random uncorrelated noise imposed initially in both cases that displaces the COM from the grid center., All spiral waves grow from random uncorrelated noise imposed initially in both cases that displaces the COM from the grid center.
" In the fixed case, where deviations of the star from the COM are not handled physically, an ordering in the small (~10 ?) amplitudes of m=4,5, and 6 develops within a small fraction of an ORP such that m=4 has a head start in its linear growth phase and reaches nonlinear amplitude about a third of an ORP before the other modes."," In the fixed case, where deviations of the star from the COM are not handled physically, an ordering in the small $\sim 10^{-4}$ ) amplitudes of $m = 4, 5,$ and 6 develops within a small fraction of an ORP such that $m = 4$ has a head start in its linear growth phase and reaches nonlinear amplitude about a third of an ORP before the other modes."
" On the other hand, in the indirect case, where the COM is treated properly, the early values of A» to Ag are more nearly the same, as they should be for white noise."," On the other hand, in the indirect case, where the COM is treated properly, the early values of $A_2$ to $A_6$ are more nearly the same, as they should be for white noise."
" Then m—5, followed closely by m—6, dominates the linear growth."," Then $m = 5$, followed closely by $m = 6$, dominates the linear growth."
" During the linear growth phase for both cases, Αι£2A3A4+A4AsAc, as expected if m=1 results from the nonlinear interaction of the m—3 to 6 modes and is not itself an independent unstable mode (e.g.,?).."," During the linear growth phase for both cases, $A_1 \approx A_3A_4 + A_4A_5 + A_5A_6$, as expected if $m = 1$ results from the nonlinear interaction of the $m = 3$ to 6 modes and is not itself an independent unstable mode \citep[e.g.,][]{laughlin1996}."
" As discussed in refSMdetailed,, the motion of the star with respect to the COM during the burst of the indirect case appears to be a response to this nonlinear interaction and should be sensitive in detail to the modes involved."," As discussed in \\ref{SMdetailed}, the motion of the star with respect to the COM during the burst of the indirect case appears to be a response to this nonlinear interaction and should be sensitive in detail to the modes involved."
" Because our initial conditions are arbitrary and the subsequent evolution is not substantively different, the qualitative difference in dominant mode during linear growth does not undermine the general conclusions aboutdisk evolution drawn from simulations with fixed stars in earlier IUHG papers."," Because our initial conditions are arbitrary and the subsequent evolution is not substantively different, the qualitative difference in dominant mode during linear growth does not undermine the general conclusions aboutdisk evolution drawn from simulations with fixed stars in earlier IUHG papers."
" On the other hand, the significant displacementof the star during the burst and subsequent phases is a potentially interesting and observable"," On the other hand, the significant displacementof the star during the burst and subsequent phases is a potentially interesting and observable"
measured by Ixennicuttetal.(1993).,measured by \citet{ken98}.
. While (his is a lo result. improved data on (he Sextans A long-period Cepheids (or those in similarly metal-poor galaxies) is needed to improve the measurenient.," While this is a $1 \sigma$ result, improved data on the Sextans A long-period Cepheids (or those in similarly metal-poor galaxies) is needed to improve the measurement."
 It is clear that the P-L relation does not have a large (~0.5 magnitudes per dex: Deaulieu et al., It is clear that the P-L relation does not have a large $\sim 0.5$ magnitudes per dex; Beaulieu et al.
 1997 and Gould 1994) dependence on metallicity., 1997 and Gould 1994) dependence on metallicity.
 We find no evidence of a correlation between metallicity and the red clump — RGB lip distance difference. which is comforting since metallicity is accounted for in our red clamp calibration.," We find no evidence of a correlation between metallicity and the red clump $-$ RGB tip distance difference, which is comforting since metallicity is accounted for in our semi-empirical red clump calibration."
 The zero points are also consistent at the lo level. providing additional evidence (hat the red. clump is an accurate distance indicator. provided that population effects are properly accounted for.," The zero points are also consistent at the $1 \sigma$ level, providing additional evidence that the red clump is an accurate distance indicator, provided that population effects are properly accounted for."
 Finally. we present distance moduli relative to the SAIC for all galaxies in Table 5..," Finally, we present distance moduli relative to the SMC for all galaxies in Table \ref{tabrelative}."
 Although the LAIC is generally the standard. for such comparisons. we chose to use the SAIC! for the comparison because it has accurate distances determined with all five distance indicators.," Although the LMC is generally the standard for such comparisons, we chose to use the SMC for the comparison because it has accurate distances determined with all five distance indicators."
 We have presented photometry of deep ΛΕΡΟΣ observations of Sextans A. Observations were made over 16 epochs in ES814W and 8 epochs in F555W. permitting a search lor variable stars.," We have presented photometry of deep WFPC2 observations of Sextans A. Observations were made over 16 epochs in F814W and 8 epochs in F555W, permitting a search for variable stars."
 We identified 82 periodic variables with clean light curves in both bands: all 82 appear to be short-period Cepheids., We identified 82 periodic variables with clean light curves in both bands; all 82 appear to be short-period Cepheids.
 We found fundamental-mode Cepheids with periods as short as 0.8 davs and first-overtone Cephleids with periods of 0.5 davs., We found fundamental-mode Cepheids with periods as short as 0.8 days and first-overtone Cepheids with periods of 0.5 days.
 Using these Cepheids. we measured a distance to Sextans A using a P-L relation computed using SAIC short-period (1 αν) Cepheids.," Using these Cepheids, we measured a distance to Sextans A using a P-L relation computed using SMC short-period $\sim 1$ day) Cepheids."
 We compared (his distance to that obtained with other means. aud find (hat short-period Cepheids are indeed a viable standard candle for objects at or below the metallicity of the SAIC.," We compared this distance to that obtained with other means, and find that short-period Cepheids are indeed a viable standard candle for objects at or below the metallicity of the SMC."
 Given the large numbers of these that should be found in low-metallicity star-forming galaxies. (ese objects can provide much more accurate distance measurements than those obtained using other distance indicators.," Given the large numbers of these that should be found in low-metallicity star-forming galaxies, these objects can provide much more accurate distance measurements than those obtained using other distance indicators."
 Combining the short-period Cepheids with distances obtained trom the RGB tip and red clump. we determined the distance modulus to Sextans A to be jn=25.61c0.07. corresponding to a distance of d—1.32£0.04 Alpe.," Combining the short-period Cepheids with distances obtained from the RGB tip and red clump, we determined the distance modulus to Sextans A to be $\mu_0 = 25.61 \pm 0.07$, corresponding to a distance of $d = 1.32 \pm 0.04$ Mpc."
 We also exeunined relative distances produced by live distance indicators for live galaxies in and near the Local Group: Sextans A. Leo A. IC 1613. and the Magellanic Clouds.," We also examined relative distances produced by five distance indicators for five galaxies in and near the Local Group: Sextans A, Leo A, IC 1613, and the Magellanic Clouds."
 We find (hat relative distances calculated using the RGB tip. red clump. and RR Lyrae are consistent for the sample.," We find that relative distances calculated using the RGB tip, red clump, and RR Lyrae are consistent for the sample."
 However. we find a metallicity dependence of —0.12£0.12 magnitudes per," However, we find a metallicity dependence of $-0.12 \pm 0.12$ magnitudes per"
Liolse.,noise.
 To satisfy the acuuissibilitv condition (1)) we choose a value of &=6., To satisfy the admissibility condition \ref{eq04}) ) we choose a value of $k=6$.
 In reality. Equation (1)) is not formally satisfied for the Morlet. Wavelet of Equation (1)).," In reality, Equation \ref{eq04}) ) is not formally satisfied for the Morlet Wavelet of Equation \ref{eq01}) )."
 ILowever if &c5. the acimissibilitv condition is satisfied to within the accuracy of computer algorithms using sinele precision απlhinetic.," However if $k \geq 5$, the admissibility condition is satisfied to within the accuracy of computer algorithms using single precision arithmetic."
 To test our technique. we rau several καΊος.," To test our technique, we ran several simulations."
 First. to investigate the ability of our technique to detect a purely periodic signal in the presence of noise we used a signal of the fori. where IN is an amplitude factor aud ο(1) a noise function that eenerates white noise.," First, to investigate the ability of our technique to detect a purely periodic signal in the presence of noise we used a signal of the form where $N$ is an amplitude factor and $n(t)$ a noise function that generates white noise."
 We show the continuous and cross transforms for j|N=10 in Figure 1.., We show the continuous and cross transforms for $N=10$ in Figure \ref{fig3}.
" The cross wavelet plot is that for a mock sienal of period 7,=2.059 vr.", The cross wavelet plot is that for a mock signal of period $\tau_n = 2.059$ yr.
 Plots of the elobal wavelet spectrum and FE. for this simulation are shown in Figure laa. As can be seen in Figure laa. the period is easily recovered using the techuique with noise of amplitude five-times that of the auplitude of the sinusoid (signal-to-noise of 0.2).," Plots of the global wavelet spectrum and $\bar{F_c}$ for this simulation are shown in Figure \ref{fig5}a a. As can be seen in Figure \ref{fig5}a a, the period is easily recovered using the technique with noise of amplitude five-times that of the amplitude of the sinusoid (signal-to-noise of 0.2)."
 Because signal-to-noise values as low as S/N=0.2 are never realized. our technique is is vali for the time series studied here.," Because signal-to-noise values as low as $S / N = 0.2$ are never realized, our technique is is valid for the time series studied here."
 Tn addition. we also applied the algorithia to a sinusoid that changes amplitude aud phase over he time window.," In addition, we also applied the algorithm to a sinusoid that changes amplitude and phase over the time window."
 The transforms are shown iu Figure 2.. and the power spectra in Figure 1bb. A change in amplitude affects the amplitude of he wavelet coefficieuts. as would be expected.," The transforms are shown in Figure \ref{fig4}, and the power spectra in Figure \ref{fig5}b b. A change in amplitude affects the amplitude of the wavelet coefficients, as would be expected."
" The effects of a discontinuous chanee in the phase o, can be seen as disturbing the structure of the rausforms in these regions.", The effects of a discontinuous change in the phase $\phi_a$ can be seen as disturbing the structure of the transforms in these regions.
 The technique gives a characteristic period of 2.0 vr. showing hat a sudden change in the shase of a signal does not effect the technique.," The technique gives a characteristic period of 2.0 yr, showing that a sudden change in the phase of a signal does not effect the technique."
 Tn practice. we arc| unge this technique to Investigate quasiperiocic behavior aud to give a characteristic time scae for a time series. rather than attempting to recover a periodic signal buried beneath noise (althoueh this certainly nav be done).," In practice, we are using this technique to investigate quasiperiodic behavior and to give a characteristic time scale for a time series, rather than attempting to recover a periodic signal buried beneath noise (although this certainly may be done)."
 To illustrate οἱr techuique in the case of pure nolse. we applied he eross-wavelet technique," To illustrate our technique in the case of pure noise, we applied the cross-wavelet technique"
[ound in the images. but we diseuss only Gl in this At 8.4 Gllz. an apparent source with a flux density of 2846 μον [corresponding to 2x107 W ! for distance modulus of (m—M)=24.42 mag (Mevlan et al.,"found in the images, but we discuss only G1 in this At 8.4 GHz, an apparent source with a flux density of $28\pm 6$ $\mu$ Jy [corresponding to $2\times 10^{15}$ W $^{-1}$ for distance modulus of $(m-M)=24.42$ mag (Meylan et al."
" 2001)] was found approximately one arcsecond from the GI optical position reported by Mevlanetal.(2001): (his radio source has J2000 coordinates of a=0032""46.54. 0=39734/39.2""."," 2001)] was found approximately one arcsecond from the G1 optical position reported by \citet{mey01}; this radio source has J2000 coordinates of $\alpha=00^h32^m46.54^s$, $\delta=39^\circ 34'39.2''$."
 Figure 1 shows our 8.4 GIIZz image of the bby rregion centered on G1: this image includes al sigma error circle of 1755 radius for the X-ray position found by IXong(2007)., Figure 1 shows our 8.4 GHz image of the by region centered on G1; this image includes a $1~sigma$ error circle of 5 radius for the X-ray position found by \citet{kon07}.
. The radio position has an estimated error of 0766 in each dimension (not shown in the figure). derived by dividing the beam size by the signal-to-noise The probability of finding a 4.5σ noise spike or background source so close to GI is quite small. as indicated by the lack of anv other contours of similar strength in Figure 1.," The radio position has an estimated error of 6 in each dimension (not shown in the figure), derived by dividing the beam size by the signal-to-noise The probability of finding a $4.5~\sigma$ noise spike or background source so close to G1 is quite small, as indicated by the lack of any other contours of similar strength in Figure 1."
 If we hypothesize that there are 9 independent beams (roughly bbv 8) within which a source would be considered to be associated with Gl. then the probability of a 4.5σ noise point close to GL is less than LO7.," If we hypothesize that there are 9 independent beams (roughly by ) within which a source would be considered to be associated with G1, then the probability of a $4.5~\sigma$ noise point close to G1 is less than $10^{-4}$."
 Similarly. the expected density of extragalactic radio sources at 28 piJy or above is 0.25 7 1993).. or 4x10? in a box oon a side. making it unlikely that we have found an unrelated background source.," Similarly, the expected density of extragalactic radio sources at 28 $\mu$ Jy or above is 0.25 $^{-2}$ \citep{win93}, or $4\times 10^{-3}$ in a box on a side, making it unlikely that we have found an unrelated background source."
" In order to search for possible data errors that might cause a spurious source. we have subjected our data set to additional tests. imaging data from the two days separately. ancl also imagine the two different intermediate lrequency. channels separately,"," In order to search for possible data errors that might cause a spurious source, we have subjected our data set to additional tests, imaging data from the two days separately, and also imaging the two different intermediate frequency channels separately."
 The GI radio source remains in (he images made [rom each data subset. with approximately the same [αν density ancl position.," The G1 radio source remains in the images made from each data subset, with approximately the same flux density and position."
 The overall significance is reduced by 2!? to approximately 30 in each image made with about half the cata. as expected for a real source will unconteminated data.," The overall significance is reduced by $2^{1/2}$ to approximately $3~\sigma$ in each image made with about half the data, as expected for a real source with uncontaminated data."
 Other 2.50 3.0 sources appear in the central bbox in some subsets of half the data. consistent with noise statisies. but none is above the 3.5σ level in the full data set.," Other $2.5~\sigma$ $3~\sigma$ sources appear in the central box in some subsets of half the data, consistent with noise statistics, but none is above the $3.5~\sigma$ level in the full data set."
 Thus. all tests indicate that the detection of Gl is real. and we will proceed on that basis for the remainder of this paper.," Thus, all tests indicate that the detection of G1 is real, and we will proceed on that basis for the remainder of this paper."
 At 4.9 GllIz. we find no detection at the GI position. but the much hieher noise level provides us only with very," At 4.9 GHz, we find no detection at the G1 position, but the much higher noise level provides us only with very"
"linear relation to stellar age with A(g—r)~0.5A(age), and, notably, do not appear to differ between BCGs and age-matched, similarly luminous non-BCGs (except for the few very young BCGs, which are redder).","linear relation to stellar age with $\Delta(g-r)\sim 0.5\Delta({\rm age})$, and, notably, do not appear to differ between BCGs and age-matched, similarly luminous non-BCGs (except for the few very young BCGs, which are redder)."
 The difference between the model and spectra-derived (aperture) colours is caused by colour gradients., The difference between the model and spectra-derived (aperture) colours is caused by colour gradients.
" We found BCGs to be at least A(g—r)~0.01 mag redder than other E/S0s in the model-magnitude CMR and CoR (Figures 1, 2, 3 and 4) with a smaller (<0.005 mag) or no significant difference in the spectra-derived colours."," We found BCGs to be at least $\Delta(g-r)\simeq 0.01$ mag redder than other E/S0s in the model-magnitude CMR and $\sigma$ R (Figures 1, 2, 3 and 4) with a smaller $<0.005$ mag) or no significant difference in the spectra-derived colours."
" This can now be explained as a combination of (i) the 0.5 Gyr greater mean age of BCGs compared with luminosity-matched non-BCGs, corresponding to A(g—r)~0.0025 in the aperture colour, and (ii) the flatter colour gradients of BCGs, meaning that even if their spectra-derived (central) colours match those of non-BCGs, their model-magnitude colours will be redder."," This can now be explained as a combination of (i) the 0.5 Gyr greater mean age of BCGs compared with luminosity-matched non-BCGs, corresponding to $\Delta(g-r)\simeq 0.0025$ in the aperture colour, and (ii) the flatter colour gradients of BCGs, meaning that even if their spectra-derived (central) colours match those of non-BCGs, their model-magnitude colours will be redder."
 This could account for the remaining ~0.0075 magnitudes., This could account for the remaining $\sim 0.0075$ magnitudes.
" To further investigate the relationshipbetween age and colour gradient,. we show mean rzt2:—1 against radius (Figure 21) 10loge+M, (Figure 22) and density (Figure 23) for the full E/SO0 sample divided by mean stellar ‘formation’ redshift."," To further investigate the relationshipbetween age and colour gradient, we show mean ${{{\rm r}_{eff}(g)}\over{{\rm r}_{eff}(r)}}-1$ against radius (Figure 21) $10~{\rm log}~\sigma+M_r$ (Figure 22) and density (Figure 23) for the full E/S0 sample divided by mean stellar `formation' redshift."
 BCGs are included to see if their different properties with respect to other E/S0s resemble the effects of increased age., BCGs are included to see if their different properties with respect to other E/S0s resemble the effects of increased age.
" We also (Figure 24) plot colour gradient against dynamic mass, estimated as 5.8; for units of kms~! and kpc, log(Mayn/Mo)=reg 6.13."," We also (Figure 24) plot colour gradient against dynamic mass, estimated as $5.8{{\rm r_{eff}\sigma^2}\over{G}}$; for units of $\rm s^{-1}$ and kpc, ${\rm log}~(M_{dyn}/M_{\odot})=\rm log~r_{eff} + 2 {\rm log}\sigma +6.13$ ."
" Colour gradients show a broad peak at Muay,~ 10''4Mo5, which is more pronounced for galaxies with younger stellar ages."," Colour gradients show a broad peak at $M_{dyn}\simeq 10^{11.4}M_{\odot}$ , which is more pronounced for galaxies with younger stellar ages."
" Colour gradients in the galaxies with the youngest stellar populations, zform«0.5, show correlations with galaxy properties, similar to the 0.5<Zform«1.0 galaxies, but offset downwards, as might result from the presence of an admixture of post-starbursts with negative gradients."," Colour gradients in the galaxies with the youngest stellar populations, $z_{form}<0.5$, show correlations with galaxy properties, similar to the $0.5<z_{form}<1.0$ galaxies, but offset downwards, as might result from the presence of an admixture of post-starbursts with negative gradients."
" Colour gradients in E/SOs depend significantly on radius, density, mass etc."," Colour gradients in E/S0s depend significantly on radius, density, mass etc."
 within each Zform interval., each $z_{form}$ interval.
" However, these correlations, especially those with radius and density,"," However, these correlations, especially those with radius and density,"
metallicities.,metallicities.
 From their results it appears that either the IMF has to be truncated. or the colors have to be dominated by a fading starburst to reproduce the observed colors. both of which would bring our results closer to the Kennicutt-Schmidt relation.," From their results it appears that either the IMF has to be truncated, or the colors have to be dominated by a fading starburst to reproduce the observed colors, both of which would bring our results closer to the Kennicutt-Schmidt relation."
 For example. FUV-NUV color of 0.34 would be observed in a galaxy which ¢1) has a Kroupa IMF (Kroupa.Tout&Gilmore1993) with metallicity 2 Z./20. an age of 107 years. and star formation was quenched after 107. years or (2) has a Kroupa IMF truncated at 5M. at the highend. solar metallicity. has been forming stars ‘or 107 years continuously or (3) has an age of 107 years and star formation was quenched after 107 years or (4) Has Kroupa IMF. solar metallicity. an age of 10° years and star formation was quenched after 107. years.," For example, FUV-NUV color of 0.34 would be observed in a galaxy which (1) has a Kroupa IMF \citep{kro93} with metallicity = $_\odot$ /20, an age of $\times$ $^8$ years, and star formation was quenched after $^8$ years or (2) has a Kroupa IMF truncated at $_\odot$ at the highend, solar metallicity, has been forming stars for $\times$ $^8$ years continuously or (3) has an age of $\times$ $^8$ years and star formation was quenched after $^8$ years or (4) Has Kroupa IMF, solar metallicity, an age of $\times$ $^8$ years and star formation was quenched after $^8$ years."
 For galaxies in our sample. UV colours range from ~0.03 to —0.8. and hence the range of yossible models is correspondingly larger.," For galaxies in our sample, FUV-NUV colours range from $\sim$ 0.03 to $\sim$ 0.8, and hence the range of possible models is correspondingly larger."
 While we don't explore his issue further. it should be noted that alternate IMFs or star ormation histories could lead to revision in the interpretation of our data.," While we don't explore this issue further, it should be noted that alternate IMFs or star formation histories could lead to revision in the interpretation of our data."
 While there have not been systematic earlier studies of star ormation recipes for similarly faint galaxies. it is interesting to compare our results with what is already known for brighter dwarfs or large spiral galaxies.," While there have not been systematic earlier studies of star formation recipes for similarly faint galaxies, it is interesting to compare our results with what is already known for brighter dwarfs or large spiral galaxies."
 Empirical studies of star formation hresholds have generally used the Ha luminosity as a tracer of he current star formation rate., Empirical studies of star formation thresholds have generally used the $\alpha$ luminosity as a tracer of the current star formation rate.
 The Ha luminosity is sensitive argely to stars with masses = 10 M. and lifetimes < 20 Myr: one hence gets a measure of the instantaneous star formation., The $\alpha$ luminosity is sensitive largely to stars with masses $>$ 10 $_\odot$ and lifetimes $<$ 20 Myr; one hence gets a measure of the instantaneous star formation.
 A study of spatially resolved star formation laws for regions of size ~ 800 pe in the spiral galaxy MSda (Kennicuttetal.2007). which uses both Ha and Infrared fluxes to estimate star formation. show very similar results to what we obtain here.," A study of spatially resolved star formation laws for regions of size $\sim$ 500 pc in the spiral galaxy M51a \citep{ken07} which uses both $\alpha$ and Infrared fluxes to estimate star formation, show very similar results to what we obtain here."
 There is no evidence of any obvious star formation threshold., There is no evidence of any obvious star formation threshold.
 Interestingly the relation between SFR surface density and HI gas surface density is quite steep. but the power law index comes down to |.5640.04 after taking molecular gas into account.," Interestingly the relation between SFR surface density and HI gas surface density is quite steep, but the power law index comes down to $\pm$ 0.04 after taking molecular gas into account."
 Thilkeretal.(2007). did a multi-wavelength study of the spiral galaxy NGC 7331., \citet{thi07} did a multi-wavelength study of the spiral galaxy NGC 7331.
 Along with looking for an azimuthally averaged Schmidt's law. they also show pixel by pixel correlations between aand ut different resolutions (400 pe and | kpe).," Along with looking for an azimuthally averaged Schmidt's law, they also show pixel by pixel correlations between and at different resolutions (400 pc and 1 kpc)."
 Their vs. yplot looks strikingly similar to tiat for our galaxies. with a Hat lower portion changing to a steep power law portion. which only reaches the Kennicutt-Sehmid law level at higher column densities.," Their vs. plot looks strikingly similar to that for our galaxies, with a flat lower portion changing to a steep power law portion, which only reaches the Kennicutt-Schmidt law level at higher column densities."
 However. unlike the galaxies in our sample. NGC 7331 ws a number of pixels lying above the level at which the KennicuSchmidt relation holds.," However, unlike the galaxies in our sample, NGC 7331 has a number of pixels lying above the level at which the Kennicutt-Schmidt relation holds."
 Even after acding molecular gas to the plot remains qualitatively unchanged. except. as expected. the »ower law portion becomes less steep and Tor a large number of pixels fall below the Kennicutt-Schmidt law evel.," Even after adding molecular gas to the plot remains qualitatively unchanged, except, as expected, the power law portion becomes less steep and for a large number of pixels fall below the Kennicutt-Schmidt law level."
 This is similar to what we expect to find on taking molecular gas into account for our sample., This is similar to what we expect to find on taking molecular gas into account for our sample.
 In another recent study. Boissier et al.," In another recent study, Boissier et al."
 (Boissieretal.2007) look for evidence for a threshold density or star formation using UV fluxes as a measure of the star ormation rate., \citep{boi07} look for evidence for a threshold density for star formation using UV fluxes as a measure of the star formation rate.
 Similarly to the results presented here. they also do not find any evidence for a threshold below which star formation is completely quenched.," Similarly to the results presented here, they also do not find any evidence for a threshold below which star formation is completely quenched."
 Finally. Wyderetal.(2009). in a paper sublished after our manuscript was submitted. tind results similar o ours when comparing the global to Tor a sample of LSB galaxies.," Finally, \citet{wyd09} in a paper published after our manuscript was submitted, find results similar to ours when comparing the global to for a sample of LSB galaxies."
 A similar pixel by pixel correlation study (at 220 pe linear resolution) was done for the Magellanic clouds by Kennicuttal.(1995).., A similar pixel by pixel correlation study (at 220 pc linear resolution) was done for the Magellanic clouds by \cite{ken95}. .
 The star formation rate in that case was traced by Ha emission., The star formation rate in that case was traced by $\alpha$ emission.
 The 9 scatter plot in Kennicuttet is qualitatively similar to those in the current paper: the power law indices that they find are 1.754:0.3 for the LMC and 1.954370.3 for the SMC., The ) scatter plot in \cite{ken95} is qualitatively similar to those in the current paper; the power law indices that they find are $1.75 \pm 0.3$ for the LMC and $1.95 \pm 0.3$ for the SMC.
 In a recent paper. Bigieletal.(2008). study the relation between the star formation rate density and the gas column density in a sample of 18 nearby galaxies at ~ 750 pe resolution using data from the THINGS survey.," In a recent paper, \citet{bigiel08} study the relation between the star formation rate density and the gas column density in a sample of 18 nearby galaxies at $\sim$ 750 pc resolution using data from the THINGS survey."
 Their sample covers a range of galaxy types. including dwarfs. but they do not present pixel by yixel correlations for galaxies fainter than the FIGGS magnitude imit of 14.9.," Their sample covers a range of galaxy types, including dwarfs, but they do not present pixel by pixel correlations for galaxies fainter than the FIGGS magnitude limit of $-$ 14.9."
 For the 4 irregular galaxies for which they do tit a power law. they find power law indices that vary from 1.59 o 2.78.," For the 4 irregular galaxies for which they do fit a power law, they find power law indices that vary from 1.59 to 2.78."
" They also find that the ""star formation efficiency"" (1.9. 9 is lower in dwarfs and the outer parts of spirals than in the inner. H» dominated regions ofspiral galaxies."," They also find that the “star formation efficiency” (i.e. ) is lower in dwarfs and the outer parts of spirals than in the inner, $_2$ dominated regions of spiral galaxies."
 This is similar o our finding that the SER in dwarfs is lower than that predicted rom the Kennicutt(1998). relation., This is similar to our finding that the SFR in dwarfs is lower than that predicted from the \cite{ken98} relation.
 They also find that the gas density in dwarfs truncates sharply at about 9M. /pc?., They also find that the gas density in dwarfs truncates sharply at about $_\odot$ $^2$.
 We show in Fig., We show in Fig.
 8. the distribution of column densities at both 400 pe and 200 pe resolutions (the data from UGC 685 was not included while calculating the distribution of column densities at 400 pe resolution. as it is unique in having some gas at column densities between ~20 and  30M. Z and it wasn’t imaged at 200 pe resolution).," \ref{fig:hst} the distribution of column densities at both 400 pc and 200 pc resolutions (the data from UGC 685 was not included while calculating the distribution of column densities at 400 pc resolution, as it is unique in having some gas at column densities between $\sim20$ and $\sim30$ $_\odot$ $^{-2}$, and it wasn't imaged at 200 pc resolution)."
 The 300 pe resolution data does indeed show a fall off in the amount of eas at column densities more than 10 . /pc. however at the higher resolution. one can see a tail in the distribution that extends to ~30M. /pe?.," The 400 pc resolution data does indeed show a fall off in the amount of gas at column densities more than $\sim 10$ $_\odot$ $^2$, however at the higher resolution, one can see a tail in the distribution that extends to $\sim 30$ $_\odot$ $^2$."
 Tt would appear that dense HI gas occurs in small clumps whose density gets smoothed out when one observes with à coarser resolution., It would appear that dense HI gas occurs in small clumps whose density gets smoothed out when one observes with a coarser resolution.
 Begumetal.(2006) compared. the morphology of the Ha emission and the HI emission (at 300 pe resolution) in a sample of IO similarly faint dwarf galaxies., \cite{begum06} compared the morphology of the $\alpha$ emission and the HI emission (at 300 pc resolution) in a sample of 10 similarly faint dwarf galaxies.
 Although the Ha emission generally occurred near the central regions where the gas column density is high. no one to one relation between the HI column density and the gas column density was found.," Although the $\alpha$ emission generally occurred near the central regions where the gas column density is high, no one to one relation between the HI column density and the gas column density was found."
 One possible explanationfor this observation is stochasticity in the Ha based estimates ofspp., One possible explanationfor this observation is stochasticity in the $\alpha$ based estimates of.
 There are two reasons why UV based estimates of would be less susceptible to stochastic fluctuations than Ha based ones. viz. C," There are two reasons why UV based estimates of would be less susceptible to stochastic fluctuations than $\alpha$ based ones, viz. ("
I) as mentioned above Ha ,1) as mentioned above $\alpha$ 
"With four classes of particles in each of three ""generations. there are 12 predicted particles.","With four classes of particles in each of three “generations”, there are 12 predicted particles."
 All 12 members of these three generations have been confirmed. experimentally (so Noon2 3). and there is a powerful piece of evidence that there are no more than three eeneralions.," All 12 members of these three generations have been confirmed experimentally (so $N_{\rm gen}\geq 3$ ), and there is a powerful piece of evidence that there are no more than three generations."
 The Z particle can decay into particle/anti-particle pairs of anv of these 12 particles. except for the top quark. since two tops have more mass than the Z.," The $Z$ particle can decay into particle/anti-particle pairs of any of these 12 particles, except for the top quark, since two tops have more mass than the $Z$."
 The rate ol decay would increase (and so the width of the Z resonance would decrease) bevond its measured value if there were particles in a fourth generation., The rate of decay would increase (and so the width of the $Z$ resonance would decrease) beyond its measured value if there were particles in a fourth generation.
 The only caveat is that if all four particles in (his putative generation were heavier (han half the Z mass. (these decay channels would be blocked (as they are for the top quark).," The only caveat is that if all four particles in this putative generation were heavier than half the $Z$ mass, these decay channels would be blocked (as they are for the top quark)."
" llence. there is excellent. though not absolutely secure evidence that there are exactly three generations (Vou,= 3)."," Hence, there is excellent, though not absolutely secure evidence that there are exactly three generations $N_{\rm gen}=3$ )."
 And so. Rabi's question can now be made more precise: “why exactlv three generations?," And so, Rabi's question can now be made more precise: “why exactly three generations”?"
" There is a broad class of answers to such questions that is subsumed under the loliv slogan ""anthropic principle’.", There is a broad class of answers to such questions that is subsumed under the lofty slogan “anthropic principle”.
" The core idea of this principle is (hat our ""universe"" is only one ol many universes. each with its own ""fundamental constants”. such as the electron mass. the fine structure constant. etc."," The core idea of this principle is that our “universe” is only one of many universes, each with its own “fundamental constants”, such as the electron mass, the fine structure constant, etc."
" These constants appear as ""Iundamental (ie. without anv further explanation — or perhaps “explained” by mathematical derivation from other constants that are themselves unexplained). but thev actually are just realizations of fields whose svauneliries are broken as (he universe cools. leaving them al some random value."," These constants appear as “fundamental” (i.e., without any further explanation – or perhaps “explained” by mathematical derivation from other constants that are themselves unexplained), but they actually are just realizations of fields whose symmetries are broken as the universe cools, leaving them at some random value."
 Then there are a huge number of universes that have various values for these constants that are incompatible with intelligent life. and so do not contain physicists to ponder the values ol these constants.," Then there are a huge number of universes that have various values for these constants that are incompatible with intelligent life, and so do not contain physicists to ponder the values of these constants."
 Our universe is among the others., Our universe is among the others.
 lence. if we see that certain constants (or combinations of constants) “happen” to be compatible with life. (he reason is the same as Why the Earth “happens” to have water: our planet mav well be in a minority that are so endowed. but the others do not have people on them to worry about this issue.," Hence, if we see that certain constants (or combinations of constants) “happen” to be compatible with life, the reason is the same as why the Earth “happens” to have water: our planet may well be in a minority that are so endowed, but the others do not have people on them to worry about this issue."
 Ol course. the full conditions for intelligent life are not known. but we can conservatively identify al least some conditions.," Of course, the full conditions for intelligent life are not known, but we can conservatively identify at least some conditions."
 For example. if big bang nucleosvnthesis had ended with >99% helium. then stars would not live long enough lor intelligent lile to evolve. even supposing that such life could form without hvdrogen.," For example, if big bang nucleosynthesis had ended with $>99\%$ helium, then stars would not live long enough for intelligent life to evolve, even supposing that such life could form without hydrogen."
 And I think that few would argue that a universe without barvons (protons and neutrons — made of quarks) could contain lile. intelligent or otherwise.," And I think that few would argue that a universe without baryons (protons and neutrons – made of quarks) could contain life, intelligent or otherwise."
 Now. before continuing. 1 must take note of the fact that many people object to the," Now, before continuing, I must take note of the fact that many people object to the"
There are several proposed mechanisms lor (he formation of quark stars.,There are several proposed mechanisms for the formation of quark stars.
 Quark stars are expected to form during the collapse of the core of a massive star. after (he supernova explosion. as a result of a first or second order phase transition. resulüng in deconfined quark matter (Daietal.1995).," Quark stars are expected to form during the collapse of the core of a massive star, after the supernova explosion, as a result of a first or second order phase transition, resulting in deconfined quark matter \citep{Da}."
. The proto-neutron star core or the neutron star core is a favorable environment for the conversion of ordinary matter to strange quark matter 1993b).., The proto-neutron star core or the neutron star core is a favorable environment for the conversion of ordinary matter to strange quark matter \citep{ChDa}.
 Another possibility is that some neutron stars in low-mass X-ray binaries can accrete sufficient mass to undergo a phase transition to become strange stars (Cheng 1996)., Another possibility is that some neutron stars in low-mass X-ray binaries can accrete sufficient mass to undergo a phase transition to become strange stars \citep{Ch96}.
. This mechanism has also been proposed by ChengandDai(1998) as a source of radiation emission for cosmological y-ray bursts., This mechanism has also been proposed by \citet{Ch98a} as a source of radiation emission for cosmological $\gamma $ -ray bursts.
 Quark stars can also be formed during (he rapid spin-down of maguetars. astroplivsical objects with extremely. high magnetic fields (Ilarkoetal.2004).," Quark stars can also be formed during the rapid spin-down of magnetars, astrophysical objects with extremely high magnetic fields \citep{HaChTa04}."
.. Based on numerical integration of (he general relativistic hydrostatic equilibrium equations a complete description of the basic astrophysical properties (1iass. radius. eccentricity. Keplerian frequency ete.)," Based on numerical integration of the general relativistic hydrostatic equilibrium equations a complete description of the basic astrophysical properties (mass, radius, eccentricity, Keplerian frequency etc.)"
 of both static and rotating strange stars can be obtained (Witten.1984:Cheng 2002a)..," of both static and rotating strange stars can be obtained \citep{Wi84,Ha86,Go00,De98,ChHa,HaCh02}."
 Rotational properties can discriminate between neutron and quark stars., Rotational properties can discriminate between neutron and quark stars.
 Strange stars can reach much shorter periods (han neutron stars. of the order of 0.5 ms (Chengetal.1998a).," Strange stars can reach much shorter periods than neutron stars, of the order of $0.5$ ms \citep{Ch98}."
. r-mocle instabilities in rapidly rotating strange stars lead to specific signatures in the evolution of pulsars with periods below 2.5 ms., $r$ -mode instabilities in rapidly rotating strange stars lead to specific signatures in the evolution of pulsars with periods below $2.5$ ms.
 If strange matter is absolutely stable. pulsars would be expected to consist of quark matter.," If strange matter is absolutely stable, pulsars would be expected to consist of quark matter."
 Some data on pulsar properles are consistent wilh Chis assumption (Madsen2000a)., Some data on pulsar properties are consistent with this assumption \citep{Ma00}.
. The structure of a realistic strange star is very complicated. but its basic properties can be described as follows (Alcocketal.1986).," The structure of a realistic strange star is very complicated, but its basic properties can be described as follows \citep{Al86}."
. Deta-equilibrated strange quark - star matter consists of an approximately equal mixture of up s. down d and strange s quarks. with a slight deficit of the latter.," Beta-equilibrated strange quark - star matter consists of an approximately equal mixture of up $u$, down $d$ and strange $s$ quarks, with a slight deficit of the latter."
 The Fermi gas of 2.1 quarks constitutes a single color-singlet barvon with barvon number 4A., The Fermi gas of $3A$ quarks constitutes a single color-singlet baryon with baryon number $A$.
 This structure of the quarks leads (o a net positive charge inside (he star., This structure of the quarks leads to a net positive charge inside the star.
 Since stars in (heir lowest energy state are supposed to be charge neutral. electrons must balance (he net positive quark charge in strange matter stus.," Since stars in their lowest energy state are supposed to be charge neutral, electrons must balance the net positive quark charge in strange matter stars."
 The electrons. being bounded to the quark matter by the electromagnetic interaction and not by the strong force. are able to move [freely across the quark surface. but clearly cannot move to infinity because of the electrostatic attraction of quarks.," The electrons, being bounded to the quark matter by the electromagnetic interaction and not by the strong force, are able to move freely across the quark surface, but clearly cannot move to infinity because of the electrostatic attraction of quarks."
 For hot stars the electron distribution could extend up to ~10* [m above the quark surface (ChengandIHarko2003)., For hot stars the electron distribution could extend up to $\sim 10^{3}$ fm above the quark surface \citep{ChHa03}.
. Photon enüssivitv is the basic parameter for determining macroscopic properties οἱ stellar tvpe objects., Photon emissivity is the basic parameter for determining macroscopic properties of stellar type objects.
 Aleockοἱal.(1986) have shown that. because of verv high. plasma frequency cj near (he strange matter edge. photon emissivity of strange matter is verv low.," \citet{Al86} have shown that, because of very high plasma frequency $\omega _p$ near the strange matter edge, photon emissivity of strange matter is very low."
 Onlv photons produced just below the surface. in a quark laver of approximately 5 fn. and," Only photons produced just below the surface, in a quark layer of approximately $5$ fm, and"
indepeudenut groups have identified some interesting behaviors iu measured nuclear decay rates hat did not arise [rom a change in the plivsical or chemical euviroumeut of the decaying 940-4121.11.15 Iu these results. there appears to be some structure in what should be ‘audoualy distributed data points.,"independent groups have identified some interesting behaviors in measured nuclear decay rates that did not arise from a change in the physical or chemical environment of the decaying \cite{ell90,fal01,par05,bau07,par10a,par10b,shn98a,shn98b} In these results, there appears to be some structure in what should be randomly distributed data points."
 More recently. however. Recent work by our has gone further aud detailed the existence of periodicities aud other non-raudom behaviors in measured nuclear decay data from Purdue Universitv!?.. Brookhaven National Laboratory (BNLPF. and the Physikalisch-Technische Bundesanstalt P..," More recently, however, Recent work by our \cite{jen09a,jen09b,fis09,stu10a,jav10,stu10b,stu11a,stu11b} has gone further and detailed the existence of periodicities and other non-random behaviors in measured nuclear decay data from Purdue \cite{jen09a}, , Brookhaven National Laboratory \cite{alb86}, , and the Physikalisch-Technische Bundesanstalt \cite{sie98}."
 The suggestion of this recent work is that there is a solar influence ou the these measured decay rates. via some particle or ield of solar origin such as solar neutriuos.," The suggestion of this recent work is that there is a solar influence on the these measured decay rates, via some particle or field of solar origin such as solar neutrinos."
" Such a proposal is. without question. going to generate eriticisiu [rom the physics community. sed ou the belief that the observed effects were the result of chauges in the environment of the detector systems (ie.."" temperature. background. etc.)"," Such a proposal is, without question, going to generate criticism from the physics community, based on the belief that the observed effects were the result of changes in the environment of the detector systems (i.e., temperature, background, etc.)"
 or systematic 372572729790OsOD However. a thorough analysis by our group of the Purdue. BNL aud PTB detector systems lias effectively refitted essentially all of this criticism’! Ln this report we will further strengthen this view by providing adcditioual perspective aud results that support the conjecture that whatever is influencing the measured decay rates is external to the terrestrial euvironmeut. and could iu [act have a solar origin.," or systematic \cite{coo09,nor09,sem09,sil09} However, a thorough analysis by our group of the Purdue, BNL and PTB detector systems has effectively refuted essentially all of this \cite{jen10} In this report we will further strengthen this view by providing additional perspective and results that support the conjecture that whatever is influencing the measured decay rates is external to the terrestrial environment, and could in fact have a solar origin."
 To begiu this discussion. it is helpful to collect together the information related to the observed decay rate changes trom multiple independent experiments.," To begin this discussion, it is helpful to collect together the information related to the observed decay rate changes from multiple independent experiments."
 Table 1 lists several experiments which utilize cilferent isotopes as well as different different detector techuologies. all ol which show anomalous behaviors. either in the form of periodicities. or a localized departure from the expected decay trend over a short duratiou.," Table \ref{tab:exp}
 lists several experiments which utilize different isotopes as well as different different detector technologies, all of which show anomalous behaviors, either in the form of periodicities, or a localized departure from the expected decay trend over a short duration."
 What should be evident [rom the information presented in Table 1 is that the “problem” olf apparent non-raudom bebavior iu nuclear decay imeasuremeuts is apparent in a numnber of different experiments., What should be evident from the information presented in Table \ref{tab:exp} is that the “problem” of apparent non-random behavior in nuclear decay measurements is apparent in a number of different experiments.
 What will probably also become evident as time passes is that the ellect is more widespread than even this list indicates., What will probably also become evident as time passes is that the effect is more widespread than even this list indicates.
 A simple search of the literature reveals multiple instances of articles discussing the discrepancies in nuclear decay measurements. particularly hall-life determinations.’238.3L385 ]t is interesting. given recent advauces in detector techuoloey. aud the precision with which we cau make measurements in the preseut day. that there would be discrepancies as large as are observed to be present in nuclear decay data.," A simple search of the literature reveals multiple instances of articles discussing the discrepancies in nuclear decay measurements, particularly half-life \cite{beg01,chi07,woo90,woo96} It is interesting, given recent advances in detector technology, and the precision with which we can make measurements in the present day, that there would be discrepancies as large as are observed to be present in nuclear decay data."
 However. if some of these measurements are of ο decays that are allected by auinfluenceexternal to tlhe Earth. and," However, if some of these measurements are of $\beta^-$ decays that are affected by aninfluenceexternal to the Earth, and"
"At 100 arcsecs from the center of NGC 1407, the 2MASS project quotes an isophotal intensity of 0.97 DN (20.82 J mag arcsecs?).","At 100 arcsecs from the center of NGC 1407, the 2MASS project quotes an isophotal intensity of 0.97 DN (20.82 $J$ mag $^{-2}$ )."
 Our project finds a value of 1.42 DN (20.41 J mag ?)., Our project finds a value of 1.42 DN (20.41 $J$ mag $^{-2}$ ).
" To determine which value more closely represents the isophote at that radius, we have plotted a histogram of intensity values for all pixels between 99.5 and 100.5 arcsecs from the galaxy center."," To determine which value more closely represents the isophote at that radius, we have plotted a histogram of intensity values for all pixels between 99.5 and 100.5 arcsecs from the galaxy center."
 This histogram is shown in Figure 6 (both regular and normalized)., This histogram is shown in Figure 6 (both regular and normalized).
" From this Figure, it is obvious that the intensity values deduced by the 2MASS project are not in agreement with the mean value of the pixels in the image, whereas our calculated intensity value is in good agreement with the mean and median value."," From this Figure, it is obvious that the intensity values deduced by the 2MASS project are not in agreement with the mean value of the pixels in the image, whereas our calculated intensity value is in good agreement with the mean and median value."
" Since NGC 1407 is a nearly perfect circle in axial ratio, this is not an effect of the ellipse fitting procedure."," Since NGC 1407 is a nearly perfect circle in axial ratio, this is not an effect of the ellipse fitting procedure."
 This is also not due to calibration errors (these are raw data numbers) nor an improper sky subtraction (the differences, This is also not due to calibration errors (these are raw data numbers) nor an improper sky subtraction (the differences
CO observations of V Thyva’s euvelope were made ou the welts of March 21-28 with the 10. li Robert D. Leighton telescope of the Caltech Subinillimeter Observatory on Manna wea. UWawaii.,"CO observations of V Hya's envelope were made on the nights of March 24-28 with the 10.4 m Robert B. Leighton telescope of the Caltech Submillimeter Observatory on Mauna Kea, Hawaii."
 The weather was excellent. with a zeuith opacity at 220 QGIIz of 7. 0.03.," The weather was excellent, with a zenith opacity at 220 GHz of $\rm \tau_{\circ} ~ \leq$ 0.03."
 The CO(I3) line at 161.0108 GIIz and the CO(65) line at 691.173 GIIz were observed., The CO(4–3) line at 461.0408 GHz and the CO(6–5) line at 691.473 GHz were observed.
 The Lue profiles are shown in Al - both the fast and normal winds are seen.," The line profiles are shown in \ref{co}
 - both the fast and normal winds are seen."
 Table 2 sunuiuarizes the CO line data obtained at the Caltech Subiuilluneter Observatorv for V Iva. giviug he brightuess temperature of the fast wind (measured at |100 kins +). the Dbrightuess teniperature of the hain colmponent (ueasured at about 10 kins i ratio T(fast wind)/T(slow wind). aud the halfpower scaumwidth of the CSO for each line.," Table 2 summarizes the CO line data obtained at the Caltech Submillimeter Observatory for V Hya, giving the brightness temperature of the fast wind (measured at +100 $\rm km~s^{-1}$ ), the brightness temperature of the main component (measured at about –10 $\rm km~s^{-1}$ ), the ratio T(fast wind)/T(slow wind), and the half-power beamwidth of the CSO for each line."
 The CO(21) aud CO(32) data are from Paper 1., The CO(2–1) and CO(3–2) data are from Paper 1.
" These data show that the ratio of the CO(21) and CO(32) line intensities for both he fast aud slow winds have about the value expected or au optically thick source which is roughly the same size as or smaller than the 20"" beam for the CO(32) ine.", These data show that the ratio of the CO(2–1) and CO(3–2) line intensities for both the fast and slow winds have about the value expected for an optically thick source which is roughly the same size as or smaller than the $\rm 20''$ beam for the CO(3–2) line.
 The ratios of the CO(65). CO(I3) and CO(32) ines. however. show that the envelope is partly resolved at 160 and 691 GITz.," The ratios of the CO(6–5), CO(4–3) and CO(3–2) lines, however, show that the envelope is partly resolved at 460 and 691 GHz."
 The fast wind does not appear to be sieuificautlv hotter than he slow sviud., The fast wind does not appear to be significantly hotter than the slow wind.
 These observations confirm the conclusions from Paper I: V Uva is ejecting a very fast molecular wind as well as slower winds. aud the circtunstellar cuvelopes formed by both the fast aud slow winds have approximately the same diameter. 207.," These observations confirm the conclusions from Paper I: V Hya is ejecting a very fast molecular wind as well as slower winds, and the circumstellar envelopes formed by both the fast and slow winds have approximately the same diameter, $\rm 20''$."
" These data eive a radius of ~8«1019 αι at a distance of 500 pc. a dvnaiica age for the slow wind of about 1600 years. anda total mass loss rate of alout ἐν{ο°AD,s.+."," These data give a radius of $\rm \sim 
8 \times 10^{16}$ cm at a distance of 500 pc, a dynamical age for the slow wind of about 1600 years, and a total mass loss rate of about $\rm 4
\times 10^{-5} ~ M_{\odot} ~ yr^{-1}$."
" This hieh mass loss rate. and the small dvnamical age of the envelope. suggestsOO that V IIa has eutered its ""superwiud"" phase."," This high mass loss rate, and the small dynamical age of the envelope, suggests that V Hya has entered its “superwind” phase."
observations (Mavromatakis 2003).,observations (Mavromatakis 2003).
 We find that the age of SNR G78.2+2.1 is about one order magnitude smaller than the spin-down age of 7~77 kyr for PSR J2021+4026., We find that the age of SNR G78.2+2.1 is about one order magnitude smaller than the spin-down age of $\tau\sim 77$ kyr for PSR J2021+4026.
" However, the discrepancy between the real age and the spin down age may be expected, if PSR J2021+4206 was born with a spin period close to current one."," However, the discrepancy between the real age and the spin down age may be expected, if PSR J2021+4206 was born with a spin period close to current one."
" It can be expected that PSR J2021+4026 is much younger than the age inferred from the spin down age, such as PSR J0538+2817, which has a spin down age of 620 kyr, but its true age is 40 kyr (Ng et al."," It can be expected that PSR J2021+4026 is much younger than the age inferred from the spin down age, such as PSR J0538+2817, which has a spin down age of 620 kyr, but its true age is 40 kyr (Ng et al."
 2007)., 2007).
" Therefore, the discrepancy between the age of SNR G78.2+2.1 and the spin down age of PSR J2021+4026 does not imply that aand the supernova remnant G78.2+2.1 are not associated with each other."," Therefore, the discrepancy between the age of SNR G78.2+2.1 and the spin down age of PSR J2021+4026 does not imply that and the supernova remnant G78.2+2.1 are not associated with each other."
" In fact, we expect that SNR G78.2+2.1 and aare associated with each other, as follows."," In fact, we expect that SNR G78.2+2.1 and are associated with each other, as follows."
" First, adopting the distance d~1 kpc toJ2021+4026,, the efficiency, η, which is defined by the ratio between y-ray luminosity and spin down luminosity, is provided as η~0.16Q(d/kpc)?, where ó€? is the solid angle."," First, adopting the distance $d\sim 1$ kpc to, the efficiency, $\eta$, which is defined by the ratio between $\gamma$ -ray luminosity and spin down luminosity, is provided as $\eta\sim 0.1\delta\Omega (d/\mathrm{kpc})^2$, where $\delta\Omega$ is the solid angle."
" This large efficiency with the distance is consistent with the typical value of the efficiency of the middle spin-down age pulsars such as Geminga, which has η~0.0760)."," This large efficiency with the distance is consistent with the typical value of the efficiency of the middle spin-down age pulsars such as Geminga, which has $\eta\sim
0.07\delta\Omega$."
" Therefore, the distance to the SNR G78.2+2.1 provides a consistent efficiency with the spin down age."," Therefore, the distance to the SNR G78.2+2.1 provides a consistent efficiency with the spin down age."
" Secondly, iis located 7.8 arcmin off-axis from the geometrical center of SNR G78.24-2.1."," Secondly, is located $\sim 7.8$ arcmin off-axis from the geometrical center of SNR G78.2+2.1."
" Assuming that off-axis of the location of iis caused by the proper motion in the space, the space velocity of PSR J2021--4026 is estimated to be vj~ 340(d/1kpc)km/s, which is a typical velocity of observed pulsars (Hansen Phinney 1997; Hobbs et al."," Assuming that off-axis of the location of is caused by the proper motion in the space, the space velocity of PSR J2021+4026 is estimated to be $v_p\sim 340 (d/1\mathrm{kpc})$ km/s, which is a typical velocity of observed pulsars (Hansen Phinney 1997; Hobbs et al."
 2005)., 2005).
" On these ground, the association between aand SNR G78.2+2.1 is more likely."," On these ground, the association between and SNR G78.2+2.1 is more likely."
 Finally we briefly discuss the association between 2XMM J202131.4-402645 andJ202144026.," Finally, we briefly discuss the association between 2XMM J202131.+402645 and."
". First, only 2XMM J202131.+402645 is a persistent and relatively bright X-ray source located within the y—ray error circle of ((see section 2)."," First, only 2XMM J202131.+402645 is a persistent and relatively bright $X$ -ray source located within the $\gamma-$ ray error circle of (see section 2)."
" Second, the nominal X-ray flux in 2-10 keV, fx~8x1077?erg/cm?/s, of 2XMM J202131.4-402645 provides a X-ray luminosity of Lx~10°°foerg/s, where fo is the solid angle divided by Απ."," Second, the nominal X-ray flux in 2-10 keV, $f_{X}\sim 
8\times 10^{-15}~\mathrm{erg/cm^2/s}$, of 2XMM J202131.+402645 provides a X-ray luminosity of $L_{X}\sim
 10^{30}f_{\Omega}~\mathrm{erg/s}$, where $f_{\Omega}$ is the solid angle divided by $4\pi$."
 Comparing the X- luminosity of other pulsars (e.g. Possenti et al., Comparing the X-ray luminosity of other pulsars (e.g. Possenti et al.
" 2002), we find that the X-ray luminosity Lx~10°°foerg/s of 2XMM J202131.4-402645 is consistent with typical values of the pulsars which have a spin down luminosity similar to that ofJ20214-4026,, Ε~1035 erg/s. It is also found that the ratio of the X-ray flux of 2XMM J202131.+402645 deduced from the best-fit blackbody model and y-ray flux ofJ2021+4026,, fx/f,~2x10?, is consistent with typical values of y-ray pulsars with a middle spin-down age like Geminga."," 2002), we find that the X-ray luminosity $L_{X}\sim 10^{30}f_{\Omega}~\mathrm{erg/s}$ of 2XMM J202131.+402645 is consistent with typical values of the pulsars which have a spin down luminosity similar to that of, $\dot{E}\sim 10^{35}$ erg/s. It is also found that the ratio of the X-ray flux of 2XMM J202131.+402645 deduced from the best-fit blackbody model and $\gamma$ -ray flux of, $f_X/f_{\gamma}\sim2\times10^{-5}$, is consistent with typical values of $\gamma$ -ray pulsars with a middle spin-down age like Geminga."
" On these ground, we suggest that 2XMM J202131.4-402645 is the plausible X-ray counter part ofJ20214-4026."," On these ground, we suggest that 2XMM J202131.+402645 is the plausible X-ray counter part of."
". Although the interpetation of the pulsar nature is tempting, we have to emphasize that small photon statistics of the existing data does not allow us to confirm this unambiguously."," Although the interpetation of the pulsar nature is tempting, we have to emphasize that small photon statistics of the existing data does not allow us to confirm this unambiguously."
" Specifically, we cannot tightly constrain the aforementioned flux ratios, spectral parameters as well as the variability."," Specifically, we cannot tightly constrain the aforementioned flux ratios, spectral parameters as well as the variability."
" Therefore, we have to admit that we cannot exclude the possible nature of aas a star or an AGN."," Therefore, we have to admit that we cannot exclude the possible nature of as a star or an AGN."
 Dedicated X-ray and optical observations are most important in discriminating these competing X-ray emission scenarios., Dedicated X-ray and optical observations are most important in discriminating these competing X-ray emission scenarios.
" Obviously, if X-ray pulsations that consistent with the rotational period of ccan be detected in the future, this will certainly provide the most decisive nature ofJ202131."," Obviously, if X-ray pulsations that consistent with the rotational period of can be detected in the future, this will certainly provide the most decisive nature of."
"0+402645.. In this study, we have investigated the multiwavelength emission nature of iin details."," In this study, we have investigated the multiwavelength emission nature of in details."
" Searching for the X-ray counterparts of this new and bright y—ray pulsar, we have identified aas the promising candidate."," Searching for the X-ray counterparts of this new and bright $\gamma-$ ray pulsar, we have identified as the promising candidate."
 We have also examined the y-ray data collected by FERMI LAT with an exposure somewhat more than one year and tightly constrained its spectral and temporal properties in MeV—GeV regime., We have also examined the $\gamma-$ ray data collected by FERMI LAT with an exposure somewhat more than one year and tightly constrained its spectral and temporal properties in $-$ GeV regime.
 We found that the X-ray position of iis consistent with that of the optimal y—ray timing solution., We found that the X-ray position of is consistent with that of the optimal $\gamma-ray$ timing solution.
 We have further modeled the y—ray light curve in the context of outer gap accelerator model and provided constraints on its emission geometry., We have further modeled the $\gamma-$ ray light curve in the context of outer gap accelerator model and provided constraints on its emission geometry.
 The nominal to—y-ray flux ratio of iis found to resemble that of Geminga., The nominal $\gamma$ -ray flux ratio of is found to resemble that of Geminga.
" Furthermore, if wwas born with a spin period close to the current one, it is likely to be born in the explosion that created SNR G78.2+2.1 and has a projected kick velocity of few hundred km/s which is typical for the known pulsar population."," Furthermore, if was born with a spin period close to the current one, it is likely to be born in the explosion that created SNR G78.2+2.1 and has a projected kick velocity of few hundred km/s which is typical for the known pulsar population."
" At the distance of SNR G78.2+2.1, the conversion efficiencies in y—ray and X-ray of this pulsar are both found to be consistent with those of Geminga."," At the distance of SNR G78.2+2.1, the conversion efficiencies in $\gamma-$ ray and X-ray of this pulsar are both found to be consistent with those of Geminga."
" Together with the non-detection of any pulsed radio signals, the high energy emission properties of ssuggest it to be a new member of Geminga-like pulsars."," Together with the non-detection of any pulsed radio signals, the high energy emission properties of suggest it to be a new member of Geminga-like pulsars."
 LT would like to thank DFG for financial support in SFB TR 7 Gravitational Wave Astronomy and the members of the neutron star group at AIU for fruitful discussions and useful comments., LT would like to thank DFG for financial support in SFB TR 7 Gravitational Wave Astronomy and the members of the neutron star group at AIU for fruitful discussions and useful comments.
 KSC is supported by a GRF grant of Hong Kong Government under HKU700908P. The authors would like to thank C.Y. Ng for useful discussion., KSC is supported by a GRF grant of Hong Kong Government under HKU700908P. The authors would like to thank C.Y. Ng for useful discussion.
The gravitational hierarchical formation of large-scale structures in the universe drives shocks in the intergalactic medium (IGM).,The gravitational hierarchical formation of large-scale structures in the universe drives shocks in the intergalactic medium (IGM).
 These convert the kinetic energy associated with cosmic flows into thermal energy. with IGM temperatures reaching values of 5-10 keV in massive clusters and «1 keV in large-scale filaments (e.g.??)..," These convert the kinetic energy associated with cosmic flows into thermal energy, with IGM temperatures reaching values of 5-10 keV in massive clusters and 1 keV in large-scale filaments \citep[e.g.][]{2002MNRAS.337..199M,2001ApJ...552..473D}."
 Shocks can re-accelerate old relativistic electron populations. released by the former AGN activity. within a cluster. or they can also directly accelerate thermal electrons of the IGM.," Shocks can re-accelerate old relativistic electron populations, released by the former AGN activity within a cluster, or they can also directly accelerate thermal electrons of the IGM."
 The detection of radio emission from intergalactic shocks has important implications for our understanding of cosmology and astrophysics: it provides a test of structure formation models. can confirm the existence of the undetected warm-hot intergalactic medium. and can trace its distribution (?)..," The detection of radio emission from intergalactic shocks has important implications for our understanding of cosmology and astrophysics: it provides a test of structure formation models, can confirm the existence of the undetected warm-hot intergalactic medium, and can trace its distribution \citep{keshet}."
 Cluster-wide relativistic electron populations are observed in several merging and post-merging clusters as diffuse steep-spectrum structures., Cluster-wide relativistic electron populations are observed in several merging and post-merging clusters as diffuse steep-spectrum structures.
 They are grouped in three classes: radio halos. relics. and mini-halos (?)..," They are grouped in three classes: radio halos, relics, and mini-halos \citep{fergiov}."
 Radio halos are unpolarized. extended (~ | Mpe or more) structures located at the cluster center.," Radio halos are unpolarized, extended $\sim$ 1 Mpc or more) structures located at the cluster center."
 Relics still have an extended shape. but they lie at the cluster periphery and show high polarization percentages (~20%).," Relics still have an extended shape, but they lie at the cluster periphery and show high polarization percentages $\sim$ $\%$ )."
 Mini-halos are detected around a powerful radio galaxy at the center of cooling core clusters and have a typical size of ~ 500 kpe., Mini-halos are detected around a powerful radio galaxy at the center of cooling core clusters and have a typical size of $\sim$ 500 kpc.
 These diffuse cluster structures provide important information on the history and evolution. of clusters. by improving our knowledge about the presence and importance of both large-scale magnetic fields and relativistic particles in the IGM.," These diffuse cluster structures provide important information on the history and evolution of clusters, by improving our knowledge about the presence and importance of both large-scale magnetic fields and relativistic particles in the IGM."
 Furthermore. since up to now they have only been found in clusters with signatures of merging in the optical and X-ray domains. their detection could be considered to indicate a perturbed dynamical state.," Furthermore, since up to now they have only been found in clusters with signatures of merging in the optical and X-ray domains, their detection could be considered to indicate a perturbed dynamical state."
 The low radio-surface brightness and steep spectrum make the detection of halos and relies rather difficult., The low radio-surface brightness and steep spectrum make the detection of halos and relics rather difficult.
 However. in the past few years several works on radio halos and their hosting clusters (e.g.??) have improved our knowledge of these radio sources.," However, in the past few years several works on radio halos and their hosting clusters \citep[e.g.][]{2003tsra.symp..209F,2005xrrc.procE8.02F} have improved our knowledge of these radio sources."
 On the other hand. the location of relics in the outermost cluster regions makes their detection very problematic because. usually. only the cluster central regions are imaged at radio wavelengths with high sensitivity.," On the other hand, the location of relics in the outermost cluster regions makes their detection very problematic because, usually, only the cluster central regions are imaged at radio wavelengths with high sensitivity."
 Detailed broad band radio studies of relics are still missing: similarly. the comparison of radio with X-ray emission is hot possible because of the lack of sensitivity of X-ray satellites in. the peripheral cluster regions.," Detailed broad band radio studies of relics are still missing; similarly, the comparison of radio with X-ray emission is not possible because of the lack of sensitivity of X-ray satellites in the peripheral cluster regions."
 A review of the current knowledge of relics is found in ?.., A review of the current knowledge of relics is found in \cite{giovferrelics}.
" One of the main goals of detecting “relic-like™ structures in galaxy clusters is to constrain their origin,", One of the main goals of detecting “relic-like” structures in galaxy clusters is to constrain their origin.
 The galaxy cluster A2255 is nearby (z=0.0806.2) anc ΠΟΠ.ROSAT," The galaxy cluster A2255 is nearby \citep[z=0.0806,][]{struble} and rich."
 X-ray observations indicate that it has recently undergone a merger (???)..," X-ray observations indicate that it has recently undergone a merger \citep{burns,fer,miller}."
 Recent observations of A2255 revealed temperature asymmetries of the ICM anc reached the conclusion that the merger happened ~ 0.15 Gyr ago. probably in the E-W direction with à. still. uncertair position angle (?)..," Recent observations of A2255 revealed temperature asymmetries of the ICM and reached the conclusion that the merger happened $\sim$ 0.15 Gyr ago, probably in the E-W direction with a still uncertain position angle \citep{sakelliou}. ."
 Optical studies of A2255 reveal kinematical substructures in the form of several associated groups (?).. anc the high ratio of velocity dispersion to X-ray temperature (6.34KeV;?) also indicates a non-relaxed system.," Optical studies of A2255 reveal kinematical substructures in the form of several associated groups \citep{yuan}, and the high ratio of velocity dispersion to X-ray temperature \citep[6.3 KeV;][]{horner} also indicates a non-relaxed system."
 When studied at radio wavelengths. A2255 shows a diffuse radio halo (located at the center of the cluster) and a relic source (at the cluster periphery). together with a large number of embedded head-tail radiogalaxies (2)..," When studied at radio wavelengths, A2255 shows a diffuse radio halo (located at the center of the cluster) and a relic source (at the cluster periphery), together with a large number of embedded head-tail radiogalaxies \citep{har}."
 This cluster is the first and only one in which polarized radio emission from a radio halo has been detected., This cluster is the first and only one in which polarized radio emission from a radio halo has been detected.
The halo shows filaments of strong polarized emission ( 20-40 %)) with the magnetic fields fluctuating up to scales of ~ 400 kpe in size (?)..,The halo shows filaments of strong polarized emission $\sim$ 20-40 ) with the magnetic fields fluctuating up to scales of $\sim$ 400 kpc in size \citep{gov}.
 We observed A2255 at several radio wavelengths to better understand the nature of the polarized emission of the filaments m the halo (whether this is intrinsic or due to a projection effect) and to search for low surface-brightness features located farfrom the cluster center., We observed A2255 at several radio wavelengths to better understand the nature of the polarized emission of the filaments in the halo (whether this is intrinsic or due to a projection effect) and to search for low surface-brightness features located farfrom the cluster center.
 We did not observe, We did not observe
dominant number of clouds oriented: perpencicularly with respect to the Galactic plane is an indication that turbulence in the Galactic ISM. must. be injected on scales. larger han those associated with feedback from massive stars.,dominant number of clouds oriented perpendicularly with respect to the Galactic plane is an indication that turbulence in the Galactic ISM must be injected on scales larger than those associated with feedback from massive stars.
 The latter conelusion is based. on the fact that supernova (SN) explosions occurring in the Galactic disk will generate ountain like structures and a laree fraction of MCs that are »erpendieular to the Galactic plane., The latter conclusion is based on the fact that supernova (SN) explosions occurring in the Galactic disk will generate fountain like structures and a large fraction of MCs that are perpendicular to the Galactic plane.
 However. to date. there is no complete theoretical/numerical model that. includes sullicient physics and that possesses enough resolution and hat is able to make predictions about the real fractions of the orientations of MCSs in a Milky Wavy-like Galaxy.," However, to date, there is no complete theoretical/numerical model that includes sufficient physics and that possesses enough resolution and that is able to make predictions about the real fractions of the orientations of MCs in a Milky Way-like Galaxy."
 In he absence of such information. the conclusions of οσα et al. (," In the absence of such information, the conclusions of Koda et al. ("
2006). still require the quantitative argument. that would definitely confirm or exlude stellar feedback as being responsible for the orientations of Galactic MCSs.,2006) still require the quantitative argument that would definitely confirm or exlude stellar feedback as being responsible for the orientations of Galactic MCs.
 The question of what causes the inclinations of MCSs with respect to the galactic plane in the Galaxy ancl in other ealaxics is intimately related to the question of the nature of the dominant energy injection mechanism into the ISAL, The question of what causes the inclinations of MCs with respect to the galactic plane in the Galaxy and in other galaxies is intimately related to the question of the nature of the dominant energy injection mechanism into the ISM.
 Numerical simulations and theoretical studies show that feedback [rom massive stars in the form of. stellar winds (Ixrumholz et al., Numerical simulations and theoretical studies show that feedback from massive stars in the form of stellar winds (Krumholz et al.
 2006) or SN explosions (Palous al., 2006) or SN explosions (Palouš et al.
 1990. Ixorpi et al.," 1990, Korpi et al."
 1999: ce Avillez Breitschwerelt )05: Slvz et al., 1999; de Avillez Breitschwerdt 2005; Slyz et al.
 2005: Joung Mac Low 2006: Dib οἱ al., 2005; Joung Mac Low 2006; Dib et al.
 2006: Booth Theuns 2007: Shetty Ostriker 2008) is able to explain the observed. velocity dispersions of the Η1 eas in the inner and intermediate regions of galactic disks and a fraction of the observed. velocity. dispersion in the outer regions., 2006; Booth Theuns 2007; Shetty Ostriker 2008) is able to explain the observed velocity dispersions of the HI gas in the inner and intermediate regions of galactic disks and a fraction of the observed velocity dispersion in the outer regions.
 SN feedback. also produces. substantial numbers of MCs with non-zero inclinations with respect to the galactic plane., SN feedback also produces substantial numbers of MCs with non-zero inclinations with respect to the galactic plane.
 Using a feedback. elficiency of 0.25 (cach SN injects {ον=0.25.10 erg). Dib et al. (," Using a feedback efficiency of 0.25 (each SN injects $E_{SN}=0.25 \times 10^{51}$ erg), Dib et al. ("
2006) showed that feedback from SNe explosions can maintain a velocity. dispersion of 35 km  of the LE gas for SN rates such as those prevailing in the outer region of ealactic disks: i.c. for. SN rates as low as 0.01 times the Galactic SN type HE rate.,2006) showed that feedback from SNe explosions can maintain a velocity dispersion of $3-5$ km $^{-1}$ of the HI gas for SN rates such as those prevailing in the outer region of galactic disks; i.e. for SN rates as low as $0.01$ times the Galactic SN type II rate.
 Dib et al. (, Dib et al. (
2006) attributed the differences between the measured. velocity dispersions of the HIE gas for such low rates and the observed values (~5lO km s... Dickey et al.,"2006) attributed the differences between the measured velocity dispersions of the HI gas for such low rates and the observed values $\sim 5-10$ km $^{-1}$, Dickey et al."
 1990: Dib et al., 1990; Dib et al.
 2006: Tamburro et al., 2006; Tamburro et al.
 2009) in the outer galactic regions to a number of potential ellects., 2009) in the outer galactic regions to a number of potential effects.
 The discrepancy can result from the unknown temperatures of the Ll eas in the outer regions of galaxies ancl our ignorance about the truc thermal component in the observed lino width. an unclerestimate of the SN ellicicney. and/or can be due to the presence of other driving mechanisms in the those regions. such as the magnetorotational instability (Sebwood Balbus 1999: Wim et al.," The discrepancy can result from the unknown temperatures of the HI gas in the outer regions of galaxies and our ignorance about the true thermal component in the observed line width, an underestimate of the SN efficiency, and/or can be due to the presence of other driving mechanisms in the those regions, such as the magnetorotational instability (Selwood Balbus 1999; Kim et al."
 2003: Dziourkevitch οἱ al., 2003; Dziourkevitch et al.
 2004: Piontek Ostriker 2007). large scale gravitational instabilities. non-axisvnunetric perturbations. and cloud-cloud. collisions (Waca et al.," 2004; Piontek Ostriker 2007), large scale gravitational instabilities, non-axisymmetric perturbations, and cloud-cloud collisions (Wada et al."
 2002: Dib Burkert 2005: Li et al., 2002; Dib Burkert 2005; Li et al.
 2006: ‘Tasker Tan 2008: Agertz et al., 2006; Tasker Tan 2008; Agertz et al.
 2009). tidal interactions ancl ram pressure effects. (Bureau ct al.," 2009), tidal interactions and ram pressure effects (Bureau et al."
 2004): collisions of high velocity clouds: with the galactic disk (Venorio-Tagle et al., 2004); collisions of high velocity clouds with the galactic disk (Tenorio-Tagle et al.
 1987: Santillánn et al., 1987; Santillánn et al.
 2007: Back et al., 2007; Baek et al.
 2008) and galactic spiral shocks (Ixim Ostriker 2006: 3onnell et al., 2008) and galactic spiral shocks (Kim Ostriker 2006; Bonnell et al.
 2006: Wim et al., 2006; Kim et al.
 2008: Dobbs et al., 2008; Dobbs et al.
 2008)., 2008).
 In the present paper. we complement the work of Ixoda al. (," In the present paper, we complement the work of Koda et al. ("
2006) by analyzing the position angles of AIC's (i.e.. 1eiy inclinations with respect to the Galactic plane. £724) in 10 outer Galactic disk using the Lever. Carpenter Snel nnolecular cloud. catalogue (ICS. Hover ct al.,"2006) by analyzing the position angles of MCs (i.e., their inclinations with respect to the Galactic plane, $PA$ ) in the outer Galactic disk using the Heyer, Carpenter Snell molecular cloud catalogue (HCS, Heyer et al."
 2001)., 2001).
 As a uantitative test to measure the signature of the turbulence river(s) in the Outer Galaxy. we measure the spatia correlations between MOS with the same PAs with respec to the Galactic plane.," As a quantitative test to measure the signature of the turbulence driver(s) in the Outer Galaxy, we measure the spatial correlations between MCs with the same PAs with respect to the Galactic plane."
 In particular. supernova feedback wil eenerate a network of MCSs of various inclinations.," In particular, supernova feedback will generate a network of MCs of various inclinations."
 Lf the PAs of the clouds are mirrored to values between O° ane 90. the spatial scales on which they might be correlatec can be compared to the expected. sizes of SN remnants in the outer Galactic disk.," If the $PA$ s of the clouds are mirrored to values between $0^{\circ}$ and $90^{\circ}$, the spatial scales on which they might be correlated can be compared to the expected sizes of SN remnants in the outer Galactic disk."
 Another possible approach would be to use shell-Iike structures as a direct tracer of feedback from massive stars., Another possible approach would be to use shell-like structures as a direct tracer of feedback from massive stars.
 Shells observed in the HE 21 em line are not an automatic tracer of star formation activity., Shells observed in the HI 21 cm line are not an automatic tracer of star formation activity.
 Although some LIL shells are e&cnerated by feedback from massive stars. Blitz et al. (," Although some HI shells are generated by feedback from massive stars, Blitz et al. ("
2007) discussed the facet that whereas Giant Molecular Clouds are founcl to be well correlated with high density regions in the LIL (see also Margulis et al.,2007) discussed the fact that whereas Giant Molecular Clouds are found to be well correlated with high density regions in the HI (see also Margulis et al.
 1988). the opposite is not true and many bright LIE Glaments are found without molecular eas.," 1988), the opposite is not true and many bright HI filaments are found without molecular gas."
 Dib Burkert (2005) and other groups have shown that LU shelllike structures that are not associated with stellar fecdhack can also be generated by laree scale turbulence and eas instabilities., Dib Burkert (2005) and other groups have shown that HI shell-like structures that are not associated with stellar feedback can also be generated by large scale turbulence and gas instabilities.
 In the SAIC. Latzicimitriou et al. (," In the SMC, Hatzidimitriou et al. ("
2005) found that 59 of the 509 LEE shell they have catalogued show no signs of being associated to any form of star formation or stellar feedback activities.,2005) found that 59 of the 509 HI shell they have catalogued show no signs of being associated to any form of star formation or stellar feedback activities.
 In Llolmbcre LL. 86 percent of the LIL holes do not show signs of being associated. with stellar feedback (Rhode ct al.," In Holmberg II, 86 percent of the HI holes do not show signs of being associated with stellar feedback (Rhode et al."
 1999)., 1999).
 Phis argument does not apply to CO shells. as it is very likely that large and complete CO shells (=το pe are associated with feedback from massive stars.," This argument does not apply to CO shells, as it is very likely that large and complete CO shells $\gtrsim 70$ pc are associated with feedback from massive stars."
 However. CO shells that would form through feedback bv massive stars will generally evolve in a turbulent and hiehlieghlv inhomogeneous|e1 mediumliu andl μιαν |lose utheir sphericaJ| svmmetry uncer the action of hydrodynamical instabilities.," However, CO shells that would form through feedback by massive stars will generally evolve in a turbulent and highly inhomogeneous medium and may lose their spherical symmetry under the action of hydrodynamical instabilities."
 This would make their recognition as tracers of feedback by massive stars very. problematic., This would make their recognition as tracers of feedback by massive stars very problematic.
 More clirect evidence for, More direct evidence for
pulse. there still remain some open problems.,"pulse, there still remain some open problems."
 Although our analysis strongly favors the thermalnonthermal interpretation. itis still unclear which of the two components dominates in the X-ray radiation ofJO437—4715.," Although our analysis strongly favors the thermal+nonthermal interpretation, it is still unclear which of the two components dominates in the X-ray radiation of."
. To establish the relative contributions of these components. energy-resolved timing and time-resolved spectral analysis are needed. which. hopefully. will be possible with the forthcoming data.," To establish the relative contributions of these components, energy-resolved timing and time-resolved spectral analysis are needed, which, hopefully, will be possible with the forthcoming data."
 We thank Leisa Townsley for the advise on the ACIS data reduction. Allyn Tennant for the discussion of the HRC timing issues. and Willem van Straten for providing the timing ephemeris given in Table 1.," We thank Leisa Townsley for the advise on the ACIS data reduction, Allyn Tennant for the discussion of the HRC timing issues, and Willem van Straten for providing the timing ephemeris given in Table 1."
 We also thank Vadim Burwitz for helping in preparation of the color image., We also thank Vadim Burwitz for helping in preparation of the color image.
" This work was partially supported by NASA through grants NAGS-7017. NAGS-10865, and SAO GOO-1126X."," This work was partially supported by NASA through grants NAG5-7017, NAG5-10865, and SAO GO0-1126X."
Bahuer line eimission aud coronal X-ray enission. however. appear to steeply decline from peak levels in carly aud 1k AL dwarfs (Pallavicinietal.1981:Vilhu&Walter1987:Cüzisetal.2000:West 2001).. leading to divergeu trends of inagnoetie activity at the bottom of the main sequence.,"Balmer line emission and coronal X-ray emission, however, appear to steeply decline from peak levels in early and mid M dwarfs \citep{pgr+81,vw87,gmr+00,whw+04}, leading to divergent trends of magnetic activity at the bottom of the main sequence."
 Tn both Πα auc X-rays there is also a clear transition from persistent cluission to a snall πο of flaring objects with duty cycles of a few percent (Reidetal.2003:West 2001)... as well as a breakdown of the rotation-activity relation (Dasri&Marcy1995:Mo-hauty&Basri2003) that is clearly seen in carly AL οποτε Rosneretal.1985:Fleming1993:MohautyctS02:Pizzolatoetal. 2003).," In both $\alpha$ and X-rays there is also a clear transition from persistent emission to a small number of flaring objects with duty cycles of a few percent \citep{rkg+99,gmr+00,rbm+00,lkc+03,whw+04}, as well as a breakdown of the rotation-activity relation \citep{bm95,mb03} that is clearly seen in early M dwarfs \citep{rgv85,fgs+93,mbs+02,pmm+03}."
. The chauge aud divergence in activity trends is most clearly evident im the breakdown of the racdio/N-rav correlation that holds for a large nuuber of early-type stars and solar flares (Cuedel&Beng1993:Coreletal.1993::Benz&Cuedel199 D.. aud is attributed to flare heating of coronal plasiua to X-ray temperatures (Neupert1968:Cmedoeletal. 1996).," The change and divergence in activity trends is most clearly evident in the breakdown of the radio/X-ray correlation that holds for a large number of early-type stars and solar flares \citep{gb93,gsb+93,bg94}, and is attributed to flare heating of coronal plasma to X-ray temperatures \citep{neu68,gbs+96}."
. While objects in the range MO obey this correlation. several objects -later than MT exhibit radio emission that is several of magnitude brighter than expected (Bergerctal.2001:Bereer2002:Dergeretal.2005:Bereer2," While objects in the range M0--M6 obey this correlation, several objects later than M7 exhibit radio emission that is several orders of magnitude brighter than expected \citep{bbb+01,ber02,brr+05,ber06}."
006 Similarly. im early M dwarts there is an overall euergv. G).-balance between N-rav and chromospheric cussion. Wwhich has led to the idea of chromospheric eating bv coronal N-ravs (6.8... Cram.1982:Hawleyetal. 1995)).," Similarly, in early M dwarfs there is an overall energy balance between X-ray and chromospheric emission, which has led to the idea of chromospheric heating by coronal X-rays (e.g., \citealt{cra82,hfs+95}) )."
 It is not kuown whether this miechanigi holdsin ultracool dwarfs. primarily because of the decline in persistent activity.," It is not known whether this mechanism holds in ultracool dwarfs, primarily because of the decline in persistent activity."
 Theoretical work on magnetic dvuzuos in ultracool dwarfs also remains incouclusive., Theoretical work on magnetic dynamos in ultracool dwarfs also remains inconclusive.
 Studies of the a? dynamo in fully convective stars suggest that a stratified and rotating turbulent medimm can lead to the build-up of a nonu and imultipolar feld (e.8.. Chabrier&Iiitkerivinnetrie2006:simplificationsDobleretal. 2006)). but these models make several for computational purposes.," Studies of the $\alpha^2$ dynamo in fully convective stars suggest that a stratified and rotating turbulent medium can lead to the build-up of a non-axisymmetric and multi-polar field (e.g., \citealt{ck06,dsb06}) ), but these models make several simplifications for computational purposes."
 It has also been argued that decreasing electrical conductivity will impede the dissipation of anv magnetic fields iu the cool auc inercasingly neutral atmospheres of ultracool cavarts (Mohlantyctal.2002)., It has also been argued that decreasing electrical conductivity will impede the dissipation of any magnetic fields in the cool and increasingly neutral atmospheres of ultracool dwarfs \citep{mbs+02}.
. The existing radio detections sugeest that field dissipation may not be a problem. but the overall field configuration aud. the effect of neutral atinospheres in the preseuce of magnetic Issipation remain largely unexplored.," The existing radio detections suggest that field dissipation may not be a problem, but the overall field configuration and the effect of neutral atmospheres in the presence of magnetic dissipation remain largely unexplored."
 As a result of the various conflicting treuds aud the trausition from persistent to flaring cinission. progress in our understanding of magnetic activity and dyiaiuos i1 ultracool chwarts requires. observations of tιο various activity bauds.," As a result of the various conflicting trends and the transition from persistent to flaring emission, progress in our understanding of magnetic activity and dynamos in ultracool dwarfs requires observations of the various activity bands."
 We have already mucertakensuch observations for the L3.5 brown dwiuf 2MASS JOO3G61G617|1821101 iu late 2002 aud discovered periodic radio enüsson (2=Isl mun). with no correspondius A-aav or Dio cinission (Dergerotal.2005).," We have already undertakensuch observations for the L3.5 brown dwarf 2MASS J00361617+1821104 in late 2002 and discovered periodic radio emission $P=184$ min), with no corresponding X-ray or $\alpha$ emission \citep{brr+05}."
. These observations indicated a iiagnuetie field of ~200 CG covering a substantial fraction of the stellar surface. as well as the first direct coufirimation that the radio/N-ray correlation is indeed violated by orders of magnitude.," These observations indicated a magnetic field of $\sim 200$ G covering a substantial fraction of the stellar surface, as well as the first direct confirmation that the radio/X-ray correlation is indeed violated by orders of magnitude."
 Follow-up observations showed that the field is stable on a z3 vi timescale. much longer than the couvective turnover time. pointing fo a stable dwuamo process.," Follow-up observations showed that the field is stable on a $\gtrsim 3$ yr timescale, much longer than the convective turnover time, pointing to a stable dynamo process."
 À receut siuultaueous observation of the L dwarf binary Welu-l resulted in au Nav detection without correspouding radio enission (Audardetal.2007).. although the radio limits still allow for a violation of the radio/N-rav correlation by up to —ὃς107.," A recent simultaneous observation of the L dwarf binary Kelu-1 resulted in an X-ray detection without corresponding radio emission \citep{aob+07}, although the radio limits still allow for a violation of the radio/X-ray correlation by up to $\sim 2\times 10^3$."
 Tere we exploit the powerful approach of siumultaucous observations to investigate the iuagnotic activity in the ΑΙ dwarf16... an object previously detected in the radio (Berger2002.2006:Ostenctal.200Gb:Hallinanetal.2006.2007) aud in Πα (Alartinetal.1991:Reidetal.x2:Mohauty&Basri 2003).," Here we exploit the powerful approach of simultaneous observations to investigate the magnetic activity in the M8.5 dwarf, an object previously detected in the radio \citep{ber02,ber06,ohb+06,had+06,hbl+07} and in $\alpha$ \citep{mrm94,rkl+02,mb03}."
.. These observations are the In a series that targets several objects in the sparselv-studied aud critical spectral type ranee MT to L3., These observations are the first in a series that targets several objects in the sparsely-studied and critical spectral type range M7 to L3.
 In the case of wwe detect radio. X-ray. aud Balmer lue emission. but no UV emission.," In the case of we detect radio, X-ray, and Balmer line emission, but no UV emission."
 The overall behavior is complex aud larecly uncorrelated between the various cussion bauds., The overall behavior is complex and largely uncorrelated between the various emission bands.
" The long time and wavelength baselines provide uuprecedeuted detail. includiug the first case to date of sinusoidal Daliner line euisson: the observed 2-hour period "" iu excelleut agreement with the rotation of513-16516."," The long time and wavelength baselines provide unprecedented detail, including the first case to date of sinusoidal Balmer line emission; the observed 2-hour period is in excellent agreement with the rotation of."
"..oni: Using the various activity indicators we inter the of the maenetic field. corona, and chromosphere. and show that the underline processes aud field configuration likely ciffer from those in early M cowarts."," Using the various activity indicators we infer the properties of the magnetic field, corona, and chromosphere, and show that the underlying processes and field configuration likely differ from those in early M dwarfs."
 We targeted the M8.5 dwart ddue to its vicinity (αἱ=10.6 pe: Dahlctal.2002)) aud known radio aud Πα activity., We targeted the M8.5 dwarf due to its vicinity $d=10.6$ pc; \citealt{dhv+02}) ) and known radio and $\alpha$ activity.
 The bolometric Iuuinositv of iis Lgc ο its rotation velocity is esuzm60 lans + (Mohauty&Dagi2003).," The bolometric luminosity of is $L_{\rm bol}\approx 10^{-3.59}$ $_\odot$, and its rotation velocity is $v{\rm sin}i\approx 60$ km $^{-1}$ \citep{mb03}."
. The nou-dotectiou of lithium. with a limit of 0.05À.. sugeests that Hs most likely a verv low mass star Detal.2002).," The non-detection of lithium, with a limit of 0.05, suggests that is most likely a very low mass star \citep{rkl+02}."
". Adaptive optics imagine of irevealed uo companions with diyx3 mae in the range 0.1-15""7 (Closeetal.2003).", Adaptive optics imaging of revealed no companions with $\delta m\lesssim 3$ mag in the range $0.1$ $15\arcsec$ \citep{csf+03}.
". wwas first detected in the racio during a 2 hr observation at 8.5 CdIz in Sep. 2001. and exhibited both persistent CF,zm190 pJv) and flaring ciission (Berger2002).. the latter with a peak brightuess of 1 ταν. a duration of 15 win. and circular polarization of r.z66%."," was first detected in the radio during a 2 hr observation at 8.5 GHz in Sep. 2001, and exhibited both persistent $F_\nu\approx
190$ $\mu$ Jy) and flaring emission \citep{ber02}, the latter with a peak brightness of 1 mJy, a duration of 15 min, and circular polarization of $r_c\approx 66\%$."
" Subsequent observations frou 1. to 8.5 GIIz in Jan. 2001 revealed a similar level of persistent{ cinission. F,(1.1)z260 qi]. ΕΙ)=280 µ.]ν. aud Εν(8.5)z230 pdx. with p<15 (Ostenetal.20000"," Subsequent observations from 1.4 to 8.5 GHz in Jan. 2004 revealed a similar level of persistent emission, $F_\nu(1.4)\approx 260$ $\mu$ Jy, $F_\nu(4.9)\approx 280$ $\mu$ Jy, and $F_\nu(8.5)\approx 230$ $\mu$ Jy, with $r_c\lesssim 15\%$ \citep{ohb+06}."
"), Observations in Jan. 2005 revealed brighter cuuission. Εν1.9)z105 μ.]ν. and Εν(δι)zLoo pJy. as well as aclaimed periodicity of about 2 hr (Wallinanal. 2006)."," Observations in Jan. 2005 revealed brighter emission, $F_\nu(4.9)\approx 405$ $\mu$ Jy, and $F_\nu(8.5)\approx 400$ $\mu$ Jy, as well as aclaimed periodicity of about 2 hr \citep{had+06}."
. Finally. observations in May. 2006 wucovered. a series of flares with durations of a few minutes. 10054 circular polarization. aud a periodicity of 1.96 hr (Hallan )..," Finally, observations in May 2006 uncovered a series of flares with durations of a few minutes, $\sim 100\%$ circular polarization, and a periodicity of 1.96 hr \citep{hbl+07}. ."
" Previous detectious of Πα emission reveal long term variability. with equivalent widths (EW) ranging from 1.7 to 3.5 A. or Lg,/Li4&107 (Martinotal.1991:Reid 2003).."," Previous detections of $\alpha$ emission reveal long term variability, with equivalent widths (EW) ranging from 1.7 to 3.5 , or $L_{\rm H\alpha}/L_{\rm bol}\approx 10^{-5}$ \citep{mrm94,rkl+02,mb03}. ."
 Our simultaneous observations were obtainedon 2007 April 20 UT for a total of 8.8 ly in the radio (01:00-12:Ls UT). 8.9 hr in the N-ravs (0 UT). and7 hr iu the optical(07:13-11:13. UT).," Our simultaneous observations were obtainedon 2007 April 20 UT for a total of $8.8$ hr in the radio (04:00-12:48 UT), $8.9$ hr in the X-rays (03:47-12:41 UT), and $7$ hr in the optical (07:13-14:13 UT)."
 δι MRNAUV/optical telescope, UV/optical telescope
galaxy of 0090205.,galaxy of 090205.
" We also carried out deep, late-time (t—To~180 d) NIR observations of the field of GRB 090205 with VLT/HAWK-I in JHK —bands."," We also carried out deep, late-time $t-T_0 \sim 180$ d) NIR observations of the field of GRB 090205 with VLT/HAWK-I in $JHK-$ bands."
" The host is not detected in any of the observed bands up to a limiting AB magnitude of J>244, H>24.2 and Ks>23.9 (30 c.l.)."," The host is not detected in any of the observed bands up to a limiting AB magnitude of $J>24.4$, $H>24.2$ and $Ks>23.9$ $3\sigma$ c.l.)."
 The results are reported in Tab., The results are reported in Tab.
 | and in Figs., \ref{tab:log} and in Figs.
" 6,7."," 6,7."
" As already mentioned, the afterglow spectrum shows an emission line at ~6873 superposed on the Ly-a absorption, corresponding to Ly-oa emission at the same redshift of the GRB."," As already mentioned, the afterglow spectrum shows an emission line at $\sim 6873$ superposed on the $\alpha$ absorption, corresponding to $\alpha$ emission at the same redshift of the GRB."
" In order to check the reliability of the line detection, and to exclude the possibility that it is due to some atmospheric emission or absorption contaminating feature, we performed a detailed analysis of the 2-D spectrum (see Fig."," In order to check the reliability of the line detection, and to exclude the possibility that it is due to some atmospheric emission or absorption contaminating feature, we performed a detailed analysis of the 2-D spectrum (see Fig."
 5)., 5).
 At the wavelength corresponding to the Ly—a line emission we measure 2101«51 counts (sky+object)., At the wavelength corresponding to the $-\alpha$ line emission we measure $2101\pm 51$ counts (sky+object).
" The counts corresponding only to sky are 1836+21, so that the object counts are 265+55 (68% c.1.)."," The counts corresponding only to sky are $1836\pm
21$, so that the object counts are $265\pm55$ $68\%$ c.l.)."
 The corresponding signal-to-noise ratio is 5.2., The corresponding signal-to-noise ratio is 5.2.
" Another striking evidence we obtain from the 2-D spectrum is the measure of a spatial displacement of 1.3+0.9 pixels (equivalent to 0.3""+ 0.2"") from the centroid of the afterglow continuum trace and the “spot” corresponding to the Ly—a@ emission (see Fig.", Another striking evidence we obtain from the 2-D spectrum is the measure of a spatial displacement of $1.3 \pm 0.9$ pixels (equivalent to $0.3'' \pm 0.2''$ ) from the centroid of the afterglow continuum trace and the “spot” corresponding to the $-\alpha$ emission (see Fig.
 5)., 5).
" Doing precise astrometry on our afterglow and host galaxy images obtained with FORSI, we measure the same offset between the afterglow and the host galaxy positions (0.4""+0.3"", corresponding to a physical offset of about 3 kpc), thus making stronger the hypothesis that this emission line is really due to Ly—a from the host galaxy."," Doing precise astrometry on our afterglow and host galaxy images obtained with FORS1, we measure the same offset between the afterglow and the host galaxy positions $0.4'' \pm 0.3''$, corresponding to a physical offset of about 3 kpc), thus making stronger the hypothesis that this emission line is really due to $-\alpha$ from the host galaxy."
 Using the flux-calibrated afterglow spectrum we derive a flux of 1.82x107! erg s! cm’., Using the flux-calibrated afterglow spectrum we derive a flux of $1.82\times 10^{-17}$ erg $^{-1}$ $^{-2}$.
 This flux transforms into a Ly—a luminosity of 4.27x10*? erg s!.," This flux transforms into a $-\alpha$ luminosity of $4.27\times
10^{42}$ erg $^{-1}$."
" We note that this value is in the range of luminosities observed for the other GRB-LAEhosts?,, i.e. 1—5x10? erg s! (Jakobsson et al."," We note that this value is in the range of luminosities observed for the other GRB-LAE, i.e. $1-5\times 10^{42}$ erg $^{-1}$ (Jakobsson et al."
 2005)., 2005).
" One interesting aspect of this burst is that, similarly to other, high-z GRBs (e.g. GRB 080913 at z—6.7, Greiner et al."," One interesting aspect of this burst is that, similarly to other, $z$ GRBs (e.g. GRB 080913 at $z=6.7$, Greiner et al."
" 2009; GRB 090423 at z=8.2, Salvaterra et al."," 2009; GRB 090423 at $z=8.2$, Salvaterra et al."
" 2009, Tanvir et al."," 2009, Tanvir et al."
" 2009), it shows a short duration in the emitter rest frame, Του,~1.6 s. A short rest frame duration was recently proposed as a possible indicator (among others) of GRBs originated from a compact-star-merger progenitor (or Type I GRBs; Zhang et al."," 2009), it shows a short duration in the emitter rest frame, $T_{90,rf}\sim 1.6$ s. A short rest frame duration was recently proposed as a possible indicator (among others) of GRBs originated from a compact-star-merger progenitor (or Type I GRBs; Zhang et al."
 2009)., 2009).
" While the spectral lag analysis is inconclusive regarding the nature of this burst, owing to the faintness of the prompt emission (Sec."," While the spectral lag analysis is inconclusive regarding the nature of this burst, owing to the faintness of the prompt emission (Sec."
" 2.1), the BAT spectrum appears to be softer with respect to typical short GRBs."," 2.1), the BAT spectrum appears to be softer with respect to typical short GRBs."
" At ζ4.65, the isotropic gamma-ray energy release in the redshifted 15-150 keV band is Ey;=7.86+1.21x10°! erg and the intrinsic peak energy is Ep;=192+85 Κεν. These values make GRB 090205 consistent with the observed E,i—Ey,iso correlation (Amati et al."," At $z=4.65$, the isotropic gamma-ray energy release in the redshifted 15-150 keV band is $E_{\gamma,iso}=7.86\pm 1.21\times 10^{51}$ erg and the intrinsic peak energy is $E_{p,i}=192\pm 85$ keV. These values make GRB 090205 consistent with the observed $E_{p,i}-E_{\gamma,iso}$ correlation (Amati et al."
" 2008), that is known to be followed only by long GRBs (see also Piranomonte et al."," 2008), that is known to be followed only by long GRBs (see also Piranomonte et al."
 2008) and proposed as an indicator of GRBs with a massive stellar collapse origin (Type II GRBs; Zhang et al., 2008) and proposed as an indicator of GRBs with a massive stellar collapse origin (Type II GRBs; Zhang et al.
 2009)., 2009).
" Indeed, the Ej;—Εγιω correlation has been used recently to support the long classification of a few rest-frame short duration bursts such as GRB 090423 (Salvaterra et al."," Indeed, the $E_{p,i}-E_{\gamma,iso}$ correlation has been used recently to support the long classification of a few rest-frame short duration bursts such as GRB 090423 (Salvaterra et al."
"4x10-14 erg s! cm~?, and adds further evidence to the presence of an obscured AGN with a reflection efficiency of ~1 per cent.","$4 \times 10^{-14}$ erg $^{-1}$ $^{-2}$, and adds further evidence to the presence of an obscured AGN with a reflection efficiency of $\sim$ 1 per cent."
" Two other objects within our selection of ULIRGs that are missed by the optical diagnostics as Seyfert galaxies but likely harbour an AGN with quasar-like luminosity, although observed in the X-rays, have never been published to date."," Two other objects within our selection of ULIRGs that are missed by the optical diagnostics as Seyfert galaxies but likely harbour an AGN with quasar-like luminosity, although observed in the X-rays, have never been published to date."
 We have therefore reduced as outlined above and then analysed the ~15 ks long observations of IRAS 01166—0844 and IRAS 07251—0248 retrieved from the archives., We have therefore reduced as outlined above and then analysed the $\sim$ 15 ks long observations of IRAS $-$ 0844 and IRAS $-$ 0248 retrieved from the archives.
" The former source is a close equivalent (althoughmuch fainter) to IRAS 01298—0744 at 5-8 um; strikingly, it turns out to be completely undetected as well."," The former source is a close equivalent (althoughmuch fainter) to IRAS $-$ 0744 at 5–8 $\mu$ m; strikingly, it turns out to be completely undetected as well."
" The latter, instead, which is a very bright source in the Revised Bright Galaxy Sample (z~0.088, feo”-6.5 Jy; Sanders et al."," The latter, instead, which is a very bright source in the Revised Bright Galaxy Sample $z \simeq 0.088$, $f_{60} \simeq 6.5$ Jy; Sanders et al."
" 2003) delivers a 3.50 detection, and its weak emission can be fitted with a steep power law of photon index ~3.6(+1.6)."," 2003) delivers a $\sigma$ detection, and its weak emission can be fitted with a steep power law of photon index $\simeq$ $\pm1.6$ )."
" In both cases, the upper limit (or estimated) 2-10 keV flux is of the order of «10:15 erg s! em?."," In both cases, the upper limit (or estimated) 2–10 keV flux is of the order of $\sim$ $^{-15}$ erg $^{-1}$ $^{-2}$."
 Assuming again the far-IR to X-ray conversion of Ranalli et al. (, Assuming again the far-IR to X-ray conversion of Ranalli et al. (
"2003), such a tiny value implies not only that the AGN is thoroughly absorbed, but also that the SB provides very little contribution to the bolometric luminosity of the host galaxy.","2003), such a tiny value implies not only that the AGN is thoroughly absorbed, but also that the SB provides very little contribution to the bolometric luminosity of the host galaxy."
" The remaining four sources in our sample similarly display strong evidence for buried nuclear activity at mid-IR wavelengths, with spectral trends that are well represented by the ones shown in Fig. 1.."," The remaining four sources in our sample similarly display strong evidence for buried nuclear activity at mid-IR wavelengths, with spectral trends that are well represented by the ones shown in Fig. \ref{f1}. ."
" At high energies, IRAS 00091—0738 and IRAS 11095—0238 have been"," At high energies, IRAS $-$ 0738 and IRAS $-$ 0238 have been"
21 em observation will possibly rule out or confirm these theoretical predictions. opening a new exciting frontier in cosmology and possibly unveiling the nature of dark matter particles.,"21 cm observation will possibly rule out or confirm these theoretical predictions, opening a new exciting frontier in cosmology and possibly unveiling the nature of dark matter particles."
 All the most popular dark matter particle cancliclates inject enerev into the ΙΙ. either via decavs or annihilations. initiating an energv cascade [rom energetic primary photons or electrons.," All the most popular dark matter particle candidates inject energy into the IGM, either via decays or annihilations, initiating an energy cascade from energetic primary photons or electrons."
 The cnerey deposition depends on the laree number of interactions taking place during the propagation of the cascade particles through the LGAL, The energy deposition depends on the large number of interactions taking place during the propagation of the cascade particles through the IGM.
 Lt is therefore very important for achieving correct results to follow in detail these cascades ancl to know exactly how much of the energy injected ionizes the gas. produces radiation by collisional excitations. and heats surrounding medium. respectively.," It is therefore very important for achieving correct results to follow in detail these cascades and to know exactly how much of the energy injected ionizes the gas, produces radiation by collisional excitations, and heats surrounding medium, respectively."
 This fundamental problem has received attention in the past (e.g. Bergeron2 Collin-Soullrin 1973). and the results achieved were corrected by an extensive study by Shull and van Steemberg (1985). which we will denote hereafter as SVS85. which was a development ofà previous work by Shull (1979). hereafter S79.," This fundamental problem has received attention in the past (e.g. Bergeron Collin-Souffrin 1973), and the results achieved were corrected by an extensive study by Shull and van Steemberg (1985), which we will denote hereafter as SVS85, which was a development of a previous work by Shull (1979), hereafter S79."
 In this work we present the results of a Monte Carlo calculation in the spirit of the one from S79 and SVSS5: in comparison. we use more recent and accurate cross sections for collisional ionization and excitations from electron. impacts. for clectron-clectron collisions. for. [rec-ree interactions and recombinations.," In this work we present the results of a Monte Carlo calculation in the spirit of the one from S79 and SVS85; in comparison, we use more recent and accurate cross sections for collisional ionization and excitations from electron impacts, for electron-electron collisions, for free-free interactions and recombinations."
 In addition to this we ollow in detail the radiation produced. by the excitations and we are able to predict precisely how much of the energy goes into photons that do not further interact with the eas (E 10.2 eV) and how much of it contributes to the Lya ickeround. which directly. alfects the physies of the 21 em ine racliation by the so called Wouthuvsen-Eielkd οσσ (e.g. Wouthuvsen 1952: Field 1959: Hirata 2005) and which can reat or cool the gas depending on the nature of the Lya photons (Chen Miralda Escudé 2004. Chuzhov Shapiro 2001).," In addition to this we follow in detail the radiation produced by the excitations and we are able to predict precisely how much of the energy goes into photons that do not further interact with the gas $\leq $ 10.2 eV) and how much of it contributes to the ${\alpha}$ background, which directly affects the physics of the 21 cm line radiation by the so called Wouthuysen-Field effect (e.g. Wouthuysen 1952; Field 1959; Hirata 2005) and which can heat or cool the gas depending on the nature of the $\alpha $ photons (Chen Miralda $\acute{e}$ 2004, Chuzhoy Shapiro 2007)."
 We calculate the effects produced by an X-photon of keV enerev injected. into the IGM. with ZQU Ix. At these energies the dominant interaction is photoionization (see e.g. Zdziarski Svensson 1989) and the X-photon ionizes an 11 or Hle atom producing an energetic primary electron., We calculate the effects produced by an X-photon of $\sim $ keV energy injected into the IGM with $T\ll 10^4$ K. At these energies the dominant interaction is photoionization (see e.g. Zdziarski Svensson 1989) and the X-photon ionizes an H or He atom producing an energetic primary electron.
 We ollow the subsequent secondary cascade products., We follow the subsequent secondary cascade products.
" For our calculations we choose two specific energies for he primary electron. £7,—3 keV and 10 keV. This energy range is of great interest. because sterile neutrinos. one of he most promising WDÀ candidates. are expected to emit ine radiation at an energy between 3-25 keV. X large elfort ias been done recently by several authors to constrain the mass and lifetime of raciatively decaving sterile neutrinos rom X-ray observations (Abazajian. Puller Tucker 2001: Abazajian 2006: Abazajian Ixoushiappas 2006: Bovarsky et al."," For our calculations we choose two specific energies for the primary electron, $E_{in}=3$ keV and $10$ keV. This energy range is of great interest because sterile neutrinos, one of the most promising WDM candidates, are expected to emit line radiation at an energy between 3-25 keV. A large effort has been done recently by several authors to constrain the mass and lifetime of radiatively decaying sterile neutrinos from X-ray observations (Abazajian, Fuller Tucker 2001; Abazajian 2006; Abazajian Koushiappas 2006; Boyarsky et al."
 2006b: Watson et al., 2006b; Watson et al.
 2006: Mapelli Ferrara. 2005: Bovarsky et al., 2006; Mapelli Ferrara 2005; Boyarsky et al.
 2006a)., 2006a).
 Once the primary electron. is injected into the LGA he code calculates the cross sections relative to a list of possible processes: Ll. He. Hel ionization: LH. Ho excitation: collisions with thermal electrons: [ree-free interactions with ionized atoms: recombinations.," Once the primary electron is injected into the IGM the code calculates the cross sections relative to a list of possible processes: H, He, HeI ionization; H, He excitation; collisions with thermal electrons; free-free interactions with ionized atoms; recombinations."
 We then estimate the mean ree paths and derive the probability for a single electron to ave any of the aforementioned interactions., We then estimate the mean free paths and derive the probability for a single electron to have any of the aforementioned interactions.
" We assume. in agreement with the 3-vr Wilkinson Microwave Anisotropy robe (INALADP) data analysis. that the helium fraction by mass is fg,= 0.248 (Sperecl ct al."," We assume, in agreement with the 3-yr Wilkinson Microwave Anisotropy Probe (WMAP) data analysis, that the helium fraction by mass is $f_{He}=$ 0.248 (Spergel et al."
 2007) and we follow he fate of a primary electron and its secondary. products or different values of the ionized. fraction ur of the gas. which. as showed by 5VYS585 and 879. is the [ree parameter which allects the results.," 2007) and we follow the fate of a primary electron and its secondary products for different values of the ionized fraction $x_e$ of the gas, which, as showed by SVS85 and S79, is the free parameter which affects the results."
" We assume. similarly. that w=n(ll)/n(l)=(lleJfn(tle). For each primary energy £5, and for each assumed value of the gas ionizecl fraction wr, we performed. 1000. Monte Carlo realizations. a number sullicient to produce consistent results not biased by the random nature of the computation."," We assume, similarly, that $x_e \equiv n\mbox{(H}^+\mbox{)}/n\mbox{(H)}\equiv n\mbox{(He}^+\mbox{)}/n\mbox{(He).}$ For each primary energy $E_{in}$ and for each assumed value of the gas ionized fraction $x_e$ we performed 1000 Monte Carlo realizations, a number sufficient to produce consistent results not biased by the random nature of the computation."
 We will return on this aspect at the end of this Sec., We will return on this aspect at the end of this Sec.
 If the primary electron. (or an energetie secondary electron) collisionally ionizes an Ll or Hle atom then the resulting two electrons have to be followed separately as they interact further with the gas., If the primary electron (or an energetic secondary electron) collisionally ionizes an H or He atom then the resulting two electrons have to be followed separately as they interact further with the gas.
 Once the electron energy. has degraded. below 10.2 eV we assume that its entire energy is deposited as heat., Once the electron energy has degraded below 10.2 eV we assume that its entire energy is deposited as heat.
 This is à simplification as the electron would actually thermalize with the gas and as a consequence the precise heating should be caleulated by taking into account the gas temperature., This is a simplification as the electron would actually thermalize with the gas and as a consequence the precise heating should be calculated by taking into account the gas temperature.
 Η the temperature is of the order of 103 I& electrons with energies lower than 1 eV could even cool the gas., If the temperature is of the order of $10^4$ K electrons with energies lower than 1 eV could even cool the gas.
 Collisional excitations of LE ad Lle produce photons that escape freely in the surrounding medium if their energy. is lower than 10.2 eV or that can further interact with the eas -- ‘they have higher energy., Collisional excitations of H ad He produce photons that escape freely in the surrounding medium if their energy is lower than 10.2 eV or that can further interact with the gas if they have higher energy.
 The study from 879 and SVSS5 derives the amount of snerey which is deposited in excitations but does not give ctails about the individual photons., The study from S79 and SVS85 derives the amount of energy which is deposited in excitations but does not give details about the individual photons.
 We want to estimate instead the amount of energy. that goes into Lya photons: iis racliation can in fact interact further with the gas by the Wouthuvsen-Eield effect and is crucial to correctly estimate 16 21 em signal., We want to estimate instead the amount of energy that goes into $\alpha$ photons: this radiation can in fact interact further with the gas by the Wouthuysen-Field effect and is crucial to correctly estimate the 21 cm signal.
 Furthermore. Lya photons hy scattering resonantly olf neutral hydrogen can cool or heat the gas. epending on whether they enter the resonance from its red or blue wing respectively. as we will explain more in detail later in this Letter.," Furthermore, $\alpha$ photons by scattering resonantly off neutral hydrogen can cool or heat the gas, depending on whether they enter the resonance from its red or blue wing respectively, as we will explain more in detail later in this Letter."
 An additional novel feature of our model is the inclusion of the previously neglected two-photon forbidden transition 255Is., An additional novel feature of our model is the inclusion of the previously neglected two-photon forbidden transition $2s \rightarrow 1s$.
 We included both the direct collisional excitation cross section to the 28 level ancl the probability. that a collisional excitation to a level»z 3 results in a cascade through the 2s level rather than through 2p., We included both the direct collisional excitation cross section to the $2s$ level and the probability that a collisional excitation to a level $n\geq $ 3 results in a cascade through the $2s$ level rather than through $2p$.
 As noted recently (Llirata 2005. ομον Shapiro 2007) this cllect is not neeligible in general and constitutes the most probable decay channel for HE atoms excited to a level η= 3 or higher.," As noted recently (Hirata 2005, Chuzhoy Shapiro 2007) this effect is not negligible in general and constitutes the most probable decay channel for H atoms excited to a level $n=$ 3 or higher."
"The remaining lifetime of a pulsar binary is defined. by (he shorter of the merger time of the binary due to the emission of GWs.Taye. or the time that the pulsar will reach the ""death line’.1975).","The remaining lifetime of a pulsar binary is defined by the shorter of the merger time of the binary due to the emission of GWs, or the time that the pulsar will reach the “death line”,."
" For voung pulsars like J1141—6545 which have relatively short radio lifetüimes. τα7,4,4."," For young pulsars like $-$ 6545 which have relatively short radio lifetimes, $<$."
. Reeveled pulsars. on the other hand. have far smaller spin-down rates than voung pulsars so that it is likely Chat close binaries containing a recycled pulsar will coalesce before the pulsar reaches the death-line 74)).," Recycled pulsars, on the other hand, have far smaller spin-down rates than young pulsars so that it is likely that close binaries containing a recycled pulsar will coalesce before the pulsar reaches the death-line $<$ )."
" For circular orbits. the results of Peters (1964) ecaleulations for the merger (ime of a binary svstem of (wo point masses n and me wilh orbital period 2, can be written as simply: where the reduced mass j(=mms/(mq+ma)."," For circular orbits, \nocite{p64} the results of Peters (1964) calculations for the merger time of a binary system of two point masses $m_1$ and $m_2$ with orbital period $P_b$ can be written as simply: where the reduced mass $\mu = m_1 m_2 / (m_1+m_2)$."
" For the eccentric binary JLI416545. we use the more detailed calculations of Peters (1964) to caleulate 74,4."," For the eccentric binary J1141–6545, we use the more detailed calculations of Peters (1964) to calculate $\tau_{\rm mrg}$."
" Most. of observed coalescing binaries as well as the DNS systems have TresLOS? vr,", Most of observed coalescing binaries as well as the DNS systems have $\sim10^{8-9}$ yr.
 Our understanding of pulsar emission is rather poor ancl therefore il is not clear how to calculate an accurate time associated with the termination of pulsar emission and hence74., Our understanding of pulsar emission is rather poor and therefore it is not clear how to calculate an accurate time associated with the termination of pulsar emission and hence.
. llere we assume the spin-down torque is dominated bv magnetic-dipole radiation with no evolution of the magnetic field., Here we assume the spin-down torque is dominated by magnetic-dipole radiation with no evolution of the magnetic field.
 The surface magnetic field of a neutron star. Z2. can be estimated [rom the current spin period 2 (s) and spin-down rate P 4): comprehensively discussed (he evolution of a pulsar period based on different magnetic field structures.," The surface magnetic field of a neutron star, $B_{\rm
s}$, can be estimated from the current spin period $P$ (s) and spin-down rate $\dot{P}$ $^{-1}$ ): comprehensively discussed the evolution of a pulsar period based on different magnetic field structures."
 Their results are consistent with previous studies1957)., Their results are consistent with previous studies.
" We adopt their case C ((9) in (heir paper) according to which (he radio emission terminales when (he 7death-period"" is reached.", We adopt their case C (9) in their paper) according to which the radio emission terminates when the “death-period” is reached.
 Assuming that the surface magnetic field remains constant. we can integrate ((5)) to caleulate the time for the pulsar period to reach P4.," Assuming that the surface magnetic field remains constant, we can integrate \ref{eq:bp1}) ) to calculate the time for the pulsar period to reach $P_{\rm d}$."
 We find that For PSR. J1141—6545. we use ((6)) and (7)) to [ind the remaining observable lifetime τι104 Myr.," We find that For PSR $-$ 6545, we use \ref{eq:pd}) ) and \ref{eq:taud}) ) to find the remaining observable lifetime $\tau_{\rm d} \sim 104$ Myr."
" This is significantly less than 7,444 for this binary system (c600 Myr)."," This is significantly less than $\tau_{\rm mrg}$ for this binary system $\sim
600$ Myr)."
subsection studies the dynamical effects of microlensing by analysing light curves.,subsection studies the dynamical effects of microlensing by analysing light curves.
" Magnification probability distributions of magnification maps are shown in Figure 4 for the base ESR as seen in image B, using unrotated maps and as viewed through HP and VP filters at two filter orientations each; unrotated, and rotated by 0;=7/4."," Magnification probability distributions of magnification maps are shown in Figure \ref{Fig:Histograms} for the base ESR as seen in image B, using unrotated maps and as viewed through HP and VP filters at two filter orientations each; unrotated, and rotated by $\theta_f = \pi/4$."
" The distributions appear very approximately Gaussian in shape, centred on the expected theoretical magnification."," The distributions appear very approximately Gaussian in shape, centred on the expected theoretical magnification."
" In Figure 4a the top and bottom panels use unrotated HP and VP filters, respectively."," In Figure \ref{Fig:LowHistogram} the top and bottom panels use unrotated HP and VP filters, respectively."
 Figure 4b presents the same data but for 0;=7/4., Figure \ref{Fig:HighHistogram} presents the same data but for $\theta_f = \pi/4$.
" By subtracting the former distribution from the latter, Figure 4c shows that a relative angle of 7/4 between polarisation filter and the band-like caustic structures, evident in Figure 3,, biases the distribution towards the mean with less extremes in magnification."," By subtracting the former distribution from the latter, Figure \ref{Fig:DiffHistogram} shows that a relative angle of $\pi/4$ between polarisation filter and the band-like caustic structures, evident in Figure \ref{Fig:MagMapExample}, biases the distribution towards the mean with less extremes in magnification."
" However, subtracting the distribution in Figure 4b from a histogram for 0;=7/2 (not shown) generates a vertical inversion of Figure 4c,, with an increased proportion of high and low magnification with respect to the average."," However, subtracting the distribution in Figure \ref{Fig:HighHistogram} from a histogram for $\theta_f =\pi/2$ (not shown) generates a vertical inversion of Figure \ref{Fig:DiffHistogram}, with an increased proportion of high and low magnification with respect to the average."
 Further simulations confirm this trend for any additional rotation of 7/2., Further simulations confirm this trend for any additional rotation of $\pi/2$.
 'The explanation of this requires consideration of how the HP and VP wings overlap with the structure of the magnification map., The explanation of this requires consideration of how the HP and VP wings overlap with the structure of the magnification map.
" If the relative orientation is such that either the HP or VP wings are parallel to the caustic bands, there is a high probability that either the wing pair crosses caustics and magnification is larger than average, or the wings are both off the caustic structure and magnification is below average."," If the relative orientation is such that either the HP or VP wings are parallel to the caustic bands, there is a high probability that either the wing pair crosses caustics and magnification is larger than average, or the wings are both off the caustic structure and magnification is below average."
" Presumably, a perpendicular orientation also leads to such extremes; if one wing lies across a caustic then the other is likely to cross the same band, and likewise if one wing is off the structure then the other is too."," Presumably, a perpendicular orientation also leads to such extremes; if one wing lies across a caustic then the other is likely to cross the same band, and likewise if one wing is off the structure then the other is too."
" In contrast, a relative angle of 7/4 does not double the magnification effect for a wing pair via simultaneous traversal of the same caustic, nor can the pair completely overlap a band as they do when parallel to the caustic structure."," In contrast, a relative angle of $\pi/4$ does not double the magnification effect for a wing pair via simultaneous traversal of the same caustic, nor can the pair completely overlap a band as they do when parallel to the caustic structure."
 Hence the probability of magnification is more tightly centred around an average., Hence the probability of magnification is more tightly centred around an average.
" Figure 5 extends this argument by displaying the joint probability distributions of the base ESR VP filter magnifications (y-axis) and HP filter magnifications (x-axis) for Q2237+0305, all as seen in image B at varying rotations of the polarisation filter and magnification maps."," Figure \ref{Fig:RotationDistributionsB} extends this argument by displaying the joint probability distributions of the base ESR VP filter magnifications $y$ -axis) and HP filter magnifications $x$ -axis) for Q2237+0305, all as seen in image B at varying rotations of the polarisation filter and magnification maps."
" Joint distributions have been fruitfully used in other works (Lewis&Ibata2004;BrewerLewis2005;Abajasetal.2007) and indicate the probability of HP and VP filtered magnifications occurring at the same source location, ie. map point, and thus how well magnifications vary in “lock-step”."," Joint distributions have been fruitfully used in other works \citep{Lewis:2004,Brewer:2005,Abajas:2007} and indicate the probability of HP and VP filtered magnifications occurring at the same source location, i.e. map point, and thus how well magnifications vary in “lock-step”."
" They therefore indicate expectations of one magnification based on the other, and can constrain models from observations."," They therefore indicate expectations of one magnification based on the other, and can constrain models from observations."
" The probability value is indicated by colour, with blue being O0 and red “most likely""."," The probability value is indicated by colour, with blue being $0$ and red “most likely”."
" All the panels represent the same measure, but for different orientations of the magnification map ($) and the various rotations applied simultaneously to both HP and VP filters (OF)."," All the panels represent the same measure, but for different orientations of the magnification map $\phi$ ) and the various rotations applied simultaneously to both HP and VP filters $\theta_f$ )."
 All distributions appear symmetric across the lines of equal magnification., All distributions appear symmetric across the lines of equal magnification.
" However, the top left and bottom right plots show widest distributions when the relative angle"," However, the top left and bottom right plots show widest distributions when the relative angle"
(see ? for a description of the catalog).,(see \citealt{SDSSDR8} for a description of the catalog).
 The emission-line measurements are from Gaussian fits to continuum-subtracted spectra (??)..," The emission-line measurements are from Gaussian fits to continuum-subtracted spectra \citep{brinchmann04,tremonti04}."
 The emission-line fluxes have been normalized to SDSS r-band photometric fiber magnitudes and have been corrected for Galactic foreground extinction following ? using the map of ?..," The emission-line fluxes have been normalized to SDSS $r$ -band photometric fiber magnitudes and have been corrected for Galactic foreground extinction following \citet{odonnell94}
 using the map of \citet{schlegel98}."
" Continuum spectral indices such as aand aare measured from data spectra after subtracting all c emission lines (??),, which, as we have checked, are consistent with those measured from best-fit continuum model spectra."," Continuum spectral indices such as and are measured from data spectra after subtracting all $\sigma$ emission lines \citep{kauffmann03c,brinchmann04}, which, as we have checked, are consistent with those measured from best-fit continuum model spectra."
 The stellar mass estimates are total stellar masses derived from population synthesis fits using the ? models to SDSS broad-band photometry (??)..," The stellar mass estimates are total stellar masses derived from population synthesis fits using the \citet{bc03} models to SDSS broad-band photometry \citep{kauffmann03c,salim07}."
" The adopted stellar mass estimate from photometry fits is a good indicator of the dynamical mass inside the effective radius (May,c? R,/G, where R, is the galaxy effective radius and G is the gravitational constant) for M,>101?M (222); At the lower mass end of our sample (M.~ 10°°Mo), M, is ~0.2 dex larger than (?).."," The adopted stellar mass estimate from photometry fits is a good indicator of the dynamical mass inside the effective radius $M_{{\rm dyn}} \propto
\sigma_{\ast}^2 R_e/G$ , where $R_e$ is the galaxy effective radius and $G$ is the gravitational constant) for $M_{\ast} >
10^{10} M_{\odot}$ \citep{brinchmann00,drory04,padmanabhan04}; At the lower mass end of our sample $M_{\ast} \sim 10^{9.5}
M_{\odot}$ ), $M_{\ast}$ is $\sim 0.2$ dex larger than $M_{{\rm
dyn}}$ \citep{drory04}."
" To characterizeMay; how the effects of tidal interactions on host star formation and BH accretion evolve in AGN pairs as the merger progresses, we examine their statistical properties as a function of pair separation and velocity offset, and compare to control samples of single AGNs."," To characterize how the effects of tidal interactions on host star formation and BH accretion evolve in AGN pairs as the merger progresses, we examine their statistical properties as a function of pair separation and velocity offset, and compare to control samples of single AGNs."
" We draw control AGNs from our of 138,070 AGNs."," We draw control AGNs from our parent sample of 138,070 AGNs."
" We match the control sample parentto the sampleAGN pair sample in redshift to mitigate selection biases in our flux-limited sample, and aperture bias due to the difference in the physical scales covered by the SDSS ffibers for galaxies at different redshifts."," We match the control sample to the AGN pair sample in redshift to mitigate selection biases in our flux-limited sample, and aperture bias due to the difference in the physical scales covered by the SDSS fibers for galaxies at different redshifts."
 We also match stellar mass distribution to control mass-dependent effects of AGN host-galaxy properties (?).., We also match stellar mass distribution to control mass-dependent effects of AGN host-galaxy properties \citep{kauffmann03}.
" We show in Figure 1 the redshift and stellar mass distributions of the pair (tidal) sample and its control sample, respectively."," We show in Figure \ref{fig:control} the redshift and stellar mass distributions of the pair (tidal) sample and its control sample, respectively."
 We match the whole distribution rather than object by object., We match the whole distribution rather than object by object.
 The control samples are drawn to have the same distribution in redshift and in stellar mass as the pair (tidal) sample by requiring that their Kolmogorov-Smirnov (KS) probabilities are larger than at least., The control samples are drawn to have the same distribution in redshift and in stellar mass as the pair (tidal) sample by requiring that their Kolmogorov-Smirnov (KS) probabilities are larger than at least.
" We have matched galaxy mass rather than luminosity in our control sample, because interacting galaxies often show younger stellar populations than do isolated galaxies, making galaxy luminosity a biased indicator of mass (seealsoe.g., ?).."," We have matched galaxy mass rather than luminosity in our control sample, because interacting galaxies often show younger stellar populations than do isolated galaxies, making galaxy luminosity a biased indicator of mass \citep[see also e.g.,][]{ellison08}."
" To the intrinsic dependence of host star formation and BH studyaccretion on and Av in AGN pairs, we first verify in Figure 2. that host-galaxyr, stellar mass does not correlate with r, or Av, obviating the need to match control samples for each subset of AGN at fixed or Av."," To study the intrinsic dependence of host star formation and BH accretion on $r_p$ and $\Delta v$ in AGN pairs, we first verify in Figure \ref{fig:control_at_fixed_r} that host-galaxy stellar mass does not correlate with $r_p$ or $\Delta v$, obviating the need to match control samples for each subset of AGN pairs at any fixed $r_p$ or $\Delta v$."
" Figure 2 also shows that galaxy pairsconcentration,any a rymeasure of the mass distribution within galaxies, does not correlate with r, or Av, which is relevant because the distribution of mass within galaxies may also regulate mergertimescales$."," Figure \ref{fig:control_at_fixed_r} also shows that galaxy concentration, a measure of the mass distribution within galaxies, does not correlate with $r_p$ or $\Delta v$, which is relevant because the distribution of mass within galaxies may also regulate merger."
". The r-band concentration index C, is defined as the ratio between the r- Petrosian half-lightradius and the radius enclosing of the r-band Petrosian luminosity of a galaxy (?)..", The $r$ -band concentration index $C_r$ is defined as the ratio between the $r$ -band Petrosian half-lightradius and the radius enclosing of the $r$ -band Petrosian luminosity of a galaxy \citep{strauss02}.
" In §?? we present the distributions of BH accretion and host recent star formation properties of the pair and tidal samples and their dependence on r, and Av, and compare them with control AGN samples."," In \ref{subsec:prop} we present the distributions of BH accretion and host recent star formation properties of the pair and tidal samples and their dependence on $r_p$ and $\Delta v$ , and compare them with control AGN samples."
 We show how these results depend on host-galaxy stellar mass ratio and concentration in, We show how these results depend on host-galaxy stellar mass ratio and concentration in
We study secular iuteracious in //D83113s planetary system under the assmuptious that the planets share a conuuon orbital plane aud that their apsides remain aligned.,We study secular interactions in $HD 83443$ 's planetary system under the assumptions that the planets share a common orbital plane and that their apsides remain aligned.
 The former asstuuption seenis reasonable for planets formed ina gaseous disk., The former assumption seems reasonable for planets formed in a gaseous disk.
 The latter asswuption is consistent with the currently observed. approximate apse alieumieut (see Table 1)) aud is justified by the analysis in 3.., The latter assumption is consistent with the currently observed approximate apse alignment (see Table \ref{table:parameter}) ) and is justified by the analysis in \ref{sec:linear}.
 These asstuptions aow us to infer paralmctors of the planetary system from he observed eccentricity ratio., These assumptions allow us to infer parameters of the planetary system from the observed eccentricity ratio.
 Ahtual secular perturbaions of the planets orbits are calculated following a method devised. by Gauss (1818)) as outlined in the appendix., Mutual secular perturbations of the planets' orbits are calculated following a method devised by Gauss \cite{gauss}) ) as outlined in the appendix.
 Equation describes the resulting periapse and ecceutricity variations., Equation describes the resulting periapse and eccentricity variations.
 However. as a result of inner planets proximity to the star. it is subject to additional precessional perturbations of which the ost miportaut arise from its related tidal aud rotational distortions (Sterne 1939))?.. and. frou eoncral relativity (Eiusteiu 1916)).," However, as a result of inner planet's proximity to the star, it is subject to additional precessional perturbations of which the most important arise from its related tidal and rotational distortions (Sterne \cite{sterne}), and from general relativity (Einstein \cite{einstein}) )."
 Expressions for these precession rates are. Note that iu equation the plauct’s spin rate. 04. is scaled by its mean motion. vy. since we expect that tidal dissipation has produced approximate spiu-orbit svuchronization.," Expressions for these precession rates are, Note that in equation the planet's spin rate, $\Omega_1$ , is scaled by its mean motion, $n_1$, since we expect that tidal dissipation has produced approximate spin-orbit synchronization."
 We neglect simaller precessional contributions due to the rotational oblateness of the star and to the tidal distortion of the star by the planet., We neglect smaller precessional contributions due to the rotational oblateness of the star and to the tidal distortion of the star by the planet.
 NMuuevically. the total rate of extra precessious amounts to. where we set O4=n4 aud introduce the dineusiouless jiuuber C=(Eoflo(RyRy) with Ry aud boyassigued values appropriate for Jupiter.," Numerically, the total rate of extra precessions amounts to, where we set $\Omega_1 = n_1$ and introduce the dimensionless number $C \equiv (k_{2}/k_{2J})(R_1/R_J)^5$, with $R_J$ and $k_{2J}$assigned values appropriate for Jupiter."
 Observations determine hoy= 0.191. close to that of an =1 polvtrope. kyzz0.51. whereas Saturn has a smaller Love umuber. fo=0.317 (Yoder 1995)) because it is more centrally condensed as a result of possessing a relatively laree," Observations determine $k_{2J}=0.494$ , close to that of an $n=1$ polytrope, $k_2\approx 0.51$, whereas Saturn has a smaller Love number, $k_2 = 0.317$ (Yoder \cite{yoder}) ) because it is more centrally condensed as a result of possessing a relatively larger core of heavy elements."
r core of , We incorporate the additional precessional terms into the secular perturbation equations (see eq. \ref{eq:secular}] ]).
hea," In a state of apse alignment, there is no secular exchange of angular momentum between the planets."
," Therefore, their orbital eccentricities are constant on the seculartime-scale."
vy ," Moreover, the eccentricity ratio, $e_1/e_2$, is a monotonically decreasing function of $\Delta$."
," To match the observationally determined value of $e_1/e_2=0.19$ requires $\Delta \approx 9.1\times 10^{-11}\,\sin^{-1} i\, \s^{-1}$."
, This value is greater than the precession rate due to general relativity and provides evidence for the tidal and rotational distortion of the inner planet.
," Because the inner planet is not observed to transit, $\sin i <
0.99$ , which implies $C \ge 0.9$."
," Nearly pole-on orbits, $\sin i <
0.20$, are excluded if we accept that $R_1 < 2 R_J$, a conservative upper-limit as judgedfrom Fig."
, 1 of Burrows \cite{burrows}. .
, Thisimplies $m_1 < 5.45 M_{\rm sat}$ .
Πω, Figure \ref{fig:secular_search} shows $e_1$ as a function of $C$ for different values of $\sin i$ with $e_2$ fixed at itsobserved value.
dusty torus.,dusty torus.
" One is the sublimation radius, rau,(0), which determines the region where hot dust can survive."," One is the sublimation radius, $r_{\rm sub}(\theta)$, which determines the region where hot dust can survive."
" In order to maintain a geometrically thick structure, energy input from stars and/or supernovae in the dusty torus is necessary (e.g., Wada&Norman2002;Thompson,Quataert,Mur-ray2005;Kawakatu&Wada 2008))."," In order to maintain a geometrically thick structure, energy input from stars and/or supernovae in the dusty torus is necessary (e.g., \citealt{WN02,Th05,KW08}) )."
" This energy input may occur outside of the critical radius, r., above which the torus is gravitationally unstable, if we adopt Toomre's stability criterion."," This energy input may occur outside of the critical radius, $r_{*}$, above which the torus is gravitationally unstable, if we adopt Toomre's stability criterion."
" Thus, the magnitude relation between Tsub(Otorus) and rx may determine the structure of the inner part of the dusty torus, as in the following three cases. ("," Thus, the magnitude relation between $r_{\rm sub}(\theta_{\rm torus})$ and $r_{*}$ may determine the structure of the inner part of the dusty torus, as in the following three cases. ("
"i) If rx< Ysub(Otorus), the inner radius of the torus, rin, may be determined by rsup(@).","i) If $r_{*} \ll r_{\rm sub}(\theta_{\rm torus})$ , the inner radius of the torus, $r_{\rm in}$, may be determined by $r_{\rm sub}(\theta)$."
 This corresponds to the case of Fig., This corresponds to the case of Fig.
 5(i). (, 5(i). (
"ii) When r.£&r&b(0corus), the structure of the dusty torus is like Fig.","ii) When $r_{*}\approx r_{\rm sub}(\theta_{\rm torus})$, the structure of the dusty torus is like Fig."
 5(ii)., 5(ii).
" As mentioned above, the dust can survive at even r<rsub(Atorus), though the structure within r. is geometrically thin because there is no energy source in this region."," As mentioned above, the dust can survive at even $r < r_{\rm sub}
(\theta_{\rm torus})$, though the structure within $r_{*}$ is geometrically thin because there is no energy source in this region."
" Thus, the NIR emission from r<rx is negligible since the covering factor becomes small."," Thus, the NIR emission from $r < r_{*}$ is negligible since the covering factor becomes small."
" That is, rin is determined by the radius for which the dusty torus is gravitationally unstable. ("," That is, $r_{\rm in}$ is determined by the radius for which the dusty torus is gravitationally unstable. ("
"iii) If r.>>rsub(@torus), the dust temperature of the whole inner edge of the dusty torus becomes lower than Tsun because rin=r. is much larger than rsup(@).","iii) If $r_{*} \gg r_{\rm sub}(\theta_{\rm torus})$, the dust temperature of the whole inner edge of the dusty torus becomes lower than $T_{\rm sub}$ because $r_{\rm in}=r_{*}$ is much larger than $r_{\rm sub}(\theta)$."
" If this is the case, the structure of the dusty torus is similar to Fig."," If this is the case, the structure of the dusty torus is similar to Fig."
 5(iii)., 5(iii).
" By exploring the relation between the region of nuclear starbursts and that of the hot dust, we may find evidence revealing the formation of the dusty torus."," By exploring the relation between the region of nuclear starbursts and that of the hot dust, we may find evidence revealing the formation of the dusty torus."
" We now discuss the evolutionary tracks of SMBH growth in the Limm,AGN/ Lbonaisc-Ütorus diagram."," We now discuss the evolutionary tracks of SMBH growth in the $L_{\rm IR,AGN}/L_{\rm bol,disc}$ $\theta_{\rm torus}$ diagram."
" As mentioned in §3.1, although the formation mechanism of the obscuring torus is still a hotly debated issue (e.g., Krolik&BegelmanPapadopoulos,&Spaans2009;Schartmannetal. 2009)), Wada&Norman(2002) proposed a dusty torus supported by turbulent pressure, in which the turbulence is produced by SN explosions (see also Kawakatu&Wada2008;Wada,Papadopoulos,&Spaans2009))."," As mentioned in $\S 3.1$, although the formation mechanism of the obscuring torus is still a hotly debated issue (e.g., \citealt{KB88,PK92,OU99,OU01,WN02,WU05,
Wa09,Sc09}) ), \citet{WN02} proposed a dusty torus supported by turbulent pressure, in which the turbulence is produced by SN explosions (see also \citealt{KW08,Wa09}) )."
" In their model, the geometrical thickness of the torus, which is determined by the balance between the gravity of the central BH and the force due to turbulent pressure, is smaller for more massive BHs."," In their model, the geometrical thickness of the torus, which is determined by the balance between the gravity of the central BH and the force due to turbulent pressure, is smaller for more massive BHs."
" This tendency is consistent with observations in which the covering factor of the dusty torus decreases with increasing BH mass (e.g., Maiolinoetal.2007;Noguchietal.2010))."," This tendency is consistent with observations in which the covering factor of the dusty torus decreases with increasing BH mass (e.g., \citealt{Ma07,No10}) )."
 This model also implies that Oorus increases with time as the BH grows., This model also implies that $\theta_{\rm torus}$ increases with time as the BH grows.
" That is, the evolution proceeds from left to right in the Lim,AGN/Lboraisc-Ütorus. diagram (see Fig."," That is, the evolution proceeds from left to right in the $L_{\rm IR,AGN}/L_{\rm bol,disc}$ $\theta_{\rm torus}$ diagram (see Fig."
 5)., 5).
 Here we consider two simple scenarios: (i) the super-Eddington growth dominated scenario where most of the mass of the SMBHs is supplied not through sub-Eddington accretion discs but through super-Eddington accretion discs. (, Here we consider two simple scenarios: (i) the super-Eddington growth dominated scenario where most of the mass of the SMBHs is supplied not through sub-Eddington accretion discs but through super-Eddington accretion discs. (
ii) the sub-Eddington growth dominated scenario where the sub-Eddington accretion disc mainly feeds the SMBH.,ii) the sub-Eddington growth dominated scenario where the sub-Eddington accretion disc mainly feeds the SMBH.
" Figure 6 shows the evolutionary tracks for these two scenarios, assuming an initial opening angle of the torus of Oorus,init=45° and initially r?gg=10°."," Figure 6 shows the evolutionary tracks for these two scenarios, assuming an initial opening angle of the torus of $\theta_{\rm torus,init}=45^{\circ}$ and initially $\dot{m}_{\rm BH}=10^{3}$."
" We find from this figure that the AGNs stay in a super-Eddington phase (7ngu> 10?) for a long time (a wide range of Oorus) in case (i), whereas in case (ii) the AGNs shift to a sub-Eddington phase when the torus is relatively thick."," We find from this figure that the AGNs stay in a super-Eddington phase $\dot{m}_{\rm BH}>10^{2}$ ) for a long time (a wide range of $\theta_{\rm torus}$ ) in case (i), whereas in case (ii) the AGNs shift to a sub-Eddington phase when the torus is relatively thick."
 The two distinct scenarios can be clearly understood from Fig., The two distinct scenarios can be clearly understood from Fig.
" 3 as follows: for case (i) the evolution proceeds from top left > top right — bottom right, whereas for case (ii) it goes from top left — bottom left — bottom right."," 3 as follows: for case (i) the evolution proceeds from top left $\to$ top right $\to$ bottom right, whereas for case (ii) it goes from top left $\to$ bottom left $\to$ bottom right."
" That is, the AGNs never undergo a phase of extremely low Lir,acn/Lpoidise for case (ii)."," That is, the AGNs never undergo a phase of extremely low $L_{\rm IR,AGN}/L_{\rm bol,disc}$ for case (ii)."
" In contrast, in case (i), many AGNs can be identified as IR faint objects."," In contrast, in case (i), many AGNs can be identified as IR faint objects."
 The NIR luminosity of such AGNs is also very small., The NIR luminosity of such AGNs is also very small.
" The dispersion of AGN/Lbodisc as well as Dntr,aGn/Lbol,disc for case (i)Lim, is significantly larger than that for case (ii)."," The dispersion of $L_{\rm IR,AGN}/L_{\rm bol,disc}$ as well as $L_{\rm NIR,AGN}/L_{\rm bol,disc}$ for case (i) is significantly larger than that for case (ii)."
" If the majority of high-z quasars (z> 7) are NIR-faint, super-Eddington growth may be inevitable for SMBH growth in the early Universe."," If the majority of $z$ quasars $z>7$ ) are NIR-faint, super-Eddington growth may be inevitable for SMBH growth in the early Universe."
" In order to compare the predictions with observations in detail, we must elucidate the evolution of Dnir,acn/Lpol,disc based on the coevolution model of SMBH growth and a circumnuclear disc such as Kawakatu&Wada(2008)."," In order to compare the predictions with observations in detail, we must elucidate the evolution of $L_{\rm NIR,AGN}/L_{\rm bol,disc}$ based on the coevolution model of SMBH growth and a circumnuclear disc such as \citet{KW08}."
. This is a subject for future work., This is a subject for future work.
" In this paper, we predicted that super-Eddington AGNs with rgg>10? have relatively low Lxig,AGN/Dbonaisc."," In this paper, we predicted that super-Eddington AGNs with $\dot{m}_{\rm BH}\geq 10^{2}$ have relatively low $L_{\rm NIR,AGN}
/L_{\rm bol,disc}$."
" SO far, more than 30 quasars have been discovered at ze6 (e.g., Fanetal.2001,2006;GotoWillott2007, 2010))."," So far, more than 30 quasars have been discovered at $z\approx 6$ (e.g., \citealt{Fa01,Fa06,Go06,Wi07,Wi10}) )."
" Jiangetal.(2010) found that two are unusually NIR-faint quasars, 1.6., their ratio of Lwin/Lsioo is one order of magnitude smaller than the average for ordinary quasars, although their properties are similar to those of low-z quasars in the rest-frame ultraviolet/optical andX-ray bands (e.g., Fanetal.2004;Jiang2006;Shemmer 2006))."," \citet{Ji10} found that two are unusually NIR-faint quasars, i.e., their ratio of $L_{\rm NIR}/L_{\rm 5100}$ is one order of magnitude smaller than the average for ordinary quasars, although their properties are similar to those of $z$ quasars in the rest-frame ultraviolet/optical andX-ray bands (e.g., \citealt{Fa04,Ji06,Sh06}) )."
" More interestingly, the two quasars have the smallest BH mass (MpHού10° Mo) and the highest Eddington ratios (Lpoi,acn/Lmaa~ 2) of z~6 quasar samples."," More interestingly, the two quasars have the smallest BH mass $M_{\rm BH}
\approx 10^{8}M_{\odot}$ ) and the highest Eddington ratios $L_{\rm bol,AGN}
/L_{\rm Edd}\sim 2$ ) of $z\sim 6$ quasar samples."
" These features can be nicely explained by our interpretation, ie., the faint NIR emission for high Eddington AGNs."," These features can be nicely explained by our interpretation, i.e., the faint NIR emission for high Eddington AGNs."
 We should note that since NIR-faint quasars can be explained, We should note that since NIR-faint quasars can be explained
Some anubieuities are preseut in the interpretation of stellar wobbles.,Some ambiguities are present in the interpretation of stellar wobbles.
 Auelada-Exscude et al. (, Anglada-Escude et al. (
2010) have warned that eccentric orbital solutious can hide two planets iu a 2:1 resonance (and vice versa?).,2010) have warned that eccentric orbital solutions can hide two planets in a 2:1 resonance (and vice versa?).
 Other degeucracics are preseut for two planet systems: exchange orbits (change in senmiauajor axis. Punk et al.," Other degeneracies are present for two planet systems: exchange orbits (change in semi-major axis, Funk et al."
 2011). eccentric resonances (change iu eccentricity. Laughlin Chambers 2002. Nauenhbere 2002). Trojan planets (Dvorak ot al.," 2011), eccentric resonances (change in eccentricity, Laughlin Chambers 2002, Nauenberg 2002), Trojan planets (Dvorak et al."
 2001). lege imoons or binary plaucts (Cabrera Schneider 2007).," 2004), large moons or binary planets (Cabrera Schneider 2007)."
 These ambiguities will finally be resolved by the detection of the candidate by direct spectro-nnaeiug., These ambiguities will finally be resolved by the detection of the candidate by direct spectro-imaging.
 For direct nuagiug. Kalas (2008) aud Wenuedy Watt (2011) have pointed out that the planet cau be surrounded by a large dust cloud leading to a significant overestimate of its radius and albedo.," For direct imaging, Kalas (2008) and Kennedy Wyatt (2011) have pointed out that the planet can be surrounded by a large dust cloud leading to a significant overestimate of its radius and albedo."
" Some special cases deserve a few comments: - Some authors designate thei discovered. substellar conrpanions as brown dwarfs” whereas they have a nass below the 25 Mj, lint."," Some special cases deserve a few comments: - Some authors designate their discovered substellar companions as ""brown dwarfs"" whereas they have a mass below the 25 $M_{Jup}$ limit."
" It is for instance the case of TIP 75530 b (M = 23.01 4 1 Mj, (Lafreuio et al.", It is for instance the case of HIP 78530 b $M$ = 23.04 $\pm$ 4 $M_{Jup}$ (Lafrenièrre et al.
 2011)., 2011).
 We have iucluded. these allegated brown dwurfs iu the main planet table. -, We have included these allegated brown dwarfs in the main planet table. -
 The oeidividual case of Gliese Sal e has deservec uuch attention because. as a one of the first poteutiallv jabitable plauets. it is enmibleiiatic.," The individual case of Gliese 581 g has deserved much attention because, as a one of the first potentially habitable planets, it is emblematic."
 It has been publishee in a refereed paper (Vost ct al., It has been published in a refereed paper (Vogt et al.
 2010) and as such shouk rormmally be in the main table., 2010) and as such should normally be in the main table.
 It las been. challenece w Pepe ct al. (, It has been challenged by Pepe et al. (
2010) and by Creeory (2011). but as of February 2011 with no published additional RV data.,"2010) and by Gregory (2011), but as of February 2011 with no published additional RV data."
 We rave chosen to transfer it (provisionnally?), We have chosen to transfer it (provisionnally?)
 iu the table of uuconfiued planets. -, in the table of unconfirmed planets. -
" 9xue objects have a published mass well bevoud the 25 Αιρ nass limit. but with a very large iiass micertaiuty AM so that the value for AfAM. is below the 25 Afj4, liit."," Some objects have a published mass well beyond the 25 $M_{Jup}$ mass limit, but with a very large mass uncertainty $\Delta M$ so that the value for $M-\Delta M$ is below the 25 $M_{Jup}$ limit."
" It is for instance the case of ΠΟ 190228 b for which Reffert Quireubach (2011) eive a mass range 5.93 - 117.2 Mj, at the 3 σ level by using IHipparcos astrometric data.", It is for instance the case of HD 190228 b for which Reffert Quirrenbach (2011) give a mass range 5.93 - 147.2 $M_{Jup}$ at the 3 $\sigma$ level by using Hipparcos astrometric data.
 We have trausfered thoi into he table of unconfirmed planets, We have transfered them into the table of unconfirmed planets.
 The situation will be clarified around 2015 with the results of the ESA Cia astrometric MUSSIOL. -, The situation will be clarified around 2015 with the results of the ESA Gaia astrometric mission. -
" They are naturally in the table"" unconfmnued'. -"," They are naturally in the table ""unconfirmed"". -"
 It is the case for caudidates suspected frou a linear trend in RV inonitoriug. or planets suspected to sculpt a debris disc or plauets suspected because they pollute a stellar spectrum.," It is the case for candidates suspected from a linear trend in RV monitoring, or planets suspected to sculpt a debris disc or planets suspected because they pollute a stellar spectrum."
 For the two first cases. the cadidate will ultimately be confirmed. or uot. bv direct imeing.," For the two first cases, the cadidate will ultimately be confirmed, or not, by direct imging."
 Ther are in the “unconfirmed” table.," They are in the ""unconfirmed"" table."
 We describe the catalogue as it is iu February 2011., We describe the catalogue as it is in February 2011.
 It nay evolve continuously., It may evolve continuously.
 It is. provisionally. organized in 8 tables. according to their discovery mcthods.," It is, provisionally, organized in 8 tables, according to their discovery methods."
" We distinguish “detection” from ""discovery: ο, Some auets are discovered by RV aud detected by trausit afterwards."," We distinguish ""detection"" from ""discovery"": e.g. some planets are discovered by RV and detected by transit afterwards."
 Iu the coming vears. planets discovered by RV will be detected bv direct. inagius aud vice-versa: herefore this categorization is likely to chauge.," In the coming years, planets discovered by RV will be detected by direct imaging and vice-versa; therefore this categorization is likely to change."
 The & ables L/ All “confirmed” 2/ Planets discovered by RV audor astrometry (note that as of February 2011 no confined planet has been discovered by astrometry. although a few of them have been observed iu an astrometric mouitoriug after their discovery by 3í A sub-table of the previous collects plaucts discovered first by transit aud confirmed later by RV. aud planets discovered first bv RWV with transits discovered Lf Planets discovered by 5/a Planets discovered by direct if Planets discovered by timing (pulsar planets. timing of eclipses of eclipsing binaries (or planetary transits) or timing of stellar τὸ Vnconfixiied or retracted δ Free floattine” planets.," The 8 tables 1/ All ""confirmed"" 2/ Planets discovered by RV and/or astrometry (note that as of February 2011 no confirmed planet has been discovered by astrometry, although a few of them have been observed in an astrometric monitoring after their discovery by 3/ A sub-table of the previous collects planets discovered first by transit and confirmed later by RV, and planets discovered first by RV with transits discovered 4/ Planets discovered by 5/ Planets discovered by direct 6/ Planets discovered by timing (pulsar planets, timing of eclipses of eclipsing binaries (or planetary transits) or timing of stellar 7/ Unconfirmed or retracted 8/ ""Free floatting"" planets."
"The ""no hair” theorem (Misueretal.1973). postulates that all black bole solutious of the Eiusteiu-Maxwell equations of gravitation and electromaguetisi iu general relativity can be completely characterized by ouly three externally observable classical parameters: mass. electric charge. aud augular momentum.","The “no hair” theorem \citep[][]{MTW} postulates that all black hole solutions of the Einstein-Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three externally observable classical parameters: mass, electric charge, and angular momentum."
 The key point in the classical proof (e.g...Price1972) is that the outside mecitua is a vacuum., The key point in the classical proof \citep[\eg][]{1972PhRvD...5.2439P} is that the outside medium is a vacuum.
 Iu contrast. the surrouudiugs of astrophysical high energy sources like pulsars and," In contrast, the surroundings of astrophysical high energy sources like pulsars and"
If the winds from these low mass companions are orders of magnitdue smaller than (he solar wind mass loss rate. this has significant implications for the angular momentum evolution of CV progenitors and CVs themselves.,"If the winds from these low mass companions are orders of magnitdue smaller than the solar wind mass loss rate, this has significant implications for the angular momentum evolution of CV progenitors and CVs themselves."
 Typically. it has been assumed that the angular momentum evolution of a CV or CV-progenitor occurred due to magnetic braking through a stellar wind. with angular momentum loss: where ο represents a cutoff rotation speed where the magnetic [field saturates.," Typically, it has been assumed that the angular momentum evolution of a CV or CV-progenitor occurred due to magnetic braking through a stellar wind, with angular momentum loss: where $\omega_{crit}$ represents a cutoff rotation speed where the magnetic field saturates."
 This equation is a modilied form of Chat used by 2.. following the work of ? αμα ?..," This equation is a modified form of that used by \citet{kawaler88}, following the work of \citet{mestel87} and \citet{weber67}."
 This prescriplion was used bv others to estimate the Gimescale for the evolution of single low nass stars. (he onset of mass transfer in CV progenitors. aud the timescale for the evolution of CVs (??7)..," This prescription was used by others to estimate the timescale for the evolution of single low mass stars, the onset of mass transfer in CV progenitors, and the timescale for the evolution of CVs \citep{sills00, g03, andronov03}."
 In all of these cases. it was implicitly assumed that the mass loss rate was approximatelv (he solar wind mass loss rate.," In all of these cases, it was implicitly assumed that the mass loss rate was approximately the solar wind mass loss rate."
" A, ancl V were essentially [ree parameters bul were chosen to be 2.7x 10! g em s and 1.5 respectively in these works.", $K_w$ and $N$ were essentially free parameters but were chosen to be $\times$ $^{47}$ g cm s and 1.5 respectively in these works.
" A, essentially collects all the uncertainties in the properties of the wind and magnetic field of a particular star and N corresponds to the particular magnetic field geometry.", $K_w$ essentially collects all the uncertainties in the properties of the wind and magnetic field of a particular star and $N$ corresponds to the particular magnetic field geometry.
 It is immediately apparent that for the given .N. JxM and the consequent angular momentum loss rate for the observed DAZs would be 1-2 orders of magnitude smaller Chan would be calculated by Equation 5..," It is immediately apparent that for the given $N$, $\dot{J}\propto\dot{M}$ and the consequent angular momentum loss rate for the observed DAZs would be 1-2 orders of magnitude smaller than would be calculated by Equation \ref{eq:ang}."
 The consequent timescale for these binaries to become CVs would be dominated by eravitational radiation. and would not be affected significantly by magnetic braking.," The consequent timescale for these binaries to become CVs would be dominated by gravitational radiation, and would not be affected significantly by magnetic braking."
 ] also investigate a plausible orbital separation cutoff where a (vpical measured. WD accretion rate can be maintained bv an M cdiwirf wind., I also investigate a plausible orbital separation cutoff where a typical measured WD accretion rate can be maintained by an M dwarf wind.
 Using a similar calculation as I used for my widely separated binaries. I place a cutoff for reasonable mass loss rates due to winds at the stellar wind upper limits for Proxima Centauri (See Table 3)).," Using a similar calculation as I used for my widely separated binaries, I place a cutoff for reasonable mass loss rates due to winds at the stellar wind upper limits for Proxima Centauri (See Table \ref{resulttab}) )."
 Figure 2. shows the result for varving levels of mass accretion that should be typical for DAZs., Figure \ref{fig:cutoff} shows the result for varying levels of mass accretion that should be typical for DAZs.
 The lowest accretion rates allow plausible companions at wider separations. but the maximum allowed is e] AU.," The lowest accretion rates allow plausible companions at wider separations, but the maximum allowed is $\sim$ 1 AU."
 li may be instructive to separate DAZs into three classes for ease of identilving the underlying mechanism for accretion., It may be instructive to separate DAZs into three classes for ease of identifying the underlying mechanism for accretion.
 The first. class would be DAZs with companions in orbits <1 AU., The first class would be DAZs with companions in orbits $\ltorder$ 1 AU.
 These are most plausibly explained by a wind scenario and can be used to, These are most plausibly explained by a wind scenario and can be used to
 ,where p is a real number. \ref{eq:inverse_theory_2d}) )
The proof can be generalized to any function which can be expressed as where p; are real numbers., can be rewritten as ) The proof can be generalized to any function which can be expressed as where $p_i$ are real numbers.
" To measure the spherically-averaged correlation function. we have shown that using one rescaling parameter, Dy. and two rescaling parameters. // and £4. are equivalent as long as the scales of interest are relatively small compared to the survey length scale. and the constraint on D: is tight enough."," To measure the spherically-averaged correlation function, we have shown that using one rescaling parameter, $D_V$, and two rescaling parameters, $H$ and $D_A$, are equivalent as long as the scales of interest are relatively small compared to the survey length scale, and the constraint on $D_V$ is tight enough."
 A similar statement can be made for the spherically-averaged power spectrum analysis., A similar statement can be made for the spherically-averaged power spectrum analysis.
 We have verified that these two rescaling methods give similar results., We have verified that these two rescaling methods give similar results.
 We use CosmoMC (Lewis&Bridle2002). in a Markov Chain Tonte-Carlo likelihood analysis., We use CosmoMC \citep{Lewis:2002ah} in a Markov Chain Monte-Carlo likelihood analysis.
" The main parameter space that we explore is 1,A7Ob?inuDy(πρ)b, and the prior ranges are (0.025.0.3). (0.01859.0.02657). ](0.865.1.059). (725.1345). (0.09.0.13). respectively."," The main parameter space that we explore is $\{\Omega_mh^2, \Omega_bh^2, n_s, D_V(z_{eff}), k_\star \}$ and the prior ranges are $\{(0.025,0.3)$, $(0.01859,0.02657)$, $(0.865,1.059)$, $(725,1345)$, $(0.09,0.13)\}$ respectively."
 The dependence on /. he curvature. and dark energy parameters are absorbed. into Dy(serr).," The dependence on $h$, the curvature, and dark energy parameters are absorbed into $D_V(z_{eff})$."
 We marginalize over the amplitude of the correlation function: his is equivalent to marginalizing over galaxy oxFa. where ox is the matter power spectrum normalization parameter and ος is the linear ratio between the correlation function in the redshift space and real space which can be derived from the linear redshift distortion parameter (Kaiser.1987)..," We marginalize over the amplitude of the correlation function; this is equivalent to marginalizing over galaxy $\times \sigma_8 \times r_\beta$, where $\sigma_8$ is the matter power spectrum normalization parameter and $r_\beta$ is the linear ratio between the correlation function in the redshift space and real space which can be derived from the linear redshift distortion parameter \citep{Kaiser:1987qv}."
" Since the LRG data alone cannot give tight constraints on ,/7 and Ες. we apply flat priors CETo ay.) on them which are wide enough so that CMB constraints will not be double counted."," Since the LRG data alone cannot give tight constraints on $\Omega_b h^2$ and $n_s$, we apply flat priors $\pm 7\sigma_{WMAP}$ ) on them which are wide enough so that CMB constraints will not be double counted."
 In other words. the effect from the wide flat priors could be ignored when combining our final results with CMB data.," In other words, the effect from the wide flat priors could be ignored when combining our final results with CMB data."
 We also marginalized over &; over the range of 0.09 to 0.13 (see Sec.3.2)., We also marginalized over $k_*$ over the range of 0.09 to 0.13 (see Sec.3.2).
" In this section. we present the model independent measurements of the parameters we explore. [24(0.35).Q,, h?\_ obtained by using the method described in previous sections."," In this section, we present the model independent measurements of the parameters we explore, $\{D_V(0.35)$, $\Omega_m h^2\}$, obtained by using the method described in previous sections."
 Although. the effective redshift we use is 0.33. the average weighted redshift. we rescale all our results to σε=0.35 for comparing with previous work easily by 105404:(0.33).," Although, the effective redshift we use is 0.33, the average weighted redshift, we rescale all our results to $z_{eff}=0.35$ for comparing with previous work easily by D_V(0.33)."
 We have checked that the results is insensitive to the effective redshift in refsec:test.., We have checked that the results is insensitive to the effective redshift in \\ref{sec:test}.
 We derive the model independent measurements of // and Di for comparison with 2D results., We derive the model independent measurements of $H$ and $D_A$ for comparison with 2D results.
 We also apply the method on two subsamples (two redshift slices) as a systematic test., We also apply the method on two subsamples (two redshift slices) as a systematic test.
 We validate our method by applying it to the LasDamas mock catalogs. and find that our measurements are consistent with the input parameters of the simulations.," We validate our method by applying it to the LasDamas mock catalogs, and find that our measurements are consistent with the input parameters of the simulations."
 We derive constraints on dark energy and cosmological parameters by combining our results with other data sets including WMAP7 (Komatsuetal.2010) and Union? SN tAmanullah2010)., We derive constraints on dark energy and cosmological parameters by combining our results with other data sets including WMAP7 \citep{Komatsu:2010fb} and Union2 SN \citep{Amanullah:2010vv}.
 Finally. we compare our results with previous works.," Finally, we compare our results with previous works."
" Without assuming a dark energy model or a flat Universe. we tind that (0.35).=1428.12 Mpe and kr()/D3(0.35)=0.1125+ 0.0030. where r.(2,) is the comoving sound horizon at the drag epoch calculated with the ((6) in Eisenstein&Hu (1905"," Without assuming a dark energy model or a flat Universe, we find that $D_V(0.35)=1428_{-73}^{+74}$ Mpc and $r_s(z_d)/D_V(0.35) =0.1143 \pm 0.0030$ , where $r_s(z_d)$ is the comoving sound horizon at the drag epoch calculated with the (6) in \cite{Eisenstein:1997ik}."
). reftig:dvSparams shows one and two-dimensional marginalized contours of the parameters. (4:(0.35). Qr. roa)£Dy(0:35). 400.35)J. where The measurements and the covariance matrix are listed in Table | and 2..," \\ref{fig:dv5params} shows one and two-dimensional marginalized contours of the parameters, $\{D_V(0.35)$, $\Omega_m h^2$, $r_s(z_d)/D_V(0.35)$, $A(0.35)\}$, where The measurements and the covariance matrix are listed in Table \ref{table:mean} and \ref{table:covar_matrix}."
 The besttit model from the MCMC likelihood analysis has V7=6.32 for 16 bins of data used tin the scale range of 40h. ΤΜροςs«120f! Mpe with the bin size 2 5h. Mpc). for a set of 6 parameters (including the overall amplitude of the correlation function).," The bestfit model from the MCMC likelihood analysis has $\chi^2=6.32$ for 16 bins of data used (in the scale range of $40 \,h^{-1}$ $<s<120\,h^{-1}$ Mpc with the bin size = $5\,h^{-1}$ Mpc), for a set of 6 parameters (including the overall amplitude of the correlation function)."
 The scale range of the correlation function we have selected iss=40120! Mpe., The scale range of the correlation function we have selected is $s=40-120\ h^{-1}$ Mpc.
 In this range. the scale dependence of the redshift distortion and galaxy bias is small.," In this range, the scale dependence of the redshift distortion and galaxy bias is small."
 We cut the tail of the correlation function ats=1204 Mpe because the high tail (large correlation at large scales) cannot be fitted to any conventional model. and could be due to systematic error or sample variance (see further discussion in refsec:test)).," We cut the tail of the correlation function at $s=120\ h^{-1}$ Mpc because the high tail (large correlation at large scales) cannot be fitted to any conventional model, and could be due to systematic error or sample variance (see further discussion in \\ref{sec:test}) )."
 At this point. we assume the high tail is simply due to sample variance. and might disappear when much larger data sets become available.," At this point, we assume the high tail is simply due to sample variance, and might disappear when much larger data sets become available."
 Unlike previous analyses by other groups. we apply very," Unlike previous analyses by other groups, we apply very"
Our treatment of a decelerating jet is borrowed from the blast wave mocel of bursts.,Our treatment of a decelerating jet is borrowed from the blast wave model of gamma-ray bursts.
 For details see. e.e.. Chiang&Dermer(1999).," For details see, e.g., \cite{cd99}."
. We assume a plasmoid moving ballisGeally with initial mass Mo and bulk Lorentz [actor D along the jet., We assume a plasmoid moving ballistically with initial mass $M_0$ and bulk Lorentz factor $\Gamma_0$ along the jet.
 Let AM be the relativistic mass of the the plasmoid in the rest-frame of (he plasmoid. (hen the momentum P of the plasmoid in the stationary AGN frame is P?—9TAMe. where 9 is the normalized velocily e/e corresponding to the bulk Lorentz factor E.," Let $M$ be the relativistic mass of the the plasmoid in the rest-frame of the plasmoid, then the momentum $P$ of the plasmoid in the stationary AGN frame is $P = \beta \, \Gamma \, M \, c$, where $\beta$ is the normalized velocity $v/c$ corresponding to the bulk Lorentz factor $\Gamma$."
 If the plasmoid radiates isotropically in its vest frame. (he equation of motion of the plasmoid can be derived [rom momentum conservation. dP/dt=0.," If the plasmoid radiates isotropically in its rest frame, the equation of motion of the plasmoid can be derived from momentum conservation, $dP/dt = 0$."
" However. in the case of a quasar. a substantial contribution {ο the (bolometrically dominant) ?-rav emission results from Compton upscattering of external raciation fields (EC: = External Compton). and a significant transfer of plasmoid momentum to Compton-scattered external radiation (""Compton drag) has to be taken into account."," However, in the case of a quasar, a substantial contribution to the (bolometrically dominant) $\gamma$ -ray emission results from Compton upscattering of external radiation fields (EC = External Compton), and a significant transfer of plasmoid momentum to Compton-scattered external radiation (“Compton drag”) has to be taken into account."
 We can therefore write For large enough P. most of the EC radiation will be beamed into a narrow cone of solid angle O~1/T?. and we can write the momentunm transfer to EC radiation as where {ως is the internal energy loss due to EC radiation in (he co-moving frame.," We can therefore write For large enough $\Gamma$, most of the EC radiation will be beamed into a narrow cone of solid angle $\Omega \sim 1/\Gamma^2$, and we can write the momentum transfer to EC radiation as where $\dot{E'}_{\rm EC}$ is the internal energy loss due to EC radiation in the co-moving frame."
 For the purpose of an approximate. quantitative analysis to extract the salient spectral ancl light curve features of this model. we assume that all Compton scattering occurs in the Thomson regime so that The [actor 1/D in Eq. (4))," For the purpose of an approximate, quantitative analysis to extract the salient spectral and light curve features of this model, we assume that all Compton scattering occurs in the Thomson regime so that The factor $1/\Gamma$ in Eq. \ref{EdotEC}) )"
 stems from the fact that £ constitutes a derivative with respect (ο time in the stationary AGN frame. ancl di!=dl/T.," stems from the fact that $\dot{E'}$ constitutes a derivative with respect to time in the stationary AGN frame, and $dt' = dt/\Gamma$."
 We ean also use Eq. (3)), We can also use Eq. \ref{dPdtEC}) )
 for a rough estimate of the magnitude of the radiation drag force. assuming that the observed -rav enmission results from Compton scattering of an isotropic radiation fiekl.," for a rough estimate of the magnitude of the radiation drag force, assuming that the observed $\gamma$ -ray emission results from Compton scattering of an isotropic radiation field."
 Then.," Then,"
are described iun Vinkoetal.2001.,are described in \cite{2ke}.
. The nuüuiuuni of the 4? was found at the following pariineters: Ty(B) = JD 2151973.0 4 0.2 Ciducial Paunaxiuuau) E(DBVW) = 0.05+0.02 uag. fo = 3136E0.11 mag and A = O1740.0E inae.," The minimum of the $\chi^2$ was found at the following parameters: $T_0(B)$ = JD 2451973.0 $\pm$ 0.2 (fiducial $B$ -maximum), $E(B-V)$ = $0.05 \pm 0.02$ mag, $\mu_0$ = $34.36 \pm 0.14$ mag and $\Delta$ = $-0.47 \pm 0.04$ mag."
" The giveu uncertainties are formal errors corresponding to the ecomoetrv of fwe A? ""uction around muni.", The given uncertainties are formal errors corresponding to the geometry of the $\chi^2$ function around minimum.
 The fitted igh curves are show rin Fig.3., The fitted light curves are shown in Fig.3.
 Note. that the Τρ) parameter given here corresponds to the maxiuun of thefiducial light curve (wit1. A=0.0). the actual iiaxinuuu of SN 2IOLV in B occured oue day later. at JD 215197I.," Note, that the $T_0(B)$ parameter given here corresponds to the maximum of the light curve (with $\Delta = 0.0$ ), the actual maximum of SN 2001V in $B$ occured one day later, at JD 2451974."
 The parameters above imply some interesting propertics of SN 2001V. Comparing the £(BV colour excess with the reddening due to Milkv Wax dust (E(B Ἑνα=0.02. Schlegeletαἲ..1998)). it is visible that the ISM in the host galaxy coutributes to the dust absorption.," The parameters above imply some interesting properties of SN 2001V. Comparing the $E(B-V)$ colour excess with the reddening due to Milky Way dust $E(B-V)_{\rm gal} = 0.02$, \cite{sfd}) ), it is visible that the ISM in the host galaxy contributes to the dust absorption."
 Since NGC 3987 is an ecec-on galaxy with strong central dust lane. it is not an unexpected result.," Since NGC 3987 is an edge-on galaxy with strong central dust lane, it is not an unexpected result."
 The host-galaxw reddening could have been even more severe if the SN had occured closer to the ceutral plane of NGC 23987. like e.g. iu the case of SN 1986€ (Phillipsetal.. 1987)). ox. iore recently SN 2002cv iu NGC 3190 (Moikle&Alattila. 2002)).," The host-galaxy reddening could have been even more severe if the SN had occured closer to the central plane of NGC 3987, like e.g. in the case of SN 1986G \cite{phil1}) ), or, more recently SN 2002cv in NGC 3190 \cite{iauc7911}) )."
" The reddening was also estimated usine the ""Lia-Phillips law” (PhilIpsefal. 1999)) as an independent check of the value eiven bv fιο MLCS method.", The reddening was also estimated using the ``Lira-Phillips law” \cite{phil2}) ) as an independent check of the value given by the MLCS method.
 This method uses the apparent homogeneity of the unreddcued (0V)y colours of SNe Ta in the 30<ty<9) phase iuterval (fj- is the phase mieastred frour V. masini)., This method uses the apparent homogeneity of the unreddened $(B-V)_0$ colours of SNe Ia in the $30 < t_V < 90$ phase interval $t_V$ is the phase measured from $V-$ maximum).
 Uufortuuatelv. there is oulv oue observed (2V) data point iu Table 3 hat call be used for this ULPose (BV)2098X0.] Qinae).," Unfortunately, there is only one observed $(B-V)$ data point in Table 3 that can be used for this purpose $(B-V) = 0.98 \pm 0.10$ mag)."
 The moment of V Inaxiun was estimated from the template light curves fitted by the MLCS inecthod., The moment of $V-$ maximum was estimated from the template light curves fitted by the MLCS method.
 It occured at Zoi) = 2151976 +1 JD., It occured at $T_0(V)$ = 2451976 $\pm 1$ JD.
 After correcting for time dilation. the phase of the observed (BV) point was found to be ty=16.3+41 davs.," After correcting for time dilation, the phase of the observed $(B-V)$ point was found to be $t_V = 46.3 ~ \pm 1$ days."
 The relation eiven by Phillipsctal.1999. resulted in (0Yjo-0.89d 0.02., The relation given by \cite{phil2} resulted in $(B-V)_0 = 0.89 \pm 0.02$ .
" This iuplies £(BPy)=0409 mae. which is uot too far from the value given by ΠΙΟο,"," This implies $E(B-V) = 0.09$ mag, which is not too far from the value given by MLCS."
" Towever. its nucertainty is probably higher. because this estimate is based ou a single observation. aud the ""Lira-Phillips law” itself may have an intrinsic uncertainty at the 0.1 mae"," However, its uncertainty is probably higher, because this estimate is based on a single observation, and the “Lira-Phillips law” itself may have an intrinsic uncertainty at the $0.1$ mag"
Deteruunation of the distance-redshift relation mace using distant Type la supernovae (Perluutteretal(1999):Schinidt (1998))). combinect with independent estimates for both the mass density in the Universe today. aud the geometry of the universe from.CAIB ieasurecments (deBeruarcdisetal(2000):Παπά (2000))) have definitively established the need. for a domiuaut conrponeut to the cuerey budect that involves a neeative pressure.,"Determination of the distance-redshift relation made using distant Type 1a supernovae \cite{perl,kirsh}) ), combined with independent estimates for both the mass density in the Universe today, and the geometry of the universe fromCMB measurements \cite{boomerang,maxima}) ) have definitively established the need for a dominant component to the energy budget that involves a negative pressure."
 While there is currently no fundamental understanding of the nature of tlis dark pressure. one particular value of the equation of state parameter carrics special weight.," While there is currently no fundamental understanding of the nature of this dark pressure, one particular value of the equation of state parameter carries special weight."
" A vacuum energy density is fixed. w Lorentz invariance. to have the form Ty,Age. aud tliis as i=1."," A vacuum energy density is fixed, by Lorentz invariance, to have the form $T_{\mu \nu} = \Lambda g_{\mu \nu}$ and thus as $w=-1$."
 Uufortunately. however. all estimates of the vacumu energy deusitv ou the vasis of fust principles calculations vield a value which is orders of magnitude too large. aud thus it was conmuouly assumed for many vears that some lew svinuetry nmechanisn gnieht vield a value or the vacuum enerey which is precisely zero.," Unfortunately, however, all estimates of the vacuum energy density on the basis of first principles calculations yield a value which is orders of magnitude too large, and thus it was commonly assumed for many years that some new symmetry mechanism might yield a value for the vacuum energy which is precisely zero."
 A παω]. scalar field. for example. that is slowly rolling down a poteutial aud has not vet achieved its wun value ean mimic vacuuu cucrey.," A uniform scalar field, for example, that is slowly rolling down a potential and has not yet achieved its minimum value can mimic vacuum energy."
 For such a field. sv is giveu by Since the kinetic energy of the scalar field as it rolls iu the potential eives a positive contribution to the pressure. any τοις nuplies a>1.," For such a field, w is given by Since the kinetic energy of the scalar field as it rolls in the potential gives a positive contribution to the pressure, any rolling implies $w > -1$."
 Of course. since we do not have any uudorlviug theory for the dark pressure one nimmst allow for the possibility that we«——1 (Caldwell (20023).," Of course, since we do not have any underlying theory for the dark pressure one must allow for the possibility that $w <-1$ \cite{caldwell}) )."
 Tt is clear that Lagrangian models that have au equation of state of this forma will be extremely exotic. lunplvine for example. a negative kinetic term.," It is clear that Lagrangian models that have an equation of state of this form will be extremely exotic, implying for example, a negative kinetic term."
 Such models will have the remarkably odd feature that the energy deusitv ofthe dark energy willποσο with time!, Such models will have the remarkably odd feature that the energy density of the dark energy will with time!
 As a result. the Hubble constant itself will continue to increase with time.," As a result, the Hubble constant itself will continue to increase with time."
 If a cosmological constant allows for an older universe for a fixed IIubble coustant today. what will be the effect of even more exotic forms of dark pressure?," If a cosmological constant allows for an older universe for a fixed Hubble constant today, what will be the effect of even more exotic forms of dark pressure?"
 If the equation of state parameter relmaius constant. for a fixed universe. the IIubble coustaut relation is given by: Tt is clear that as Ὃy approaches uuity. the age of the Universe can approach infinity if (ex.1.," If the equation of state parameter remains constant, for a fixed universe, the age-Hubble constant relation is given by: It is clear that as $\Omega_X$ approaches unity, the age of the Universe can approach infinity if $w \le -1$."
" However. we have good estimates on the density of dark matter today. coming from eravitational eusiug of clusters ?.. X-Ray studies of clusters?.. and studies of large scale structure ?7.. tha conservatively iuplv 0,=0.2."," However, we have good estimates on the density of dark matter today, coming from gravitational lensing of clusters \cite{tony}, X-Ray studies of \cite{evrard}, and studies of large scale structure \cite{sloan,2df}, that conservatively imply $\Omega_m \ge 0.2$."
 If we assume lis nüunual value. then the miplicatious. of the above relation between age aud Iubble coustau ‘or exotic forms of energy become quite different.," If we assume this minimal value, then the implications of the above relation between age and Hubble constant for exotic forms of energy become quite different."
 If we normalize to the ITubble hex Project best ft value Ly=72 lau | | (Freceamaneta (2001))) then we can plot the above relation for age as function of το shown in figure 1.," If we normalize to the Hubble Key Project best fit value $H_0 =72$ km $^{-1}$ $^{-1}$ \cite{keyproj}) ) then we can plot the above relation for age as function of $w$, shown in figure 1."
 Also shown in this figure is the ITubbleudepoeudeut product Πρίν., Also shown in this figure is the Hubble-independent product $H_0t_0$.
 As is clearly secu in the figure the age of the Universe is a sharply increasing function of —a for wo0. but then it quickly beeius to asviuptote. so that fora<<10 the age increases by less than 0.5 Cir for a>301," As is clearly seen in the figure the age of the Universe is a sharply increasing function of $-w$ for $w < 0$, but then it quickly begins to asymptote, so that for $w < -10$ the age increases by less than 0.5 Gyr for $w>-30$!"
 This behavior is easilv understood., This behavior is easily understood.
 As has been descibed. as uw decreases below -1. the net enerev density stored mereases with tune.," As has been descibed, as $w$ decreases below -1, the net energy density stored increases with time."
 Thus. the relative coutributiou of this exotic energv to the total energv budget of the Universe was snnaller at carlicr times (hieher redshifts) than. sav. the enerewv deusity stored in a cosmological constant.," Thus, the relative contribution of this exotic energy to the total energy budget of the Universe was smaller at earlier times (higher redshifts) than, say, the energy density stored in a cosmological constant."
 Iu short. this exotic euergv has just become important.," In short, this exotic energy has 'just' become important."
 As a result. the more negative is v. the less time there has been for it to have an effect. even though the acceleration rate mmereases diving the period in which it is sguificaut.," As a result, the more negative is $w$, the less time there has been for it to have an effect, even though the acceleration rate increases during the period in which it is significant."
 The uet result is that. for fixed fraction of the closure density today iu iaatter.there is effectively a maxinnun age for the universe. independent of how negative a is!," The net result is that, for fixed fraction of the closure density today in matter,there is effectively a maximum age for the universe, independent of how negative $w$ is!"
 For My=72 today. oue finds. for example. that for wo 600. ty< 20Car.," For $H_0=72$ today, one finds, for example, that for $w >-600$ , $t_0 <20 $ Gyr."
 Put, Put
of realizations are fitted with much steeper slopes both in the inner ancl outer disk.,of realizations are fitted with much steeper slopes both in the inner and outer disk.
 Given our previous cliscussion of a dichotomy resulting from the combination of two samples with dillerent selection criteria. it is natural to ask whether the two subsamples can be identified with distinct. loci in Fig. 4..," Given our previous discussion of a dichotomy resulting from the combination of two samples with different selection criteria, it is natural to ask whether the two subsamples can be identified with distinct loci in Fig. \ref{fig_mm}."
 Indeed. selecting only those realizations of the bootstrapping procedure that vield best fits at ro«0.9. Le. those associated with what we consider the true truncation radius. produces fits solely in a well-confined region with Ay<2.5 and As«9. which we have indicated: with filled circles.," Indeed, selecting only those realizations of the bootstrapping procedure that yield best fits at $r_0<0.9$, i.e., those associated with what we consider the true truncation radius, produces fits solely in a well-confined region with $\lambda_1<2.5$ and $\lambda_2<9$, which we have indicated with filled circles."
 “Phe remaining fits with ry20.9 are represented. by empty circles., The remaining fits with $r_0>0.9$ are represented by empty circles.
 We will focus our analysis on the ry«0.9 peak. which we believe to be uninlluenced by the warps in several of our sample galaxies.," We will focus our analysis on the $r_0<0.9$ peak, which we believe to be uninfluenced by the warps in several of our sample galaxies."
 A further important observation from Fig., A further important observation from Fig.
 4. is that the outer disk slopes À» for the Ho. component are slightly displaced. from those for the stellar continuum. towards steeper slopes. indicating that Ho crops olf slightly: faster.," \ref{fig_mm} is that the outer disk slopes $\lambda_2$ for the $\alpha$ component are slightly displaced from those for the stellar continuum towards steeper slopes, indicating that $\alpha$ drops off slightly faster."
 Neither component is extremely large. (210): with a mock catalogue. we have verified that a sharp truncation would vield. values of Azο20.," Neither component is extremely large $(>10)$; with a mock catalogue, we have verified that a sharp truncation would yield values of $\lambda_2>20$."
 Projection elfects. as noted earlier. wil soften the outer edge «of the surface brightness clistributior 1only slightly and do no change this conclusion.," Projection effects, as noted earlier, will soften the outer edge of the surface brightness distribution only slightly and do not change this conclusion."
" ""Therefore. his result confirms that he truneation in neither component is particularly sudden. ie. {ο is ruled out for the composite profile. as we had anticipated earlier based on visual inspection alone."," Therefore, this result confirms that the truncation in neither component is particularly sudden, i.e., $H_2$ is ruled out for the composite profile, as we had anticipated earlier based on visual inspection alone."
 Finally. we turn our attention to the comparison between the Eo. and stellar continuum profiles.," Finally, we turn our attention to the comparison between the $\alpha$ and stellar continuum profiles."
 Irrespective of the influence of warped galaxies on the fit. we note that the two probability. distributions are distinct. from. each other.," Irrespective of the influence of warped galaxies on the fit, we note that the two probability distributions are distinct from each other."
 In. particular. fits to the stellar continuum are somewhat closer to the condition Ay=A». meaning that the truncation is relatively softer.," In particular, fits to the stellar continuum are somewhat closer to the condition $\lambda_1=\lambda_2$, meaning that the truncation is relatively softer."
 The fits to the Lla component. on the other hand. are marked by a significantly. larger difference between inner and outer slopes. ie. the truncation is sharper.," The fits to the $\alpha$ component, on the other hand, are marked by a significantly larger difference between inner and outer slopes, i.e., the truncation is sharper."
 LE we consider only the peak associated with he ry80.7 fits. we find the slope Ay of the Ho. profile in the inner cisk to be fairly shallow ancl much shallower han for the stellar continuum.," If we consider only the peak associated with the $r_0\approx0.7$ fits, we find the slope $\lambda_1$ of the $\alpha$ profile in the inner disk to be fairly shallow and much shallower than for the stellar continuum."
 In the outer disk. however. he situation appears reversed: The values of A» appear to indicate a slightly steeper slope for the Lla component than or the stellar continuum.," In the outer disk, however, the situation appears reversed: The values of $\lambda_2$ appear to indicate a slightly steeper slope for the $\alpha$ component than for the stellar continuum."
 The preceding observations also apply when we consider he samples of warped and unwarped: galaxies separately: most dillerences are. quantitative. but not qualitative.," The preceding observations also apply when we consider the samples of warped and unwarped galaxies separately; most differences are quantitative, but not qualitative."
 The most striking dillerence is the fact that the surface rightness profile of the warped galaxies ds fitted: with shallower inner slopes., The most striking difference is the fact that the surface brightness profile of the warped galaxies is fitted with shallower inner slopes.
 One possible explanation is that re warped galaxies were selected to be highly edge-on systems. so that the surface. brightness measured. in the inner disk is strongly alfected by dust in the ealactic plane.," One possible explanation is that the warped galaxies were selected to be highly edge-on systems, so that the surface brightness measured in the inner disk is strongly affected by dust in the galactic plane."
 llowever. since our analysis is not designed. to. probe the inner disks. we cannot pursue this observation further.," However, since our analysis is not designed to probe the inner disks, we cannot pursue this observation further."
 More relevant to our investigation. in the uncdisturbed subsample. 1e tail of the probability distribution of fits to the stellar continuum profile extends to much steeper inner and outer slopes.," More relevant to our investigation, in the undisturbed subsample, the tail of the probability distribution of fits to the stellar continuum profile extends to much steeper inner and outer slopes."
" ""This leads to a significant overlap between the probability. clistributions for the Ha and stellar continuum", This leads to a significant overlap between the probability distributions for the $\alpha$ and stellar continuum
We consider à model in which space-time is endowed with a Friedmann-Robertson-Walker (FRW) metric. given by the formula where sink=siny.sinhy according to the value &=1.0.—1 of the parameter κ describing the spatial curvature. and a£) is the scale factor.,"We consider a model in which space-time is endowed with a Friedmann-Robertson-Walker (FRW) metric, given by the formula where $\rm{sink}=\sin \chi, \chi, \sinh \chi$ according to the value $k=1, 0, -1$ of the parameter $k$ describing the spatial curvature, and $a(t)$ is the scale factor."
 For such a FRW metric. the time-time and space-space components of the Einstein tensor των take the forms 3 Gii. On scales larger than the characteristic size of the emulsion. the presence of equal quantities of matter with positive mass and antimatter with negative mass nullifies the stress-energy tensor T.," For such a FRW metric, the time-time and space-space components of the Einstein tensor $G_{\mu\nu}$ take the forms G_0^0=3 G_i^i= On scales larger than the characteristic size of the emulsion, the presence of equal quantities of matter with positive mass and antimatter with negative mass nullifies the stress-energy tensor $T_{\mu\nu}$."
" Using Einstein equation G,,,=8#GT,,.. we therefore have the equivalence 0 att)t tk=-l."," Using Einstein equation $G_{\mu\nu}= 8\pi G T_{\mu\nu}$, we therefore have the equivalence }=0 t k=-1."
 The metric of the Dirac-Milne universe then reads As in the standard ACDM ).cosmology. the Dirac-Milne universe has a distinetive geometry: while the standard ACDM model has a curved space-time and flat spatial sections. the Dirac-Milne universe has a flat space-time and negatively curved spatial sections.," The metric of the Dirac-Milne universe then reads As in the standard $\Lambda$ CDM cosmology, the Dirac-Milne universe has a distinctive geometry: while the standard $\Lambda$ CDM model has a curved space-time and flat spatial sections, the Dirac-Milne universe has a flat space-time and negatively curved spatial sections."
 The Friedmann equation for the Dirac-Milne universe reads where do is the present value of the scale factor.," The Friedmann equation for the Dirac-Milne universe reads )^2, where $a_0$ is the present value of the scale factor."
 Integrating this equation enables one to compute the present age of the Universe fy: where Hy is the Hubble constant., Integrating this equation enables one to compute the present age of the Universe $t_U$ where $H_0$ is the Hubble constant.
 It should be emphasized that this is a strict equality. whereas in the standard ACDM model. the age of the Universe is only approximatively equal to 1/Ho.," It should be emphasized that this is a strict equality, whereas in the standard $\Lambda$ CDM model, the age of the Universe is only approximatively equal to $1/H_0$."
 It should also be noted that the linear evolution of the scale factor solves the age problem of the Universe (?).. which was a prime concern before the introduction of dark energy. and does not affect the Dirac-Milne cosmology.," It should also be noted that the linear evolution of the scale factor solves the age problem of the Universe \citep{Chaboyer98}, which was a prime concern before the introduction of dark energy, and does not affect the Dirac-Milne cosmology."
 Using the metric in Eq. (1)).," Using the metric in Eq. \ref{metric1}) ),"
 the particle horizon.i.e.. the distance a photon can travel since the origin. is given by the limit which diverges logarithmically in the case of the Dirac-Milne universe.," the particle horizon, the distance a photon can travel since the origin, is given by the limit which diverges logarithmically in the case of the Dirac-Milne universe."
 This simple relation has profound implications as it signifies that any two given places in space were causally connected in the past., This simple relation has profound implications as it signifies that any two given places in space were causally connected in the past.
 The Dirac-Milne universe therefore does not have an horizon problem. which removes the main motivation for the introduction of inflation theories.," The Dirac-Milne universe therefore does not have an horizon problem, which removes the main motivation for the introduction of inflation theories."
 Therefore. the linear evolution of the scale factor and the property that the space-time is flat and spatial sections are open naturally solves two major problems in standard cosmology without requiring additional ingredients such as dark energy or inflation. and is an important motivation for studying in detail such a cosmology.," Therefore, the linear evolution of the scale factor and the property that the space-time is flat and spatial sections are open naturally solves two major problems in standard cosmology without requiring additional ingredients such as dark energy or inflation, and is an important motivation for studying in detail such a cosmology."
 Before presenting the properties of the Dirac-Milne universe and for the sake of clarity. we list the underlying hypothesis and necessary constraints that have been assumed so far:," Before presenting the properties of the Dirac-Milne universe and for the sake of clarity, we list the underlying hypothesis and necessary constraints that have been assumed so far:"
estimates by Thomas et al. (,estimates by Thomas et al. (
2008) which pertain to the entire galaxies.,2008) which pertain to the entire galaxies.
" We also recall that observations suggest that the observed radial gradient slope in the [o/Fe] has, on average, a null value (e.g. Mehlert et al."," We also recall that observations suggest that the observed radial gradient slope in the $\alpha$ /Fe] has, on average, a null value (e.g. Mehlert et al."
 2003)., 2003).
" As shown by Pipino, D'Ercole Matteucci (20088). in fact, even though the observed gradients (Carollo et al."," As shown by Pipino, D'Ercole Matteucci (2008a), in fact, even though the observed gradients (Carollo et al."
" 1993, Davies et al."," 1993, Davies et al."
" 1993) suggest that most ellipticals form outside-in, the expected strong and positive [a/Fe] gradient can be affected by the metal rich gaseous flows inside the galaxy acting together with the SFR."," 1993) suggest that most ellipticals form outside-in, the expected strong and positive $\alpha$ /Fe] gradient can be affected by the metal rich gaseous flows inside the galaxy acting together with the SFR."
 The net result is a gradient in the [c/Fe] ratio nearly flat., The net result is a gradient in the $\alpha$ /Fe] ratio nearly flat.
" Hence, we can safely neglect the presence of gradients in our study."," Hence, we can safely neglect the presence of gradients in our study."
" Instead, they might affect the MMR (see discussion in Sec. 5))"," Instead, they might affect the MMR (see discussion in Sec. \ref{mm}) )"
 The results for our fiducial GalICS version are presented in Fig. 3.., The results for our fiducial GalICS version are presented in Fig. \ref{mfmr}.
 In agreement with Nagashima et al. (, In agreement with Nagashima et al. (
"2005), the a/Fe ratios do not show any correlation with mass (Fig. 3,,","2005), the $\alpha/Fe$ ratios do not show any correlation with mass (Fig. \ref{mfmr},"
" top panel), in strong contrast with the clear positive correlation derived observationally."," top panel), in strong contrast with the clear positive correlation derived observationally."
" The simulations seem to produce decreasing [a/Fe] ratios with increasing galaxy mass, with a slight upturn at the high-mass end."," The simulations seem to produce decreasing $\alpha$ /Fe] ratios with increasing galaxy mass, with a slight upturn at the high-mass end."
 As a result the scatter is large., As a result the scatter is large.
 A linear fit of the simulation results in the [a/Fe]-mass plane would give a flat relationship., A linear fit of the simulation results in the $\alpha$ /Fe]-mass plane would give a flat relationship.
" It is interesting to note that this result does not depend on the environment in the sense that, if we restrict the regression analysis to a sub-sample of galaxies living in haloes whose mass is comparable to rich cluster of galaxies, we do not notice substantial changes in the predicted relationships."," It is interesting to note that this result does not depend on the environment in the sense that, if we restrict the regression analysis to a sub-sample of galaxies living in haloes whose mass is comparable to rich cluster of galaxies, we do not notice substantial changes in the predicted relationships."
 We notice that the most massive galaxies attain a typical level of a-enhancement that is only lo off the value suggested by the observations., We notice that the most massive galaxies attain a typical level of $\alpha$ -enhancement that is only $\sigma$ off the value suggested by the observations.
 This is an improvements with respect to previous results and mainly caused by the implementation of AGN feedback (see Discussion)., This is an improvements with respect to previous results and mainly caused by the implementation of AGN feedback (see Discussion).
 There are two possible formation paths for these objects: i) either these galaxies assemble through dry (gas-poor) mergers or ii) assemble most of their mass over very short time-scales (less than 0.5 Gyr)., There are two possible formation paths for these objects: i) either these galaxies assemble through dry (gas-poor) mergers or ii) assemble most of their mass over very short time-scales (less than 0.5 Gyr).
" Indeed, this ensures that the pollution from SNIa is kept at a low level and, hence, that they maintain an over-solar [a/Fe] ratio in their stars."," Indeed, this ensures that the pollution from SNIa is kept at a low level and, hence, that they maintain an over-solar $\alpha$ /Fe] ratio in their stars."
" However, as showed by Pipino Matteucci (2008), low-mass and highly a-enhanced galaxies are needed if one wants to create the most massive spheroids with a suitable @ enhancement by means of dry-mergers."," However, as showed by Pipino Matteucci (2008), low-mass and highly $\alpha$ -enhanced galaxies are needed if one wants to create the most massive spheroids with a suitable $\alpha$ enhancement by means of dry-mergers."
" GallICS then predicts that a small number of them, with masses ~0.5—1x10!!Me should survive down to redshift zero."," GalICS then predicts that a small number of them, with masses $\sim 0.5-1\times 10^{11}M_{\odot}$ should survive down to redshift zero."
 Unfortunately such galaxies are not observed., Unfortunately such galaxies are not observed.
" In a sense one could turn the argument around and say that a robust prediction of semi-analytic models of hierarchical galaxy formation is the presence of low-mass, highly [o/Fe-enhanced galaxies at high redshift because it is the only way in these models to build local massive ellipticals with the observed [oc/Fe] ratios."," In a sense one could turn the argument around and say that a robust prediction of semi-analytic models of hierarchical galaxy formation is the presence of low-mass, highly $\alpha$ /Fe]-enhanced galaxies at high redshift because it is the only way in these models to build local massive ellipticals with the observed $\alpha$ /Fe] ratios."
 We know from observations that such objects do not seem to exist at moderately high redshifts around z~0.4 (Ziegler et al., We know from observations that such objects do not seem to exist at moderately high redshifts around $z\sim 0.4$ (Ziegler et al.
 If we consider the subsample of galaxies whose luminosity-weighted ages are larger than 10 Gyr (lighter points in fig. 4)), If we consider the subsample of galaxies whose luminosity-weighted ages are larger than 10 Gyr (lighter points in fig. \ref{mfmr_bis}) )
 we notice that the galaxies populating the region below the observed area in the [@/Fe]-mass plane disappear., we notice that the galaxies populating the region below the observed area in the $\alpha$ /Fe]-mass plane disappear.
From its position in the L-R diagram. suspected CEILT-PI-12 to be a brown dwarf binary.,"From its position in the H-R diagram, suspected CFHT-Pl-12 to be a brown dwarf binary."
 Similarly. from their photometric analvsis. suspected this object to be multiple.," Similarly, from their photometric analysis, suspected this object to be multiple."
 Using our WEPC? and ACS images. we resolve and calculate a mass ratio consistent wilh the one (μον derive from the photometry.," Using our WFPC2 and ACS images, we resolve CFHT-Pl-12 and calculate a mass ratio consistent with the one they derive from the photometry."
 It is interesting to note that the (wo resolved binaries IPMDD-25 and IPMDD-29. which have ἐς. and AY photometric measurements available. fall just on the binary. sequence of the ÁN vs. Ue— N) colou-magnitude diagram (CMD) defined by(2003)... as shown in Figure 6.. although they were not included in their study.," It is interesting to note that the two resolved binaries IPMBD-25 and IPMBD-29, which have $I_{C}$ and $K$ photometric measurements available, fall just on the binary sequence of the $K$ vs. $I_{C}-K$ ) colour-magnitude diagram (CMD) defined by, as shown in Figure \ref{pinfield}, although they were not included in their study."
 From this diagram we can predict a mass ratio of 0.60.9 for IPAIBD-25. very similar to that of CEILT-PI-12 since the two objects are very close in the diagram. and consistent with the mass ratio we derive from the relative photometry of the (wo components.," From this diagram we can predict a mass ratio of 0.6–0.9 for IPMBD-25, very similar to that of CFHT-Pl-12 since the two objects are very close in the diagram, and consistent with the mass ratio we derive from the relative photometry of the two components."
 Similarly. (ae CALD predict a mass ratio of O.71.0 for IPAIBD-29. in good agreement with the one we derive [rom the relative photometry of the (wo components.," Similarly, the CMD predict a mass ratio of 0.7–1.0 for IPMBD-29, in good agreement with the one we derive from the relative photometry of the two components."
 From their positions in the II-R. ciagram. suspected ΕΙΤ-1-16 to be a brown dwarf binary.," From their positions in the H-R diagram, suspected CFHT-Pl-16 to be a brown dwarf binary."
 It is not resolved in our ACS images., It is not resolved in our ACS images.
 From their photometric study. also classify this object as binary. and derive a mass ratio of about 0.751.," From their photometric study, also classify this object as binary, and derive a mass ratio of about 0.75–1."
 According to the DUSTY models. this mass ratio corresponds to a difference ol magnitude between 0.0 Amae<6 mag in the J band. thus just at/above the limit of sensitivity of our study.," According to the DUSTY models, this mass ratio corresponds to a difference of magnitude between $\le\Delta$ $\le$ 6 mag in the $I$ band, thus just at/above the limit of sensitivity of our study."
 This indicates that. if multiple. this svstem should have a separation less than 5.4n34 AU depending on the flux ratio (see Figure 1. and Table 4)).," This indicates that, if multiple, this system should have a separation less than 5.4–34 AU depending on the flux ratio (see Figure \ref{limit_detection_all} and Table \ref{binary_candidates}) )."
 Due (ο its peculiar proper motion. suggested that CEIFET-PI-15 might be a multiple svstem.," Due to its peculiar proper motion, suggested that CFHT-Pl-15 might be a multiple system."
 found evidence for high residuals after PSF subtiraction on their NICMOS image.c» and suspected the presence of a companion ab a than ," found evidence for high residuals after PSF subtraction on their NICMOS image, and suspected the presence of a companion at a separation less than 22."
070040.," Using ACS, we do not resolve any companion at separation larger than 040."
 I£ multiple. this object should have a separation smaller than 5.4 AU and/or a difference in magnitude larger than 5.9 mag in the F314W band.," If multiple, this object should have a separation smaller than 5.4 AU and/or a difference in magnitude larger than 5.9 mag in the F814W band."
 From their photometric analysis. suspected CEILT-DI-25. P1-23 and CFILT-PI-21 to be binaries.," From their photometric analysis, suspected CFHT-Pl-25, CFHT-Pl-23 and CFHT-Pl-21 to be binaries."
 Using our. ACS images. we do not find any evidence of companions around (hese three objects.," Using our ACS images, we do not find any evidence of companions around these three objects."
 also. predict. mass ratios ol q ~1 lor CEILTI-DI-23. ¢ <0.751 for CEITT-PI-25. and 0.5g «0.7 lor CEILT-DPI-21. corresponding to differences of magnitude of respectively 0 mag. 203 mag. and 3.3.8.8 mag.," also predict mass ratios of $q\sim$ 1 for CFHT-Pl-23, $q<$ 0.75–1 for CFHT-Pl-25, and $<q<$ 0.7 for CFHT-Pl-21, corresponding to differences of magnitude of respectively 0 mag, $>$ 0–3 mag, and 3.3–8.8 mag."
candles. sensitive to Luminosity clistance) ane DAO or acoustic peaks (standard rulers. sensitive to angular diameter clistance) has already been noticed ancl discussed bv Lazkoz. Nesseris Perivolaropoulos (2007) and hy Linder Roberts (2008).,"candles, sensitive to luminosity distance) and BAO or acoustic peaks (standard rulers, sensitive to angular diameter distance) has already been noticed and discussed by Lazkoz, Nesseris Perivolaropoulos (2007) and by Linder Roberts (2008)."
" Jearing in mind similar mutual inconsistency in the Llubble constant values inferred. [rom lensing time delavs 44,2526kins+Alpe1 (IxXochanek Schechter 2003) anc from the LIST Ixey Project 44,=ΕΝkrstAlpe3 (Freedman ct al."," Bearing in mind similar mutual inconsistency in the Hubble constant values inferred from lensing time delays $H_0 = 52 \pm 6 \; km\; s^{-1}\;Mpc^{-1}$ (Kochanek Schechter 2003) and from the HST Key Project $H_0 = 72 \pm 8 \;
km\; s^{-1}\;Mpc^{-1}$ (Freedman et al."
 2001) our resul suggests the need. for taking a closer look at compatibility of results derived by using angular clameter distances anc umiinosity distances respectively., 2001) our result suggests the need for taking a closer look at compatibility of results derived by using angular diameter distances and luminosity distances respectively.
 Lt is also worth noticing hat the ideas of testingὃν the Etheringtono reciprocity relation γαοσα these two distance measures have been cliscusse: ov Basset Ixuntz (2004) and by Uzan. Aghanim Alellicr (2005).," It is also worth noticing that the ideas of testing the Etherington reciprocity relation between these two distance measures have been discussed by Basset Kuntz (2004) and by Uzan, Aghanim Mellier (2005)."
 1n conclusion our results demonstrated that the methoc discussed in Biesiacla (2006) and extensively investigate »v Grillo ct al. (, In conclusion our results demonstrated that the method discussed in Biesiada (2006) and extensively investigated by Grillo et al. (
2008) on simulated. cata can be used. in owactice to constrain Cosmological models.,2008) on simulated data can be used in practice to constrain cosmological models.
 It turned: ou ο give reasonable results on already. accessible samples of stronglv lensed svstems., It turned out to give reasonable results on already accessible samples of strongly lensed systems.
" Desides the uncertainties relate o velocity dispersion. measurements and their conversion o relevant. lens model parameters (as well as the impac of SIS assumption) the issue of svstematies associated with Di,£D. ratio in the sample turned out to be important.", Besides the uncertainties related to velocity dispersion measurements and their conversion to relevant lens model parameters (as well as the impact of SIS assumption) the issue of systematics associated with $D_{ls}/D_s$ ratio in the sample turned out to be important.
 In xuwticular it implies that strong lensing survey strategies like he one adopted in SLACS survey are better from this point of view., In particular it implies that strong lensing survey strategies like the one adopted in SLACS survey are better from this point of view.
 Lensing systems are gathered around something like ).58 in distance ratio because it is roughly the configuration or which lensing probability (for a given lens mass) is the ighest., Lensing systems are gathered around something like $0.58$ in distance ratio because it is roughly the configuration for which lensing probability (for a given lens mass) is the highest.
 Earlier searches were focused on source population (quasars) seeking for close pairs or multiples ancl checking if they are multiple images of a single source. lensecl by an intervening galaxy., Earlier searches were focused on source population (quasars) seeking for close pairs or multiples and checking if they are multiple images of a single source lensed by an intervening galaxy.
 Pherefore a high lensing probability was an important selection. [actor there., Therefore a high lensing probability was an important selection factor there.
 On the other hand SLACS survey is focused on possible lens population (massive elipticals) with good spectroscopic. data., On the other hand SLACS survey is focused on possible lens population (massive elipticals) with good spectroscopic data.
 Using SDSS templates spectra are carefully checked. for. residual emission (at least three distinct common atomic transitions) coming [rom higher redshifts., Using SDSS templates spectra are carefully checked for residual emission (at least three distinct common atomic transitions) coming from higher redshifts.
 Such candidates undergo image processing by subtracting parametrized brightness distribution tvpical for early type galaxies in order to reveal multiple images of the quasar., Such candidates undergo image processing by subtracting parametrized brightness distribution typical for early type galaxies in order to reveal multiple images of the quasar.
 Details can be found in Bolton et al. (, Details can be found in Bolton et al. (
2006).,2006).
" Therefore. besides the obvious bonus of having central velocity dispersion measured. such strategy is better suited for. discovering systems with lareer D;,/D., ratios which in turn can be used for testing cosmological models."," Therefore, besides the obvious bonus of having central velocity dispersion measured, such strategy is better suited for discovering systems with larger $D_{ls}/D_s$ ratios which in turn can be used for testing cosmological models."
 Finally. one important effect — neglected here — should » mentioned. which is the influence of line of sight mass contamination.," Finally, one important effect – neglected here – should be mentioned, which is the influence of line of sight mass contamination."
 Phe debate on this issue started with Dar-kana (1996) and Ixeeton ct al. (, The debate on this issue started with Bar-Kana (1996) and Keeton et al. (
L997) who were among the irst to convineinely demonstrate that the elfect of large scale structure on strong lensing could be significant.,1997) who were among the first to convincingly demonstrate that the effect of large scale structure on strong lensing could be significant.
 More recent results on this issue can be found in Dalal et al. (, More recent results on this issue can be found in Dalal et al. (
2005) (in he context. of cluster lensing) or Momcheva. ct aL(2006).,2005) (in the context of cluster lensing) or Momcheva et al.(2006).
 This rises the issue of an impact this effect might have on our results. since the sample was small.," This rises the issue of an impact this effect might have on our results, since the sample was small."
 Straightforward naive first guess (based on Poissonian statistics) might sugeest that sample size of order of a few hundred. lenses müght reduce line of sight ‘noise’ contamination down to a few percent., Straightforward naive first guess (based on Poissonian statistics) might suggest that sample size of order of a few hundred lenses might reduce line of sight `noise' contamination down to a few percent.
 This is however not that simple since the ine of sight contamination is in [fact a systematic effect., This is however not that simple since the line of sight contamination is in fact a systematic effect.
 mele massive carly type galaxies (ie.," Namely, massive early type galaxies (ie."
 typical lenses) refer overdense environments. so one consistent approach would be to follow light rays (rav-shooting simulation) hrough many lens planes (obtained from cosmological N-xdv simulation) up to high source redshift.," typical lenses) prefer overdense environments, so one consistent approach would be to follow light rays (ray-shooting simulation) through many lens planes (obtained from cosmological N-body simulation) up to high source redshift."
 This was done o» Wambseanss et al. (, This was done by Wambsganss et al. (
"2005) with the result that up to 2.=lo most ιο, 95% ) of lenses involved only a single mass concentration. whereas for sources at ος=3.8 important contribution of intervening mass could be significant in 38% of strong lensing svstems.","2005) with the result that up to $z_s=1$ most (i.e. $95\%$ ) of lenses involved only a single mass concentration, whereas for sources at $z_s=3.8$ important contribution of intervening mass could be significant in $38\%$ of strong lensing systems."
 This result suggests that the line of sight contamination should be ackclressecl separately. for each. particular survey., This result suggests that the line of sight contamination should be addressed separately for each particular survey.
 For the SLACS survey (where the bulk of our sample comes from) this was assessed in Treu et al. (, For the SLACS survey (where the bulk of our sample comes from) this was assessed in Treu et al. (
2009) where the authors found that SLACS lens galaxies are unbiased. population (ie. with environmenta ollects tvpical to the over-all population of carly type galaxies) ancl typical contribution from. external mass. clistribution is small ono more than a few percent.,2009) where the authors found that SLACS lens galaxies are unbiased population (i.e. with environmental effects typical to the over-all population of early type galaxies) and typical contribution from external mass distribution is small – no more than a few percent.
 Fortunately. the SLACS survey is ongoing i.e. the sample of spectroscopically investigated strong lenses is growing.," Fortunately, the SLACS survey is ongoing i.e. the sample of spectroscopically investigated strong lenses is growing."
 However this survey is relatively shallow. so for cosmological applications one is forced to combine it with deeper surveys (with dilferent designs — hence dillerent svstematies) and the problem of line of sightD contamination remains challenging.," However this survey is relatively shallow, so for cosmological applications one is forced to combine it with deeper surveys (with different designs – hence different systematics) and the problem of line of sight contamination remains challenging."
ots Authors thank to the referee for suggesting inclusion of line of sight contamination elfects. which was very beneficial for," Authors thank to the referee for suggesting inclusion of line of sight contamination effects, which was very beneficial for"
"From Eq.(9)) aud (13)). one nüght think that it is possible to ecneralize the ""nou-bliud phase reconstruction method to the “blind” variant simply using the «;,, coefficients in Eq.(13)) as an estimator for the reconstructed phases of the pre-CMD signal.","From \ref{eq9}) ) and \ref{eq12}) ), one might think that it is possible to generalize the “non-blind” phase reconstruction method to the “blind” variant simply using the $\alm$ coefficients in \ref{eq12}) ) as an estimator for the reconstructed phases of the pre-CMB signal."
 Such generalization. however. would be incorrect because of the following reason.," Such generalization, however, would be incorrect because of the following reason."
 Below we consider only for the multipole range f<50 to avoid the iustruuneutal noise and beam shape properties., Below we consider only for the multipole range $\ell \le 50$ to avoid the instrumental noise and beam shape properties.
" According to Eq.(5)) the moduli of the 0;,, cocficients are related with the moduli of the foregrounds and CMD for cach hand as (with the plases BY? in Eq.(5)) being replaced by 8977, the resultant foreground plases) where [a""|-<[GU]."," According to \ref{eq5}) ) the moduli of the $\alm$ coefficients are related with the moduli of the foregrounds and CMB for each band as (with the phases $\Ks^{(j)}$ in \ref{eq5}) ) being replaced by $\Ph^{(j),f}$, the resultant foreground phases) where $|\a^{cmb}| \ll |\G^{(j)}|$."
 Using Taylor scries oue can obtain fal}~[G7||[aουο€).," Using Taylor series one can obtain $|\a^{(j)}| \sim |\G^{(j)}|+|\a^{cmb}|\cos(\Ph^{(j),f}-\ks)$."
 Then. from Eq.(12)) we ect The comparison of Eq.(A2)) aud Eq.(12)) allow us to conclude that the deviation of the reconstructed plases frou. the CAIB phases should be very hieh even for the small values of A-piuiuueter.," Then, from \ref{eq11}) ) we get The comparison of \ref{a2}) ) and \ref{eq11}) ) allow us to conclude that the deviation of the reconstructed phases from the CMB phases should be very high even for the small values of $\Delta$ -parameter."
 This meaus that the recoustructed phases of the CAIB signal would be close to the foreground plases aud the corresponding power spectra should have very significant crrors., This means that the reconstructed phases of the CMB signal would be close to the foreground phases and the corresponding power spectrum should have very significant errors.
 It is important to note that such a conclusion means that in order to extract the correct pliases and amplitudes of the CAIB signal from the data using a “blind” method of separation. it Is necessary to decrease the contamination in Eq.CÀ1)) of the linear term (7[a'mh)Cosplat &)).," It is important to note that such a conclusion means that in order to extract the correct phases and amplitudes of the CMB signal from the data using a “blind” method of separation, it is necessary to decrease the contamination in \ref{a1}) ) of the linear term $\sim|\a^{cmb}|\cos(\Ph^{(j),f}-\ks)$ )."
" The only way to do this is to take iuto account that $2,eanμαουκο ϱ).»0 for high fa."," The only way to do this is to take into account that $\sum_m|\a^{cmb}|\cos(\Ph^{(j),f}-\ks)
\rightarrow 0$ for high $\ell,m$."
 Tn such a case NC0HwyUlaUP]sOffa’?) and corresponding error of the CMB phase recoustruction should be of the order |a|/iiuf[|G|].," In such a case $\sum_j(-1)^{j+1} \w^{(j)}|\a^{(j)}|\sim
{\cal O}(|\a^{cmb}|^2)$ and corresponding error of the CMB phase reconstruction should be of the order $|\a^{cmb}|/\min\{|\G^{(j)}| \}$."
 Moreover. averagius over tle i values ineans that the corresponding weighting coefficients wl!) is à fiction of { oulv. but uot of in. which is ideologically close to Teemark&Efstathiou(1996) and the ΤΟΠ method. where wl?=ο)," Moreover, averaging over the $m$ values means that the corresponding weighting coefficients $\w^{(j)}$ is a function of $\ell$ only, but not of $m$, which is ideologically close to \citet{te96} and the TOH method, where $\w^{(j)}=w^{(j)}(\ell)$."
 We would like to poiut out. however. tliat for such an optimization. as indicated in Eq.(12)). the reconstructed CAIB plases will have the cross correlations with the foregrounds phases at different levels for differeut modes.," We would like to point out, however, that for such an optimization, as indicated in \ref{eq11}) ), the reconstructed CMB phases will have the cross correlations with the foregrounds phases at different levels for different modes."
 Asstunine that the reconstructed phase VV should be close to the CAMB phase £. from Eq.(12)). we obtain As inentioncd above. a new clement of the “blind” reconstruction of the CMD signal is the correlation between the derived. phases SV and the foreground. phases y;NEN.yjNBN for¢ all linear. combinations. of. the maps.," Assuming that the reconstructed phase $\Ph^{M}$ should be close to the CMB phase $\ks$, from \ref{eq11}) ), we obtain As mentioned above, a new element of the “blind” reconstruction of the CMB signal is the correlation between the derived phases $\Ph^{M}$ and the foreground phases $
\Ph^{(j),f}_1,\Ph^{(j),f}_2$ for all linear combinations of the maps."
" Moreover. if-- then BW~€ while for some of the (in modes which corespouds to equality |a""|cos&<Ng""IGcosV. reconstruction of the CMD phases needs more specific investigation. which will be discussed at the cud of the| section."," Moreover, if then $\Ph^{M} \simeq \ks$ while for some of the $\ell,m$ modes which corresponds to inequality $|\a^{cmb}| \cos{\ks} \ll \sum_j \g^{(j)}|\G^{(j)}|\cos{\Ph^{(j)}}$, reconstruction of the CMB phases needs more specific investigation, which will be discussed at the end of the section."
 For all f£.i0 modes satisfiug Eq.(D2)) in order to decrease the correlation between the foregrounds aud. CAIB phases we introduce the optimization scheme based ou the iterative solution of the Eq.(D1)).," For all $\ell,m$ modes satisfying \ref{b2}) ) in order to decrease the correlation between the foregrounds and CMB phases we introduce the optimization scheme based on the iterative solution of the \ref{b1}) )."
 The first step of iterations is to minimize the variauce, The first step of iterations is to minimize the variance
increasingH ofB the light+ curve is+ more rapidly+ than 2fy.,increasing of the light curve is more rapidly than $t_{\rm obs}^{\rm 2p}$.
 ForB FasFass as long as ολ is not much smaller than 1. the [actor a!772 jinereases rapidly.," For $t_{\rm obs}>t_{\rm obs,
\times}$, as long as $\gamma \Delta \theta$ is not much smaller than 1, the factor $a^{\rm (p+5)/2}$ increases rapidly."
" ""Therefore. at early. tine. the optical emission increases. rather than decreases with time."," Therefore, at early time, the optical emission increases, rather than decreases with time."
 At much later time. σολ51. the factor ai?77 increases only slightly.," At much later time, $\gamma \Delta
\theta\rightarrow 1$, the factor $a^{\rm (p+5)/2}$ increases only slightly."
 So the lisht. curve of RS emission drops as xA47. (Figure 1. the thin solid line).," So the light curve of RS emission drops as $\propto
t_{\rm obs}^{-2}$ (Figure 1, the thin solid line)."
" Taking ep,=0.01. 6.4=ος (the subscript f represents the forward. shock). we have: At fous Beysud7 0.04mJvy."," Taking $\epsilon_{\rm B,f}=0.01$, $\epsilon_{\rm
e,f}=\epsilon_{\rm e}$ (the subscript $f$ represents the forward shock), we have: At $t_{\rm \times,obs}$, $F_{\rm \nu_{\rm
R,obs(off)},f}\approx 0.04{\rm mJy}$ ."
 For foFosse αμαXfH5 (oe. SPN).," For $t>t_{\rm \times,obs}$, $F_{\rm \nu_{\rm R,obs }(on),f}\propto t^{-1/3}$ (e.g., SPN)."
 With eq. (2)), With eq. \ref{Eq:Flux}) )
 and tas=EA|(Eyyee. the sample early. light curve of the FS emission has been presented in Figure 1. (Phe dotted line).," and $t_{\rm obs}\approx {5(a_0-1)\over
4a_0}t_{\times}+[1+{7\over 4 }({1-a_0\over a_0})({t_{\times}\over
t})^{6/7}]t$, the sample early light curve of the FS emission has been presented in Figure 1 (The dotted line)."
" Lor à Gaussian jet. the observed isotropic energy £o,=LicaoiOxp(8/265) "," For a Gaussian jet, the observed isotropic energy $E_{\rm
iso(\theta_{\rm v})}=E_{\rm iso(\theta_{\rm v}=0)}
\exp({-\theta_{\rm v}^2/2\theta_0^2})$ ."
"Typically, the observed peal enerev of NRE is about 0.08 times that of GRBs and Finn~1?Bie,ais "," Typically, the observed peak energy of XRF is about 0.03 times that of GRBs and $E_{\rm
iso(\theta_{v})}\sim 10^{-3}E_{\rm iso(\theta_{\rm v}=0)}$."
Phe corresponding viewing angle is θςzz3.105.," The corresponding viewing angle is $\theta_{\rm v}\approx
3.7\theta_0$."
 Taking (A)=150. equation (3) gives Ruse~ em.," Taking $\eta(\theta_{\rm v})=150$, equation (3) gives $R_{\rm dec}\sim 8.8\times 10^{15}{\rm cm}$ ."
 Correspondingly. fcc725s. which is much shorter than the tvpical duration of the NREs Loy100s. je.thick.," Correspondingly, $t_{\rm dec}\sim 25~{\rm s}$, which is much shorter than the typical duration of the XRFs $T_{\rm 90}\sim
100~{\rm s}$, i.e.,."
 So. locally /.zmουρές| z). with which /?. and 5. can be calculated self-consistentLy.," So, locally $t_{\rm \times}\approx T_{90}/(1+z)$ with which $R_{\rm \times}$ and $\gamma_{\rm \times}$ can be calculated self-consistently."
 At R.. the energy conservation of the svstem. i.o.. the shocked ISAT and the shocked viewing outflow. gives where Al. (Mow) is the mass of the viewed ejecta (the swept ISM).," At $R_{\rm \times}$, the energy conservation of the system, i.e., the shocked ISM and the shocked viewing outflow, gives where $M_{\rm ej}$ $M_{\rm sw}$ ) is the mass of the viewed ejecta (the swept ISM)."
 In the thick shell case. the RS is mild-relativistic and 44.clA.)f2- ," In the thick shell case, the RS is mild-relativistic and $\gamma_{34,\times}\approx \eta(\theta_{\rm
v})/2\gamma_{\rm \times}$."
Now equation. (10) reduces. to SAL.GxWAALG/2.," Now equation (10) reduces to $\gamma_{\rm \times}^2M_{\rm sw}\approx \eta(\theta_{\rm v})
M_{\rm ej}/2$ ."
" Considering that Aa=LEqenin, and Loo/(1|z)zzBR./2*57e. we have Now 544.%1.55. which is mild-relativistic."," Considering that $M_{\rm sw}={4\pi\over 3}R_{\rm
\times}^3n_1m_{\rm p}$ and $T_{90}/(1+z)\approx R_{\rm
\times}/2\gamma_{\rm \times}^2c$ , we have Now $\gamma_{34,\times}\approx 1.55$, which is mild-relativistic."
 So the assumption mace before is reasonable., So the assumption made before is reasonable.
 Similar to section 3.1. the typical frequency. of RS emission can be estimated by where F|—64ustIL).," Similar to section 3.1, the typical frequency of RS emission can be estimated by where $F_1\equiv \epsilon_{\rm e,-0.5}({\gamma_{\rm
34,\times}-1\over 0.55})$."
 Similarly. taking ος=1 and z=0.3 we have mo.~2.910Lz.," Similarly, taking $Q_{\rm x}=1$ and $z=0.3$ we have $\nu_{\rm c,\times}\sim 2.9\times 10^{16}{\rm
Hz}$."
 Following Wu et al. (, Following Wu et al. (
"2003). the svnchrotron self-absorption frequency IS Wa,~1510Lz.","2003), the synchrotron self-absorption frequency is $\nu_{\rm a,\times}\sim 4.5\times 10^{10}~{\rm Hz}$."
 Therefore. both of them can not allect the Ro band spectrum significantly., Therefore both of them can not affect the R band spectrum significantly.
 “Phe peak lux of RS emission can be estimated. bv fasτ−2NmJw(⊥↝−1.3Messasot1.2quαταΠα1/2οep.bye112 οτι o," The peak flux of RS emission can be estimated by $F_{\rm \nu, max}\approx 28{\rm mJy}~({1+z\over 1.3})E_{\rm {\rm
iso(\theta_{\rm v})},50}\eta_{2.18}^{-1}\gamma_{\rm
\times,1.74}^2n_{1,0}^{1/2}\epsilon_{\rm B,-1}^{1/2}D_{\rm
L,27.7}^{-2}$ ."
pPhen the observed. peak energy Lux can be estimated by (SPN) the magnitude mpez16. which is also bright enough to be detected. by the upcoming UVOT or the telescopes on work today. as long as the response to the XI is fast enough.," Then the observed peak energy flux can be estimated by (SPN) the magnitude $m_{\rm R}\approx 16$, which is also bright enough to be detected by the upcoming UVOT or the telescopes on work today, as long as the response to the XRF is fast enough."
 In the case of thick shell. the very early light curve of a stanclarel fireball takes the form (For the parameters adopted in this Letter. the reverse/FS emission are all in slow cooling. for td.)," In the case of thick shell, the very early light curve of a standard fireball takes the form (For the parameters adopted in this Letter, the reverse/FS emission are all in slow cooling, for $t>t_{\rm \times}$ )."
 Thanks to the beaming elfect. these scaling laws may be applied to the current work as well.," Thanks to the beaming effect, these scaling laws may be applied to the current work as well."
 Llere we simply take equation (15) to plot the sample very carly light curve powered by Gaussian. jetLSAL interaction (See figure 1. the thick clash line).," Here we simply take equation (15) to plot the sample very early light curve powered by Gaussian jet—ISM interaction (See figure 1, the thick dash line)."
 The corresponding light curve of the FS emission (see figure 1. the thick cdash-clotted line) is plotted. as follows: Following SPN. at foun.=(11τή Bayt©009mJy.," The corresponding light curve of the FS emission (see figure 1, the thick dash-dotted line) is plotted as follows: Following SPN, at $t_{\rm \times,obs}=(1+z)t_{\times}$, $F_{\rm \nu_{\rm
R,obs},f}\approx 0.09{\rm mJy}$."
 For £mdo. Beyox ος fy is determined by £yua(lu)=(11 ern): For!fu. Baytxb," For $t<t_0$, $F_{\rm \nu_{\rm
R,obs} ,f}\propto t^{1/2}$ (where $t_0$ is determined by $\nu_{\rm
m,f}(t_0)=(1+z)\nu_{\rm R,obs}$ ); For $t>t_0$, $F_{\rm \nu_{\rm
R,obs} ,f}\propto t^{-0.9}$."
 As shown in Figure 1. in many respects. ic.. the peak time and the temporal behavior. the current light curve is much different from that powered by the oll-beam jet interaction. which max help us to distinguish them.," As shown in Figure 1, in many respects, i.e., the peak time and the temporal behavior, the current light curve is much different from that powered by the off-beam jet---ISM interaction, which may help us to distinguish them."
 For example.the FS peak emission of theolf-beam jet ismuch brighter than that ofGaussian jet. which is mainly due to: In the olf-beam jet model. we take A@= 0.019rad.," For example,the FS peak emission of theoff-beam jet ismuch brighter than that of Gaussian jet, which is mainly due to: In the off-beam jet model, we take $\Delta\theta=0.019{\rm rad}$ ."
 At several, At several
(Debesetal.2008).,\citep{deb08}.
. present multi-wavelength observations -1 showing that the outer disk cannot be modeled as a single dust component; these authors adopt a two-component model with two different grain sizes., present multi-wavelength observations -1 showing that the outer disk cannot be modeled as a single dust component; these authors adopt a two-component model with two different grain sizes.
" Here we present new ground-based near-infrared imaging data at high spatial resolution, revealing the tapered outer regions of the debris disk."," Here we present new ground-based near-infrared imaging data at high spatial resolution, revealing the tapered outer regions of the debris disk."
" Our observations of HR 4796 A were obtained with the Subaru on 24, 2011, within the SEEDS survey (StrategicTelescopeExplorationMayofExoplanetsandDiskswith 2009)."," Our observations of HR 4796 A were obtained with the Subaru Telescope on May 24, 2011, within the SEEDS survey \citep[Strategic 
Exploration of Exoplanets and Disks with Subaru/HiCIAO,][]{tamura09}."
. The HiCIAO instrument (Hodappetal.2008) with a x field of view and a plate scale of 9.50-Ε0.02 mmas/pixel was used., The HiCIAO instrument \citep{hodapp08} with a $\times$ field of view and a plate scale of $\pm$ mas/pixel was used.
" The image rotator operated in pupil-tracking mode to enable angular differential imaging (ADI,Marois2006)."," The image rotator operated in pupil-tracking mode to enable angular differential imaging \citep[ADI,][]{marois06}."
". A sequence of 260 images was taken in H-band with an exposure time of 10ss, for a total integration time of mmin and a total field rotation of23?."," A sequence of 260 images was taken in $H$ -band with an exposure time of s, for a total integration time of min and a total field rotation of."
". Weather conditions were 0755—0/88 in V-band), and the AO188 adaptive goodoptics (seeingsystem (Minowaetal.2010) provided a FWHM of 6.5 pixels — mmas."," Weather conditions were good (seeing 8 in $V$ -band), and the AO188 adaptive optics system \citep{minowa10} provided a FWHM of 6.5 pixels $=$ mas."
 The images were corrected for flatfield and field distortion (Suzukietal.2010)., The images were corrected for flatfield and field distortion \citep{suzuki10}.
". Stellar was estimated in each frame by two different methods: (1) positionFitting a Moffat profile to the PSF halo, and (2) triangulating between symmetrical pairs of static speckles."," Stellar position was estimated in each frame by two different methods: (1) Fitting a Moffat profile to the PSF halo, and (2) triangulating between symmetrical pairs of static speckles."
 Both were consistent with an empirical drift model (7;=7+toi1/2 9i?) plus measurement noise.," Both were consistent with an empirical drift model $\vec{r}_i = \vec{r}_0 + \vec{v}_0 i + 1/2\,\vec{a_0} i^2$ ) plus measurement noise."
" The difference between the two sets of centroids showed no systematic behavior, and was consistent with incoherent combination of the two measurement noise sources."," The difference between the two sets of centroids showed no systematic behavior, and was consistent with incoherent combination of the two measurement noise sources."
" We therefore used the drift model for image registration, for an estimated centering accuracy of ~0.3 pixels = mmas in the co-added image."," We therefore used the drift model for image registration, for an estimated centering accuracy of $\sim$ 0.3 pixels $=$ mas in the co-added image."
 ADI combined with the LOCI algorithm (LocallyOp- is currently the most successful ground-based imaging technique for the detection of planets and substellar companions (Thalmannetal.2009;Biller2010;Jansonetal.2011).," ADI combined with the LOCI algorithm \citep[Locally Optimized Combination of 
Images,][]{lafreniere07} is currently the most successful ground-based imaging technique for the detection of planets and substellar companions \citep
{thalmann09,biller10,janson11}."
". Furthermore, it has proven useful in revealing high-contrast circumstellar disks (Thalmannetal.2010;Buenzlietal. 2010)."," Furthermore, it has proven useful in revealing high-contrast circumstellar disks \citep{thalmann10,buenzli10}."
". We applied three implementations of the ADI technique to our data: (I) “Simple ADI’, consisting of subtracting a median background from the entire dataset before derotating and co-adding."," We applied three implementations of the ADI technique to our data: (I) “Simple ADI”, consisting of subtracting a median background from the entire dataset before derotating and co-adding."
 This method causes the least amount of flux loss and is therefore useful for estimating the surface brightness profile of the disk. (, This method causes the least amount of flux loss and is therefore useful for estimating the surface brightness profile of the disk. (
"II) ""Aggressive LOCI"", using frame selection criteria of 0.5 FWHM (minimum differential field rotation between images to be used for mutual subtraction, to limit self-subtraction of physical sources) and an region with an area of 300 PSF footprints.","II) “Aggressive LOCI”, using frame selection criteria of 0.5 FWHM (minimum differential field rotation between images to be used for mutual subtraction, to limit self-subtraction of physical sources) and an optimization region with an area of 300 PSF footprints."
" Althoughoptimization most of the disk signal is lost and negative over-subtraction effects appear, this method achieves excellent speckle suppression and provides the best constraints on point sources, such as planets. ("," Although most of the disk signal is lost and negative over-subtraction effects appear, this method achieves excellent speckle suppression and provides the best constraints on point sources, such as planets. ("
"III) “Conservative LOCI’, a compromise between the previous two methods, first described in Thalmannetal. (2010).","III) “Conservative LOCI”, a compromise between the previous two methods, first described in \citet{thalmann10}."
. This method preserves more disk flux than aggressive LOCI while achieving significantly better speckle subtraction than simple ADI., This method preserves more disk flux than aggressive LOCI while achieving significantly better speckle subtraction than simple ADI.
 The resulting image proves ideal for deriving geometric parameters of the inner disk edge., The resulting image proves ideal for deriving geometric parameters of the inner disk edge.
" Due to the dataset’s limited field rotation budget, we do not use an increased frame selection criterion to conserve more disk flux, as Thalmannetal.(2010) do."," Due to the dataset's limited field rotation budget, we do not use an increased frame selection criterion to conserve more disk flux, as \citet{thalmann10}
 do."
" Instead, we enlarge the optimization area to 10,000 PSF footprints, lowering the of the disk on the optimization process, as first impactdemonstrated in signalBuenzlietal.(2010)."," Instead, we enlarge the optimization area to 10,000 PSF footprints, lowering the impact of the disk signal on the optimization process, as first demonstrated in \citet{buenzli10}."
". Unless otherwise noted, we use the default numerical and geometric LOCI settings as defined in Table 1 and Fig."," Unless otherwise noted, we use the default numerical and geometric LOCI settings as defined in Table 1 and Fig."
 1 of Lafreniéreetal., 1 of \citet{lafreniere07}.
" (2007).. Figure 1 shows the results of applying the three ADI reduction methods to our data: Simple ADI in (a), conservative LOCI in (b), and aggressive LOCI in (c)."," Figure \ref{f:images} shows the results of applying the three ADI reduction methods to our data: Simple ADI in (a), conservative LOCI in (b), and aggressive LOCI in (c)."
 In panel, In panel
Similarly. we find that for the UT2-UT4 baseline of the flux is emitted from the inner 13 AU.,"Similarly, we find that for the UT2-UT4 baseline of the flux is emitted from the inner 13 AU."
 For the UT3-UT4 baseline of the 8-13y;an flix comes from the inner 20 AU., For the UT3-UT4 baseline of the $\mu$ m flux comes from the inner 20 AU.
 The spatially resolved. MIR. spectra of the MIDI instrument make it possible to study the radial dependence of the dust composition in (he protoplanetary disk 2004).., The spatially resolved MIR spectra of the MIDI instrument make it possible to study the radial dependence of the dust composition in the protoplanetary disk \citep{boekel}.
 In section 4 we showed (hat the spatially unresolved (total) spectrum of FU Ori can be fitted with mainly large amorphous dust erains., In section 4 we showed that the spatially unresolved (total) spectrum of FU Ori can be fitted with mainly large amorphous dust grains.
 The shape of the spatially resolved (correlated) [ux spectra contains information about the dust composition of the inner parts of the disk., The shape of the spatially resolved (correlated) flux spectra contains information about the dust composition of the inner parts of the disk.
" To compare (he shape of (he correlated spectra to the total spectrum we first subtracted the continuum for which we fitted a straight line between the flux al 8.25 ancl 12.95,an. Then we normalized all continuum subtracted correlated flix spectra aud (he total spectrum by where ἔ aud Freonsup denote the continuum subtracted spectra aud (heir mean value. respectively."," To compare the shape of the correlated spectra to the total spectrum we first subtracted the continuum for which we fitted a straight line between the flux at 8.25 and $\mu$ m. Then we normalized all continuum subtracted correlated flux spectra and the total spectrum by where $F_{sub}$ and $F_{mean, sub}$ denote the continuum subtracted spectra and their mean value, respectively."
 By applying this formula all correlated. spectra conserve their shape and can be compared (o the total spectrum (Fieure 7))., By applying this formula all correlated spectra conserve their shape and can be compared to the total spectrum (Figure \ref{shape_correl}) ).
" To identify those parts where the spectra differ significantly we furthermore computed the deviation from the total spectrum for each wavelength in units of the data error: Frorpmeory A Fuuuq; re Lhe normalized correlated spectra ancl the normalized total spectrum and 0,4, denotes the standard deviation of the correlated spectra MIDI errors) al a given wavelength."," To identify those parts where the spectra differ significantly we furthermore computed the deviation from the total spectrum for each wavelength in units of the data error: $F_{norm, corr}$ and $F_{norm, total}$ are the normalized correlated spectra and the normalized total spectrum and $\sigma_{corr}$ denotes the standard deviation of the correlated spectra (MIDI errors) at a given wavelength."
 We applied the same normalization factors to the errors as we did to the spectra., We applied the same normalization factors to the errors as we did to the spectra.
 Figure 7 shows that no clear deviations from (he total unresolved spectirum are observed for any of the correlated spectra., Figure \ref{shape_correl} shows that no clear deviations from the total unresolved spectrum are observed for any of the correlated spectra.
 This means that with the given spatial resolution and sensitivity no significant chemical difference in the dust composition is observed ancl the spectra of the inner parts of the disk look very similar to the total unresolved disk spectrum., This means that with the given spatial resolution and sensitivity no significant chemical difference in the dust composition is observed and the spectra of the inner parts of the disk look very similar to the total unresolved disk spectrum.
 This finding is somewhat surprising., This finding is somewhat surprising.
 As seen in section + the silicate dust grains apparently already underwent noticeable coagulation., As seen in section 4 the silicate dust grains apparently already underwent noticeable coagulation.
 Thus. the disk does not consist of purely ISM dust anvmore and must already have a significant age.," Thus, the disk does not consist of purely ISM dust anymore and must already have a significant age."
 In. addition it is known that apart from erain growth also thermal annealing takes place within protoplanetary disks aud. transform, In addition it is known that apart from grain growth also thermal annealing takes place within protoplanetary disks and transform
density fluctuations.,density fluctuations.
" Due (o sell-gravitational instability. the f[Inetuations of dark matter have collapsed and virialized into objects which are so-called ‘dark matter halos’ or ""dark halos’."," Due to self-gravitational instability, the fluctuations of dark matter have collapsed and virialized into objects which are so-called `dark matter halos' or `dark halos'."
 The larger halos are generally considered to have formed via the merger of smaller ones collapsed first., The larger halos are generally considered to have formed via the merger of smaller ones collapsed first.
 The distribution of mass in the eravilationally collapsed structures. such as galaxies and groups (or clusters) of galaxies. which is usually called (he mass or multiplicity function. has been determined by observation.," The distribution of mass in the gravitationally collapsed structures, such as galaxies and groups (or clusters) of galaxies, which is usually called the mass or multiplicity function, has been determined by observation."
 As the observational data relevant (ο these issues improve. the need for accurate theoretical predictions increases.," As the observational data relevant to these issues improve, the need for accurate theoretical predictions increases."
 By lar the most widely used analvtic formulae for halo mass functions are based on extensions of the theoretical framework first sketched by ?.., By far the most widely used analytic formulae for halo mass functions are based on extensions of the theoretical framework first sketched by \cite{1974ApJ...187..425P}.
 The Press-Schechter (PS) model theory did not draw much attention until 1938. when the first relative large simulation revealed a good agreement with it.," The Press-Schechter (PS) model theory did not draw much attention until 1988, when the first relative large N-Body simulation revealed a good agreement with it."
 The mystery of the /fudge factor of 2 in PS theory was solved by approaching the cloud-in-cloud. problem with a rigorous wav(??)..," The mystery of the `fudge factor' of 2 in PS theory was solved by approaching the 'cloud-in-cloud' problem with a rigorous \citep{1990MNRAS.243..133P,1991ApJ...379..440B}."
 The reliability of the PS formula has been tested using N-Bocly simulation by several authors. which turus out the PS formula indeed provides an overall satisfactory description of mass function for virialized objects.," The reliability of the PS formula has been tested using N-Body simulation by several authors, which turns out the PS formula indeed provides an overall satisfactory description of mass function for virialized objects."
 Unfortunately. none of (hese derivations is sufficiently rigorous such that the resulting formulae can be considered accurate bevond the regime where they have been tested against N-body simulations.," Unfortunately, none of these derivations is sufficiently rigorous such that the resulting formulae can be considered accurate beyond the regime where they have been tested against N-body simulations."
 Although the analvtical framework of the PS model has been ereatly refined. and extended in recent vears. in particular to allow predictions for the merger histories of dark matter halos (?).. il is well known (hat the PS mass function. while qualitatively correct. disagrees in detail with the results of N-bodx simulations.," Although the analytical framework of the PS model has been greatly refined and extended in recent years, in particular to allow predictions for the merger histories of dark matter halos \citep{1991ApJ...379..440B}, it is well known that the PS mass function, while qualitatively correct, disagrees in detail with the results of N-body simulations."
 Specifically. the. PS formula overestimates the abundance of halos near the characteristic mass and underestimates the abundance in the high mass tail.," Specifically, the PS formula overestimates the abundance of halos near the characteristic mass and underestimates the abundance in the high mass tail."
 In order to overcome this discrepancy. ? proposed an analvte mass function which gives a [it to their numerical multiplicity function.," In order to overcome this discrepancy, \cite{2001MNRAS.321..372J} proposed an analytic mass function which gives a fit to their numerical multiplicity function."
" In particular. a power spectrum of primordial fluctuation. 2,04). should be assumed in advance in the calculation of mass function."," In particular, a power spectrum of primordial fluctuation, $P_p(k)$, should be assumed in advance in the calculation of mass function."
" Inflationary models predict a approximately scale-invariant power spectra for primordial density (scalar metric) fuctuation. P,(E)xA"" with index »=1 (??).."," Inflationary models predict a approximately scale-invariant power spectra for primordial density (scalar metric) fluctuation, $P_p(k)\propto k^n$ with index $n=1$ \citep{1982PhRvL..49.1110G,1983PhRvD..28..679B}."
 The combination of the first-vear Wilkinson Microwave Anisotropy Probe (WAIAP) data with other liner scale cosmic background (CMD) experiments (Cosmic Background Imager [CDI]. Arcminute Cosmology. Dolometer Array Receiver [ACBAR]} and {wo observations of large-scale structure (the Anglo-Australian Telescope Two-Degree Field Galaxy Redshift Survey [24FGBS] and Lyman a forest) favour à ACDM cosmological model wilh a running index of the primordial power spectrum. (RSI-ACDM). while the WMADP data alone still suggest a best-fit standard power-law ACDM model with the spectral index ol n£z1 (PL-ACDAI) (??)..," The combination of the first-year Wilkinson Microwave Anisotropy Probe (WMAP) data with other finer scale cosmic background (CMB) experiments (Cosmic Background Imager [CBI], Arcminute Cosmology Bolometer Array Receiver [ACBAR]) and two observations of large-scale structure (the Anglo-Australian Telescope Two-Degree Field Galaxy Redshift Survey [2dFGRS] and Lyman $\alpha$ forest) favour a $\Lambda$ CDM cosmological model with a running index of the primordial power spectrum $\Lambda$ CDM), while the WMAP data alone still suggest a best-fit standard power-law $\Lambda$ CDM model with the spectral index of $n\approx 1$ $\Lambda$ CDM) \citep{2003ApJS..148..175S,2003ApJS..148..213P}."
 However. there still exist the intriguing discrepancies between theoretical predictions and observations on both the largest and smallest scales.," However, there still exist the intriguing discrepancies between theoretical predictions and observations on both the largest and smallest scales."
 While the enmiergence of a running spectral index max improve problems on small scales. (here remain," While the emergence of a running spectral index may improve problems on small scales, there remain"
known (ransiüng exoplanets to demonstrate that this diagnostic has the potential to be very effective in the pre-selection of the best candidates.,known transiting exoplanets to demonstrate that this diagnostic has the potential to be very effective in the pre-selection of the best candidates.
" To aid in (his process. we derive a new equation for calculating stellar densiües using other. more tangible transit parameters often available in papers that quote neither a/R, nor the stellar density."," To aid in this process, we derive a new equation for calculating stellar densities using other, more tangible transit parameters often available in papers that quote neither $a/R_\star$ nor the stellar density."
 This equation includes orbital parameters (eccentricity and angle of periastron). which make it possible to analvze the impact of an unknown orbital eccentricity on the measured stellar density.," This equation includes orbital parameters (eccentricity and angle of periastron), which make it possible to analyze the impact of an unknown orbital eccentricity on the measured stellar density."
 It is based on the equations in Sackett(1999) ancl Tinglev&Sackett(2005) and may also be used as a consistency check of fitted (transit parameters., It is based on the equations in \citet{sac1999} and \citet{tin2005} and may also be used as a consistency check of fitted transit parameters.
 In § 2.. we derive (he equations (hat will be used for the analvsis.," In $\S$ \ref{equations}, we derive the equations that will be used for the analysis."
 In 8 3.. we discuss the independent density measures that compliment the stellar densities from transit parameters.," In $\S$ \ref{independent}, we discuss the independent density measures that compliment the stellar densities from transit parameters."
 In 5 4.. we apply these equations to those transiting exoplanets lor which (he necessary parameters have beenpublished.," In $\S$ \ref{planets}, we apply these equations to those transiting exoplanets for which the necessary parameters have beenpublished."
 In 5 5.. we examine the use of the payo combined with (he densities derived lrom J—A colors on the CohoT candidates.," In $\S$ \ref{corot}, we examine the use of the $\rho_{\rm
 SMO}$ combined with the densities derived from $J-K$ colors on the CoRoT candidates."
" In 8 ον, we analvze the impact of eccentricity on this technique."," In $\S$ \ref{eccentricity}, we analyze the impact of eccentricity on this technique."
 Lastly. we discuss our conclusions in 8 7..," Lastly, we discuss our conclusions in $\S$ \ref{conclusions}."
 Calculating the stellar densities [rom transit parameters is not difficult., Calculating the stellar densities from transit parameters is not difficult.
" The most straightforward wav begins wilh the equation for the density of a spherical star: where p, is the density of the star and A, is the mass of the star.", The most straightforward way begins with the equation for the density of a spherical star: where $\rho_\star$ is the density of the star and $M_\star$ is the mass of the star.
" Then. one can use Ixepler's 3rd. law to substitute oul άν. needing only the rather safe assumption that Al,M,> AM. obtaining an equation for the densitvdensity of the star starEFbasedLon on the transit parameterparamete affi, (pa)"," Then, one can use Kepler's 3rd law to substitute out $M_\star$, needing only the rather safe assumption that $M_\star \gg
M_p$ , obtaining an equation for the density of the star based on the transit parameter $a/R_\star$ $\rho_{t1}$ ):"
of 0.265.<Kk»0.379.,of $0.265 < k_2 < 0.379$.
 It can be expected that this smaller region of allowed &»-values will significantly narrow the allowed range of solutions for the interior of HAT-P-13b., It can be expected that this smaller region of allowed $k_2$ -values will significantly narrow the allowed range of solutions for the interior of HAT-P-13b.
 For our models we use the mean values for the mass and radius of HAT-P-13b (?):: The uncertainties introduced by the error bars in mass and radius are discussed in 4.2.., For our models we use the mean values for the mass and radius of HAT-P-13b \citep{Bakosetal09}: The uncertainties introduced by the error bars in mass and radius are discussed in \ref{subsec:MRuncertainties}.
 We assume a two-layer structure. consisting of a rocky core and one homogeneous envelope of hydrogen. helium and metals.," We assume a two-layer structure, consisting of a rocky core and one homogeneous envelope of hydrogen, helium and metals."
 It is not necessary to consider three-layer models in this work because they are within the range of solutions confined by the two-layer models (see refsec:Results. for à discussion)., It is not necessary to consider three-layer models in this work because they are within the range of solutions confined by the two-layer models (see \\ref{sec:Results} for a discussion).
 We set the helium abundance in the envelope to the solar value Y=0.27 (?).., We set the helium abundance in the envelope to the solar value $Y=0.27$ \citep{Bahcalletal95}.
 The amount of heavy elements Z was varied from Z=0. which gives a model with the biggest possible core when the other parameters are fixed. to à maximum value where the core vanishes.," The amount of heavy elements $Z$ was varied from $Z=0$, which gives a model with the biggest possible core when the other parameters are fixed, to a maximum value where the core vanishes."
 Due to the proximity to its star. the temperature profile of HAT-P-13b ts likely to be strongly influenced by the radiation of the star.," Due to the proximity to its star, the temperature profile of HAT-P-13b is likely to be strongly influenced by the radiation of the star."
 The various processes in an exoplanet's atmosphere influencing its temperature are very complex and beyond the scope of this work., The various processes in an exoplanet's atmosphere influencing its temperature are very complex and beyond the scope of this work.
 As we aim to study the effects of input parameters important for planet modeling on the structure and Love number of a planet. we vary the envelope temperature within the widest possible range. even though extremely cold or hot models may be unrealistic.," As we aim to study the effects of input parameters important for planet modeling on the structure and Love number of a planet, we vary the envelope temperature within the widest possible range, even though extremely cold or hot models may be unrealistic."
 For HAT-P-13b we change the kkbar temperatures from 3800 to KK. Zi;=3800 KK gives the most homogeneous planet with zero core mass and models with Τμ> 9000KK would have κ. values smaller than the BBL-interval (see also refsec:Results)).," For HAT-P-13b we change the kbar temperatures from 3800 to K. $T_{1\,\mathrm{kbar}}=3800$ K gives the most homogeneous planet with zero core mass and models with $T_{1\,\mathrm{kbar}}>9000$ K would have $k_2$ values smaller than the BBL-interval (see also \\ref{sec:Results}) )."
 In the outermost layer of the planet from bbar to kkbar we assume the temperature profile to be either adiabatic or isothermal., In the outermost layer of the planet from bar to kbar we assume the temperature profile to be either adiabatic or isothermal.
 This is supposed to account for the uncertainty of how the star's radiation influences the outer envelope of the planet., This is supposed to account for the uncertainty of how the star's radiation influences the outer envelope of the planet.
 As the planet is very close to its star. it is likely that there will be an isothermal layer to some extent (?)..," As the planet is very close to its star, it is likely that there will be an isothermal layer to some extent \citep{Fortneyetal07}."
 In every case. for pressures P>| kkbar the planet is adiabatic.," In every case, for pressures $P>1$ kbar the planet is adiabatic."
 In addition. we compute à model series that is consistent with the nongray model atmospheres from ? ΠΠ order to further pin down the outer boundary condition.," In addition, we compute a model series that is consistent with the nongray model atmospheres from \citet{Fortneyetal07} in order to further pin down the outer boundary condition."
" Based on their pressure-temperature profiles of Jupiter-like planets around Sun-like stars (Fig.3in?).. we interpolated a model atmosphere for HAT-P-13b. assuming that the incoming energy flux remains constant: L./(42u7)=const. where L, is the stellar luminosity and a is the planet's semi-major axis."," Based on their pressure-temperature profiles of Jupiter-like planets around Sun-like stars \citep[Fig. 3
in][]{Fortneyetal07}, we interpolated a model atmosphere for HAT-P-13b, assuming that the incoming energy flux remains constant: $L_*/(4\pi a^2) =
\mathrm{const.}$, where $L_*$ is the stellar luminosity and $a$ is the planet's semi-major axis."
" Our interpolation yields Ty)pa,=2080 KK as new outer boundary condition."," Our interpolation yields $T_{1\,\mathrm{bar}} = 2080$ K as new outer boundary condition."
 It further showed that an isothermal layer may reach down to P44~I00 bbar., It further showed that an isothermal layer may reach down to $P_\mathrm{ad}\sim 100$ bar.
 Our interpolated model atmosphere is in agreement with an atmosphere model specifically calculated for HAT-P-I3b. using the methods of ?..," Our interpolated model atmosphere is in agreement with an atmosphere model specifically calculated for HAT-P-13b, using the methods of \citet{Fortneyetal07}."
 The thickness of the isothermal layer ts a variable parameter (influenced by the age of the planet)., The thickness of the isothermal layer is a variable parameter (influenced by the age of the planet).
 Hence. in our model series based on the model atmosphere. we vary P44 as a free parameter while keeping Typar fixed at KK. Our modeling procedure constitutes an. improvement compared to the modeling done by ? because we do not approximate the core material by a constant density and we include the effects of different temperatures and temperature profiles in the atmosphere.," Hence, in our model series based on the model atmosphere, we vary $P_\mathrm{ad}$ as a free parameter while keeping $T_{1\,\mathrm{bar}}$ fixed at K. Our modeling procedure constitutes an improvement compared to the modeling done by \citet{Batyginetal09} because we do not approximate the core material by a constant density and we include the effects of different temperatures and temperature profiles in the atmosphere."
 This allows us to draw some general conclusions about the capability of K» to constram interior models of extrasolar giant planets., This allows us to draw some general conclusions about the capability of $k_2$ to constrain interior models of extrasolar giant planets.
 We present in Figs., We present in Figs.
 2. and 3 results for the calculated core mass. A». and envelope metallicity.," \ref{fig:HAT-P-13b} and \ref{fig:HAT-P-13b_k2Z} results for the calculated core mass, $k_2$, and envelope metallicity."
" The area between an adiabatic and isothermal line of the same kkbar temperature accounts for the uncertainty about the outer temperature profile as the thickness of a potential isothermal layer is not known,", The area between an adiabatic and isothermal line of the same kbar temperature accounts for the uncertainty about the outer temperature profile as the thickness of a potential isothermal layer is not known.
 Also shown are the models based on our model atmosphere with an isothermal layer of KK. reaching down to | (fully adiabatic). 5. 10. 50. or bbar. where the core disappears.," Also shown are the models based on our model atmosphere with an isothermal layer of K, reaching down to 1 (fully adiabatic), 5, 10, 50, or bar, where the core disappears."
 In Fig. 2..," In Fig. \ref{fig:HAT-P-13b},"
 the line connecting zero metallicity fully adiabatic models separates the region of all possible planetary models from the prohibited area which ts not accessible for models of HAT-P-13b., the line connecting zero metallicity fully adiabatic models separates the region of all possible planetary models from the prohibited area which is not accessible for models of HAT-P-13b.
 A general trend that can be seen in Fig., A general trend that can be seen in Fig.
 2 and 3 is that the Love number &» increases as more metals are put in the envelope.," \ref{fig:HAT-P-13b}
 and \ref{fig:HAT-P-13b_k2Z} is that the Love number $k_2$ increases as more metals are put in the envelope."
 This is the result of &» being a measure of the level of central condensation of an object., This is the result of $k_2$ being a measure of the level of central condensation of an object.
 Since the total mass of the planet must always be M. the enrichment of the envelope with metals leads to a decrease in core mass.," Since the total mass of the planet must always be $M_\mathrm{p}$, the enrichment of the envelope with metals leads to a decrease in core mass."
 A smaller core and higher metal content in the envelope means that the planet is more homogeneous. which is why the Love number grows.," A smaller core and higher metal content in the envelope means that the planet is more homogeneous, which is why the Love number grows."
 The maximum metallicity is reached when the core of the planet vanishes., The maximum metallicity is reached when the core of the planet vanishes.
 This marks the maximum possible Love number of a planet for a given temperature., This marks the maximum possible Love number of a planet for a given temperature.
 The temperature itself also has a significant influence on the metallicity. core mass. and consequently Love number of the planet.," The temperature itself also has a significant influence on the metallicity, core mass, and consequently Love number of the planet."
 Higher temperatures reduce the Love number κ»., Higher temperatures reduce the Love number $k_2$.
 The higher the envelope temperature. the lower its density.," The higher the envelope temperature, the lower its density."
 Low densities in the envelope require à more massive core in order to ensure mass conservation., Low densities in the envelope require a more massive core in order to ensure mass conservation.
 High envelope temperatures thus lead to a strong central condensation. reflecting in a small Love number.," High envelope temperatures thus lead to a strong central condensation, reflecting in a small Love number."
 For HAT-P-13b we find a minimum kkbar temperature of KK for fully adiabatic models., For HAT-P-13b we find a minimum kbar temperature of K for fully adiabatic models.
 At this low temperature the zero metallicity envelope is so dense that the core is almost vanished (M.=0.2 ME))., At this low temperature the zero metallicity envelope is so dense that the core is almost vanished $M_\mathrm{core}=0.2$ ).
 Hence. there is no enrichment of heavy elements possible in the envelope.," Hence, there is no enrichment of heavy elements possible in the envelope."
 At this temperature maximum homogeneity is reached., At this temperature maximum homogeneity is reached.
 That translates into a maximum possible Love number for HAT-P-13b of &»=0.379. well below the upper limit given by the BBL-interval.," That translates into a maximum possible Love number for HAT-P-13b of $k_2=0.379$, well below the upper limit given by the BBL-interval."
 At high temperatures. on the other hand. the density in the envelope is low enough to enable the existence of massive cores.," At high temperatures, on the other hand, the density in the envelope is low enough to enable the existence of massive cores."
 That creates the possibility to enrich the envelope with metals., That creates the possibility to enrich the envelope with metals.
1n principle. the helium-burning red clump stars as defined bv Paczviisski Stanek (1908) olfer real advantages as distance indicators.,"In principle, the helium-burning red clump stars as defined by Paczyńsski Stanek (1998) offer real advantages as distance indicators."
 Phey are a relatively numerous. well-defined population. ancl hundreds. of red. clump stars with quite accurate parallaxes can be found in. the llipparcos catalog.," They are a relatively numerous, well-defined population, and hundreds of red clump stars with quite accurate parallaxes can be found in the Hipparcos catalog."
 At first. attention centred on distance determination using the | bane (Paczvásski Stanek 1998. Stanek (ιαΠανός 1998. Udalski et al.," At first, attention centred on distance determination using the I band (Paczyńsski Stanek 1998, Stanek Garnavich 1998, Udalski et al."
 1998. Uclalski 2000). but the ellects of stellar population dillerences on the mean V-band or I-band red clump magnitude can be considerable (Alves et al.," 1998, Udalski 2000), but the effects of stellar population differences on the mean V-band or I-band red clump magnitude can be considerable (Alves et al."
 2002. Grocholski Sarajecdini 2002. Cirardi Salaris 2001. Groenewegen 2008. Pietrzvisski et al.," 2002, Grocholski Sarajedini 2002, Girardi Salaris 2001, Groenewegen 2008, Pietrzyńsski et al."
 2010)., 2010).
 In the Ix band. the effects of stellar population cdilferences and reddening are generally less (Salaris Girardi: 2002. Alves et al.," In the K band, the effects of stellar population differences and reddening are generally less (Salaris Girardi 2002, Alves et al."
 2Y02. Cirocholski Sarajecini 2002. Pietrzvnski et al.," 2002, Grocholski Sarajedini 2002, Pietrzynski et al."
 2010). although not always negligible.," 2010), although not always negligible."
 In. particular. the estimated. corrections are predicted to be much smaller when comparing the red clump populations in the solar neighbourhood and in the LMC field. (Salaris Cirareli 2002). and the data suggest that this is indeed the case (Alves et al.," In particular, the estimated corrections are predicted to be much smaller when comparing the red clump populations in the solar neighbourhood and in the LMC field (Salaris Girardi 2002), and the data suggest that this is indeed the case (Alves et al."
 2002. Pietrzviisski et al.," 2002, Pietrzyńsski et al."
 2010)., 2010).
 Jut ever since Alves (2000) first. determined a mean Ix-band. absolute magnitude for nearby red. clump stars. a fundamental weakness of this approach has been the quality of the infrared. photometry available for nearby. red chump stars.," But ever since Alves (2000) first determined a mean K-band absolute magnitude for nearby red clump stars, a fundamental weakness of this approach has been the quality of the infrared photometry available for nearby red clump stars."
 As pointed. out by Alves. the stars with the best Hipparcos parallaxes are all saturated in the 2\LASS survey data. and modern LR array detectors are too sensitive [or stars with Ix«5.," As pointed out by Alves, the stars with the best Hipparcos parallaxes are all saturated in the 2MASS survey data, and modern IR array detectors are too sensitive for stars with $<$ 5."
 Indeed. a typical Ht telescope/array combination like the Infraltecd Survey Facility (RSE) in South Africa has a bright limit of INS despite a telescope aperture of only αμα. The catalog. cata used. by Alves were therefore a miscellaneous collection on no well-defined system. and the more modern data used by. Croenewegen (2008) (giving a rather dillerent. result) were restricted. to fainter stars.," Indeed, a typical IR telescope/array combination like the InfraRed Survey Facility (IRSF) in South Africa has a bright limit of $=$ 8 despite a telescope aperture of only 1.4m. The catalog data used by Alves were therefore a miscellaneous collection on no well-defined system, and the more modern data used by Groenewegen (2008) (giving a rather different result) were restricted to fainter stars."
 llere it may be useful to quote Grocnewegen: For this study we have determined. accurate Ix-band magnitudes for 226 bright. nearby red. clump stars with magnitudes brighter than Ix — 5.," Here it may be useful to quote Groenewegen: For this study we have determined accurate K-band magnitudes for 226 bright, nearby red clump stars with magnitudes brighter than K $\sim$ 5."
 With these data we have determined. the mean Ix-band. absolute magnitude Lor red clump stars in the solar neighbourhood to within2%., With these data we have determined the mean K-band absolute magnitude for red clump stars in the solar neighbourhood to within.
. JI. observations for 226 nearby red clump stars with lx magnitudes between -0.3. and 4.9 were obtained. with the O.75m telescope at the South African Astronomical Observatory (SAAQO). using the Mk.," JHK observations for 226 nearby red clump stars with K magnitudes between -0.3 and 4.9 were obtained with the 0.75m telescope at the South African Astronomical Observatory (SAAO), using the Mk."
" Lb infrared photometer and the same filter set usec (Carter 1990) to celine the SAAO ΗΝ, standard svstem.", II infrared photometer and the same filter set used (Carter 1990) to define the SAAO JHKL standard system.
 Program stars were chosen from those identified. by Paczviisski Stanek (1998). selecting for declinations observable from SAAO.," Program stars were chosen from those identified by Paczyńsski Stanek (1998), selecting for declinations observable from SAAO."
 As pointed, As pointed
 As pointed., As pointed
depends on the ratios of these (μου characteristic (ime scales.,depends on the ratios of these three characteristic time scales.
" Note fist. (hat if particle escape is controlled by diffusion [rom the region between the shocks. which is characterized by a thickness D. then the condition /5,>[ο reads for strong turbulence. where the particle mean lree path is comparable to the particle evroradius. aad for inverse-Compton losses comparable to svnchrotron losses (Appendix F)."," Note first, that if particle escape is controlled by diffusion from the region between the shocks, which is characterized by a thickness $D$, then the condition $t'_{\rm esc} > t'_{\rm rad}$ reads for strong turbulence, where the particle mean free path is comparable to the particle gyroradius, and for inverse-Compton losses comparable to synchrotron losses (Appendix F)."
 Thus. if D is of oxder of the jet radius (~1 kpc). then particle escape is inefficient compared to the radiative losses. independent of particle energy.," Thus, if $D$ is of order of the jet radius $\sim 1$ kpc), then particle escape is inefficient compared to the radiative losses, independent of particle energy."
 Also. if the mean separation of theshocks is less than ~1 kpe. particles cannot escape belore passing through many shocks. and therefore (μον experience multiple (and not single) shock acceleration.," Also, if the mean separation of theshocks is less than $\sim 1$ kpc, particles cannot escape before passing through many shocks, and therefore they experience multiple (and not single) shock acceleration."
" In such a case. as shown bv the analvsis of Schneider(1993).. one should expect the formation of a flat power-law spectrum for particles satisfying /L,4/>/p. a steep power-law spectrum (but not necessarily an exponential cut-off) for particles satisfying (4,/ἡρ. and a spectral pile-up at particle energies Lor which [7.4cf1."," In such a case, as shown by the analysis of \citet{sch93}, one should expect the formation of a flat power-law spectrum for particles satisfying $t'_{\rm rad} > t'_{\rm b}$, a steep power-law spectrum (but not necessarily an exponential cut-off) for particles satisfying $t'_{\rm rad} < t'_{\rm b}$, and a spectral pile-up at particle energies for which $t'_{\rm rad} \sim t'_{\rm b}$."
 Now consider what the shock separation has to be in order to obtain a piled-up distribution of particles emitting the observed svuchrotvon keV photons., Now consider what the shock separation has to be in order to obtain a piled-up distribution of particles emitting the observed synchrotron keV photons.
" If the radiating plasma between the shocks is highly relativisie (with the respective bulk Lorentz factor D2»1). then the condition {ο~/1, reads where d' is (he shock separation as measured in the radiating plasma rest frame (Appendices D and F)."," If the radiating plasma between the shocks is highly relativistic (with the respective bulk Lorentz factor $\Gamma \gg 1$ ), then the condition $t'_{\rm rad} \sim t'_{\rm b}$ reads where $d'$ is the shock separation as measured in the radiating plasma rest frame (Appendices D and F)."
" The parameter d"" as a function of E. for the observed. critical svuchrotvon photon energv fi.~1 keV and diflerent magnetic field intensities. is shown on figure +."," The parameter $d'$ as a function of $\Gamma$, for the observed critical synchrotron photon energy $h \nu_{\rm cr} \sim 1$ keV and different magnetic field intensities, is shown on figure 4."
 For D3-10and 210?—10 Gone gets d'~10—100 pe., For $\Gamma \sim 3 - 10$ and $B \sim 10^{-5} - 10^{-4}$ G one gets $d' \sim 10 - 100$ pc.
 For larger shock separations. are expected to occur at lower energies of the svnchrotron photons.," For larger shock separations, pile-ups are expected to occur at lower energies of the synchrotron photons."
 However. these values should be considered as illustrative only. because the analysis above refers (o a very simplified situation. in which we neglect the effects of turbulent second-order Fermi acceleration and assume identical properties for all the shocks.," However, these values should be considered as illustrative only, because the analysis above refers to a very simplified situation, in which we neglect the effects of turbulent second-order Fermi acceleration and assume identical properties for all the shocks."
 For reasonable laree-scale jet. parameters. however. an ensemble of shock waves present within the extended. knot region can result in the formation of a flat power-law electron energy. distiibution followed by a hieh-enerey pile-up announced by its X-ray. svnchrotron emission.," For reasonable large-scale jet parameters, however, an ensemble of shock waves present within the extended knot region can result in the formation of a flat power-law electron energy distribution followed by a high-energy pile-up announced by its X-ray synchrotron emission."
" This situation is similar (o the model discussed bv Stawarz&Ostrowski(2002).. but here the time scale between subsequent shock events. and not the second-order Fermi acceleration (ime scale. /14,. determines the critical electron energv."," This situation is similar to the model discussed by \citet{sta02}, but here the time scale between subsequent shock events, and not the second-order Fermi acceleration time scale, $t'_{\rm F \, II}$ , determines the critical electron energy."
 The ratio of these two time scales. for D.ο1 and electron Lorentz factor," The ratio of these two time scales, for $B_{-4} \sim 1$ and electron Lorentz factor"
Vhe X-ray. transient SAN JISQS.43658 was first. detected by the Wide Field Camera (AVEC) on the X-ray satellite in September 1996 (in 1 Zand et al.,The X-ray transient SAX J1808.4–3658 was first detected by the Wide Field Camera (WFC) on the X-ray satellite in September 1996 (in 't Zand et al.
 1998)., 1998).
 Lt was detectable for a period of ~20 days but had not been visible during an earlier long exposure of the same region in August 1996., It was detectable for a period of $\sim$ 20 days but had not been visible during an earlier long exposure of the same region in August 1996.
 ltecentlv. the Proportional Counter Array (PCA) experiment on the Rossi X-ray Timing Explorer(RAPE) satellite detected a transient. (NTE JISOSN369) in the same &eneral location during à routine scan between targets., Recently the Proportional Counter Array (PCA) experiment on the Rossi X-ray Timing Explorer satellite detected a transient (XTE J1808–369) in the same general location during a routine scan between targets.
 A series of Target OF Opportunity (POO) observations with refined. the error box and. indicated: it was probably a repeat occurrence of the earlier transient outburst (Marshall 1998)., A series of Target Of Opportunity (TOO) observations with refined the error box and indicated it was probably a repeat occurrence of the earlier transient outburst (Marshall 1998).
 The PCA cata also revealed. a high frequency signal at ~400 [lz with a moclulation of 4.3 per cent rms in the 260 keV. band (Wijnands van der Ilis 1998a.b).," The PCA data also revealed a high frequency signal at $\sim$ 400 Hz with a modulation of 4.3 per cent rms in the 2–60 keV band (Wijnands van der Klis 1998a,b)."
 This is the first X-ray source to show coherent. millisecond. periodicity in its persistent emission., This is the first X-ray source to show coherent millisecond periodicity in its persistent emission.
 Further analysis of the PCA data showed this signal to be modulated: with a sinusoidal doppler shift about a mean frequeney of 400.9752106 Lz indicating a binary period of 7249.119 seconds (Chakrabarty Morgan 1998a.b).," Further analysis of the PCA data showed this signal to be modulated with a sinusoidal doppler shift about a mean frequency of 400.9752106 Hz indicating a binary period of 7249.119 seconds (Chakrabarty Morgan 1998a,b)."
 The rav [lux has a weak modulation of 2 per cent with a broad minimum when the neutron star is behind the companion., The X-ray flux has a weak modulation of 2 per cent with a broad minimum when the neutron star is behind the companion.
 The mass estimates for the companion suggest a very low value of probably «0.1 ALS (Chakrabarty Morgan 1998h)., The mass estimates for the companion suggest a very low value of probably $<$ 0.1 $\sun$ (Chakrabarty Morgan 1998b).
 The X-ray flux from SAX 1505.3658 peaked close to April ll. just after the commencement of the series. of observations.," The X-ray flux from SAX J1808.4–3658 peaked close to April 11, just after the commencement of the series of observations."
 A relatively rapid. X-ray decline. alter April 25 has been reported by Cilfanov. Revnivisey Sunvaev (1998a) ancl Gilfanov et al. (," A relatively rapid X-ray decline after April 25 has been reported by Gilfanov, Revnivtsev Sunyaev (1998a) and Gilfanov et al. ("
1998b).,1998b).
 At higher energies the Ligh Energy X-ray Timing Experiment (ΗΝTIZ) on found the source to be one of the hardest. known X-ray pulsars with a power law index of 2.0240.05 and a spectrum extending to at least 120 keV (Hoindl. Marsden Blanco 1998. Leinedl Smith 1998).," At higher energies the High Energy X-ray Timing Experiment (HEXTE) on found the source to be one of the hardest known X-ray pulsars with a power law index of $2.02\pm0.05$ and a spectrum extending to at least 120 keV (Heindl, Marsden Blanco 1998, Heindl Smith 1998)."
 Roche et al. (, Roche et al. (
1998). reported a probable optical counterpart with a magnitude of V=16.6 that was not on an earlier. Ul Schmidt. Digitised Sky. Survey. plate dating [rom 1987.,1998) reported a probable optical counterpart with a magnitude of =16.6 that was not on an earlier UK Schmidt Digitised Sky Survey plate dating from 1987.
 We had also commenced. optical photometry of the X-ray error box and were able to support the proposed identification since the candidate appeared to show a ~2 hour band modulation of —0.12 magnitudes peak to peak (Giles. Hill CGreenhill 1998).," We had also commenced optical photometry of the X-ray error box and were able to support the proposed identification since the candidate appeared to show a $\sim$ 2 hour band modulation of $\sim$ 0.12 magnitudes peak to peak (Giles, Hill Greenhill 1998)."
 Phe band intensity decreased: by 0.1 magnitudes over the 4 day period [rom April 18.22 further supporting the identification (Giles et al., The band intensity decreased by $\sim$ 0.1 magnitudes over the 4 day period from April 18–22 further supporting the identification (Giles et al.
 1998)., 1998).
 The orbital doppler solution derived by Chakrabarty Morgan. (1998a.b) is of sullicicnt precision to define a relatively small error box which also includes the candida star.," The orbital doppler solution derived by Chakrabarty Morgan (1998a,b) is of sufficient precision to define a relatively small error box which also includes the candidate star."
 The assertion that the companion was a low mass star was supported by optical spectra obtained. by. Filippenko Leonard. (1998)., The assertion that the companion was a low mass star was supported by optical spectra obtained by Filippenko Leonard (1998).
 heir spectra revealed absorption lines throughout the spectrum. which are characteristic of mid to late type stars., Their spectra revealed absorption lines throughout the spectrum which are characteristic of mid to late type stars.
 They. also reported a possible broad. fa , They also reported a possible broad $H\alpha$ 
This letter has (wo goals.,This letter has two goals.
 The first is to determine if the observed star formation intensity distribution is a natural consequence of empirical laws such as the Schmidt. law ancl the Schechter mass function., The first is to determine if the observed star formation intensity distribution is a natural consequence of empirical laws such as the Schmidt law and the Schechter mass function.
 The second is to determine which parameters in (he empirical law most influence (he shape of the distribution., The second is to determine which parameters in the empirical law most influence the shape of the distribution.
 Galaxy. modelers can then predict the evolution of the distribution with redshift aud compare it against future observations., Galaxy modelers can then predict the evolution of the distribution with redshift and compare it against future observations.
 The star formation intensity distribution developed by Lanzetlaetal.(1999) has received significant. attention both as a constraint on models of galaxy. lormation (Barkana2002) and as a method of correcting for star formation missed bv the effects of surface brightness dining αἱ high redshifts (Thompson.WevmannandStorrie-Lombarcdial. 2002).," The star formation intensity distribution developed by \citet{lanz99} has received significant attention both as a constraint on models of galaxy formation \citep{brk02} and as a method of correcting for star formation missed by the effects of surface brightness diming at high redshifts \citep{thm01,lanz02}."
. Al present. the distribution is only empirically derived [rom the observations by filling the distribution at low redshift.," At present, the distribution is only empirically derived from the observations by fitting the distribution at low redshift."
 Correction of higher redshilt observations for surface brightness dimmiug is achieved by matching the bright end of the fitted distribution to the bright end of the observations at. higher redshift., Correction of higher redshift observations for surface brightness dimming is achieved by matching the bright end of the fitted distribution to the bright end of the observations at higher redshift.
 In. particular, In particular
has an observable optical spectrum (Mignani.Pavlov&Ixargaltsev2010)... aud the flux is slightly stnaller than the extrapolation from non-thermal X-ray emission.,"has an observable optical spectrum \citep{MPK10}, and the flux is slightly smaller than the extrapolation from non-thermal X-ray emission."
 The pulse profile has not vet been determiued. but tlie peaks should appear at a phase 0.3«o<0.6 and be due to outward emissiou.," The pulse profile has not yet been determined, but the peaks should appear at a phase $<\phi<0.6$ and be due to outward emission."
 We have calculated. the light curves of emissious using the TCSOs outer gap model and compared them with observed imulti-waveleugth light curves., We have calculated the light curves of emissions using the TCS08 outer gap model and compared them with observed multi-wavelength light curves.
 We find that the model cau successfully explain the peak positious of multi-wavelength light curves., We find that the model can successfully explain the peak positions of multi-wavelength light curves.
 In order to determine the altitude of he emission region. the observed X-ray. ligit curve is important. especially when there is a single yeak in the 5-ray light curve.," In order to determine the altitude of the emission region, the observed X-ray light curve is important, especially when there is a single peak in the $\gamma$ -ray light curve."
 The fit of a light curve based ou a simple emissivity distribution can be iniproved by takin[n]) into account the limitation of azimuthal extension in which a reasonable value of the y-ray photon uean free path is adopted., The fit of a light curve based on a simple emissivity distribution can be improved by taking into account the limitation of azimuthal extension in which a reasonable value of the $\gamma$ -ray photon mean free path is adopted.
 The resulting cdiffereuce between model aud observed 7-ray light curves jecomes stall: however. there may still be au unseen peak. such as the minor third peak in Vela.," The resulting difference between model and observed $\gamma$ -ray light curves becomes small; however, there may still be an unseen peak, such as the minor third peak in Vela."
 The best-fit values of the altitude of tle emission region for PSRs J0659-2-111Laud J1120-60Ls. suggestMOD a eviation from the last-opeu field lines of a vacuum clipole field.," The best-fit values of the altitude of the emission region for PSRs J0659+1414 and J1420-6048, suggest a deviation from the last-open field lines of a vacuum dipole field."
 The real last-opeu field ines lie inside those of vacuum dipole fiekl. rj«1.0.," The real last-open field lines lie inside those of vacuum dipole field, $r_{ov}<1.0$."
 This shift suggests that the lower boundary is very similar to that of a force-free ruagnetospliere., This shift suggests that the lower boundary is very similar to that of a force-free magnetosphere.
 We find that the altitude of the emission region is correlated. with inclination angle., We find that the altitude of the emission region is correlated with inclination angle.
 This relationship is also very similar to that in a [orce-Iree uaguetospliere., This relationship is also very similar to that in a force-free magnetosphere.
 The lower boundary of emission region has been assumed to r4.=1 so lar. but our uodel fits do uot support it.," The lower boundary of emission region has been assumed to $r_{ov}=1$ so far, but our model fits do not support it."
 This modification of the boundary of the magnetosphere suggestsMOD tliat he pulsars with low inclination aud viewing augles are likely to be detectable., This modification of the boundary of the magnetosphere suggests that the pulsars with low inclination and viewing angles are likely to be detectable.
 Thus the expected uunber in the Πο observation tu the previous works(Takata.Wane&ChengRomani (2011))) is underestiniated for the sources with low inclination and viewing angles.," Thus the expected number in the future observation in the previous \citet{TWC11, WR11}) ) is underestimated for the sources with low inclination and viewing angles."
 The authors thank S. Shibata aud J. Takata for much valuable discussion., The authors thank S. Shibata and J. Takata for much valuable discussion.
 This work was supported in part by the Grant-in-Aid for Scientific Research from the Japan Society for Promotion ol Science(S.Ix.) aud from tle Japauese Ministry of Education. Culture. Sports. Science aud Technology(YIs. No.21510271).," This work was supported in part by the Grant-in-Aid for Scientific Research from the Japan Society for Promotion of Science(S.K.) and from the Japanese Ministry of Education, Culture, Sports, Science and Technology(Y.K. No.21540271)."
Darth) su(GEHT (tha) | G0 1 fV) ug 7 9 PLο ει |] I DPIο oL ~2 ΓΕ... ΕΕ (eq |]. where the quantities f ave obtained from Eqs.(31))- (38)).,"P_M(k) P_L(k) (kq) + (k) + 2 - 3 P_L(k) (k q) ] + P_L(k) (kq)^2 + 2 (k) 2 3 P_L(k) (kq)^2 ], where the quantities $\tf$ are obtained from \ref{tfabb}) \ref{tfbab}) )."
 As discussed. below Eq.(U31)). the terms fo.(h) and Ευ] im Eq.(132)) were already obtained by Matarrese Verde (2008). following also Ivaiser (1981) by identifving massive halos with rare fluctuations in the linear deusitv field.," As discussed below \ref{xiMlin}) ), the terms $\tf_{2;11}(k)$ and $2\tf_{1;12}(k)$ in \ref{PkM}) ) were already obtained by Matarrese Verde (2008), following also Kaiser (1984) by identifying massive halos with rare fluctuations in the linear density field."
" Defining the Fourier-space bias as (uote that this is not the Fourier transform of the real- spacebias (118))) Pt IPLA where we used Pk}2Perth) at low & for the matter power spectrum. we obtain. λε)Di from,J qe Eq.(132))."," Defining the Fourier-space bias as (note that this is not the Fourier transform of the real-space bias \ref{biasdef}) )) b_M^2(k) = , where we used $P(k) \simeq P_L(k)$ at low $k$ for the matter power spectrum, we obtain $b_M^2(k)$ from \ref{PkM}) )."
 We can also obtain the bias of cifferent-niass halos im a simular fashion. first expanding Eq.(115)) and next takine he Fourier trausforii," We can also obtain the bias of different-mass halos in a similar fashion, first expanding \ref{xiM1M2}) ) and next taking the Fourier transform."
 Iu order to take iuto account the displacement of the halos (1.6. 0E 5). we can also make he approximation πλ where we use the explici expression (117)) for ος).," In order to take into account the displacement of the halos (i.e. $x \neq s$ ), we can also make the approximation P_M(k) )^3 ), x=, where we use the explicit expression \ref{sx}) ) for $s(x)$."
 This expressesthe fact that because of the displacement of massive halos. which usually have come closer bec“ATISC of thei mutual attraction (60 s). Lagrangian-space wavelengths 7s (0. measured in the linear density field) correspond to salle Euleriaespace waveleneths ~wr (1.6. measured in the uoulinear density field).," This expressesthe fact that because of the displacement of massive halos, which usually have come closer because of their mutual attraction $x<s$ ), Lagrangian-space wavelengths $\sim s$ (i.e. measured in the linear density field) correspond to smaller Eulerian-space wavelengths $\sim x$ (i.e. measured in the nonlinear density field)."
 This also follows the spirit of the ITuniltou et al. (, This also follows the spirit of the Hamilton et al. (
1991) ansatz. translated in Fourier space in Peacock Dodds (1996).,"1991) ansatz, translated in Fourier space in Peacock Dodds (1996)."
 We can note that for lavee nesativo [νι the alo power spectrum (132)) can become negative., We can note that for large negative $\fNL$ the halo power spectrum \ref{PkM}) ) can become negative.
" This is due to the fact that we looked for an expression of the alo correlation. or of halo power at Inear order over fw ax m Eq.(1the"""" 2j)."," This is due to the fact that we looked for an expression of the halo correlation, or of the halo power spectrum, at linear order over $\fNL$ as in \ref{PkM}) )."
 However. by “pecdefiuitioi the power spectrum Pa(4) be positive.," However, by definition the power spectrum $P_M(k)$ must be positive."
 Then. in cUses Wiere the expression (132)) turus negative one should consider lieher-order terms over fxp. which would custre that the power spectrum reais positive.," Then, in cases where the expression \ref{PkM}) ) turns negative one should consider higher-order terms over $\fNL$, which would ensure that the power spectrum remains positive."
" Nevertlieless. since such lieh-order terms are bevoud the scope of this article. Wwe consider below the following simple procedure tlat ensures that Paj(k). or the squared biasB Di03,(&). remainB positive."," Nevertheless, since such high-order terms are beyond the scope of this article, we consider below the following simple procedure that ensures that $P_M(k)$, or the squared bias $b_M^2(k)$, remain positive."
eye Up to linear order over fxzp. the bias (133)) reads as INL = Day(1.0) ία | where AP.fx)Path.fxy)λε.0) is the deviation from the Caussian halo power spectrum and we oxpauced the square-root.," Up to linear order over $\fNL$, the bias \ref{bkdef}) ) reads as ) = b_M(k,0) ( 1 + ), where $\Delta P_M(k,\fNL) = P_M(k,\fNL) - P_M(k,0)$ is the deviation from the Gaussian halo power spectrum and we expanded the square-root."
 Then. we may use the last expression (135)) as the prediction for the halo bias.," Then, we may use the last expression \ref{Dbk}) ) as the prediction for the halo bias."
 This amounts to make the transformation μμ.0) (see i πο where the two sides ouly differ x hnieher-order terius OVCL [xL (Gu lleztilie/2)* up to linear order over €) and the right side is always positive.," This amounts to make the transformation ) b_M^2(k,0) ( - 1 ) ]^2 , where the two sides only differ by higher-order terms over $\fNL$ (as $1+\epsilon \simeq (1+\epsilon/2)^2$ up to linear order over $\epsilon$ ) and the right side is always positive."
" TadTt we the Πιτ of very rare eveuts. that is 0,(uote»ü 32) . we can onlv keep the last two terius that fX2 . see Eq.(115)) below). OST) Parte) PLT Ug)? oen] | 5OL 8H 1"," If we take the limit of very rare events, that is $\sigma_q\rightarrow 0$ in \ref{PkM}) ), we can only keep the last two terms (note that $\tf \propto \sigma_q^2$ , see \ref{f112asymp}) ) below), _q 0: P_M(k) P_L(k) (kq)^2 - 6 ] + 2 ( + 2 )."
 2A yh). ke with TWky)~1. and at linear order over fx. the square root of Eq.(133)) eives with Eq.(138)) the bias σος :0.(130] 0: bath) 32k |o," At low $k$, with $\tW(kq)\simeq 1$, and at linear order over $\fNL$, the square root of \ref{bkdef}) ) gives with \ref{PkM1}) ) the bias _q 0, 0: b_M(k) - 3 +."
"L The first teria. óg, is the result obtained by Naiser (1981) for rare massive ση.halos (ie. with a large bias) for Gaussian mitial conditions."," The first term, $\delta_L/\sigma_q^2$, is the result obtained by Kaiser (1984) for rare massive halos (i.e. with a large bias) for Gaussian initial conditions."
 It is interesting to note that the second term gives a scale-3udepeudoeut correction to the Gaussian bias., It is interesting to note that the second term gives a scale-independent correction to the Gaussian bias.
 The presence of such a term was already noticed in Slosar et al. (, The presence of such a term was already noticed in Slosar et al. (
2008) and Afshordi Tolley (2009).,2008) and Afshordi Tolley (2009).
 As stressed) in Desjacques ct al. (, As stressed in Desjacques et al. (
2009). takiue tus term mto account is required to obtain a good latch to ποπΊσα. simulations.,"2009), taking this term into account is required to obtain a good match to numerical simulations."
 We checked. that this is indeed the case to match the iuuercal results i1 Fies., We checked that this is indeed the case to match the numerical results in Figs.
 9 aud 10 low using Eq.(1 32))., \ref{figbiask_M2d13_Desj} and \ref{figbiask_M1.5d13_Desj} below using \ref{PkM}) ).
 The last two terms depeud onu the waveuunber fr., The last two terms depend on the wavenumber $k$ .
 There is an additional terii. that we ueelect iu this paper. that arises fromthe cepeidence of the matter power spectrin on fx (i.e. the denominator in Eq.(133))).," There is an additional term, that we neglect in this paper, that arises fromthe dependence of the matter power spectrum on $\fNL$ (i.e. the denominator in \ref{bkdef}) ))."
 However. since this teria is muc1 3ualler than theother ones we disregard it here (sce Desjacques," However, since this term is much smaller than theother ones we disregard it here (see Desjacques"
even by Lauzettas figure { directly with a break at z2 (seo Fieure 9 where we replot the Lanzctta figure to illustrate the tine depeudence aud our fit to Lauzetta’s points).,"given by Lanzetta's figure 4 directly with a break at $z\approx2$ (see Figure \ref{fig:lanzetta}
 where we replot the Lanzetta figure to illustrate the time dependence and our fit to Lanzetta's points)."
 The results of fitting these ΕΤΕ are eiven iu Table 2.., The results of fitting these SFHs are given in Table \ref{tab:lanz}.
 We use a weighted combination of FOAL A with FOM D in the ratio of 1-to-5 based ou uncertainties deteriuued frou the Moute-Carlo eror estimation frou our different sky regious., We use a weighted combination of FOM A with FOM B in the ratio of 1-to-5 based on uncertainties determined from the Monte-Carlo error estimation from our different sky regions.
 For reference we also eive the sienificance levels of a fiducial a= 0. 9=3 model aud a a=. ο)=2 model.," For reference we also give the significance levels of a fiducial $\alpha=0$ $\beta=3$ model and a $\alpha=1$, $\beta=2$ model."
 The first gives a best-fit model with about halfsolar metallicity aud the second with about solar metallicity., The first gives a best-fit model with about half-solar metallicity and the second with about solar metallicity.
 The IIICIT model is rejected at =99% confidence for cosmic spectra from both the SDSS aud 2dFCRS sirvers., The HIGH model is rejected at $\ge 99$ confidence for cosmic spectra from both the SDSS and 2dFGRS surveys.
" Iu fact. the ΠΙΑ model oulv fits at this level if the average metallicitv becomes rather low (Z< 0.5Z.). if we restrict the range to Z>0.5Z... the model is rejected very severcly,"," In fact, the HIGH model only fits at this level if the average metallicity becomes rather low $Z<0.5 Z_{\odot}$ ), if we restrict the range to $Z>0.5 Z_{\odot}$, the model is rejected very severely."
 The LOW iuodel is also rejected by the SDSS data because of the low >. though more mareinally.," The LOW model is also rejected by the SDSS data because of the low $\beta$, though more marginally."
 None of these models fit the cosimic spectra as well as our fiducial a=0. 9=3 model which is well motivated bv the high redshitt bhuuinositv denusitv iueasurements.," None of these models fit the cosmic spectra as well as our fiducial $\alpha=0$, $\beta=3$ model which is well motivated by the high redshift luminosity density measurements."
 Thus it appears the cosmic spectrum does not provide any strous evidence for large amounts ΕΕ light in the current high redshift census., Thus it appears the cosmic spectrum does not provide any strong evidence for large amounts of missing light in the current high redshift census.
 Quauntitativelv. uo iore than about of stars formed at z>1.," Quantitatively, no more than about of stars formed at $z>1$."
 This is shehtly hieher than the BOO2 upper limit of, This is slightly higher than the BG02 upper limit of.
 The differences are that we include the SDSS data. include oulv the 2dFCRS low-redshift range. give some weight to the low-pass components of the cosmic spectra aud allow tenn=LO for the Lauzetta models.," The differences are that we include the SDSS data, include only the 2dFGRS low-redshift range, give some weight to the low-pass components of the cosmic spectra and allow $\zform=10$ for the Lanzetta models."
 It is of course possible that some of our assimiptious may be wrong. such as a universal IME: however the data can be well fitted by imodels which assume a Universal IMFE.," It is of course possible that some of our assumptions may be wrong, such as a universal IMF; however the data can be well fitted by models which assume a Universal IMF."
 The slope of the high-mass TATF can be constrained by cosmic spectra. if near-IR data is included.," The slope of the high-mass IMF can be constrained by cosmic spectra, if near-IR data is included."
 This will be addressed. by a forthcoming paper (Baldry&Clazebrook2003)., This will be addressed by a forthcoming paper \citep{BG03}.
. We have shown that we have derived a nonualized cosinic spectrum which is consistent between SDSS aud 2dFCRS surveys. is close to being volume limited aud is robust against aperture effects (bv comparing with SDSS « r colors).," We have shown that we have derived a normalized cosmic spectrum which is consistent between SDSS and 2dFGRS surveys, is close to being volume limited and is robust against aperture effects (by comparing with SDSS $u-r$ colors)."
 Au advantage of the SDSS survey is the excellent spectrophotometry as standard stars are included on cach plate., An advantage of the SDSS survey is the excellent spectrophotometry as standard stars are included on each plate.
 Iu particulary we would expect that the relative fliuxiug with waveleneth of the SDSS cosmic spectrum should be much more accurate than for 21FCRS (DGO2 indicate crrors are Likely iu the latter)., In particular we would expect that the relative fluxing with wavelength of the SDSS cosmic spectrum should be much more accurate than for 2dFGRS (BG02 indicate errors are likely in the latter).
 We do indeed find that the SDSS cosmic spectrum is in agreciuent with the 2dFCRS cosiuic spectrin has been applied to the latter (see BOO? for details of this procedure. esseutiallv it uses a good fit high-pass model to set the fiuxiug).," We do indeed find that the SDSS cosmic spectrum is in agreement with the 2dFGRS cosmic spectrum has been applied to the latter (see BG02 for details of this procedure, essentially it uses a good fit high-pass model to set the fluxing)."
 So far we have Όσοι dealing with the normalized cosmic spectrum. aud principally fitting to the high-pass spectral information.," So far we have been dealing with the normalized cosmic spectrum, and principally fitting to the high-pass spectral information."
 However we can put the cosmic spectrum on an absolute huumositv scale by normaliziug to the rband hunainositv deusitv., However we can put the cosmic spectrum on an absolute luminosity scale by normalizing to the $r$ -band luminosity density.
 For consistencev. we calculate this ourselves from a more recent large-scale structure (LSS) sample bv calculating the + buuinositv function Wine VivesVias Weighting aud A-correctiug to the rest-frame r-biud (keorrectvi11..20025).," For consistency, we calculate this ourselves from a more recent large-scale structure (LSS) sample by calculating the $r$ luminosity function using $V_{\rm survey}/V_{\rm max}$ weighting and $k$ -correcting to the rest-frame $r$ -band \citep[{\tt kcorrect v1\_11},."
 The LSS ziuuple is simular to our cosiic-spectra sample but has a well defined area.includes nearest-ucighhor redshifts to replace galaxies unissed due to fiber collisions and has stricter limits ou the selection magnitude of ιο«r17.5 (takenfromsampleiO described," The LSS sample is similar to our cosmic-spectra sample but has a well defined area,includes nearest-neighbor redshifts to replace galaxies missed due to fiber collisions and has stricter limits on the selection magnitude of $14.5<r<17.5$ \citep[taken from {\tt sample10}
 described"
of the outcome of our simulation.,of the outcome of our simulation.
" In the following we analyze the velocity structure of a typical pillar in the Mach 5 simulation which has a similar morphology and mass as the only trunk with well observed line-of-sight velocities, the Dancing Queen (DQ) trunk in NGC 7822 (?,, see Fig. 8))."," In the following we analyze the velocity structure of a typical pillar in the Mach 5 simulation which has a similar morphology and mass as the only trunk with well observed line-of-sight velocities, the Dancing Queen (DQ) trunk in NGC 7822 \citealt{2006A&A...454..201G}, see Fig. \ref{DQ}) )."
" The authors give the diameter as dogs©0.12—0.15pc, the total estimated mass from 1200 is Mops©9.2Mo."," The authors give the diameter as $d_\mathrm{obs}\approx0.12-0.15\pc$, the total estimated mass from $^{12}$ CO is $M_\mathrm{obs}\approx9.2\Msun$."
" This is similar the simulated pillar (da70.12pc, Mii*12.6Mo, see Table 2))."," This is similar the simulated pillar $d_\mathrm{sim}\approx0.12\pc$, $M_\mathrm{sim}\approx12.6\Msun$, see Table \ref{TAB_compare}) )."
 If we subdivide the pillar into a head and a body the mass, If we subdivide the pillar into a head and a body the mass
statistics. essentially a stacked residual image. was denotedfils.,"statistics, essentially a stacked residual image, was denoted."
 Onfils.. the only stars visible were variable starsprimarily RR Lyraes.," On, the only stars visible were variable stars--primarily RR Lyraes."
 A routine was then run to search for objects infis., A routine was then run to search for objects in.
" To avoid missing variables in the erowcde core. the detection limit was set. to only one. stanclare deviation. so that the program found all objects whose ""brightness! was more than 1o above the local background."," To avoid missing variables in the crowded core, the detection limit was set to only one standard deviation, so that the program found all objects whose `brightness' was more than $\sigma$ above the local background."
" Due to this low thresholel a substantial number of detected objects were ""false positives’ in that they did no represent actual variable objects."," Due to this low threshold, a substantial number of detected objects were `false positives' in that they did not represent actual variable objects."
 The majority of. these detections were associated with the extremely noisy edges of the lile. which are an artifact of the ISM.," The majority of these detections were associated with the extremely noisy edges of the file, which are an artifact of the ISM."
 These clear false positives were removed manually., These clear false positives were removed manually.
 A smaller number of objects were later found to have constant Light curves. an were then removed from the data sample.," A smaller number of objects were later found to have constant light curves, and were then removed from the data sample."
 One exception is the star v224. which is discussed in $4.2. For each of the remaining candidate variable stars. an unphased light curve was produced.," One exception is the star v224, which is discussed in $\S 4.2.$ For each of the remaining candidate variable stars, an unphased light curve was produced."
 “Phe built-in routine for PSE photometry caleulated the dilferential [ux for each of the residual images by convolving the reference frame PSE to the individual frame using the previously calculated local kernel., The built-in routine for PSF photometry calculated the differential flux for each of the residual images by convolving the reference frame PSF to the individual frame using the previously calculated local kernel.
 Lor stars 2 40 aresee from the core. the internal dispersion of our photometry is  23-6 per cent of the differential flux.," For stars $\ga$ 40 arcsec from the core, the internal dispersion of our photometry is $\sim$ 3-6 per cent of the differential flux."
 X direct conversion into instrumental magnitudes gives an upper limit to the internal error as 0.03 - 0.06 mae for this group of stars., A direct conversion into instrumental magnitudes gives an upper limit to the internal error as 0.03 - 0.06 mag for this group of stars.
 For stars closer to the crowded: core. the errors rise to tvpical values of 8-10. per cent (0.08 - 0.10 mag).," For stars closer to the crowded core, the errors rise to typical values of 8-10 per cent (0.08 - 0.10 mag)."
 Several stars within 25 arcsec of the core have dispersions as high as 20 per cent (0.20 mae)., Several stars within 25 arcsec of the core have dispersions as high as 20 per cent (0.20 mag).
 It should. however. be kept in mind that the Duxes of these stars are certainly greater than the dillerential Huxes caleulated. and thus the errors given here represent generous upper limits.," It should, however, be kept in mind that the fluxes of these stars are certainly greater than the differential fluxes calculated, and thus the errors given here represent generous upper limits."
 To search for the periods of the suspected. variables. Lomb-Scargle periodogram (Scargle1982). and. phase dispersion minimization (PDM) (StellinewerlLOTS) methods. were used. as implemented in the I. Barbera’sprogram.," To search for the periods of the suspected variables, Lomb-Scargle periodogram \citep{s82} and phase dispersion minimization (PDM) \citep{s78} methods were used, as implemented in the R. Barbera's."
 For each star. both methocds were used to search for the best- period. as deseribed in this section.," For each star, both methods were used to search for the best-fit period as described in this section."
 In. nearly. all cases. the resulting periods agreed to the fourth or fifth decimal place.," In nearly all cases, the resulting periods agreed to the fourth or fifth decimal place."
 When discrepancies existed. visual inspection of the resulting light curves was used to choose the period that minimized the scatter in the light curve.," When discrepancies existed, visual inspection of the resulting light curves was used to choose the period that minimized the scatter in the light curve."
 Since the focus of the search was on Ribs. the period range 0.2-0.8 davs was searched.," Since the focus of the search was on RRLs, the period range 0.2-0.8 days was searched."
 Hn à lew cases. when no accurate period could be found in that interval. the range was extended at both ends to allow for the rare possibility ofa Cepheid. ROB. or SX Phe star.," In a few cases, when no accurate period could be found in that interval, the range was extended at both ends to allow for the rare possibility of a Cepheid, RGB, or SX Phe star."
 For the majority of the stars in the outer portions of the images. the PDAL/periodogram (PDMP) analysis showed a single clear period ancl produced a relatively. clean light curve when fit to the data.," For the majority of the stars in the outer portions of the images, the PDM/periodogram (PDMP) analysis showed a single clear period and produced a relatively clean light curve when fit to the data."
 For those stars closer to the core. however. the PDAIP analysis did not always suggest a single period.," For those stars closer to the core, however, the PDMP analysis did not always suggest a single period."
 In these cases. periods corresponding to all of the respective PDMP extrema were tried. and the resulting light curves were compared.," In these cases, periods corresponding to all of the respective PDMP extrema were tried, and the resulting light curves were compared."
 In many cases it was possible to eliminate other periods because they were incompatible with the type of the RRL. as indicated. by the shape of the light curve.," In many cases it was possible to eliminate other periods because they were incompatible with the type of the RRL, as indicated by the shape of the light curve."
 Lf these methods still left multiple possible periods. the candidate light curves were inspected: visually. to ascertain the most accurate period.," If these methods still left multiple possible periods, the candidate light curves were inspected visually to ascertain the most accurate period."
 For a small number of cases. no such determination could be mace. and no period was assigned.," For a small number of cases, no such determination could be made, and no period was assigned."
 For à few stars. the noise in the light curve can be at least. partially attributed to the presence of a nearby. star (variable or not). whose light interferes with the signal [rom the variable star.," For a few stars, the noise in the light curve can be at least partially attributed to the presence of a nearby star (variable or not), whose light interferes with the signal from the variable star."
" Phese stars have been marked as ""merged in Table 1.", These stars have been marked as `merged' in Table 1.
 After caleulating preliminary. periods for all of the detected variables in the images. RA/Dee coordinates were [ound [or cach star.," After calculating preliminary periods for all of the detected variables in the images, RA/Dec coordinates were found for each star."
 To do this. 20 variables were identified using the finder charts in Carrettaetal.(1998). σσ].," To do this, 20 variables were identified using the finder charts in \citet{c98} [C98]."
 Each variable hac its identity confirmed using rough period matching from values given in the same source., Each variable had its identity confirmed using rough period matching from values given in the same source.
 Since complete astrometry for all previously known variables ds given in Bakosetal.(2000) BOO]. it was possible to obtain accurate. RAYDee values for each of these. known HltLs.," Since complete astrometry for all previously known variables is given in \citet{b00} [B00], it was possible to obtain accurate RA/Dec values for each of these known RRLs."
 The tasks and were then used to compute transformation equations from physical (pixel) to world (RA/Dec) coordinates for the images. and thus assign RA/Dee coordinates to cach variable star in the sample.," The tasks and were then used to compute transformation equations from physical (pixel) to world (RA/Dec) coordinates for the images, and thus assign RA/Dec coordinates to each variable star in the sample."
 Since the accuracy of the BOO astrometry was < 0.2 aresec. the process of matching variables in the saniple to known RRLs was greatly. facilitated.," Since the accuracy of the B00 astrometry was $\leq$ 0.2 arcsec, the process of matching variables in the sample to known RRLs was greatly facilitated."
 For nearly all detected variables. the RA/Dec matches provided an accurate means of identifving ltütLs in our sample.," For nearly all detected variables, the RA/Dec matches provided an accurate means of identifying RRLs in our sample."
 X second means of verification was period matching., A second means of verification was period matching.
 For each variable. the period was taken from the most recent source available. which was usually CorwinandCarney(2001) οςο).," For each variable, the period was taken from the most recent source available, which was usually \citet{cc01} [CC01]."
 If the star was not included in the CCOL sample. an older period. determination could sometimes be found in catalogue of Clementctal.(2001) 0). an updated version of (SawyerLloge1973).," If the star was not included in the CC01 sample, an older period determination could sometimes be found in catalogue of \citet{c01} [C01], an updated version of \citep{s73}."
. We identified 140 variable star candidates using the above procedures., We identified 140 variable star candidates using the above procedures.
 Of these 140. 131 proved to be variable.," Of these 140, 131 proved to be variable."
 ποσο variables previously known are listed in Table 1., Those variables previously known are listed in Table 1.
 The new ancl published. periods are. compared. and. comments. are added: where appropriate.," The new and published periods are compared, and comments are added where appropriate."
 Data for new and. suspected variables is given in Table 2., Data for new and suspected variables is given in Table 2.
 The method. used. here calculates light curves using, The method used here calculates light curves using
"Fullv-uupled images of 11L1 were obtained usine the SCUBA sub-uuu camera during 1997 July and 1998 Alay,",Fully-sampled images of 114 were obtained using the SCUBA sub-mm camera during 1997 July and 1998 May.
 We used the 9l-clemenut short-wave array at jnu( TMS PWT Afbeamλα Πο elementlony eacearreagatsbü pau (LIT ENTIM beam) diving excelleut conditions., We used the 91-element short-wave array at $\micron$ $7\farcs8$ FWHM beam) and the 37-element long-wave array at $\micron$ $14\farcs7$ FWHM beam) during excellent conditions.
 Typical 850-40. zenith opacities were approxinatelv 0.2. determined from hourly— skydips.," Typical $\micron$ zenith opacities were approximately 0.2, determined from hourly skydips."
 We obtained kks of useful on-source integration time at 850 jmnueand5.1 πα ju., We obtained ks of useful on-source integration time at $\micron$ and ks at $\micron$.
 Fluxes were calibrated50 against Uranus and the flux densities determined for ναι at 150 aud S50 μα ο ουσ aud +11 respectively. including errors induced by opacity uucertaiunties aud the absolute flux uucertaimty of Uranus.," Fluxes were calibrated against Uranus and the flux densities determined for 114 at 450 and $\micron$ are accurate to $\pm 18$ and $\pm 14$, respectively, including errors induced by opacity uncertainties and the absolute flux uncertainty of Uranus."
 The uncertainty iu the L50pau/s50¢n flux ratio is approximately dats» which represcuts the full dispersion iu the measurenme mace ou the separate nights.," The uncertainty in the $\micron$ $\micron$ flux ratio is approximately $\pm7$, which represents the full dispersion in the measurements made on the separate nights."
 The error in the £5051n/850422 fox ratio is less than total uncertainty at either wavelcueth since the absolute flux calibration error of Uranus cancels for the ratio., The error in the $\micron$ $\micron$ flux ratio is less than total uncertainty at either wavelength since the absolute flux calibration error of Uranus cancels for the ratio.
 Pointing was checked regularly using a nearby blazar., Pointing was checked regularly using a nearby blazar.
" We estimate the overall positional accuracy of the subanillimeter maps to be £2”,"," We estimate the overall positional accuracy of the submillimeter maps to be $\pm
2\arcsec$."
 Nowurufrared. J- aud Jv-baucd. nuagiug of 1114 was obtained during the uieht of 1998 October 19 using the new UKIRT Fast-Track huager ΤΕΤΙ) ou the 3.8m UK Infrared Telescope (UKIRT) on Manna Kea.," Near-infrared, $J$ - and $K$ -band, imaging of 114 was obtained during the night of 1998 October 19 using the new UKIRT Fast-Track Imager (UFTI) on the 3.8-m UK Infrared Telescope (UKIRT) on Mauna Kea."
 UFTI comprises a 101 CCdTTe ILAWAII iuvav cooled to 77& and scusitive fom 0.8. to ΜΕ, UFTI comprises a $1024^2$ Te HAWAII array cooled to $77\K$ and sensitive from 0.8 to $\micron$.
 Ομ ugquistsamplingofthebggtspggagewpopndee d Ισ ΕΙ» 27 ," The pixel scale is $0\farcs091$, allowing Nyquist sampling of the best seeing experienced on UKIRT, and the field of view is $92\arcsec$ ."
"""Theobs evid with 971 spacing."," The observations of 114 consisted of three sets of 9 exposures, two in $K$ $2.2\micron$ ) and one in $J$ $1.2\micron$ ), each of s, dithered on a $3\times 3$ grid with $9\farcs1$ spacing."
 These were iuterspersed by similar leugth observations of an offset sky region aud car exposures to allow the removal of the sky aud instrumental backerounds., These were interspersed by similar length observations of an offset sky region and dark exposures to allow the removal of the sky and instrumental backgrounds.
 The final stacked. exposures represcuts 2jÜ0ss iu J and 5105s in A., The final stacked exposures represents s in $J$ and s in $K$.
 The tip/tilt secoudary ou URIRT was used to provide standard adaptive correction within our field. although the conditions were nou-photometric and the secius achieved was only mediocre. ~UT.," The tip/tilt secondary on UKIRT was used to provide standard adaptive correction within our field, although the conditions were non-photometric and the seeing achieved was only mediocre, $\sim 0\farcs7$."
 Nevertheless. these dmages represent a substantial iurproveiient in resolution over those preseuted by I&uop et (01991).," Nevertheless, these images represent a substantial improvement in resolution over those presented by Knop et (1994)."
 Figures la 1b show the 150-. and 850-421: images of L111 taken with SCUBA., Figures 1a 1b show the 450- and $\micron$ images of 114 taken with SCUBA.
 Theiucerated flix densities sununed over the cussion regions are 2.13+0.11Jv and 0.273+0.038Jy at £5042n. ancl 850/21. respectively (Table 1).," The integrated flux densities summed over the emission regions are $2.43\pm0.44\jy$ and $0.273\pm0.038\jy$ at $\micron$ and $\micron$, respectively (Table 1)."
 At s50y;nu. we detect cinission extended in the cast-awest direction. while at ἱοῦμα we appear to resolve the central eiiission iuto two μπα in Table1).," At $\micron$, we detect emission extended in the east-west direction, while at $\micron$ we appear to resolve the central emission into two peaks $\micron$ [1] and $\micron$ [2] in Table 1)."
 Gaven that the separation of the two L50j;nu|2|150r peaks is near the resolving limit of SCUBA. observations at higher resolution are required to confir this doublepeaked morphology.," Given that the separation of the two $\micron$ peaks is near the resolving limit of SCUBA, observations at higher resolution are required to confirm this double–peaked morphology."
 When the [50-512 data are couvolved to the resolution of the 850-41. map. the data at both wavelengths show a similar shape. size. and position.," When the $\micron$ data are convolved to the resolution of the $\micron$ map, the data at both wavelengths show a similar shape, size, and position."
" At this resolution we fail to detect any significant variations iu the5((LUT),150721)/S(850;12) flux ratio."," At this resolution $14\farcs7$ ), we fail to detect any significant variations in the $S(450\micron)/S(850\micron)$ flux ratio."
 Iutegratius over all enüssion regious. we find a flux ratio of 8.9+0.6. which is also the ratio measured for the peak of the πια enudssion (at a resolution of 1177).," Integrating over all emission regions, we find a flux ratio of $8.9\pm0.6$, which is also the ratio measured for the peak of the sub-mm emission (at a resolution of $14\farcs7$ )."
 The consisteucies 1u he 150-512. and 850-41 data would be expected if the bulk of the sub-auni euission is on the blackbody tail of spectral energy. distribution with dust teiiperatures T>104., The consistencies in the $\micron$ and $\micron$ data would be expected if the bulk of the sub-mm emission is on the black–body tail of spectral energy distribution with dust temperatures $T\ga 10\K$.
 Observations at higher resolution are required to search for possible varialons lu the οί15050)/5(85tya) raio on smaller spatial scales., Observations at higher resolution are required to search for possible variations in the $S(450\micron)/S(850\micron)$ ratio on smaller spatial scales.
 The sub-uiui enadssion los along the CO xu-like structure (Fie., The sub-mm emission lies along the CO bar-like structure (Fig.
 lc). extending east-west between he two optica coniponents.," 1c), extending east-west between the two optical components."
 Doth tιο CO and sub-miun cussion peak near the xiehtest AC bud source of 111 which is hy far the reddest part of the 1111 svsteWl. as indicated bv the JA color map (Fig.," Both the CO and sub-mm emission peak near the brightest $K-$ band source of 114 which is by far the reddest part of the 114 system, as indicated by the $J-K$ color map (Fig."
 Hd)., 1d).
 Ahough the NIR data were not taken iu plotometiic conditions. an approximate JA inagnitude scale was derived by matching the data with the previously determine: JN color of WW (Isnop ct 11991).," Although the NIR data were not taken in photometric conditions, an approximate $J-K$ magnitude scale was derived by matching the data with the previously determined $J-K$ color of W (Knop et 1994)."
 The resolution data preseuted here suggests a color of (.7Nix) for he bright compact red component iu LEE. These results are 'nsÓsteunt with those found fex the Nour-Infrared Couπα and Multi-ObMject) Spectrometcr (NICALOS) data taken with the IIub Space Telescope (Scoville et 11999)., The higher--resolution data presented here suggests a color of $(J-K)\simeq 3$ for the bright compact red component in E. These results are consistent with those found for the Near-Infrared Camera and Multi-Object Spectrometer (NICMOS) data taken with the Hubble Space Telescope (Scoville et 1999).
 The sub-uiuui. radio contiuuuu. aud CO ωςΓΙ from 1111 all have roughly the same spatial extent.," The sub-mm, radio continuum, and CO emission from 114 all have roughly the same spatial extent."
 However. there are ssienificant differeuces in their detailed structure.," However, there are significant differences in their detailed structure."
 Iu particular. the radio sources (Condon et pnd s near-infrared (NIR) enission peaks (I&nop et 1991). sugecsting that these regions are responsible for the majority of the oneoiug star formation.," In particular, the radio sources (Condon et 1990; Condon et 1991) are located near the near-infrared (NIR) emission peaks (Knop et 1994), suggesting that these regions are responsible for the majority of the ongoing star formation."
 The SULπι and CO peaks do not appear to be correlated with the radio and NIR pealss but tend to lie primary iu between WW. The CO peal lis. approximately 2” from the subnmülluneter peak. which is consistent within the positional uncertainties of he data sets.," The sub-mm and CO peaks do not appear to be correlated with the radio and NIR peaks but tend to lie primary in between W. The CO peak lies approximately $2\arcsec$ from the submillimeter peak, which is consistent within the positional uncertainties of the data sets."
 The eecneral simularities of the €Ὁ aud sSub-nuin inaps suggest tlat both the :uid. ΠΕ emissiou probe the same material the molecular gas aud ¢ust reservolr assoclated with the merser eveut., The general similarities of the CO and sub-mm maps suggest that both the and sub-mm emission probe the same material: the molecular gas and dust reservoir associated with the merger event.
 Despite these consisteucies. there aro cüfferences du their detailed structure which may iudicate optical depth or excitation effects in thie CO ΕΠ," Despite these consistencies, there are differences in their detailed structure which may indicate optical depth or excitation effects in the CO emission."
 The CO emission is distributed more suxothlv along the bar-like structure between EE and VVIILIWW. while the sunuu emission IS iore stronelv peak nea EE. The tidal tails are also luore apparent in the CO map. whiletthe 150401 e1issiou is 11016 extended in the east aud south-west directions.," The CO emission is distributed more smoothly along the bar-like structure between E and W, while the sub-mm emission is more strongly peaked near E. The tidal tails are also more apparent in the CO map, while the $\micron$ emission is more extended in the east and south-west directions."
 The excess sub-nuni enisson iu the east and south-west directions nav be associated with tidal debris iufalliug iuo the central regions (ITiblxuxl Yun 1999)., The excess sub-mm emission in the east and south-west directions may be associated with tidal debris infalling into the central regions (Hibbard Yun 1999).
 VVILLEE is located near a peal of the suπι Cluission which is «musistent with the lieh level o| dust obscurationinferred frou. its extremely red NIR colors (Fig., E is located near a peak of the sub-mm emission which is consistent with the high level of dust obscurationinferred from its extremely red NIR colors (Fig.
 ld: also see E&uop et 11991)., 1d; also see Knop et 1994).
 VVIIIIWW. ou the other haud. lies along a line of sight which is rearly free of sub-nua emission (Fig.," W, on the other hand, lies along a line of sight which is nearly free of sub-mm emission (Fig."
 la) and is consisten with, 1a) and is consistent with
"a correlation between A, and X-ray flux.",a correlation between $K_\textnormal{\tiny S}$ and X-ray flux.
" The distribution of unclassified sources is similar to that of known AGNS, although a correlation of unclassified sources seems to be weak."," The distribution of unclassified sources is similar to that of known AGNs, although a correlation of unclassified sources seems to be weak."
" Because FSC sources are mainly gathered sources fainter than the count rate of ~0.05 counts !, there is a small number of sources in therange of Fx>2.8xs107? erg cm? s! (corresponding to 0.05 counts s)."," Because FSC sources are mainly gathered sources fainter than the count rate of $\sim0.05$ counts $^{-1}$, there is a small number of sources in therange of $F_\textnormal{\tiny X}>2.8 \times 10^{-13}$ erg $^{-2}$ $^{-1}$ (corresponding to 0.05 counts $^{-1}$ )."
 Figure 2. shows the (J— Ks)- (Px/F;) diagrams., Figure \ref{JK-XJ-CCD} shows the $J-K_\textnormal{\tiny S}$ )- $F_\textnormal{\tiny X}/F_\textnormal{\tiny J}$ ) diagrams.
" As to candidates in the BSC, Fx/F; is nearly constant though FX/HEKgdecreaseswith(J—Kg)colour."," As to candidates in the BSC, $F_\textnormal{\tiny X}/F_\textnormal{\tiny J}$ is nearly constant though $F_\textnormal{\tiny X}/F_\textnormal{\tiny K$ $}$ decreases with $(J-K_\textnormal{\tiny S})$ colour."
"Ontheotherhand,as to candidates in Jnownéun"," On the other hand, as to candidates in the FSC, $F_\textnormal{\tiny X}/F_\textnormal{\tiny J}$ is directly proportional to $(J-K_\textnormal{\tiny S})$ colour and $F_\textnormal{\tiny X}/F_\textnormal{\tiny K$ $}$ decreases with $(J-K_\textnormal{\tiny S})$ colour compared with $F_\textnormal{\tiny X}/F_\textnormal{\tiny J}$."
, A similarity between candidates in the BSC and the FSC is that $F_\textnormal{\tiny X}/F_\textnormal{\tiny K$ $}$ decreases with $(J-K_\textnormal{\tiny S})$ colour.
," This is probably due to extinctions because the light at the J-band suffers extinction than the light at the $_\textnormal{\tiny S}$ band (i.e., $F_\textnormal{\tiny J}$ should be absorbed than $F_\textnormal{\tiny K$ $}$ )."
kne, \citet{Haakonsen2009-ApJS} reported loci of various types of objects in a $J-K_\textnormal{\tiny S}$ $F_\textnormal{\tiny X}/F_\textnormal{\tiny J}$ ) diagram using both 2MASS photometry and X-ray flux in the ROSAT BSC.
wn ES," Their diagram shows that the AGN locus is well separated from those of other types of objects such as normal stars, where almost all of the AGNs have $(J-K_\textnormal{\tiny S})>0.6$ and $F_\textnormal{\tiny X}/F_\textnormal{\tiny J}>3 \times 10^{-2}$."
G., The locus of our candidates is consistent with their AGN locus.
"are, alike be"," Some unclassified sources in the BSC or the FSC have $(J-K_\textnormal{\tiny S})<1.0$, where few known AGNs are distributed."
tween ," These sources might be spurious AGNs or other kinds of AGNs (e.g., AGNs having extremely small extinction and low luminosity) that have not been found by previous surveys."
c, The AGNs with $(J-K_\textnormal{\tiny S})>2.0$ are defined as red AGNs \citep{Cutri2001-ASPC}.
andi, It is believed that many red AGNs are found at $z\la 0.5$ \citep{Cutri2002-ASPC}.
dates in the BSC and t ," In our sample, there are 234 (192) red AGNs in the BSC (FSC) and it is highly probable that they are AGNs at $z \la 0.5$."
"Figure 3 shows histograms of two hardness ratios (HR1 and HR2), where HR1 and HR2 are given using four energy bands, that is, A (Pulse Height Amplitude (PHA) channels 11—41), B (52-201), C (52-90), and D (91-201): HR1=(B-A)/(B+A) and HR2=(D-C)/(D4C), respectively."," Figure \ref{HR-hist} shows histograms of two hardness ratios (HR1 and HR2), where HR1 and HR2 are given using four energy bands, that is, A (Pulse Height Amplitude (PHA) channels 11–41), B (52–201), C (52–90), and D (91–201): HR1=(B-A)/(B+A) and HR2=(D-C)/(D+C), respectively."
" In the HR1 histogram for the BSC, both known AGNs andunclassified sources show a flat distribution in —0.5 SHRIS1.0 and the number of sources decreases in HRIS —0.5, although the number of unclassified sources is relatively larger in HR1>0.8."," In the HR1 histogram for the BSC, both known AGNs andunclassified sources show a flat distribution in $-0.5 \la$ $\la 1.0$ and the number of sources decreases in $\la-0.5$ , although the number of unclassified sources is relatively larger in $\ga 0.8$."
 Vogesetal.(1999) presented that X-ray counterparts for AGNs in the catalogue of Veron-Cetty&(1998) show flat distribution in the range between —0.5 to 4-1.0., \citet{Voges1999-AA} presented that X-ray counterparts for AGNs in the catalogue of \citet{Veron1998-BOOK} show a flat distribution in the range between $-0.5$ to $+1.0$.
" Hence, the HR1a property of these candidates is consistent with Vogesetal.(1999).."," Hence, the HR1 property of these candidates is consistent with \citet{Voges1999-AA}."
" On the other hand, although known AGNs in the FSC have a similar shape in Vogesetal.(1999),, the number of unclassified sources in the FSC increase towards larger HR1 values (i.e., they are relatively harder as compared to known AGNs)."," On the other hand, although known AGNs in the FSC have a similar shape in \citet{Voges1999-AA}, the number of unclassified sources in the FSC increase towards larger HR1 values (i.e., they are relatively harder as compared to known AGNs)."
" Therefore, some candidates in the FSC might be contaminated by galaxies because Abell clusters of galaxies (ACO) objects tend to have harder than stars and AGNS in their diagrams (Vogeset 1999).."," Therefore, some candidates in the FSC might be contaminated by galaxies because Abell clusters of galaxies (ACO) objects tend to have harder than stars and AGNs in their diagrams \citep{Voges1999-AA}."
" In the HR2 histograms, they have peaks at HR2~0.2 and this is also consistent with the HR2 histograms of AGNs in al. (1999).."," In the HR2 histograms, they have peaks at $\sim0.2$ and this is also consistent with the HR2 histograms of AGNs in \citet{Voges1999-AA}."
" It should be noted that in the range over HR2~0.2 there are relatively large number of unclassified candidates in the BSC than known AGNS (i.e., there are harder samples) though the for Soureesdnothe."," It should be noted that in the range over $\sim0.2$ there are relatively large number of unclassified candidates in the BSC than known AGNs (i.e., there are harder samples) though the distributions for known/unknown sources in the FSC are alike."
" In Figure 4,, HR1 versus HR2 diagrams are shown."," In Figure \ref{HR1-HR2}, HR1 versus HR2 diagrams are shown."
" Both known AGNs and unclassified sources in the BSC have similar distribution each other, although there are a relatively large number of unclassified sources in HR1Z;0.8 as pointed out the above."," Both known AGNs and unclassified sources in the BSC have similar distribution each other, although there are a relatively large number of unclassified sources in $\ga0.8$ as pointed out the above."
 Most of them are located in HR1»—0.6 and —0.5 «HR2«0.5 space and show a flat distribution with respect to HR1., Most of them are located in $>-0.6$ and $-0.5<$ $<0.5$ space and show a flat distribution with respect to HR1.
" Vogesetal.(1999) compared distributions among three types of objects (namely, TYCHO stars, ACO objects, and AGNs) and presented that AGNs are found mostly in the central part with HR1>—0.5 and —0.5 <HR2< 0.5."," \citet{Voges1999-AA} compared distributions among three types of objects (namely, TYCHO stars, ACO objects, and AGNs) and presented that AGNs are found mostly in the central part with $>-0.5$ and $-0.5<$ $<	0.5$ ."
 The distribution of our samples are very similar to that of Vogesetal. (1999).., The distribution of our samples are very similar to that of \citet{Voges1999-AA}. .
" Therefore, our candidates in the BSC is consistent with the property of AGNs in Voges (1999).."," Therefore, our candidates in the BSC is consistent with the property of AGNs in \citet{Voges1999-AA}. ."
" On the other hand, candidates in the FSC tend to have a dispersion distribution compared to candidates in the BSC."," On the other hand, candidates in the FSC tend to have a dispersion distribution compared to candidates in the BSC."
" Although errors of hardness ratios affectthe distribution, there may be many spurious AGNs in the candidates detected in the FSC."," Although errors of hardness ratios affectthe distribution, there may be many spurious AGNs in the candidates detected in the FSC."
stripped planetesimals of Figures 2. or 34 for the appropriate ratio 2/1.,stripped planetesimals of Figures \ref{strip40_100_dots} or \ref{strip10_40_dots} for the appropriate ratio $m_p/m_c$.
 As an example of this calculation. we list in Table 3. the miss distance d. and stripping factor s; for each spectral type of the stellar encounters undergone by the Sun for the first 100 Myr after its birth in a cluster characterized by c=km/s and the initial stellar density 2o=3000pew? (Adams Laughlin. 2001).," As an example of this calculation, we list in Table \ref{sun} the miss distance $d_{enc}$ and stripping factor $s_i$ for each spectral type of the stellar encounters undergone by the Sun for the first 100 Myr after its birth in a cluster characterized by $\sigma=5~km/s$ and the initial stellar density $n_0=3000~pc^{-3}$ (Adams Laughlin, 2001)."
 In these conditions. the total fraction of planetesimals left is <95% after 100 Myrs in our model.," In these conditions, the total fraction of planetesimals left is $< 95 \%$ after 100 Myrs in our model."
 The present day Kuiper Belt has only ~ of the mass that the minimun mass solar nebula hypothesis predicts. and. the hypothesis of the late heavy bombardement at 700 Myr has been put forth as an explaination (Morbidelli et al 2005).," The present day Kuiper Belt has only $\sim$ of the mass that the minimun mass solar nebula hypothesis predicts, and, the hypothesis of the late heavy bombardement at 700 Myr has been put forth as an explaination (Morbidelli et al 2005)."
 In Table 4.. we search the parameter space (7. 719) to find out the conditions in which a debris disk can be most severely depleted during the first 100 Myr of its lifetime.," In Table \ref{strip}, we search the parameter space $m_c$, $n_0$ ) to find out the conditions in which a debris disk can be most severely depleted during the first 100 Myr of its lifetime."
 The fractions of planetesimals left after 100 Myr in a standard size disk (40—100 AU) and compact disk (10—40 AU) are estimated for the central star masses. 7.(=0.25. 0.5. 1.0 or 2.5 M... which cover the mass range of stars searched for debris disks in surveys.," The fractions of planetesimals left after 100 Myr in a standard size disk $40-100$ AU) and compact disk $10-40$ AU) are estimated for the central star masses, $m_c= 0.25$, 0.5, 1.0 or 2.5 $M_{\odot}$, which cover the mass range of stars searched for debris disks in surveys."
 The cluster dispersion velocity adopted is c=5 km/s. as observed in 11 nearby open clusters and associations with ages between SMyrs (Upper Sco) and 757 Myrs (Praesepe) by Madsen. Dravins Lindegren (2002). and as measured in the N-body simulation of the dynamicalvá evolution of embedded clusters from which open clusters emerge (Proszkow Adams 2009).," The cluster dispersion velocity adopted is $\sigma= 5$ km/s, as observed in 11 nearby open clusters and associations with ages between 5Myrs (Upper Sco) and 757 Myrs (Praesepe) by Madsen, Dravins Lindegren (2002), and as measured in the N-body simulation of the dynamical evolution of embedded clusters from which open clusters emerge (Proszkow Adams 2009)."
 In Table 4.. the initial star number density 70 is chosen to be 100. 1000. 3000. 10 000. 20 000. or 30 000 pc for several reasons; most embedded clusters have stellar densities of ~100pe (Carpenter 2000. Porras et al 2003. Lada Lada 2003). the Sun is thought to be born in a cluster of stellar density ~3000pc (Adams Laughlin 2001). and the densest and closest embedded cluster is the Orion nebula cluster with ~20000pc (Hillenbrand Hartmann. 1998).," In Table \ref{strip}, , the initial star number density $n_0$ is chosen to be 100, 1000, 3000, 10 000, 20 000, or 30 000 $pc^{-3}$ for several reasons; most embedded clusters have stellar densities of $\sim 100~pc^{-3}$ (Carpenter 2000, Porras et al 2003, Lada Lada 2003), the Sun is thought to be born in a cluster of stellar density $\sim 3000~pc^{-3}$ (Adams Laughlin 2001), and the densest and closest embedded cluster is the Orion nebula cluster with $\sim 20~000~pc^{-3}$ (Hillenbrand Hartmann, 1998)."
 We note also that the central stellar density of the Arches cluster close to the Galactic center reaches ~10°pc (Portegies Zwart et al., We note also that the central stellar density of the Arches cluster close to the Galactic center reaches $\sim 10^5~pc^{-3}$ (Portegies Zwart et al.
 2007) but we have not included this extreme case in our study., 2007) but we have not included this extreme case in our study.
" According to our search of the parameter space (,../0) in Table 4.. severe depletion by close stellar encounters occurs only for a disk of standard size (40—100 AU) surrounding à star born in an embedded cluster with a high star-density no greater than 20000ο."," According to our search of the parameter space $m_c, n_0$ ) in Table \ref{strip}, , severe depletion by close stellar encounters occurs only for a disk of standard size $40-100$ AU) surrounding a star born in an embedded cluster with a high star-density $n_0$ greater than $20~000~pc^{-3}$."
 In these conditions. fewer than 585c of the planetesimals are left around an intermediate-mass star after 100 Myr. fewer than 37% around a solar-mass star. and fewer than only around a low-mass star.," In these conditions, fewer than $58\%$ of the planetesimals are left around an intermediate-mass star after 100 Myr, fewer than $37\%$ around a solar-mass star, and fewer than only around a low-mass star."
 In common low star-density embedded clusters where mq is <1000pe. stellar flybys have a relatively small effect on disks.," In common low star-density embedded clusters where $n_0$ is $ < 1000~pc^{-3}$, stellar flybys have a relatively small effect on disks."
 The turning point in Table 4. where disks start to lose their planetesimals in 100 Myr is the intermediate star density ny~3000pc. which ts thought to have prevailed in the birthplace of the Sun.," The turning point in Table \ref{strip} where disks start to lose their planetesimals in 100 Myr is the intermediate star density $n_0 \sim 3000~pc^{-3}$, which is thought to have prevailed in the birthplace of the Sun."
 In contrast. disks of compact size (10—40 AU) are almost insensitive to their stellar environment as seen in Table 4..," In contrast, disks of compact size $10-40$ AU) are almost insensitive to their stellar environment as seen in Table \ref{strip}."
 These conclusions remain qualitatively the same regardless of whether the disk is dynamically excited at the start of the simulation or not., These conclusions remain qualitatively the same regardless of whether the disk is dynamically excited at the start of the simulation or not.
 In agreement with these results. Spurzem et al. (," In agreement with these results, Spurzem et al. ("
2009) demonstrated that disruptions of some wide-orbit planetary systems in ai Orion-type cluster are expected on a timescale of a few 10% yrs. leaving free-floating planets as relies.,"2009) demonstrated that disruptions of some wide-orbit planetary systems in an Orion-type cluster are expected on a timescale of a few $10^8$ yrs, leaving free-floating planets as relics."
" We can make a rough estimate of the fraction of stars born in low and high star-density environments by comparing the numbers of stars N, and N> that are. respectively. in the closest high star-density embedded cluster. the Orion Nebula Cluster at 450 pe. and in all low star-density embedded clusters closer than this distance: these numbers are Nj,=2520 andNz=1324 based on the catalog of LadaLada (2003)."," We can make a rough estimate of the fraction of stars born in low and high star-density environments by comparing the numbers of stars $N_1$ and $N_2$ that are, respectively, in the closest high star-density embedded cluster, the Orion Nebula Cluster at 450 pc, and in all low star-density embedded clusters closer than this distance; these numbers are $N_1=2520$ and$N_2=1324$ based on the catalog of LadaLada (2003)."
 Thus. the corresponding fractions are ΑΝ+No)=34% and ΑΝ+No)=66% for stars born in low and high star-density embedded clusters. respectively.," Thus, the corresponding fractions are $N_2/(N_1+N_2) = 34$ and $N_1/(N_1+N_2) = 66$ for stars born in low and high star-density embedded clusters, respectively."
 If this rough, If this rough
Lage. J. Juréákk. T. Magara. aud ο. Tsuneta for fruitful comments.,"Lagg, J. Jurčákk, T. Magara, and S. Tsuneta for fruitful comments."
 Hinocde is a Japaiese tissiou developed aud launched by ISAS/JANA. with NAOJ as domestic partuer aud. NASA aud STFC (UIx) as international partners.," Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners."
 It is operated by these agencies in co-operation with ESA and NSC Norway., It is operated by these agencies in co-operation with ESA and NSC Norway.
" This work was partly carried out at the NAOJ Hinode Science Center. which is supported by the Curant-in-Aicd for Creative Scientific Research ""The Basic Study of Space Weather Preciction” from MENT. Japan (Head Luvestigator: lx. Shibata). generous donatious from Sun Alicrosystems. aud NAOJ internal funciusg."," This work was partly carried out at the NAOJ Hinode Science Center, which is supported by the Grant-in-Aid for Creative Scientific Research “The Basic Study of Space Weather Prediction” from MEXT, Japan (Head Investigator: K. Shibata), generous donations from Sun Microsystems, and NAOJ internal funding."
The spectral type of IID 358623 D was determined iu Sect.,The spectral type of HD 358623 B was determined in Sect.
 3.2 roughly to be earlv- to imid-M from its JU. uaenuitudes., 3.2 roughly to be early- to mid-M from its JHK magnitudes.
 To coufirma aud refine this classification. we obtained au Παπ spectiuu ou 8 Dec 2001 with 5ο. We ook 20 specra with 60 sec exposure each through a 1 slit wit ia red eiu iucludiug both the IT- aud Ik-baud (1.53 o 2.52 sau) with a resolution of &21000.," To confirm and refine this classification, we obtained an H-band spectrum on 8 Dec 2001 with SofI. We took 20 spectra with 60 sec exposure each through a $1^{\prime \prime}$ slit with a red grism including both the H- and K-band (1.53 to $2.52~\mu$ m) with a resolution of $R \simeq 1000$."
 Data reduction Was do1¢ in the normal way with IRAF: Dark subtraction. LOYualization. flat fielding. skv subtraction. wavelength calibration. co-adding the spectra. then correction for iustruimenta sensitivitv and atmospheric respouse.," Data reduction was done in the normal way with IRAF: Dark subtraction, normalization, flat fielding, sky subtraction, wavelength calibration, co-adding the spectra, then correction for instrumental sensitivity and atmospheric response."
 The spectra were not fiux-calibrated., The spectra were not flux-calibrated.
 The final spectra of both the primary ΠΙΟ 358623 A and the secoudary TD 358623 D are shown in Fie., The final spectra of both the primary HD 358623 A and the secondary HD 358623 B are shown in Fig.
 |., 4.
 Because we have comparison spectra of IkX- to ALtype «warts available oulv for the U-hbancd. we use aud show oilv the IT-baud part of the Soff ITI|1ν-band spectrum.," Because we have comparison spectra of K- to M-type dwarfs available only for the H-band, we use and show only the H-band part of the SofI H+K-band spectrum."
 The I-baud spectrum of the comparison star GSC 7210 1352. a known Ml-dwarf in the TW Iva region. has been taτοι by us with ISAAC at the VET aud was publishee before in Neulauuser et al. (," The H-band spectrum of the comparison star GSC 7210 1352, a known M1-dwarf in the TW Hya region, has been taken by us with ISAAC at the VLT and was published before in Neuhäuuser et al. ("
2002).,2002).
 As seen di Fig., As seen in Fig.
" 1, ΠΟ 358623 A shows the typical features of laο to carly-AL type sars. naiuclv Me. Si. Al. and Na absorption (see ee. Cacen Lada 1996. Alever et al."," 4, HD 358623 A shows the typical features of late-K to early-M type stars, namely Mg, Si, Al, and Na absorption (see e.g. Green Lada 1996, Meyer et al."
 J998)., 1998).
 Those lines are clearly weaker in the COMpaLISOL 5ar GSC 7210 1352. a kuown ALL dw.," Those lines are clearly weaker in the comparison star GSC 7210 1352, a known M1 dwarf."
 It is very simular for the secondary. where these lines are even a bit weaker.," It is very similar for the secondary, where these lines are even a bit weaker."
 Hence. regarding the presence of lies. the relative streugth oftrem. and the general shape ofthe continua. we can classify the seconary as M2 chwart (41 sub-class).," Hence, regarding the presence of lines, the relative strength of them, and the general shape of the continuum, we can classify the secondary as M2 dwarf $\pm 1$ sub-class)."
 This is consistent with is JT colors (1001 and our Table 2)., This is consistent with its JHK colors (JB01 and our Table 2).
 It cannot be later than M23. because a stronger than observed absorption liue appears at 1.76 jn in dwarts later than MO (Green Lada 1996. Mower et al.," It cannot be later than M3, because a stronger than observed absorption line appears at $1.76~\mu$ m in dwarfs later than M3 (Green Lada 1996, Meyer et al."
 1998)., 1998).
 This classification ids also consistent with the primary being K7-30 aud the magnitude ciffereuce between primary and secondary beme 1.7 mag in J aud II (and 1.6 mae in I&). assuming that they are at tle same age and distance.," This classification is also consistent with the primary being K7-M0 and the magnitude difference between primary and secondary being 1.7 mag in J and H (and 1.6 mag in K), assuming that they are at the same age and distance."
 We have shown that the ΠΟ 358623 primary A and its colupanion candidate D indeed show the same proper motion aud that the spectral type of the companion (M2) is consistent with the observed colors and magnitude differeuces. so that it is a trucly bound companion.," We have shown that the HD 358623 primary A and its companion candidate B indeed show the same proper motion and that the spectral type of the companion (M2) is consistent with the observed colors and magnitude differences, so that it is a truely bound companion."
 We would like to point out again the hieh precision achieved in the relative astrometry: After just one vear. we could measure the proper motion (~LOO mas) of both TID 358623 A and D with sufficient precision to show that hey form à colmuon proper motion pair. using the 150 uas pixel scale of the Soff small field auc several nou-noving background stars.," We would like to point out again the high precision achieved in the relative astrometry: After just one year, we could measure the proper motion $\sim 100$ mas) of both HD 358623 A and B with sufficient precision to show that they form a common proper motion pair, using the 150 mas pixel scale of the SofI small field and several non-moving background stars."
 The incan apparent angular separation between ID 358623 A aud D (2.2054 0.0287) corresponds to a srojected physical separation of 105.2+6.6 AU (at the Tipparcos distance of TID 199118. which is prestually he sgunue as for ΠΟ 358623. see vadAOO).," The mean apparent angular separation between HD 358623 A and B $2.205 \pm 0.028^{\prime \prime}$ ) corresponds to a projected physical separation of $105.2 \pm 6.6$ AU (at the Hipparcos distance of HD 199143, which is presumably the same as for HD 358623, see vdA00)."
" The xojected uivsical separation between WD 199113 A and B js [N.N3.9 AU. namely 1.023£0.031"" (our separation neasured with SITARP-I) at 17.7£2.1 pe."," The projected physical separation between HD 199143 A and B is $48.8 \pm 3.9$ AU, namely $1.023 \pm 0.031^{\prime \prime}$ (our separation measured with SHARP-I) at $47.7 \pm 2.4$ pc."
 Let us investigate the sensitivity uuits deteruined for the dynamic rauge achieved in the images: The dux ratio is determined from our actual images of the two stars iu all Sof and SITARP-I images as the 30 backerouud, Let us investigate the sensitivity limits determined for the dynamic range achieved in the images: The flux ratio is determined from our actual images of the two stars in all SofI and SHARP-I images as the $3 \sigma$ background
huninosity.,luminosity.
 However. this has been substautiallv relaxed in view of the recently revised source distance of 188 pc (ESA 1997) ax opposed to the previously assumed. value of 250 pe.," However, this has been substantially relaxed in view of the recently revised source distance of 188 pc (ESA 1997) as opposed to the previously assumed value of 250 pc."
 When coupled wijio a re-evaluation of wind xuiueters bv Stee e al. (, When coupled with a re-evaluation of wind parameters by Stee et al. (
1995). the observed luuinosity is uo longer in conflict with current limits on the orbital notion.,"1995), the observed luminosity is no longer in conflict with current limits on the orbital motion."
 The lack of N-rav. pulsidious nav indicate that he white dwarf docs lot possess a strong maenetic field or hat the orbital period is long compared to the timeline of he cient X-ray database., The lack of X-ray pulsations may indicate that the white dwarf does not possess a strong magnetic field or that the orbital period is long compared to the time–line of the current X-ray database.
 The latter explanation would xc consistent with the caleulatious of I&ubo et al. (, The latter explanation would be consistent with the calculations of Kubo et al. (
1998) who derive an orbital period fr the svstem of 150 davs.,1998) who derive an orbital period for the system of 150 days.
 Lastly. in a critical review of X-ray emission models. Kaho et al. (," Lastly, in a critical review of X-ray emission models, Kubo et al. ("
1998) οποιος there is uo compelling evidence for the coronal model of οτα et al. (,1998) conclude there is no compelling evidence for the coronal model of Smith et al. (
1998) since the very properties they claim are characteristic ofcoronal emission are also seen iu the dwarf uova SS Cre (Watson ct al.,1998) since the very properties they claim are characteristic of coronal emission are also seen in the dwarf nova SS Cyg (Watson et al.
 L985)., 1985).
 Iu sunuuary. our results confirm previous ASC'A and ROSAT ineastvements aud support the view of Kubo et al. (," In summary, our results confirm previous ASCA and ROSAT measurements and support the view of Kubo et al. ("
1998) that the characteristics of the N-ray cuaissio are fully consistent with the conventional picture of? Cas asa binary svstem coutaimiue an accreting non-naeguetic white dwarf. rather than neutrou star binary or coronal enission models.,"1998) that the characteristics of the X-ray emission are fully consistent with the conventional picture of $\gamma$ –Cas as a binary system containing an accreting non-magnetic white dwarf, rather than neutron star binary or coronal emission models."
In moment space. this amounts (o restrict il (to ils mass shell positive frequency components.,"In momentum space, this amounts to restrict it to its mass shell positive frequency components."
 In coordinate space. (his amount (o spread out the della function to a full solution of the Wlein Gordon equation. which as ils happens al Gime or? is concentrated around τὰ bui at other “mes is spread around the future and past light cones of (v...pP).," In coordinate space, this amount to spread out the delta function to a full solution of the Klein Gordon equation, which –as its happens– at time $x^{0}$ is concentrated around $\vec x$, but at other times is spread around the future and past light cones of $(\vec x,x^{0})$ ."
" The state [7.2py, is à physical state. and has a physical interpretation consistent with the dwnaiics: it is a (Ileisenberg) state in which the particle is in 7 at lime 20 and has appropriately moved around in space at other limes."," The state $|\vec x,x^{0}\rangle_{Ph}$ is a physical state, and has a physical interpretation consistent with the dynamics: it is a (Heisenberg) state in which the particle is in $\vec x$ at time $x^{0}$, and has appropriately moved around in space at other times."
 The transition amplitude between (wo such states is a physically meaningful quantity., The transition amplitude between two such states is a physically meaningful quantity.
 Iideed. 1 is nothing else that the familiar propagator in Minkowski space.," Indeed, it is nothing else that the familiar propagator in Minkowski space."
 But notice Lad Namely (he propagator is nothing but the matrix element of the projector operator {2 between the states |.c)!," But notice that Namely the propagator is nothing but the matrix element of the projector operator $P$ between the states $|\vec x,x^{0}\rangle$!"
 It is clear that the structure illustrated is (he precisely the same as in quantum gravitv., It is clear that the structure illustrated is the precisely the same as in quantum gravity.
 A classical three-eeometry is determined by three degrees of lreeclom per space point., A classical three-geometry is determined by three degrees of freedom per space point.
 Two of these correspond to physical degrees of freedom of the gravitational field. in analogy with the dependent variable 7 above.," Two of these correspond to physical degrees of freedom of the gravitational field, in analogy with the dependent variable $\vec x$ above."
 The third is the independent temporal variable. in analogy with the iU variable in the example Therefore s. precisely as (r.c)includes the dependent as well as the independent (time) variables.," The third is the independent temporal variable, in analogy with the $x^{0}$ variable in the example Therefore $s$, precisely as $(\vec
x,x^{0})$includes the dependent as well as the independent (time) variables."
 The states |s) are quantum states concentrated at a single three-geometry., The states $|s\rangle$ are quantum states concentrated at a single three-geometry.
" Precisely as the states Lr.2). these are unphysical. because spacetime cannot be concentrated on a unique three-eeometry, in the very same sense in which a particle cannot be al a unique point of Minkowski space."," Precisely as the states $|\vec
x,x^{0}\rangle$, these are unphysical, because spacetime cannot be concentrated on a unique three-geometry, in the very same sense in which a particle cannot be at a unique point of Minkowski space."
 The projector P project à slate [s) into a physical state which spreads across three-geometries. and (he transition amplitude (2)) gives the amplitude of measuring the three-eeomelry corresponding to s after wehave measured the three geometry corresponding to s'.," The projector $P$ project a state $|s\rangle$ into a physical state which spreads across three-geometries, and the transition amplitude \ref{eq:W2}) ) gives the amplitude of measuring the three-geometry corresponding to $s$ after wehave measured the three geometry corresponding to $s'$ ."
 This amplitude is well defined and diffeomorphism invariant., This amplitude is well defined and diffeomorphism invariant.
their bispectrum is indeed large compared to the bispectrum value (see Appendix ?7)).,their bispectrum is indeed large compared to the bispectrum value (see Appendix \ref{appendix:wngvar}) ).
" We now present the results when the two populations of sources contribute to the signal at the frequencies 30, 90, 148, 219, 277, and 350 GHz."," We now present the results when the two populations of sources contribute to the signal at the frequencies 30, 90, 148, 219, 277, and 350 GHz."
" To do so, we simply add the simulated maps at each frequency."," To do so, we simply add the simulated maps at each frequency."
" We illustrate the angular bispectrum dependence on frequency for one single configuration, namely equilateral, see Fig. 8.."," We illustrate the angular bispectrum dependence on frequency for one single configuration, namely equilateral, see Fig. \ref{equibisp-IRAD}."
 The frequency behaviour is as expected from an independent combination of the IR and RAD bispectra., The frequency behaviour is as expected from an independent combination of the IR and RAD bispectra.
 The radio source contribution dominates at low frequencies 30 and 90 GHz (blue and purple lines) and its bispectrum is flat., The radio source contribution dominates at low frequencies 30 and 90 GHz (blue and purple lines) and its bispectrum is flat.
 Infrared galaxies dominate at the highest frequencies 277 and 350 GHz (black and red upper lines) and show the characteristic power-law dependence due to clustering followed by a flattening of the bispectrum., Infrared galaxies dominate at the highest frequencies 277 and 350 GHz (black and red upper lines) and show the characteristic power-law dependence due to clustering followed by a flattening of the bispectrum.
 At intermediate frequencies both populations contribute to the signal., At intermediate frequencies both populations contribute to the signal.
 The clustering-induced term of IR-galaxies dominates on large angular scale while the random-noise term of radio-galaxies dominates at small angular scale., The clustering-induced term of IR-galaxies dominates on large angular scale while the random-noise term of radio-galaxies dominates at small angular scale.
 The cross-over between radio and IR-galaxy bispectra is shifted to higher £s with increasing frequency., The cross-over between radio and IR-galaxy bispectra is shifted to higher $\ell$ s with increasing frequency.
 It is worth noting in Fig., It is worth noting in Fig.
" 9 that at the lowest multipoles and at highest frequencies, the IR galaxies produce a bispectrum at least 10 times more important than the radio sources."," \ref{speconfratio} that at the lowest multipoles and at highest frequencies, the IR galaxies produce a bispectrum at least 10 times more important than the radio sources."
As noted. cartier. the luminosity function. presented. in Section 4.2. is expected. to. sulfer from. Malmequist-tvpe biases. and. we were not able to estimate the uncertainty on it.,"As noted earlier, the luminosity function presented in Section \ref{sec:obsphi} is expected to suffer from Malmquist-type biases, and we were not able to estimate the uncertainty on it."
" Biases in luminosity functions computed by the LiVines method are discussed in detail by Geijoetal.(2006)... and ""Torresetal."," Biases in luminosity functions computed by the $1/V_{max}$ method are discussed in detail by \\cite{StobieIshidaPeacock89}, , \cite{Geijo06}, and \cite{Torres07}."
 (2007).. Stobieetal.(1989). show that even when unbiased distance estimates are used. Φ is still biased.," \cite{StobieIshidaPeacock89} show that even when unbiased distance estimates are used, $\Phi$ is still biased."
 In order to correct for these ellects. we have to assume a functional form for the true luminosity function.," In order to correct for these effects, we have to assume a functional form for the true luminosity function."
 We will model it as a power lav. and then determine the power law index that best reproduces the observations we have.," We will model it as a power law, and then determine the power law index that best reproduces the observations we have."
 In the same wav as described in Section 3.2.3.. we populate a mocdel galaxy with CVs from an input luminosity function: here the form is for the range 28.2<log(Lx/ergs+)32.0. and —0 elsewhere. (in practice. of course the input ᾧ is discrete).," In the same way as described in Section \ref{sec:test}, we populate a model galaxy with CVs from an input luminosity function; here the form is for the range $28.2<\mathrm{log}(L_X/\mathrm{erg\,s^{-1}})<32.0$, and $\Phi=0$ elsewhere (in practice, of course the input $\Phi$ is discrete)."
 Using the [ux limit and area of the combined RBS and NEP survey. we then find the sample that would be detected and calculate an output exactly as in Section 4.2..," Using the flux limit and area of the combined RBS and NEP survey, we then find the sample that would be detected and calculate an output $\Phi$ exactly as in Section \ref{sec:obsphi}."
" Errors in Lx similar to those of the real CV sample are assigned to the ""detected"" CVs (these errors are Gaussian in loe(Lx). which is not quite the case for all the real svstenis: see Table 1))."," Errors in $L_X$ similar to those of the real CV sample are assigned to the “detected” CVs (these errors are Gaussian in $\mathrm{log}(L_X)$, which is not quite the case for all the real systems; see Table \ref{tab:distances}) )."
" For à given input 9. we repeat this many times (note that he ""detected? CV samples do not all have the same size)."," For a given input $\Phi$, we repeat this many times (note that the “detected” CV samples do not all have the same size)."
 Then we compare the distribution of the output in every Lx in with the observed & presented in Section 4.2.., Then we compare the distribution of the output in every $L_X$ bin with the observed $\Phi$ presented in Section \ref{sec:obsphi}.
 We vary the power-law index o. to find the best input «b.," We vary the power-law index $\alpha$, to find the best input $\Phi$."
 Phe normalization constant is fixed (for a given a) so that he integral of Φ over the range 20.8<log(Lx/eres31.8 is the same for the assumed input as for the observed cb. plotted in Fig. 3..," The normalization constant is fixed (for a given $\alpha$ ) so that the integral of $\Phi$ over the range $29.8<\mathrm{log}(L_X/\mathrm{erg\,s^{-1}})<31.8$ is the same for the assumed input as for the observed $\Phi$, plotted in Fig. \ref{fig:obsphi}."
 The position of the faint cutolf in he input @ is not importantwe would obtain the same result if it extended. to fainter Ly., The position of the faint cutoff in the input $\Phi$ is not important—we would obtain the same result if it extended to fainter $L_X$.
 However. allowing the input & to be non-zero to log(LyJeres1jzo32 results in output. values much higher than the data in the brightest [ow Lx bins (the brightest position of the ο consistent with the data depends on the the power lav index. but we performed only a single-parameter fit. with both bright and faint cutoll Ly fixed. because the calculations are computationally expensive).," However, allowing the input $\Phi$ to be non-zero to $\mathrm{log}(L_X/\mathrm{erg\,s^{-1}}) \ga 32$ results in output values much higher than the data in the brightest few $L_X$ bins (the brightest position of the cutoff consistent with the data depends on the the power law index, but we performed only a single-parameter fit, with both bright and faint cutoff $L_X$ fixed, because the calculations are computationally expensive)."
" We use a single scale height in these simulations (260 pe). because Ly is the only. property that à simulated €V has (we cannot assign an age. because. as mentioned before in Section 2> Ly is not a clean indicator of 2,4)."," We use a single scale height in these simulations (260 pc), because $L_X$ is the only property that a simulated CV has (we cannot assign an age, because, as mentioned before in Section \ref{sec:xlum}, $L_X$ is not a clean indicator of $P_{orb}$ )."
" Since the ""detected"" CV. samples in these simulations are subject to the same selection criteria as the real sample. they are allected by Alalmeauist-type biases in the same wav as the data."," Since the “detected” CV samples in these simulations are subject to the same selection criteria as the real sample, they are affected by Malmquist-type biases in the same way as the data."
 Therefore. to the extent that our simple Galaxy model is suitable. the best-estimate power-law index. found by comparing these simulations to the observations. is unbiased.," Therefore, to the extent that our simple Galaxy model is suitable, the best-estimate power-law index, found by comparing these simulations to the observations, is unbiased."
 The assumed « resulting. in the best-fit model output is shown in Fig. 5..," The assumed $\Phi$ resulting in the best-fit model output is shown in Fig. \ref{fig:obssimphi},"
 together with the output from the simulation. as well the observed 9 [rom Section. 4.2..," together with the output from the simulation, as well the observed $\Phi$ from Section \ref{sec:obsphi}."
 We lind à—0.80dE0.05. where the error on à. is based on 4? increasing by 1.," We find $\alpha=-0.80 \pm 0.05$, where the error on $\alpha$ is based on $\chi^2$ increasing by 1."
 For this best-fit. the reduced X7 is 1.1.," For this best-fit, the reduced $\chi^2$ is 1.1."
 Note that the output is lower than input P at the faint end: this is the expected elfect of the [ux limit., Note that the output is lower than input $\Phi$ at the faint end; this is the expected effect of the flux limit.
 Also. at the bright end. the sharp cutolf in the input is not recovered. because of error in Ly.," Also, at the bright end, the sharp cutoff in the input is not recovered, because of error in $L_X$."
 We expect that the errors on the out from these simulations give a reliable indication of the put.uncertainty on the observed. o., We expect that the errors on the output from these simulations give a reliable indication of the uncertainty on the observed $\Phi$.
 This calculation also allows us to check the distribution in height above the Galactic plane of the CV. sample., This calculation also allows us to check the distribution in height above the Galactic plane of the CV sample.
 Since it is a high Galactic latitude. Uusx-limitecl sample. it is not expected to have the same z-distribution as the underlving population.," Since it is a high Galactic latitude, flux-limited sample, it is not expected to have the same $z$ -distribution as the underlying population."
 Llowever. we can check that the observed: sample is consistent with the assumed. Galaxy model.," However, we can check that the observed sample is consistent with the assumed Galaxy model."
 Using the best-fit power law input . we construct a smooth. cumulative probability distribution function for >. from many “detected” CV. samples.," Using the best-fit power law input $\Phi$, we construct a smooth cumulative probability distribution function for $z$, from many “detected” CV samples."
 We then use a Ixolmogorov-Smirnov (INS) test to compare this to the z-distribution of the real sample of 20 systems: this is done many times. in order to sample the large errors in z of the real CVs.," We then use a Kolmogorov-Smirnov (KS) test to compare this to the $z$ -distribution of the real sample of 20 systems; this is done many times, in order to sample the large errors in $z$ of the real CVs."
 We find that the probability that the moclel ancl observed distributions are drawn from the same parent population is 0.56. for our model seale-height of 260. pc.," We find that the probability that the model and observed distributions are drawn from the same parent population is 0.56, for our model scale-height of 260 pc."
 Given that theobserved: sample is small. this is not a," Given that theobserved sample is small, this is not a"
funnelecl into this phase space if the collisions discussed in 2 and3 are to plausibly account lor the existence of 0-3.,funneled into this phase space if the collisions discussed in \ref{sec:anal} and \ref{sec:numer} are to plausibly account for the existence of S0-2.
 Gerhard(2001) suggested Chat the Hel stars in (he central parsec of the Galactic center were born in a 104—LO’AL. cluster that was formed more than 30pc away [rom Sag A* (like the Arches and Quintuplet clusters)., \citet{gerhard} suggested that the HeI stars in the central parsec of the Galactic center were born in a $10^4-10^6M_\odot$ cluster that was formed more than 30pc away from Sag A* (like the Arches and Quintuplet clusters).
 The cluster sank inward to Sag À* due to dynamical friction and was tidally disrupted by (he massive black hole. (lus leaving massive stars within the central parsec.," The cluster sank inward to Sag A* due to dynamical friction and was tidally disrupted by the massive black hole, thus leaving massive stars within the central parsec."
 Consider a cluster of mass M4 ancl velocity dispersion σοι that has been formed outside the central pe of the Galactic center., Consider a cluster of mass $M_\cl$ and velocity dispersion $\sigma_\cl$ that has been formed outside the central pc of the Galactic center.
 Dy (the virial theorem. it will have an elfective radius Ry~GMa/o4.," By the virial theorem, it will have an effective radius $R_\cl\sim G M_\cl/\sigma_\cl^2$."
 The cluster will sink by dynamical friction until it is tidallv ripped apart at a separation from Ser Αν ry. For a star from this disrupted cluster to come within qii of Ser A*. it must have angular momentum J<(26Mundin4/7. and therefore transverse velocity ο<(OGMungini)7/rg.," The cluster will sink by dynamical friction until it is tidally ripped apart at a separation from Sgr A*, $r_d$, For a star from this disrupted cluster to come within $q_\init$ of Sgr A*, it must have angular momentum $J<(2GM_\bh q_\init)^{1/2}$, and therefore transverse velocity $v_\perp < (2GM_\bh q_\init)^{1/2}/r_d$."
 Ilence. where (ire=(CM/rj)? is the circular speed at breakup and vy=6450kms as the velocity at. peribothron.," Hence, where $v_\circ=(G M/r_d)^{1/2}$ is the circular speed at breakup and $v_q=6450\,\kms$ is the velocity at peribothron."
 Hence. if (he cluster is on a roughly circular orbit when it is disrupted. then essentially none of its stars will have a close passage to Ser A*.," Hence, if the cluster is on a roughly circular orbit when it is disrupted, then essentially none of its stars will have a close passage to Sgr A*."
 On the other hand. if the cluster is on a roughly racial orbit. then a traction will have close passages.," On the other hand, if the cluster is on a roughly radial orbit, then a fraction $f\sim 1 - \exp[(-q v_q/r_d\sigma_\cl)^2/2]$ will have close passages."
 That is. so that lor parameters (hat are plausible for a cluster lormed in the deep eravitational well of the Galactic center. a substantial fraction of its members could come within following a radial-orbit disruption.," That is, so that for parameters that are plausible for a cluster formed in the deep gravitational well of the Galactic center, a substantial fraction of its members could come within $q_\init\sim 130\,\au$ following a radial-orbit disruption."
 In the above example. a massive-star cluster wilh Ma~LOPAL. would contain of order 107 100AL. stars.," In the above example, a massive-star cluster with $M_\cl\sim 10^4\,M_\odot$ would contain of order $10^2$ $100\,M_\odot$ stars."
 OF these 1/3 would come within q=130AU of Ser Α and as estimated above. of order of these might kick out companions onto S0-2-lke orbits.," Of these 1/3 would come within $q=130\,\au$ of Sgr A* and as estimated above, of order of these might kick out companions onto S0-2-like orbits."
 Over the lifetime of S0-2. several such clusters might form and disrupt.," Over the lifetime of S0-2, several such clusters might form and disrupt."
 Assuming that these clusters were on radial orbits. thev are a plausible source ol S0-2-like stars.," Assuming that these clusters were on radial orbits, they are a plausible source of S0-2-like stars."
 The final question then is whether it is plausible (hat such clusters will find themselves on radial orbits., The final question then is whether it is plausible that such clusters will find themselves on radial orbits.
 To address (his question. we first show Chat for a power-law density prolile," To address this question, we first show that for a power-law density profile"
pulsars in that area of the sky that could also be plausible gamma-ray sources were therefore discovered before llaunch. especially when adding those discovered in deep pointed observations of known pulsar wind nebulae (e.g..Camiloetal. 2002).,"pulsars in that area of the sky that could also be plausible gamma-ray sources were therefore discovered before launch, especially when adding those discovered in deep pointed observations of known pulsar wind nebulae \citep[e.g.,][]{cmgl02}."
. In time. several of these pulsars were detected by LAT (e.g..Abdoetal.2010d).," In time, several of these pulsars were detected by LAT \citep[e.g.,][]{abdo11}."
. Subsequent to the Parkes multibeam survey an even deeper Parkes survey extended Galactic plane coverage out to /=60° (Camilo et al..," Subsequent to the Parkes multibeam survey an even deeper Parkes survey extended Galactic plane coverage out to $l = 60\arcdeg$ (Camilo et al.,"
" in preparation). and the on-going PALFA Arecibo survey is doing so out to /z75"" (Cordesetal.20006)."," in preparation), and the on-going PALFA Arecibo survey is doing so out to $l \approx 75\arcdeg$ \citep{cfl+06}."
". In our view. the above suggests that the answer to ""why have more radio pulsars not been detected among the unidentified Galactic plane LAT sources?"""," In our view, the above suggests that the answer to “why have more radio pulsars not been detected among the unidentified Galactic plane LAT sources?”"
 is that the vast majority of ordinary radio pulsars accessible to the current generation of telescopes and located within a few degrees of the plane at /X75° that can yield an appreciable gamma-ray flux at the Earth were discovered a long time ago (it is possible that in rare but important cases very high L. distant pulsars will have their radio pulses scattered beyond practical detectability)., is that the vast majority of ordinary radio pulsars accessible to the current generation of telescopes and located within a few degrees of the plane at $l \la 75\arcdeg$ that can yield an appreciable gamma-ray flux at the Earth were discovered a long time ago (it is possible that in rare but important cases very high $L_{\gamma}$ distant pulsars will have their radio pulses scattered beyond practical detectability).
 Many of the LAT sources that remain unidentified along the Galactic plane are surely pulsars — but they may not be detectable asradio sources. and should be searched anew in gamma rays (someofthesemaybeinbinaries.andinacces-sibletocurrentblindsearches:see.e.g..Corbetetal. 2011).," Many of the LAT sources that remain unidentified along the Galactic plane are surely pulsars — but they may not be detectable asradio sources, and should be searched anew in gamma rays \citep[some of
these may be in binaries, and inaccessible to current blind searches;
see, e.g.,][]{cck+11}."
. iis bright enough that it would have been discovered in blind searches of 18 months of LAT data. if the photon selection criteria had been adjusted to take into account its flat spectrum (e.g.. if only photons with E=0.8 GGeV had been searched for pulsations). as we confirmed after discovery.," is bright enough that it would have been discovered in blind searches of 18 months of LAT data, if the photon selection criteria had been adjusted to take into account its flat spectrum (e.g., if only photons with $E\ga0.8$ GeV had been searched for pulsations), as we confirmed after discovery."
 Spectral analysis of a region can improve the signal-to-noise ratio by selecting events based on the probability that they come from the source of interest (seeBelfiore2011).. and applying this technique to the Cygnus region also resulted in the unbiased detection of pulsations fromJ203043641.," Spectral analysis of a region can improve the signal-to-noise ratio by selecting events based on the probability that they come from the source of interest \citep[see][]{bel11}, and applying this technique to the Cygnus region also resulted in the unbiased detection of pulsations from."
. For fainter point sources superimposed on the large and uncertain diffuse Galactic background. spectral analysis and localization are harder wwas only 0/4 from the actual pulsar position). but these and other improvements in search techniques are already resulting in the discovery of many more gamma-ray pulsars2011).," For fainter point sources superimposed on the large and uncertain diffuse Galactic background, spectral analysis and localization are harder was only $0\farcm4$ from the actual pulsar position), but these and other improvements in search techniques are already resulting in the discovery of many more gamma-ray pulsars."
. As a consequence. the ratio of known gamma-ray-only to gamma-ray-and-radio ordinary pulsars. which is currently slightly under 1.0. should increase substantially.," As a consequence, the ratio of known gamma-ray-only to gamma-ray-and-radio ordinary pulsars, which is currently slightly under 1.0, should increase substantially."
 When will we ever learn all that we can (in the eera) about the geometry and emission properties of gamma-ray and radio pulsar accelerators?, When will we ever learn all that we can (in the era) about the geometry and emission properties of gamma-ray and radio pulsar accelerators?
 Perhaps when full details emerge from the continuing collaborative radio and gamma-ray observational and modeling work., Perhaps when full details emerge from the continuing collaborative radio and gamma-ray observational and modeling work.
 The future is bright (at some wavelength). but requires publication of all searches. including radio non-detections. and consideration of the detection by LAT of radio pulsars with very large E flux at the Earth (e.g..Romanietal.2011).," The future is bright (at some wavelength), but requires publication of all searches, including radio non-detections, and consideration of the non-detection by LAT of radio pulsars with very large $\dot E$ flux at the Earth \citep[e.g.,][]{rkc+11}."
. The GBT is operated by the National Radio Astronomy Observatory. a facility of the National Science Foundation operated under cooperative agreement by Associated Universities. Inc. The LLAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis.," The GBT is operated by the National Radio Astronomy Observatory, a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. The LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis."
 These include the National Aeronautics and Space Administration (NASA) and the Department of Energy in the United States. the Commissariat à l'Energie Atomique and the Centre National de la Recherche Sctentifique/Institut National de Physique Nucléaaire et de Physique des Particules in France. the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy. the Ministry of Education. Culture. Sports. Science and Technology (MEXT). High Energy Accelerator Research Organization (KEK) and. Japan Aerospace Exploration Agency (JAXA) in Japan. and the K. A. Wallenberg Foundation. the Swedish Research Council and the Swedish National Space Board in Sweden.," These include the National Aeronautics and Space Administration (NASA) and the Department of Energy in the United States, the Commissariat à l'Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the Swedish National Space Board in Sweden."
 Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PFO-110073 issued by the Chandra X-ray Observatory Center. which 1s operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. (LAT).. (," Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PF0-110073 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. , ,"
 Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PFO-110073 issued by the Chandra X-ray Observatory Center. which 1s operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. (LAT).. (G," Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PF0-110073 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. , ,"
 Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PFO-110073 issued by the Chandra X-ray Observatory Center. which 1s operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. (LAT).. (GU," Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PF0-110073 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. , ,"
 Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PFO-110073 issued by the Chandra X-ray Observatory Center. which 1s operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. (LAT).. (GUP," Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PF0-110073 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. , ,"
 Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PFO-110073 issued by the Chandra X-ray Observatory Center. which 1s operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. (LAT).. (GUPP," Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PF0-110073 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. , ,"
 Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PFO-110073 issued by the Chandra X-ray Observatory Center. which 1s operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. (LAT).. (GUPPD," Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PF0-110073 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. , ,"
 Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PFO-110073 issued by the Chandra X-ray Observatory Center. which 1s operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. (LAT).. (GUPPD.," Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PF0-110073 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. , ,"
 Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PFO-110073 issued by the Chandra X-ray Observatory Center. which 1s operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. (LAT).. (GUPPD..," Support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PF0-110073 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. , ,"
The qualitative treuds in our results could have been auticipated ou the basis of previous studies of the influence of the IME aud the sar formation history ou the calibratlo1 of luminosity densities ist terms of star formaion rates (e.g.Schaerer1999).,The qualitative trends in our results could have been anticipated on the basis of previous studies of the influence of the IMF and the star formation history on the calibration of luminosity densities in terms of star formation rates \citep[e.g.][]{Sch99}.
. Our study slows quaUitatively that 1tempts to infer the SFR cleusity locally ane over a range of redshifts cau be conipromised by the p'eselice [9]. dillerent. galaxy tyyes. whose inix evolves clifferentialy.," Our study shows quantitatively that attempts to infer the SFR density locally and over a range of redshifts can be compromised by the presence of different galaxy types, whose mix evolves differentially."
 Such differentlal evolutiou is 1 almost inevitable consecuetrce of models jsed ou pure IuimiOs]ty evolution Or. iuceed. other cescriptiois of cosmic evolution.," Such differential evolution is an almost inevitable consequence of models based on pure luminosity evolution or, indeed, other descriptions of cosmic evolution."
 lusofar as t1e uocel of Pozzettielal.(1996). is M7dical iu respect M its indXlure of galaxy types. systematic er‘ors can be anticipaec of the order of a [actor of at least 2 1 tli the absolute vaue of SFR aidini s relative evouti=ou in 0aot2.," Insofar as the model of \citet{Poz96} is typical in respect of its mixture of galaxy types, systematic errors can be anticipated of the order of a factor of at least 2 in both the absolute value of SFR and in its relative evolution in $0 < z < 2$."
 Some of the intriusic p'obleijs that arise from the adoption of fixed calibratioik icbors for the relation between SFR deisly and luminosity deisity can be partially acdressed by cotypuine the luminosity deusity explicitly rou a model universe for comparison wih observatious (cL., Some of the intrinsic problems that arise from the adoption of fixed calibration factors for the relation between SFR density and luminosity density can be partially addressed by computing the luminosity density explicitly from a model universe for comparison with observations (cf.
 Figure 1))., Figure \ref{fig:ldens}) ).
 At irst sielt. the inconsistency between the SFR inferred [roi1 200 win aud ccalibraIOUS COLkd be regardede as a serious problem.," At first sight, the inconsistency between the SFR inferred from 200 nm and calibrations could be regarded as a serious problem."
 However. the cdillereice between the two values Contains potentialy useful diaguostic power regardiug tlie star foruation history.," However, the difference between the two values contains potentially useful diagnostic power regarding the star formation history."
 €)bservations of a variety of differeut cliaguostics of the star formation rate in a saliple of galaxies «οι] provide a more robusly corstrained star formation |istory. by allowing the cdeteruiration of other important factors (suchi as tvpe-specilic ΤΙΜΕΣ).," Observations of a variety of different diagnostics of the star formation rate in a sample of galaxies could provide a more robustly constrained star formation history, by allowing the determination of other important factors (such as type-specific IMFs)."
 However. the uumber of star ormation diaguosties accessible to observatiou is not large. and there are 1iany parameters to be c«yustraineck.," However, the number of star formation diagnostics accessible to observation is not large, and there are many parameters to be constrained."
 Clearly. tle possible existence of type-specilic INES aud star-formation histories presen sa slgnificaut Challenge to any systelnat16 investigation of the COSLDIC evoution of star formation.," Clearly, the possible existence of type-specific IMFs and star-formation histories presents a significant challenge to any systematic investigation of the cosmic evolution of star formation."
 We wis 110 thank Michael Rowan-Robiuson for helpful comments aud SugeestMODLOLS., We wish to thank Michael Rowan-Robinson for helpful comments and suggestions.
 JA eratefully ackuowledges support in the form of a seiolarship from the Scieuce aud Technology. Foundation (ECT. Portigal) through Program Praxis XXI.," JA gratefully acknowledges support in the form of a scholarship from the Science and Technology Foundation (FCT, Portugal) through Program Praxis XXI."
"units the correlation strength of the excursion set regions per Gaussian expectations (left panel), the difference (middle panel) and the ratio (right panel) between the clustering of hot and cold pixels when |v|=2.00.","units the correlation strength of the excursion set regions per Gaussian expectations (left panel), the difference (middle panel) and the ratio (right panel) between the clustering of hot and cold pixels when $|\nu|=2.00$."
 No smoothing is applied., No smoothing is applied.
" Shaded areas represent the 1 and 2σ zones, while different symbols are used for different values of fwr, as specified in the plots."," Shaded areas represent the 1 and $\sigma$ zones, while different symbols are used for different values of $f_{\rm NL}$, as specified in the plots."
" When fwr,=100, departures from Gaussianity lie always below the lo level, unlike for the abundance case (see Figure 5 for a direct comparison)."," When $f_{\rm NL}=100$, departures from Gaussianity lie always below the $\sigma$ level, unlike for the abundance case (see Figure \ref{nd_sigma_distances_fig}
 for a direct comparison)."
 The situation does not improve significantly if we consider the clustering difference or ratio between hot and cold patches., The situation does not improve significantly if we consider the clustering difference or ratio between hot and cold patches.
" Only when fwri=500 there is a noticeable effect, which exceeds 2c around the Doppler scale, at 0~Τὸ arcmin."," Only when $f_{\rm NL}=500$ there is a noticeable effect, which exceeds $\sigma$ around the Doppler scale, at $\theta \simeq 75$ arcmin."
" 'The scatter in the clustering strength is mainly due to cosmic variance, which causes large fluctuations among different full-sky realizations (m- and £-modes)."," The scatter in the clustering strength is mainly due to cosmic variance, which causes large fluctuations among different full-sky realizations $m$ - and $\ell$ -modes)."
" As a result, errorbars are large."," As a result, errorbars are large."
" To minimize its effect, we propose a statistical test, which involves the clustering information alone."," To minimize its effect, we propose a statistical test, which involves the clustering information alone."
 The procedure can be summarized as follows., The procedure can be summarized as follows.
"perpendicular and parallel to the line of sight: r=r,+r) aud k=ky,+kj.",perpendicular and parallel to the line of sight: $\rr=\rr_p+\rr_\parallel$ and $\kk=\kk_p+\kk_\parallel$.
 The projected 2PCFE is obtained by integrating £(r) aloug the line of sight. After substitutiug‘ equation1 (1)) into equation1 (2)) and Iputting‘ variables into the form of perpeucdicular aud parallel components. we have Equation (1)) follows (rom equation (3)) because the rightmost integral in equation (3)) is just 27 times the Dirac à-[uuction Oph).," The projected 2PCF is obtained by integrating $\xi(\rr)$ along the line of sight, After substituting equation \ref{eqn:xi}) ) into equation \ref{eqn:wp}) ) and putting variables into the form of perpendicular and parallel components, we have Equation \ref{eqn:wp_b}) ) follows from equation \ref{eqn:wp_a}) ) because the rightmost integral in equation \ref{eqn:wp_a}) ) is just $2\pi$ times the Dirac $\delta$ -function $\delta_D(k_\parallel)$."
 Equation (1)) states that the projected 2PCF is the two-climeusioual Fourler transform of the power spectrum. and because we have projected out redshift-space distortions. we can use the isotropic. real-space P(&) tu the integral.," Equation \ref{eqn:wp_b}) ) states that the projected 2PCF is the two-dimensional Fourier transform of the power spectrum, and because we have projected out redshift-space distortions, we can use the isotropic, real-space $P(k)$ in the integral."
 We cau evaluate equation (1)) in polar coordinates., We can evaluate equation \ref{eqn:wp_b}) ) in polar coordinates.
 The augular part can be caleulatecl by using the expausiou expGkr)=ὃνmAn(heryexplin(o—&)] (plane waves in terms of cylindrical waves). where Oo—@ is the angle between k and x aud μα) is the Bessel function of integer order.," The angular part can be calculated by using the expansion $\exp(i\kk \bcdot \rr) = \sum_{n=-\infty}^{+\infty} J_n(kr)i^n
\exp[in(\phi-\Phi)]$ (plane waves in terms of cylindrical waves), where $\phi-\Phi$ is the angle between $\kk$ and $\rr$ and $J_n(x)$ is the Bessel function of integer order."
 Finally. equation (1)) reduces to a one-climenusional integral. This equation mimics the relation for the real-space. tliree-diimiensioual 2PCF which involves the spherical Bessel function jyGr).," Finally, equation \ref{eqn:wp_b}) ) reduces to a one-dimensional integral, This equation mimics the relation for the real-space, three-dimensional 2PCF which involves the spherical Bessel function $j_0(x)$."
 This kind of result can be found in papers that deal with projected observations. such as variants of Limber's equation (e.g.. Baugh&Elstathiou 1993)).," This kind of result can be found in papers that deal with projected observations, such as variants of Limber's equation (e.g., \citealt{Baugh93}) )."
 The projected 3PCFs cau be derived in a similar way to the 2PCFEs., The projected 3PCFs can be derived in a similar way to the 2PCFs.
" The three-cimensional 3PCF is the Fourier transform of the bispectrum B(k,.ko.k3). The Dirac 6-fuuctionu selects wavevectors (Kj.ko.κι) that form a triangle."," The three-dimensional 3PCF is the Fourier transform of the bispectrum $B(\kk_1,\kk_2,\kk_3)$, The Dirac $\delta$ -function selects wavevectors $(\kk_1,\kk_2,\kk_3)$ that form a triangle."
 From now on. we adopt the notation that a subscript of one number represents one side lor a wavevector triaugle. while it represents oue vertex lor a real-space triangle.," From now on, we adopt the notation that a subscript of one number represents one side for a wavevector triangle, while it represents one vertex for a real-space triangle."
 Each side of a real-space triangle is denoted by subscript of two numbers. e.g.. rjj—rjrj; G27= 1.2.3).," Each side of a real-space triangle is denoted by subscript of two numbers, e.g., $\rr_{ij}=\rr_i-\rr_j$ $i, j=1, 2, 3$ )."
 Equation (6)) reduces to, Equation \ref{eqn:xithree_a}) ) reduces to
Fig.,Fig.
 4. shows the average cumulative mass function M(V) derived from the phase space density distribution for the spheroidal components in the local Universe with masses of ~5x10'M.., \ref{fig:builde} shows the average cumulative mass function $M(V)$ derived from the phase space density distribution for the spheroidal components in the local Universe with masses of $\sim 5 \times 10^{10} M_\odot$.
 Also shown on this figure is the average M(V) curve derived from all the galaxies in the sample with total stellar masses between 1x10*M.. and 5x109M...," Also shown on this figure is the average $M(V)$ curve derived from all the galaxies in the sample with total stellar masses between $1 \times
10^8 M_\odot$ and $5 \times 10^8 M_\odot$."
 The individual galaxy curves that make up this latter average have been normalized by multiplying both M and V by the factor required to generate from them a system containing ~5x10A... of stars., The individual galaxy curves that make up this latter average have been normalized by multiplying both $M$ and $V$ by the factor required to generate from them a system containing $\sim 5 \times 10^{10} M_\odot$ of stars.
 Thus. it represents the M(V) curve of the progenitors of these higher-mass spheroids if the latter systems form from random galaxy mergers of the lower-mass systems.," Thus, it represents the $M(V)$ curve of the progenitors of these higher-mass spheroids if the latter systems form from random galaxy mergers of the lower-mass systems."
 The fact that M(V) for the small galaxies does not lie above the curve for the large spheroids at all values of V means that these functions violate the mixing inequality of Eq. (2)).," The fact that $M(V)$ for the small galaxies does not lie above the curve for the large spheroids at all values of $V$ means that these functions violate the mixing inequality of Eq. \ref{eq:mixing}) ),"
 so we can state quite generally that no combination of collisionless merger processes bringing small systems like these together could have produced the final large spheroids., so we can state quite generally that no combination of collisionless merger processes bringing small systems like these together could have produced the final large spheroids.
 In this case. it is interesting to note that the issue does not arise at the highest phase densities (lowest values of V). as the compact spheroidal components of the small galaxies provide more than enough stars at these densities to produce the bigger spheroids.," In this case, it is interesting to note that the issue does not arise at the highest phase densities (lowest values of $V$ ), as the compact spheroidal components of the small galaxies provide more than enough stars at these densities to produce the bigger spheroids."
 Rather 1t 15 at intermediate phase densities where one runs out of spheroid stars. but has yet to tap into the lower phase densities of disk stars. that the deficit arises.," Rather it is at intermediate phase densities where one runs out of spheroid stars, but has yet to tap into the lower phase densities of disk stars, that the deficit arises."
 As such. this apparent violation of the mixing theorem is somewhat harder to explain away than the original result comparing a single disk to a single spheroid. where the discrepancy occurs just in the extreme tail of the phase density distribution.," As such, this apparent violation of the mixing theorem is somewhat harder to explain away than the original result comparing a single disk to a single spheroid, where the discrepancy occurs just in the extreme tail of the phase density distribution."
 Although this violation of the mixing theorem is formally statistically significant — with samples of galaxies of this size. one can re-sample the distribution to get a good handle on the random errors in M(V) — it is nonetheless probably still not a major problem for the fundamental paradigm of hierarchical galaxy formation.," Although this violation of the mixing theorem is formally statistically significant – with samples of galaxies of this size, one can re-sample the distribution to get a good handle on the random errors in $M(V)$ – it is nonetheless probably still not a major problem for the fundamental paradigm of hierarchical galaxy formation."
 As with the single galaxy result. it only involves a rather small fraction of the total mass of the system. and a relatively minor addition of extra mass through star formation could reorder the curves.," As with the single galaxy result, it only involves a rather small fraction of the total mass of the system, and a relatively minor addition of extra mass through star formation could reorder the curves."
 In addition. presumably today’s large spheroids did not form from progenitors exactly akin to today’s small galaxies. so one might not expect this inequality to be met even if the large spheroids did form purely from collisionless mergers of pre-existing galaxies.," In addition, presumably today's large spheroids did not form from progenitors exactly akin to today's small galaxies, so one might not expect this inequality to be met even if the large spheroids did form purely from collisionless mergers of pre-existing galaxies."
 Indeed. there is now strong evidence that the structural parameters of even non-star-forming systems have evolved strongly over time (?.andreferencestherein)..," Indeed, there is now strong evidence that the structural parameters of even non-star-forming systems have evolved strongly over time \citep[][and references therein]{Williamsetal10}."
 Nonetheless. this example illustrates the potential power in using phase space constraints to study the possible evolutionary. paths that galaxies might follow. and where extra stars would have to be added in to allow other paths to be pursued.," Nonetheless, this example illustrates the potential power in using phase space constraints to study the possible evolutionary paths that galaxies might follow, and where extra stars would have to be added in to allow other paths to be pursued."
 It also underlines the point that there is more to such analyses than considering just the maximum phase density., It also underlines the point that there is more to such analyses than considering just the maximum phase density.
 In this paper. we have introduced a methodology for modeling the full stellar phase space density of any combination of disk and spheroidal stellar systems. including that which makes up the local galaxy population in the Universe.," In this paper, we have introduced a methodology for modeling the full stellar phase space density of any combination of disk and spheroidal stellar systems, including that which makes up the local galaxy population in the Universe."
 We have also discussed the general inequality that limits the possible ways in which this phase density distribution can evolve., We have also discussed the general inequality that limits the possible ways in which this phase density distribution can evolve.
 As we have seen. such analyses can make use of more than just the rather non-robust constraint provided by the maximum phase density. and offer a potentially powerful tool for determining the possible paths by which these systems could have evolved.," As we have seen, such analyses can make use of more than just the rather non-robust constraint provided by the maximum phase density, and offer a potentially powerful tool for determining the possible paths by which these systems could have evolved."
 Of necessity. the phase space model considered here has been rather simple. but the explosion of available data means that over time many of the simplifying assumptions can be eliminated.," Of necessity, the phase space model considered here has been rather simple, but the explosion of available data means that over time many of the simplifying assumptions can be eliminated."
 Large infrared surveys like Two Micron ΑΙ-Sky Survey offer a more direct window on the stellar mass distribution in galaxies. and its decomposition into disk and bulge components (e.g.?)..," Large infrared surveys like Two Micron All-Sky Survey offer a more direct window on the stellar mass distribution in galaxies, and its decomposition into disk and bulge components \citep[e.g.][]{MendezAbreuetal08}."
 Further. extensive spectroscopic studies of galaxies using integral field units (e.g.?) and detailed dynamical modeling of such data (e.g.?) mean that the simple generalized parameterizations of both the photometric and kinematic properties of galaxies can soon be replaced by reasonably direct. measurements of the phase-space density distribution on a galaxy-by-galaxy basis.," Further, extensive spectroscopic studies of galaxies using integral field units \citep[e.g.][]{Krajnovicetal06} and detailed dynamical modeling of such data \citep[e.g.][]{DeLorenzietal08} mean that the simple generalized parameterizations of both the photometric and kinematic properties of galaxies can soon be replaced by reasonably direct measurements of the phase-space density distribution on a galaxy-by-galaxy basis."
 Aother obvious direction in which to extend this analysis is to the more distant Universe., Another obvious direction in which to extend this analysis is to the more distant Universe.
" At these greater distances. it is challenging to obtain the necessary high-quality photometric and kinematic observations. but steps are already being taken both to determine the distribution of light within such distant galaxies (e.g.?).. and in establishing at least the broad kinematic scaling relations analogous to those used here (e.g. ?,."," At these greater distances, it is challenging to obtain the necessary high-quality photometric and kinematic observations, but steps are already being taken both to determine the distribution of light within such distant galaxies \citep[e.g.][]{HuertasCompanyetal07}, and in establishing at least the broad kinematic scaling relations analogous to those used here \citep[e.g.][]{MacArthuretal08}."
 Comparison between the phase density distributions of stars in distant galaxies and that in the local Universe will allow à more direct test as to which evolutionary paths are available to galaxies of different types., Comparison between the phase density distributions of stars in distant galaxies and that in the local Universe will allow a more direct test as to which evolutionary paths are available to galaxies of different types.
" It also offers the prospect of a new perspective on the star formation history of the Universe. in that by determining the phase densities of stars that have to be added over time so as to avoid violation of the mixing constraint. we will be able to go beyond the simple numbers game of how many stars form at different epochs to learn about the smaller-scale environments in which these stars must have formed,"," It also offers the prospect of a new perspective on the star formation history of the Universe, in that by determining the phase densities of stars that have to be added over time so as to avoid violation of the mixing constraint, we will be able to go beyond the simple numbers game of how many stars form at different epochs to learn about the smaller-scale environments in which these stars must have formed."
Understanding the rotation of gravitationally interacting bodies with an ever increasing accuracy is an important challenge of celestial mechanics.,Understanding the rotation of gravitationally interacting bodies with an ever increasing accuracy is an important challenge of celestial mechanics.
" Many authors have modelled with very good accuracy the rotation of the Earth as Woolard (1953), Kinoshita (1977)."," Many authors have modelled with very good accuracy the rotation of the Earth as Woolard (1953), Kinoshita (1977)."
" The other planets of the Solar system followed logically (see for instance Yoder, 1997; Rambaux, 2007)."," The other planets of the Solar system followed logically (see for instance Yoder, 1997; Rambaux, 2007)."
" Today thanks to new and very precise observational astrometric techniques the dynamical study of celestial bodies extended to comets, asteroids and satellites (Meyer, 2008; Sinclair, 1977; Wisdom, 1984, 1987)."," Today thanks to new and very precise observational astrometric techniques the dynamical study of celestial bodies extended to comets, asteroids and satellites (Meyer, 2008; Sinclair, 1977; Wisdom, 1984, 1987)."
" Nevertheless a few studies have been made on the rotational motion of Phoebe, the ninth satellite of Saturn, since its discovery in 1899 by W.H Pickering."," Nevertheless a few studies have been made on the rotational motion of Phoebe, the ninth satellite of Saturn, since its discovery in 1899 by W.H Pickering."
" In 1905, F.Ross etablished that this motion is retrograde and gave for the first time the orbital elements refering to the mean equinox and ecliptic of date."," In 1905, F.Ross etablished that this motion is retrograde and gave for the first time the orbital elements refering to the mean equinox and ecliptic of date."
 Jacobson (1998) determined new orbital elements thanks to Earth based astrometric observations from 1904 to 1996., Jacobson (1998) determined new orbital elements thanks to Earth based astrometric observations from 1904 to 1996.
 More recently Emelyanov(2007) elaborated ephemerides of Phoebe from 1904 to 2027., More recently Emelyanov(2007) elaborated ephemerides of Phoebe from 1904 to 2027.
" Others studies have been made on the composition and the inertial parameters of Phoebe (Aleshkina et al.,"," Others studies have been made on the composition and the inertial parameters of Phoebe (Aleshkina et al.,"
 2010)., 2010).
" Phoebe is the only non-synchronous satellite of Saturn with rather well known physical parameters, as the moments of inertia."," Phoebe is the only non-synchronous satellite of Saturn with rather well known physical parameters, as the moments of inertia."
 As Phoebe is a dissymetric body (large dynamical flattening and large triaxiality) it is interesting to study its rotation., As Phoebe is a dissymetric body (large dynamical flattening and large triaxiality) it is interesting to study its rotation.
" Here for the first time, we propose to determine the combined motion of precession and nutation of Phoebe considered as a rigid body."," Here for the first time, we propose to determine the combined motion of precession and nutation of Phoebe considered as a rigid body."
" After presenting the model (Sect.??)), we describe the orbital motion of Phoebe by fitting the curves of the temporal variations of the orbital elements a,e,M and L, with polynomial functions."," After presenting the model \ref{2}) ), we describe the orbital motion of Phoebe by fitting the curves of the temporal variations of the orbital elements $a, e, M$ and $L_{s}$ with polynomial functions."
" Thanks to a fast Fourier transform (FFT), the large periodic variations around the mean elements are analysed and show that the orbital motion of Phoebe is far from being keplerian (Sect.??))."," Thanks to a fast Fourier transform (FFT), the large periodic variations around the mean elements are analysed and show that the orbital motion of Phoebe is far from being keplerian \ref{3}) )."
 Then we determine the motion of precession and nutation of Phoebe by numerical integration using the value of the obliquity obtained in section ??.., Then we determine the motion of precession and nutation of Phoebe by numerical integration using the value of the obliquity obtained in section \ref{4}.
" Finally, after quantifying the validity of the developments done by Kinoshita (1977) for the Earth, when applied to Phoebe, an analytical model is constructed."," Finally, after quantifying the validity of the developments done by Kinoshita (1977) for the Earth, when applied to Phoebe, an analytical model is constructed."
 All our results are compared to the results obtained by Kinoshita for the Earth., All our results are compared to the results obtained by Kinoshita for the Earth.
 We show in section ?? that the numerical approach is significantly more accurate to determine the precession and the nutation motion of Phoebe than the analytical model on the opposite of the Earth for which a very good agreement is reached., We show in section \ref{6} that the numerical approach is significantly more accurate to determine the precession and the nutation motion of Phoebe than the analytical model on the opposite of the Earth for which a very good agreement is reached.
 This is due to the large periodic departure from the keplerian motion of the orbit of Phoebe., This is due to the large periodic departure from the keplerian motion of the orbit of Phoebe.
 We note however that it gives a fairly good approximation for the precession which is sensitive to the average value., We note however that it gives a fairly good approximation for the precession which is sensitive to the average value.
" 'The present study of the rotation of Phoebe considered as a rigid body, is based on the theoritical framework set by Kinoshita (1977) who adopted an Hamiltonian formulation using Andoyer variables (1923) to evaluate the motion of the precession-nutation of the rigid Earth."," The present study of the rotation of Phoebe considered as a rigid body, is based on the theoritical framework set by Kinoshita (1977) who adopted an Hamiltonian formulation using Andoyer variables (1923) to evaluate the motion of the precession-nutation of the rigid Earth."
 Here a simplified model is described and only the variables and the equations used in this paper are detailed., Here a simplified model is described and only the variables and the equations used in this paper are detailed.
" The rotation of a rigid Phoebe involves three axes: the figure axis, which coincides with the axis of the"," The rotation of a rigid Phoebe involves three axes: the figure axis, which coincides with the axis of the"
in each component for quasars in each a biu. a. b. and c are the uuknown paranieters to be fitted. and o is du degree.,"in each component for quasars in each $\alpha$ bin, a, b, and c are the unknown parameters to be fitted, and $\alpha$ is in degree."
" For μιcosó. the best-fitting result of he function is jn,cosó=(0.59|2.95sn(eT8.Im)."," For $\mu_{\alpha}\cos\delta$, the best-fitting result of the function is $\overline{\mu_{\alpha}\cos\delta}=-0.59+2.95\sin(\alpha+78.48)$."
 For us. the best-fitting result of the function is fry=2.5000ία.| 61.02).," For $\mu_{\delta}$, the best-fitting result of the function is $\overline{\mu_{\delta}}=-2.30-0.99\sin(\alpha+61.02)$ ."
 The best-fittine function or the proper motions i cach component is plotted as vellow dash dot line iu each top panel of Figure 8.., The best-fitting function for the proper motions in each component is plotted as yellow dash dot line in each top panel of Figure \ref{fg8}.
 The 6» two panels of Figure & also indicate that there is uo systematic dependence of the random error of the proper notions in cach component on a., The top two panels of Figure \ref{fg8} also indicate that there is no systematic dependence of the random error of the proper motions in each component on $\alpha$.
" The dispersion of the randon errors im 44,cosó and pi for quasars in cdiffercut à ns js LO aud OS mas +t. respectively,"," The dispersion of the random errors in $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$ for quasars in different $\alpha$ bins is $1.0$ and $0.8$ mas $^{-1}$, respectively."
 This dispersion is Snaller than the raudon eror of proper motions for all quasars iu our sanuple by a factor of |. 6., This dispersion is smaller than the random error of proper motions for all quasars in our sample by a factor of 4 – 6.
" The bottom two panels of Figure 8— shows the distribution of i,cos9 and jis along with 6.", The bottom two panels of Figure \ref{fg8} shows the distribution of $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$ along with $\delta$.
 The bottom-left panel of Figure & indicates that. for quasars with à>0.the systematic errors of μμcosó in the six à bins are sinaller than zero.," The bottom-left panel of Figure \ref{fg8} indicates that, for quasars with $\delta >0$,the systematic errors of $\mu_{\alpha}\cos\delta$ in the six $\delta$ bins are smaller than zero."
" On the other hand. for quasars with à«0. the systematic errors of jn,cosó in the four à bins are bigeer than zero."," On the other hand, for quasars with $\delta <0$, the systematic errors of $\mu_{\alpha}\cos\delta$ in the four $\delta$ bins are bigger than zero."
" For quasars with à>0. there is no à dependence of the svstematic aud random errors in 44,cos à. the dispersion of the systematic aud random errors of νιcos for quasars in different 8 bins is 0.5 aud LTauas +. respectively,"," For quasars with $\delta >0$, there is no $\delta$ dependence of the systematic and random errors in $\mu_{\alpha}\cos\delta$ , the dispersion of the systematic and random errors of $\mu_{\alpha}\cos\delta$ for quasars in different $\delta$ bins is 0.5 and 0.7 mas $^{-1}$, respectively."
" For quasars with à«0. the ΠΕΠ svstematic error of qp,cosó=L6 mas ντ lias in the nearby of ὁ-30°."," For quasars with $\delta <0$, the maximum systematic error of $\mu_{\alpha}\cos\delta=4.6$ mas $^{-1}$ is in the nearby of $\delta=-30\degr$."
 The bottomrright panel of Figure 8 indicates that. Or quasars with à« 0. there is no à dependence of the systematic aud random errors of gs. but the quasars in he uearbv of 6=30° have the maxinuun svstematic error of πρ=5.3 mas |.," The bottom-right panel of Figure \ref{fg8} indicates that, for quasars with $\delta <0$ , there is no $\delta$ dependence of the systematic and random errors of $\mu_{\delta}$ but the quasars in the nearby of $\delta=-30\degr$ have the maximum systematic error of $\overline{\mu_{\delta}}=-5.3$ mas $^{-1}$."
 For quasars with à>0. he bottom-right panel of Figure 8. indicates that there is Ó dependence of the svstematic error of p.," For quasars with $\delta >0$, the bottom-right panel of Figure \ref{fg8} indicates that there is $\delta$ dependence of the systematic error of $\mu_{\delta}$."
 A line of fs=3.65|0.076 can best fit the à. dependence of Ha. Where qp is the systematic error of gry for quasars iu different 9 bins. 6 is in degree.," A line of $\overline{\mu_{\delta}}=-3.65+0.07\delta$ can best fit the $\delta$ dependence of $\mu_{\delta}$, where $\overline{\mu_{\delta}}$ is the systematic error of $\mu_{\delta}$ for quasars in different $\delta$ bins, $\delta$ is in degree."
 This line is plotted as vellow dash dot line in the bottoumright panel of Figure 8., This line is plotted as yellow dash dot line in the bottom-right panel of Figure \ref{fg8}.
 For quasars with 6>0. there is no ó depeudence of the random errors of p. the dispersion of the random errors of p for quasars in different 6 bius is 0:3 mas 4.," For quasars with $\delta >0$, there is no $\delta$ dependence of the random errors of $\mu_{\delta}$, the dispersion of the random errors of $\mu_{\delta}$ for quasars in different $\delta$ bins is 0.3 mas $^{-1}$."
 Tu the previous sections. we have pointed out that there is only 13520 or quasars in our sample with the 2ATASS observation data.," In the previous sections, we have pointed out that there is only 13520 or quasars in our sample with the 2MASS observation data."
 Thus. the proper motions for most of quasars in our sample were derived ouly from the photographic data.," Thus, the proper motions for most of quasars in our sample were derived only from the photographic data."
 But it is important to compare the derived proper motions with aud without the 2\TASS data to understand the importance of the 2MASS data in derivation of the proper motions in the PPMXL catalog., But it is important to compare the derived proper motions with and without the 2MASS data to understand the importance of the 2MASS data in derivation of the proper motions in the PPMXL catalog.
 A appropriate quasar sample was chosen before this comparison., A appropriate quasar sample was chosen before this comparison.
 The top two panels of Figure 9. show the photographic D magnitude distributions of quasars with (left panel) and without (right panel) the 2M1ASS data., The top two panels of Figure \ref{fg9} show the photographic $B$ magnitude distributions of quasars with (left panel) and without (right panel) the 2MASS data.
 These two panels indicate that the B magnitude distributions for these two eroups of quasars are very different., These two panels indicate that the $B$ magnitude distributions for these two groups of quasars are very different.
 Most of quasars with 2MÀASS data are bright and the median of the P imiagnuitude distribution is ~15.0 mae., Most of quasars with 2MASS data are bright and the median of the $B$ magnitude distribution is $\sim18.0$ mag.
" On the other ας, most ofquasars without 2\TASS data are faint and the median of the D magnitude distribution is ~20.0 mae."," On the other hand, most of quasars without 2MASS data are faint and the median of the $B$ magnitude distribution is $\sim20.0$ mag."
 Furthermore. for quasars with D19.0. the wmuber of quasars without 2\LASS data is mich bigecr than that of quasars with 2MLASS data. aud all quasars without 221ASS data whose B iiaguitudes are bieeer than 17.0 mae.," Furthermore, for quasars with $B>19.0$, the number of quasars without 2MASS data is much bigger than that of quasars with 2MASS data, and all quasars without 2MASS data whose $B$ magnitudes are bigger than 17.0 mag."
 Thus. quasars with B magnitudes in the range between 17.3 aud 18.3 mae were cliosen as the comparison sample.," Thus, quasars with $B$ magnitudes in the range between 17.3 and 18.3 mag were chosen as the comparison sample."
 The nunuber of quasars with aud without the 2\TASS data in the comparison sample is G013 aud 5878. respectively.," The number of quasars with and without the 2MASS data in the comparison sample is 6013 and 5878, respectively."
 The iniddle and bottom panels of Figure 9. show the histograms of the proper motions in cach component for quasars with (loft panels) aud without (vight panels) the 2QATASS data in the comparison sample. respectively.," The middle and bottom panels of Figure \ref{fg9} show the histograms of the proper motions in each component for quasars with (left panels) and without (right panels) the 2MASS data in the comparison sample, respectively."
 Suinilu to Figure 5.. A Gaussian function wasused to fit the proper motions iu cach comipouenut aud was plotted as red solid line iu cach panel of Figure 9..," Similar to Figure \ref{fg5}, A Gaussian function wasused to fit the proper motions in each component and was plotted as red solid line in each panel of Figure \ref{fg9}."
 These four panels in Figure 9 indicate that there is no obvious difference in the raudon errors of the proper motions m both components for quasars with aud without 241ÀSS data., These four panels in Figure \ref{fg9} indicate that there is no obvious difference in the random errors of the proper motions in both components for quasars with and without 2MASS data.
" But the systematic error of j5,cos for quasars with 2MASS data is much smaller than that for quasars without 2MASS data.", But the systematic error of $\mu_{\alpha}\cos\delta$ for quasars with 2MASS data is much smaller than that for quasars without 2MASS data.
 The systematic error of gry for quasars with 2\TASS data is also a little smaller than that for quasars without 2\TASS data., The systematic error of $\mu_{\delta}$ for quasars with 2MASS data is also a little smaller than that for quasars without 2MASS data.
 Figure 9 indicates that the 2\TASS data are very important in the derivation of the proper motions in the PPAUINL catalog., Figure \ref{fg9} indicates that the 2MASS data are very important in the derivation of the proper motions in the PPMXL catalog.
 They cau sienificautly reduce the svstematic errors of the derived proper motions in the PPMXL catalog., They can significantly reduce the systematic errors of the derived proper motions in the PPMXL catalog.
 The USNO-SDSS proper motion uses the USNO-D catalog as the carly echo data. but links its zero-poiut to the galaxies.," The USNO-SDSS proper motion uses the USNO-B catalog as the early echo data, but links its zero-point to the galaxies."
 The SDSS photometric data as the later echo data used in deriviug the USNO-SDSS proper motion are much deeper than the 2MÁSS plhotoimetry used by the PPMXL catalog., The SDSS photometric data as the later echo data used in deriving the USNO-SDSS proper motion are much deeper than the 2MASS photometry used by the PPMXL catalog.
 quasars in the PPMXL catalog are also found iu the SDSS DR., quasars in the PPMXL catalog are also found in the SDSS DR7.
 Thus. it is nuportaut to compare the proper motions of quasars in the PPAINE catalog to that in the SDSS catalog to see whether the new SDSS photometric data used in the derivation of the USNO-SDSS proper metion can nuprove the derived proper motions for the eiven quasar saluple.," Thus, it is important to compare the proper motions of quasars in the PPMXL catalog to that in the SDSS catalog to see whether the new SDSS photometric data used in the derivation of the USNO-SDSS proper motion can improve the derived proper motions for the given quasar sample."
 Siuilar to Figure 5.. Figure 10. shows the histograms of the USNO-SDSS proper motions of quasars cross- iu the PPNMXL aud SDSS DR7 catalogs with a bin of 1.0 mas H1.," Similar to Figure \ref{fg5}, Figure \ref{fg10} shows the histograms of the USNO-SDSS proper motions of quasars cross-identified in the PPMXL and SDSS DR7 catalogs with a bin of 1.0 mas $^{-1}$."
 A Gaussian function was used to fit the USNO-SDSS proper motions iu cach coimponout and was plotted as red solid liue in cach panel of Figure 10.., A Gaussian function was used to fit the USNO-SDSS proper motions in each component and was plotted as red solid line in each panel of Figure \ref{fg10}.
 Figure 109 inclicates that the svstematic error of the USNO-SDSS proper motions of quasars iu the SDSS DR? catalog is 0.9 and 0.5 mas ban Hacosó and fis. respectively.," Figure \ref{fg10} indicates that the systematic error of the USNO-SDSS proper motions of quasars in the SDSS DR7 catalog is $0.9$ and $0.5$ mas $^{-1}$ in $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$ , respectively."
" The random error of the USNO-SDSS proper motions of quasars in the SDSS DR7 catalog is 3.3 and 3.3 mas + dmn gr,coxsd and pty. respectively.", The random error of the USNO-SDSS proper motions of quasars in the SDSS DR7 catalog is $3.3$ and $3.3$ mas $^{-1}$ in $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$ respectively.
 The derived svstematic and randoni errors are mich sanallerthan those of the proper motions of quasars iuthe PPMXL catalog.which indicates the improvement in the derivation of proper motions iucludiug the SDSS astrometric auc photometric cata.," The derived systematic and random errors are much smallerthan those of the proper motions of quasars inthe PPMXL catalog,which indicates the improvement in the derivation of proper motions including the SDSS astrometric and photometric data."
 Suuilu to Figure 6.. Figure 11. shows the SDSS r magnitude depeudeuce of the USNO-SDSS. proper motionsin each component of quasars cross-ideutified iu the PPMXL iud SDSS DR? catalogs.," Similar to Figure \ref{fg6}, , Figure \ref{fg11} shows the SDSS $r$ magnitude dependence of the USNO-SDSS proper motionsin each component of quasars cross-identified in the PPMXL and SDSS DR7 catalogs."
 Quasars with SDSS r maguitude in the range between 16.0 and 21.0, Quasars with SDSS $r$ magnitude in the range between 16.0 and 21.0
obvious that the trend of [Is/bhs] with respect to metallicity of RCB aud. EHes is quite different from that shown by post-ACB stars.,obvious that the trend of [ls/hs] with respect to metallicity of RCB and EHes is quite different from that shown by post-AGB stars.
 It also. probably. suggestsMOD the s-processing in RCBs aud EHes is not a result of the third dredgeup aud could have happened when the stars passed through a second ACB phase (presumably).," It also, probably, suggests the $s$ -processing in RCBs and EHes is not a result of the third dredgeup and could have happened when the stars passed through a second AGB phase (presumably)."
 Are the minority RCBs born-again giants?, Are the minority RCBs born-again giants?
 The similarity of the abundance pattern of V851CCen, The similarity of the abundance pattern of Cen
"Was ebwarfs with observed proper motions to determine their last pericentre and apocentre distances r, and p.",Way dwarfs with observed proper motions to determine their last pericentre and apocentre distances $r_p$ and $r_a$.
 We found:, We found:
"solving (he equations [or. roog and Eoz. ut""pe Sean be related to dark halo mass AZ.","solving the equations for $r_{200}$ and $\sigma_\mathrm{v}^2$, $\kappa_\mathrm{c}^{\mathrm{CIS}}$ can be related to dark halo mass $M$."
 :The above analvsisκ for. the NTIS profile then is also (rue for the CIS model. if core radius ro; is large enough to be able to fit the observed rotation curves of the dwarl and LSB clisk galaxies.," The above analysis for the NTIS profile then is also true for the CIS model, if core radius $r_\mathrm{core}$ is large enough to be able to fit the observed rotation curves of the dwarf and LSB disk galaxies."
 Note that our conclusion (hat a CIS model as a cored mass profile is ruled out. bv statistical strong gravitational lensing seems inconsistent with previous works (Ilinshaw&Krauss1987:Chiba&Yoshii1999:ChengIxrauss 2000).. since these authors used this model to constrain cosmological parameters.," Note that our conclusion that a CIS model as a cored mass profile is ruled out by statistical strong gravitational lensing seems inconsistent with previous works \citep{hinshaw,chiba,cheng}, since these authors used this model to constrain cosmological parameters."
 A simple analvsis. however. shows us that there is no discrepancy.," A simple analysis, however, shows us that there is no discrepancy."
 The central convergence can be expressed in teris of the mass and (he core radius of a lens halo., The central convergence can be expressed in terms of the mass and the core radius of a lens halo.
 For NTIS. [rom equation (2)) and equation (4)). we have a.xMrz: for CIS. from equation (11)). equation (13)) and equation (15)) we have (approximately) ROSxMTpoe.," For NTIS, from equation \ref{r0}) ) and equation \ref{kc1}) ), we have $\kappa_\mathrm{c}\propto M/r_0^2$ ; for CIS, from equation \ref{kc2}) ), equation \ref{mball}) ) and equation \ref{sigmav}) ) we have (approximately) $\kappa_\mathrm{c}^{\mathrm{CIS}}\propto
M^{2/3}/r_\mathrm{core}$."
" A larger ri, needs a larger M. to ensure eC>Lor. for a fixed value of mass AL. an appropriate smaller value of roe. would ensure Ros>Ll."," A larger $r_\mathrm{core}$ needs a larger $M$ to ensure $\kappa_\mathrm{c}^{\mathrm{CIS}}\geq 1$, or, for a fixed value of mass $M$, an appropriate smaller value of $r_\mathrm{core}$ would ensure $\kappa_\mathrm{c}^{\mathrm{CIS}}\geq 1$."
 Therelore. if rag is not determined by currently observed rotation curves of the dwarf ancl LSB clisk galaxies. but rather is adjustable (Hinshaw&vauss1987:ChibaYoshii 2000).. then no cliscrepaney appears.," Therefore, if $r_\mathrm{core}$ is not determined by currently observed rotation curves of the dwarf and LSB disk galaxies, but rather is adjustable \citep{hinshaw,chiba,cheng}, then no discrepancy appears."
 A more realistic mass profile should not be divergent ad the center (cusp). that is. it should have a flat core. but the core radius r4 should be small enough to ensure that the lensing probability matehesthe observations of CLÀASS/JVAS.," A more realistic mass profile should not be divergent at the center (cusp), that is, it should have a flat core, but the core radius $r_\mathrm{core}$ should be small enough to ensure that the lensing probability matchesthe observations of CLASS/JVAS."
indicate a pair of skeletons crossing over cach other.,indicate a pair of skeletons crossing over each other.
 The possible deviation from the length distribution is totally negligible according to various tests., The possible deviation from the length distribution is totally negligible according to various tests.
 On a pixelised. 2D) random field. the key step in tracing he local skeleton is to locate the skeleton knot which is always within the line connecting the centres of the two canceling neighbouring pixels (one edge of the secondary pixel). ancl whose position is conventionally estimated. by incar interpolation. since the skeleton realisation S can be considered as a linear function alone the line connecting just à few pixels at a very high resolution-level.," On a pixelised 2D random field, the key step in tracing the local skeleton is to locate the skeleton knot which is always within the line connecting the centres of the two canceling neighbouring pixels (one edge of the secondary pixel), and whose position is conventionally estimated by linear interpolation, since the skeleton realisation $\mathcal{S}$ can be considered as a linear function along the line connecting just a few pixels at a very high resolution-level."
 “Phis is an approximation that makes things easier to handle. especially for the HIZALDix. pixelization scheme.," This is an approximation that makes things easier to handle, especially for the HEALPix pixelization scheme."
 However. he skeleton is actually a cubic function. so that 10 is necessary to test whether linear interpolation is sullicient for its computation.," However, the skeleton is actually a cubic function, so that it is necessary to test whether linear interpolation is sufficient for its computation."
 In this appendix. we investigate the linear properties at the skeleton knots derived by linear ancl cubic spline interpolation methods.," In this appendix, we investigate the linear properties at the skeleton knots derived by linear and cubic spline interpolation methods."
 The characteristic equation (I5q. 2)), The characteristic equation (Eq. \ref{eq_det}) )
 for the 2D random Ποιά must be satisfied at. the skeleton knots., for the 2D random field must be satisfied at the skeleton knots.
" It can be reexpressed for a CMD temperature field as We define ancl A should satisfy the following with two real roots Ay ancl As (A,> Av)."," It can be reexpressed for a CMB temperature field as We define and $\lambda$ should satisfy the following with two real roots $\lambda_1$ and $\lambda_2$ $\lambda_1 \ge
\lambda_2$ )."
 In principle. rm should be equal to ο ancl also equal to Ay or Az along the underlving skeleton.," In principle, $r_1$ should be equal to $r_2$ and also equal to $\lambda_1$ or $\lambda_2$ along the underlying skeleton."
 However. in practice. we have to investigate such a property at the position of the estimated skeleton knots on the pixelisecl sphere where ry ancl re are not exactly equal because of estimation. errors.," However, in practice, we have to investigate such a property at the position of the estimated skeleton knots on the pixelised sphere where $r_1$ and $r_2$ are not exactly equal because of estimation errors."
 The irst ancl second derivatives there can be obtained safely by inear interpolation as in Iq. AG.., The first and second derivatives there can be obtained safely by linear interpolation as in Eq. \ref{eq_T_intpl}.
 We define a new quantity roydr)/2., We define a new quantity $r \equiv (r_1+r_2)/2$.
 Phe numerical robustness of the equivalence oween r and A indicates the quality of the estimation methoc., The numerical robustness of the equivalence between $r$ and $\lambda$ indicates the quality of the estimation method.
 In this test. we pick αρ two six-pixel-arrays Groorpo.rs) from one simulated. Gaussian| realisation (resolution parameter μις= 1024) smoothed by Gaussian xums with PWHAL=30° and. 60°," In this test, we pick up two six-pixel-arrays $x_0, x_1, ..., x_5$ ) from one simulated Gaussian realisation (resolution parameter $N_{\rm side}=1024$ ) smoothed by Gaussian beams with $\rm
FWHM=30\arcmin$ and $60\arcmin$."
 Lhe pixel location of he two arravs are exactly the same with cach other., The pixel location of the two arrays are exactly the same with each other.
 The corresponding values of S in Eq., The corresponding values of $\mathcal{S}$ in Eq.
 4 are marked by Lilled riangles in Figure Bl., \ref{eq_CMB_ske} are marked by filled triangles in Figure \ref{fig_lin_cub}.
 For the case of FWHAL=30’. tory is a pai of canceling pixels and Py point (P point) is the estimated skeleton knot determined by a linear (cubic spline) interpolation method.," For the case of $\rm
FWHM=30\arcmin$, $x_2 x_3$ is a pair of canceling pixels and $P_f$ point $P$ point) is the estimated skeleton knot determined by a linear (cubic spline) interpolation method."
 The linear properties at. the, The linear properties at the
motion of a clump in the gas then this corresponds to a tangential velocity of 120216km!.,motion of a clump in the gas then this corresponds to a tangential velocity of $\pm$.
. Even though the measured velocity is comparable to the velocities inferred. [rom near-IR emission line profiles for massive YSO winds the direction of motion is not that of a clump ol gas moving racially outwards and is not at all like the jet motions seen in other objects., Even though the measured velocity is comparable to the velocities inferred from near-IR emission line profiles for massive YSO winds the direction of motion is not that of a clump of gas moving radially outwards and is not at all like the jet motions seen in other objects.
 It is more consistent with a straightening or opening out of the curved structure seen in the first epoch and in Tolani οἱ al., It is more consistent with a straightening or opening out of the curved structure seen in the first epoch and in Tofani et al.
's November 1992 VLA image.,'s November 1992 VLA image.
 Since this likely to be the bright part of a larger. over-resolved structure then it is also possible Chat the distribution ol material has remained the same but the illumination by ionizing radiation has change between the epochs to highlight a different patch (see below).," Since this likely to be the bright part of a larger, over-resolved structure then it is also possible that the distribution of material has remained the same but the illumination by ionizing radiation has change between the epochs to highlight a different patch (see below)."
 Figure 4 shows the MERLIN map just 50 davs alter (hat in Figure 2.., Figure \ref{fig:ep3} shows the MERLIN map just 50 days after that in Figure \ref{fig:ep2}.
 Here the changes in morphology of the source are much more dramatic., Here the changes in morphology of the source are much more dramatic.
 Several checks were made (o see if the periods of rain during the observations were affecting the resulting source morphology. but they did not.," Several checks were made to see if the periods of rain during the observations were affecting the resulting source morphology, but they did not."
 Simall changes in morphology can occur due to differentwe coverage of the same source. but all (he observations were very similar full tracks.," Small changes in morphology can occur due to different coverage of the same source, but all the observations were very similar full tracks."
 In the third epoch the emission is concentrated in a compact region to the SW of the original core position. although again the integrated [αν has staved remarkably constant. (Table 1)).," In the third epoch the emission is concentrated in a compact region to the SW of the original core position, although again the integrated flux has stayed remarkably constant (Table \ref{tab:params}) )."
 Emission in the NE part οἱ the elongated core is now almost absent., Emission in the NE part of the elongated core is now almost absent.
 The patch of emission which showed significant proper motion over the previous 5 vears is unchanged over this much shorter interval., The patch of emission which showed significant proper motion over the previous 5 years is unchanged over this much shorter interval.
 This is as expected and bolsters (he signilicance of the other changes in morpholoey., This is as expected and bolsters the significance of the other changes in morphology.
 50. what is the nature of the radio emission from $140 IRS 1?," So, what is the nature of the radio emission from S140 IRS 1?"
 The highly elongated. cIumpy and curving structure is highly reminiscent of the jet from the luminous YSO GGD?7T.," The highly elongated, clumpy and curving structure is highly reminiscent of the jet from the luminous YSO GGD27."
 llowever. as noted by Schwartz who first put forward the jet interpretation. there is a major problem with (his in that such a jet would be perpendicular (ο the laree scale bipolar molecular outflow in the region. which appears to be powered by IRS 1.," However, as noted by Schwartz who first put forward the jet interpretation, there is a major problem with this in that such a jet would be perpendicular to the large scale bipolar molecular outflow in the region, which appears to be powered by IRS 1."
 The (rue nature of the radio source is revealed through high resolution observations in the near-IR., The true nature of the radio source is revealed through high resolution observations in the near-IR.
 Figure shows a grevscale of (he MERLIN map from Figure 1. overlaid with contours of near-IR K-band (2.2j/1)) emission from a reconstructed speckle image obtained by Alvarez et al. (, Figure \ref{fig:5K} shows a greyscale of the MERLIN map from Figure \ref{fig:ep1} overlaid with contours of near-IR K-band ) emission from a reconstructed speckle image obtained by Alvarez et al. (
2004a).,2004a).
 The unresolved near-IR. point source as been arbitrarily aligned wilh the peak of {he radio emission given the lack of accurate near-IR astrometry., The unresolved near-IR point source as been arbitrarily aligned with the peak of the radio emission given the lack of accurate near-IR astrometry.
 The position of the 2\IASS counterpart of IRS 1L., The position of the 2MASS counterpart of IRS 1.
 is located EE and 55 of the peak MEBRLLEN position., is located E and S of the peak MERLIN position.
 Given that the extended nebular emission dominates over ihe point source in the K-band (Alvarez et al., Given that the extended nebular emission dominates over the point source in the K-band (Alvarez et al.
 200da) this is consistent with the adopted, 2004a) this is consistent with the adopted
in the Calactic relation for »—r (Braun Walterbos 1992). unlike the considerably higher temperature >=775+100 at was derived earlier.,"in the Galactic relation for $\tau$ (Braun Walterbos 1992), unlike the considerably higher temperature $= 775 \pm 100$ K that was derived earlier."
 This is the first redshifted systet1 lor which it cau be shown that Tj; is less tlan>.. de.," This is the first redshifted system for which it can be shown that $T_{\mathrm k}$ is less than, ie."
 that the kinetic temperature in the incivicual cold phase gas clouds is less than the «lerivec harmonie mean spin temperature lor all of the neitral eas on the sightline., that the kinetic temperature in the individual cold phase gas clouds is less than the derived harmonic mean spin temperature for all of the neutral gas on the sightline.
" The kinetic temyerature of the third line. derived [rom the velocity widh of the line. is 7,€5016£953 Ik. i reasonable agreement with meastuements of temperatu‘e lu the WNAL of our owl Galaxy (sulktoi Heiles 1988: Carilli. Dwarakanath Coss 1998). where typical temperaures fall in the rane 2000-3000. Is. For a given cloud. 7422 Tj une istial couciious found in the ISM (Ixulkarni Heiles 1985)."," The kinetic temperature of the third line, derived from the velocity width of the line, is $T_{\mathrm k}
\leq 5046 \pm 953$ K, in reasonable agreement with measurements of temperature in the WNM of our own Galaxy (Kulkarni Heiles 1988; Carilli, Dwarakanath Goss 1998), where typical temperatures fall in the range 5000-8000 K. For a given cloud, $T_{\mathrm s} \approx$ $T_{\mathrm k}$ under usual conditions found in the ISM (Kulkarni Heiles 1988)."
 For the two cold absorptlon 6ΟΜΙΡΟΙΙΘΙts. we set T;= Tj atd f—0.98 (because the Arecibo beam covers both the core and the exteuded lobes of tle Quasar). :1d calculate the columu ceusity lor each 2lem liue componeit [rom equatious (1 alid (2).," For the two cold absorption components, we set $T_{\mathrm s} =$ $T_{\mathrm k}$ and $f= 0.98$ (because the Arecibo beam covers both the core and the extended lobes of the quasar), and calculate the column density for each 21cm line component from equations (1) and (2)."
" Adding he two togeher. and bearing iu iind that our values [or Tjx are upper limits. we ind a totalL coUmu of Noteluzd0.1x10?"" 7> iu tlie 1arrow absorption features."," Adding the two together, and bearing in mind that our values for $T_{\mathrm k}$ are upper limits, we find a total column of $_\mathrm{21cm} \leq 5.4
\pm 0.1 \times 10^{20}$ $^{-2}$ in the narrow absorption features."
 This is approxinmaely o1e. third of the measured ccoluma density in te DLA line: Αιρ=1ct0.2x107! > (Rao Τιrushek. |LOO8).," This is approximately one third of the measured column density in the DLA line: $_\mathrm{DLA} = 1.5 \pm 0.2 \times 10^{21}$ $^{-2}$ (Rao Turnshek, 1998)."
" The calcuated column density in the warm «‘olnponent is p0.[4E2.3x1007 u> forJ a covering"" factor"" o Df=0.98."," The calculated column density in the warm component is $ \leq
9.4 \pm 2.3 \times 10^{20} $ $^{-2}$ for a covering factor of $f =
0.98$."
 Altlough we do 100 have the needed sensitivity to determi1e the core covering [acto ‘for this component in the VLBA data. warm gas in our Galaxy is distribute more widely and more uniformly tha ithe cold gas (Dickey Lockinau 1990). so it seems uulikey that the eas would have a lower core covering factor tla he cold gas.," Although we do not have the needed sensitivity to determine the core covering factor for this component in the VLBA data, warm gas in our Galaxy is distributed more widely and more uniformly than the cold gas (Dickey Lockman 1990), so it seems unlikely that the gas would have a lower core covering factor than the cold gas."
 There is the possibilin hat the warm gas covers oue or both of the weak extende radio lobes as well as the core (i7, There is the possibility that the warm gas covers one or both of the weak extended radio lobes as well as the core (ie.
" lat [2 0.98). but given that 30""zzI5/-4 kpe at 2,=0.0912. it seems unlikely."," that $f > 0.98$ ), but given that $30\arcsec \approx 45 h_{75}^{-1}$ kpc at $z_1=0.0912$, it seems unlikely."
 The absorption lunits against the extended lobes (W. Laue. in preparation) aulthe El» oL the warum absorption i ithe Arecibo spectrum rule out the possibility that the abso‘plion covers one of the lobes but not tlie core as well.," The absorption limits against the extended lobes (W. Lane, in preparation) and the $EW_{21}$ of the warm absorption in the Arecibo spectrum rule out the possibility that the absorption covers one of the lobes but not the core as well."
 When the wari anc cold Component column densities are added together. the otal coltunn density in 2lem absorption on this sightline is Nyyopem<1.154-0.21x105 −↓∢∙⋯−⋅⊺↥⊔⊳∖," When the warm and cold component column densities are added together, the total column density in 21cm absorption on this sightline is $_\mathrm{21cm} \leq 1.48 \pm 0.24 \times 10^{21}$ $^{-2}$."
↥⊳∖⋯5 ⋅⋅⋅ remarkable agreemeut wih the column deusity [roi the fit to the DLA line., This is in remarkable agreement with the column density from the fit to the DLA line.
 The existence of a second gas phase has oieu beeu suggested to explain tlie large harmonic 1 spin temperature values. typically 1000 Ix (c£.," The existence of a second gas phase has often been suggested to explain the large harmonic mean spin temperature values, typically $\approx 1000$ K (cf."
 Carilli et al., Carilli et al.
 1996) found in redshifed DLA/21e absorbers., 1996) found in redshifted DLA/21cm absorbers.
" If the gas on the sightline lias wo (or more) teruperature phases. then tle T, caleulated by comparing the 21cm and DLA absorption profiles will uot be equal to the kiielic temperature in eitlier phase. but rather to a columu-deusity weighted barmonic mean of the temperature of each phase."," If the gas on the sightline has two (or more) temperature phases, then the $T_{\mathrm s}$ calculated by comparing the 21cm and DLA absorption profiles will not be equal to the kinetic temperature in either phase, but rather to a column-density weighted harmonic mean of the temperature of each phase."
 Thus a sightline with mostly warum phase eas will have a higher calcuated, Thus a sightline with mostly warm phase gas will have a higher calculated
allows us to neglect the 0.2 uncertainty in the wavelength scale.,allows us to neglect the 0.2 uncertainty in the wavelength scale.
 We also show the error in the mean flux (based on shot noise)., We also show the error in the mean flux (based on shot noise).
 This shot noise error is small because the combined integration time for all targets is 13.200.000 s. But as discussed above. we have verified independently (hat svstematic effects can be neglected for integration times of up to about 800.000 s. not necessarily For 13.200.000 s. Therefore in the the analvsis below we take as the 1 sigma uneertainty in each line flux a value corresponding (ο the shot noise limit for an ~800.000 sec integration. and show this uncertaintv in Table 1.," This shot noise error is small because the combined integration time for all targets is 13,200,000 s. But as discussed above, we have verified independently that systematic effects can be neglected for integration times of up to about 800,000 s, not necessarily for 13,200,000 s. Therefore in the the analysis below we take as the 1 sigma uncertainty in each line flux a value corresponding to the shot noise limit for an $\sim$ 800,000 sec integration, and show this uncertainty in Table 1."
 The faintness of the EUV emission makes characterizing its origin difficult., The faintness of the EUV emission makes characterizing its origin difficult.
 Before launch we expected. or al least hoped. that CIUPS would record signals of ~50 LU or more.," Before launch we expected, or at least hoped, that CHIPS would record signals of $\sim$ 50 LU or more."
 Such signals could be detected to 3 sigma significance in observing times of —200 Ίνκου., Such signals could be detected to 3 sigma significance in observing times of $\sim$ 200 Ksec.
 The first vears data sel would provide nearly 70 independent spectra al (his sensitivity. level. facilitating study of how the EUV brightness might vary. wilh astrophysical parameters or with orbital conditions (dav/nieht cvele. zenith angle. sum avoidance. ete.).," The first year's data set would provide nearly 70 independent spectra at this sensitivity level, facilitating study of how the EUV brightness might vary with astrophysical parameters or with orbital conditions (day/night cycle, zenith angle, sun avoidance, etc.)."
 In the actual data. the (vpical fluxes are an order of magnitude fainter. demanding integrations roughly 100 limes deeper (o achieve a given S/N. The narrow slit data set important limits on the brightness of EUV enission lines. ancl indicate that the periods when EUV emission is detected are probably contaminated by a foreground source associated will orbital day time.," In the actual data, the typical fluxes are an order of magnitude fainter, demanding integrations roughly 100 times deeper to achieve a given S/N. The narrow slit data set important limits on the brightness of EUV emission lines, and indicate that the periods when EUV emission is detected are probably contaminated by a foreground source associated with orbital day time."
 However. the narrow slit data provide too lew independent measurements at sufficient sensitivity to allow the spatial / temporal / or other variability of the emission to be explored in detail.," However, the narrow slit data provide too few independent measurements at sufficient sensitivity to allow the spatial / temporal / or other variability of the emission to be explored in detail."
 Accordingly. the instrument was switched to wide-slit observing mode in early 2004.," Accordingly, the instrument was switched to wide-slit observing mode in early 2004."
 In this section we analvze the complete integrated spectrum. without. excluding the LEUV-bright observations or otherwise correcting for the day time [oreground emission.," In this section we analyze the complete integrated spectrum, without excluding the EUV-bright observations or otherwise correcting for the day time foreground emission."
 This is because the detailed foreground contribution is diffieult to quantify. ancl because. at the conlidence level. the constraints on plasma emission measure are dominated bv the limiting uncertainties rather than the best-fit EUV line fluxes.," This is because the detailed foreground contribution is difficult to quantify, and because, at the confidence level, the constraints on plasma emission measure are dominated by the limiting uncertainties rather than the best-fit EUV line fluxes."
 Η the positive best-fit [Inx(es) in (he integrated spectrum were shown (o arise entirely from (he loreground. the constraints on plasma emission measure would fall bv at most a factor of 1.8 compared to those presented below.," If the positive best-fit flux(es) in the integrated spectrum were shown to arise entirely from the foreground, the constraints on plasma emission measure would fall by at most a factor of 1.8 compared to those presented below."
 To interpret the CHIPS data. we apply the predictions of the APEC plasma. code. utilizing a grid of line eniissivilies at temperature steps of 0.1 dex provided by N. Brickhouse.," To interpret the CHIPS data, we apply the predictions of the APEC plasma code, utilizing a grid of line emissivities at temperature steps of 0.1 dex provided by N. Brickhouse."
 We also include featiwes of Fe from the CIILANTI line list (version 4.2) 2003).. as these features are not. present in the current release of APEC.," We also include features of Fe from the CHIANTI line list (version 4.2) \citep{Yetal03}, as these features are not present in the current release of APEC."
 Emissivities are, Emissivities are
1997).,1997).
 The first three (13) make use of the expected eeneral characteristics of nmicroleusiug candidates: sinele various on otherwise constant light curves; which coincide iu time for data taken iu both colors.," The first three (1–3) make use of the expected general characteristics of microlensing candidates: single variations on otherwise constant light curves, which coincide in time for data taken in both colors."
 The nest two cuts (Ll and 5) are designed o reject a known backeround of variable stars. while the last two (6 aud T) improve the signal-to-noise of the set of selected candidates.," The next two cuts (4 and 5) are designed to reject a known background of variable stars, while the last two (6 and 7) improve the signal-to-noise of the set of selected candidates."
 The criteria were sufficiently loose not to reject eveuts affected by blending or by the finite size of the source. or events Involving multiple leuses or sources.," The criteria were sufficiently loose not to reject events affected by blending or by the finite size of the source, or events involving multiple lenses or sources."
 We define a positive (negative) fluctuation as a series of data points that (1) starts by one point deviating by at least lo from the base flux. (ii) stops with at least three consecutive points below basefiux|lo (above baseflux ia} aud (id) contains at least1 poiuts above baseflux|lo (below baseflux. 1o).," We define a positive (negative) fluctuation as a series of data points that (i) starts by one point deviating by at least $1\sigma$ from the base flux, (ii) stops with at least three consecutive points below ${\rm base\:flux} + 1\sigma$ (above ${\rm base\:flux} - 1\sigma$ ) and (iii) contains at least4 points above ${\rm
base\:flux} + 1\sigma$ (below ${\rm base\:flux} - 1\sigma$ )."
 The significance LP of a given variation is defined as the negative of the logarithi of the product. over the data poiuts it contaius. of the probability that cach point deviates from the base flux by more than the observed fluctuation Ge; is the deviation of the poiut taken at tie f;. in 0 x N is the παο: of points within the fluctuation): We order the fluctuations along a light curve by decreasing significauce.," The significance $LP$ of a given variation is defined as the negative of the logarithm of the product, over the data points it contains, of the probability that each point deviates from the base flux by more than the observed fluctuation $x_i$ is the deviation of the point taken at time $t_i$, in $\sigma$ 's, $N$ is the number of points within the fluctuation): We order the fluctuations along a light curve by decreasing significance."
 The cuts of the analysis are described. lereatiY: The tuuiug of cach cut and the estimate of the eficicney of the analysis is done with Monte Carlo suuulated light curves., The cuts of the analysis are described hereafter: The tuning of each cut and the estimate of the efficiency of the analysis is done with Monte Carlo simulated light curves.
 To ensure similar plotometric dispersion ou simulated eveuts and on the data. the events are added to elt curves.," To ensure similar photometric dispersion on simulated events and on the data, the events are added to light curves."
 The mücroleusiug ρααλλοους are drawn unifonuly in the following intervals: time of niaxinmun imaguification fyC[fai150.|150] davs. inpact parameter normalized to the Eimsteinfj. radius ugC[0.2] aud time-scale (Einstein radius crossiug tine) AfC[0.150] days.," The microlensing parameters are drawn uniformly in the following intervals: time of maximum magnification $t_0 \in [t_{\rm first}-150,
t_{\rm last}+150]$ days, impact parameter normalized to the Einstein radius $u_0 \in [0,2]$ and time-scale (Einstein radius crossing time) $\Delta t \in
[0,150]$ days."
 We correct for blending statistically. using a study of the typical fiux distribution ofthe source stars Which coutzibute to the flux of a reconstructed star. depending on its position in the coloranaguitude diagram.," We correct for blending statistically, using a study of the typical flux distribution of the source stars which contribute to the flux of a reconstructed star, depending on its position in the color-magnitude diagram."
 Table 1 sununarizes the müpact of the cuts., Table \ref{cuts} summarizes the impact of the cuts.
 The first requirement removes of the data lieht curves which are just flat elt curves., The first requirement removes of the data light curves which are just flat light curves.
 It also removes a large fraction of the simulated events of too low amplitiucle (large inpact paraucter) or s«hort-duration eveuts peaking well outside the observational period [fuf] ," It also removes a large fraction of the simulated events of too low amplitude (large impact parameter) or short-duration events peaking well outside the observational period $[t_{\rm first},t_{\rm last}]$ ."
The other cuts remove a large fraction of remaimine data light, The other cuts remove a large fraction of remaining data light
more than a factor of 3 relative to its value at r=109 aud is cropping fast with cecreasing raclius.,more than a factor of 3 relative to its value at $r=10M$ and is dropping fast with decreasing radius.
 The classical ovikov-Thorue predictiou for tlie radiative efficiency of a perlectly-radiatiug disk around a Scluwarzschild BH is 1—8/3~0.0572. the binding energy at the ISCO.," The classical Novikov-Thorne prediction for the radiative efficiency of a perfectly-radiating disk around a Schwarzschild BH is $1 - \sqrt{8}/3 \simeq 0.0572$, the binding energy at the ISCO."
 Although few photons raciatecd his far out are captured by the BH. this nunuber must still be corrected for such ellects.," Although few photons radiated this far out are captured by the BH, this number must still be corrected for such effects."
 If he phoous are radiated isotropically iu the local fluid frame (i.e.. our “optically thin” approximalion). tie actual efficiency of photons reaching infinity [alls to 0.0553: if they are radiated with an aieular clistribution correspoucliug to an optically thick disk haviug he limb-darkeuiug of a scattere-domiuated :tunospliere. it is a jt larger. 0.0570 (the lower effi‘iency of au optically thin NT disk is die to the larger photo] Capture rate. with more photons initlally emittecl in the plane of 11e clisk).," If the photons are radiated isotropically in the local fluid frame (i.e., our “optically thin"" approximation), the actual efficiency of photons reaching infinity falls to 0.0553; if they are radiated with an angular distribution corresponding to an optically thick disk having the limb-darkening of a scattering-dominated atmosphere, it is a bit larger, 0.0570 (the lower efficiency of an optically thin NT disk is due to the larger photon capture rate, with more photons initially emitted in the plane of the disk)."
 By couUrast. we find that the racliati veeficiency preccted by a simulatio1 incorporating MHD dynamics | ssomewhat la‘eer: 0.0608 [or he optically thin nocdel. 0.0606 [or the optically thick (iow the opticaly thin model leads tohigher elficieucy. siuce tlere is euliauced eimisslou near the ISCO. where velccities are hieler aid nore energy gets beamed Lin the forward direction towarcs observers).," By contrast, we find that the radiative efficiency predicted by a simulation incorporating MHD dynamics is somewhat larger: 0.0608 for the optically thin model, 0.0606 for the optically thick (now the optically thin model leads to efficiency, since there is enhanced emission near the ISCO, where velocities are higher and more energy gets beamed in the forward direction towards high-inclination observers)."
 These amount to an increase in ὁliciency of ~10% or the opticaly thin Case or & with the aieular distribution of an optically thick disk., These amount to an increase in efficiency of $\simeq 10\%$ for the optically thin case or $\simeq 6\%$ with the angular distribution of an optically thick disk.
" As we remarked above. these numbers Heht in princidle be increased by auoher 6% if à larger fraction of the lui""s hea were racli:(οι."," As we remarked above, these numbers might in principle be increased by another $\simeq 6\%$ if a larger fraction of the fluid's heat were radiated."
 Becase of geometric ‘projection. limb-ceing iu he clisk atmosphere. aud relativistic peal elTe‘ts. de perceived efliciency varies witl üug angle.," Because of geometric projection, limb-darkening in the disk atmosphere, and relativistic beaming effects, the perceived efficiency varies with viewing angle."
 Our two ray-traciug methods ¢Που in their asstuptions about the clisk’s opacity. : ierefo'e differ 1 their predictions for this augular clepencler'e.," Our two ray-tracing methods differ in their assumptions about the disk's opacity, and therefore differ in their predictions for this angular dependence."
 This coutras is illustrated ii e» iu radiative efficiency units.," This contrast is illustrated in Figure \ref{fig:dldOmega}
 in radiative efficiency units."
 Tje. racdiatiol is nearly isotropic i1 opticaly thin conditi le Olv augular variation is that dij/d2 rises N 50% a high incliuaticoi angles as a resilt oL Doppler boostiig aud bearing by te lunernksl orbiine later., The radiation is nearly isotropic in optically thin conditions; the only angular variation is that $d\eta/d\Omega$ rises by $\sim 50\%$ at high inclination angles as a result of Doppler boosting and beaming by the innermost orbiting matter.
 TIis ellect is slightly stronger or TunHR tan for the VT inocel because Its einissiviiv exends to stnaller radii where velocitles are greater., This effect is slightly stronger for ThinHR than for the NT model because its emissivity extends to smaller radii where velocities are greater.
 On the otler hanc. he opticathic &onsslnption leads to a angular dependence douinated yw the cos? area projection. li darkening. aid the finite thickness of the disk. which gives (0>8257)=0 due to self-eclipsiug.," On the other hand, the opticallythick assumption leads to an angular dependence dominated by the $\cos\theta$ area projection, limb darkening, and the finite thickness of the disk, which gives $\eta(\theta \gtrsim
85^\circ)=0$ due to self-eclipsing."
 In the opticaly thick case. te perceived eíficieney car vary [rot a 1uaximuinm &0.12 (face-on) to esseutially ni (edge-on).," In the optically thick case, the perceived efficiency can vary from a maximum $\simeq 0.12$ (face-on) to essentially nil (edge-on)."
 Using the methods described iu ?7.. we lave computed the spectrum emitted if all the raciation is emitted thermally.," Using the methods described in \ref{sec:calcmethod}, we have computed the spectrum emitted if all the radiation is emitted thermally."
 In the two panels of Figure 6.. we show how both the optically thin," In the two panels of Figure \ref{fig:thermspec_ang}, , we show how both the optically thin"
As outlined above. triple systems may be a source of false positives but how relevant are they?,"As outlined above, triple systems may be a source of false positives but how relevant are they?"
 Since the CoRoT and Kepler mission focus on main-sequence F. G. and K stars (M.=0.5 to 1.7 Mj). only these stars are discussed in the following.," Since the CoRoT and Kepler mission focus on main-sequence F, G, and K stars $M_{*}=0.5$ to 1.7 $M{_\odot}$ ), only these stars are discussed in the following."
 According to Tokovinin (2008)) at least of the solar-type stars are in systems containing three or more stars., According to Tokovinin \cite{tokovinin08}) ) at least of the solar-type stars are in systems containing three or more stars.
" Dynamically stable triple systems have to be hierarchical with P,/Ps>5 (Eggleton 2006)).", Dynamically stable triple systems have to be hierarchical with $P_{L}/P_{S}>5$ (Eggleton \cite{eggleton06}) ).
 This means that even for an eclipsing system with an orbital period of one year. the separation between the primary and the eclipsing system can be as small as 3.0 AU.," This means that even for an eclipsing system with an orbital period of one year, the separation between the primary and the eclipsing system can be as small as 3.0 AU."
 If we consider the canonical 12th magnitude G-star. this means that for the given semi-major axis. the ratio of the ratio of semi-major axis to distance can produce a maximum separation as small as 0.01 aresec.," If we consider the canonical 12th magnitude G-star, this means that for the given semi-major axis, the ratio of the ratio of semi-major axis to distance can produce a maximum separation as small as 0.01 arcsec."
 Using the results obtained by Tokovinin (2008)). we find that the probability of a triple system containing two M-stars with an orbital period of one year is between 0.1 and0.," Using the results obtained by Tokovinin \cite{tokovinin08}) ), we find that the probability of a triple system containing two M-stars with an orbital period of one year is between 0.1 and."
4%.. The probability of a triple system containing two eclipsing stars with an orbital period of up to one year is >1077., The probability of a triple system containing two eclipsing M-stars with an orbital period of up to one year is $\geq 10^{-4}$.
 Since the CoRoT and Kepler both survey 10? stars. triple systems are an important source of false positives.," Since the CoRoT and Kepler both survey $10^{5}$ stars, triple systems are an important source of false positives."
 It is thus unsurprising that CoRoT has already found at least one such system., It is thus unsurprising that CoRoT has already found at least one such system.
 The positives aspect of a triple star is that all three components are at about the same distance from the Earth., The positives aspect of a triple star is that all three components are at about the same distance from the Earth.
" Thus. given the depth of the transit. the spectral type of the primary, and the period of the transit. all relevant parameters of a hypothetical triple star system can be fixed."," Thus, given the depth of the transit, the spectral type of the primary, and the period of the transit, all relevant parameters of a hypothetical triple star system can be fixed."
 For example. an eclipsing binary that mimics a transiting planet such as the Earth would have to consist of two M-stars.," For example, an eclipsing binary that mimics a transiting planet such as the Earth would have to consist of two M-stars."
 The most interesting case is a transit that mimics a planet such as the Earth., The most interesting case is a transit that mimics a planet such as the Earth.
 What would be the properties of a triple star causing such a LC?, What would be the properties of a triple star causing such a LC?
 The triple star will consist of a E. G. K-star primary and eclipsing M-star binary.," The triple star will consist of a F, G, K-star primary and eclipsing M-star binary."
 The two relevant cases for the M-star binary are: Unequal mass (M-star) binaries for which the secondary eclipse is detectable do not have to be considered here. as these false positives would already be removed in the analysis of the LC.," The two relevant cases for the M-star binary are: Unequal mass (M-star) binaries for which the secondary eclipse is detectable do not have to be considered here, as these false positives would already be removed in the analysis of the LC."
 There are two other less relevant cases., There are two other less relevant cases.
 One is that 7.. and e are such that the primary eclipse is observed but not the secondary.," One is that $i, \Omega$, and $e$ are such that the primary eclipse is observed but not the secondary."
 We do not have to discuss this case separately. because the method applied to remove this case is identical to when one component is much fainter than the other.," We do not have to discuss this case separately, because the method applied to remove this case is identical to when one component is much fainter than the other."
 The method for excluding these two cases are identical., The method for excluding these two cases are identical.
 Another possibility is a binary with an eccentric orbit in which the impact parameter is such that two transits of equal duration and depth are produced by stars of different radii., Another possibility is a binary with an eccentric orbit in which the impact parameter is such that two transits of equal duration and depth are produced by stars of different radii.
 This case Is very unlikely., This case is very unlikely.
 Since the nethod for excluding this case is the same as for the case of identical stars. we do not have to discuss this case separately either.," Since the method for excluding this case is the same as for the case of identical stars, we do not have to discuss this case separately either."
 We thus have to exclude only the two relevant cases given above., We thus have to exclude only the two relevant cases given above.
 Transits of binaries can be either central or grazing., Transits of binaries can be either central or grazing.
 For a given transit depth. the eclipsing stars are brighter if the transit is grazing rather than central.," For a given transit depth, the eclipsing stars are brighter if the transit is grazing rather than central."
 Since binaries with central eclipses are more difficult to detect. we focus on central eclipses.," Since binaries with central eclipses are more difficult to detect, we focus on central eclipses."
 In additional. all values are given for a transiting planet as the Earth but can be scaled to larger or smaller planets.," In additional, all values are given for a transiting planet as the Earth but can be scaled to larger or smaller planets."
 Since the depth of the transit is simply the squared of the ratio of the radii. the depth depends not only on the size of the planet but also the size of the star.," Since the depth of the transit is simply the squared of the ratio of the radii, the depth depends not only on the size of the planet but also the size of the star."
 The transit is shallower if the star has a larger diameter. and deeper if the star has a smaller diameter.," The transit is shallower if the star has a larger diameter, and deeper if the star has a smaller diameter."
 The depth of the transit of a terrestrial planet is 55.8x107? for an FSV-star. 9.6x107 for a GSV-star. and 1.55x107 for a K5V star.," The depth of the transit of a terrestrial planet is $5.8\times10^{-5}$ for an F5V-star, $9.6\times10^{-5}$ for a G5V-star, and $1.5\times10^{-4}$ for a K5V star."
 What would be the properties of an eclipsing binary that mimics the transit of a terrestrial planet?, What would be the properties of an eclipsing binary that mimics the transit of a terrestrial planet?
" In the case of an FSV star. the brightness-ratio of the primary to the secondary (the brighter of the two eclipsing stars) would be 74,7, 1077."," In the case of an F5V star, the brightness-ratio of the primary to the secondary (the brighter of the two eclipsing stars) would be $I_{sec}/I_{prim}\leq
5.8\times10^{-5}$ ."
 This corresponds to a brightness-difference mag in the visual., This corresponds to a brightness-difference $m_{sec}-m_{prim}\leq 10.6$ mag in the visual.
 refdiff shows the maximum difference in mag between primary and the secondary in the V.J.H.K-band (Amy.Anis.Aug. Ani) for main-sequence stars of different spectral types.," \\ref{diff}
 shows the maximum difference in mag between primary and the secondary in the V,J,H,K-band $\Delta m_{V},\Delta m_{J},\Delta m_{H},\Delta
m_{K}$ ) for main-sequence stars of different spectral types."
 The brightness difference between the hypothetical companion and the primary depends on the spectral type of the primary star. because the depth of the transit depends on the size of the host star.," The brightness difference between the hypothetical companion and the primary depends on the spectral type of the primary star, because the depth of the transit depends on the size of the host star."
 The brightness difference is thus smaller for a main, The brightness difference is thus smaller for a main
lt has been shown that the products of main-sequence main-sequence collisions appear in the colour-magnitucde diagrams of clusters as blue stragelers (Sillsetal.1997:Sandquistetal. 1997).,"It has been shown that the products of main-sequence – main-sequence collisions appear in the colour-magnitude diagrams of clusters as blue stragglers \cite{SLBDRS97,SBH97}."
.. Since blue stragelers are. reaclily observable in clusters. they form an ideal population with which to probe the dynamical evolution of the cluster.," Since blue stragglers are readily observable in clusters, they form an ideal population with which to probe the dynamical evolution of the cluster."
 The dynamical state of a globular cluster (ts density profile. velocity. dispersion. amount of mass segregation etc.)," The dynamical state of a globular cluster (its density profile, velocity dispersion, amount of mass segregation etc.)"
 will determine the rate and nature of the collisions which occur in the cluster., will determine the rate and nature of the collisions which occur in the cluster.
 As the cluster evolves. the kinds of collision that occur will change.," As the cluster evolves, the kinds of collision that occur will change."
 Therefore. the population of collision products in a cluster can be used to probe the history of the cluster (Sillsetal.2000:Llurley2001).," Therefore, the population of collision products in a cluster can be used to probe the history of the cluster \cite{SBEG00,HTAP01}."
.. However. in order to use collision products in this wav. there are. two issues which must first be understood.," However, in order to use collision products in this way, there are two issues which must first be understood."
 First. we know that blue stragelers can also be formed through the merger of two components of a binary system.," First, we know that blue stragglers can also be formed through the merger of two components of a binary system."
 These blue stragglers will probably have dilferent. properties than those formed. from collisions., These blue stragglers will probably have different properties than those formed from collisions.
 We must either be confident that the population we are observing is collisional in origin. (c.g. from cluster density considerations). or be able to distinguish. between the two populations.," We must either be confident that the population we are observing is collisional in origin (e.g. from cluster density considerations), or be able to distinguish between the two populations."
 Secondly. we also need. to be sure that we understand. the formation and evolution. of the collision products themselves.," Secondly, we also need to be sure that we understand the formation and evolution of the collision products themselves."
 This paper is concerned with acdressing the second. point., This paper is concerned with addressing the second point.
 In this paper. we present the highest resolution smoothed particle hyelrocvnamic (SPI) simulations of collisions between main-sequence stars to date.," In this paper, we present the highest resolution smoothed particle hydrodynamic (SPH) simulations of collisions between main-sequence stars to date."
 Most. recent computations have ~jo! particles (Lombardictal.1996:Sandeuistetal. 1997)... with the highest resolution simulation using 107 particles (Sillsetal.2001).," Most recent computations have $\sim 10^4$ particles \cite{LRS96,SBH97}, with the highest resolution simulation using $10^5$ particles \cite{SFLRW01}."
". Ln this paper. we increase the number of particles to 10""."," In this paper, we increase the number of particles to $10^6$."
 Phere are three main reasons to extend this kind. of simulation to such high resolution., There are three main reasons to extend this kind of simulation to such high resolution.
 The first. and simplest. is to make sure that no fundamental change in our understanding of," The first, and simplest, is to make sure that no fundamental change in our understanding of"
particularly potent targets for asteroseismic investigation.,particularly potent targets for asteroseismic investigation.
 Prior to theKepler discoveries. these stars were relatively rare. with only 5 examples found in ground-based studies.," Prior to the discoveries, these stars were relatively rare, with only 5 examples found in ground-based studies."
 In all of those cases. the stronger pulsations are in the p-mode frequency range.," In all of those cases, the stronger pulsations are in the $p$ -mode frequency range."
 The lone p-mode pulsator had a single low-amplitude oscillation at low frequencies (Paper ID. suggesting that it behaves like the already-known hybrid pulsators.," The lone $p$ -mode pulsator had a single low-amplitude oscillation at low frequencies (Paper II), suggesting that it behaves like the already-known hybrid pulsators."
 For theKepler sdBV stars from the first part of the survey. we found that many of the g-mode pulsators showed suggestive evidence for shorter period pulsations in the p mode regime (Paper IID at lower amplitude.," For the sdBV stars from the first part of the survey, we found that many of the $g$ -mode pulsators showed suggestive evidence for shorter period pulsations in the $p-$ mode regime (Paper III) at lower amplitude."
 This pattern is not seen in any of the sdBV pulsators observed using ground-based data., This pattern is not seen in any of the sdBV pulsators observed using ground-based data.
 This is likely a signal-to-noise issue., This is likely a signal-to-noise issue.
 The g-modes are low amplitude to begin with. and at problematie frequencies for adequate observing: the possible p-modes we see are at even lower amplitude.," The $g$ -modes are low amplitude to begin with, and at problematic frequencies for adequate observing; the possible $p$ -modes we see are at even lower amplitude."
 Based on their effective temperatures. almost all the potential Kepler hybrid candidates (fivestarsinthispapertogetherwithWOfrompaperbyReedetal.2010) have a typical Thar close to 27kkKK. The only exception is the slightly-cooler 55807616 with only one barely detected peak at high frequencies.," Based on their effective temperatures, almost all the potential hybrid candidates \citep[five stars in this paper together with two stars from paper by][]{reed10} have a typical $_{\rm eff}$ close to kK. The only exception is the slightly-cooler 5807616 with only one barely detected peak at high frequencies."
" Their location in logg and Z;,r diagram is right between hybrid stars dominated by p-modes and HHer class stars.", Their location in $\log g$ and $T_{\rm eff}$ diagram is right between hybrid stars dominated by $p$ -modes and Her class stars.
 This would be consistent with the idea that there is a transition temperaure between p-mode pulsations at the hot end and. g-modes at the cool end: the p-mode dominant stars are in general hotter than the g-modedominant hybrids., This would be consistent with the idea that there is a transition temperature between $p$ -mode pulsations at the hot end and $g$ -modes at the cool end; the $p$ -mode dominant stars are in general hotter than the $g$ -modedominant hybrids.
 If the singlehigh-frequency periodicities are confirmed. this could explain their presence.," If the singlehigh-frequency periodicities are confirmed, this could explain their presence."
We plot the radial epicvelie frequency Ky as a functiou of radius for several values of the parameter e aud a spin ofa=0.24 in Fieure 2..,We plot the radial epicyclic frequency $\kappa_{\rm r}$ as a function of radius for several values of the parameter $\epsilon$ and a spin of $a=0.2M$ in Figure \ref{omegarfig}.
 The radial oscillation fequency oeicreases with decreasing values of the radius and reaches a ΛΙ at krzcTAL for this spin, The radial oscillation frequency increases with decreasing values of the radius and reaches a maximum at $r\approx7M$ for this spin.
 Decreasing values of the parameter e slift the maximi to smaller raclii., Decreasing values of the parameter $\epsilon$ shift the maximum to smaller radii.
 Iu Figure 3. we plot the Leuse-Thirrineg frequency as a fiction of radius for several values of the paralcter ε at a spin value a=0.2.4., In Figure \ref{omegalthfig} we plot the Lense-Thirring frequency as a function of radius for several values of the parameter $\epsilon$ at a spin value $a=0.2M$.
" The Lense-Thirring frequency describes the precession of the orbital plane of a particle moving around the black hole aud vanishes iu the case of a Schwarzschild black hole. where O,,=OQ»."," The Lense-Thirring frequency describes the precession of the orbital plane of a particle moving around the black hole and vanishes in the case of a Schwarzschild black hole, where $\Omega_{\rm \phi}=\Omega_{\rm \theta}$."
 The Lense-Thirring frequency increases with decreasing values of the radius aud of the parameter e., The Lense-Thirring frequency increases with decreasing values of the radius and of the parameter $\epsilon$.
 This frequency depends significantly on the parameter € and changes by a factor of ~5 at the ISCO for values of the parameter e=£0.2., This frequency depends significantly on the parameter $\epsilon$ and changes by a factor of $\sim5$ at the ISCO for values of the parameter $\epsilon=\pm0.2$.
 Note that both the Leuse-Thirriug frequency aud the radial oscillation. frequeucy are significauflv simualler than the IEepleriaun frequency οMM , Note that both the Lense-Thirring frequency and the radial oscillation frequency are significantly smaller than the Keplerian frequency $\Omega_{\rm \phi}$.
Tn this section. we determine the location of the ISCO iu the quasi-I&err spacetime which separates the reeion of space where circular orbits are stable from the reeion where circular orbits are unstable.," In this section, we determine the location of the ISCO in the quasi-Kerr spacetime which separates the region of space where circular orbits are stable from the region where circular orbits are unstable."
 The location of this orbit. iu turn. cletermuines the maxima Keplerian frequency for that particular ceutral object.," The location of this orbit, in turn, determines the maximum Keplerian frequency for that particular central object."
 Iu Paper I we found the location of the ISCO from equation (16)) by solving Iu this paper. we ceteruine the location of the 1οςὉ by computing the radius r at which the frequeney of," In Paper I we found the location of the ISCO from equation \ref{energy}) ) by solving In this paper, we determine the location of the ISCO by computing the radius $r$ at which the frequency of"
While the cetectection of solalike. p-inode oscillatious in other stars is difficult to do in a reasonable amount of time. even wihi sub-millimagnitude photometry (see for example 1993)). we cau still probe a relatively uuexplored regime of stellar variability.,"While the detectection of solar-like, p-mode oscillations in other stars is difficult to do in a reasonable amount of time, even with sub-millimagnitude photometry (see for example \citealt{gilliland93}) ), we can still probe a relatively unexplored regime of stellar variability."
 Another exciting application o‘this technology could be to survey stellar clusters for la as sinall as Neptune., Another exciting application of this technology could be to survey stellar clusters for planets as small as Neptune.
 Iu FigWes 3-+) |. we slowed the 6.50 detection limits for planets as 5na Neptune assiimius one observed κ)+) ‘ull ransits with NNT/Megacaim., In Figures \ref{lcstat_separate}- \ref{apcompare} we showed the $\sigma$ detection limits for planets as small as Neptune assuming one observed 3 full transits with MMT/Megacam.
 For the second night. the two minute exposure tirje. there are 23.062 stars below the Jupiter detection limit. ai stars below the Neptune detection luni.," For the second night, with the two minute exposure time, there are 23,062 stars below the Jupiter detection limit, and 1664 stars below the Neptune detection limit."
 Ou the third uight. with the 1 Minute exposures. are 19.5[3 stars below the Jupiter detection limit. ancl OLS stars )elow tlie Neyume detectio ," On the third night, with the 1 minute exposures, there are 19,843 stars below the Jupiter detection limit, and 648 stars below the Neptune detection limit."
We have mace no attempt bere to distinguisli betwee:1 field stars alid cluser members., We have made no attempt here to distinguish between field stars and cluster members.
 The ability o detect Jipiters in tlis system is uot |Initec by precision but rather the time baseline over wuch observaious are carried out., The ability to detect Jupiters in this system is not limited by precision but rather the time baseline over which observations are carried out.
 If oile οserve5 Ole enowh to have a resonable chauce of detectiο 2-3 full rausits. then oue would be able to fitd essenlay every short-»eriod. transiting. Jupiter-sized platet in the stellar cluster.," If one observes long enough to have a resonable chance of detecting 2-3 full transits, then one would be able to find essentially every short-period, transiting, Jupiter-sized planet in the stellar cluster."
 Since here are only tlree known planets with a lower nmiass-luuit near that of Neptune (Santosetal.20()[:MeArt1ret2001:Butler2001).. esseutially nothing is kuowr about the statistics of Neptule-s]zec| planes.," Since there are only three known planets with a lower mass-limit near that of Neptune \citep{santos04a,mcarthur04,butler04}, essentially nothing is known about the statistics of Neptune-sized planets."
 Moreover. because all ol these planets have been detected ouly via their in]ueuce on tle Facli:i| velocities of their host stars. we do not kuow anything about their radii.," Moreover, because all of these planets have been detected only via their influence on the radial velocities of their host stars, we do not know anything about their radii."
 Therelo'e. the very [ας ἰiat there are huucdreds OL stars around which we could detect trausitiug. Neple-sizecl panels i| ley exist represents ati excitiug new opportunity for the study of extra-solar glanets.," Therefore, the very fact that there are hundreds of stars around which we could detect transiting, Neptune-sized planets if they exist represents an exciting new opportunity for the study of extra-solar planets."
 As noted by Pepper&Gaudii(2005).. as a result «) ‘the relations betwe tass. luminosity. and radius for main sequence stars. if one can identify a t‘ausiting planet aroutrd αν cluster member nith source-limitecl precision. ilen one could find th:1 sale transitiug plauet around essentially al cluster members. with souce-linited precision.," As noted by \citet{pepper05}, as a result of the relations betwen mass, luminosity, and radius for main sequence stars, if one can identify a transiting planet around any cluster member with source-limited precision, then one could find that same transiting planet around essentially all cluster members with source-limited precision."
 Tle effect of this is tlal τί is not essential. fe ‘planet finding. to achieve SOice-lIimited photometry at he brightest eud whe‘e there are few stars. rather it is most imporali to achieve soiree-limitec p1lo0tomeltry Or a large julyer of stars.," The effect of this is that it is not essential, for planet finding, to achieve source-limited photometry at the brightest end where there are few stars, rather it is most important to achieve source-limited photometry for a large number of stars."
 Tjerefore; even if our photorjet‘y shows some simall (<1 inijag) consta|| error te ‘ina tlie bright οιcda. we would still have sensiivity to Neptue-sized planets around jaliy stals.," Therefore, even if our photometry shows some small $<$ 1 mmag) constant error term at the bright end, we would still have sensitivity to Neptune-sized planets around many stars."
 This it is not [uucdamentally the ability Oclo ueh-precision photometry jtst below sauration tl aloyeus up the possibility of finding small plaets. but ratherit is the fact tlal we are sing a large telescope hat can collect a greater signa per expost'e for every star compares with sing a simmaller elescope.," Thus it is not fundamentally the ability to do high-precision photometry just below saturation that opens up the possibility of finding small planets, but rather it is the fact that we are using a large telescope that can collect a greater signal per exposure for every star compared with using a smaller telescope."
 We can estimate tlie luinver ol panets one could cdeect in alb alnjlious. παν1ight survey of NGC 6791 usinϱ Megacam o1 the MMT.," We can estimate the number of planets one could detect in an ambitious, many-night survey of NGC 6791 using Megacam on the MMT."
 Adoptitο the parameers of NGC 6791 liste( previously [E(B—V)=0.1. cdistauce=Ls S|ye age= SCvr]. and assumug a mass function slope anc 10rinalizatlou that reprocluces tie enupirical E-baud luulnosity fuuction of ]xaluziv&Udalski(1992).. we calcilate the number of plauets oue weJilc| detect as a function of tie. plaretary radius using tle forma]snu ol Pepper&Caudi(2005).," Adopting the parameters of NGC 6791 listed previously $E(B-V)=0.1$, $=4.8$ kpc, $=8$ Gyr], and assuming a mass function slope and normalization that reproduces the empirical I-band luminosity function of \citet{kaluzny92}, we calculate the number of planets one would detect as a function of the planetary radius using the formalism of \citet{pepper05}."
. We assuje that the planets are utiformily distributed ir log period. aud we cousider planets witli yeriods >=1-3 ays alle 2—9 days separately.," We assume that the planets are uniformly distributed in log period, and we consider planets with periods $P=1-3$ days and $3-9$ days separately."
 For our fidiClal, For our fiducial
The mass distribution in dark-matter halos and the level of substructure in them are among the central predictions of the CDM paradigm for cosmic structure formation.,The mass distribution in dark-matter halos and the level of substructure in them are among the central predictions of the CDM paradigm for cosmic structure formation.
" The density profile should asymptotically fall off cc7? at large radii r and flatten considerably within a radial scale r, (?).", The density profile should asymptotically fall off $\propto r^{-3}$ at large radii $r$ and flatten considerably within a radial scale $r_\mathrm{s}$ \citep{Navarro1996}.
".The mass distribution should be richly substructured by sublumps of matter with a differential mass function approximated by a power law, dn/dMο.M*' with a slope slighly shallower than a= -2(?0).."," .The mass distribution should be richly substructured by sublumps of matter with a differential mass function approximated by a power law, $d n/d M\propto M^{\alpha}$ with a slope slighly shallower than $\alpha=-2$ \citep{Madau2008,Springel2008}."
" Galaxy clusters should be weakly influenced by baryonic physics, thus their density profiles and mass distributions outside the cooling radius should well reflect those expected for dark matter."," Galaxy clusters should be weakly influenced by baryonic physics, thus their density profiles and mass distributions outside the cooling radius should well reflect those expected for dark matter."
 Do they?, Do they?
" Although tentative answers exist, showing that estimated density profiles do at least not contradict the CDM expectation, accurate constraints are still missing."," Although tentative answers exist, showing that estimated density profiles do at least not contradict the CDM expectation, accurate constraints are still missing."
" Due to its insensitivity to the physical state of the matter, gravitational lensing is perhaps the most promising tool for determining matter distributions."," Due to its insensitivity to the physical state of the matter, gravitational lensing is perhaps the most promising tool for determining matter distributions."
" Weak lensing lacks the resolution necessary to constrain the density profile in cluster centres, while strong lensing is confined to the innermost cluster cores."," Weak lensing lacks the resolution necessary to constrain the density profile in cluster centres, while strong lensing is confined to the innermost cluster cores."
" In combination, they may be able to test the CDM predictions on density profiles well."," In combination, they may be able to test the CDM predictions on density profiles well."
 Several methods have been suggested to combine weak and strong cluster lensing (???)..," Several methods have been suggested to combine weak and strong cluster lensing \citep{Bradav2005,Cacciato2006,Diego2007}."
 Among them is our own algorithm aiming at the lensing potential., Among them is our own algorithm aiming at the lensing potential.
 It is based on minimising a y? function comparing observed shear measurements with suitable second derivatives of the potential., It is based on minimising a $\chi^2$ function comparing observed shear measurements with suitable second derivatives of the potential.
 Expressing the derivatives in terms of finite differences leads to a system of linear equations whose direct inversion yields the solution., Expressing the derivatives in terms of finite differences leads to a system of linear equations whose direct inversion yields the solution.
 We extend our earlier work in several ways., We extend our earlier work in several ways.
" First, we no longer use the lowest-order approximation in which measured ellipticities estimate the shear, and introduce the reduced shear instead."," First, we no longer use the lowest-order approximation in which measured ellipticities estimate the shear, and introduce the reduced shear instead."
 The non-linearity accommodated in this way can be resolved into an iterative scheme using linear inversion in each step., The non-linearity accommodated in this way can be resolved into an iterative scheme using linear inversion in each step.
" Second, we wrap the algorithm into an outer iteration loop in which the grid resolution is progressively enhanced."," Second, we wrap the algorithm into an outer iteration loop in which the grid resolution is progressively enhanced."
" While this step introduces correlations between adjacent pixels that have to be dealt with, it prepares the insertion of the strong-lensing constraints available in cluster cores."," While this step introduces correlations between adjacent pixels that have to be dealt with, it prepares the insertion of the strong-lensing constraints available in cluster cores."
" Third, we introduce a regularisation term for the two purposes of avoiding overfitting and smoothly joining the strong- and weak-lensing solutions."," Third, we introduce a regularisation term for the two purposes of avoiding overfitting and smoothly joining the strong- and weak-lensing solutions."
" Finally, to account for the additional computational time we enabled the code to run on parallel machines."," Finally, to account for the additional computational time we enabled the code to run on parallel machines."
" We investigate the performance of our algorithm using two sets of synthetic data, one idealised and one realistic, before we proceed to apply it to the well-known strong-lensing cluster MS 2137, for which we obtain a high-resolution, parameter- reconstruction."," We investigate the performance of our algorithm using two sets of synthetic data, one idealised and one realistic, before we proceed to apply it to the well-known strong-lensing cluster MS 2137, for which we obtain a high-resolution, parameter-free reconstruction."
 A brief summary of the lensing notation in Sect., A brief summary of the lensing notation in Sect.
 D] is followed by an outline of the method in Sect., \ref{lensingformalism} is followed by an outline of the method in Sect.
 B| and a description of its implementation in Sect. A]., \ref{outlineofthemethod} and a description of its implementation in Sect. \ref{implementation}.
 We present the results in Sect., We present the results in Sect.
 and conclude in Sect. [B]., \ref{results} and conclude in Sect. \ref{conclusions}.
 Details of the algorithm are given in Appendix [Appendix Aj}. , Details of the algorithm are given in Appendix \ref{linearisationingridspace}. .
"We adopt the standard notation introduced to describe isolated lenses in the thin-lens approximation (e.g. ???)) Two-dimensional,"," We adopt the standard notation introduced to describe isolated lenses in the thin-lens approximation (e.g. \citealt{P.1992,Narayan1996,P.2006}) ). Two-dimensional,"
" projected lensing mass distributions are covered by angular coordinates 6=(06,65)."," projected lensing mass distributions are covered by angular coordinates $\vec{\theta}=(\theta_{1},\theta_{2})$."
" The lensing potential y(6), which is the appropriately scaled Newtonian potential projected on the sky, contains all information necessary to describe a single-plane lens."," The lensing potential $\psi(\vec\theta)$, which is the appropriately scaled Newtonian potential projected on the sky, contains all information necessary to describe a single-plane lens."
" The deflection angle, convergence and shear are derivatives of WB) with respect to 0; and 62,"," The deflection angle, convergence and shear are derivatives of $\psi(\vec{\theta})$ with respect to $\theta_{1}$ and $\theta_{2}$,"
deviation is at the level of 2.5-3 6 and we cannot rule out the P3 law with confidence.,deviation is at the level of 2.5-3 $\sigma$ and we cannot rule out the $P^{-\frac{1}{3}}$ law with confidence.
" We have also checked. for the dependence of R on a by using 3 sub-sets. cach of range 307 iu o. The best fit values forR iu the different o segnieuts are η, Oaths 0.528 for à ranges QU 307,307.GOP GO""907, respectively."," We have also checked for the dependence of $R$ on $\alpha$ by using 3 sub-sets, each of range $30^{\circ}$ in $\alpha$ The best fit values for$R$ in the different $\alpha$ segments are $1\pm^{0.4}_{0.2}$ , $0.8\pm^{0.4}_{0.2}$ $0.5\pm^{0.4}_{0.2}$ for $\alpha$ ranges $0^{\circ}-30^{\circ}$, $30^{\circ}-60^{\circ}$ $60^{\circ}-90^{\circ}$, respectively."
 This dependence of A; ou 6. even if it were significant. is quite consistent with our values of A1. W2 (Table 2) as well as with he results of Dieesao (1990).," This dependence of $R_{\circ}$ on $\alpha$, even if it were significant, is quite consistent with our values of $K1$ , $K2$ (Table 2) as well as with the results of Biggs (1990)."
 ITowever. eiven the uncertainties in the R estimates for the three ranges. it is not possible preseutlv to rule out a dependence of R on 6.," However, given the uncertainties in the $R$ estimates for the three ranges, it is not possible presently to rule out a dependence of $R$ on $\alpha$."
 IDudecd. this par of the eoocduess-of-Bt is neclieible. 04 (the standard deviation) is 0.187 when A1 and A240 aud 0.27 when A1.A?=0.," Indeed, this part of the goodness-of-fit is negligible, $\sigma_{\circ}$ (the standard deviation) is $0.18^{\circ}$ when $K1$ and $K2 \neq 0$ and $0.2^{\circ}$ when $K1, K2 = 0$."
 Earlicr Naravan Vivekanaud (1983) had argued hat R is a function of the pulsar period., Earlier Narayan Vivekanand (1983) had argued that $R$ is a function of the pulsar period.
 To assess this claim. our sample was divided iuto three period rauges aud the correspouding A estimates compared.," To assess this claim, our sample was divided into three period ranges and the corresponding $R$ estimates compared."
 However. no )oriod dependence was evident and it was possible to rule out such a depeudence with ligh confidence.," However, no period dependence was evident and it was possible to rule out such a dependence with high confidence."
 As already noted and can be secu in Figure [. we do see evidence for a possible cone outside the two cones discussed by Rankin (1993a).," As already noted and can be seen in Figure \ref{fig:fig4}, we do see evidence for a possible cone outside the two cones discussed by Rankin (1993a)."
 Also. presence of a “further inner cone has been sugeested by Rankin BRathuasree (1997) in the case of PSR 1929|10.," Also, presence of a `further inner' cone has been suggested by Rankin Rathnasree (1997) in the case of PSR 1929+10."
" The pulsars suggestive of this outer cone (refer Figure 1)) are PSRs 0656|L1. 18211605. 1911]17 and 1952|29 (at frequencies 231 MITz and Ποιο),"," The pulsars suggestive of this outer cone (refer Figure \ref{fig:fig4}) ) are PSRs 0656+14, 1821+05, 1944+17 and 1952+29 (at frequencies 234 MHz and higher)."
 We have examined the possibility that these cases really belong to the ceutral-cone. but are well outside of 1 due to an error in the asstuned values of a.," We have examined the possibility that these cases really belong to the central-cone, but are well outside of it due to an error in the assumed values of $\alpha$."
 We rule out the possibility as the implied error iu à turus out o be too high to be likely., We rule out the possibility as the implied error in $\alpha$ turns out to be too high to be likely.
 It is important to point out lat a noisy sample like the preseut one would appear increasinely cousisteut. judeine bv the best-fit criterion. with models that include more cones.," It is important to point out that a noisy sample like the present one would appear increasingly consistent, judging by the best-fit criterion, with models that include more cones."
 The question. rerefore is whether we can coustrain the uuuber of coues wv sole independent method.," The question, therefore is whether we can constrain the number of cones by some independent method."
 In this coutext. we wish to liscuss£p.," In this context, we wish to discuss."
.. Since 1e deficit reflects the absence of coual singles and conal loubles iu our data set. the size ofthe related ‘gap at large 0 values. can be used to estimate the possible thickness of 16 conal rues.," Since the deficit reflects the absence of conal singles and conal doubles in our data set, the size of the related `gap' at large $\theta$ values, can be used to estimate the possible thickness of the conal rings."
 The absence of poiuts at 05607 (Figure 1) sugeests that the coual rugs are rather thin. since a radial lickness ór Comparable to the ring radius would imply a wider eap in 0.," The absence of points at $\theta\gsim 60^{\circ}$ (Figure \ref{fig:fig4}) ) suggests that the conal rings are rather thin, since a radial thickness $\delta r$ comparable to the ring radius would imply a wider gap in $\theta$."
" To quautify this. we write the following relation. where 0, is the 0 at the start of the gap (as illustrated in Fig. 2))"," To quantify this, we write the following relation, where $\theta_{g}$ is the $\theta$ at the start of the gap (as illustrated in Fig. \ref{fig:fig2}) )"
".With 0,~ 60°. drfr would be about",".With $\theta_{g} \sim 60^{\circ}$ , $\delta r/r$ would be about."
 Thepresence of more thanone distiunguishable peak iu the distribution of beam radii (shown in the bottom paucl of Fig. 13), Thepresence of more thanone distinguishable peak in the distribution of beam radii (shown in the bottom panel of Fig. \ref{fig:fig4}) )
 clearly indicates that the conal separation is, clearly indicates that the conal separation is
distances are from 0.24 to1.6Ape and their los relative velocities with respect to Fornax are at most S.7253.6kins,distances are from 0.24 to$1.6~kpc$ and their los relative velocities with respect to Fornax are at most $8.7\pm 3.6\kms$.
 As observers. we have no knowledge of the third spatial dimension (depth). nor the motion in the plane of the sky.," As observers, we have no knowledge of the third spatial dimension (depth), nor the motion in the plane of the sky."
 What we do know. is that if we assume these GCs are a representative sample. then there is very little chance that all 5 have los distances from Fornax that are considerably ereater than the maximum projected distance. although one might.," What we do know, is that if we assume these GCs are a representative sample, then there is very little chance that all 5 have los distances from Fornax that are considerably greater than the maximum projected distance, although one might."
 Therefore. it is a safe bet that all 5 currently spend the majority of their orbits at projected distances less than 1.6&pe and their orbits must reflect this.," Therefore, it is a safe bet that all 5 currently spend the majority of their orbits at projected distances less than $1.6~kpc$ and their orbits must reflect this."
 Phere is more freedom in the orbital velocity. since only one of the three coordinates are measured (los. not the two dimensions in the plane of the sky) ancl with far poorer precision than the projected radius.," There is more freedom in the orbital velocity, since only one of the three coordinates are measured (los, not the two dimensions in the plane of the sky) and with far poorer precision than the projected radius."
 Three out of four of the GCs have los velocities of between 7 and Ὁkms+ worst Fornax. but there is no real statistical significance attached to this.," Three out of four of the GCs have los velocities of between 7 and $9~\kms$ w.r.t Fornax, but there is no real statistical significance attached to this."
 Several studies (Readctal.2006:Gooerdtοἱ 2009)) have suggested that the mere presence of GC's near Fornax represents a fundamental problem for concordance cosmology (Spergelctal. 20072) or the modified Newtonian dvnamies of Milgrom(1983)..," Several studies \citealt{read06,goerdt06,sanchez06,strigari06,inoue09}) ) have suggested that the mere presence of GCs near Fornax represents a fundamental problem for concordance cosmology \citealt{spergel07}) ) or the modified Newtonian dynamics of \cite{milgrom83a}."
 Phev claim that the timescale over which the orbital angular momentum of these CC's is drained by the background of stars and DM. through which thes orbit. is a fraction of the age of the Universe.," They claim that the timescale over which the orbital angular momentum of these GCs is drained by the background of stars and DM, through which they orbit, is a fraction of the age of the Universe."
 Despite this. there is no bright nucleus of stars at the centre as there would be if other GC's had decaved. (Lremaine 1976)).," Despite this, there is no bright nucleus of stars at the centre as there would be if other GCs had decayed \citealt{tremaine76}) )."
 This process which bleeds the orbital angular momentum is called dynamical friction (DE) and. in the classical sense. is given bv (Binney&Tremaine 2008)) (He) πω. ons where In.X is the Coulomb logarithm and is taken to be approximately 3.," This process which bleeds the orbital angular momentum is called dynamical friction (DF) and, in the classical sense, is given by \citealt{bt08}) ) ) - ) ] where $\ln \Lambda$ is the Coulomb logarithm and is taken to be approximately 3."
 Ἐν) is the circular. velocity of Fornax. C—44.10ο. is Newton's constant. Mess ds the mass of the GC and σ is the measured. VD of Fornax which is roughly LLkms 1.," $V_c(r)$ is the circular velocity of Fornax, $G=4.4\times10^{-6}\kms kpc^{-1}\msun^{-1}$ is Newton's constant, $M_{GC}$ is the mass of the GC and $\sigma$ is the measured VD of Fornax which is roughly $11~\kms$ ."
 We have knowledge of all relevant parameters in the Newtonian case once a density profile. ptr). of luminous plus DM has been fitted to the losVD.," We have knowledge of all relevant parameters in the Newtonian case once a density profile, $\rho(r)$ , of luminous plus DM has been fitted to the losVD."
 We use the procedure of Angusctal.(2008) ancl Angus(2008) to match the losVD profile of Fornax by solving the Jeans equation assuming a cusped NEW profile (Navarroetal. LO97)) ancl the same corecl DAL profile. emploved by (Readetal.2006:GoerdtctSánchez-Salcedoetal.2006:Inoue 2009:: hereafter. ROG. COG. SOG ancl 109 respectively).," We use the procedure of \cite{aftcz} and \cite{angus08} to match the losVD profile of Fornax by solving the Jeans equation assuming a cusped NFW profile \citealt{nfw97}) ) and the same cored DM profile employed by \citealt{read06,goerdt06,sanchez06,inoue09}; hereafter R06, G06, S06 and I09 respectively)."
 We neglect the density corresponding to the stars. since it has no direct bearing on the dynamics and can be simply subtracted if one wants to infer the exact density of DM. which is not our goal here.," We neglect the density corresponding to the stars, since it has no direct bearing on the dynamics and can be simply subtracted if one wants to infer the exact density of DM, which is not our goal here."
 The fits to the losVD are shown in Fig 1 (solid lino) and the NEW density prolile Ga=e) is plotted. in Fig 2 with parameters p.=DAbpe. po=14210M.Epe7. à concentration zs—7.0 and the5 velocity. distribution of stars is isotropic (οὐ=1se0.0).," The fits to the losVD are shown in Fig \ref{fig:losvd} (solid line) and the NFW density profile $\left(\rho(r)={\rho_o r_s^3 \over r(r+r_s)^2}\right)$ is plotted in Fig \ref{fig:rho} with parameters $r_s=2.5~kpc$, $\rho_o=1.2\times10^7\msun kpc^{-3}$, a concentration of $c={r_{200} \over r_s}=7.0$ and the velocity distribution of stars is isotropic $\beta(r) \equiv 1-{\sigma^2_{\theta}\over \sigma^2_r}=0.0$ )."
 Vhe enclosed: mass of stars and DAL is given in Fig 3.., The enclosed mass of stars and DM is given in Fig \ref{fig:mass}.
 lt is this constraint. and not the mere existence of GC's in orbit that must fix the DM halo since the NEN profile works perfectly well in this case and d is not possible to have a better match to the data. regardless of whether 7.0 is a sensible concentration parameter for this size of halo. nor if the DM density is suspiciously low for a cold DM particle.," It is this constraint, and not the mere existence of GCs in orbit that must fix the DM halo since the NFW profile works perfectly well in this case and it is not possible to have a better match to the data, regardless of whether $7.0$ is a sensible concentration parameter for this size of halo, nor if the DM density is suspiciously low for a cold DM particle."
" Nevertheless. to compare with the work of 106. (06 ancl LOO we take the corecl density profile they use (p(r)=p.r|2Us where p,=10734.kpe? and re=0.91 Ape) cy]and attempt to match the losVD."," Nevertheless, to compare with the work of R06, G06 and I09 we take the cored density profile they use $\rho(r)=\rho_o \left[1+({r \over r_s})^2\right]^{-1.5}$; where $\rho_o=10^8\msun kpc^{-3}$ and $r_s=0.91~kpc$ ) and attempt to match the losVD."
 lt is not possible to obtain a good match even with a variable anisotropy and to have a satisfactory fit one needs highly racial orbits. J(r)=0.46.," It is not possible to obtain a good match even with a variable anisotropy and to have a satisfactory fit one needs highly radial orbits, $\beta(r)=0.46$."
" A more aesthetic cored profile has parameters p,=2.21011.kpe5. r2=05kpe ancl isotropic velocity anisotropy (3(r)=0). but we only mention it here."," A more aesthetic cored profile has parameters $\rho_o=2.2\times10^8\msun kpc^{-3}$, $r_s=0.5~kpc$ and isotropic velocity anisotropy $\beta(r)=0$ ), but we only mention it here."
 La any case. as one sees from Fig 5.. which plots the deceleration from dynamical friction given by Eq ??.. the two DM profiles are inclistinguishable bevond 0.3Ape and so we discuss them jointly hereafter.," In any case, as one sees from Fig \ref{fig:df}, which plots the deceleration from dynamical friction given by Eq \ref{eqn:df}, the two DM profiles are indistinguishable beyond $0.3~kpc$ and so we discuss them jointly hereafter."
 Knowledge of the mass profile also tells us the circular velocity. profile (Ao=cpP)Ax Pr). thus. we have all the pertinent information nthat allows us to follow the orbits of the GCs.," Knowledge of the mass profile also tells us the circular velocity profile $V_c(r)^2={G \over r} \int_0^r \rho(\tilde{r}).4\pi \tilde{r}^2 d\tilde{r}$ ), thus, we have all the pertinent information that allows us to follow the orbits of the GCs."
 ‘This case where the Fornax ανα is dominated by the existence of DAL particles. as opposed to modifiecl gravity. requires very little discussion because it has absolutely. no problem with sustaining the orbits ofGC's for a Llubble time.," This case where the Fornax dwarf is dominated by the existence of DM particles, as opposed to modified gravity, requires very little discussion because it has absolutely no problem with sustaining the orbits of GCs for a Hubble time."
 Our procedure is to numerically solve the equations of motion fora GC witha starting © and jy position and velocity wart Fornax (we use zero z distance - line of sight - and velocity for ease)., Our procedure is to numerically solve the equations of motion for a GC with a starting $x$ and $y$ position and velocity w.r.t Fornax (we use zero $z$ distance - line of sight - and velocity for ease).
 The acceleration due to gravity (Fig 4)) is computed from the circular speed (Fig 6)). V;(rYyr sand the deceleration from dynamical friction is given by Eq ?? and shown in Fig 5..," The acceleration due to gravity (Fig \ref{fig:grav}) ) is computed from the circular speed (Fig \ref{fig:vc}) ), $V_c(r)^2r^{-1}$, and the deceleration from dynamical friction is given by Eq \ref{eqn:df} and shown in Fig \ref{fig:df}."
" Combining all this allows us to follow the orbit of the GC using simple Eulerian time-stepping such that for the « coordinate d |. |dI,(D where the time step df=0.01.Agr. is less than 1 per cent of the dynamical time at LlApe."," Combining all this allows us to follow the orbit of the GC using simple Eulerian time-stepping such that for the $x$ coordinate -dt ], +dt where the time step $dt=0.01~Myr$, is less than 1 per cent of the dynamical time at $1~kpc$."
 To update the y coordinate we simply swap the wr subscripts for jy., To update the $y$ coordinate we simply swap the $x$ subscripts for $y$ .
 Although in the DM scenario we use only circular orbits.the use of both rand y coordinates (and not merely à) allows us to use more exotic orbits like highly elliptical ones.," Although in the DM scenario we use only circular orbits,the use of both $x$ and $y$ coordinates (and not merely $r$ ) allows us to use more exotic orbits like highly elliptical ones."
In Fig 7 πο show the decav of the GC's [rom a distance. of LAApe from Fornax which is close to the maximumobservecl projected. distance.,In Fig \ref{fig:idf} we show the decay of the GCs from a distance of $1.4~kpc$ from Fornax which is close to the maximumobserved projected distance.
 This starting, This starting
Finally. one obtains the X-ray heating rate per baryon. cx from eq. (11)),"Finally, one obtains the X-ray heating rate per baryon, $\epsilon_{\rm X}$ from eq. \ref{eq:dTkdz}) )"
" by integrating over frequency and z: where r, is the proper. null-geodesic separation of z and z. and the frequency integral includes a sum over species. ;= HI. Hel. or Hell. in which f; is the number fraction. .'; is the cell's species ionization fraction [which forHI and Hel is (Ίο) and for Hell is 7. ]. 0; the ionization cross-section. and ££!"" is the ionization threshold energy of species ;."," by integrating over frequency and $z''$: where $r_p$ is the proper, null-geodesic separation of $z'$ and $z''$, and the frequency integral includes a sum over species, $i=$ HI, HeI, or HeII, in which $f_i$ is the number fraction, $x_i$ is the cell's species' ionization fraction [which forHI and HeI is $(1-x_e)$ , and for HeII is $x_e$ ], $\sigma_i$ the ionization cross-section, and $E^{\rm th}_i$ is the ionization threshold energy of species $i$."
 The factor fiiihieEp(κ.σ’Ἱ is defined as the fraction of theenergy. hiLi.deposited as heat.," The factor $f_{\rm heat}[h\nu - E^{\rm th}_i, x_e({\bf x, z'})]$ is defined as the fraction of the, $h\nu - E^{\rm th}_i$,deposited as heat."
" We use the new results of ?.. to compute fi... as well as των and fps, below."," We use the new results of \citet{FS09}, to compute $f_{\rm heat}$, as well as $f_{\rm ion}$ and $f_{\rm Ly\alpha}$ below."
" These fractions take into account the cell's local ionization state. ο, as opposed to the global ΤΟΝΤ value... used to calculate the optical depth in eq. 1600)."," These fractions take into account the cell's local ionization state, $x_e$, as opposed to the global IGM value, $\bar{x}_e$, used to calculate the optical depth in eq. \ref{eq:tau}) )."
 Unfortunately. the double integral eq. C173) ," Unfortunately, the double integral eq. \ref{eq:eps}) )"
is slow to evaluate due to the attenuation term. which depends on both redshift and frequency (eq. 16).," is slow to evaluate due to the attenuation term, which depends on both redshift and frequency (eq. \ref{eq:tau}) )."
 To speed-up computation. we make the additional approximation that all photons with optical depth. τν<l are absorbed. while no photons with optical depth zx>1 are absorbed.," To speed-up computation, we make the additional approximation that all photons with optical depth, $\tau_{\rm X} \leq 1$ are absorbed, while no photons with optical depth $\tau_{\rm X} > 1$ are absorbed."
 Such a step-function attenuation has been shown to yield fairly accurate ionizing photon flux probability distributions (see Fig., Such a step-function attenuation has been shown to yield fairly accurate ionizing photon flux probability distributions (see Fig.
 2 in ?.. although comparisons were limited to a single set of parameters).," 2 in \citealt{MF09}, although comparisons were limited to a single set of parameters)."
 This approximation allows us to separate the frequency and redshift integrals in eq. (17)).," This approximation allows us to separate the frequency and redshift integrals in eq. \ref{eq:eps}) ),"
" removing the exponential attenuation term from dóx/dz"" and setting the lower bound of the frequency integral to either # or the frequency corresponding to an optical depth of unity. vp—pGrizz""). whichever is larger."," removing the exponential attenuation term from $d\phi_{\rm X}/dz''$ and setting the lower bound of the frequency integral to either $\nu_0$ or the frequency corresponding to an optical depth of unity, $\nu_{\tau=1}(\bar{x}_e, z,' z'')$, whichever is larger."
 Expanding and grouping the terms. we obtain: Now the integrand in both integrals only depends on a single variable. and the entire frequency integral can be treated as a function of z.," Expanding and grouping the terms, we obtain: Now the integrand in both integrals only depends on a single variable, and the entire frequency integral can be treated as a function of $z''$."
 Analogously. we can also express the ionization rate per particle in eq. (100) ," Analogously, we can also express the ionization rate per particle in eq. \ref{eq:ion_rate}) )"
as: where figheο.(x.z).j] is now the fraction ofthe electrons energy going intosecondary ionizations of species j. with the unity term inside the sum accounting for the primary ionization of species /.," as: where $f_{\rm ion, j}[h\nu - E^{\rm th}_i, x_e({\bf x, z'}), j]$ is now the fraction ofthe electron's energy going into ionizations of species $j$, with the unity term inside the sum accounting for the primary ionization of species $i$."
" The Lyman à background has two main contributors: X-ray excitation of HI. J/,x: and direct stellar emission of photons between aand the Lyman limit. /,,..."," The Lyman $\alpha$ background has two main contributors: X-ray excitation of HI, $J_{\rm \alpha, X}$; and direct stellar emission of photons between and the Lyman limit, $J_{\alpha, \ast}$."
 The former can easily be related to the X-ray heating rate. assuming that the X-ray energy injection rate is balanced by photons redshifting out of resonance (2): where fisheE.4OX.z)] is the fraction of the electron’s energy going into pphotons.," The former can easily be related to the X-ray heating rate, assuming that the X-ray energy injection rate is balanced by photons redshifting out of resonance \citep{PF07}: where $f_{\rm Ly\alpha}[h\nu - E^{\rm th}_i, x_e({\bf x, z})]$ is the fraction of the electron's energy going into photons."
 Because of the high resonant optical depth of neutral hydrogen. photons redshifting into any Lyman-» resonance at (x.2) will be absorbed in the IGM.," Because of the high resonant optical depth of neutral hydrogen, photons redshifting into any $n$ resonance at $\xz$ will be absorbed in the IGM."
 They then quickly and locally cascade with a fraction ficco(7) passing through aand inducing strong coupling (22)..," They then quickly and locally cascade with a fraction $f_{\rm recycle}(n)$ passing through and inducing strong coupling \citep{Hirata06, PF06}."
 Therefore. the direct stellar emission component of the bbaekground (in ? | + Jj ean be estimated with a sum over the Lyman resonance backgrounds (e.g. 29) the emissivity per unit↔ redshift (no.," Therefore, the direct stellar emission component of the background (in $^{-2}$ $^{-1}$ $^{-1}$ $^{-1}$ ) can be estimated with a sum over the Lyman resonance backgrounds (e.g. \citealt{BL05_WF}) ):, where the emissivity per unit redshift (no."
". ofl photons sl  Hz.) Where calculated analogously to the X-ray luminosity above: Here =(7) is the number of photons produced per Hz per stellar baryon, and is evaluated at the emitted (rest frame) frequency: The upper limit of the redshift integral in eg. (21))"," of photons $^{-1}$ $^{-1}$ ) is calculated analogously to the X-ray luminosity above: Here $\varepsilon(\nu)$ is the number of photons produced per Hz per stellar baryon, and is evaluated at the emitted (rest frame) frequency: The upper limit of the redshift integral in eq. \ref{eq:Jalpha_stars}) )"
 corresponds to the redshift of the next Lyman resonance: Following ?.. we truncatethe sum at rax 23. and use their Population II and Population III spectral models for οί).," corresponds to the redshift of the next Lyman resonance: Following \citet{BL05_WF}, , we truncatethe sum at $n_{\rm max}=23$ and use their Population II and Population III spectral models for $\varepsilon(\nu)$ ."
 For computational efficiency. one can rearrange the terms in eq. (21)).," For computational efficiency, one can rearrange the terms in eq. \ref{eq:Jalpha_stars}) ),"
 placing the sum over Lyman transitions inside the redshift integral., placing the sum over Lyman transitions inside the redshift integral.
 Substituting in eq. (229) , Substituting in eq. \ref{eq:Lya_emiss}) )
and simplifying. we obtain:," and simplifying, we obtain:"
conjunction of the companion (i.e. when is at its closest position with respect to the observer) and phase 0.75 (to the superior conjunclion.,conjunction of the companion (i.e. when is at its closest position with respect to the observer) and phase 0.75 to the superior conjunction.
 In order (ο determine (he amplitude A of the radial velocity curve ancl the svstemic velocity > of the binary. system. we have fitted the data by using a function whieh is the sum of a constant and a sinusoid. adequate to describe the almost perfectly circular orbit of COM J1911—5958A. The best [it curve vields A.=237.5420.0 km ! and 4=—28.149 (1o uncertainties are used here and evervwhere in (he paper) ancl is reported in Figure 1..," In order to determine the amplitude $K$ of the radial velocity curve and the systemic velocity $\gamma$ of the binary system, we have fitted the data by using a function which is the sum of a constant and a sinusoid, adequate to describe the almost perfectly circular orbit of COM $-$ 5958A. The best fit curve yields $K=237.5\pm 20.0$ km $^{-1}$ and $\gamma = -28.1 \pm 4.9$ $1\sigma$ uncertainties are used here and everywhere in the paper) and is reported in Figure \ref{RVel}."
 The systemic velocity of the binary svstem is in agreement will the published racial motion of the globular cluster (Cexcicszss=—21.9x0.8. Harris et al.," The systemic velocity of the binary system is in agreement with the published radial motion of the globular cluster $v_{\rm NGC6752} =
-27.9 \pm 0.8$, Harris et al."
 1996. catalog revision 2003).," 1996, catalog revision 2003)."
 This lends further support to the cluster membership of the binary., This lends further support to the cluster membership of the binary.
 Given (he central 1-D dispersion velocity of NGC 6752 (9-15 kms !. Drukier et al.," Given the central 1-D dispersion velocity of NGC 6752 (9-15 km $^{-1}$, Drukier et al."
 2003). the expected 1-1) dispersion velocily for objects of mass 1.4—1.7 M. (corresponding to the most likely total nass of the binary. see later) and located at the projected position of with respect to the cluster center is 2-3 kins ! (Mapelli. private communication).," 2003), the expected 1-D dispersion velocity for objects of mass $1.4-1.7$ $_{\odot}$ (corresponding to the most likely total mass of the binary, see later) and located at the projected position of with respect to the cluster center is 2-3 km $^{-1}$ (Mapelli, private communication)."
 This is fully compatible with the value of the difference Ary=|5—txccurs2)z6 km 1 Moreover. the small value of Ney may indicate that the binary is now near apoastron of a uehlv elliptical orbit in the potential well of the elobular cluster.," This is fully compatible with the value of the difference $\Delta v_{\rm 1D}=|{\gamma}-v_{\rm NGC6752}|\lapp 6$ km $^{-1}.$ Moreover, the small value of $\Delta v_{\rm 1D}$ may indicate that the binary is now near apoastron of a highly elliptical orbit in the potential well of the globular cluster."
 In fact. were the binary on an almost cireular orbit al 74 core radii from the GC center. its line of sight velocity with respect to the cluster center (Sabbi et al.," In fact, were the binary on an almost circular orbit at 74 core radii from the GC center, its line of sight velocity with respect to the cluster center (Sabbi et al."
 2004). as estimated [rom the enclosed mass. would be of the order 212 km |. All these considerations support the hypothesis that the binary has been recently kicked out of the core of NGC 6752 due to a dynamical interaction (see 51).," 2004), as estimated from the enclosed mass, would be of the order $\gapp 12$ km $^{-1}.$ All these considerations support the hypothesis that the binary has been recently kicked out of the core of NGC 6752 due to a dynamical interaction (see 1)."
 We are in (he position of inlerring the ratio between the masses of the (wo stars in the binary., We are in the position of inferring the ratio between the masses of the two stars in the binary.
 The mass function of the pulsar. as measured [rom radio observation. is (Corongiu el al.," The mass function of the pulsar, as measured from radio observation, is (Corongiu et al."
" 2006): whereas (he mass function of (he companion. derived [rom (he present spectroscopic observations results: where-. 1.1,20.82111341100(1) davs (Corongiu et al."," 2006): whereas the mass function of the companion, derived from the present spectroscopic observations results: where $P_{\rm orb}=0.83711347700(1)$ days (Corongiu et al."
 2006). IX is the ;unplitude of the racial velocily curve. Mpag and. Meo; ave the masses of the pulsar and (he companion. / is the," 2006), K is the amplitude of the radial velocity curve, $M_{\rm PSR}$ and $M_{\rm COM}$ are the masses of the pulsar and the companion, $i$ is the"
in the course of lo1g slijulations).,in the course of long simulations).
 iil) Perhaps tle nxmt striking feature of the time-averaged plots is the suggestion of stroug cylindreal collimation iithe hiel-sdin models: whereas the 5 model shows a time-averaged patteru with a consta open180 augle of approximately 16 clegrees. tle plos of the hiel-spin moclels iudicate that the itra-relativist» components of the jets 1u roughly parallel to tve axis for r/AL= 300.," iii) Perhaps the most striking feature of the time-averaged plots is the suggestion of strong cylindrical collimation in the high-spin models; whereas the S model shows a time-averaged pattern with a constant opening angle of approximately 16 degrees, the plots of the high-spin models indicate that the ultra-relativistic components of the jets run roughly parallel to the axis for $r/M \gtrsim$ 300."
 For the tmocles with no initial ver‘al field. we find similar patteris for VW(r0) and (WV(0); with one imp«lant exceptio1> the uunul1 values seen in the time-averaged jxlots are systematically lower where 1o luit external fi is present.," For the models with no initial vertical field, we find similar patterns for $W(r,\theta)$ and $\langle W(r,\theta) \rangle_t$ with one important exception: the maximum values seen in the time-averaged plots are systematically lower where no initial external field is present."
 Collitmationli is uot euliauced by the initial external field IL Olr sinulations: : isis Che case in the simulationsi with uo itiitial exte‘hal field. the properties of the flLuel magnetic ield are areely determiued by the accretion flow (0090).," Collimation is not enhanced by the initial external field in our simulations; as is the case in the simulations with no initial external field, the properties of the funnel magnetic field are largely determined by the accretion flow (D05)."
 The dashed line in lhe top left parel of Figure 1. uxcates tie angle at whitchi a cut was take hroel ile knots for 1odel Εν., The dashed line in the top left panel of Figure \ref{f1} indicates the angle at which a cut was taken through the knots for model ${\rm E}_{\rm vf}$.
 Data along this cut is show 1 Figure [., Data along this cut is shown in Figure \ref{f2}.
 Tle top. panel shows Wr as a solid 1Ine alc| ο”H as a ¢ashedc line., The top panel shows $W(r)$ as a solid line and $\langle W(r)\rangle_{\rm t}$ as a dashed line.
 The grey slacecd regiois extending to the lower nne 1el» locae the Xhots ag€)ainst other code variables., The grey shaded regions extending to the lower panels help locate the knots against other code variables.
 Τιe second panel [rom the top shows )less Otal. gas. aud magietic). referenced to the ititial OFUus Duaximunm pressure: the knots sit it le roughs of outbouud pressure waves.," The second panel from the top shows pressure (total, gas, and magnetic), referenced to the initial torus maximum pressure; the knots sit in the troughs of outbound pressure waves."
 The bottom panel shows temperature. referenced oth πιlal torIs 1naxiinuna teimperature: the knots. which are at least in part heated by shocks. are sighificantly hotter than tle surrounding jet material. aud considerably hotter than the initial OJflls.," The bottom panel shows temperature, referenced to the initial torus maximum temperature; the knots, which are at least in part heated by shocks, are significantly hotter than the surrounding jet material, and considerably hotter than the initial torus."
 The jets show a prea deal of temporal variability., The jets show a great deal of temporal variability.
 Figure 5 shows the time clepeuceuce of radial mass flux (M=(pl? j) and energy flux (E=(775). including both the dominant fluid. entlalpy compotet and the electromaguetie component) of jet material (ejigq.27. 1.5) at r/AL= 15. near the base of the jet. and at r/A/= 100. iu the acceleration zone for model Evy.," Figure \ref{f3} shows the time dependence of shell-averaged radial mass flux $\dot{M}=\langle \rho\,U^r\rangle$ ) and energy flux $\dot{E}=\langle{T^r}_t\rangle$, including both the dominant fluid enthalpy component and the electromagnetic component) of jet material $e_{\rm bind} > 1.5$ ) at $r/M = $ 15, near the base of the jet, and at $r/M =$ 100, in the acceleration zone for model ${\rm E}_{\rm vf}$."
 Close to he black hole. fiue structure is detectable at a time scale comparable to the horizon üne.," Close to the black hole, fine structure is detectable at a time scale comparable to the horizon light-crossing time."
 Energy [ltx comes in intense bursts corresponcdiug to the passage of knots through the reeion. followed by exteusive quiescent periods.," Energy flux comes in intense bursts corresponding to the passage of knots through the region, followed by extensive quiescent periods."
 At larger radii. variability follows a similar pattern. out the fine stricture tends to be smoothed out by processes taking place higher iu the funnel. stch as entrainment (DO»5) aud shocks.," At larger radii, variability follows a similar pattern, but the fine structure tends to be smoothed out by processes taking place higher in the funnel, such as entrainment (D05) and shocks."
 Table 2. sumiuarizes the normalized rates of mass (M) aud energy (E) trausported by the jets and coronal wiud: tliese quantities are computed by integrating numerical fluxes through shells al r/AL= 100 (to compare 2D and 3D models) aud. normalized to initial torus mass (Mo) aud euergy (Ay). aud heuce are in units of inverse simulation time (A lj," Table \ref{results} summarizes the normalized rates of mass $\dot{M}$ ) and energy $\dot{E}$ ) transported by the jets and coronal wind; these quantities are computed by integrating numerical fluxes through shells at $r/M=$ 100 (to compare 2D and 3D models) and normalized to initial torus mass $M_0$ ) and energy $E_0$ ), and hence are in units of inverse simulation time $M^{-1}$ )."
 [tds üunportant to emphasize, It is important to emphasize
Ol course. this can be derived from Special Relativity. but the orientation here is {ο derive equation (4)) with no recourse to Relativity. nor to concepts of a similar vintage. such as photons.,"Of course, this can be derived from Special Relativity, but the orientation here is to derive equation \ref{eqn:emc2}) ) with no recourse to Relativity, nor to concepts of a similar vintage, such as photons."
 Jackson(1975) recapitulates Poynting(1884) s manipulations of Maxwell's equations to derive the electromagnetic energy [lux density S=(c/1x)ExH. where E and H are the electric and magnetic fields.," \citet{jackson} recapitulates \citet{poynting}' 's manipulations of Maxwell's equations to derive the electromagnetic energy flux density ${\bf S} = (c/4\pi){\bf E \times H}$, where ${\bf E}$ and ${\bf H}$ are the electric and magnetic fields."
 Ile (hen develops a similar manipulation of Maxwell's equations (logether with the Lorentz forcelaw) to derive the momentum density g=ExD/4zc. where D is the magnetic induction.," He then develops a similar manipulation of Maxwell's equations (together with the Lorentz forcelaw) to derive the momentum density ${\bf g} = {\bf E \times B}/4\pi c$, where ${\bf B}$ is the magnetic induction."
 Combining (hese two equations for monocdirectional electromagnetic waves in [ree space vields equation (6))., Combining these two equations for monodirectional electromagnetic waves in free space yields equation \ref{eqn:pegamma}) ).
 This shows that this relation rests directly on the Maxwell/Lorentz equations. allhough whether auvone actually derived the expression for g prior to the simplification of vector notation 1s not clear.," This shows that this relation rests directly on the Maxwell/Lorentz equations, although whether anyone actually derived the expression for ${\bf g}$ prior to the simplification of vector notation is not clear."
 llowever. Doltzmann(1884) already uses 2?=4/3 for isotropic electromagnetic radiation in his thermodynamic derivation of Stefans law.," However, \citet{boltzmann} already uses $P=u/3$ for isotropic electromagnetic radiation in his thermodynamic derivation of Stefan's law."
 Here 2 is (he pressure and wu is (he energy density., Here $P$ is the pressure and $u$ is the energy density.
 This expression already implies p—6 lor monodirectional electromagnetic waves., This expression already implies $p=E/c$ for monodirectional electromagnetic waves.
 As emphasized in 2.. bv carrving out the derivation only to first order in (v/c). I ultimatelv restricted its validitv to bodies at rest.," As emphasized in \ref{sec:derivation}, by carrying out the derivation only to first order in $(v/c)$, I ultimately restricted its validity to bodies at rest."
 Put. differently. if the (rue relation between mass and energy had the form. E=mer(l+s(ve/c)4...). the derivation would have proceeded exactly (he same way.," Put differently, if the true relation between mass and energy had the form, $E=m c^2(1 + \kappa(v/c)^2 + \ldots)$, the derivation would have proceeded exactly the same way."
 There are two paths to generalizing (he result to moving bodies., There are two paths to generalizing the result to moving bodies.
 The first is to adopt the results of Special Relativity., The first is to adopt the results of Special Relativity.
 This is the approach of (2003).. who derived E=mie? using momentum conservation when light is emitted in an arbitrary direction.," This is the approach of \citet{brown}, who derived $E=m c^2$ using momentum conservation when light is emitted in an arbitrary direction."
 Ia Special Relativity. equation (2)) is exact. so the derived. relation between mass and energy is exact (o all orders in (¢/e).," In Special Relativity, equation \ref{eqn:pgammamov}) ) is exact, so the derived relation between mass and energy is exact to all orders in $(v/c)$."
 This approach is pedagogicallyv useful like Einstein's derivation. it makes use of Special Relativity. but it is simpler and more direct.," This approach is pedagogically useful: like Einstein's derivation, it makes use of Special Relativity, but it is simpler and more direct."
 llowever. as a historical ancl logical exercise. one may also ask how equation (5)) could have been generalized if it had been discovered prior to Special Belativity.," However, as a historical and logical exercise, one may also ask how equation \ref{eqn:em0c2}) ) could have been generalized if it had been discovered prior to Special Relativity."
 Such a eeneralization [follows [rom a simple thought experiment., Such a generalization follows from a simple thought experiment.
 Imagine a box filled with warm eas. whose thermal enerev ultimately resides in the kinetic energv of the atoms.," Imagine a box filled with warm gas, whose thermal energy ultimately resides in the kinetic energy of the atoms."
 At the lime. (his picture was controversial but at least some plivsicists (e.g.. Doltzmaun) held to it.," At the time, this picture was controversial but at least some physicists (e.g., Boltzmann) held to it."
 Light is emitted [rom two holes in the box. similarly (o the situation in 2..," Light is emitted from two holes in the box, similarly to the situation in \ref{sec:derivation}. ."
 The energy of the lisht packets is drawn from the kinetic energv of the atoms in the box. some of which," The energy of the light packets is drawn from the kinetic energy of the atoms in the box, some of which"
ias the lowest entropy.,has the lowest entropy.
 When halos merge to form a new alo this low entropy gas. which would normally settle into he inner parts of the halo. is missing.," When halos merge to form a new halo this low entropy gas, which would normally settle into the inner parts of the halo, is missing."
 We take this into account by increasing the core radius of later generations of ialos so that the gas density at the virial racius is the same as Hb would have been if no gas had cooled in. progenitors (for a full description see Coleetal. 20000)., We take this into account by increasing the core radius of later generations of halos so that the gas density at the virial radius is the same as it would have been if no gas had cooled in progenitors (for a full description see \pcite{coleetal99}) ).
 The mode also allows us the option of keeping the core radius fixed. which we explore below.," The model also allows us the option of keeping the core radius fixed, which we explore below."
 The inclusion of a core in the 100 gas profile prevents the formation of extremely brigh galaxies in the centres of groups and clusters. which woule otherwise lead to a disagreement with the shape of the brigh end of the observed galaxy luminosity function.," The inclusion of a core in the hot gas profile prevents the formation of extremely bright galaxies in the centres of groups and clusters, which would otherwise lead to a disagreement with the shape of the bright end of the observed galaxy luminosity function."
 The reasons for choosing this particular profile ave therefore identical in spirit to those for preventing runaway cooling in the SPL simulations (see po[sec:SPLHass))., The reasons for choosing this particular profile are therefore identical in spirit to those for preventing runaway cooling in the SPH simulations (see \\ref{sec:SPHass}) ).
 Semi-analvtic models make several assumptions in the treatment of gas in order to obtain simple. analytic solutions to complex. hyvdrodyvnamical. processes.," Semi-analytic models make several assumptions in the treatment of gas in order to obtain simple, analytic solutions to complex hydrodynamical processes."
 We have already. mentioned the important. assumptions of spherical symmetry and of the shock-heating of the gas to the virial temperature of its associated halo., We have already mentioned the important assumptions of spherical symmetry and of the shock-heating of the gas to the virial temperature of its associated halo.
 The hot gas is then further assumed to settle into a distribution with a universal form., The hot gas is then further assumed to settle into a distribution with a universal form.
 Finally. the amount of gas that is able to cool by time | after the formation of the halo is identified with the gas contained within the radius at which the cooling time equals /.," Finally, the amount of gas that is able to cool by time $t$ after the formation of the halo is identified with the gas contained within the radius at which the cooling time equals $t$."
 Once it has cooled. this gas is assumed to low to the centre ofthe halo. where it is available for star formation. provided that the free-fall time for the gas is also less than /.," Once it has cooled, this gas is assumed to flow to the centre of the halo, where it is available for star formation, provided that the free-fall time for the gas is also less than $t$."
" We shall refer to this as the ""cooling radius? prescription.", We shall refer to this as the “cooling radius” prescription.
 In this section we compare several properties of the galaxy populations that form in our mocdoels anc consider how this comparison is allectec by varving certain assumptions and parameter values., In this section we compare several properties of the galaxy populations that form in our models and consider how this comparison is affected by varying certain assumptions and parameter values.
 We begin by comparing the most basic quantities calculated by cach technique. namely the fraction of gas in the hot and cold phases. both globally aud as a function of dark matter halo mass.," We begin by comparing the most basic quantities calculated by each technique, namely the fraction of gas in the hot and cold phases, both globally and as a function of dark matter halo mass."
" For these purposes. we define a ""hot halo gas phase’ as gas hotter than LOK: a ""galaxy. phase’ represented by cool. dense gas in the SPLE simulation and SDSA. and also including stars in disks and. spheroids in the FSA: and an ""uncollapsed. gas phase” consisting of everything else Le. gas outside virialised halos."," For these purposes, we define a `hot halo gas phase' as gas hotter than $10^5$ K; a `galaxy phase' represented by cool, dense gas in the SPH simulation and SDSA, and also including stars in disks and spheroids in the FSA; and an `uncollapsed gas phase' consisting of everything else — i.e. gas outside virialised halos."
 Note that for the galaxy phase. we consider. only galaxies. with. a mass greater than IN» σας particles in the SPII and mmoclels. but include galaxies of all masses in the niniodel.," Note that for the galaxy phase, we consider only galaxies with a mass greater than $N'_{\rm SPH}$ gas particles in the SPH and models, but include galaxies of all masses in the model."
 1n the Press-Schechter (or Sheth-Mo-Tormen) theory. all the matter in the universe is deemed to be in halos of some mass. and semi-analvtic models assume that gas in iios is shock heated to the halo virial temperature.," In the Press-Schechter (or Sheth-Mo-Tormen) theory, all the matter in the universe is deemed to be in halos of some mass, and semi-analytic models assume that gas in halos is shock heated to the halo virial temperature."
" We can herefore determine the fraction of gas in the uncollapsed gas phase in the numodel simply by integrating over the analytical mass unction (Sheth.Alo&VYormen1990). [fron zero mass o the mass corresponding to a virial temperature of 10""Ix. According to the spherical top-hat model of halo formation. he mass corresponding to 101 is: where Ac(s) is the overdensityv of a newly formed. virialised dark matter halo at recshilt z (e.g. Eke.Cole&Frenk 1996))."," We can therefore determine the fraction of gas in the uncollapsed gas phase in the model simply by integrating over the analytical mass function \cite{smt} from zero mass to the mass corresponding to a virial temperature of $10^5$ K. According to the spherical top-hat model of halo formation, the mass corresponding to $10^5$ K is: where $\Delta _{\rm c}(z)$ is the overdensity of a newly formed, virialised dark matter halo at redshift $z$ (e.g. \pcite{eke96}) )."
 Since some halos hotter than 107Ix. are not resolved in the mmoclel. the integration in this case is carried out from zero mass to Adjgsy or to INZpg dark matter particle masses. whichever is largest.," Since some halos hotter than $10^5{\rm K}$ are not resolved in the model, the integration in this case is carried out from zero mass to $M_{10^5{\rm K}}$ or to $N'_{\rm SPH}$ dark matter particle masses, whichever is largest."
 This estimate does not correspon exactly to the situation in the SPLIE simulation in which the largest halos are surrounded by gas at temperatures above 101 which extends bevond the virial radius., This estimate does not correspond exactly to the situation in the SPH simulation in which the largest halos are surrounded by gas at temperatures above $10^5$ K which extends beyond the virial radius.
 Because of this. the mmoclel calculation will elfectivelv overestimate the amoun of uncollapsed gas relative to the SPIEL simulation.," Because of this, the model calculation will effectively overestimate the amount of uncollapsed gas relative to the SPH simulation."
 On the other hand. gas in the SPLIT simulation tends to be slightly more extended than assumed. in the semi-analytic mode (i.c. the simulated. clusters tend to have a barvonic conten slightly smaller than the universal barvon fraction within a radius enclosing an overdensity of 200.— see e.g. Frenkeal. 19993).," On the other hand, gas in the SPH simulation tends to be slightly more extended than assumed in the semi-analytic model (i.e. the simulated clusters tend to have a baryonic content slightly smaller than the universal baryon fraction within a radius enclosing an overdensity of 200 – see e.g. \pcite{frenk99}) )."
 These two elfects counteract cach other to some degree., These two effects counteract each other to some degree.
 The amount of gas in the hot and galaxy phases depends upon the rate at which gas cools., The amount of gas in the hot and galaxy phases depends upon the rate at which gas cools.
 Therefore this comparison ests model. assumptions relating to the process of gas cooling. such as spherical symmetry and the cooling radius oescription in the semi-analvtie models or the clleets of smoothing in SPILL.," Therefore this comparison tests model assumptions relating to the process of gas cooling, such as spherical symmetry and the cooling radius prescription in the semi-analytic models or the effects of smoothing in SPH."
 This test will therefore be sensitive to he choice of gas density profile in the semi-analvtic modcls and to Nero in the simulations., This test will therefore be sensitive to the choice of gas density profile in the semi-analytic models and to $N_{\rm SPH}$ in the simulations.
 Since this comparison is concerned only with the total amount of gas in cillerent ohases. it is insensitive to the way in which the gas is apportioned into galaxies within a single halo. at least in he SPIIL and SDSA mocdels.," Since this comparison is concerned only with the total amount of gas in different phases, it is insensitive to the way in which the gas is apportioned into galaxies within a single halo, at least in the SPH and SDSA models."
 In the Πωπα some dependence on galaxy merger rates may exist. since merging can allect the star formation rate in a galaxy and thus alter the amount of gas reheated by [eedback. as well as the rate of chemical evolution. which in turn alters the cooling rates in subsequent generations of halos.," In the model, some dependence on galaxy merger rates may exist, since merging can affect the star formation rate in a galaxy and thus alter the amount of gas reheated by feedback, as well as the rate of chemical evolution, which in turn alters the cooling rates in subsequent generations of halos."
 Figure 2. shows the fraction of gas in each of the three, Figure \ref{fig:gastemp} shows the fraction of gas in each of the three
(Stohmaver&Watts2006).,\citep{key-8}.
. Ht is not clear whether they are associated to erustal modes. or to modes of the magnetic field or both: if the spacing between the observed Lrequencics would be explained. one may gain information on the internal structure of the star (Sotanietal.2007).," It is not clear whether they are associated to crustal modes, or to modes of the magnetic field or both; if the spacing between the observed frequencies would be explained, one may gain information on the internal structure of the star \citep{key-9}."
. The existence of a magnetar motivates to study the effects. of strong magnetic. field. on NS. properties., The existence of a magnetar motivates to study the effects of strong magnetic field on NS properties.
 A strong magnetic field. alfects. the structure of a NS through its influence on the underlying metric (Boequetetal.1995:Cardall2001) and Eos through the Landau quantization of charged. particles ancl then the interaction of magnetic moments of charged particles with the magnetic field.," A strong magnetic field affects, the structure of a NS through its influence on the underlying metric \citep{bbgn,cpl} and EoS through the Landau quantization of charged particles and then the interaction of magnetic moments of charged particles with the magnetic field."
 For the NAL with ao n-p-c system. the ellect of magnetic field was studied by several authors (Chakrabartyetal.L997:Yuan&Zhang1999:3roclericketal.," For the NM with a $n$ $p$ $e$ system, the effect of magnetic field was studied by several authors \citep{cbs,yz,bpl1,czl,wmkksg}."
2001:Chen2005:Wei 2006).. Llowever. as discussed. earlier the composition of the core of a NS is very uncertain. ancl different EoSs have been proposed to describe the matter at such extreme condition.," However, as discussed earlier the composition of the core of a NS is very uncertain, and different EoSs have been proposed to describe the matter at such extreme condition."
 The matter in the star may contain only deconfined quarks. which are known as SS. or the hyperons may appear. making hvperonic matter.," The matter in the star may contain only deconfined quarks, which are known as SS, or the hyperons may appear, making hyperonic matter."
 The cllect of magnetic field on quark matter using the MEE bag model has been. studied earlier (Chakrabarty1996:Ghosh&Chakrabarty2001:Felipeetal.," The effect of magnetic field on quark matter using the MIT bag model has been studied earlier \citep{chakra,gc,fmro}."
 2008).. Phere are other models of quark matter with phenomenological density dependent quark. masses (Fowleretal.1981:Chakrabarty1991:Dev1998:Lietal. 2010).," There are other models of quark matter with phenomenological density dependent quark masses \citep{fowler,chak,d98,lxl}."
. Broclerick et al., Broderick et al.
 (Brodericketal.2002) studied the effect. of strong magnetic field. on. hyperonic matter. where the field strength does not depend on density.," \citep{bpl2} studied the effect of strong magnetic field on hyperonic matter, where the field strength does not depend on density."
 Llowever. in reality. we expect the field strength should. be higher at core than at surface of a NS.," However, in reality, we expect the field strength should be higher at core than at surface of a NS."
 Pherefore. the field strength should vary with radius. and hence with density.," Therefore, the field strength should vary with radius, and hence with density."
 So the study of magnetic field in NS may provide with new different results ancl will help in understanding the basic properties of NS in a much better way., So the study of magnetic field in NS may provide with new different results and will help in understanding the basic properties of NS in a much better way.
 The magnetic field will also play an important role in the conversion of NS to Ss., The magnetic field will also play an important role in the conversion of NS to SS.
 The NS may convert to a SS bv several different wavs., The NS may convert to a SS by several different ways.
 A few possible mechanisms for the production of SQAL in a NS have been discussed by Aleock ct al (Aleocketal.1986)., A few possible mechanisms for the production of SQM in a NS have been discussed by Alcock et al \citep{al}.
. The conversion from hadron matter to quark matter is expected to start as the star comes in contact with a seed of external strange quark nugect., The conversion from hadron matter to quark matter is expected to start as the star comes in contact with a seed of external strange quark nugget.
 Another mechanism for the initiation of the conversion process was given bv Cilencdenninge (Clendenning1982.1992., Another mechanism for the initiation of the conversion process was given by Glendenning \citep{key-10}.
1992)... Lt was suggested. there that a sudden spin down of the star may increase the density at its core thereby triggering the Conversion process spontancouslv., It was suggested there that a sudden spin down of the star may increase the density at its core thereby triggering the conversion process spontaneously.
 Conversion of NM to SQAL has been studied by several authors. which are discussed in detail by Bhattacharyya et al (Bhattacharyyaetal.2006) and for brevity we clo not discuss them here.," Conversion of NM to SQM has been studied by several authors, which are discussed in detail by Bhattacharyya et al \citep{abhi} and for brevity we do not discuss them here."
 In this paper we plan to study the ellect of the density dependent magnetic field LoS on the conversion front., In this paper we plan to study the effect of the density dependent magnetic field EoS on the conversion front.
 We will write down the Rankine-Llugoniot condition Lor the matter velocities ancl solve them with the LoS derived. in presence of magnetic field., We will write down the Rankine-Hugoniot condition for the matter velocities and solve them with the EoS derived in presence of magnetic field.
 In. presence of magnetic field. both pressure (2?) ancl energy. density (2) of the system are alfected.," In presence of magnetic field, both pressure $P$ ) and energy density $\varepsilon$ ) of the system are affected."
 Vhis will indirectly give the ellect of magnetic field on the conversion front., This will indirectly give the effect of magnetic field on the conversion front.
 Phe paper is arranged in theFollowing wav: In the next section we construct our mocel for the magnetic field. dependent LoS. In section 3 we will discuss the kinematics of the phase transition for the magnetic field dependent LoS. In section 4. we will discuss about the propagation of the front along the star and in thefinal section we will summarize our results., The paper is arranged in thefollowing way: In the next section we construct our model for the magnetic field dependent EoS. In section \ref{rankine} we will discuss the kinematics of the phase transition for the magnetic field dependent EoS. In section \ref{dynamic} we will discuss about the propagation of the front along the star and in thefinal section we will summarize our results.
 First we construct the magnetic field. induced. Los. We use nonlinear Walecka model (Ellisetal.1991).. which was been successful in describing the nuclear ground. state »operties and clastic scattering (Walecka1974:Chin1977:Serot1979:&Walecka 1986).," First we construct the magnetic field induced EoS. We use nonlinear Walecka model \citep{wal}, which has been successful in describing the nuclear ground state properties and elastic scattering \citep{walecka,chin,serot,sw}."
".. In. addition to the model. here we consider the possibilitv of appearance of ivperons (X.EN.N.Wyτ2B"")ou and muons (jp. ) at higherRn clensitv."," In addition to the model, here we consider the possibility of appearance of hyperons $\Lambda, \Sigma^-, \Sigma^0, \Sigma^+,
\Xi^-, \Xi^0$ ) and muons $\mu^-$ ) at higher density."
 The detail of the calculation is similar to that of Sinha et al (Sinha&Müukhopadhyay2010) anc for brevity we only mention the important results of the model here.," The detail of the calculation is similar to that of Sinha et al \citep{sinha}
 and for brevity we only mention the important results of the model here."
 For the magnetic field. inclusion. we choose the gauge to. be. AY—(0.gyB.0.0). B being the magnitude of magnetic field. and. ος) the charge of the particle with e the positive unit of charge.," For the magnetic field inclusion we choose the gauge to be, $A^{\mu}\equiv(0,-y{\cal B},0,0)$, ${\cal B}$ being the magnitude of magnetic field and $eQ$ the charge of the particle with $e$ the positive unit of charge."
 For this particular gauge choice B=84., For this particular gauge choice ${\vec {\cal B}}={\cal B}\hat{z}$.
 In the presence of magnetic field. the motion of the charged particles is Landau quantized in the perpendicular direction to the magnetic field.," In the presence of magnetic field, the motion of the charged particles is Landau quantized in the perpendicular direction to the magnetic field."
 The momentum in the w-y plane is quantized and hence the energy in the nth Landau level is eiven by With the above consideration we can write down the total energy density of matter as where ON denotes charge. neutral barvons. C' charged barvons and. ?¢ leptons.," The momentum in the $x$ $y$ plane is quantized and hence the energy in the $n$ th Landau level is given by With the above consideration we can write down the total energy density of matter as where $N$ denotes charge neutral baryons, $C$ charged baryons and $l$ leptons."
" cg.cp0.w and p are. fields of barvons. leptons. 0-mesons. d-niesons and p-mesons. with masses rmg.nmg.ne.nma and om, respectively. gee.dex and gog are coupling constants for interactions of aw and p mesons respectively with the barvon D."," $\psi_B,\psi_l,\sigma,\omega$ and $\rho$ are fields of baryons, leptons, $\sigma$ -mesons, $\omega$ -mesons and $\rho$ -mesons, with masses $m_B, m_l, m_\sigma,
m_\omega$ and $m_\rho$ respectively, $g_{\sigma B},
g_{\omega B}$ and $g_{\rho B}$ are coupling constants for interactions of $\sigma, \omega$ and $\rho$ mesons respectively with the baryon $B$ ."
 ((a) is the scalar. self interaction term (Glendenning1982.," $U(\sigma)$ is the scalar self interaction term \citep{glend8,bb}. ."
1985.1987:—Boguta&Boclmer L977).. We define pon)=pp πο. where pr is the Fermi momentum.," We define $p(n)~=~\sqrt{p_F^2 - 2ne|Q|{\cal B}}$ , where $p_F$ is the Fermi momentum."
where Llere the sum 7 runs over all clatapoints (dg) with standard deviation σι. £ is the fractional uncertainty in the predictions of the model (which following the discussion in section 3. Is taken to be £= 0.08) and the term GrGPn» is added. in quadrature to the denominator to account for systematic uncertainties in the model.,"where Here the sum $i$ runs over all datapoints $d_i$ $r^i_0$ ) with standard deviation $\sigma_i$, $E$ is the fractional uncertainty in the predictions of the model (which following the discussion in section \ref{sec-simulations} is taken to be $E=0.08$ ) and the term $\left(E r^{\rm X}_0(d^i)\right)^2$ is added in quadrature to the denominator to account for systematic uncertainties in the model."
 Given a set of moce parameters and. prior distributions for those parameters. 1. calculate la and 2a confidence limits by computing the likelihood threshold above which the integrated. likelihoo accounts for 69 and 95 per cent respectively of the tota probability.," Given a set of model parameters and prior distributions for those parameters, I calculate $1\sigma$ and $2\sigma$ confidence limits by computing the likelihood threshold above which the integrated likelihood accounts for 69 and 95 per cent respectively of the total probability."
 Finally. all model predictions are computed a the median. redshift of each sample. which L take to be >=0.08. although the precise value used. has little effec on the results.," Finally, all model predictions are computed at the median redshift of each sample, which I take to be $z=0.08$, although the precise value used has little effect on the results."
 i, Fig.
rο. 3.2 shows confidence limits in the Foax plane clerived from the observations shown in bie. 2.., \ref{fig-square} shows confidence limits in the $\Gamma-\sigma_8$ plane derived from the observations shown in Fig. \ref{fig-data}.
" Given values for ox and E. each model is fully specified: once we know Qu, and the conditional probability distribution relating the ""inferred? mass for the cluster observations in question to the truce cluster mass."," Given values for $\sigma_8$ and $\Gamma$, each model is fully specified once we know $\Omega_{\rm m}$ and the conditional probability distribution relating the “inferred” mass for the cluster observations in question to the true cluster mass."
" “Phe shaded: area labeled ""Cτο shows lo (dark region) and 2a (light region) confidence limits derived using the SM'T model and the C97 data. in an £0,20.3 background cosmology. with zero scatter between inferred. ancl true cluster mass (use of an open Qu,=0.3 cosmology makes virtually no difference to the results)."," The shaded area labeled “Croft” shows $\sigma$ (dark region) and $\sigma$ (light region) confidence limits derived using the SMT model and the C97 data, in an $\Omega_m=0.3$ background cosmology with zero scatter between inferred and true cluster mass (use of an open $\Omega_{\rm m}=0.3$ cosmology makes virtually no difference to the results)."
 Four other confidence regions are also shown in this fieure. cach one the result. of changing one aspect of the first. analvsis.," Four other confidence regions are also shown in this figure, each one the result of changing one aspect of the first analysis."
" First. the shaded: area labeled ""MW"" gives the le confidence region which results from using the MW model rather than the SAPP model."," First, the shaded area labeled “MW” gives the $1\sigma$ confidence region which results from using the MW model rather than the SMT model."
 Phe limits in this case are quite different. and given the poor performance of the MW. model when compared to simulations. should be disregarded.," The limits in this case are quite different, and given the poor performance of the MW model when compared to simulations, should be disregarded."
" Second. the shaded. region labeled. ""Lec? shows the le limits resulting from using the LDP99 data (with its higher values lor rg) rather than the COS data."," Second, the shaded region labeled “Lee” shows the $\sigma$ limits resulting from using the LP99 data (with its higher values for $r_0$ ) rather than the C98 data."
 Vhe LP99 cata favours dramatically lower values of E for a given. value of ox. and since the majority of alternative datasets (see LP99 for a detailed: discussion) also prefer higher values of ry. the high E region to the right of the “Croft” confidence limits is likely to be excluded: by al current observations.," The LP99 data favours dramatically lower values of $\Gamma$ for a given value of $\sigma_8$, and since the majority of alternative datasets (see LP99 for a detailed discussion) also prefer higher values of $r_0$ , the high $\Gamma$ region to the right of the “Croft” confidence limits is likely to be excluded by all current observations."
 Thirdlv. the long-cash lines delineate the le confidence region resulting from an analysis identica to the “Croft” analysis. except. for the choice. of a Ila On=1 cosmology.," Thirdly, the long-dash lines delineate the $\sigma$ confidence region resulting from an analysis identical to the “Croft” analysis except for the choice of a flat $\Omega_{\rm m}=1$ cosmology."
" Increasing ©, slightly increases the amplification of clustering by redshift space distortion. anc slightly reduces the growth factor at the median redshift of the sample."," Increasing $\Omega_{\rm
m}$ slightly increases the amplification of clustering by redshift space distortion, and slightly reduces the growth factor at the median redshift of the sample."
 Both of these ellects are small. and the resulting confidence region is very similar to the Le limits resulting from the ιν=0.3 analysis.," Both of these effects are small, and the resulting confidence region is very similar to the $1\sigma$ limits resulting from the $\Omega_{\rm m}=0.3$ analysis."
 Lastly. the short dashed. lines delineate La confidence regions obtained when a significant scatter is introduced. between the inferred. and true cluster masses.," Lastly, the short dashed lines delineate $\sigma$ confidence regions obtained when a significant scatter is introduced between the inferred and true cluster masses."
 In. particular. pMt[A) is modeled as a log-normal distribution with a natural logarithmic stancard deviation σ=04.," In particular, $p({\cal M}|M)$ is modeled as a log-normal distribution with a natural logarithmic standard deviation $\sigma=0.4$."
 This value of σ corresponds to roughly a 50. per cent scatter in the inferred. mass for a given truc mass., This value of $\sigma$ corresponds to roughly a 50 per cent scatter in the inferred mass for a given true mass.
" Even for such a large scatter. the 1e confidence region is virtually unchanged. demonstrating that robust constraints can be obtained even if clusters of a given mass have a wide distribution of ""richness"" values - the only. requirement is that there is some monotonic transformation which loosely correlates the richness (for instance. N-rav. luminosity or ealaxy counts) with the true mass."," Even for such a large scatter, the $\sigma$ confidence region is virtually unchanged, demonstrating that robust constraints can be obtained even if clusters of a given mass have a wide distribution of “richness” values - the only requirement is that there is some monotonic transformation which loosely correlates the richness (for instance, X-ray luminosity or galaxy counts) with the true mass."
 Fig., Fig.
 3. demonstrates that observations of the cluster correlation length place constraints on the amplitude shape of the matter power spectrum in the universe which are almost independent. of cosmology., \ref{fig-square} demonstrates that observations of the cluster correlation length place constraints on the amplitude shape of the matter power spectrum in the universe which are almost independent of cosmology.
 As one final. point. ] illustrate the type of cosmological constraints which can be obtained when these limits are combined with independent observations of the mass power spectrum.," As one final point, I illustrate the type of cosmological constraints which can be obtained when these limits are combined with independent observations of the mass power spectrum."
 Fig., Fig.
" + shows confidence limits in the Qy,ax plane from a combination of cluster correlation length data ancl cluster number abundance data.", \ref{fig-square_omega} shows confidence limits in the $\Omega_{\rm m}-\sigma_8$ plane from a combination of cluster correlation length data and cluster number abundance data.
Ehe dark and light hashed regions show lec and 2e confidence bandsderived. from the local cluster temperature function by Ike. Cole Lrenk (ECE - 1996).,"The dark and light hashed regions show $\sigma$ and $\sigma$ confidence bandsderived from the local cluster temperature function by Eke, Cole \markcite{ECF} (ECF - 1996)."
 The other confidence bands show, The other confidence bands show
As described in the first paper of this series (Bareza2010.. hereafter Paper D) à new method can be used to determine fundamental parameters. of RR Lyrae (RR) stars. using broad-band optical photometry and. the conservation laws of mass and momentum in the pulsating atmosphere.,"As described in the first paper of this series \citealt{barc4}, hereafter Paper I) a new method can be used to determine fundamental parameters of RR Lyrae (RR) stars using broad-band optical photometry and the conservation laws of mass and momentum in the pulsating atmosphere."
 The first. version of the method (Bareza2003.2006) used. the Law of momentum conservation in the frame of a uniform atmosphere approximation (UNA). that is. the pulsation of the atmosphere. is taken into account as if the atmosphere were a rigid shell.," The first version of the method \citep{barc2,barc5} used the law of momentum conservation in the frame of a uniform atmosphere approximation (UAA), that is, the pulsation of the atmosphere is taken into account as if the atmosphere were a rigid shell."
" The available Johnson-Cousins (PV(RL¢: photometries of SU Dra and T Sex (Bareza2002.2006) were processed as examples because these uniformly cover the whole evele of pulsation and allow a solution of the Euler equation of hydrocdsnamics for the mass M,, of the star and distance d to it. ("," The available Johnson-Cousins $UBV(RI)_C$ photometries of SU Dra and T Sex \citep{barc0,barc5} were processed as examples because these uniformly cover the whole cycle of pulsation and allow a solution of the Euler equation of hydrodynamics for the mass ${\cal M}_{\rm a}$ of the star and distance $d$ to it. ("
Lhe subseript ‘a’ indicates that this mass is a civnanmical mass derived. from an analysis of the motion of the atmosphere.),The subscript 'a' indicates that this mass is a dynamical mass derived from an analysis of the motion of the atmosphere.)
 In Paper L an extended. hydrodynamic treatment. in which the UAA is dropped. was reported.," In Paper I, an extended hydrodynamic treatment, in which the UAA is dropped, was reported."
 Phe following two main steps were involved., The following two main steps were involved.
 Because the ATLAS models apply to the atmosphere of non-variable stars. quantitative photometric ane hiverodyvnamic conditions (Conditions | anc Ll in Paper I. hereafter C and CH. respectively) were. formulate [or the applicability of the quasi-static atmosphere approximation (QSAA) in order to find the time| intervals of the pulsation when dynamical phenomena have a negligible elect on the colours and brightness. (ic. the structure au colours of the atmosphere are identical to those of a selectec ATLAS model).," Because the ATLAS models apply to the atmosphere of non-variable stars, quantitative photometric and hydrodynamic conditions (Conditions I and II in Paper I, hereafter ${\rm C}^{\rm (I)}$ and ${\rm C}^{\rm (II)}$, respectively) were formulated for the applicability of the quasi-static atmosphere approximation (QSAA) in order to find the time intervals of the pulsation when dynamical phenomena have a negligible effect on the colours and brightness, (i.e. the structure and colours of the atmosphere are identical to those of a selected ATLAS model)."
 Ao summary of the conditions is as follows., A summary of the conditions is as follows.
 €m| is satisfied if the clifference of the continuum. Luxes of the observed. and. selected. ATLAS model does not exceed the error of the observation in the optical spectrum: covered. by the colours C., ${\rm C}^{\rm (I)}$ is satisfied if the difference of the continuum fluxes of the observed and selected ATLAS model does not exceed the error of the observation in the optical spectrum covered by the colours $U$ $I_C$.
.ide. (ub is satisfied if the acceleration in the atmosphere is equal to the instantaneous elfective gravity” golf) (CLedoux&Whitney1900) of the selected: ATLAS model., ${\rm C}^{\rm (II)}$ is satisfied if the acceleration in the atmosphere is equal to the instantaneous 'effective gravity' $g_{\rm e}(t)$ \citep{ledo1} of the selected ATLAS model.
"scale of 0.463 kpe for fp=T1. ο,=0.27 and Qy=0.73 (Carter et al.","scale of 0.463 kpc $^{-1}$ for $h=71$ , $\Omega_m=0.27$ and $\Omega_\lambda=0.73$ (Carter et al."
 2008)., 2008).
 In this paper. all magnitudes are in the AB system.," In this paper, all magnitudes are in the AB system."
 The HST ACS Coma cluster treasury survey is a deep two-passband imaging survey of one of the nearest rich cluster of galaxies., The HST ACS Coma cluster treasury survey is a deep two-passband imaging survey of one of the nearest rich cluster of galaxies.
 The completed survey covers 274 aremin? area of sky inthe core and infall region of the Coma cluster., The completed survey covers 274 $^2$ area of sky in the core and infall region of the Coma cluster.
 25 tields were imaged by ACS Wide Field Camera with the F475W (g-band) and F475W (I-band) filters., 25 fields were imaged by ACS Wide Field Camera with the F475W (g-band) and F475W (I-band) filters.
 Of 25 fields. 19 were located within 0.5 Mpe (0.3 deg) of Coma centre.," Of 25 fields, 19 were located within 0.5 Mpc (0.3 deg) of Coma centre."
 For the purpose of this study. we used the images of Data Release 2 (DR2). which include several improvements to the initial release.," For the purpose of this study, we used the images of Data Release 2 (DR2), which include several improvements to the initial release."
 Among the galaxies with DEIMOS spectroscopic data. 32 have HST/ACS images.," Among the galaxies with DEIMOS spectroscopic data, 32 have HST/ACS images."
 Reliable velocity dispersions were derived for 28 of these galaxies., Reliable velocity dispersions were derived for 28 of these galaxies.
 Four remaining galaxies were therefore excluded from the analysis., Four remaining galaxies were therefore excluded from the analysis.
 Moreover. velocity dispersion measurements were available for 4l more galaxies (34 from MGOS and 9 from Co09) in Coma for which ACS images at the above bands were available.," Moreover, velocity dispersion measurements were available for 41 more galaxies (34 from MG05 and 9 from Co09) in Coma for which ACS images at the above bands were available."
 The final sample consists of 71 galaxies with ACS images and determined velocity dispersion covering a luminosity range from Alyzc -22 to -15., The final sample consists of 71 galaxies with ACS images and determined velocity dispersion covering a luminosity range from $M_R\approx$ -22 to -15.
" For the purpose of this study. galaxies in. both FSIJW/FA75W images were extracted. usingSExtractor (Bertin Arnouts 1996) for photometry and measuring the initial model independent shape parameters such as the effective radius. /7,.. position angle and ellipticity."," For the purpose of this study, galaxies in both F814W/F475W images were extracted using (Bertin Arnouts 1996) for photometry and measuring the initial model independent shape parameters such as the effective radius, $R_e$, position angle and ellipticity."
 For each galaxy. the initial central position as well as the concentration parameter (i.e. C=5{ου(Γκυroo). where reo ου) iS the radius within which {SO (420) of the total galaxy light is collected) and the Kron radius. i.e. a characteristic radius as weighted by the light profile originally detined by Kron (19500. were measured using SExtractor.," For each galaxy, the initial central position as well as the concentration parameter (i.e. $C=5~log_{10}({r_{80}/r_{20})}$, where $r_{80}$ $r_{20}$ ) is the radius within which $\%80$ $\%20$ ) of the total galaxy light is collected) and the Kron radius, i.e. a characteristic radius as weighted by the light profile originally defined by Kron (1980), were measured using SExtractor."
 For each galaxy. we used both F8I4W/F475W bands to run SExtraetor in dual-image mode where F814W-band was used for object detection.," For each galaxy, we used both F814W/F475W bands to run SExtractor in dual-image mode where F814W-band was used for object detection."
 The SExtractor input parameters are directly taken from Table | of Hammer et al., The SExtractor input parameters are directly taken from Table 1 of Hammer et al.
 2010., 2010.
 Sérrsic function. defined as log Taner’. describes the structure of most. elliptical galaxies remarkably wel (Kormendy. 2009).," Sérrsic function, defined as log $\propto$ $^{1/n}$, describes the structure of most elliptical galaxies remarkably well (Kormendy, 2009)."
 To tind the best Sérrsic fit to the ligh profile. we used (version 3. Peng et al.," To find the best Sérrsic fit to the light profile, we used (version 3, Peng et al."
 2010)., 2010).
 For ACS images. the anisotropic PSF shape depends on the location of each object on ACS CCD chips (WFCI WFC2) and was modelled by (Krist. 1993).," For ACS images, the anisotropic PSF shape depends on the location of each object on ACS CCD chips (WFC1 WFC2) and was modelled by (Krist, 1993)."
 To run Galfit. initia values of the /?.. pi. galaxy position and galaxy position angle were taken from SExtractor initial run. and the initia value of the Sérrsic index 7 was set to 3.," To run Galfit, initial values of the $R_e$, $\mu_e$, galaxy position and galaxy position angle were taken from SExtractor initial run, and the initial value of the Sérrsic index $n$ was set to 3."
> Tests show tha with the well detined psf of ACS data the tinal solution does not depend strongly upon the initial value of » (see also Hoyos et al., Tests show that with the well defined psf of ACS data the final solution does not depend strongly upon the initial value of $n$ (see also Hoyos et al.
 2011)., 2011).
 Any object in the vicinity of the target galaxies was masked out., Any object in the vicinity of the target galaxies was masked out.
 It is important to leave enough sky background for a reliable estimation of the background level. as the estimated Sérrsic index. n. is slightly sensitive to the masked regions.," It is important to leave enough sky background for a reliable estimation of the background level, as the estimated Sérrsic index, $n$, is slightly sensitive to the masked regions."
 This sensitivity is higher for larger Sérrsic indices., This sensitivity is higher for larger Sérrsic indices.
" Comparing the estimated effective radius. C2... ie. the radius encompassing half-light of the galaxy) and effective surface brightness. C07... Le. the mean surface brightness within /7,.). from Galfit and SExtractor. we found that the difference in results (the scatter around the line with the slope ""one) is minimized when the size of the fitted area (galaxy and background) is about 2.5 times the Kron radius."," Comparing the estimated effective radius, $R_e$, i.e. the radius encompassing half-light of the galaxy) and effective surface brightness, $\langle \mu \rangle_e$, i.e. the mean surface brightness within $R_e$ ), from Galfit and SExtractor, we found that the difference in results (the scatter around the line with the slope “one"") is minimized when the size of the fitted area (galaxy and background) is about 2.5 times the Kron radius."
 In each case. the modelled galaxy and the Galfit residual images were inspected by eye to identify galaxies that are well described by Sérrsic model.," In each case, the modelled galaxy and the Galfit residual images were inspected by eye to identify galaxies that are well described by Sérrsic model."
 The galaxies with internal spiral structure or those with poor fit were excluded from the analysis., The galaxies with internal spiral structure or those with poor fit were excluded from the analysis.
 To study the dependency of measured Sérrsic indices on the observing wavelengths. surface brightness fitting was performed on both F475W/F8|4W images.," To study the dependency of measured Sérrsic indices on the observing wavelengths, surface brightness fitting was performed on both F475W/F814W images."
 The Sérrsic indices in F8I4W band are about higher than those of F475W band (see Figure 19)., The Sérrsic indices in F814W band are about higher than those of F475W band (see Figure \ref{fig:ser81475}) ).
 To study the wavelength dependency of the FP and PHP in 33.2.. for each band. the corresponding Sérrsie index and effective radius were used.," To study the wavelength dependency of the FP and PHP in \ref{chap:ppanalysis}, for each band, the corresponding Sérrsic index and effective radius were used."
 In addition to Galfit and SExtractor. the IRAP task inSTSDAS package is used to find and compare the radial light profile of each galaxy and its corresponding estimated. Sérrsic model.," In addition to Galfit and SExtractor, the IRAF task in package is used to find and compare the radial light profile of each galaxy and its corresponding estimated Sérrsic model."
 This helps to examine the reliability of the fitted profiles., This helps to examine the reliability of the fitted profiles.
 Moreover. the central surface brightness of galaxies. sry. are obtained from their estimated surface brightness profiles.," Moreover, the central surface brightness of galaxies, $\mu_0$, are obtained from their estimated surface brightness profiles."
 Figure 2. shows the example of two galaxies modelled by Sérrsic function., Figure \ref{fig:galfit} shows the example of two galaxies modelled by Sérrsic function.
 GMP 3080 seems to have an extra component at its centre which is well modelled by additional Gaussian function with FWHM s0.137. in another iteration.," GMP 3080 seems to have an extra component at its centre which is well modelled by additional Gaussian function with FWHM $\approx 0.13""$, in another iteration."
 The importance and physical meaning of this excess light is discussed in $4.2.., The importance and physical meaning of this excess light is discussed in \ref{subsec:extralight}.
 The estimated photometric and kinematic parameters of our 71 sample galaxies are presented in Table |.., The estimated photometric and kinematic parameters of our 71 sample galaxies are presented in Table \ref{tab:results}.
 Hoyos et al. (, Hoyos et al. (
2011) present a detailed comparison of effective radius and surface brightness with the ground-based data of Gutierrez et al. (,2011) present a detailed comparison of effective radius and surface brightness with the ground-based data of Gutierrez et al. (
2004) and Aguerri et al. (,2004) and Aguerri et al. (
2005).,2005).
 They find a good agreement. with a few outliers where complex structure is not well resolved in the ground-based data.," They find a good agreement, with a few outliers where complex structure is not well resolved in the ground-based data."
 Our derived values are in general in good agreement with those of Hoyos et al. (, Our derived values are in general in good agreement with those of Hoyos et al. (
2011) although. our derived values of the Sefssic index are somewhat lower.,"2011) although, our derived values of the Seŕssic index are somewhat lower."
 This difference can be attributed to the fact that we allow a separate nuclear component in some of the fits., This difference can be attributed to the fact that we allow a separate nuclear component in some of the fits.
 Taking all essential kinematic and photometric parameters. we have investigated the most well known scaling relations for our sample galaxies.," Taking all essential kinematic and photometric parameters, we have investigated the most well known scaling relations for our sample galaxies."
 Our sample consists of 7l dwarf galaxies which are fainter and lessmassive than the previously studied galaxies in the Coma cluster., Our sample consists of 71 dwarf galaxies which are fainter and lessmassive than the previously studied galaxies in the Coma cluster.
 The distribution of magnitude. velocity dispersion and Sérrsic index of our galaxies are represented in Figure 3..," The distribution of magnitude, velocity dispersion and Sérrsic index of our galaxies are represented in Figure \ref{fig:histogram}. ."
 In this, In this
Idan. L et al.,"Idan, I. et al."
 1998. in preparation King. AR. 1997. in ος.," 1998, in preparation King, A.R. 1997, in ed."
 J.-A. Marck J.-P. Lasota. (Cambridge: CUP). p. 105 Lasota. J.-P. 1996. inObjects. LÀU Coll.," J.-A. Marck J.-P. Lasota, (Cambridge: CUP), p. 105 Lasota, J.-P. 1996, in, IAU Coll."
 158. ed.," 158, ed."
 J.IT. Wood et al. (, J.H. Wood et al. (
"Dordrecht: IKIuwer). p. 385 Lasota. J.-P.. Tamemy. J.-M. Πιτόν, J.-M... 1995. AA, 302. L29 Liu. D.N.C.. Williams. R.E. Stover. R.J. 1958. ApJ. 327. 231 Livio. M. Spruit. IL. 1991. AA. 252. 150 Livio. M. Priugle J.. 1992. AINRAS 259. 23p Abuwsh. T. R. 1957. MNRAS. 228. 779 AMever EF. Moever-Hofiucister E. 1991. AA 288. 175 Alineshige. S. Wood. J.I. 1989. NENRAÀS. 211. 259 Abu. K.. Wood. J.IL.. Navlor. T.. Schlegel. EAL Swauk. J.D. 1997. ApJ. 175. NI2 Patterson. J. 1981. ApJS. 15. 517 Rutten. R.CLNLIC. van Paradijs.J. Tinbergen. J. 1992. AA, 260. 213 Shaviv. C. Welinse. R. 19856. A&AA. 169. L5 Shaviv. C. Welirse. R. 1991. A&AA. 251. 117 Sinak J. 198 l..Acta astron..","Dordrecht: Kluwer), p. 385 Lasota, J.-P., Hameury, J.-M. Huré,, J.-M., 1995, A, 302, L29 Lin, D.N.C., Williams, R.E. Stover, R.J. 1988, ApJ, 327, 234 Livio, M. Spruit, H. 1991, A, 252, 189 Livio, M. Pringle J., 1992, MNRAS 259, 23p Marsh, T. R. 1987, MNRAS, 228, 779 Meyer F. Meyer-Hofmeister E. 1994, A 288, 175 Mineshige, S. Wood, J.H. 1989, MNRAS, 241, 259 Mukai, K., Wood, J.H., Naylor, T., Schlegel, E.M. Swank, J.H. 1997, ApJ, 475, 812 Patterson, J. 1981, ApJS, 45, 517 Rutten, R.G.M.R., van Paradijs,J. Tinbergen, J. 1992, A, 260, 213 Shaviv, G. Wehrse, R. 1986, A, 169, L5 Shaviv, G. Wehrse, R. 1991, A, 251, 117 Smak J. 1984, Acta astron.,"
 31. 161 Sinak J. 1991. Acta astrou..," 34, 161 Smak J. 1994, Acta astron.,"
 LL. 265 Snak J. 1996. inObjects. TAU Coll.," 44, 265 Smak J. 1996, in, IAU Coll."
 195. ed.," 158, ed."
 J.II. Wood et al. (, J.H. Wood et al. (
"Dordrecht: νο), p. 15 Snak J. 1998. this volume Tyleuda. B. 1981. Acta astron..","Dordrecht: Kluwer), p. 45 Smak J. 1998, this volume Tylenda, R. 1981, Acta astron.,"
" 31. 127 Vrichnann. 8. 1997. PhD Thesis. University of Cótttingeu Wade. R.A. 1988. ApJ. 335. 391 Warner. D. 1995.Stars, (Cabridec: CUP) Wenzel. W. 1987. Astron."," 31, 127 Vrielmann, S. 1997, PhD Thesis, University of Götttingen Wade, R.A. 1988, ApJ, 335, 394 Warner, B. 1995, (Cambridge: CUP) Wenzel, W. 1987, Astron."
 Nachr.," Nachr.,"
" 308. 75 Williams. CoA. 1991. AJ. 101. 1929 Williams. R.E. 1980. ApJ. 235. 939 Wood. JID. 1990. AINRAS. 213. 219 Wood. J.IL. Morne. IK. Venues. S. 1992. ApJ 385. 291 Wood. JID. Horne. K.. Berriman. €. Wade. R. 1989. ApJ. 311. 971 Wood. IL. Navlor. T.. Hassal. DJ.M. Ramsaver. T.F. 1995. NINBAS. 273. 772 Wood. JIL. Ποιο, I... Berriman. C.. Wade. R. O'Donoghue. D. Warner. D. 1986. NINRAS. 219. 629 Zhang. E.-IT.. Robinson. E.L. Nather. R.E. 1986. ApJ. 305. 710"," 308, 75 Williams, G.A. 1991, AJ, 101, 1929 Williams, R.E. 1980, ApJ, 235, 939 Wood, J.H. 1990, MNRAS, 243, 219 Wood, J.H., Horne, K. Vennes, S. 1992, ApJ 385, 294 Wood, J.H., Horne, K., Berriman, G. Wade, R. 1989, ApJ, 341, 974 Wood, J.H., Naylor, T., Hassal, B.J.M. Ramsayer, T.F. 1995, MNRAS, 273, 772 Wood, J.H., Horne, K., Berriman, G., Wade, R. O'Donoghue, D. Warner, B. 1986, MNRAS, 219, 629 Zhang, E.-H., Robinson, E.L. Nather, R.E. 1986, ApJ, 305, 740"
the young outlier galaxies are the few brightest ones. which do not count as much towards the final residuals as the more numerous older and fainter population.,"the young outlier galaxies are the few brightest ones, which do not count as much towards the final residuals as the more numerous older and fainter population."
 Hence. luminosity-weighted residuals would be more useful for this purpose.," Hence, luminosity-weighted residuals would be more useful for this purpose."
 The stellar mass-to-light ratios can also be computed using the population synthesis models from BC99., The stellar mass-to-light ratios can also be computed using the population synthesis models from BC99.
 The ratio of mass to luminosity is a very age-sensitive quantity. thereby making it one of the most useful observables for breaking the age and metallicity degeneracy.," The ratio of mass to luminosity is a very age-sensitive quantity, thereby making it one of the most useful observables for breaking the age and metallicity degeneracy."
 Unfortunately. observed M/L ratios have large uncertainties so that a large sample in a wide range of redshifts is necessary in order to discriminate between formation scenarios.," Unfortunately, observed $M/L$ ratios have large uncertainties so that a large sample in a wide range of redshifts is necessary in order to discriminate between formation scenarios."
 Figures 6a and 6b show the predictions from our chemical enrichment model for the main parameters of the correlation between logM/Ly and log , Figures 6a and 6b show the predictions from our chemical enrichment model for the main parameters of the correlation between $\log M/L_V$ and $\log M$.
A non-zero slope yields the tilt of the fundamental plane M.relative to the expectation using the virial theorem., A non-zero slope yields the tilt of the fundamental plane relative to the expectation using the virial theorem.
 A range of chemical enrichment toy models results in a degeneracy for the slope. zero point and residuals of this correlation.," A range of chemical enrichment toy models results in a degeneracy for the slope, zero point and residuals of this correlation."
 In analogy with the CM relation. these parameters are most sensitive to age differences as shown in figure 6b for three star formation scenarios.," In analogy with the CM relation, these parameters are most sensitive to age differences as shown in figure 6b for three star formation scenarios."
 The middle panels show there is good agreement in the zero points with M/L observations measured for five clusters: Coma (z= 0.02). C11358462 (z= 0.33). CI0024416 (z= 0.39). MS2053+03 (z= 0.58) and MS1054-03 (z2 0.83). obtained from the compilation of Van Dokkum et al. (1998). ," The middle panels show there is good agreement in the zero points with $M/L$ observations measured for five clusters: Coma $z=0.02$ ), Cl1358+62 $z=0.33$ ), Cl0024+16 $z=0.39$ ), MS2053+03 $z=0.58$ ) and MS1054-03 $z=0.83$ ), obtained from the compilation of Van Dokkum et al. \markcite{vdk98}. ."
The trend with redshift gives a linear fit AlogM/Ly=—0.34z for the range θ«zlI. in agreement with Van Dokkum et al. (1998).," The trend with redshift gives a linear fit $\Delta\log M/L_V=-0.34z$ for the range $0<z<1$, in agreement with Van Dokkum et al. \markcite{vdk98},"
. who find AlogzM/Lj=—0.4z., who find $\Delta\log M/L_B=-0.4z$.
 However. we can see in the figures that this evolution is not linear. and so a fit using a wider range of redshifts 0<z«2 gives a flatter slope AlogM/Ly2—0.28z.," However, we can see in the figures that this evolution is not linear, and so a fit using a wider range of redshifts $0<z<2$ gives a flatter slope $\Delta\log M/L_V=-0.28z$."
 The residuals could represent a way of discerning the formation history. but given realistic values for the error bars. we doubt that cluster observations. at least in the redshift range 0<zI could be used for this purpose.," The residuals could represent a way of discerning the formation history, but given realistic values for the error bars, we doubt that cluster observations, at least in the redshift range $0<z<1$ could be used for this purpose."
 A comparison of the slopes obtained with purely stellar masses — around M/LyxM!5 for a monolithic model — with actual observations: M/Lο. (e.g. Mobasher et al. 1999)), A comparison of the slopes obtained with purely stellar masses — around $M/L_V\propto M^{0.075-0.085}$ for a monolithic model — with actual observations: $M/L\propto M^{0.15-0.25}$ (e.g. Mobasher et al. \markcite{mob99}) )
 shows that stellar masses alone cannot account for this. and dark matter (DM) should therefore be included.," shows that stellar masses alone cannot account for this, and dark matter (DM) should therefore be included."
 The slope mismatch is caused by a correlation between stellar mass and dark matter. so that there is more invisible mass in galaxies with more mass in stars.," The slope mismatch is caused by a correlation between stellar mass and dark matter, so that there is more invisible mass in galaxies with more mass in stars."
 Given that the model presented in this paper only gives the average. qualitative trend of different observables. we should only take these slopes as indicative.," Given that the model presented in this paper only gives the average, qualitative trend of different observables, we should only take these slopes as indicative."
 However. if we speculate that the actual mismatch between mass in stars and DMis similar to the one obtained here (1.9. between a slope of ~0.15—0.25 for DM and ~0.075—0.085P for stars). then the trend should be Mpa:xMz. with a=1.154 0.08. re. the scaling between dark matter and luminous matter is roughly linear. which implies à mass-independent bias for ellipticals.," However, if we speculate that the actual mismatch between mass in stars and DMis similar to the one obtained here (i.e. between a slope of $\sim 0.15-0.25$ for DM and $\sim 0.075-0.085$ for stars), then the trend should be $M_{\rm DM}\propto M_{\rm St}^\alpha$, with $\alpha=1.15\pm 0.08$ , i.e. the scaling between dark matter and luminous matter is roughly linear, which implies a mass-independent bias for ellipticals."
 This renders the studies of (stellar) M/L ratios using population synthesis models applicable to dynamical masses as Well. with the proviso that an offset should be added when dealing with the total mass.," This renders the studies of (stellar) $M/L$ ratios using population synthesis models applicable to dynamical masses as well, with the proviso that an offset should be added when dealing with the total mass."
 The abundance of magnesium traces the star formation history of the population of massive stars in the galaxy., The abundance of magnesium traces the star formation history of the population of massive stars in the galaxy.
 It is strongly correlated with the central velocity dispersion (c) which implies an enhanced star formation rate in more massive ellipticals., It is strongly correlated with the central velocity dispersion $\sigma$ ) which implies an enhanced star formation rate in more massive ellipticals.
 This correlation might possibly depend on the environment as found by Guzmánn etal., This correlation might possibly depend on the environment as found by Guzmánn etal.
 and Jérgensen. Franx Kjegaard (1996)...," \markcite{gu92} and rgensen, Franx gaard \markcite{jo96}. ."
 Furthermore. there is an overabundance of magnesium in the cores of the," Furthermore, there is an overabundance of magnesium in the cores of the"
image region.,image region.
 A percentage variation in the overall scalings ofthe halo. disc and bar components will make less dilference to the lensing than a change in the bulge value.," A percentage variation in the overall scalings of the halo, disc and bar components will make less difference to the lensing than a change in the bulge value."
 These results demonstrate the nature of stacking these mass coniponents., These results demonstrate the nature of stacking these mass components.
 An increase in the halo mass (for example. due to à small core region) would necessitate a decrease in the bulge.," An increase in the halo mass (for example, due to a small core region) would necessitate a decrease in the bulge."
 For this to be an adequate solution. however. the halo cannot be too large. otherwise it contributes too much rotation at the HE points. and the loss in shear from the bulge must be compensated for in another elliptical component.," For this to be an adequate solution, however, the halo cannot be too large, otherwise it contributes too much rotation at the HI points, and the loss in shear from the bulge must be compensated for in another elliptical component."
 Thus. the combination of requiring correct. convergence shear ds able to break the disc/halo degeneracy. removing the need to consider both maximal and. minimal disces (Maller et al.," Thus, the combination of requiring correct convergence shear is able to break the disc/halo degeneracy, removing the need to consider both maximal and minimal discs (Maller et al."
 2000)., 2000).
luminosities (e.g.. Caldwell et 11993. van Dokkum et 11998b. Kuntschner Davies 1998). ,"luminosities (e.g., Caldwell et 1993, van Dokkum et 1998b, Kuntschner Davies 1998). }}"
There are several ways in which this conflict can be solved., There are several ways in which this conflict can be solved.
 First. we can adapt the starformation histories.," First, we can adapt the starformation histories."
 The model assumes that star formation in elliptical and SO. galaxies commenced at z2x. and that their star formation rate was approximately constant from fa to fup.," The model assumes that star formation in elliptical and S0 galaxies commenced at $z=\infty$, and that their star formation rate was approximately constant from $\tstart$ to $\tstop$."
 If star formation in elliptical galaxies commenced at a later time the systematic difference between elliptical and SO galaxies ts reduced., If star formation in elliptical galaxies commenced at a later time the systematic difference between elliptical and S0 galaxies is reduced.
 If. £44=0.2% for elliptical galaxies (e.. star formation commenced at z 2.5) the systematic difference in M/L ratio between elliptical and SO galaxies at z=O is very small.," If $\tstart = 0.2 \t0$ for elliptical galaxies (i.e., star formation commenced at $z \approx 2.5$ ) the systematic difference in $M/L$ ratio between elliptical and S0 galaxies at $z=0$ is very small."
 However. it increases to z:0.3 in In(M/Lg) at z=0.8.," However, it increases to $\approx 0.3$ in $\ln (M/L_B)$ at $z=0.8$."
 This corresponds to a systematic difference in U—B color of 0.06. which is inconsistent with the low scatter 1n the CM relation of early type galaxies at z20.83 (van Dokkum et 22000).," This corresponds to a systematic difference in $U-B$ color of $0.06$, which is inconsistent with the low scatter in the CM relation of early type galaxies at $z=0.83$ (van Dokkum et 2000)."
 An alternative explanation for the small observed difference between luminous elliptical and SO galaxies is that most of their stars were formed at very high redshift., An alternative explanation for the small observed difference between luminous elliptical and S0 galaxies is that most of their stars were formed at very high redshift.
 In our models. this corresponds to low values of f.. the parameter describing the star formation history.," In our models, this corresponds to low values of $\fstar$ the parameter describing the star formation history."
 The systematic difference in M/L ratio scales linearly with f... and for values of f.<0.2 the systematic age difference between elliptical and SO galaxies Is <5 This explanation. can. be tested with the help of direct measurements of the star formation rates of the spiral galaxies in intermediate redshift clusters.," The systematic difference in $M/L$ ratio scales linearly with $\fstar$, and for values of $\fstar \lesssim 0.2$ the systematic age difference between elliptical and S0 galaxies is $\lesssim 5$ This explanation can be tested with the help of direct measurements of the star formation rates of the spiral galaxies in intermediate redshift clusters."
 A third possibility ts that the effects of metallicity cancel the effects of age (e.g.. Worthey. Trager. Faber 1996. Shioya Bekki 1998. Trager et 22000).," A third possibility is that the effects of metallicity cancel the effects of age (e.g., Worthey, Trager, Faber 1996, Shioya Bekki 1998, Trager et 2000)."
 The spiral galaxies would be enriched in metals compared to the elliptical galaxies of the same luminosity. and hence their colors would be redder. and their M/L ratios higher than that of elliptical galaxies with the same age.," The spiral galaxies would be enriched in metals compared to the elliptical galaxies of the same luminosity, and hence their colors would be redder, and their $M/L$ ratios higher than that of elliptical galaxies with the same age."
 This solution requires exact fine tuning between age and metallicity to keep the seatter small., This solution requires exact fine tuning between age and metallicity to keep the scatter small.
 It can be tested by direct observations of absorption line strengths of elliptical and SO galaxies in nearby and distant clusters., It can be tested by direct observations of absorption line strengths of elliptical and S0 galaxies in nearby and distant clusters.
 The first studies do not appear to indicate significant differences between massive elliptical and SO galaxies (e.g.. Kuntschner Davies 1998. Jones et 22000. Kelson et 22001).," The first studies do not appear to indicate significant differences between massive elliptical and S0 galaxies (e.g., Kuntschner Davies 1998, Jones et 2000, Kelson et 2001)."
 Finally. the separation of ellipticals and SO's 1 very difficult. and it is not clear whether a clear distinction can be made between elliptical galaxies and SO galaxies with L luminosities (e.g.. Jorrgensen Franx 1994. Rix White 1990).," Finally, the separation of ellipticals and S0's is very difficult, and it is not clear whether a clear distinction can be made between elliptical galaxies and S0 galaxies with $L_*$ luminosities (e.g., rgensen Franx 1994, Rix White 1990)."
 The latter study demonstrated that many elliptical galaxies contain significant disks. and would be classified as SO galaxies when seen edge-on.," The latter study demonstrated that many elliptical galaxies contain significant disks, and would be classified as S0 galaxies when seen edge-on."
 Jorgensen and Franx argued that the Coma elliptical and SO galaxies can be approximated well by a population of galaxies which has a homogeneous distribution in the ratio of bulge light to total light., Jorgensen and Franx argued that the Coma elliptical and S0 galaxies can be approximated well by a population of galaxies which has a homogeneous distribution in the ratio of bulge light to total light.
 In this case. no clearcut distinction would exist between SO galaxies and elliptical galaxies. and the evolutionary histories would not be so different between the galaxies.," In this case, no clearcut distinction would exist between S0 galaxies and elliptical galaxies, and the evolutionary histories would not be so different between the galaxies."
 This might also explain the fact that the classifications between different authors agree well when the total fraction of elliptical and SO galaxies is considered. but not when the classes are separated (e.g.. Andreon 1998. Fabricant et 22000).," This might also explain the fact that the classifications between different authors agree well when the total fraction of elliptical and S0 galaxies is considered, but not when the classes are separated (e.g., Andreon 1998, Fabricant et 2000)."
 Quantitative classifications would be able to resolve this issue. especially if detailed attention is given to the classification uncertainties due to projection effects.," Quantitative classifications would be able to resolve this issue, especially if detailed attention is given to the classification uncertainties due to projection effects."
 In this paper we have quantified the effects of morphological evolution on the observed properties of early-type galaxies in clusters at 0<zI., In this paper we have quantified the effects of morphological evolution on the observed properties of early-type galaxies in clusters at $0<z<1$.
 A manifestation of morphological evolution is the “progenitor bias”: at high redshift. the progenitors of the youngest present-day early-type galaxies drop out of the sample.," A manifestation of morphological evolution is the “progenitor bias”: at high redshift, the progenitors of the youngest present-day early-type galaxies drop out of the sample."
 In general. the observed evolution of the mean luminosity and color of early-type galaxies 1s slower than the true evolution of all progenitors of early-type galaxies. and the scatter in luminosity and color is smaller.," In general, the observed evolution of the mean luminosity and color of early-type galaxies is slower than the true evolution of all progenitors of early-type galaxies, and the scatter in luminosity and color is smaller."
 If morphological evolution is strong the observed mean evolution is similar to that of a single age stellar population formed at z2x. and the scatter Is approximately constant with redshift.," If morphological evolution is strong the observed mean evolution is similar to that of a single age stellar population formed at $z=\infty$, and the scatter is approximately constant with redshift."
 These results can be derived analytically AAppendix A))., These results can be derived analytically Appendix \ref{equations.sec}) ).
 In traditional models it is difficult to explain the low number fractions of early-type galaxies in. distant clusters and the homogeneity and slow evolution of their stellar populations simultaneously., In traditional models it is difficult to explain the low number fractions of early-type galaxies in distant clusters and the homogeneity and slow evolution of their stellar populations simultaneously.
 We have shown that the observed constant scatter in the CM relation and the FP and the slow evolution of the mean M/L ratio are natural consequences of morphological evolution., We have shown that the observed constant scatter in the CM relation and the FP and the slow evolution of the mean $M/L$ ratio are natural consequences of morphological evolution.
 Observations of early-type galaxies in. clusters. at θ«z| are well fitted by our models. and we can constrain the morphological transformation rate and the star formation histories of galaxies prior to transformation from the fits.," Observations of early-type galaxies in clusters at $0<z<1$ are well fitted by our models, and we can constrain the morphological transformation rate and the star formation histories of galaxies prior to transformation from the fits."
 The observed evolution of the early-type galaxy fraction constrains the transformation rate. the evolution of the mean M/L ratio constrains the time of onset of star formation. and the scatter in the color-magnitude relation and the Fundamental Plane constrain the star formation histories of galaxies prior to transformation.," The observed evolution of the early-type galaxy fraction constrains the transformation rate, the evolution of the mean $M/L$ ratio constrains the time of onset of star formation, and the scatter in the color-magnitude relation and the Fundamental Plane constrain the star formation histories of galaxies prior to transformation."
 The best fits are obtained if approximately present-day early-type galaxies were transformed from other morphological types at <<|. star formation commenced at early times (z> 2.5). and star formation was approximately constant prior to transformation.," The best fits are obtained if approximately present-day early-type galaxies were transformed from other morphological types at $z<1$, star formation commenced at early times $z>2.5$ ), and star formation was approximately constant prior to transformation."
 Such gradual star formation histories are consistent with the low numbers of star burst galaxies seen in intermediate redshift clusters (e.g.. Abraham et 11996. Balogh et 11998.Ellingson et 22000). although some star bursts could be concealed by dust (Poggianti et," Such gradual star formation histories are consistent with the low numbers of star burst galaxies seen in intermediate redshift clusters (e.g., Abraham et 1996, Balogh et 1998,Ellingson et 2000), although some star bursts could be concealed by dust (Poggianti et"
Methanol masers are commonly found in massive star-forming regions. with more than twenty different centimetre and millimetre wavelength masing transitions discovered to date (e...Mülleretal. 20043.,"Methanol masers are commonly found in massive star-forming regions, with more than twenty different centimetre and millimetre wavelength masing transitions discovered to date \citep[e.g.,][]{mul04}."
. All methanol maser transitions do not share the same behaviour., All methanol maser transitions do not share the same behaviour.
 Empirically. they form two classes (Batrlaetal.1987).," Empirically, they form two classes \citep{bat87}."
 Class I methanol masers (e.g. at 36. 44. 84. and 95 GHz) usually oceur in multiple locations across the star-forming region scattered around an area up to a parsec in extent (e...Kurtzetal.2004:Voronkovetal.2006:Cyganowski 2009).," Class I methanol masers (e.g. at 36, 44, 84, and 95 GHz) usually occur in multiple locations across the star-forming region scattered around an area up to a parsec in extent \citep[e.g.,][]{kur04,vor06,cyg09}."
. In contrast. class II methanol masers (e.g. at 6.7. 12 and 107 GHz) reside in the close vicinity of exciting young stellar objects (YSOs) and are typically ound as a single cluster of emission at arcsecond resolution (e.g..Phillipsetal. 1998).," In contrast, class II methanol masers (e.g. at 6.7, 12 and 107 GHz) reside in the close vicinity of exciting young stellar objects (YSOs) and are typically found as a single cluster of emission at arcsecond resolution \citep[e.g.,][]{phi98}."
. Theoretical calculations are able to explain his empirical classification and strongly suggest that the pumping orocess of class I masers is dominated by collisions with molecular ivdrogen. in contrast to class TT masers which are pumped by radiative excitation (e.g.Voronkovetal.2005.andreferences herein).," Theoretical calculations are able to explain this empirical classification and strongly suggest that the pumping process of class I masers is dominated by collisions with molecular hydrogen, in contrast to class II masers which are pumped by radiative excitation \citep[e.g.][and references therein]{vor05}."
 The morphology of class I methanol masers has recently become the focus of high angular resolution studies aimed at searching for associations with other phenomena commonly observed in regions of high-mass star-formation (e.g..Cyganowskietal. 2009)..," The morphology of class I methanol masers has recently become the focus of high angular resolution studies aimed at searching for associations with other phenomena commonly observed in regions of high-mass star-formation \citep[e.g.,][]{cyg09}."
 The common consensus is that the majority of class I masers trace interface regions between outflows and molecular gas. although direct observational evidence of this has been obtained for a limited number of sources only (e.g..Plam-beck&Menten1990:Kurtzetal.2004:Voronkov 20060.," The common consensus is that the majority of class I masers trace interface regions between outflows and molecular gas, although direct observational evidence of this has been obtained for a limited number of sources only \citep[e.g.,][]{pla90,kur04,vor06}."
 The alternative scenarios involving cloud-cloud collisions (e.g.. as well as the interaction of expanding regions with the ambient molecular environment (Voronkov.etal.2010) may also be realised in some sources.," The alternative scenarios involving cloud-cloud collisions \citep[e.g.,][]{sob92,sal02,sjo10} as well as the interaction of expanding regions with the ambient molecular environment \citep{vor10} may also be realised in some sources."
 The common point of all these scenarios is the presence of shocked gas. where the physical conditions are favouring class T methanol masers (see the discussion in section 4.1. below).," The common point of all these scenarios is the presence of shocked gas, where the physical conditions are favouring class I methanol masers (see the discussion in section \ref{hv_discussion} below)."
" Apart from the outflow associations cited above (based on the 2.12-//m H» emission. which is a well known shock tracer). Cvganowskietal.(2009). reported association of some class I maser spots with the extended features showing a prominent excess of the 4.5-//m emission in the images obtained with the Spitzer Space Telescope's Infrared Array Camera (RAC). also known as extended green objects (EGOs:Cyganowskietal.2009) or ""green fuzzies” (Chambersetal.2009)."," Apart from the outflow associations cited above (based on the $\mu$ m $_2$ emission, which is a well known shock tracer), \citet{cyg09} reported association of some class I maser spots with the extended features showing a prominent excess of the $\mu$ m emission in the images obtained with the Spitzer Space Telescope's Infrared Array Camera (IRAC), also known as extended green objects \citep[EGOs;][]{cyg09} or “green fuzzies” \citep{cha09}."
. The excess of the ὅ- μπι (TRAC band 2) emission could be a result of shock excitation of molecular hydrogen and carbon monoxide in protostellar outflows (Cyganowskietal.2009:Chambers2009:DeBuizer&Vacca 2010).," The excess of the $\mu$ m (IRAC band 2) emission could be a result of shock excitation of molecular hydrogen and carbon monoxide in protostellar outflows \citep{cyg09,cha09,deb10}."
. It is worth noting that Chenetal.(2009). demonstrated statistically the presence of an EGO in the vicinity of a large fraction of elass I methanol masers at low angular resolution (single dish positions)., It is worth noting that \citet{che09} demonstrated statistically the presence of an EGO in the vicinity of a large fraction of class I methanol masers at low angular resolution (single dish positions).
 To increase the number of class I masers studied at high angular resolution and to compare, To increase the number of class I masers studied at high angular resolution and to compare
10 ionisation [reeze-out but. as with ionisation [reeze-out. results in a luminosity exceeding that of the instantaneous radioactive decay deposition.,"the ionisation freeze-out but, as with ionisation freeze-out, results in a luminosity exceeding that of the instantaneous radioactive decay deposition."
 There is general agreement jut by day. 1200. the ejecta are predominantly neutral. but with a fraction of singlv-ionised species resulting from the ionisation [reeze-out and/or direct ionisation by non-thermal electrons.," There is general agreement that by day 1200, the ejecta are predominantly neutral, but with a fraction of singly-ionised species resulting from the ionisation freeze-out and/or direct ionisation by non-thermal electrons."
 During 1350.2000 days the electron. [raction is ~10? in the L-envelope. rising to 0.1 in the Fe-Lle zone (IxI958a).," During 1350–2000 days the electron fraction is $\sim10^{-3}$ in the H-envelope, rising to 0.1 in the Fe-He zone (KF98a)."
 At 3425 days. Lundavist et al. (," At 3425 days, Lundqvist et al. ("
2001) caleulate that the fraction of iron that is singlv-ionised. is in the range 0.20.4.,"2001) calculate that the fraction of iron that is singly-ionised, is in the range 0.2–0.4."
 The acdiabatic cooling becomes significant when the radiative cooling timescale becomes. longer than t1c expansic211 timescale., The adiabatic cooling becomes significant when the radiative cooling timescale becomes longer than the expansion timescale.
 For pure adiabatic cooling. Tx/7.," For pure adiabatic cooling, $\propto t^{-2}$."
 Owing to their lower density anc metallicity. adiabatic cooling is already. dominant as carly as ~250 days in the H-envelope and ~S00 clavs in the He-envelope (xb98a).," Owing to their lower density and metallicity, adiabatic cooling is already dominant as early as $\sim$ 250 days in the H-envelope and $\sim$ 800 days in the He-envelope (KF98a)."
 For the LLLe zones within the core. the higher densities mean that adiabatie cooling begins to dominate at SOO-I000. clays.," For the H/He zones within the core, the higher densities mean that adiabatic cooling begins to dominate at 800-1000 days."
 While fine-structure line cooling Ht catastrophe below) becomes the dominant radiative cooling mechanism in these zones. ib never supersedes adiabatic cooling.," While fine-structure line cooling IR catastrophe below) becomes the dominant radiative cooling mechanism in these zones, it never supersedes adiabatic cooling."
 Nevertheless. fine-structure line coolinge may be significante in these regionso (COT).," Nevertheless, fine-structure line cooling may be significant in these regions (C97)."
 IXF98a find that the H-envelope temperature lies in he range 400-1000 Ix on αν 1350. falling to a range of 150 Ix bv day 2000.," KF98a find that the H-envelope temperature lies in the range 400-1000 K on day 1350, falling to a range of 150--300 K by day 2000."
 The temperatures of the 11Πο zones within the core fall from. ~900 Ix to 7300 Ix over the same »eriod., The temperatures of the H/He zones within the core fall from $\sim$ 900 K to $\sim$ 300 K over the same period.
 “Phe day 2000 δα value compares well with the 300 Ix derived from the Balmer continuum by Wang et al. (, The day 2000 KF98a value compares well with the $\sim$ 300 K derived from the Balmer continuum by Wang et al. (
1996) for about the same time.,1996) for about the same time.
 The model of COT vields ~130 Ix for the L-envelope at 2875 days. compared with 3504100 Ix. derived from the Balmer continuum at that time.," The model of C97 yields $\sim$ 130 K for the H-envelope at 2875 days, compared with $\pm$ 100 K derived from the Balmer continuum at that time."
 Once the nebular heating/cooling rate drops below a certain level. cooling via low-lying fine-structure transitions dramatically overtakes optical ancl near-L1t transitions as the dominant radiative cooing mechanism.," Once the nebular heating/cooling rate drops below a certain level, cooling via low-lying fine-structure transitions dramatically overtakes optical and near-IR transitions as the dominant radiative cooling mechanism."
 Consequently the stabilising temperature falls abruptiy rom 2000 Ix toa [ew 100 Ix. and the bull of 1e nebulas. luminosity shifts to far-LR emission.," Consequently the stabilising temperature falls abruptly from $\sim$ 2000 K to a few $\times100$ K, and the bulk of the nebula's luminosity shifts to far-IR emission."
" This elec is known as the ""LH Catastrophe”. ancl was. predicted. by Axelrod (1980). in his pioneeringe work on type la spectral models."," This effect is known as the “IR Catastrophe”, and was predicted by Axelrod (1980) in his pioneering work on type Ia spectral models."
 Fransson Chevalier (1989). predicted: that. it. could. also occur in core-collapse SNe such as SN. 1987X. The first. clirect evidence for this phenomenon occurring in SN. LOSTA was obtained through the detailed: study of the evolution of the near-IRoptical Fe 1) lines during the second. vear, Fransson Chevalier (1989) predicted that it could also occur in core-collapse SNe such as SN 1987A. The first direct evidence for this phenomenon occurring in SN 1987A was obtained through the detailed study of the evolution of the near-IR/optical [Fe II] lines during the second year
emitter as a discrete source which emits a packet of line and continuum radiation spanning a certain frequency range.,emitter as a discrete source which emits a packet of line and continuum radiation spanning a certain frequency range.
 The packet is absorbed along the path of propagation subject to the optical depth., The packet is absorbed along the path of propagation subject to the optical depth.
 The strength of the emission from each emitter yo aand jj) is weighted according to a distribution profile in the envelope., The strength of the emission from each emitter $\eta_{c}$ and $\eta_l$ ) is weighted according to a distribution profile in the envelope.
 We consider 50000 emitters in each simulation., We consider 50000 emitters in each simulation.
 Phe observed Dux is the sum of the contribution of all emitters in the non-obscured region jt., The observed flux is the sum of the contribution of all emitters in the non-obscured region $\Re$.
 This quick-fix method allows us to handle complicatec ecometry due to obscuration easilv., This quick-fix method allows us to handle complicated geometry due to obscuration easily.
 Lt also enables us to survey various functional forms for the distribution profiles of the velocity. emissivity ancl absorption coefficients. arc obtain qualitative features of the line emission with sensible computational time.," It also enables us to survey various functional forms for the distribution profiles of the velocity, emissivity and absorption coefficients and obtain qualitative features of the line emission with sensible computational time."
 In Fig., In Fig.
 Al we show examples of line profiles for three cases in which the racial velocity distribution is apower-law function (with indices —1. 0 and. |1 rrespectively).," \ref{fig:A1} we show examples of line profiles for three cases in which the radial velocity distribution is apower-law function (with indices $-1$, 0 and $+1$ respectively)."
 In these cases. i£ the line absorption is weaker than the continuum absorption. x;«X. an asvmmetrie bluc-shilted profile can be obtained.," In these cases, if the line absorption is weaker than the continuum absorption, $\chi_l
< \chi_c$, an asymmetric blue-shifted profile can be obtained."
 H£ x;zye. the line is svimetric with no obvious shift of the line centre frequency.," If $\chi_l \approx \chi_c$, the line is symmetric with no obvious shift of the line centre frequency."
 LE yy29 ye. a profile will be obtained.," If $\chi_l > \chi_c$ , a P-Cygni profile will be obtained."
Chiappini et al. (,Chiappini et al. (
"2006) ou the other hand argue that the [C/O] πηρα can be explained through fast stellar rotation at very low inetallicifies. so that due to lower average core temperature, the couversion of C into O would be less efficient.","2006) on the other hand argue that the [C/O] upturn can be explained through fast stellar rotation at very low metallicities, so that due to lower average core temperature, the conversion of C into O would be less efficient."
 However. they also make it clear that it is not erauted that the high C/O values should necessarily imply the signature of massive Pop.," However, they also make it clear that it is not granted that the high C/O values should necessarily imply the signature of massive Pop."
 IIT stars. since their own results cau be achieved without includius zero-netallicity vields.," III stars, since their own results can be achieved without including zero-metallicity yields."
 Carigi et al. (, Carigi et al. (
2005) successfully fitted the observed radial eradieuts of C/O and O/II iu the Milky Way with models which use a steep IMF aud in which the relative proportions of carbou released iuto the iuterstellar nmuediuni by massive stars on the one haud. aud low- aud iutermecdiate-niass stars on the other. vary with time aud ealactocentric distance.,"2005) successfully fitted the observed radial gradients of C/O and O/H in the Milky Way with models which use a steep IMF and in which the relative proportions of carbon released into the interstellar medium by massive stars on the one hand, and low- and intermediate-mass stars on the other, vary with time and galactocentric distance."
 Their models are iu reasonably eood agreement. with the observed trends of the ratios IC/O]. [C/Fe| aud |O/Fe| reported here.," Their models are in reasonably good agreement with the observed trends of the ratios [C/O], [C/Fe] and [O/Fe] reported here."
 Nissen ct al. (, Nissen et al. (
2007) reported evidence for au mucrease in the abundance of Zu relative to Fe at the lowest mctallicities. with [Zu/Fe|z|0.5 at <n ,"2007) reported evidence for an increase in the abundance of Zn relative to Fe at the lowest metallicities, with $\simeq +0.5$ at $\apprle -3$."
Traditional viclds of Type Π SNe (Nomoto ct al., Traditional yields of Type II SNe (Nomoto et al.
 L997) cannot reach the high observed |Zu/Fo] values. which instead seem to require either the ejecta of Population III hyperuovae. or high Zu production from core-collapse. very nassive (M~500°1000 37.) stars (Obkubo ct al.," 1997) cannot reach the high observed [Zn/Fe] values, which instead seem to require either the ejecta of Population III hypernovae, or high Zn production from core-collapse, very massive $M \sim 500{-}1000\,M_{\odot}$ ) stars (Ohkubo et al."
 2006)., 2006).
 Ixobavashi et al. (, Kobayashi et al. (
2006) caleulated vields for a wide range of inetallicities (Z=O Z..) aud explosion energies. including hypernovac.,"2006) calculated yields for a wide range of metallicities $Z =0 - Z_{\odot}$ ) and explosion energies, including hypernovae."
 Their predicted and relatious seen to 11ateli our derived abunudances for halo stars (assuming Sy=0 and 1 for carbon and oxvecn respectively) fairly closely., Their predicted and relations seem to match our derived abundances for halo stars (assuming $_{\rm H}=0$ and $1$ for carbon and oxygen respectively) fairly closely.
 Ta particular for carbon. the agreement seenis to indicate that cnrichinent from stellar winds and the contribution of low- and intermeciate-lass stars are not muportaut for this clement at low metallicity. since those are not included iu the calculations by Ixobavashi et al. (," In particular for carbon, the agreement seems to indicate that enrichment from stellar winds and the contribution of low- and intermediate-mass stars are not important for this element at low metallicity, since those are not included in the calculations by Kobayashi et al. ("
2006).,2006).
 Those authors poiuted out that in order to explain simultaneously the high C abundances observed in extremely moetal-poor stars aud the supersolar Zu/Fo ratios at low metallicities. other euriclinent sources (c.g. a few Pop.," Those authors pointed out that in order to explain simultaneously the high C abundances observed in extremely metal-poor stars and the supersolar Zn/Fe ratios at low metallicities, other enrichment sources (e.g. a few Pop."
 III supernova explosions in the very carly inhomeegcucous intergalactic iuediuni or externa chrichinent frou a binary companion) are needed.," III supernova explosions in the very early inhomogeneous intergalactic medium, or external enrichment from a binary companion) are needed."
 The final C vields may in fact turn out to be even higher han predicted by I&obavashi aud collaborators. if winds of uassive stars at very low mictallicity contribute siguificaut additional amounts of carbon.," The final C yields may in fact turn out to be even higher than predicted by Kobayashi and collaborators, if winds of massive stars at very low metallicity contribute significant additional amounts of carbon."
 Finally. Suiüiljiuüic ct al. (," Finally, Smiljanic et al. ("
2008) very recently discussec ooswpble signatures of hvpernova uucleosvuthesis iu106038.. one of the stars iu our sample. for which we derive [Fe/TII]2.—1.37.,"2008) very recently discussed possible signatures of hypernova nucleosynthesis in, one of the stars in our sample, for which we derive ${\rm [Fe/H]} = -1.37$."
 Even though their livpothesis is uainlv based on very large beryllium eubancemeut. they also discuss available literature values for other elemoeuts.," Even though their hypothesis is mainly based on very large beryllium enhancement, they also discuss available literature values for other elements."
 For carbon aud oxygen in this star. we find .== |0.23/10.09 and .== |0.62/10.55. depending on whether IH collisious are included or uot.," For carbon and oxygen in this star, we find = +0.23/+0.09 and = +0.62/+0.55, depending on whether H collisions are included or not."
 The values of wwe deduce are iu good agreement with the mouLTE determination by Meléundez et al. (, The values of we deduce are in good agreement with the non–LTE determination by Melénndez et al. (
2006) of .=10.5640.10.,2006) of $=+0.56 \pm 0.10$.
" We have presented nonLTE corrected element abundances in a xuuple of 13 uactal-poor halo stars, and carried ouf the most extensive study to date of the relative abundances of carbon and oxvecu as a function of ietallicitv."," We have presented non–LTE corrected element abundances in a sample of 43 metal-poor halo stars, and carried out the most extensive study to date of the relative abundances of carbon and oxygen as a function of metallicity."
 Updated— estimates of stellar parameters for stars with Linthesampleof Akermanetal (, Updated estimates of stellar parameters for stars with $< -1$ in the sample of Akerman et al. (
200Dweredericedeonsistentlgwitht ο.,2004) were derived consistently with the rest of our sample stars following Nissen et al. (
.,2007).
. , Akerman et al. (
Ffectsomthe iamdO Winestheganat ReffeCsirsre quiredtocon f,"2004) estimated that, to a first approximation, non--LTE and 3D effects on the formation of the and lines they analysed are of similar magnitude so that their neglect should not lead to a systematic bias in the values of [C/O] deduced."
orinationoftheC firnithe realityofthe int ntatie," However, they also warned that a quantitative assessment of non--LTE effects was required to confirm the reality of their tentative findings."
r fi Ecorrections forbothCandQandceonsidercdadd, Here we have included non--LTE corrections for both C and O and considered additional lines; taken together these two aspects of the present work represent significant improvements over earlier published studies by reducing both systematic and statistical uncertainties in the determinations of the C and O abundances.
, The sample of stars analysed by Akerman et al. (
,2004) was subsequently used by Melénndez et al. (
itional€ ,2006) in their study of oxygen at low metallicity.
Hines: Ecorrcectionsdircetlgtopublishedealues.wehacer ncwlygobserce," However, while Melénndez and collaborators applied their non--LTE corrections directly to published values, we have re-derived the abundances to complement our sample of newly observed stars in a consistent fashion."
dst:, Our main findings are as follows.
"When the ISM effects are included, asymmetries develop in the disk due to the eccentricity and pericenter evolution forced by the ISM perturbation.","When the ISM effects are included, asymmetries develop in the disk due to the eccentricity and pericenter evolution forced by the ISM perturbation."
" These asymmetries are barely detectable when r=10 (Fig.1,, upper right plot) but they become more pronounced? for lower values of 7 (Fig.1,, bottom plots) since the grains have more time to accumulate the perturbative effects."," These asymmetries are barely detectable when $\tau = 10^{-3}$ \ref{f1}, upper right plot) but they become more pronounced for lower values of $\tau$ \ref{f1}, bottom plots) since the grains have more time to accumulate the perturbative effects."
 When T=107? the two peaks at the particles pericenters and apocenters are still visible but the disk begins to develop an eccentric shape., When $\tau = 10^{-3}$ the two peaks at the particles pericenters and apocenters are still visible but the disk begins to develop an eccentric shape.
 The alteration in the disk shape is more noteworthy for T1075 when the disk appears as the superposition of two ellipses., The alteration in the disk shape is more noteworthy for $\tau = 10^{-6}$ when the disk appears as the superposition of two ellipses.
 'This feature can be explained by inspecting the orbital behaviour of the grains under the effect of the ISM neutral gas., This feature can be explained by inspecting the orbital behaviour of the grains under the effect of the ISM neutral gas.
" In Fig.2 we show the evolution with time of the grain orbits in the(e,cz) plane."," In \ref{f2}
 we show the evolution with time of the grain orbits in the$(e,\varpi)$ plane."
" Particles evolve towards high eccentricity values (~ 1) while, at the same time, the pericenter values tend to 270?."," Particles evolve towards high eccentricity values $\sim 1$ ) while, at the same time, the pericenter values tend to $270^{\circ}$ ."
 When large values of, When large values of
 , 
stars.,stars.
 These illustrate that the higher quality of the Kepler data improved the classification of those targets (they turn out to be binaries indeed)., These illustrate that the higher quality of the Kepler data improved the classification of those targets (they turn out to be binaries indeed).
" Figure 15 shows some examples of variables whose classification from TrES and are equal: both the TrES and the light curves are plotted for an eclipsing binary with additional variability, a candidate y Dor pulsator and a candidate 6 Sct pulsator."," Figure \ref{tres} shows some examples of variables whose classification from TrES and are equal: both the TrES and the light curves are plotted for an eclipsing binary with additional variability, a candidate $\gamma$ Dor pulsator and a candidate $\delta$ Sct pulsator."
" The TrES light curves have been phased according to the dominant frequency found in the data, for visibility reasons."," The TrES light curves have been phased according to the dominant frequency found in the data, for visibility reasons."
" These ground-based data have a much poorer quality than the data, and the variability is very difficult to see by eye in the original light curve."," These ground-based data have a much poorer quality than the data, and the variability is very difficult to see by eye in the original light curve."
" Nevertheless, those objects were classified correctly using the TrES data, showing the robustness of our methods."," Nevertheless, those objects were classified correctly using the TrES data, showing the robustness of our methods."
" For the pulsating stars, we also find exactly the same dominant frequency peaks in the TrES and light curves, showing the reliability of the frequencies and the stability of the pulsation modes."," For the pulsating stars, we also find exactly the same dominant frequency peaks in the TrES and light curves, showing the reliability of the frequencies and the stability of the pulsation modes."
" The latter is very useful when doing asteroseismological studies of individual objects, since analysing two independent datasets is the best way to have certainty about detected frequencies."," The latter is very useful when doing asteroseismological studies of individual objects, since analysing two independent datasets is the best way to have certainty about detected frequencies."
" Obviously, the data allow many more significant frequencies to be detected than the TrES data do, but we could at least verify the reliability of the three most dominant frequencies in ground-based data which were assembled with a completely different goal than asteroseismology, and, along with it, the suitability of target selection for follow-up dedicated studies of the best class candidates."," Obviously, the data allow many more significant frequencies to be detected than the TrES data do, but we could at least verify the reliability of the three most dominant frequencies in ground-based data which were assembled with a completely different goal than asteroseismology, and, along with it, the suitability of target selection for follow-up dedicated studies of the best class candidates."
" We have presented a global variability study of the public data, measured in the first quarter of the mission."," We have presented a global variability study of the public data, measured in the first quarter of the mission."
" In total, we analysed more than 1500000 light curves using automated classification and extractor methods."," In total, we analysed more than 000 light curves using automated classification and extractor methods."
" This database is unprecedented, never before did we have access to such a large sample of very-well sampled light curves with such a high photometric precision."," This database is unprecedented, never before did we have access to such a large sample of very-well sampled light curves with such a high photometric precision."
 It is therefore an excellent dataset to perform statistical studies on the relative class populations of variable stars of all kinds and better constrain their instability domains., It is therefore an excellent dataset to perform statistical studies on the relative class populations of variable stars of all kinds and better constrain their instability domains.
" To improve our detection capabilities, we have introduced two ‘new’ classes in our classification scheme: variables showing rotational modulation and active stars."," To improve our detection capabilities, we have introduced two `new' classes in our classification scheme: variables showing rotational modulation and active stars."
 We have also supplemented our classifiers with a dedicated extracted method, We have also supplemented our classifiers with a dedicated extracted method
The two cases markecl l-and-10. aud LO-aucd-1L. show the result of separatingMm grain> input by planetesimals from those carried in by nebular gas.,"The two cases marked 1-and-10, and 10-and-1, show the result of separating grain input by planetesimals from those carried in by nebular gas."
 The l-aud-10 case (in ciamoucl markers) corresponds to having «o=1jun for the grains entering with the gas. aud dy=10pan for the grains coming from plauetesimals.," The 1-and-10 case (in diamond markers) corresponds to having $a_0=1\unit{\mu{m}}$ for the grains entering with the gas, and $a_0=10\unit{\mu{m}}$ for the grains coming from planetesimals."
 The LO-aucl-l case (iu plus sigus) is just the reverse., The 10-and-1 case (in plus signs) is just the reverse.
 These cases demonstrate the [act that planetesimal grains. because they are released mostly in the deep atmosphere. only iuflueuce tle size distribution iu the deep layers.," These cases demonstrate the fact that planetesimal grains, because they are released mostly in the deep atmosphere, only influence the size distribution in the deep layers."
 While graius carried in by uebular eas. because they are deposited iu the uppermost layer. influence the size distribution throughout —jost. of the atimosRm)ere.," While grains carried in by nebular gas, because they are deposited in the uppermost layer, influence the size distribution throughout most of the atmosphere."
 The [act that the opacity profiles are sensitive to he choice of monomer size is perhaps a rawback of the procedure used to calculate them., The fact that the opacity profiles are sensitive to the choice of monomer size is perhaps a drawback of the procedure used to calculate them.
 Iu pa‘ticular there is uo reason that the source of new erains will contain ouly monomers. or even cont:vin monomers at all. but since our moclel oes not include processes that the grain size. like wreakup or evaporation. there is wo reason ο cousider auy grains smaller than those brought. iu frnm outside the planet.," In particular there is no reason that the source of new grains will contain only monomers, or even contain monomers at all, but since our model does not include processes that the grain size, like breakup or evaporation, there is no reason to consider any grains smaller than those brought in from outside the planet."
 In future work we ——ope to include these processes., In future work we hope to include these processes.
 The seusitivity to the sticking coellicient. 5. is shown in Fig. 10..," The sensitivity to the sticking coefficient, $\gamma$, is shown in Fig. \ref{fig:stick}."
 It turus out that the resulting opacity is ον seusitive to chauges in this parameter., It turns out that the resulting opacity is mildly sensitive to changes in this parameter.
 The opacity profiles in Fig., The opacity profiles in Fig.
 10. show the same behavior. with approximately the same values. [or a range of sticking coefficients from 1 to 0.1.," \ref{fig:stick} show the same behavior, with approximately the same values, for a range of sticking coefficients from $1$ to $0.1$."
 As can be seen. the opacity and optical depth increase somewhat as the sticking coellicient decreases by an order of magnitude. but the overall values of the opacity are still low.," As can be seen, the opacity and optical depth increase somewhat as the sticking coefficient decreases by an order of magnitude, but the overall values of the opacity are still low."
 The time to reach steady state when +=0.1 is ~3500 vrs. as opposed to LOOO ves for +=1.," The time to reach steady state when $\gamma=0.1$ is $\about 3500$ yrs, as opposed to $\about 1000$ yrs for $\gamma=1$."
 This is still muuch lower thau the time scale for siguificant changes in the envelope structure., This is still much lower than the time scale for significant changes in the envelope structure.
 During most of phase 2 of core accretion the protoplanet eaius ou the order of 10°ALvr1 oL high-Z material [rom accreting planetesinals., During most of phase 2 of core accretion the protoplanet gains on the order of $10^{-6}\unit{M_{\oplus}~yr^{-1}}$ of high-Z material from accreting planetesimals.
 But most of this mass is added to the planet's atinosphliere. the radiative zone. or possibly adde| directly to the core.," But most of this mass is added to the planet's atmosphere the radiative zone, or possibly added directly to the core."
 In thetr model of planet formation. ? calculate first the rate of solid planetesimal accretion by the protoplauet. then calculate the interaction between a single planetesimal aud the planet's atmosphere to cetermine how much mass and energyOe are deposited at different heights.," In their model of planet formation, \citeauthor{hubickyj} calculate first the rate of solid planetesimal accretion by the protoplanet, then calculate the interaction between a single planetesimal and the planet's atmosphere to determine how much mass and energy are deposited at different heights."
e They assume. for the purpose of this Ccculation. that the planetestinals all have a radius of 100 kim.," They assume, for the purpose of this calculation, that the planetesimals all have a radius of 100 km."
 Iu general. stualler planetesimals are expected to deposit more of thelr mass higher up in the atmosphere while larger planetesiuials deposit their 1uass deeper in the atmosphere or even survive to reach the core nearly intact.," In general, smaller planetesimals are expected to deposit more of their mass higher up in the atmosphere while larger planetesimals deposit their mass deeper in the atmosphere or even survive to reach the core nearly intact."
 Rather than repeat these lenethy calculations with plauetesimals of different sizes. we have tested the ellect of varying the assumed plauetesiinal size by varying directly the mass deposition," Rather than repeat these lengthy calculations with planetesimals of different sizes, we have tested the effect of varying the assumed planetesimal size by varying directly the mass deposition"
primary inversions based on the equations of hivdrostatic equilibritin aloug with the adiabatic oscillation equations. however. eive only the mechanical variables like pressure. density aud souud speed.,"primary inversions based on the equations of hydrostatic equilibrium along with the adiabatic oscillation equations, however, give only the mechanical variables like pressure, density and sound speed."
 This provides us with the ratio Τμ. where pois the mcan molecular weight.," This provides us with the ratio $T/\mu$, where $\mu$ is the mean molecular weight."
" Ta order to determine Laud p separately. it becomes necessary to use the equations of thermal equilibrimu. 1.6.. where £,. is the total energy eeucrated within a sphere of radius r. σ is the Stefau-Boltzimanu coustaut. & is the BRosseland mean opacity. p is the deusitv and € is the nuclear cucrey generation rate per unit mass."," In order to determine $T$ and $\mu$ separately, it becomes necessary to use the equations of thermal equilibrium, i.e., where $L_r$ is the total energy generated within a sphere of radius $r$, $\sigma$ is the Stefan-Boltzmann constant, $\kappa$ is the Rosseland mean opacity, $\rho$ is the density and $\epsilon$ is the nuclear energy generation rate per unit mass."
 Iu addition. the equation of state needs to be adopted to relate the sound speed to chemical composition and temperature: e—Tip.X. Z).," In addition, the equation of state needs to be adopted to relate the sound speed to chemical composition and temperature: $c=c(T,\rho,X,Z)$ ."
" These three equations are sufficicut to determine the three unknowns T.L,..X. provided the Z xofile is prescribed (Αα Chitre 1998))."," These three equations are sufficient to determine the three unknowns $T,L_r,X$, provided the $Z$ profile is prescribed (Antia Chitre \cite{ac98}) )."
 The resulting seismic model will not in general have he correct solar huninosity which is au observed quantity., The resulting seismic model will not in general have the correct solar luminosity which is an observed quantity.
 It turus out that we need to adjust the nuclear reaction rates sliehtlv to obtain the correct luminosity and we leve this boundary condition can be profitably usec or constraimiung the unclear reaction rates., It turns out that we need to adjust the nuclear reaction rates slightly to obtain the correct luminosity and we believe this boundary condition can be profitably used for constraining the nuclear reaction rates.
 The rate of miclear enerev generation iu the Sun is mainly controllec * the cross-section for the pp nuclear reaction. which ins nof been measured in the laboratory.," The rate of nuclear energy generation in the Sun is mainly controlled by the cross-section for the pp nuclear reaction, which has not been measured in the laboratory."
 This nuclear reaction rate is thus calculated theoretically aud it woul ο Interesting to test the validity of calculated results using the lelioscismuc constraints., This nuclear reaction rate is thus calculated theoretically and it would be interesting to test the validity of calculated results using the helioseismic constraints.
" Since the compute Tuninositv m seiunie models also depends on Z,.. the reavy Clement abundance in solar core. we attempt to deteiuiue the region in the Z. Sy, plane which vields the correct solar Iuuinositv."," Since the computed luminosity in seismic models also depends on $Z_c$, the heavy element abundance in solar core, we attempt to determine the region in the $Z_c$ $S_{11}$ plane which yields the correct solar luminosity."
 Usine the deusitv profile along with the equation of hydrostatic equilibrium. it should be possible to determine the pressure profile also frou primary inversions.," Using the density profile along with the equation of hydrostatic equilibrium, it should be possible to determine the pressure profile also from primary inversions."
 It may even be argued that if we use the additional constraint. p=p(T.p..NLZ) it should be possible to determine the Z profile sides other profiles.," It may even be argued that if we use the additional constraint, $p=p(T,\rho,X,Z)$ it should be possible to determine the $Z$ profile besides other profiles."
 However. it is not clear if these constraints are independent and in section 3.2 we exanune this possibility.," However, it is not clear if these constraints are independent and in section 3.2 we examine this possibility."
 We use the observed frequencies from GONG. (Cloba Oscillation Network Croup) data for mouths |10 (IHHil et al. 1996)), We use the observed frequencies from GONG (Global Oscillation Network Group) data for months 4–10 (Hill et al. \cite{hil96}) )
 which corresponds to the period from 23 August 1995 to 30 April 1996. to calculate the sou speed aud density profiles.," which corresponds to the period from 23 August 1995 to 30 April 1996, to calculate the sound speed and density profiles."
 A Reeularized Least Squares (RLS) technique for inversion is adopted for this purpose., A Regularized Least Squares (RLS) technique for inversion is adopted for this purpose.
 With the help of the inverted profiles for sound spec and density. along with the Z profile from Model 5 of Richard et al. (1996)).," With the help of the inverted profiles for sound speed and density, along with the $Z$ profile from Model 5 of Richard et al. \cite{ric96}) ),"
 we obtain the temperature and hydrogen abundance profiles x cluploving the equations of thermal equilibriun., we obtain the temperature and hydrogen abundance profiles by employing the equations of thermal equilibrium.
 We adopt the OPAL opacitics (lelesias Rogers 19963). OPAL equation of state (Rogers. Swenson Telesias 1996)) and uuclear reaction rates from Adelherecr et al. (1998))," We adopt the OPAL opacities (Iglesias Rogers \cite{igl96}) ), OPAL equation of state (Rogers, Swenson Iglesias \cite{rog96}) ) and nuclear reaction rates from Adelberger et al. \cite{fusion}) )"
 for obtaiming the herimal structure., for obtaining the thermal structure.
 Receutlv. Elliot aud Nosovichey (1998) ) ie demonstrated that tuclision of relativistic effects in the equation of state imuiproves the aerecien with aclioscisinic data.," Recently, Elliot and Kosovichev \cite{ell98}) ) have demonstrated that inclusion of relativistic effects in the equation of state improves the agreement with helioseismic data."
 Since the OPAL equation of state does rot inch|o this effect we lave applied corrections as outlined by Elliot aud I&osovichev (1998)) to incorporate he relativistic effects., Since the OPAL equation of state does not include this effect we have applied corrections as outlined by Elliot and Kosovichev \cite{ell98}) ) to incorporate the relativistic effects.
 The inferred mean molecular weight xofile is displaved iu Fie., The inferred mean molecular weight profile is displayed in Fig.
 1., 1.
 The ouly difference νοποσα he present calculations aud earlier work of Autia Chitre (1998)) is in the adopted nuclear reaction rates aud application of the relativistic correction to tle equation of state., The only difference between the present calculations and earlier work of Antia Chitre \cite{ac98}) ) is in the adopted nuclear reaction rates and application of the relativistic correction to the equation of state.
 With the help of the inverted density. telaperature aud hydrogen abundance profiles. it is possible to conipute the total enerev generated by nuclear reactions. aud this should be compared with the observed solar luuinesity. L. Όνδίος107 ergs/sec.," With the help of the inverted density, temperature and hydrogen abundance profiles, it is possible to compute the total energy generated by nuclear reactions, and this should be compared with the observed solar luminosity, $L_\odot=3.846\times10^{33}$ ergs/sec."
 As emphasized by Autia Chitre (1998)) there is au (20) uucertaüutv of about in conmiputiug the luminosity of seiuic models., As emphasized by Antia Chitre \cite{ac98}) ) there is an $2\sigma$ ) uncertainty of about in computing the luminosity of seismic models.
 This arises from possible errors iu. primary inversion. solar radius. equation of state. nuclear reaction rates for other reactions.," This arises from possible errors in primary inversion, solar radius, equation of state, nuclear reaction rates for other reactions."
 The uncertainty arising from errors in Z profiles is nmmch larger and hence in this work we use seine models with homogeneous Z profile. covering a wide range of Z values.," The uncertainty arising from errors in $Z$ profiles is much larger and hence in this work we use seismic models with homogeneous $Z$ profile, covering a wide range of $Z$ values."
 For each central value of Z we estimate the range of cross-section ofpp nuclear reaction. which reproduces the hWnuuinositv to within of the observed value.," For each central value of $Z$ we estimate the range of cross-section ofpp nuclear reaction, which reproduces the luminosity to within of the observed value."
 The results ave shown iu Fie., The results are shown in Fig.
 2. which delineates the," 2, which delineates the"
unknown class components.,unknown class components.
" For example. if an unknown class has a small mass. one or more components will only be 7deploved"" for its representation if the model has many components."," For example, if an unknown class has a small mass, one or more components will only be “deployed” for its representation if the model has many components."
 Likewise. if the unknown class has à very large mass (and significant within-class variation). quite a few components mav be needed to represent il well.," Likewise, if the unknown class has a very large mass (and significant within-class variation), quite a few components may be needed to represent it well."
 For the neural network. the choice of the entropy threshold affects performance.," For the neural network, the choice of the entropy threshold affects performance."
 We have performed several experimental evaluations of the mixture model and neural network. based on different approaches [or choosing these operating parameters.," We have performed several experimental evaluations of the mixture model and neural network, based on different approaches for choosing these operating parameters."
 In one set of experiments. shown for the ESOLV ancl 5D55 data sets in Tables 3. and 4.. we picked both the mixture order (over the range 10 to 80) and the NN's entropy thireshold (by an exhaustive search) to maximize Criterion 1 performance.," In one set of experiments, shown for the ESOLV and SDSS data sets in Tables \ref{tab:etf} and \ref{tab:stf}, we picked both the mixture order (over the range 10 to 80) and the NN's entropy threshold (by an exhaustive search) to maximize Criterion 1 performance."
 Note (that these approaches cannot be used in practice since. in performing (he model selection. (hese methods require evaluating a cost (Criterion 1) that depends on knowledge of the unknown class labels.," Note that these approaches cannot be used in practice since, in performing the model selection, these methods require evaluating a cost (Criterion 1) that depends on knowledge of the unknown class labels."
 However. this experiment does allow a comparison ol best-case performances achieved by the mixture and neural network approaches.," However, this experiment does allow a comparison of best-case performances achieved by the mixture and neural network approaches."
 For the mixture model. we have also applied BIC-hasecl selection as described earlier.," For the mixture model, we have also applied BIC-based selection as described earlier."
 This approach is Wholly unsupervised. and (hus feasible in practice.," This approach is wholly unsupervised, and thus feasible in practice."
 Tables 3. and 4. show the results lor the ESOLV data and the SDSS data using the best (lowest) value for Criterion 1., Tables \ref{tab:etf} and \ref{tab:stf} show the results for the ESOLV data and the SDSS data using the best (lowest) value for Criterion 1.
 The first column shows the classes that were treated as unknown for that series of runs., The first column shows the classes that were treated as unknown for that series of runs.
" The value of ΠΟΠΗ is the number of components used bv the mixture model corresponding to the best value of Criterion 1. while ""nonpre"" is the number of nonpredefined components used bv Chat model."," The value of “ncomp” is the number of components used by the mixture model corresponding to the best value of Criterion 1, while “nonpre” is the number of nonpredefined components used by that model."
 The remaining columns under “Mixture Model” list error fractions for the three criteria discussed above., The remaining columns under “Mixture Model” list error fractions for the three criteria discussed above.
" Under. ""Neural Network we list the value of Criterion 1. the only error measure evaluated for the neural network."," Under “Neural Network” we list the value of Criterion 1, the only error measure evaluated for the neural network."
 The last column shows the percentage change in (he Criterion 1 value between the neural network and (he mixture model. with a negative value indicating a lower Criterion 1 error for the mixture model compared to the neural network.," The last column shows the percentage change in the Criterion 1 value between the neural network and the mixture model, with a negative value indicating a lower Criterion 1 error for the mixture model compared to the neural network."
 The bracketed values al the bottom of each column are (he average values (across all experiments) over (hat column., The bracketed values at the bottom of each column are the average values (across all experiments) over that column.
 For (he moment we will restrict discussion to the Criterion 1 performance., For the moment we will restrict discussion to the Criterion 1 performance.
 Tables 3. and 4 show that. with both methods optimized lor Criterion 1 performance. significantly better inference accuracy is achieved by (he mixture-based approach.," Tables \ref{tab:etf} and \ref{tab:stf} show that, with both methods optimized for Criterion 1 performance, significantly better inference accuracy is achieved by the mixture-based approach."
 For the ESOLNV data we find an average decrease in Criterion | error of 20% and a maximum decrease of 50%., For the ESOLV data we find an average decrease in Criterion 1 error of $20\%$ and a maximum decrease of $50\%$.
 For the SDSS data we find an average decrease in Criterion 1 error of 57% and a maximum decrease of 96%., For the SDSS data we find an average decrease in Criterion 1 error of $57\%$ and a maximum decrease of $96\%$.
 This is nol especially surprising. since the mixture is learned using the unknown class data (bul without use of the labels). while the neural network is only trained on labeled known class data.," This is not especially surprising, since the mixture is learned using the unknown class data (but without use of the labels), while the neural network is only trained on labeled known class data."
 In Tables 5. ancl 6.. we compare (he neural network. again with the threshold optimized for Criterion 1. against the mixture model. but with the order now selected based on the BIC criterion.," In Tables \ref{tab:emdl} and \ref{tab:smdl}, we compare the neural network, again with the threshold optimized for Criterion 1, against the mixture model, but with the order now selected based on the BIC criterion."
 Since (he neural network decision making (hreshold is optimized based on, Since the neural network decision making threshold is optimized based on
redenime and small feld star contanuinatiou make it a very good target for photometric studies.,reddening and small field star contamination make it a very good target for photometric studies.
 The first CCD colormaguitide diagrain (CAID) for NGC 1261 has been obished by Bolte Miirleani (1989)., The first CCD color–magnitude diagram (CMD) for NGC 1261 has been published by Bolte Marleau (1989).
 They observed the cluscr in 2 aud V. down to maguitude V.—23.," They observed the cluster in $B$ and $V$, down to magnitude $V\sim23$."
 From he appareut naguitude of the IB aud the fitting of the niil sequence to two subdawarts. they derived an appareut cistauce modilus GyAL)=16.0540.25.," From the apparent magnitude of the HB and the fitting of the main sequence to two subdwarfs, they derived an apparent distance modulus $(m-M)_V=16.05\pm0.25$."
 By matching hei observatious to the VancdenBere aud Bell (1985) isochrones auk assunmniue E(B-V)=0.02. Bolte and Marleau obtained an age of 15 Cyr aud a ietallicity |M/II|2.1.09.," By matching their observations to the VandenBerg and Bell (1985) isochrones and assuming E(B-V)=0.02, Bolte and Marleau obtained an age of 15 Gyr and a metallicity [M/H]=–1.09."
 By adopting E(BV)=0.0L. the best fitting isochrone eives an age of 15 €wr and a metallicity ΕΠΣ1.27.," By adopting E(B–V)=0.04, the best fitting isochrone gives an age of 15 Gyr and a metallicity [M/H]=–1.27."
 Alcaino (1992) published a BV photometric study of NCC 1261., Alcaino (1992) published a $BVR$ photometric study of NGC 1261.
 They found a distance iiodulus (77M)©=16.004 0.23. from the apparent magnitude oft1ο ID. and. using the saue set of isochrones of the previous stuVv. al age of 15+2 Car. and a reddening of Vj-OUT. asstuning a iictallicity |Fe/II|2.—1.27.," They found a distance modulus $(m-M)_V=16.00\pm 0.23$ , from the apparent magnitude of the HB, and, using the same set of isochrones of the previous study, an age of $15\pm2$ Gyr, and a reddening of $=0.07$, assuming a metallicity $=-1.27$."
 More receutly. Ferraro (1993) presented a BY CMD aud a luunosity fimction for the evolved stars in this cluster.," More recently, Ferraro (1993) presented a $BV$ CMD and a luminosity function for the evolved stars in this cluster."
 From the CMD metallicity tudicators. calibrated with tie Zinn West (L980) metallicity scale. they estimated a slightly lower metal coutent than iu the previous studies: «σε0.2.," From the CMD metallicity indicators, calibrated with the Zinn West (1984) metallicity scale, they estimated a slightly lower metal content than in the previous studies: $=-1.4\pm0.2$."
 They. also detected for the first tie the “RGB bump ofthe cluster. as a chuup of stars in the LF of the red giant brauch. at maeuitucde V.—16.7040.05.," They also detected for the first time the `RGB bump' of the cluster, as a clump of stars in the LF of the red giant branch, at magnitude $V=16.70\pm0.05$."
 The paper is organized as follows: in Section 2 we discuss our data and the method we followed to obtain the photonmetry., The paper is organized as follows: in Section 2 we discuss our data and the method we followed to obtain the photometry.
 Iu Section 3 we present the luninosity functions in three radial annuli., In Section 3 we present the luminosity functions in three radial annuli.
 Section 1 coucerus the lass functions and the correction for the effects of the lnass segregation., Section 4 concerns the mass functions and the correction for the effects of the mass segregation.
" Finally. iu the last Section the MIF of NGC 1261 is compared with the MES for other 19 Galactic GCs,"," Finally, in the last Section the MF of NGC 1261 is compared with the MFs for other 19 Galactic GCs."
 The database cousists of two I.baud image sets., The database consists of two I–band image sets.
 The first Ol Is a sape of seven 15 unin exposures obtained on November 2730. 1991. with EFOSC? | CCD 17 at the ESO/AIPI 2.2 in telescope of La Silla.," The first one is a sample of seven 15 min exposures obtained on November 27–30, 1991, with EFOSC2 + CCD 17 at the ESO/MPI 2.2 m telescope of La Silla."
 These images have dinenusiois of 1021« pixels. corresponding to an area of 5/5 «5/8 ou the sky. aud. cover a regiou frou ~Ut to ~το frou the ceuter of the cluster.," These images have dimensions of $1024 \times 1024$ pixels, corresponding to an area of $\primip$ $\times$ $\primip$ 8 on the sky, and cover a region from $\sim 1 \primip 4$ to $\sim 7 \primip 0$ from the center of the cluster."
 The second set consists of 9 frames. for a total exposure time of 95 nüuutes. otained with EMMI | CCD 31 at the," The second set consists of 9 frames, for a total exposure time of 95 minutes, obtained with EMMI + CCD 34 at the"
"Multiwavelength observations of supernova remnants (SNRs) allow one, in certain cases, to determine the temperatures Τε and T, of both electrons and protons behind the shock, (see review)..","Multiwavelength observations of supernova remnants (SNRs) allow one, in certain cases, to determine the temperatures $T_e$ and $T_p$ of both electrons and protons behind the shock, \citep[see][for a recent review]{rakowski2005}."
" The ratio Τε/Ty of these temperatures varies significantly, from <0.07 for SN 1006 (?,, ?)) to in the Cygnus Loop (?).."," The ratio $T_e/T_p$ of these temperatures varies significantly, from $\lesssim 0.07$ for SN 1006 \citealt{Laming1996}, , \citealt{Ghavamian2002}) ) to $0.67-1$ in the Cygnus Loop \citep{Ghavamian2001}."
 From a theoretical point of view there are two limits for this ratio., From a theoretical point of view there are two limits for this ratio.
" The lower limit, given by the electron to proton mass ratio Τε/Τρ=mMe/mMp, is the so called total non-equilibrium case, which corresponds to equal thermal velocities for electrons and protons; the upper limit, Τε=Τρ is the total equilibrium case, which corresponds to equal energies of electron and proton plasmas."," The lower limit, given by the electron to proton mass ratio $T_e /T_p=m_e/m_p$, is the so called total non-equilibrium case, which corresponds to equal thermal velocities for electrons and protons; the upper limit, $T_e=T_p$ is the total equilibrium case, which corresponds to equal energies of electron and proton plasmas."
" As was shown by ?? for the SNRs Cygnus Loop, RCW 86, Tyco and SN 1006, observed values lie between these two limits."," As was shown by \cite{Ghavamian2001, Ghavamian2002} for the SNRs Cygnus Loop, RCW 86, Tyco and SN 1006, observed values lie between these two limits."
" A compilation of current electron-ion equilibration measurements at SNRs shocks has been presented in ?,, where an inverse relationship between the shock velocity and the level of temperatures equilibration has been claimed."," A compilation of current electron-ion equilibration measurements at SNRs shocks has been presented in \cite{rakowski2005}, where an inverse relationship between the shock velocity and the level of temperatures equilibration has been claimed."
" Namely, older SNRs, characterized by a lower value of the shock velocity, exhibit a T./T; ratio closer to, and in some cases consistent with 1."," Namely, older SNRs, characterized by a lower value of the shock velocity, exhibit a $T_e/T_p$ ratio closer to, and in some cases consistent with 1."
" It is important to stress that, even in the case of total non-equilibrium at the shock (T./T,= me/mp), electrons are unavoidably heated sufficiently far downstream of the shock through Coulomb collisions with hot thermal protons (?).."," It is important to stress that, even in the case of total non-equilibrium at the shock $T_e/T_p = m_e/m_p$ ), electrons are unavoidably heated sufficiently far downstream of the shock through Coulomb collisions with hot thermal protons \citep{Spitzer}."
" This constitutes a sort of minimal heating scenario for electrons, which will be studied in details in this paper."," This constitutes a sort of minimal heating scenario for electrons, which will be studied in details in this paper."
 The temperature of this electrons is measured directly from X-ray spectra (e.g 22).," The temperature of this electrons is measured directly from X-ray spectra \citep[e.g][]{Decourchelle2001,Vink2003}."
" However, the electron heating through Coulomb interactions has been claimed to be too slow to explain the level of equilibration measured from optical lines observations in the vicinity of the shock for some SNRs (?) and other mechanisms based on the generation of plasma waves are believed to proceed faster than Coulomb heating (e.g.?).."," However, the electron heating through Coulomb interactions has been claimed to be too slow to explain the level of equilibration measured from optical lines observations in the vicinity of the shock for some SNRs \citep{Laming2000} and other mechanisms based on the generation of plasma waves are believed to proceed faster than Coulomb heating \citep[e.g.][]{Laming2001}."
" Several of such collisionless mechanisms have been investigated, amongst others, by ????.."," Several of such collisionless mechanisms have been investigated, amongst others, by \cite{Cargill1988,Laming2001,Ghavamian2007,Rakowski2008}."
" The efficient acceleration of cosmic rays at SNR shocks also plays a role, by reducing the total energy available for shock heating and consequently suppressing the proton "," The efficient acceleration of cosmic rays at SNR shocks also plays a role, by reducing the total energy available for shock heating and consequently suppressing the proton temperature \citep{blasi2005,Ellison2007,Vink2008,Helder2008,Drury2009,Patnaude2009}."
"The aim of this work is to present a simple model for electron Coulomb heating at SNR shocks, that could help to estimate the need for, and magnitude of, heating processes adjunctive to the Coulomb mechanism."," The aim of this work is to present a simple model for electron Coulomb heating at SNR shocks, that could help to estimate the need for, and magnitude of, heating processes adjunctive to the Coulomb mechanism."
 Our work is based on Chevalier's self-similar model which describes the evolution of SNRs in presence of effective cosmic ray acceleration at the SNR shock (?))., Our work is based on Chevalier's self-similar model which describes the evolution of SNRs in presence of effective cosmic ray acceleration at the SNR shock \citealt{Chevalier1983}) ).
 We coupled Chevalier's model with the equations for electron heating by Coulomb exchange., We coupled Chevalier's model with the equations for electron heating by Coulomb exchange.
" The model lacks some important features; it does not include magnetic fields explicitly and the shock compression ratio is limited to a maximum value of 7 (since it does not include possibility for cosmic rays to escape from the shock), whereas in numerical simulations this ratio in some cases could reach much higher values (see for example ?))."," The model lacks some important features; it does not include magnetic fields explicitly and the shock compression ratio is limited to a maximum value of 7 (since it does not include possibility for cosmic rays to escape from the shock), whereas in numerical simulations this ratio in some cases could reach much higher values (see for example \citealt{Ellison2005}) )."
" However it does include a minimal set of the key physical processes and provides, we feel, a useful reference calculation for more complicated estimates and models."," However it does include a minimal set of the key physical processes and provides, we feel, a useful reference calculation for more complicated estimates and models."
 The paper is organized as follows., The paper is organized as follows.
" In section 2] we briefly summarize the Chevalier model, introduce the equation for heating, and discuss projection effects in relating the 3D model to 2D observations."," In section \ref{sec:SNR dynamics} we briefly summarize the Chevalier model, introduce the equation for heating, and discuss projection effects in relating the 3D model to 2D observations."
" In section 3] we summarize the results of the numerical solution of the equations of our model, and in section] we apply the results of our model to the case of SN 1006."," In section \ref{sec:Results} we summarize the results of the numerical solution of the equations of our model, and in section \ref{sec:Application} we apply the results of our model to the case of SN 1006."
 We conclude in Sec.[Bl., We conclude in Sec. \ref{sec:Conclusions}.
 A formal approach to the hydrodynamics of a SNR in adiabatic expansion phase including cosmic rays (CRs) acceleration was developed by ?.., A formal approach to the hydrodynamics of a SNR in adiabatic expansion phase including cosmic rays (CRs) acceleration was developed by \cite{Chevalier1983}.
" In his work Chevalier generalized the self-similar model of Sedov, which describes a point explosion in a uniform medium with negligible pressure."," In his work Chevalier generalized the self-similar model of Sedov, which describes a point explosion in a uniform medium with negligible pressure."
 Chevalier's model describes the interior of a spherically symmetric SNR by the two- (relativistic cosmic rays and non-relativistic thermal gas) hydrodynamicalequations without diffusion (including diffusion would in general break the self-similarity)., Chevalier's model describes the interior of a spherically symmetric SNR by the two-fluid (relativistic cosmic rays and non-relativistic thermal gas) hydrodynamicalequations without diffusion (including diffusion would in general break the self-similarity).
 In terms of the radial coordinate 0€r<rsnock(t) the equations are:, In terms of the radial coordinate $0\le r\le r_{shock}(t)$ the equations are:
an analogous. (hough much narrower. capture loss cone.,"an analogous, though much narrower, capture loss cone."
 Some estimates indicate that the density of dark matter dominates (he stellar potential at 0.001 parsec (e.g. Bertone Merritt 2005)., Some estimates indicate that the density of dark matter dominates the stellar potential at $0.001$ parsec (e.g. Bertone Merritt 2005).
 If dark matter is less effective al scattering. particularly ibit is not sell-interacting. πακαν may be an excellent mechanism to drive significant amounts of dark matter into ihe SMDLIL.," If dark matter is less effective at scattering, particularly if it is not self-interacting, triaxiality may be an excellent mechanism to drive significant amounts of dark matter into the SMBH."
 The capture and inspiral rate for an eternally full loss cone in a spherical galaxy. has often been used as an upper limit. with the argument that a [ull loss cone cannot be more [ull," The capture and inspiral rate for an eternally full loss cone in a spherical galaxy has often been used as an upper limit, with the argument that a full loss cone cannot be more full."
 Note. however. that since triaxial galaxies have many more centrophilie orbits. the distribution function of a full triaxial loss cone can be ‘supersaturated’ compared to the full loss cone for a spherical isotropic galaxy.," Note, however, that since triaxial galaxies have many more centrophilic orbits, the distribution function of a full triaxial loss cone can be 'supersaturated' compared to the full loss cone for a spherical isotropic galaxy."
 This could occur even the orbits were only able to change angular momentum via 2-bodwv processes., This could occur even the orbits were only able to change angular momentum via 2-body processes.
 The surprisingly large replenishinent rates imply large tidal disruption rates as well. since the tidal loss cone width is about 1000 times larger (han the capture ancl inspiral loss cone.," The surprisingly large replenishment rates imply large tidal disruption rates as well, since the tidal loss cone width is about 1000 times larger than the capture and inspiral loss cone."
 This suggests tidal disruption rates as high as 1x10.7 stars per vear in a triaxial svstem with the same p(r) as M32., This suggests tidal disruption rates as high as $1 \times 10^{-3}$ stars per year in a triaxial system with the same $\rho(r)$ as M32.
 In fact. this tidal disruption rate is consistent with what is inlerred by the large amplitude N-ray. outbursts observed at the centers of galaxies (Doulev et al.," In fact, this tidal disruption rate is consistent with what is inferred by the large amplitude X-ray outbursts observed at the centers of galaxies (Donley et al."
 2002)., 2002).
 Our inferred tidal disruption rate is rather large when our model is scaled to the Milky Way bar: however. it may be (rue that (he angular momentum reshuffling process is less efficient in rotating bar potentials.," Our inferred tidal disruption rate is rather large when our model is scaled to the Milky Way bar; however, it may be true that the angular momentum reshuffling process is less efficient in rotating bar potentials."
 Our numerical models also suggest that captures aud tidal disruption events can originate rom radii much larger (han what is typically assumed: most centrophilie orbits in our model had apocenters much lareer (han LOO pe and though each centrophilie orbit contributes very little to the total rate. there are enough centrophilic orbits in our (triaxial model to influence the capture or tidal disruption rate at large raclii.," Our numerical models also suggest that captures and tidal disruption events can originate from radii much larger than what is typically assumed; most centrophilic orbits in our model had apocenters much larger than 100 pc and though each centrophilic orbit contributes very little to the total rate, there are enough centrophilic orbits in our triaxial model to influence the capture or tidal disruption rate at large radii."
 We have shown (hat (rianxiality can increase (he capture rate of single stars. but it may be even more important for binary svstems.," We have shown that triaxiality can increase the capture rate of single stars, but it may be even more important for binary systems."
 Binaries are Ihunneled from large distances to the SMDII along centrophilic orbits in a triaxial galaxy., Binaries are funneled from large distances to the SMBH along centrophilic orbits in a triaxial galaxy.
 A close pericenter pass tidally separates the binary. wilh one member of the binary captured by the SMDIIL. ancl one ejected αἱ hieh velocity.," A close pericenter pass tidally separates the binary, with one member of the binary captured by the SMBH, and one ejected at high velocity."
 Since tidal separation can occur without significant. energy. loss. the typical captured star Irom a binary (dal separation can have an apocenter hundreds of times larger (han a single stellar capture: (his max make binary interactions a much more efficient capture mechanism (Miller οἱ al.," Since tidal separation can occur without significant energy loss, the typical captured star from a binary tidal separation can have an apocenter hundreds of times larger than a single stellar capture; this may make binary interactions a much more efficient capture mechanism (Miller et al."
 2005). leading to a vet higher EMBI rate.," 2005), leading to a yet higher EMRI rate."
 In addition. the binary EMRI signal itself will be unique.," In addition, the binary EMRI signal itself will be unique."
 When capture occurs at such large separations from the SALDIIL. there is ample time for the orbit to circularize by the time it becomes detectable by," When capture occurs at such large separations from the SMBH, there is ample time for the orbit to circularize by the time it becomes detectable by"
no cusp in the spherically averaged density profile for CDM haloes according to the present model.,no cusp in the spherically averaged density profile for CDM haloes according to the present model.
" However, the finite central value is approached very slowly, in fact slightly more slowly than the Einasto profile (see Fig. 5))."," However, the finite central value is approached very slowly, in fact slightly more slowly than the Einasto profile (see Fig. \ref{f4}) )."
" 'The main differences the density profiles predicted by the present model and by DelPopoloetal.(2000) and Ascasibaretal.(2004) models, both of which also use the SI framework, are that we do not assume spherical seeds with convolved BBKS profiles and we make use of inside-out growth instead of an adiabatic invariant to determine (p)(r)."," The main differences the density profiles predicted by the present model and by \citet{DPea00} and \citet{As04} models, both of which also use the SI framework, are that we do not assume spherical seeds with convolved BBKS profiles and we make use of inside-out growth instead of an adiabatic invariant to determine $\srho(r)$."
 The model presented here is essentially equivalent to the Salvador-Soléetal.(2007) model., The model presented here is essentially equivalent to the \citet{smgh07} model.
" The key difference is that Salvador-Soléetal.(2007) used the typical cosmological accretion rate onto haloes, whereas here we explicitly make use of the typical density profile of halo seeds."," The key difference is that \citet{smgh07} used the typical cosmological accretion rate onto haloes, whereas here we explicitly make use of the typical density profile of halo seeds."
" However, the typical halo mass accretion rate arises, as mentioned, from the typical protohalo density profile, so this difference is just a matter of presentation, motivated by the distinct theoretical framework of the two models: the peak and the excursion set formalisms."," However, the typical halo mass accretion rate arises, as mentioned, from the typical protohalo density profile, so this difference is just a matter of presentation, motivated by the distinct theoretical framework of the two models: the peak and the excursion set formalisms."
" The only formal difference between the two models, apart from the fact that Salvador-Soléetal. also assumed spherical symmetry, is that the radius encompassing a given mass adopted by these authors was inferred from equation (90)) although not using the spherical total energy of the real protoobject but of its according to prescription."," The only formal difference between the two models, apart from the fact that \citeauthor{smgh07} also assumed spherical symmetry, is that the radius encompassing a given mass adopted by these authors was inferred from equation \ref{vir0}) ) although not using the spherical total energy of the real protoobject but of its according to prescription."
 This should introduce additional numerical differences between the density profiles predicted by the two models., This should introduce additional numerical differences between the density profiles predicted by the two models.
" It is also important to mention that the models by DelPopoloetal.(2000) and Ascasibaretal.(2004) and Salvador-Soléetal.(2007) include free parameters to be adjusted (the density contrast and filtering radius of the peak in the two former cases, and the value of AM/M setting the frontier between minor and major mergers in the latter), while the present model includes no free parameter at all."," It is also important to mention that the models by \citet{DPea00} and \citet{As04} and \citet{smgh07} include free parameters to be adjusted (the density contrast and filtering radius of the peak in the two former cases, and the value of $\Delta
M/M$ setting the frontier between minor and major mergers in the latter), while the present model includes no free parameter at all."
" In Figure 7,, the spherically averaged halo density profile predicted by the present model is compared to those predicted by the DelPopoloetal.(2000),, Ascasibaretal.(2004) and Salvador-Soléetal.(2007) models, all of them in the concordance model here considered."," In Figure \ref{f5}, the spherically averaged halo density profile predicted by the present model is compared to those predicted by the \citet{DPea00}, \citet{As04} and \citet{smgh07} models, all of them in the concordance model here considered."
" As expected, the theoretical profile predicted by the present model is quite similar to that predicted by Salvador-Soléetal. model, while these two profiles substantially deviate from those predicted by the remaining models."," As expected, the theoretical profile predicted by the present model is quite similar to that predicted by \citeauthor{smgh07} model, while these two profiles substantially deviate from those predicted by the remaining models."
" On the other hand, the two former profiles are in better agreement with the NFW profile with Zhaoetal.(2009) mass-concentration relation."," On the other hand, the two former profiles are in better agreement with the NFW profile with \citet{ZJMB09} mass-concentration relation."
" Moreover, the theoretical profile derived here is the one in best agreement with such a NFW profile, which is remarkable because it is also the only theoretical profile with no free parameter to be adjusted."," Moreover, the theoretical profile derived here is the one in best agreement with such a NFW profile, which is remarkable because it is also the only theoretical profile with no free parameter to be adjusted."
The velocity ὃς of freely expanding ejecta at a distance r from the explosion site iswritten as ος=r/l ad a (ime / alter the explosion.,The velocity $v_{\rm e}$ of freely expanding ejecta at a distance $r$ from the explosion site iswritten as $v_{\rm e} = r/t$ at a time $t$ after the explosion.
 The corresponding Lorentz [actor is 5e=αν1--v2., The corresponding Lorentz factor is $\gamma_{\rm e} = 1/\sqrt{1-v_{\rm e}^2}$.
 We set the speed of light equal to unity. throughout this paper., We set the speed of light equal to unity throughout this paper.
 In the relativistic limit. self-similar solutions lor (he emergence of a shock wave at the stellar surface (Nakavama&Shigevama2005) suggest that the density in the outer laver of ejecta has a power law distribution in terms of the Lorentz [actor as. where p. is the density of ejecta measured in the co-moving frame ancl pf in the fixed frame. that is. ο=pox (hereafter densities denoted with primes mean that they are measured in the fixed [rame).," In the relativistic limit, self-similar solutions for the emergence of a shock wave at the stellar surface \citep{Nakayama05} suggest that the density in the outer layer of ejecta has a power law distribution in terms of the Lorentz factor as, where $\rho_{\rm e}$ is the density of ejecta measured in the co-moving frame and $\rho_{\rm e}^\prime$ in the fixed frame, that is, $\rho_{\rm e}^\prime = \rho_{\rm e} \gamma$ (hereafter densities denoted with primes mean that they are measured in the fixed frame)."
 Here the non-dimensional parameter » can be estimated (to be ~1.1 if the stellar envelope is in radiative equilibrium and (he acliabatic index is 4/3., Here the non-dimensional parameter $n$ can be estimated to be $\sim 1.1$ if the stellar envelope is in radiative equilibrium and the adiabatic index is $4/3$.
 The constant α has the dimension of a mass., The constant $a$ has the dimension of a mass.
 On the other hand. a self-similar solution for the non-relativistic shock breakout in a plane-parallel geometry (Sakurai1960:Fieldsetal.2002) results in the clensity distribution in the same form with »~2.6.," On the other hand, a self-similar solution for the non-relativistic shock breakout in a plane-parallel geometry \citep{Sakurai60, Fields02} results in the density distribution in the same form with $n\sim2.6$."
 Though this self-similar solution asstunes non-relativistic flow. the resultant density distribution agrees with that obtained bv munerical calculations solving special relativistic hydrocdwuamics equations Nakamura&Shigevama2004) even for large Lorentz [actors 4.>10.," Though this self-similar solution assumes non-relativistic flow, the resultant density distribution agrees with that obtained by numerical calculations solving special relativistic hydrodynamics equations \citep{Nakamura04} even for large Lorentz factors $\gamma_{\rm e}>10$."
 The transition between {hese solutions occurs when the pressure to the mass density /?/p at the shock front becomes of the order of unity., The transition between these solutions occurs when the pressure to the mass density $P/\rho$ at the shock front becomes of the order of unity.
 Thus the outermost lavers should be governed by the solution in the relativistie limit., Thus the outermost layers should be governed by the solution in the relativistic limit.
 Flows located between (two shock fronts are considered by connecting (wo sell-similar solutions., Flows located between two shock fronts are considered by connecting two self-similar solutions.
 Suppose Chat the shock front in the ambient medium propagates at a speed Vy and the shock front in the ejecta al V5., Suppose that the shock front in the ambient medium propagates at a speed $V_1$ and the shock front in the ejecta at $V_2$.
 If we deline a—5/(5 1). where 5 is the adiabatic index. the flow in each of the shocked regions is described by the following equations.," If we define $\alpha = \hat{\gamma}/(\hat{\gamma}-1)$ , where $\hat{\gamma}$ is the adiabatic index, the flow in each of the shocked regions is described by the following equations."
knot (A) is actually composed of four subknots (Al through. ΑΕ).,knot (A) is actually composed of four subknots (A1 through A4).
" We refer to the inner 45"" of the jet. which includes these compact radio knots. as the inner jet."," We refer to the inner $45''$ of the jet, which includes these compact radio knots, as the inner jet."
 Figure 6 contains a contour map of the unresolved. diffuse emission from (he jet with the contribution from the knots removed overplotted onto the aclaplively smoothed image of the jet (Figure 4)).," Figure \ref{diffuse} contains a contour map of the unresolved, diffuse emission from the jet with the contribution from the knots removed overplotted onto the adaptively smoothed image of the jet (Figure \ref{jetbw}) )."
" This contour map was created using a wavelet decomposition and retaining only emission on scales of 8"" and larger.", This contour map was created using a wavelet decomposition and retaining only emission on scales of $8''$ and larger.
" As described in detail below. many of the radio and X-ray knots of the inner jet region do not exactly coincide, aud all of the previously reported knots bevond the inner jet are actually composed of several smaller subknots."," As described in detail below, many of the radio and X-ray knots of the inner jet region do not exactly coincide, and all of the previously reported knots beyond the inner jet are actually composed of several smaller subknots."
 To avoid confusion. we will refer to the A-ray knots of the inner jet as ANIL. AX. ete.," To avoid confusion, we will refer to the X-ray knots of the inner jet as AX1, AX2, etc.,"
 and knots bevond the inner jet as DXI. DN2. CXL. CX2. et(c..," and knots beyond the inner jet as BX1, BX2, CX1, CX2, etc.,"
 depending on their location relative to the knots of Feigelsone£a£.(1981). to clearly distinguish them from the radio knots., depending on their location relative to the knots of \citet{fei81} to clearly distinguish them from the radio knots.
 The nomenclature of Burns.(1983) will be used when referring specilically to the radio knots., The nomenclature of \citet{bur83} will be used when referring specifically to the radio knots.
 A summary of previously known radio and X-ray. knots and their distances from the nucleus is contained in Table 1.., A summary of previously known radio and X-ray knots and their distances from the nucleus is contained in Table \ref{rxknots}.
 When discussing X-ray jets. il is common {ο use the term to specilically describe the sites of enhanced emission where shocks may be accelerating the emitüng particles.," When discussing X-ray jets, it is common to use the term to specifically describe the sites of enhanced emission where shocks may be accelerating the emitting particles."
 We have detected. 31 sites of enhanced emission. but it is certainly not clear that thev are all sites of shocks ancl particle acceleration. particularly the enhancements bevoud knot D. For simplicity. however. we will use the termfof throughout this paper to describe these enhancements.," We have detected 31 sites of enhanced emission, but it is certainly not clear that they are all sites of shocks and particle acceleration, particularly the enhancements beyond knot B. For simplicity, however, we will use the term throughout this paper to describe these enhancements."
 In (he inner jet region. X-ray emission from the nuclear jet (radio knot NI) is clearly detected within 3” of the nucleus. and detectable X-ray emission is clearly present between ihe nuclear jet and the first bright radio/X-rav knot AL/AXI as seen from Figure 5..," In the inner jet region, X-ray emission from the nuclear jet (radio knot N1) is clearly detected within $\sim 3''$ of the nucleus, and detectable X-ray emission is clearly present between the nuclear jet and the first bright radio/X-ray knot A1/AX1 as seen from Figure \ref{gsjet}."
" The position of the first bright X-ray knot ANI coincides. (within our absolute uncertainty in astromeltrv ~ 0.5"") with radio knot Al (see below).", The position of the first bright X-ray knot AX1 coincides (within our absolute uncertainty in astrometry $\sim 0.5''$ ) with radio knot A1 (see below).
 knot AXI is clearly extended both along the jet and perpendicular to it., Knot AX1 is clearly extended both along the jet and perpendicular to it.
 For reference. the PSF of the observation at the position of the nucleus (FWIIM) is shown on the righthand side of Figure 5..," For reference, the PSF of the observation at the position of the nucleus (FWHM) is shown on the righthand side of Figure \ref{gsjet}."
 There is continuous dilfuse emission and several X-ray. knots between radio knots Al and D. and there is a kink or bend in the jet direction between knots AX? and ANS.," There is continuous diffuse emission and several X-ray knots between radio knots A1 and B, and there is a kink or bend in the jet direction between knots AX2 and AX3."
 An image of the N-rav. contours in the 0.4-1.5 keV bandpass overlaid onto an optical (LIST) image of Cen A is shown in Figure 7.., An image of the X-ray contours in the 0.4-1.5 keV bandpass overlaid onto an optical (HST) image of Cen A is shown in Figure \ref{optovl}.
 The region of low X-ray surface brightness between knots ΑΝ. and ANG corresponds with dark dust bands in the optical., The region of low X-ray surface brightness between knots AX5 and AX6 corresponds with dark dust bands in the optical.
 The jet appears to widen dramatically before knot B just as it emerges [rom behind (he dust lane. although it appears to remain collimated.," The jet appears to widen dramatically before knot B just as it emerges from behind the dust lane, although it appears to remain collimated."
 Devond knot D. the jet is composed of both knots and diffuse emission.," Beyond knot B, the jet is composed of both knots and diffuse emission."
 The width of the jet is approximately constant out to knot E (c2.5' from the nucleus). where the jet apparently begins to narrow (see Figure 3)). aldhough whether (his is a real feature or just due to a decrease in the X-ray surface brightness is not clear.," The width of the jet is approximately constant out to knot E $\sim 2.5'$ from the nucleus), where the jet apparently begins to narrow (see Figure \ref{cena}) ), although whether this is a real feature or just due to a decrease in the X-ray surface brightness is not clear."
curve) on the left ancl orbital period on the right.,curve) on the left and orbital period on the right.
 The predictions are marginally consistent with the null hvpothesis (p-values between 0.03 and 0.10) except Lor no as a [function of the eut in Aq. for which the null hypothesis is excluded.," The predictions are marginally consistent with the null hypothesis $p$ -values between 0.03 and 0.10) except for $n_2$ as a function of the cut in $K_\mathrm{RV}$, for which the null hypothesis is excluded."
 These results confirm that in many cases the separabilitv approximation and equation (12)) provide useful tools [or removing survey selection effects and converting the observable multiplicity function between surveys., These results confirm that in many cases the separability approximation and equation \ref{eq:ccccc}) ) provide useful tools for removing survey selection effects and converting the observable multiplicity function between surveys.
 Throughout this paper we shall assume that tranets are in circular orbits., Throughout this paper we shall assume that tranets are in circular orbits.
 estimate that the mean eccentricity of planets discovered in (he Kepler survey is only 0.10.25. so this assumption should not cause signilicant errors.," \cite{moor11} estimate that the mean eccentricity of planets discovered in the Kepler survey is only 0.1–0.25, so this assumption should not cause significant errors."
 We shall also assume that a transit occurs when the line of sight to the center of the planet intersects the stellar disk., We shall also assume that a transit occurs when the line of sight to the center of the planet intersects the stellar disk.
 This assumption should be approximately correct so long as the planetary. raclius is much smaller than the stellar radius (the median ratio of planetary radius to stellar radius in the Ixepler survey is only 0.026)., This assumption should be approximately correct so long as the planetary radius is much smaller than the stellar radius (the median ratio of planetary radius to stellar radius in the Kepler survey is only 0.026).
" Let 2, be the radius of the star. α the semianajor axis of a planet in a circular orbit. and e=να."," Let $R_\star$ be the radius of the star, $a$ the semi-major axis of a planet in a circular orbit, and $\epsilon\equiv R_\star/a$."
 Consider à svstem containing » planets with semi-major axes specified by €4..sssἐμ.," Consider a system containing $n$ planets with semi-major axes specified by $\epsilon_1,\ldots,\epsilon_n$."
" Let gout...€,) be the probability that a randomly oriented observer will detect m. dranets in (his svstem."," Let $g_{mn}(\epsilon_1,\ldots,\epsilon_n)$ be the probability that a randomly oriented observer will detect $m$ tranets in this system."
 First consider (he case n=I., First consider the case $n=1$.
 We define three unit vectors: ο points towers (he observer. n is normal (to the planetary orbit. aud z is normal (o the reference plane from which inclinations / are measured.," We define three unit vectors: $\hat\bfo$ points towards the observer, $\hat\bfn$ is normal to the planetary orbit, and $\hat\bfz$ is normal to the reference plane from which inclinations $i$ are measured."
 Thus z:n=cos; and o:n=cos.," Thus $\hat\bfz\cdot\hat\bfn=\cos i$ and $\hat\bfo\cdot\hat\bfn=\cos
\gamma$."
 If the planets size is negligible. it transits if and only if |o:n|€e or |cos5«€ SO Let h(i)= Lif [i|<| and zero otherwise.," If the planet's size is negligible, it transits if and only if $|\hat\bfo\cdot\hat\bfn|<\epsilon$ or $|\cos\gamma|<\epsilon$ so Let $h(w)=1$ if $|w|<1$ and zero otherwise."
 Then transits occur if and only if h(ebeos>) is unity and we may write, Then transits occur if and only if $h(\epsilon^{-1}\cos\gamma)$ is unity and we may write
or common envelope evolution.,or common envelope evolution.
 Changes in the stellar wind properties will certainly impact this balance., Changes in the stellar wind properties will certainly impact this balance.
 A low SNla production rate is actually observed in elliptical galaxies (e.g. Sullivan et al., A low SNIa production rate is actually observed in elliptical galaxies (e.g. Sullivan et al.
 2006) and in low-redshift galaxy clusters (Sharon οἱ al., 2006) and in low-redshift galaxy clusters (Sharon et al.
 2007) relative to star forming galaxies., 2007) relative to star forming galaxies.
 This has been interpreted as evidence (hat a prompt channel for SNla is more important than (he slower phase which had previously been believed to be the main channel (e.g. Panagia et al., This has been interpreted as evidence that a prompt channel for SNIa is more important than the slower phase which had previously been believed to be the main channel (e.g. Panagia et al.
 2007)., 2007).
 ILowever. a metallicity dependent production efficiency could explain the same observations ancl should be explored.," However, a metallicity dependent production efficiency could explain the same observations and should be explored."
 Our understanding of the formation of planetary nebulae (PNe) ancl whether (they. all require binary companions or not is questionable (Moe De Marco 2006)., Our understanding of the formation of planetary nebulae (PNe) and whether they all require binary companions or not is questionable (Moe De Marco 2006).
 If both binary and single stars produce PNe. another interesting consequence of our finding is that. these low-mass. helium core WDs would most likely not produce PNe. as they completely avoid ihe AGB phase.," If both binary and single stars produce PNe, another interesting consequence of our finding is that these low-mass, helium core WDs would most likely not produce PNe, as they completely avoid the AGB phase."
 Indeed. Gesicki Zijlstra (2007) find that the central stars of PNe have a very sharply peaked mass distribution. with a mean mass of M=0.61A. and a range of 0.55—0.66AL.," Indeed, Gesicki Zijlstra (2007) find that the central stars of PNe have a very sharply peaked mass distribution, with a mean mass of $M=0.61\; M_{\odot}$ and a range of $0.55-0.66$."
.. The relatively low number of PNe (per unit galaxy luminosity) in more metal-rich elliptical galaxies (Duzzoni et al., The relatively low number of PNe (per unit galaxy luminosity) in more metal-rich elliptical galaxies (Buzzoni et al.
 2006: see their Figure 11) is consistent with this prediction., 2006; see their Figure 11) is consistent with this prediction.
 We examined the age-metallicitv relation for the local Galactic disk and found that there have been super-solar metallicity stars in (he solar neighborhood in (hie past LO Gyr., We examined the age-metallicity relation for the local Galactic disk and found that there have been super-solar metallicity stars in the solar neighborhood in the past 10 Gyr.
 Since hieh metallicity stars in NGC! 6791. produced single low mass WDs. we expect that there should be a population of single low mass WDs in the fiekl WD population as well.," Since high metallicity stars in NGC 6791 produced single low mass WDs, we expect that there should be a population of single low mass WDs in the field WD population as well."
 Such a population of single low mass WDs is actually observed in several survevs including the Palomar Green ssunple aud the SPY survey., Such a population of single low mass WDs is actually observed in several surveys including the Palomar Green sample and the SPY survey.
 The observed Iraction of single low mass WDs is around50%... corresponding to a formation rate of among the entire WD population.," The observed fraction of single low mass WDs is around, corresponding to a formation rate of among the entire WD population."
 By comparing the lraction of high metallicity stars in the solar neighborhood. we show that 23% of the stars in the solar neighborhood have had. [Fe/II] > +0.3 in the past LO Gyr. therefore such stars are likely progenitors of the single low mass WDs observed today.," By comparing the fraction of high metallicity stars in the solar neighborhood, we show that $\geq$ of the stars in the solar neighborhood have had [Fe/H] $>$ +0.3 in the past 10 Gyr, therefore such stars are likely progenitors of the single low mass WDs observed today."
 Our analvsis indicates that this channel of stellar evolution actually happens not only in NGC 6191. but in the field stars as well.," Our analysis indicates that this channel of stellar evolution actually happens not only in NGC 6791, but in the field stars as well."
 The major implication of our finding is (hat a substantial fraction of old metal-rich. stars end their lives prior to igniting helium and skip interesting and visible phases of stellar evolution that such stars would ordinarily experience., The major implication of our finding is that a substantial fraction of old metal-rich stars end their lives prior to igniting helium and skip interesting and visible phases of stellar evolution that such stars would ordinarily experience.
 This also, This also
Also note that both scripts require a connection with the host that uses a no password’ public key (easy to step up for machines vou own).,Also note that both scripts require a connection with the host that uses a 'no password' public key (easy to step up for machines you own).
 Η the script requires a password. you will be prompted for it (hus. failing for a cron job).," If the script requires a password, you will be prompted for it (thus, failing for a cron job)."
 Automatic passwords are more difficult in scripts as they must come from ply rather than stdiu., Automatic passwords are more difficult in scripts as they must come from pty rather than stdin.
 Ane iab information is too powerful for this paper., And that information is too powerful for this paper.
 Sunple trausfers seem the least necessary to automate., Simple transfers seem the least necessary to automate.
 If one controls both systems. the trausfers are uot time critical.," If one controls both systems, the transfers are not time critical."
 However. oue can imagine scenarios where scripts of this type may be useful.," However, one can imagine scenarios where scripts of this type may be useful."
 For example. one could run a seript in background. say every 2 müuutes. that identilies recent data. and ships it down rauge to avoid loses from catastrophic [zilures at oue eud (e.g.. telescope computer hard drive failure).," For example, one could run a script in background, say every 5 minutes, that identifies recent data, and ships it down range to avoid loses from catastrophic failures at one end (e.g., telescope computer hard drive failure)."
 By the 1990s. the staucard method of distributiug data was through the use of websites.," By the 1990's, the standard method of distributing data was through the use of websites."
 In fact. for a majority of projects maudated to distribute data. a webpage is the fastest technique to comply to the requirements.," In fact, for a majority of projects mandated to distribute data, a webpage is the fastest technique to comply to the requirements."
 A remote system interacts with websites through the use of URLs (uniform resource locator)., A remote system interacts with websites through the use of URL's (uniform resource locator).
 Access through URLs is the responsibility of theurllib module in Python., Access through URL's is the responsibility of the module in Python.
 This moctle allows a script to seid a request to a website. read the returu HTML file aud store iu memory.," This module allows a script to send a request to a website, read the return HTML file and store in memory."
 A simple example is the following: Of course. the returning data is the HTML that inakes up tlie webpage. which ts usually not the most transparent format [or extracting data.," A simple example is the following: Of course, the returning data is the HTML that makes up the webpage, which is usually not the most transparent format for extracting data."
 Parsing the HTML to extract a value cau be tricky. although there are modules for extracting tabular data (e.g. BeautifulSoup. www.crummyv.com/software/BeautifulSoup).," Parsing the HTML to extract a value can be tricky, although there are modules for extracting tabular data (e.g. BeautifulSoup, www.crummy.com/software/BeautifulSoup)."
" A simple comunand to strip all the HTML commancs uses the regular expression (re) module (i.e. ,page))."," A simple command to strip all the HTML commands uses the regular expression ) module (i.e., )."
 This will leave you with all the words ad uumbers outside the hypertext tags., This will leave you with all the words and numbers outside the hypertext tags.
 Its also possible to ideutily specilic pieces of information in a webpage., It's also possible to identify specific pieces of information in a webpage.
" For example. a lavorite comic strip iage by searchine on “sre une="" tag. then striping the identilier tag."," For example, a favorite comic strip image by searching on ""src img="" tag, then striping the identifier tag."
 Again. usiug an urllib script as a crou job allows a user to monitor websites for changes or new data.," Again, using an urllib script as a cron job allows a user to monitor websites for changes or new data."
 The user can be alerted by email using the module. where the script can email a message through au approved SAITP server (see example below).," The user can be alerted by email using the module, where the script can email a message through an approved SMTP server (see example below)."
 This is particular useful for time critical informatiou (sudden change in your bank account?, This is particular useful for time critical information (sudden change in your bank account?
 opening ln a class vou want to atteud?)., opening in a class you want to attend?).
and where rds the binary separation (defined as the distance between the black hole and the center of mass of the strange star).,and where $r$ is the binary separation (defined as the distance between the black hole and the center of mass of the strange star).
 The corresponding acceleration on cach binary component is then given by: where e is the velocity of the quark star and PA that of the black hole. q is the mass ratio of the components.," The corresponding acceleration on each binary component is then given by: where $v^{*}$ is the velocity of the quark star and $v^{\rm BH}$ that of the black hole, $q$ is the mass ratio of the components."
 The application of the above equations is trivial in the case of the black hole. since we always treat ib as a point mass.," The application of the above equations is trivial in the case of the black hole, since we always treat it as a point mass."
 For the star. we apply the same acceleration to cach SPL uid particle. using equation (6)) evaluated at the center of mass of the IEuid. so that we have: Once the star is tically disrupted. this approximation clearly becomes meaningless. and so we switch olf the corresponding terms when the binary separation becomes smaller than the tidal disruption radius CastAlouMaz)! ?. where C isa constant of order unity.," For the star, we apply the same acceleration to each SPH fluid particle, using equation \ref{eq:reaction}) ) evaluated at the center of mass of the fluid, so that we have: Once the star is tidally disrupted, this approximation clearly becomes meaningless, and so we switch off the corresponding terms when the binary separation becomes smaller than the tidal disruption radius $r_{tidal}=CR_{\rm SS}(M_{\rm BH}/M_{\rm SS})^{1/3}$ , where $C$ is a constant of order unity."
 This formulation of gravitational radiation backreaction has been used before for coalescing compact binaries (e.g. Davies et al., This formulation of gravitational radiation back–reaction has been used before for coalescing compact binaries (e.g. Davies et al.
 1994: Iosswog ct al., 1994; Rosswog et al.
 1999: Lee IxIuznniak 1990b)., 1999; Lee Kluźnniak 1999b).
 We initially construct a spherical star by placing No particles of equal mass on a cubic threedimensional grid. and. including a damping term in the equations of motion for an isolated star., We initially construct a spherical star by placing $N$ particles of equal mass on a cubic three–dimensional grid and including a damping term in the equations of motion for an isolated star.
 Ehe system then relaxes for approximately twenty [reefall times (App%(Crp) He?)," The system then relaxes for approximately twenty freefall times $t_{ff}\approx
(G\overline{\rho})^{-1/2}$ )."
 Table P. shows the initial parameters used for our dynamical runs., Table \ref{IC} shows the initial parameters used for our dynamical runs.
 We have used three different values for the initial mass of the strange star. corresponding to the matxiniin mass for a given value of po (as noted by Witten 1984]. L7. for a discussion of physical hounds on Mis see Zdunik et al. ," We have used three different values for the initial mass of the strange star, corresponding to the maximum mass for a given value of $\rho_{0}$ (as noted by Witten [1984], $M_{\rm max} \propto \rho_{0}^{-1/2}$ ; for a discussion of physical bounds on $M_{\rm max}$ see Zdunik et al. ["
2000]).,2000]).
 The black hole is modeled as a spherical vacuum cleanerà point mass producing a Newtonian potential $= GAlpa/r. with an absorbing boundary at the Schwarzschild radius rs=2€Mgg/c.," The black hole is modeled as a spherical vacuum cleaner—a point mass producing a Newtonian potential $\Phi=-GM_{BH}/r$ , with an absorbing boundary at the Schwarzschild radius $r_{Sch}=2GM_{BH}/c^{2}$."
 The mass ratio is defined as q=Mix/Mpg., The mass ratio is defined as $q=M_{\rm SS}/M_{\rm BH}$.
 For each value of Λος we have performed calculations for two cifferent values of q. giving a total of six dynamical runs. shown in Table 1..," For each value of $M_{SS}$ we have performed calculations for two different values of $q$, giving a total of six dynamical runs, shown in Table \ref{IC}."
 To perform the dynamical simulations (described below). we place the star a distance r; from the black hole and give the binary componentsthe azimuthal velocity corresponding to a Ixeplerian binary. with angular," To perform the dynamical simulations (described below), we place the star a distance $r_{i}$ from the black hole and give the binary componentsthe azimuthal velocity corresponding to a Keplerian binary with angular"
llowever. in DDO 43 there are also rreeions found at lower column densities and not associated wilh anv apparent peak inILI.,"However, in DDO 43 there are also regions found at lower column densities and not associated with any apparent peak in."
" There are two small rreeions in (he northeast part of the galaxy Chat lie at ccolumn densities of about 7κ107""7...", There are two small regions in the northeast part of the galaxy that lie at column densities of about $7\times10^{20}$.
" In addition there are several rregions lving in the central hholes. also at column densities of 7x10?""7.."," In addition there are several regions lying in the central holes, also at column densities of $7\times10^{20}$."
 One would expect that cloud formation in (hese regions would be harder because of the lower column densities. especially so [ον the outer rreelons where the critical gas density for gravitational instabilities is dropping (Salronov 1960. Toomre 1964).," One would expect that cloud formation in these regions would be harder because of the lower column densities, especially so for the outer regions where the critical gas density for gravitational instabilities is dropping (Safronov 1960, Toomre 1964)."
 We have identified [our holes in the in DDO 43., We have identified four holes in the in DDO 43.
 The largest has a diameter of 850 pe ancl Che smallest is only 110 pe in size., The largest has a diameter of 850 pc and the smallest is only 110 pc in size.
 lloles have been found in the mnmaps of other disk galaxies as well., Holes have been found in the maps of other disk galaxies as well.
 Im galaxies with cataloged gas holes include ICLO with 8 holes (Wileots Miller 1998). DDO 47 with 19 holes (Walter Brinks 2001). DDO 50 with 51 holes (Puche 11992). DDO 81 with 48 holes (Walter Brinks 1999). NGC 6822 with one hole (de Blok Walter 2000). and the LMC with many holes (Ixim 11999).," Im galaxies with cataloged gas holes include IC10 with 8 holes (Wilcots Miller 1998), DDO 47 with 19 holes (Walter Brinks 2001), DDO 50 with 51 holes (Puche 1992), DDO 81 with 48 holes (Walter Brinks 1999), NGC 6822 with one hole (de Blok Walter 2000), and the LMC with many holes (Kim 1999)."
 Some of the holes in these galaxies reach 2.0 kpe in diameter. but most are several hundred parsecs in size.," Some of the holes in these galaxies reach 2.0 kpc in diameter, but most are several hundred parsecs in size."
 Thus. the hholes in DDO 43 are (vpical in size.," Thus, the holes in DDO 43 are typical in size."
 Ilowever. we have not detected (he signature of expansion in any of DDO 43's holes.," However, we have not detected the signature of expansion in any of DDO 43's holes."
 Therefore. they must be relatively old.," Therefore, they must be relatively old."
" DDO 43's largest hole (""Ποιος 17) resembles that surrounding the OB association NGC 206 (=OB7s) in M31 (Brinks 1951).", DDO 43's largest hole (“Hole 1”) resembles that surrounding the OB association NGC 206 $=$ OB78) in M31 (Brinks 1981).
 The hhole around NGC 206 has clearly been produced by (he mechanical energy. input. [rom the concentration of massive stars in the enclosed OB association., The hole around NGC 206 has clearly been produced by the mechanical energy input from the concentration of massive stars in the enclosed OB association.
 Not only do massive stars explode as supernovae. but they dump a comparable amount of energv into their surroundings over their lifetimes in the form of strong winds.," Not only do massive stars explode as supernovae, but they dump a comparable amount of energy into their surroundings over their lifetimes in the form of strong winds."
 Brinks estimates that 2x105 ool iis “nussine” trom the NGC 206 hole., Brinks estimates that $\times 10^6$ of is “missing” from the NGC 206 hole.
 If we assume that the column density prior to the formation of DDO 43s hole was the same as the average we see in the knots (1.3x107! 7)). and covered the area out to the current 0.8x107! ," If we assume that the column density prior to the formation of DDO 43's hole was the same as the average we see in the knots $\times 10^{21}$ ), and covered the area out to the current $\times 10^{21}$ "
dense that the lensed star itself cannot be imaged by the telescope used for monitoring (see. e.g.. Alard Lupton 1998).,"dense that the lensed star itself cannot be imaged by the telescope used for monitoring (see, e.g., Alard Lupton 1998)."
 In order for a photometrie deviation above baseline to be detectable. we must receive an additional amount of light per unit time from the region. producing a fractional change of at least fy. Typical values of fj used so far in monitoring programs have been in the range 0.1—0.5.Let the index / label an individual source star that lies close to the path of the lens.," In order for a photometric deviation above baseline to be detectable, we must receive an additional amount of light per unit time from the region, producing a fractional change of at least $f_T.$ Typical values of $f_T$ used so far in monitoring programs have been in the range $0.1-0.5.$Let the index $i$ label an individual source star that lies close to the path of the lens."
 If the approach between this source and the lens is to produce a detectable photometric event. the required angular distance of closest approach ts 05;. Because it is convenient to express angles in terms of the Einstein angle of the lens. we define 5;= If an individual star must experience a magnification >| in order for the magnification of the monitored region to be (14+fr). then This limit of small 5; is the limit used to compute the event rates presented below.," If the approach between this source and the lens is to produce a detectable photometric event, the required angular distance of closest approach is $\theta_{b,i}.$ Because it is convenient to express angles in terms of the Einstein angle of the lens, we define $b_i = \theta_{b,i}/\theta_E.$ If an individual star must experience a magnification $>>1$ in order for the magnification of the monitored region to be $(1+f_T)$, then This limit of small $b_i$ is the limit used to compute the event rates presented below."
 It is possible. however for 5; to be even larger than unity.," It is possible, however for $b_i$ to be even larger than unity."
" If. e.g.. a single bright star is the dominant source of light in the monitored region. then 5,=1.2.8.3.5 corresponds to fy approximately equal to 0.34.0.02.0.01. respectively."," If, e.g., a single bright star is the dominant source of light in the monitored region, then $b_1 = 1, 2.8, 3.5$ corresponds to $f_T$ approximately equal to $0.34, 0.02, 0.01,$ respectively."
 For point-source/point-lens events. the event duration 1s the only measurable parameter related to the lens mass.," For point-source/point-lens events, the event duration is the only measurable parameter related to the lens mass."
 The Einstein crossing time Is The measurable duration of an event Is b;7p.," The Einstein crossing time is The measurable duration of an event is $b_i\, \tau_E$."
 We parametrize the source density in terms of an angle (|. the average angular separation between sources in the background field.," We parametrize the source density in terms of an angle $\theta_1,$ the average angular separation between sources in the background field."
 The rates of and characteristics of detectable photometric effects of mesolensing depend on the method of detection and on the physical parameters of the lens and of the background source field., The rates of and characteristics of detectable photometric effects of mesolensing depend on the method of detection and on the physical parameters of the lens and of the background source field.
" The rate of events caused by an individual lens of mass M. located a distance D, from us. lensing à source located at a distance Ds (v=Dj /D«s) is given by the expression below (Di Stefano 20063)."," The rate of events caused by an individual lens of mass $M$, located a distance $D_L$ from us, lensing a source located at a distance $D_S$ $x=D_L/D_S$ ) is given by the expression below (Di Stefano 2006a)."
" In this expression 0, represents the Einstein angle. and w is the relative angular speed between the lens and source."," In this expression $\theta_E$ represents the Einstein angle, and $\omega$ is the relative angular speed between the lens and source."
 For nearby lenses. ιο is almost exactly equal to the angular speed of the lens with respect to Earth.," For nearby lenses, $\omega$ is almost exactly equal to the angular speed of the lens with respect to Earth."
 The transverse velocity of the lens is represented by €. and the effects of the Earth's motion are incorporated by the vector $. whose direction depends on position relative to the ecliptic and whose magnitude is of order unity.," The transverse velocity of the lens is represented by ${\bf {\hat v}_L},$ and the effects of the Earth's motion are incorporated by the vector ${\bf \hat g}$, whose direction depends on position relative to the ecliptic and whose magnitude is of order unity."
" The validity of this expression requires that the background field is dense enough that the monitored region (yon\0,,,) Is likely to contain stars.", The validity of this expression requires that the background field is dense enough that the monitored region $\theta_{mon} \times \theta_{mon}$ ) is likely to contain stars.
" Note that the value of Rieter increases as (,,,, and fy decrease.", Note that the value of $R_1^{detect}$ increases as $\theta_{mon}$ and $f_T$ decrease.
" The total rate of detectable events for a population of lenses. each with mass M. can be written as follows. where we assume that x<<I. O,, is the surface area of the galaxy expressed in square degrees."," The total rate of detectable events for a population of lenses, each with mass $M,$ can be written as follows, where we assume that $x << 1.\, $ $\Omega_{gal}$ is the surface area of the galaxy expressed in square degrees."
 We assume that the density of potential lenses is constant., We assume that the density of potential lenses is constant.
 It might be supposed that. when the Einstein ring of the lens is large enough to encompass the positions of several source stars. multiple-source effects could be important.," It might be supposed that, when the Einstein ring of the lens is large enough to encompass the positions of several source stars, multiple-source effects could be important."
 Indeed. as discussed below. in rare cases the presence of multiple sources produces distinctive signals.," Indeed, as discussed below, in rare cases the presence of multiple sources produces distinctive signals."
 Nevertheless. most light curves caused by nearby lenses have the same functional form as light curves caused by more distant lenses.," Nevertheless, most light curves caused by nearby lenses have the same functional form as light curves caused by more distant lenses."
 This is because events in which there is a significant deviation above baseline tend to be produced by: (a) bright stars: it is not likely that there are two or more bright stars in any specific monitored region: (b) close approaches to an individual source star: it is even less likely that the positions of two bright source stars lie within a small fraction of an Einstein angle., This is because events in which there is a significant deviation above baseline tend to be produced by: (a) bright stars; it is not likely that there are two or more bright stars in any specific monitored region; (b) close approaches to an individual source star; it is even less likely that the positions of two bright source stars lie within a small fraction of an Einstein angle.
 Against very dense source backgrounds. or if the observations are sensitive enough. the event rate can be so high that sequences of events are be caused by a single lens. particularly if the lens in near enough to have a proper motion of several Jy per year.," Against very dense source backgrounds, or if the observations are sensitive enough, the event rate can be so high that sequences of events are be caused by a single lens, particularly if the lens in near enough to have a proper motion of several $\theta_E$ per year."
" The likelihood of sequences of events increases with the value of 05;/0,."," The likelihood of sequences of events increases with the value of $\theta_{b,i}/\theta_1$."
" Indeed. as the value of Ü5i/Ü, becomes as large as roughly 0.1. the probability that two or more stars will be detectable lensed simultaneously increases."," Indeed, as the value of $\theta_{b,i}/\theta_1$ becomes as large as roughly $0.1,$ the probability that two or more stars will be detectable lensed simultaneously increases."
 The simultaneous lensing of two stars produces light curve shapes that differ from the standard Paczynsski form. but which can nevertheless be well fit by a lensing model in which the event is produced by light from à small number of source stars.," The simultaneous lensing of two stars produces light curve shapes that differ from the standard Paczyǹsski form, but which can nevertheless be well fit by a lensing model in which the event is produced by light from a small number of source stars."
 The event rate is proportional to the total area monitored., The event rate is proportional to the total area monitored.
 This means that wide-field monitoring programs can play an important role in detecting lensing., This means that wide-field monitoring programs can play an important role in detecting lensing.
 Within the next 5 to 10 years two wide-field monitoring projects will begin., Within the next $5$ to $10$ years two wide-field monitoring projects will begin.
 Pan-STARRS.System. will monitor the sky as seen from Hawarn. (Chambers te 2004) and LSST (the Telescope). will operate from Chile (Stubbs et 2004) .," Pan-STARRS, will monitor the sky as seen from Hawaii, (Chambers te 2004) and LSST (the ), will operate from Chile (Stubbs et 2004) ."
 Together. these surveys will cover the sky.," Together, these surveys will cover the sky."
 In addition. they will be able to achieve smaller values of fy than monitoring programs until now.," In addition, they will be able to achieve smaller values of $f_T$ than monitoring programs until now."
 As we will discuss in 83. the combination of wide-field coverage.," As we will discuss in 3, the combination of wide-field coverage,"
width of the broad component of the LL3 as measured by ? and ?.. around. 4000 and 3200 km s+. respectively.,"width of the broad component of the $\beta$ as measured by \citet{fh84} and \citet{win92}, , around $4\,000$ and $3\,200$ km $^{-1}$, respectively."
 Finally. the doublet has a EWILM consistent with that of the doublet and the narrow Ho. component. while the doublet is broader. but all in agreement with an origin in the Narrow Line Reeion.," Finally, the doublet has a FWHM consistent with that of the doublet and the narrow $\alpha$ component, while the doublet is broader, but all in agreement with an origin in the Narrow Line Region."
 Dillerently from all the other Sevlert 1s with broachane X-ray observations. NGC 7213 lacks a Compton rellection component. the clearest’ signature for the presence of a Compton-thick material.," Differently from all the other Seyfert 1s with broadband X-ray observations, NGC 7213 lacks a Compton reflection component, the clearest signature for the presence of a Compton-thick material."
 Pherefore. the observed: neutra iron line must originate in a Compton-thin material. be i the BLR. or a Compton-thin torus.," Therefore, the observed neutral iron line must originate in a Compton-thin material, be it the BLR or a Compton-thin torus."
 The IEG spectrum of NGC 7213. allowec us to resolve. for the first. time. the iron line width a 2400OOO117 kn f (pWIIMD).," The HEG spectrum of NGC 7213 allowed us to resolve, for the first time, the iron line width at $2\,400^{+1\,100}_{-600}$ km $^{-1}$ (FWHM)."
 Phe analysis of a cquzisi-simultaneous optical observation confirmed the presence of a broad component of the Ho line. for which we measured a PWHAM=264022 km s.+.," The analysis of a quasi-simultaneous optical observation confirmed the presence of a broad component of the $\alpha$ line, for which we measured a $2640^{+110}_{-90}$ km $^{-1}$."
 Phe widths of the two lines are in very good agreement. which suggests that they are likely to be produced in the same material.," The widths of the two lines are in very good agreement, which suggests that they are likely to be produced in the same material."
 To test if this scenario is possible. we have to. verify if the observed EW of the iron line is in agreement with an origin in the BLR.," To test if this scenario is possible, we have to verify if the observed EW of the iron line is in agreement with an origin in the BLR."
 Following the detailed: procedure described bv. 2.. derived from? adopting updated atomic data. the expected. EW for the BLR in NGC 7213 can be wrltten as: This estimate assumes a spherically symmetric cloud distribution for the BLR. with a covering factor of f. a column density of Ny for each cloud and an iron abundance relative to hvdrogen of Ap.=468.10.7 (2)..," Following the detailed procedure described by \citet{yaq01}, derived from \citet{kk87} adopting updated atomic data, the expected EW for the BLR in NGC 7213 can be written as: This estimate assumes a spherically symmetric cloud distribution for the BLR, with a covering factor of $f_c$, a column density of $N_\mathrm{H}$ for each cloud and an iron abundance relative to hydrogen of $A_\mathrm{Fe}=4.68\times10^{-5}$ \citep{ag89}. ."
 The powerlaw index of P=1.69 derived from the and the observations was further adopted in the derivation of C19)., The powerlaw index of $\Gamma=1.69$ derived from the and the observations was further adopted in the derivation of \ref{formulaew}) ).
 Assuming f.Ξ 0.35. a column density. around 31077 em7 can reproduce an EW100 eV. which is the order of magnitude found by anclNewton.," Assuming $f_c=0.35$ , a column density around $3\times10^{23}$ $^{-2}$ can reproduce an $\simeq100$ eV, which is the order of magnitude found by and."
.. Phese values for f£ and Ny are within the ranges usually assumed. in photoionization models of BLRs (?).., These values for $f_c$ and $N_\mathrm{H}$ are within the ranges usually assumed in photoionization models of BLRs \citep{netzer90}.
" In particular. f,=0.35 is the value derived by ?7/— from observational constraints in the Sevfert 1.NGC 5548. even if more ‘canonical’ values around 0.1 and 0.25 are generally found."," In particular, $f_c=0.35$ is the value derived by \citet{gk98} from observational constraints in the Seyfert 1 NGC 5548, even if more `canonical' values around 0.1 and 0.25 are generally found."
 Phe Iarge covering factor needed to account for the iron line EW may be at odds with the regular intensity of the observed. broad optical lines. but the weakness or absence of an UV bump in NGC 7213 (e.g.7). may result in a deficit of UY phototonizing photons and compensate the geometrical factor.," The large covering factor needed to account for the iron line EW may be at odds with the regular intensity of the observed broad optical lines, but the weakness or absence of an UV bump in NGC 7213 \citep[e.g.][]{starl05} may result in a deficit of UV photoionizing photons and compensate the geometrical factor."
 In any case. f. and Ny can be lower. provided that Ap. is larger than solar and/or the X-ray illumination of the BLR is anisotropic (seec.g.2.andreferencestherein)..," In any case, $f_c$ and $N_\mathrm{H}$ can be lower, provided that $A_\mathrm{Fe}$ is larger than solar and/or the X-ray illumination of the BLR is anisotropic \citep[see e.g.][and references therein]{yaq01}."
 On the other hand. we cannot exclude a further contribution to the iron line EW from a Compton-thin torus. located on a peescale. but we stress here that we do not have any other piece of evidence to support its presence.," On the other hand, we cannot exclude a further contribution to the iron line EW from a Compton-thin torus, located on a pc-scale, but we stress here that we do not have any other piece of evidence to support its presence."
" The presence of emission lines from highly ionised iron in the LEG spectrum of NGC 7213 confirms the results by ον,", The presence of emission lines from highly ionised iron in the HEG spectrum of NGC 7213 confirms the results by \citet{bianchi03b}.
 As suggested Lhby these authors. heir originC may be in Ingas photoionised bà~ the AGN. as ound in many Sevlert 1s anc 2s (c.g.2]??)..," As suggested by these authors, their origin may be in gas photoionised by the AGN, as found in many Seyfert 1s and 2s \citep[e.g.][]{bm02,bianchi05}."
 However. the eratings data presented here revealed that the resonant line is the dominant component in the Fe triplet (unless its Xueshift is significantly larger thanthe one measured [or he Fe lino). which is suggestive of anorigin in σας in collisionalequilibrium.," However, the gratings data presented here revealed that the resonant line is the dominant component in the Fe triplet (unless its blueshift is significantly larger thanthe one measured for the Fe line), which is suggestive of anorigin in gas in collisionalequilibrium."
 This is in agreement with the results ound by ? using diagnostic tools based on the O triplet, This is in agreement with the results found by \citet{starl05} using diagnostic tools based on the O triplet
period of pulsation of the excited modes (see below).,period of pulsation of the excited modes (see below).
 A sequence of evolutionary models is analvzed. starting from a central temperature κο=3. ~ 300 vr before explosion. to Teo= 7. corresponding to ~ 10 minutes before explosion.," A sequence of evolutionary models is analyzed, starting from a central temperature $T_{8,\rm c} = 3$ , $\sim$ 300 yr before explosion, to $T_{8,\rm c} =
7$ , corresponding to $\sim$ 10 minutes before explosion."
" All models analyzed show that the ""undamental and higher order modes are unstable.", All models analyzed show that the fundamental and higher order modes are unstable.
 As in Baralle et ((2001). the assumed time dependence for (he eieenfunctions is of the form exp(io/)xexpCA/). where o=27/TII is (he eigen-Irequency. II the corresponding period aud A the stability coefficient.," As in Baraffe et (2001), the assumed time dependence for the eigenfunctions is of the form $\exp({\rm i} \sigma t) \,\times
\,\exp(Kt)$ , where $\sigma = 2\pi/\Pi$ is the eigen-frequency, $\Pi$ the corresponding period and $K$ the stability coefficient."
" The e- time characterizing the growth (ünmescale of the pulsation amplitude is defined. by 74,=1.", The $e$ -folding time characterizing the growth timescale of the pulsation amplitude is defined by $\taud = 1/K$.
 In all models analvzed. (this fundamental growth. (nmescale is. by at least one order of magnitude. shorter than 74 of the higher order modes.," In all models analyzed, this fundamental growth timescale is, by at least one order of magnitude, shorter than $\taud$ of the higher order modes."
 Our analysis below can thus be restricted to the fundamental mode. since it is the mode which grows the fastest.," Our analysis below can thus be restricted to the fundamental mode, since it is the mode which grows the fastest."
 Table 2 summarizes the stability analvsis results., Table 2 summarizes the stability analysis results.
" The hudamental mode pulsation period Il, is ~ 2 s. close to the dynamical timescale."," The fundamental mode pulsation period $\Pi_0$ is $\sim$ 2 s, close to the dynamical timescale."
" Note that the shortest convective timescale is ~10! s in the first model analysed (74, — 3) and ~100 s in the last models."," Note that the shortest convective timescale is $\sim \, 10^4$ s in the first model analysed $T_{8,\rm c}$ = 3) and $\sim \, 100$ s in the last models."
 For a model with νι=5 (e 6 davs before explosion). Fig.," For a model with $T_{8,\rm c} = 5$ $\sim$ 6 days before explosion), Fig."
 G displays (he work dV ALU. which is proportional to the energy. transferred to the pulsation. with J the so-called work integral (Cox 1980: Unno et al.," \ref{fig2} displays the work $W$ $M$, which is proportional to the energy transferred to the pulsation, with $W$ the so-called work integral (Cox 1980; Unno et al."
 1939)., 1989).
 Positive work indicates driving regions whereas negative work corresponds (o camping zones., Positive work indicates driving regions whereas negative work corresponds to damping zones.
 The positive value of dV /dA in the center is due to the perturbation of the nuclear enerey generation rate and characterizes the e-mechanism., The positive value of $W$ $M$ in the center is due to the perturbation of the nuclear energy generation rate and characterizes the $\epsilon$ -mechanism.
 As expected for a gas wilh Py74/3. (the displacement àr/r is essentially constant through the wholestructure.," As expected for a gas with $\Gamma_1 \sim 4/3$, the displacement $\delta r/r$ is essentially constant through the wholestructure."
 Dampingprocesses are smallin the rest of (he white dwarl and the total work integral W is essentially determined by the driving zone in the center.," Dampingprocesses are smallin the rest of the white dwarf, and the total work integral $W$ is essentially determined by the driving zone in the center."
which are approximately isotropic not in the blob frame. but in the rest frame of the broad line region )).,"which are approximately isotropic not in the blob frame, but in the rest frame of the broad line region )."
 In the Thomson limit. Dermer(1995) has shown Chat the beaming pattern in this case is D!En7°.," In the Thomson limit, \cite{dermer95} has shown that the beaming pattern in this case is ${\cal D}^{4+2\alpha}$."
" In terms of the power-law index of the electron distribution. this is equivalent to D,"," In terms of the power-law index of the electron distribution, this is equivalent to ${\cal D}^{3+p}$."
 In 2 we show that this expression arises immediately. from (he (ransformation properties of the electron distribution and is valid for arbitrary electron enerev., In \ref{math} we show that this expression arises immediately from the transformation properties of the electron distribution and is valid for arbitrary electron energy.
 Thus. in the case of EC emission. the beaming is most simply expressed in ternis ol the underlving electron distribution. whereas for SSC and svnchrotron emission it can be obtained straightforwiuaxlly from the observed. photon distribution.," Thus, in the case of EC emission, the beaming is most simply expressed in terms of the underlying electron distribution, whereas for SSC and synchrotron emission it can be obtained straightforwardly from the observed photon distribution."
" In. addition to the beanmüng pattern for a power-law distribution. Dermer(1995) also demonstrated (hat a characteristic energy. such as a cut-off or break in the spectrum. is observed αἱ a photon energv that scales as €,xD7."," In addition to the beaming pattern for a power-law distribution, \citet{dermer95} also demonstrated that a characteristic energy, such as a cut-off or break in the spectrum, is observed at a photon energy that scales as $\epsilon_{max}\propto {\cal D}^2$."
 This contrasts with the situation lor svnchrotron and SSC radiation. where the scaling is linear with D.," This contrasts with the situation for synchrotron and SSC radiation, where the scaling is linear with ${\cal D}$."
" Once again. the dillerence can be understood from the transformation properties of electrons and photons. respectively,"," Once again, the difference can be understood from the transformation properties of electrons and photons, respectively."
 We show that the scaling changes when Ixlein-Nishina CINN) effects intervene: lor hard. electron distributions (p« 3) with an upper cut-off. the peak in the spectral energy. distribution is limited to a value €peasSl/ey Chat is independent of D. where ej is the energy of the seed photons in unitsκ of. >moc. (," We show that the scaling changes when Klein-Nishina ) effects intervene: for hard electron distributions $p<3$ ) with an upper cut-off, the peak in the spectral energy distribution is limited to a value $\epsilon_{peak} \lesssim 1/\epsilon_0$ that is independent of ${\cal D}$, where $\epsilon_0$ is the energy of the seed photons in units of $m_e c^2$. ("
Energy units. of. οE are used throughout thisκ work.),Energy units of $m_e c^2$ are used throughout this work.)
5 Assuming that the EGRET--detected. GeV emission from blazars is due to inverse Compton scattering of broad line region photons we show in 3 that (he spectra are significantly affected by INN effects. which result in a softening of the spectrum.," Assuming that the -detected GeV emission from blazars is due to inverse Compton scattering of broad line region photons we show in 3 that the spectra are significantly affected by KN effects, which result in a softening of the spectrum."
 This effect. has been noted in connection with blazar spectra by Bottcher. (1997).. who computed model spectra using anisotropically distributed accretion disk photons as targets. rather (han photons from the broad line region.," This effect has been noted in connection with blazar spectra by \citet{boettchermauseschlickeiser97}, who computed model spectra using anisotropically distributed accretion disk photons as targets, rather than photons from the broad line region."
 We map the observed sspectral indices to the index of the electron distribution. and find that these are grouped around (he value p=3.2. in agreement with recent theoretical work on particle acceleration in relativistic shocks (Bednarz&Ostrowski1998:irketal.2000: 2001).," We map the observed spectral indices to the index of the electron distribution, and find that these are grouped around the value $p=3.2$, in agreement with recent theoretical work on particle acceleration in relativistic shocks \citep{bednarzostrowski98,kirk00,achterbergetal01}."
. Svnchrotron cooling or. alternatively. cooling by IC scattering in the Thomson limit produces a break of Ap=IL in the electron spectrum.," Synchrotron cooling or, alternatively, cooling by IC scattering in the Thomson limit produces a break of $\Delta p=1 $ in the electron spectrum."
 The spectrum of IC radiation in the Thomson limit therefore shows a break of Aa=0.5., The spectrum of IC radiation in the Thomson limit therefore shows a break of $\Delta \alpha=0.5$.
 However. some 5-rav sources that peak al MeV energies show a more pronounced break (MeNaron-Drownetal...1995).. which has been interpreted. as evidence for gamma-ray absorption bv pair production (Blancllord&Levinson1995;Marcowith.Henri&Pelletier 1995).," However, some $\gamma$ -ray sources that peak at MeV energies show a more pronounced break \citep{mcnaron95}, which has been interpreted as evidence for gamma-ray absorption by pair production \citep{blandfordlevinson95,marcowithhenripelletier95}."
. We show that spectral soltening can explain these observations. provided the electron distribution is determined by svnchrotron cooling.," We show that spectral softening can explain these observations, provided the electron distribution is determined by synchrotron cooling."
 A summary of our results ancl their implications is presented in 4.., A summary of our results and their implications is presented in \ref{discussion}. .
"spatial The pipeline for IBIS data reduction takes care of normal calibration processes (dark frame, flat field, etc.)","spatial The pipeline for IBIS data reduction takes care of normal calibration processes (dark frame, flat field, etc.)"
 and also corrects for blue-shift effects (?) and instrumental polarization: the latter is important for minimizing residual cross-talk between the Stokes profiles., and also corrects for blue-shift effects \citep{MSreardon08} and instrumental polarization: the latter is important for minimizing residual cross-talk between the Stokes profiles.
" For further details on the calibration pipeline see ? The estimated mean spatial resolution of the line-of-sight (LoS) velocity fields computed from the spectropolarimetric scans used in this work is 0.36 In addition to IBIS data, we also used Hinode SOT/SP observations of the same active regions taken three and half hours before the IBIS data set."," For further details on the calibration pipeline see \cite{2009ApJ...700L.145V} The estimated mean spatial resolution of the line-of-sight (LoS) velocity fields computed from the spectropolarimetric scans used in this work is $0.36$ In addition to IBIS data, we also used Hinode SOT/SP observations of the same active regions taken three and half hours before the IBIS data set."
" When dealing with waves, knowledge of the formation heights of the spectral lines and their position with respect to the equipartition layer (namely the layer in which the MHD mode conversion takes place), is fundamental."," When dealing with waves, knowledge of the formation heights of the spectral lines and their position with respect to the equipartition layer (namely the layer in which the MHD mode conversion takes place), is fundamental."
" As mentioned earlier, IBIS observations were obtained using two spectral lines: the chromospheric Ca 854.2 nm and the photospheric Fe 617.3 As for the Ca 854.2 nm line, ? and ? pointed out that this low chromosphere spectral line actually spans a wide range of atmospheric heights starting from the mid-high photosphere to the low chromosphere (line ? estimated the quiet Sun height of formation of the Fe 617.3 nm core to be around 300 km above the photosphere."," As mentioned earlier, IBIS observations were obtained using two spectral lines: the chromospheric Ca $854.2$ nm and the photospheric Fe $617.3$ As for the Ca $854.2$ nm line, \cite{2008A&A...480..515C} and \cite{2009A&A...494..269V} pointed out that this low chromosphere spectral line actually spans a wide range of atmospheric heights starting from the mid-high photosphere to the low chromosphere (line \citet{2006ASPC..358..193N} estimated the quiet Sun height of formation of the Fe $617.3$ nm core to be around $300$ km above the photosphere."
 This has to be compared with the altitude of the equipartition layer in our region of interest in order to estimate the plasma £8 regime sampled by our observations., This has to be compared with the altitude of the equipartition layer in our region of interest in order to estimate the plasma $\beta$ regime sampled by our observations.
" For this purpose, we estimated the equipartition layer position using spectropolarimetric inversions obtained through the SIR code (?) performed on SOT/SP data."," For this purpose, we estimated the equipartition layer position using spectropolarimetric inversions obtained through the SIR code \citep{1992ApJ...398..375R} performed on SOT/SP data."
" Our estimate reveals that the equipartition layer is slightly below the height of formation of the Fe 617.3 nm spectral line throughout the FoV, this means that we are sampling the onset of the low-G regime in the solar atmosphere, very close to the conversion altitude."," Our estimate reveals that the equipartition layer is slightly below the height of formation of the Fe $617.3$ nm spectral line throughout the FoV, this means that we are sampling the onset of the $\beta$ regime in the solar atmosphere, very close to the conversion altitude."
" As mentioned, in this work we explore the characteristics of the power spectral density at different magnetic field inclinations with respect to the local gravity vector."," As mentioned, in this work we explore the characteristics of the power spectral density at different magnetic field inclinations with respect to the local gravity vector."
 This is done by comparing the information encoded in the temporal sampling to the spectro-polarimetric data provided by the, This is done by comparing the information encoded in the temporal sampling to the spectro-polarimetric data provided by the
ccontinuum emission is a mixture of shorter wavelength starlight transiently reprocessed by tiny particles (see 4.2)) and reflected NIR starlight (Sellgrenetal.1992).,continuum emission is a mixture of shorter wavelength starlight transiently reprocessed by tiny particles (see \ref{nircont}) ) and reflected NIR starlight \citep{SWD92}.
. Sellgrenetal.(1992) reported that in7023.. the polarization rises from short to long optical wavelengths.is strongest at J. and then steadily decreases to longer NIR wavelengths. with the lowest measured polarization values at their longest observed wavelength. K(13.1%...4.6%.. and at positions A. B. and C. respectively. in Fig. 4)).," \citet{SWD92} reported that in, the polarization rises from short to long optical wavelengths,is strongest at $J$, and then steadily decreases to longer NIR wavelengths, with the lowest measured polarization values at their longest observed wavelength, $K$, and at positions A, B, and C, respectively, in Fig. \ref{f4}) )."
 Based on this result. they conclude that scattered starlight contributes no more than ~20% to K measurements at positions near the 2 ccontinuum emission peak in7023.," Based on this result, they conclude that scattered starlight contributes no more than $\sim$ to $K$ measurements at positions near the 2 continuum emission peak in."
. Thus. although optical polarimetry demonstrates that the optical nebulosity at the 2.4m ccontinuum emission peak is primarily scattered starlight (Gehrels1967;Watkinetal.1991:Sellgren1992).. we believe that scattered starlight makes a negligible contribution to the overall 2 ccontinuum emission.," Thus, although optical polarimetry demonstrates that the optical nebulosity at the 2 continuum emission peak is primarily scattered starlight \citep{Ge67,WGS91,SWD92}, we believe that scattered starlight makes a negligible contribution to the overall 2 continuum emission."
 The brightest nebulosity in the 2 ccontinuum images is the extended peak roughly halfway between the filaments and200775., The brightest nebulosity in the 2 continuum images is the extended peak roughly halfway between the filaments and.
. This 2 ccontinuum emission peak is centered near W N («53 mpe) from200775.. with a diameter of - (6-63 mpc) parallel to the filaments.," This 2 continuum emission peak is centered near W N $\sim$ 53 mpc) from, with a diameter of $\sim$ $\sim$ 63 mpc) parallel to the filaments."
 The 2 ccontinuum emission peak roughly corresponds to the cclump detected by Fuenteetal.(1996).., The 2 continuum emission peak roughly corresponds to the clump detected by \citet{FMN96}.
 The ring structure seen in the 3.29 image is only partially observed in the 2 ccontinuum images., The ring structure seen in the 3.29 image is only partially observed in the 2 continuum images.
 Filament Lis clearly seen. but Filament I] is only weakly present and Filament HII may be faintly present only in the 2.18 image (Lemaireetal.1996).," Filament I is clearly seen, but Filament II is only weakly present and Filament III may be faintly present only in the 2.18 image \citep{LFG96}."
. The filaments appear more diffuse in the 2 ccontinuum emission than in the 3.29 IIEF emission or lline emission images., The filaments appear more diffuse in the 2 continuum emission than in the 3.29 IEF emission or line emission images.
 Standard PDR models (seereferencesinHollenbach&Tielens1997) predict that. in PDRs. UV-pumped fluorescent eemission lines are confined to a narrow transition region between aandH».," Standard PDR models \citep[see references in][]{HT97} predict that, in PDRs, UV-pumped fluorescent emission lines are confined to a narrow transition region between and."
. Spectroscopie studies (Martinietal.1997.1999) and narrowband imaging (Lemaireetal.1996:Takami2000). of different rro-vibrational emission lines in sshow that the observed eemission is UV-pumped fluorescence.," Spectroscopic studies \citep{MSH97,MSD99} and narrowband imaging \citep{LFG96,TUS00} of different ro-vibrational emission lines in show that the observed emission is UV-pumped fluorescence."
 These authors also find evidence that the lower level populations are redistributed collisionally due to higher ddensity. especially in the ffilaments. in agreement with rresults (Fuenteetal.1996).," These authors also find evidence that the lower level populations are redistributed collisionally due to higher density, especially in the filaments, in agreement with results \citep{FMN96}."
. Observations of theBar.. at a distance of ~450 pe (O'Dell2001).. show that the 3.29 HEF emission ts strongest Just outside the ionization front (Aitkenetal.1979;Sellgren1981:Roche.Aitken.&Smith1989;Bregmanetal.1989:Sellgren1990b:Tielens1993;Sloan 1997).," Observations of the, at a distance of $\sim$ 450 pc \citep{O2001}, show that the 3.29 IEF emission is strongest just outside the ionization front \citep*{ARS79,Se81,RAS89,BAW89,STN90,TMW93,SBG97}."
. This has been interpreted to mean that the IEF carriers are destroyed in rregions. perhaps by chemical attack or two-photon transient excitation.," This has been interpreted to mean that the IEF carriers are destroyed in regions, perhaps by chemical attack or two-photon transient excitation."
" The peak 3.29 eemission in the aalso lies significantly closer 15"".. or 22-33 mpo) to the star than does the peak fluorescent emission.", The peak 3.29 emission in the also lies significantly closer or 22-33 mpc) to the star than does the peak fluorescent emission.
 A similar result is found for the planetary nebula, A similar result is found for the planetary nebula
from which we obtain a being the viscosity parameter. and Lakes into account null boundary condition for the torque al Fr—ry. the inner radius of the disk.,"from which we obtain $\alpha$ being the viscosity parameter, and takes into account null boundary condition for the torque at $r=r_{1}$, the inner radius of the disk."
 Assuming the disk to be cooled bv radiative transport in z direction. we may write. in the diffusion approximation. with e. FL. 7. D. being. respectively. velocity of light. radiative [Iux in z direction. optical depth. and radiation pressure.," Assuming the disk to be cooled by radiative transport in $z$ direction, we may write, in the diffusion approximation, with $c$, $F_{z}$, $\tau$, $P_{r}$ being, respectively, velocity of light, radiative flux in $z$ direction, optical depth, and radiation pressure."
 Replacing differentials bv finite dillerences. and recalling the definition of effective temperature. ie. eq.(18) may be written as with σ being the Stefan-Doltzmann constant. and TZ the temperature al the mid plane of (he disk.," Replacing differentials by finite differences, and recalling the definition of effective temperature, i.e., eq.(18) may be written as with $\sigma$ being the Stefan-Boltzmann constant, and $T$ the temperature at the mid plane of the disk."
 In the outer parts of the disk. the opacity is mainly given by (he [ree-Iree opacily.," In the outer parts of the disk, the opacity is mainly given by the free-free opacity."
"so. using a Rosseland mean opacity. averaged over z. eq.(20) will be rewritten as Finally. for a gas pressure dominated disk. we obtain [rom ec.(21). where Mig. Maj. er. y are. respectively, accretion rate in units of LOMgs|. mass of the central object in units of 10? g. the radial distance in units of the inner radius.the disk scale height in units of the inner radius.","So, using a Rosseland mean opacity, averaged over $z$, eq.(20) will be rewritten as 	Finally, for a gas pressure dominated disk, we obtain from eq.(21), where ${\dot M_{17}}$, ${M_{34}}$, $x$, $y$ are, respectively, accretion rate in units of $10^{17}\, g\, s^{-1}$, mass of the central object in units of $10^{34}\, g$, the radial distance in units of the inner radius,the disk scale height in units of the inner radius."
" The inner radius ry is assumed to be 322,. 2, being the gravitational radius."," The inner radius $r_{1}$ is assumed to be $3\, R_{g}$, $R_{g}$ being the gravitational radius."
 According to Nineetal.(2007).. if constraints on a are required. one should make resource to observations of svstems subject to temporal behavior. such as cwarf nova outbursts (Warner2003:Cannizzo 2001).. outbursts of X-ray (rausients," 	According to \citet{kin07}, if constraints on $\alpha$ are required, one should make resource to observations of systems subject to temporal behavior, such as dwarf nova outbursts \citep{war03, can01}, outbursts of X-ray transients"
presumably associated with the first period of star formation is al a surprisingly high redshift. corresponding to an age of approximately 200 Myr.,"presumably associated with the first period of star formation is at a surprisingly high redshift, corresponding to an age of approximately 200 Myr."
 At the same time. the WAIAP collaboration reported a tight measurement of the age of the Universe. of 13.70.2 Gvr (Spergeletal(2003))). by combining their data with earlier CAIB ancl laree scale structure data. supporting earlier CAIB-derivecl age estimates (Ixnoxetal.(2001);Goldsteinal (2002))) (Note that all parameters we «quote here are extracted [rom this “best-fit” analvsis from WMADP).," At the same time, the WMAP collaboration reported a tight measurement of the age of the Universe, of $13.7 \pm 0.2$ Gyr \cite{spergel}) ), by combining their data with earlier CMB and large scale structure data, supporting earlier CMB-derived age estimates \cite{knox,boomer}) ) (Note that all parameters we quote here are extracted from this ""best-fit"" analysis from WMAP)."
 While the former two observations may force revisions in our thinking about the early Universe. the latter measurement. combined with constraints on the age of globular clusters can provide new inlormation on the formation of large scale structure. star formation. and (he formation history of the Milkv. Was.," While the former two observations may force revisions in our thinking about the early Universe, the latter measurement, combined with constraints on the age of globular clusters can provide new information on the formation of large scale structure, star formation, and the formation history of the Milky Way."
 In addition. one can put a new independent lower bound on the equation of state parameter. w=(p/p). for the dark energy that appears to dominate the Universe. (INrauss. (2003))).," In addition, one can put a new independent lower bound on the equation of state parameter, $w=(p/{\rho})$, for the dark energy that appears to dominate the Universe. \cite{krauss}) )."
 Conventional wisdom. supported by estimates of relative ages of halo vs disk clusters. suggest that halo elobular elusters formed during the earliest stages of the formation of our galaxy. before the primordial gas cloud dissipated energy ancl collapsed to form a disk.," Conventional wisdom, supported by estimates of relative ages of halo vs disk clusters, suggest that halo globular clusters formed during the earliest stages of the formation of our galaxy, before the primordial gas cloud dissipated energy and collapsed to form a disk."
 Thus. determination of the age of the oldest globular clusters in the halo lead to a robust lower limit on the age of the Universe (i.e. see KraussandChahbover (2003))).," Thus, determination of the age of the oldest globular clusters in the halo lead to a robust lower limit on the age of the Universe (i.e. see \cite{krausschab}) )."
 While elobular cluster ages have (hus presented a good lower bound on cosmic ages. (μον are less successful al providing an upper limit.," While globular cluster ages have thus presented a good lower bound on cosmic ages, they are less successful at providing an upper limit."
 This is simply because there has been no easy wav to directly determine what the maximum period between the Die Dang aud the formation of our own galaxy actually is., This is simply because there has been no easy way to directly determine what the maximum period between the Big Bang and the formation of our own galaxy actually is.
 Measurements of cosmic structure formation, Measurements of cosmic structure formation
achieved with a oservation of a reasonably «cep exposure for nearby galaxiesCD2;20 Mpc).,achieved with a observation of a reasonably deep exposure for nearby galaxies$D\lesssim 20$ Mpc).
 The residual contribution from fainter TAINBs aud LAINBs cau then be esuated from thei correlation with the star formation rate ai stellar mass anc subtractecL from the data with little uncertainty., The residual contribution from fainter HMXBs and LMXBs can then be estimated from their correlation with the star formation rate and stellar mass and subtracted from the data with little uncertainty.
 However. oue still needs to be careful wit1 Poisson fluctuations of sotrees just below the detection limit.," However, one still needs to be careful with Poisson fluctuations of sources just below the detection limit."
 Such flacuations lay siguificantlv affect the reliability of Χαν morphoogical analvsis oa galaxy., Such fluctuations may significantly affect the reliability of X-ray morphological analysis of a galaxy.
 Iu addition to the sutraction of relatively brigi Norav binaries. one also needs to accouit for a sjenificaut (even dominant) stellar coutributiou from catacvsnude variabes and coronally active stars. which are numerous. though iucdisdualV aut.," In addition to the subtraction of relatively bright X-ray binaries, one also needs to account for a significant (even dominant) stellar contribution from cataclysmic variables and coronally active stars, which are numerous, though individually faint."
 Very deep imaenmeg of a region toward the Galactic bulee (7). 1iis resolved out iore than of the background Cluission at energies of 6-7 keV. where the observed promiicut Fe 6.7-keV line was thought as the evidence for the presence of diffuse hot pasua at T—105 K. This hiel-cuerev backeround cussion is now s10W1l to be eutirely cousisteut with this collective stellar contrinition iu the Calactic bulee/ridee.," Very deep imaging of a region toward the Galactic bulge \cite{rev09} has resolved out more than of the background emission at energies of 6-7 keV, where the observed prominent Fe $6.7$ -keV line was thought as the evidence for the presence of diffuse hot plasma at $T \sim 10^8$ K. This high-energy background emission is now shown to be entirely consistent with this collective stellar contribution in the Galactic bulge/ridge."
 It showd be LOed. however. that the resolvec fraction is muuch snaller :vt lower energies (~50% at ZE keV). which niv be considered as an idication fcx the presence of cμπιIsc rot eas at much lower temperatures.," It should be noted, however, that the resolved fraction is much smaller at lower energies $\sim 50\%$ at $\lesssim 4$ keV), which may be considered as an indication for the presence of diffuse hot gas at much lower temperatures."
 The sellar CΜπΊο is unresolved for exnal galaxies. eve1i nearby ones.," The stellar contribution is unresolved for external galaxies, even nearby ones."
 Fortunately. the average X-ray spectru and specific Iuuniuositv (per stellar nass) of the coutribution have been calibrated. based on the OOservations of M32. which is too light to hold significant amount of diffuse hot eas). together with the cirect deection of stellar A-ray sources in the solar neigliborhood (8).," Fortunately, the average X-ray spectrum and specific luminosity (per stellar mass) of the contribution have been calibrated, based on the observations of M32, which is too light to hold significant amount of diffuse hot gas), together with the direct detection of stellar X-ray sources in the solar neighborhood \cite{rev08}."
". The coutribution cau be readily included iu a spectral analysis of the ""«lffuse N-ray emission o: a galaxy.", The contribution can be readily included in a spectral analysis of the “diffuse” X-ray emission of a galaxy.
 Iu an Πασπα analysis. oue mav subtract the COitribution scaled according to the stellar mass distribution (e.9.. traced by the near-IR K-baud iuteusitv of a galaxy).," In an imaging analysis, one may subtract the contribution scaled according to the stellar mass distribution (e.g., traced by the near-IR K-band intensity of a galaxy)."
 The properties of the elobal hot ooOas ou scales comparable to the size of the Galaxy remained largely 1uuxnown uutil recently., The properties of the global hot gas on scales comparable to the size of the Galaxy remained largely unknown until recently.
 BeforeChandra.. we did have various broad-baud N-ray emission surveys of the skv such as the one made by iu the 0.1-2.1. keV range. which is seusitive to the hot eas (9)..," Before, we did have various broad-band X-ray emission surveys of the sky such as the one made by in the 0.1-2.4 keV range, which is sensitive to the hot gas \cite{sno97}. ."
 But such a survey aloue caunot be, But such a survey alone cannot be
We have worked out predictions for the clustering properties of SCUBA-selected galaxies. in the framework of an astrophysically erouncecl model. relating the formation of QSOs and spheroics (ellipticals. SO galaxies ancl bulges of spirals).,"We have worked out predictions for the clustering properties of SCUBA-selected galaxies in the framework of an astrophysically grounded model, relating the formation of QSOs and spheroids (ellipticals, S0 galaxies and bulges of spirals)."
 “Phe theoretical angular correlation function. has been derived. for dillerent. bias functions. corresponding to ΠΠ values of the ratio MiaAM.ou between the mass of a spheroid locked in stars and the mass of its host halo.," The theoretical angular correlation function has been derived for different bias functions, corresponding to different values of the ratio $M_{\rm
halo}/M_{\rm sph}$ between the mass of a spheroid locked in stars and the mass of its host halo."
 SCUBA sources are predicted to be strongly clustered. with a clustering strength which increases with increasing mass (or equivalentlv with increasing luminosity). as a consequence of the fact that they are very massive and shining at substantial redshifts.," SCUBA sources are predicted to be strongly clustered, with a clustering strength which increases with increasing mass (or equivalently with increasing luminosity), as a consequence of the fact that they are very massive and shining at substantial redshifts."
 Since the clustering amplitude strongly depends on the quantity MivaMa future measurements of the angular correlation function w(A) will be able to discriminate amongst cillerent models of SCUBA ealaxics and in particular to determine the amount of barvonic mass actively partaking the process of star ormation.," Since the clustering amplitude strongly depends on the quantity $M_{\rm
halo}/M_{\rm sph}$, future measurements of the angular correlation function $w(\theta)$ will be able to discriminate amongst different models of SCUBA galaxies and in particular to determine the amount of baryonic mass actively partaking the process of star formation."
 Under the hypothesis of low- to. intermecdiate-niass wimeval spheroids to show up in the optical band as LBCs (as argued by Ciranato ct al., Under the hypothesis of low- to intermediate-mass primeval spheroids to show up in the optical band as LBGs (as argued by Granato et al.
 2000). we have then compared our predictions with the clustering measurements obtained w Ciavalisco ct al. (," 2000), we have then compared our predictions with the clustering measurements obtained by Giavalisco et al. ("
1998) for a wide sample of LBGs at 2c3.,1998) for a wide sample of LBGs at $z\simeq 3$.
 phe agreement is good for a mass ratio between the dark halo and the stellar component in the range LO100: veh values for this ratio secm to be favoured., The agreement is good for a mass ratio between the dark halo and the stellar component in the range 10–100; high values for this ratio seem to be favoured.
 Also. the predicted: amplitude of the angular correlation unction of SCUBA galaxies is consistent with the one determined by Dacddi et al. (," Also, the predicted amplitude of the angular correlation function of SCUBA galaxies is consistent with the one determined by Daddi et al. ("
"2000) for EROs with 2Av.35.3 and Av,19.2.",2000) for EROs with $R-K_s \geq 5.3$ and $K_s \leq 19.2$.
 This would support the observational evidence for a substantial fraction of SCUBA galaxies to be identified with EROs (Small et al., This would support the observational evidence for a substantial fraction of SCUBA galaxies to be identified with EROs (Smail et al.
 1999: Ivison et al., 1999; Ivison et al.
 2000)., 2000).
 We have also considered. the effect. of clustering on, We have also considered the effect of clustering on
was proved bv finding a solution for the particular case of stellar winds.,was proved by finding a solution for the particular case of stellar winds.
 In the following subsection { show that general criteria lor the existence/nonexistence of local solutions [ου arbitrary geometries can be established through the nozzle ΠΟΙΟmolion., In the following subsection I show that general criteria for the existence/nonexistence of local solutions for arbitrary geometries can be established through the nozzle function.
 A local solution in the vicinitv of the critical point exists if. upon integration. the solution maintains itself in Region IL [see eqs. (10))," A local solution in the vicinity of the critical point exists if, upon integration, the solution maintains itself in Region II [see eqs. \ref{equ_region_map}) )"
 and (12))]., and \ref{equ_region_sol}) )].
 This is equivalent to the condition that at the critical point where Ag is a variation of q in the vicinity of qi. and Aw is the corresponding variation of w determined upon the integration of the equation of motion.," This is equivalent to the condition that at the critical point where $\Delta q$ is a variation of $q$ in the vicinity of $q_c$, and $\Delta \omega$ is the corresponding variation of $\omega$ determined upon the integration of the equation of motion."
 Therefore. a local steady solution exists if 2 d3 From equation (24)). if the critical point conditions hold for a given q. then a local solution in (he vicinitv of that. point. exists providing For a given q. the variables à. ie’. and i can be determined through equations (.A15)). (A16)). and (A17)). respectively.," Therefore, a local steady solution exists if I define From equation \ref{equ_local2}) ), if the critical point conditions hold for a given $q$, then a local solution in the vicinity of that point exists providing For a given $q$, the variables $\omega$ , $\omega'$, and $\dot{m}$ can be determined through equations \ref{equ_critical18}) ), \ref{equ_critical19}) ), and \ref{equ_critical20}) ), respectively."
 Considering the definition of οί} leq. (πλ).," Considering the definition of $\beta(\omega)$ [eq. \ref{equ_beta}) )],"
 ?'(w) and Mw) are given by the followingequations:, $\beta'(\omega)$ and $\beta''(\omega)$ are given by the followingequations:
090515 does not have an identified host galaxy.,090515 does not have an identified host galaxy.
" However, GRB 0707244. does share many similarities with GRB 090515 so we cannot rule out the possibility that they originate from a similar progenitor."," However, GRB 070724A does share many similarities with GRB 090515 so we cannot rule out the possibility that they originate from a similar progenitor."
" Figure 4((a) shows the lightcurves for the observed R band optical afterglows associated with SGRBs (published values converted from magnitudes into flux density in Jy), GRB 090515 is the faintest observed and one of the earliest detections after the trigger time."," Figure \ref{optical_lcs}( (a) shows the lightcurves for the observed R band optical afterglows associated with SGRBs (published values converted from magnitudes into flux density in Jy), GRB 090515 is the faintest observed and one of the earliest detections after the trigger time."
 In Figure 4((b) we have divided the optical fluxes by the XRT flux at 1000 s after the trigger time., In Figure \ref{optical_lcs}( (b) we have divided the optical fluxes by the XRT flux at 1000 s after the trigger time.
" When we have considered the XRT flux at 1000 s, the optical afterglow of GRB 090515 is not unusually faint compared to other SGRBs."," When we have considered the XRT flux at 1000 s, the optical afterglow of GRB 090515 is not unusually faint compared to other SGRBs."
 We also show the optical light curve for GRB 080503 (ashortburstwithex-tendedemissionPerleyetal.20098) in Figure 4((c) in comparison to GRB 090515., We also show the optical light curve for GRB 080503 \citep[a short burst with extended emission][]{perley2009b} in Figure \ref{optical_lcs}( (c) in comparison to GRB 090515.
" As the fluence of GRB 090515 inthe 15 — 150 keV energy band was one of the lowest fluences observed for SGRBs, here we compare it to other low fluence GRBs."," As the fluence of GRB 090515 in the 15 – 150 keV energy band was one of the lowest fluences observed for SGRBs, here we compare it to other low fluence GRBs."
 GRB 050509B and GRB 050813 were short GRBs detected by the satellite that were similar to GRB 090515 during the prompt emission phase., GRB 050509B and GRB 050813 were short GRBs detected by the satellite that were similar to GRB 090515 during the prompt emission phase.
" However, the combined BAT and XRT light curves for GRBs 050509B and 050813, shown in Figure 5((b), do not show the same X-ray plateau extending to ~200 s after the burst."," However, the combined BAT and XRT light curves for GRBs 050509B and 050813, shown in Figure \ref{fig4}( (b), do not show the same X-ray plateau extending to $\sim$ 200 s after the burst."
 GRBs 050509B and 050813 have both been used to place constraints on the compact binary merger model of SGRBs (Gehrelsetal.2005;Hjorth2005b;Bloom2006;Ferreroetal. 2007)..," GRBs 050509B and 050813 have both been used to place constraints on the compact binary merger model of SGRBs \citep{gehrels2005, hjorth2005b, bloom2006, ferrero2007}."
 The observed upper limits for GRB 090515 at late times (after 400s) are consistent with the later emission observed for GRBs 050509B and 050813., The observed upper limits for GRB 090515 at late times (after 400s) are consistent with the later emission observed for GRBs 050509B and 050813.
 This suggests that the plateau and steep decay are an additional component in the light curve of GRB 090515., This suggests that the plateau and steep decay are an additional component in the light curve of GRB 090515.
" GRB 051105 is a SGRB with an identical fluence to GRB 090515, but its afterglow was undetectable by XRT in observations starting 68 s after the burst (Mineoetal.2005a)."," GRB 051105 is a SGRB with an identical fluence to GRB 090515, but its afterglow was undetectable by XRT in observations starting 68 s after the burst \citep{mineo2005b}."
. GRB 070209 had the lowest SGRB fluence and was also undetectable by XRT in observations starting 78 s after the burst (Satoetal.2007).., GRB 070209 had the lowest SGRB fluence and was also undetectable by XRT in observations starting 78 s after the burst \citep{sato2007a}.
" In Figure 5((c), the X-ray light curve of GRB 090515 is compared to the two lowest fluence LGRBs in theSwift sample which were detected by XRT."," In Figure \ref{fig4}( (c), the X-ray light curve of GRB 090515 is compared to the two lowest fluence LGRBs in the sample which were detected by XRT."
" These are GRB 080520A and GRB 0607174, they both have significantly higher fluence in the 15 — 150 keV band than GRB 090515 (due to having longer durations), but are a lot fainter in X-rays, again suggesting additional X-ray emission in GRB 090515."," These are GRB 080520A and GRB 060717A, they both have significantly higher fluence in the 15 – 150 keV band than GRB 090515 (due to having longer durations), but are a lot fainter in X-rays, again suggesting additional X-ray emission in GRB 090515."
 It is possible that these GRBs had plateau phases which end prior to the XRT observations., It is possible that these GRBs had plateau phases which end prior to the XRT observations.
" However, asSwift slewed promptly to these GRBs (observations typically starting within 100 S), a plateau phase would need to be significantly shorter than that observed for GRB 090515."," However, as slewed promptly to these GRBs (observations typically starting within 100 s), a plateau phase would need to be significantly shorter than that observed for GRB 090515."
" The main exception to this is GRB 0607174, which had XRT observations begining when GRB 090515 was in the steep decay phase."," The main exception to this is GRB 060717A, which had XRT observations begining when GRB 090515 was in the steep decay phase."
" The GRB with an X-ray light curve most similar to GRB 090515 is GRB 090607, which has a Too just above the short-long boundary."," The GRB with an X-ray light curve most similar to GRB 090515 is GRB 090607, which has a $T_{90}$ just above the short-long boundary."
 They are compared in Figure 5((d)., They are compared in Figure \ref{fig4}( (d).
 Both light curves show a distinctive steep decay at ~200s., Both light curves show a distinctive steep decay at $\sim$ 200s.
" However, the emission of GRB 090607 between 80 and 100 s is not a plateau as observed in GRB"," However, the emission of GRB 090607 between 80 and 100 s is not a plateau as observed in GRB"
at the coefficients of the weighted linear fits to the the radial trends of metallicity that are summarized in Table 4..,at the coefficients of the weighted linear fits to the the radial trends of metallicity that are summarized in Table \ref{tab:fits}.
 Following is a brief discussion of the results obtained from the individual abundance The interpretation of the R23-based abundances (top right-hand panel of Fig. 3)), Following is a brief discussion of the results obtained from the individual abundance The interpretation of the $_{23}$ -based abundances (top right-hand panel of Fig. \ref{fig:abund}) )
 requires some important considerations., requires some important considerations.
" All the inner disc rregions in NGC 4625 have {-aand 0.8, which, accordingtotheK DO2photoionisationmodels, "," All the inner disc regions in NGC 4625 have $>$ $-0.8$ , which, according to the KD02 photoionisation models, corresponds to the upper branch of $_{23}$."
"The result could be more ambiguous for the outer disc rregions, which are closer to the turnover region in the Ώρα mmetallicity relationship, even though virtually al lie in the upper-branch regime, according to the criterion, d — 1.1."," The result could be more ambiguous for the outer disc regions, which are closer to the turnover region in the $_{23}$ metallicity relationship, even though virtually all lie in the upper-branch regime, according to the criterion, $>$ $-1.1$ ."
Wereachthesameconclusion f 1i]))values(ranging. 1.land-0.7)., We reach the same conclusion from the ) values (ranging between $-1.1$ and $-0.7$ ).
"T'herefore, romthelog weusedtheupperbranchsolution f ortheinnerdisc, whi "," Therefore, we used the upper branch solution for the inner disc, whilst for the outer disc we used both the lower branch (light blue) and the upper branch (dark blue) calibrations of for comparison."
"Taking at face value the information obtained from the correspollistotátiupperbmowukbbR»led to favour the upper branch solution for the whole sample of rregions, leading, in particular, to"," Taking at face value the information obtained from the and line ratios we would be led to favour the upper branch solution for the whole sample of regions, leading, in particular, to"
The growth of large-scale structure. as revealed in the clustering of galaxies observed in large redshift surveys. has historically been one of our most important cosmological probes.,"The growth of large-scale structure, as revealed in the clustering of galaxies observed in large redshift surveys, has historically been one of our most important cosmological probes."
 This growth is driven by a competition between gravitational attraction and the expansion of space-time. allowing us to test our model of gravity and the expansion history of the Universe.," This growth is driven by a competition between gravitational attraction and the expansion of space-time, allowing us to test our model of gravity and the expansion history of the Universe."
 Despite the fact that galaxy light doesn't faithfully trace the mass. even on large scales. galaxies are expected to aet nearly as test particles within the cosmological matter flow.," Despite the fact that galaxy light doesn't faithfully trace the mass, even on large scales, galaxies are expected to act nearly as test particles within the cosmological matter flow."
 Thus the motions of galaxies carry an imprint of the rate of growth of large-scale structure and allows us to probe both dark energy and test General Relativity (e.g.Jain&val&White2008:McDonaldSeljak2008.forrecent studies).," Thus the motions of galaxies carry an imprint of the rate of growth of large-scale structure and allows us to probe both dark energy and test General Relativity \cite[e.g.][for recent studies]{jain08,Song08a,Song08b,PerWhi08,McDSel08}."
 This measurement of the growth of structure relies on redshift-space distortions seen in galaxy surveys (Kaiser1987)., This measurement of the growth of structure relies on redshift-space distortions seen in galaxy surveys \citep{Kai87}.
.. Even though we expect the clustering of galaxies in real space to have no preferred direction. galaxy maps produced by estimating distances from redshifts obtained in spectroscopic surveys reveal an anisotropic galaxy distribution.," Even though we expect the clustering of galaxies in real space to have no preferred direction, galaxy maps produced by estimating distances from redshifts obtained in spectroscopic surveys reveal an anisotropic galaxy distribution."
 The anisotropies arise because galaxy recession velocities. from which distances are inferred. include components from both the Hubble flow and peculiar velocities driven by the clustering of matter (seeHamilton1998.fora review).," The anisotropies arise because galaxy recession velocities, from which distances are inferred, include components from both the Hubble flow and peculiar velocities driven by the clustering of matter \citep[see][for a review]{HamiltonReview}."
. Measurements of the anisotropies allow constraints to be placed on the rate of growth of clustering., Measurements of the anisotropies allow constraints to be placed on the rate of growth of clustering.
 Ever larger surveys have provided ever tighter constraints., Ever larger surveys have provided ever tighter constraints.
 Analyses using the 2-degree Field Galaxy Redshift Survey (2dFGRS:Collessetal.2003). have measured. redshift-space distortions in both the correlation function (PeacockHawkinsetal.2003) and power spectrum 2004).," Analyses using the 2-degree Field Galaxy Redshift Survey \citep[2dFGRS;][]{colless03} have measured redshift-space distortions in both the correlation function \citep{peacock01,hawkins03} and power spectrum \citep{percival04}."
 Using the Sloan Digital Sky Survey (SDSS:Yorketal. 2000). redshift-space distortions have also been measured in the correlation function (Zehavietal.2005:Okumura.al.2008:Cabré&Gaztanaga 2008). and using an Eigenmode decomposition to separate real and redshift-space effects2006).," Using the Sloan Digital Sky Survey \citep[SDSS;][]{york00}, redshift-space distortions have also been measured in the correlation function \citep{Zeh05,Oku08,cabre08}, and using an Eigenmode decomposition to separate real and redshift-space effects."
. These studies were recently extended to z5| (Guzzoetal.2007) using the VIMOS-VLT Deep Survey (VVDS:LeFevreetal.2005:Garilli 2008).," These studies were recently extended to $z\simeq1$ \citep{guzzo08} using the VIMOS-VLT Deep Survey \citep[VVDS;][]{lefevre05,garilli08}."
. In addition to measuring clustering growth at z=0.8. this work has emphasized the importance of using large-scale peculiar velocities for constraining models of cosmic acceleration.," In addition to measuring clustering growth at $z=0.8$, this work has emphasized the importance of using large-scale peculiar velocities for constraining models of cosmic acceleration."
 Current constraints on the growth rate are at the several tens of percent level (e.g.Nesseris&Perivolaropoulos2008:Song&Percival 2008). but observational progress is rapid.," Current constraints on the growth rate are at the several tens of percent level \citep[e.g.][]{NesPer08,Song08b}, but observational progress is rapid."
 In the next section we shall outline the formalism for forecasting constraints on cosmological quantities from measurements of redshift space distortions. and compare it with previous forecasts.," In the next section we shall outline the formalism for forecasting constraints on cosmological quantities from measurements of redshift space distortions, and compare it with previous forecasts."
 We begin with the simplest model and then investigate various retinements., We begin with the simplest model and then investigate various refinements.
 We finish in refsec:conclusions with a discussion of future directions., We finish in \\ref{sec:conclusions} with a discussion of future directions.
 For illustration we shall assume a fiducial ACDM cosmology with On=0.25. h=0.72. n=0.97 and oy=0.8 (Gn good agreement with a variety of observations) when computing specific predictions for future surveys.," For illustration we shall assume a fiducial $\Lambda$ CDM cosmology with $\Omega_{\rm m}=0.25$, $h=0.72$, $n=0.97$ and $\sigma_8=0.8$ (in good agreement with a variety of observations) when computing specific predictions for future surveys."
 The Fisher matrix provides a method for determining the sensitivity of a particular measurement to a set of parameters and has been extensively used in cosmological forecasting and optimization., The Fisher matrix provides a method for determining the sensitivity of a particular measurement to a set of parameters and has been extensively used in cosmological forecasting and optimization.
 Here we adapt this methodology to our particular problem., Here we adapt this methodology to our particular problem.
 Under the assumption that the density field has Gaussian statistics and uncorrelated Fourier modes. the Fisher matrix for a set of parameters 1p;] is (e.g.Tegmarketal.1998) ," Under the assumption that the density field has Gaussian statistics and uncorrelated Fourier modes, the Fisher matrix for a set of parameters $\{p_i\}$ is \citep[e.g.][]{Teg98}
 "
arising from the presence of the black hole). gravitational radiation reaction acceleration. and the smoothing kernel respectively.,"arising from the presence of the black hole), gravitational radiation reaction acceleration, and the smoothing kernel respectively."
 For the kernel we use the spline form of Monaghan Lattanzio (1985)., For the kernel we use the spline form of Monaghan Lattanzio (1985).
 The viscous term is eiven by where and f; is the form-function for particle defined by The factoryc10. tin the denominator prevents numerical divergences., The viscous term is given by where and $f_{i}$ is the form-function for particle defined by The factor $\eta'\simeq 10^{-4}$ in the denominator prevents numerical divergences.
 The sound speed at the location of particle is denoted by ¢;. and o and 3 are constants of order unity.," The sound speed at the location of particle is denoted by $c_{i}$ , and $\alpha$ and $\beta$ are constants of order unity."
 The divergence and curl of the velocity Ποια are evaluated. through and This form of the viscosity vanishes in regions of strong vorticity. when VodiVoor. but remains in elfect if compression dominates in the llow (VoVOS d).," The divergence and curl of the velocity field are evaluated through and This form of the viscosity vanishes in regions of strong vorticity, when $\nabla \times \vec{v} \gg \nabla \cdot \vec{v}$, but remains in effect if compression dominates in the flow $\nabla \cdot \vec{v} \gg
\nabla \times \vec{v}$ )."
 This allows us to minimize the effects of artificial viscosity on the evolution of disk.like structures in the simulations. when they appear.," This allows us to minimize the effects of artificial viscosity on the evolution of disk–like structures in the simulations, when they appear."
 In this study. unlike before. we take the gravitational acceleration. of a volume of Εις to be proportional to its total energy. density. Le. we reinterpret p in all the above equations (but not in the sell-gravity term implicit in ;) as the energy density divided by c7. and we add any changes in the internal energy. (eq. ," In this study, unlike before, we take the gravitational acceleration of a volume of fluid to be proportional to its total energy density, i.e., we reinterpret $\rho$ in all the above equations (but not in the self-gravity term implicit in $\Phi_i$ ) as the energy density divided by $c^2$, and we add any changes in the internal energy (eq. ["
2]) to pc.,2]) to $\rho c^2$.
 To model quark matter we use the simplest. MIT. equation of state (c.o.s.).," To model quark matter we use the simplest MIT equation of state (e.o.s.),"
 where the pressure is given by P=F(pρι)3 Lor pzpo. and is zero otherwise.," where the pressure is given by $P=c^{2}(\rho-\rho_{0})/3$ for $\rho >\rho_{0}$, and is zero otherwise."
 Note that for pXpo the viscous stress vanishes (eq. , Note that for $\rho\le\rho_0$ the viscous stress vanishes (eq. [
3]). and when the radiation reaction is turned olf as well the equation of motion (1) is that of dust.,"3]), and when the radiation reaction is turned off as well the equation of motion (1) is that of dust."
 In compact binaries. the orbital decay isdriven primarily by the emission of gravitational waves.," In compact binaries, the orbital decay is driven primarily by the emission of gravitational waves."
 To take this elect into account. we include the back reaction on the system. computed in the quadrupole approximation [or point masses (see e.g. Landau Lifshitz 1975). so that the rates ofenergy and angular momentunm [oss are given respectively by," To take this effect into account, we include the back reaction on the system, computed in the quadrupole approximation for point masses (see e.g. Landau Lifshitz 1975), so that the rates ofenergy and angular momentum loss are given respectively by"
constant and dominated by (he radiation pressure.,constant and dominated by the radiation pressure.
" Under (his assumption each zone of the presupernova model is heated up to a temperature Toyo, given bv: where a is the Stelan-Doltzmann constant. Ej is the explosion energy. Tapyoek and 2 are the temperature behind (he shock and its location."," Under this assumption each zone of the presupernova model is heated up to a temperature $T_{\rm shock}$ given by: where $a$ is the Stefan-Boltzmann constant, $E_{\rm expl}$ is the explosion energy, $T_{\rm shock}$ and $R$ are the temperature behind the shock and its location."
 The shock density can be easily derived by imposing the shock to be mildly strong. i.e.. where /=4.," The shock density can be easily derived by imposing the shock to be mildly strong, i.e., where $f=4$."
 By the way let us underline that the final vields would not significantly change even assuming a strong shock (/= 7)., By the way let us underline that the final yields would not significantly change even assuming a strong shock $f=7$ ).
 The temporal variation of the temperature and density in each mass laver is obtained by assuming (the matter to expand adiabatically (Tx pt) ab the escape velocity (6=V26 MR) and (he density to decline following an exponential low. i.e.: where In these computations (unless explicitly stated) we assume always a final explosion energy equal to 1.2x10°! erg (1.2 foe) and an initial collapse of all the mass zones outside the iron core over a time of 0.5 s (Thielemann.Nomoto&Hashimoto1996).," The temporal variation of the temperature and density in each mass layer is obtained by assuming the matter to expand adiabatically $T\propto \rho^{\gamma-1}$ ) at the escape velocity $v_{\rm}=\sqrt{2GM/R}$ ) and the density to decline following an exponential low, i.e.: where In these computations (unless explicitly stated) we assume always a final explosion energy equal to $\rm 1.2\times10^{51}$ erg (1.2 foe) and an initial collapse of all the mass zones outside the iron core over a time of 0.5 s \citep{tnh96}."
. The chemical evolution has been followed by solving the same nuclear network adopted into the prestpernova. evolutions together to the temporal variation of temperature aud density., The chemical evolution has been followed by solving the same nuclear network adopted into the presupernova evolutions together to the temporal variation of temperature and density.
" The elemental vields coming from set Il have been already. published by (2002).. while the ones obtained [ον the set L are reported in Tables 2-7: lor each nass we provide. as we usuallv do. the elemental vields in solar masses for different possible choices of the ""Ni ejected (shown in the first row). after all unstable isotopes have been decaved into their stable form."," The elemental yields coming from set H have been already published by \cite{lc02pasa}, while the ones obtained for the set L are reported in Tables 2-7: for each mass we provide, as we usually do, the elemental yields in solar masses for different possible choices of the $\rm ^{56}Ni$ ejected (shown in the first row), after all unstable isotopes have been decayed into their stable form."
 In addition to the full set of explosions computed within the frame of the radiation dominated shock approximation. we have also computed one explosion with an hvdro code.," In addition to the full set of explosions computed within the frame of the radiation dominated shock approximation, we have also computed one explosion with an hydro code."
 In particular we computed the explosion of the 35M... (set ID)., In particular we computed the explosion of the $\rm 35 M_\odot$ (set H).
 The hydro code solves the full hvdrodynanmical equations (ncluded the gravitational field) in spherical sviumetry. ancl in lagrangean form together (o (he same nuclear network adopted into the presupernova evolutions., The hydro code solves the full hydrodynamical equations (included the gravitational field) in spherical symmetry and in lagrangean form together to the same nuclear network adopted into the presupernova evolutions.
 In this case the explosion has been induced by imposing the innermost edge of, In this case the explosion has been induced by imposing the innermost edge of
"and for ESO269-066, which have a more metal-rich extension than CenA-dE1.","and for ESO269-066, which have a more metal-rich extension than CenA-dE1."
" Given the number of stars in the low completeness region, we estimate that there could additionally be at least ~10 undetected AGB stars for SGC1319.1-4216 and ~40 for ESO269-066."," Given the number of stars in the low completeness region, we estimate that there could additionally be at least $\sim10$ undetected AGB stars for SGC1319.1-4216 and $\sim40$ for ESO269-066."
" There are in total 13 AGB candidates for CenA-dE1, 41 for SGC1319.1-4216 and 176 for ESO269-066."," There are in total 13 AGB candidates for CenA-dE1, 41 for SGC1319.1-4216 and 176 for ESO269-066."
" For CenA-dE1, we can see that the four brightest candidates are detached from the rest of the red dots, so we perform a visual inspection of the images and conclude that they are barely resolved background galaxies."," For CenA-dE1, we can see that the four brightest candidates are detached from the rest of the red dots, so we perform a visual inspection of the images and conclude that they are barely resolved background galaxies."
" In general, the above reported numbers are lower limits to the total number of luminous AGB stars in the target galaxies, given the NIR incompleteness limits."," In general, the above reported numbers are lower limits to the total number of luminous AGB stars in the target galaxies, given the NIR incompleteness limits."
" The lower panels of Fig. 7,,"," The lower panels of Fig. \ref{cmdcomb1},"
 8 and 9 show the composite Vo—Ko versus Κο CMDs for the three studied galaxies., \ref{cmdcomb2} and \ref{cmdcomb3} show the composite $V_0-K_0$ versus $K_0$ CMDs for the three studied galaxies.
 We plot the stars found in the combined lists and mark in red the AGB candidates., We plot the stars found in the combined lists and mark in red the AGB candidates.
" To show the expected TRGB position and to stress the metallicity spread of these galaxies, we also plot the same isochrones as in Fig."," To show the expected TRGB position and to stress the metallicity spread of these galaxies, we also plot the same isochrones as in Fig."
 1 and 4.., \ref{cmdopt} and \ref{cmdnir}.
" When looking at the combined CMDs, we notice that there are many objects that are found in the region above the TRGB, but that are not identified as candidate AGB stars."," When looking at the combined CMDs, we notice that there are many objects that are found in the region above the TRGB, but that are not identified as candidate AGB stars."
" These sources are mostly foreground contaminants, which are distributed all over the CMDs for these magnitude combinations, but some of them might be unresolved background galaxies."," These sources are mostly foreground contaminants, which are distributed all over the CMDs for these magnitude combinations, but some of them might be unresolved background galaxies."
" In particular, ? study deep ISAAC observations to derive the number counts of unresolved high-redshift galaxies."," In particular, \citet{saracco01} study deep ISAAC observations to derive the number counts of unresolved high-redshift galaxies."
 From their Fig., From their Fig.
" 1 we estimate a number of galaxies of up to ~300 for our field of view, for magnitudes 18«Ko22 and distributed on the CMD as shown in their Fig."," 1 we estimate a number of galaxies of up to $\sim300$ for our field of view, for magnitudes $18<K_0<22$ and distributed on the CMD as shown in their Fig."
 3., 3.
" Due to the combination of high resolution HST data in addition to excellent seeing ISAAC images, as well as to the quality cuts applied to our PSF photometry, most of these galaxies will be rejected from the final combined catalogs, but there is still the possibility of having a few high-redshift and compact contaminants among our AGB candidates, although this cannot be clarified with the current data."," Due to the combination of high resolution HST data in addition to excellent seeing ISAAC images, as well as to the quality cuts applied to our PSF photometry, most of these galaxies will be rejected from the final combined catalogs, but there is still the possibility of having a few high-redshift and compact contaminants among our AGB candidates, although this cannot be clarified with the current data."
" The objects found at colors Vo—Koz8 are indeed barely resolved background galaxies, as confirmed by visual inspection."," The objects found at colors $V_0-K_0\gtrsim8$ are indeed barely resolved background galaxies, as confirmed by visual inspection."
" From the combined optical and NIR CMD analysis of the previous Section, we are left with 9 luminous AGB candidates for CenA-dE1, 41 for SGC1319.1-4216 and 176 for ESO269-066."," From the combined optical and NIR CMD analysis of the previous Section, we are left with 9 luminous AGB candidates for CenA-dE1, 41 for SGC1319.1-4216 and 176 for ESO269-066."
 We report the coordinates and magnitudes of these candidate AGB stars in Tab., We report the coordinates and magnitudes of these candidate AGB stars in Tab.
 3 (the complete table is available electronically)., \ref{agb_list} (the complete table is available electronically).
" These stars belong to the IAP of the target dwarfs, while a few old and metal-rich AGB stars could be also present for SGC1319.1-4216 and ESO269-066, given the red extension of their RGBs."," These stars belong to the IAP of the target dwarfs, while a few old and metal-rich AGB stars could be also present for SGC1319.1-4216 and ESO269-066, given the red extension of their RGBs."
" We stress that the old and metal- stars in our sample are a very small percentage of the whole luminous AGB population, given the low fraction of stars with [Fe/H]x—0.7."," We stress that the old and metal-rich stars in our sample are a very small percentage of the whole luminous AGB population, given the low fraction of stars with $\lesssim-0.7$."
" Therefore, in the subsequent analysis, we will neglect their contribution, thus considering all our AGB candidates to belong to the IAP."," Therefore, in the subsequent analysis, we will neglect their contribution, thus considering all our AGB candidates to belong to the IAP."
 We now want to look at their properties in more detail., We now want to look at their properties in more detail.
profile distortion relative to the mean spectrum at phases 0.193 and 0.378.,profile distortion relative to the mean spectrum at phases 0.193 and 0.378.
 The variability of is also clearly seen for the phase 0.463., The variability of is also clearly seen for the phase 0.463.
 In addition. the lines of and also marginally deviate from the corresponding average profiles at phases 0.827. 0.920 and 0.741. 0.827 respectively.," In addition, the lines of and also marginally deviate from the corresponding average profiles at phases 0.827, 0.920 and 0.741, 0.827 respectively."
 The observed spectral variability occurs with the period of the orbital motion., The observed spectral variability occurs with the period of the orbital motion.
 For all four chemical elements with variable lines we found a distinct change of the radial velocity and. especially. equivalent width with the orbital period.," For all four chemical elements with variable lines we found a distinct change of the radial velocity and, especially, equivalent width with the orbital period."
 Since our observations cover only two rotation cycles. we cannot determine variability period with a high precision.," Since our observations cover only two rotation cycles, we cannot determine variability period with a high precision."
 However. we observed that the integral properties of variable lines and their shapes repeat closely after one orbital period.," However, we observed that the integral properties of variable lines and their shapes repeat closely after one orbital period."
 This strongly suggests that the orbital motion and the stellar rotation are synchronized., This strongly suggests that the orbital motion and the stellar rotation are synchronized.
 To study surface distribution of chemical elements in 66 Eri A. we applied the Doppler imaging (DI) method.," To study surface distribution of chemical elements in 66 Eri A, we applied the Doppler imaging (DI) method."
 We used INVERSIO code (?) to determine abundance maps. ignoring magnetic field.," We used INVERS10 code \citep{Piskunov:2002} to determine abundance maps, ignoring magnetic field."
 This analysis was applied. to several non-blended spectral lines of Ti and Y that exhibit a significant variability and to all available spectral lines of Sr and Ba., This analysis was applied to several non-blended spectral lines of Ti and Y that exhibit a significant variability and to all available spectral lines of Sr and Ba.
 In total. we used two spectral lines ofSri. two ofBam. six lines ofΥΠ. and nine spectral lines ofTit.," In total, we used two spectral lines of, two of, six lines of, and nine spectral lines of."
 These lines are marked with bold font in Table 5.., These lines are marked with bold font in Table \ref{tab:varprofs}.
 Multi-line DI is applied here to study spots in an HgMn star for the first time., Multi-line DI is applied here to study spots in an HgMn star for the first time.
 This allowed us to reconstruct the surface maps with a higher precision than what was usually achieved using a single spectral line., This allowed us to reconstruct the surface maps with a higher precision than what was usually achieved using a single spectral line.
 Doppler inversions were performed using the inclination angle of75°.. as determined earlier (Sect. 6)).," Doppler inversions were performed using the inclination angle of, as determined earlier (Sect. \ref{fp}) )."
 The initial abundances of Ti. Sr. Y. and Ba were taken from ?..," The initial abundances of Ti, Sr, Y, and Ba were taken from \citet{Yuschenko:1999}."
 Spectra were caleulated employing the revised model atmosphere of 66 Eri A with parameters z11100 Kandlogg =4.25.," Spectra were calculated employing the revised model atmosphere of 66 Eri A with parameters $\,=11100$ K and $\log g=4.25$."
 The rotational velocity was adjusted to give a better fit to the observed line profiles. yielding the final value of sini=17.540.2 kms!.," The rotational velocity was adjusted to give a better fit to the observed line profiles, yielding the final value of $\,=17.5\pm0.2$ ."
. The reconstructed surface maps are shown in Fig. 7.., The reconstructed surface maps are shown in Fig. \ref{DImaps}.
 Online Figs. 8--10, Online Figs. \ref{DI_fit1}-
 illustrate the comparison of observed and model line profiles., \ref{DI_fit3} illustrate the comparison of observed and model line profiles.
 First of all. we can see from these maps that there is à general asymmetry. of chemical composition. for. two hemispheres of the star.," First of all, we can see from these maps that there is a general asymmetry of chemical composition for two hemispheres of the star."
 For all four studied chemical elements we find a larger abundance at rotational phases from 0.5 to 0.1 and a smaller abundance for phases 0.1—0.5., For all four studied chemical elements we find a larger abundance at rotational phases from 0.5 to 0.1 and a smaller abundance for phases 0.1–0.5.
 Secondly. there is a different spot structure for the hemisphere with element overabundances.," Secondly, there is a different spot structure for the hemisphere with element overabundances."
 The spots of Ba and other chemical elements except Ti extend from —30° tto un latitude. showing the highest concentrations at the phase 0.65.," The spots of Ba and other chemical elements except Ti extend from $-30$ to in latitude, showing the highest concentrations at the phase 0.65."
 For Y and Sr we also find the secondary spot at the phases 0.95-1.05., For Y and Sr we also find the secondary spot at the phases 0.95–1.05.
 The spots of Sr and Ti are more extended azimuthally. while the spots of Ba and Y are stretched meridionally.," The spots of Sr and Ti are more extended azimuthally, while the spots of Ba and Y are stretched meridionally."
 Sr is also the only element of the four that shows a relative overabundance at thepole., Sr is also the only element of the four that shows a relative overabundance at thepole.
 Finally. Ti shows the spot," Finally, Ti shows the spot"
han the main sequence turn-oll.,than the main sequence turn-off.
 They are thought to oe produced by the merger. of two normal cluster stars. either in a primordial binary system. or through direct stellar collisions. or both.," They are thought to be produced by the merger of two normal cluster stars, either in a primordial binary system, or through direct stellar collisions, or both."
 All Galactic elobular clusters that iive been surveved contain some blue stragelers. though he fraction of blue stragelers varies greatly. even. between similar clusters.," All Galactic globular clusters that have been surveyed contain some blue stragglers, though the fraction of blue stragglers varies greatly, even between similar clusters."
 Some Galactic open clusters also contain due stragelers., Some Galactic open clusters also contain blue stragglers.
 Blue stragelers are found in open clusters of all ages CXhumacda&Lapasset1995)., Blue stragglers are found in open clusters of all ages \cite{Ahum95}.
. In the Magellanic Clouds. blue strageler stars have been found in old (NGC191 (Sharaetal.1998).. Ναιού NCGC2257 (Johnsonοἱal. 9093)) and voung (NGC330 (Ixellerctal. 2000))) clusters.," In the Magellanic Clouds, blue straggler stars have been found in old (NGC121 \cite{Shar98}, NGC1466 NGC2257 \cite{John99}) ) and young (NGC330 \cite{Kell00}) ) clusters."
 Je stars are non-supergiant (Luminosity class V to LL) D tvpe stars that show or once have shown Balmer emission (Jascheketal.1981)., Be stars are non-supergiant (luminosity class V to III) B type stars that show or once have shown Balmer emission \cite{Jasc81}.
.. Lt is widely accepted: that the Be »henomenon is associated with rapid rotation of the stellar whotosphere. and the presence of a circumstellar disk that eives rise to the line emission.," It is widely accepted that the Be phenomenon is associated with rapid rotation of the stellar photosphere, and the presence of a circumstellar disk that gives rise to the line emission."
 Lt has also been observed hat Be stars are receler in V-L than normal B stars (Cirebel 1999).. and tha those with the strongest llo emission are also the recelest c.g. (Dachsetal.LOSS).," It has also been observed that Be stars are redder in V-I than normal B stars \cite{Greb97,Kell99}, and that those with the strongest $\alpha$ emission are also the reddest e.g. \cite{Dach88}."
. LOSS), 1988).
 The reason for this reddening is not entirely clear. but it seems likely that continuum emission from the clisk plays a Large part.," The reason for this reddening is not entirely clear, but it seems likely that continuum emission from the disk plays a large part."
 Phere is also possibly some effect. [rom a change in spectral energy. distribution due to rotational distortion of the stellar atmosphere., There is also possibly some effect from a change in spectral energy distribution due to rotational distortion of the stellar atmosphere.
 Weller et shorteitelcllOO find that the 3e star fraction peaks at the main sequence turn-olf. which suggests that the 2 star phenomenon occurs at à specific evolutionary stage.," Keller et \\shortcite{Kell00} find that the Be star fraction peaks at the main sequence turn-off, which suggests that the Be star phenomenon occurs at a specific evolutionary stage."
 There are however dillerences in Be star fraction amongst clusters of the same age. anc some evidence that metallicity also allects the Be star fraction (Maecderetal.1999).," There are however differences in Be star fraction amongst clusters of the same age, and some evidence that metallicity also affects the Be star fraction \cite{Maed99}."
.. The two young clusters discussed in this paper are the LAIC clusters. NGC 1505 and NGC 1818.," The two young clusters discussed in this paper are the LMC clusters, NGC 1805 and NGC 1818."
 Both clusters are located in the north west part of the LMC. ~3.2 kpe from the centre. in fairly low density regions.," Both clusters are located in the north west part of the LMC, $\sim 3.2$ kpc from the centre, in fairly low density regions."
 Previous measurements of the cluster parameters are summarized in ‘Table r, Previous measurements of the cluster parameters are summarized in Table \ref{tab:clusprops}.
ior to this work. no colour-magnituce cdiagran (CAID). ground based. or other. existed. lor NGC 1505.," Prior to this work, no colour-magnitude diagram (CMD), ground based or other, existed for NGC 1805."
 NGC ISIS has been relatively well studied., NGC 1818 has been relatively well studied.
 There have been several attempts to measure the abundances of stars in NGCISLS., There have been several attempts to measure the abundances of stars in NGC1818.
 High resolution spectroscopy of LMC cluster and field stars (Ixornοἱal.2000:Jüttner1993:etal.1993). has found similar abundances for the clusters and the Field.," High resolution spectroscopy of LMC cluster and field stars \cite{Korn00,Jutt93a,Jutt93b} has found similar abundances for the clusters and the field."
 Lt is likely therefore that NGCISIS and Νις1505 have metallicities of Fe/1]z-0.4 (the canonical value for the LMC)., It is likely therefore that NGC1818 and NGC1805 have metallicities of $\approx$ -0.4 (the canonical value for the LMC).
 However. we note that no abundance measurements exist. for NOGCT1805. and that there are only two stars with reliably measured. abundances in NGCISIS (stars DI and D12 in Worn et 22000 and DI2 in Jütttner et 11993).," However, we note that no abundance measurements exist for NGC1805, and that there are only two stars with reliably measured abundances in NGC1818 (stars D1 and D12 in Korn et 2000 and D12 in Jütttner et 1993)."
 Previous LIST observations of ας1515 have been used to derive a mass function (Hunteretal.LOOT) investigate the binary [raction and mass segregation (Elsonetal.1998).. and search for Be stars ancl blue stragelers (elleret. 2000).," Previous HST observations of NGC1818 have been used to derive a mass function \cite{Hunt97}
 investigate the binary fraction and mass segregation \cite{Elso98}, and search for Be stars and blue stragglers \cite{Kell00}."
. The new observations in this paper are part of the laree LIST project GO7T307. details of whichcan be found in Beaulicu ct shortciteDBeautlü.," The new observations in this paper are part of the large HST project GO7307, details of whichcan be found in Beaulieu et \\shortcite{Beau00}."
. The format of this paper is as follows: Section 2 describes the data and. reductions. Section 3/— presents the results and these are compared. with simulations in Section 4..," The format of this paper is as follows: Section \ref{sec:data}
 describes the data and reductions, Section \ref{sec:res} presents the results and these are compared with simulations in Section \ref{sec:sim}."
 For both clusters we obtained LIST. WEPC2 F555W (zV) and FSIAW (zl) and NICAIOS Camera 2 FIGOW (5511) observations., For both clusters we obtained HST WFPC2 F555W $\approx$ V) and F814W $\approx$ I) and NICMOS Camera 2 F160W $\approx$ H) observations.
 Our original intention was to use the larger ield of view NICAIOS Camera 3. but unfortunately this was out of focus during NICMOS lifetime.," Our original intention was to use the larger field of view NICMOS Camera 3, but unfortunately this was out of focus during NICMOS' lifetime."
 Phe images discussed were were centred on the clusters. and the PC anc NIC2 contain most of the cluster cores (diameters. zz20 arcsec)," The images discussed here were centred on the clusters, and the PC and NIC2 contain most of the cluster cores (diameters $\ltsim
20$ arcsec)."
 We obtained both short exposures to avoid. saturating the xiehtest stars. and long exposures to provide good signal- well below the main-sequence turnolls.," We obtained both short exposures to avoid saturating the brightest stars, and long exposures to provide good signal-to-noise well below the main-sequence turnoffs."
 Full details of the image set are given in Table 2.., Full details of the image set are given in Table \ref{tab:imdetails}.
 Images of the cluster cores taken with both the PC and C2 are shown in Figures 1. and 2.., Images of the cluster cores taken with both the PC and NIC2 are shown in Figures \ref{fig:n1818pics} and \ref{fig:n1805pics}. .
 The individual exposures were combined. using the LAL task erre]. which sums the images anc rejects cosmicravys.," The individual exposures were combined using the IRAF task crrej, which sums the images and rejects cosmicrays."
 After combining we checked the magnitudes of bright stars, After combining we checked the magnitudes of bright stars
We denote torsion by Q. and total angular momentum by $...,We denote torsion by $Q^{\mu}_{.\ \alpha\beta}$ and total angular momentum by $S^{\mu}_{.\ \alpha\beta}$.
" At the weak interaction scale Rj,=OUO07'em) torsion is dominated by fermion spin densities (2).. while at the largest scale R=co torsion could be dominated only by the angular momentum of the whole Universe (galaxies. groups. clusters. ...) (???).."," At the weak interaction scale $R_{min}={\cal O}(10^{-16}cm)$ torsion is dominated by fermion spin densities \citep{Palle4}, while at the largest scale $R=\infty$ torsion could be dominated only by the angular momentum of the whole Universe (galaxies, groups, clusters, ...) \citep{Ray,Obukhov,Palle4}."
 The contribution of the torsion at present (RyΟἱ107 em) is much smaller than the mass density if the Hubble constant is small or could be much larger if the Hubble constant is large (2).., The contribution of the torsion at present $R_{0}={\cal O}(10^{28}cm)$ ) is much smaller than the mass density if the Hubble constant is small or could be much larger if the Hubble constant is large \citep{Palle8}.
 This is à consequence of the strong constraints from the age of the Universe. inevitable negative contribution to the integrated Sachs-Wolfe effect and the observed large peculiar velocities of clusters at large scales.," This is a consequence of the strong constraints from the age of the Universe, inevitable negative contribution to the integrated Sachs-Wolfe effect and the observed large peculiar velocities of clusters at large scales."
 The second scenario with large Hubble constant and large torsion at present is more probable from the theoretical and observational points of view (?).., The second scenario with large Hubble constant and large torsion at present is more probable from the theoretical and observational points of view \citep{Palle8}.
 The contribution of the torsion terms to the effective energy-momentum tensor is always negative with respect to the mass density., The contribution of the torsion terms to the effective energy-momentum tensor is always negative with respect to the mass density.
 The primordial mass density contrast is evolved from quantum fluctuations of the spin to the value at the photon decoupling defined by parameters of metric beyond that of Robertson-Walker (222).," The primordial mass density contrast is evolved from quantum fluctuations of the spin to the value at the photon decoupling defined by parameters of metric beyond that of Robertson-Walker \citep{Palle5a,Palle5b,Palle5c}."
 The question posed is whether it is possible to generate a vorticity of the Universe and to fix its chirality?, The question posed is whether it is possible to generate a vorticity of the Universe and to fix its chirality?
 The answer is positive. provided the local and global theories of spacetime are BY and EC theories.," The answer is positive, provided the local and global theories of spacetime are BY and EC theories."
 Within this framework the evolution scenario is the following: (1) Assuming CP violation in lepton sector. a dynamics of heavy Majorana neutrinos produces imbalance between leptons and antileptons (?) before their decoupling from primordial plasma.," Within this framework the evolution scenario is the following: (1) Assuming CP violation in lepton sector, a dynamics of heavy Majorana neutrinos produces imbalance between leptons and antileptons \citep{Sakharov}
 before their decoupling from primordial plasma."
 An example of leptogenesis generated with a Higgs mechanism and with heavy leptons can be find in the literature (?).. but heavy leptons are then cosmologically unstable.," An example of leptogenesis generated with a Higgs mechanism and with heavy leptons can be find in the literature \citep{Luty}, but heavy leptons are then cosmologically unstable."
 The masses of heavy Majorana neutrinos in the BY theory are in the range from O(TeV) to OC10TeV). thus leptogenesis happens arround Τ>TOCIO?eV). (," The masses of heavy Majorana neutrinos in the BY theory are in the range from ${\cal O}(TeV)$ to ${\cal O}(10^{3}TeV)$, thus leptogenesis happens arround $T > {\cal O}(10^{3}TeV)$. ("
2) Before light Majorana neutrino decoupling (Ty...=few MeV) the imbalance in the number of baryons and antibaryons appears as a consequence of the surplus of leptons against antileptons and conserved B-L (???).. (,"2) Before light Majorana neutrino decoupling $T_{dec}=few\ MeV$ ) the imbalance in the number of baryons and antibaryons appears as a consequence of the surplus of leptons against antileptons and conserved B-L \citep{tHoofta,tHooftb,Kolb}. ("
3) Now follows the crucial observation: Part of the survived leptons. like electron. are produced together with neutrinos through charged current:W—eva and the helicity (22) of the Majorana neutrino ον) is predominantly positive (έν)= +1).,"3) Now follows the crucial observation: Part of the survived leptons, like electron, are produced together with neutrinos through charged $W^{-} \rightarrow e^{-}\nu_{M}$ and the helicity \citep{Bjorkena,Bjorkenb}
 of the Majorana neutrino $\lambda (\nu_{M})$ is predominantly positive $\lambda (\nu_{M})=+1$ )."
 This is the consequence of the two facts: (a) helicity of Dirac antineutrinos (=helicity of Majorana neutrinos) produced in W->e7vp is positive for left-handed weak interactions and (b) production of the negative helicity relativistic Majorana neutrinos is suppressed in the same process with weak charged currents by the kinematical factor 4+«1 (??)..," This is the consequence of the two facts: (a) helicity of Dirac antineutrinos (=helicity of Majorana neutrinos) produced in $W^{-} \rightarrow e^{-}
\stackrel{-}{\nu_{D}}$ is positive for left-handed weak interactions and (b) production of the negative helicity relativistic Majorana neutrinos is suppressed in the same process with weak charged currents by the kinematical factor $\frac{m_{\nu}}{E} \ll 1$ \citep{Kayser,Palle1}."
 Note that the ratio of the partial decay widths of weak bosons is I(W—evy/I(Z>vv)= 1.35., Note that the ratio of the partial decay widths of weak bosons is $\Gamma (W^{-} \rightarrow e^{-}\nu)/\Gamma (Z \rightarrow \nu\nu) \simeq 1.35$ .
 Neutral currents do not generate imbalance in neutrino's helicities. because one relativistic neutrino of a produced pair has negative and the," Neutral currents do not generate imbalance in neutrino's helicities, because one relativistic neutrino of a produced pair has negative and the"
Space Astronomy Centre (ESAC).,Space Astronomy Centre (ESAC).
 We thank Andrea Merloni. Eric Feigelson. EF. Massaro and G. Miniutti for useful discussions. and Craig Gordon for all his efforts in solving problems related toXSPEC.," We thank Andrea Merloni, Eric Feigelson, F. Massaro and G. Miniutti for useful discussions, and Craig Gordon for all his efforts in solving problems related to."
. We thank the anonymous referee for valuable suggestions., We thank the anonymous referee for valuable suggestions.
 Based on observations obtained with XMM-Newton. an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.," Based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA."
of 5107 M...,of $5\times10^8$ $_\odot$.
 Ht thus seems that either more sophisticated dynamical modeling is necessary to. properly: understand the central mass concentration in Sombrero. or it. truly has an exceptionally massive black hole.," It thus seems that either more sophisticated dynamical modeling is necessary to properly understand the central mass concentration in Sombrero, or it truly has an exceptionally massive black hole."
 Mternatively. the halo mass has also to be accounted for.," Alternatively, the halo mass has also to be accounted for."
 These results urge one to question thus how the halo in Sombrero cid form. and why such structure is seen in some galaxies but not in all.," These results urge one to question thus how the halo in Sombrero did form, and why such structure is seen in some galaxies but not in all."
 For instance. NGC 4565. is also an edge-on galaxy. which was observed at the same wavelength. also using Spitzer(2).. more deeply than the Sombrero image used here. and. vet it does not show such an extended. halo.," For instance, NGC 4565 is also an edge-on galaxy, which was observed at the same wavelength also using Spitzer, more deeply than the Sombrero image used here, and yet it does not show such an extended halo."
" Conversely, NGC 5866. also. observed by does exhibit an extended. halo."," Conversely, NGC 5866, also observed by does exhibit an extended halo."
 Early merger events are a likely formation mechanism for the Sombrero halo(?)., Early merger events are a likely formation mechanism for the Sombrero halo.
. Therefore. the properties of such haloes and their host galaxies. and how often they are present in galaxies. can provide constraints to physically characterise merger events. ancl elucidate how often and in which circumstances they occur.," Therefore, the properties of such haloes and their host galaxies, and how often they are present in galaxies, can provide constraints to physically characterise merger events, and elucidate how often and in which circumstances they occur."
 This is evidently an important issue for theories of structure growth in the universe., This is evidently an important issue for theories of structure growth in the universe.
 In this context. ib is worthy to point out that and found that the haloes in BCCs (Brightest Cluster Galaxies) are better described with exponential luminosity profiles than with Sérrsic profiles with n~4. as in the case of Sombrero's halo.," In this context, it is worthy to point out that and found that the haloes in BCGs (Brightest Cluster Galaxies) are better described with exponential luminosity profiles than with Sérrsic profiles with $n\sim4$, as in the case of Sombrero's halo."
 Εις also lenels support to the arguments above that the main spheroidal in Sombrero is indeed a massive stellar halo., This also lends support to the arguments above that the main spheroidal in Sombrero is indeed a massive stellar halo.
 Finally. one is left wondering on the impact of such extended haloes in our view of [ace-on galaxies.," Finally, one is left wondering on the impact of such extended haloes in our view of face-on galaxies."
 Since they nueht not be readily. discernible in such cases. results [rom image decomposition can be substantially altered. if they are not included in the model fitted. as seen above.," Since they might not be readily discernible in such cases, results from image decomposition can be substantially altered if they are not included in the model fitted, as seen above."
 Anti-truneated outer profiles can some times be a signature of the presence of a massive stellar halo. as pointed. out. byE," Anti-truncated outer profiles can some times be a signature of the presence of a massive stellar halo, as pointed out by."
nd5639] Note that such a feature is clearly seen in Erwthe Beeouter Poh05.parts of Sombrero's radial surface brightness profiles shown in Sect. 2.., Note that such a feature is clearly seen in the outer parts of Sombrero's radial surface brightness profiles shown in Sect. \ref{sec:struc}.
 The rightmost circle in the right panel of Fig., The rightmost circle in the right panel of Fig.
 2. marks the position where the anti-truncation begins., \ref{fig:profs_bd} marks the position where the anti-truncation begins.
 As mentioned in the Introduction. 44594 is often regarded as a prototypical earlv-tvpe. dise. galaxy.," As mentioned in the Introduction, 4594 is often regarded as a prototypical early-type disc galaxy."
 With its massive spheroid and the almost edge-on disc. it is usually classified as an Sa spiral(2).. although some authors prefer to consider it an SO (e.g...2.. RZO4 hereafter).," With its massive spheroid and the almost edge-on disc, it is usually classified as an Sa spiral, although some authors prefer to consider it an S0 (e.g., RZ04 hereafter)."
 The results presented in the previous sections. however. raise the intriguing possibility that the spheroid may not be a classical bulge. but to a laree extent a stellar halo or an elliptical galaxy (sce SS).," The results presented in the previous sections, however, raise the intriguing possibility that the spheroid may not be a classical bulge, but to a large extent a stellar halo or an elliptical galaxy (see 8)."
 The latter possibility could in principle be considered just a matter of semantics if one takes the view that bulges are simply. ellipticals surrounced bv a prominent disc??7).. but Fig.," The latter possibility could in principle be considered just a matter of semantics if one takes the view that bulges are simply ellipticals surrounded by a prominent disc, but Fig."
 S. shows that. at least at the high mass end. bulges and ellipticals follow different scaling relations.," \ref{fig:scale} shows that, at least at the high mass end, bulges and ellipticals follow different scaling relations."
 At fixed stellar mass. ellipticals tend to have larger cllective radii than bulges. and. it is noteworthy that Sombrero’s spheroid as a whole lies much closer to the sequence defined. by the former.," At fixed stellar mass, ellipticals tend to have larger effective radii than bulges, and it is noteworthy that Sombrero's spheroid as a whole lies much closer to the sequence defined by the former."
 While this does not necessarily preclude that they might share similar formation mechanisms. it clearly inclicates that at least their formation histories must. clilfer.," While this does not necessarily preclude that they might share similar formation mechanisms, it clearly indicates that at least their formation histories must differ."
 The resemblance of Sombrero's spheroid with elliptical galaxies has of course been noted earlier., The resemblance of Sombrero's spheroid with elliptical galaxies has of course been noted earlier.
 pointed out that the mild. colour ancl (absorption) line strength gradients. and the central kinematics. indicate such similarity.," pointed out that the mild colour and (absorption) line strength gradients, and the central kinematics, indicate such similarity."
 Indeed. the red. colours of the spheroid inner regions gradually turn bluer with radius. matching those of the metal-rich globular cluster system (GCS) at about Skkpe from the centre(?).," Indeed, the red colours of the spheroid inner regions gradually turn bluer with radius, matching those of the metal-rich globular cluster system (GCS) at about kpc from the centre."
. This behaviour appears to hold out to large ealactocentric radii. as found that the metallicity distribution function (AIDE) of stars in a field at about Iskkpe from the centre peaks at the same value (Fe/H] &0.5) as the metal-rich GCS potentially indicating a link between the formation of both components.," This behaviour appears to hold out to large galactocentric radii, as found that the metallicity distribution function (MDF) of stars in a field at about kpc from the centre peaks at the same value ([Fe/H] $\approx -0.5$ ) as the metal-rich GCS – potentially indicating a link between the formation of both components."
 This peak is significantly more metal-rich than the halo of the Milkv Way analog SS9L (Fe/L] 1: ?2)). but comparable to what is found in other elliptical ealaxies (e.g. 55128: ?2)).," This peak is significantly more metal-rich than the halo of the Milky Way analog 891 ([Fe/H] $\approx -1$ ; ), but comparable to what is found in other elliptical galaxies (e.g. 5128; )."
 The GCS in Sombrero perhaps provides the most compelling evidence of its spheroic’s peculiar nature., The GCS in Sombrero perhaps provides the most compelling evidence of its spheroid's peculiar nature.
 It has long been known that 44594 possesses the largest GC population ever found in a disc galaxy., It has long been known that 4594 possesses the largest GC population ever found in a disc galaxy.
 IUZ04. uncovered a GCS exceeding Ny.=1900 globular clusters that extends out to ~ kkpc. with ~ of them being metal-rich.," RZ04 uncovered a GCS exceeding $N_{gc} = 1900$ globular clusters that extends out to $\sim$ kpc, with $\sim$ of them being metal-rich."
 Figure 11. shows the GC mass specific for a compilation of ALc107 AL. elliptical. lenticular and spiral galaxies in different environments — from field/groups to the Virgo ‘luster(2).," Figure \ref{sombrero_gcs} shows the GC mass specific for a compilation of $_{\star} > 10^{10}$ $_{\odot}$ elliptical, lenticular and spiral galaxies in different environments – from field/groups to the Virgo cluster."
.. With a factor 44 more GC's than M31. anc inhabiting a [ow-density environment. it is clear that both the mass anc Zw of Sombrero are more characteristic of elliptical galaxies than of lenticulars or spirals.," With a factor $\sim$ 4 more GCs than M31, and inhabiting a low-density environment, it is clear that both the mass and $T_{N}$ of Sombrero are more characteristic of elliptical galaxies than of lenticulars or spirals."
 Vhis plot also indicates that a major merger event between two ALS1-like spirals cannot reproduce the GC abundance of NGC 4594 not even that of the old. metal-poor population. which dilfers by a factor of about 3.5 between AIZ1 and Sombrero.," This plot also indicates that a major merger event between two M31-like spirals cannot reproduce the GC abundance of NGC 4594 – not even that of the old, metal-poor population, which differs by a factor of about 3.5 between M31 and Sombrero."
 pointed out that Sombrero has the largest: specific frequeney of τος CC's amongὃν all spirals and thus its value is more characteristic of more massive ὃνgalaxies., pointed out that Sombrero has the largest specific frequency of red GCs among all spirals and thus its value is more characteristic of more massive galaxies.
 Moreover. they iscovered that metal-poor GCs follow a colour-magnitude relation. making 44594 the [irst disc galaxy where such trend was observed.," Moreover, they discovered that metal-poor GCs follow a colour-magnitude relation, making 4594 the first disc galaxy where such trend was observed."
 More recently. showed. that this. mass-metallicitvEM relation.. scales as ZEx[EAL. pretty much equivalent to what has been found in most massive ellipticals.," More recently, showed that this mass-metallicity relation scales as $Z \propto L^{0.3}$, pretty much equivalent to what has been found in most massive ellipticals."
 In summary. the spheroid in Sombrero has properties that cliffer significantlv from those of classical. bulges. including its mass-size relation: the richness of its GCS (ancl especially the metal-rich population): and the high metallicity of the outer halo when compared to other disc ealaxies.," In summary, the spheroid in Sombrero has properties that differ significantly from those of classical bulges, including its mass-size relation; the richness of its GCS (and especially the metal-rich population); and the high metallicity of the outer halo when compared to other disc galaxies."
 ]t is also pertinent to ask ourselves whether the embedded: dise (see. 11) displays peculiar. properties., It is also pertinent to ask ourselves whether the embedded disc (see 1) displays peculiar properties.
" show that the neutral eas mass fraction in the CLASS sample strongly decreases as a function. of stellar mass. with M,2/107 AL. galaxies having a weighted median Mg; /M,=0.016. with a 0.386 dex scatter (see refsombrero,fatisl mess... loppanct)."," show that the neutral gas mass fraction in the GASS sample strongly decreases as a function of stellar mass, with $_{\star} \approx 2\times10^{11}$ $_{\odot}$ galaxies having a weighted median $_{HI}/$ $_{\star} = 0.016$, with a 0.386 dex scatter (see \\ref{sombrero_sf_dust_smass}, top panel)."
 44594. withastellarmasscom para ALL: cdistance.)) deviates 22 556 from this relation.," 4594, with a stellar mass comparable to this value but a much lower neutral gas content $_{HI} \approx 3.1\times10^{8}$ $_{\odot}$; ) deviates $\approx$ $\sigma$ from this relation."
 ConsideringEN instead.. the 5107| M. disc. mass would bringe this ratio to within 222260. of the observed relation in the CLASS. sample., Considering instead the $5\times10^{10}$ $_{\odot}$ disc mass would bring this ratio to within $\approx$ $\sigma$ of the observed relation in the GASS sample.
 As discussed. by 2.. this. massive," As discussed by , this massive"
Data reduction was accomplished by converting the raw AO data to Continuum and Line Analvsis Single-dish Software (CLASS) format.,Data reduction was accomplished by converting the raw AO data to Continuum and Line Analysis Single-dish Software (CLASS) format.
 To prevent contamination of the data bv REI signals. each sean was examined by eve. and anv scans with apparent REI (ie. those with prominent. rapidly varving signals) were eliminated.," To prevent contamination of the data by RFI signals, each scan was examined by eye, and any scans with apparent RFI (i.e. those with prominent, rapidly varying signals) were eliminated."
 The remaining scans were summed to produce a total spectrum [or each observed frequency., The remaining scans were summed to produce a total spectrum for each observed frequency.
 The total. spectrum was then smoothed. using the CLASS “smooth” macro. resulting in a smoothed velocity resolution of 1.1kms.τν," The total spectrum was then smoothed, using the CLASS “smooth” macro, resulting in a smoothed velocity resolution of $1.1\,{\rm km\,s^{-1}}$."
 A first order polynomial baseline was subtracted [rom the smootheel data., A first order polynomial baseline was subtracted from the smoothed data.
 In the case of the OIL main lines. an emission feature was readilv apparent in the final data. and a Gaussian prolile was lit to each feature.," In the case of the OH main lines, an emission feature was readily apparent in the final data, and a Gaussian profile was fit to each feature."
 The calibrated main line spectra. together with the Gaussian fits. are displaved in Figure 1..," The calibrated main line spectra, together with the Gaussian fits, are displayed in Figure \ref{spec}."
 The fit parameters for these lines are listed in Table 1.., The fit parameters for these lines are listed in Table \ref{linefit}.
 The errors listed in the table are lo: thus the 1665 and 1667 MlIEZ lines are delected al a significance of 4.70 and 8.86. respectively.," The errors listed in the table are $1\sigma$ ; thus the $1665$ and $1667\,$ MHz lines are detected at a significance of $4.7\sigma$ and $8.8\sigma$, respectively."
" We determine an average fractional abundance for ΟΠ of (ΟΠ)~4x10 using the 1667 MIIz line flux. Frees !. and the relationship between Figg; and the munber of OI molecules. N(OID=4zD?Εμf,Auhv. where D= 170pe is the distance to IRC+10216. fy=5/16 is the fraction of molecules in the upper state (the value of 5/16 is plausible Lor ihe most likely excitation conditions). μις7.8x10Ha lis the Einstein A coefficient [or the transition and fv is the energy of the transition."," We determine an average fractional abundance for OH of $x({\rm OH})\sim 4 \times 10^{-8}$ using the $1667\,$ MHz line flux, $F_{1667}=39\,{\rm mK\, km\, s^{-1}}
=4.8\,{\rm mJy\, km\, s^{-1}}$ , and the relationship between $F_{1667}$ and the number of OH molecules, $N({\rm OH})=4 \pi D^2 F_{1667}/f_u A_{ul} h\nu$, where $D=170\,$ pc is the distance to IRC+10216, $f_u=5/16$ is the fraction of molecules in the upper state (the value of 5/16 is plausible for the most likely excitation conditions), $A_{ul}=7.8 \times 10^{-11}\,{\rm s^{-1}}$ is the Einstein A coefficient for the transition and $h\nu$ is the energy of the transition."
 Once we have found. N(OID. we may divide by the munber of Il nuclei in the Arecibo beam to find (ΟΙ).," Once we have found $N({\rm OH})$, we may divide by the number of H nuclei in the Arecibo beam to find $x({\rm OH})$."
" Based on a density of H nuclei of ny=3xLO(ALs/ο)/em. * (Glassgold. 1996). where MI.=3 is the stellar mass loss rate in units of LOM.vr.|, and v,πρό— Lis the expansion of the circumstellar envelope in units of 105ems! we find 7.8x10°? hvdrogen nuclei. assuming a maximum radius of rye»=LOM em."," Based on a density of H nuclei of $n_H=3\times 10^{37}(\dot M_{-5}/v_{exp,6})/r^2\,$ $^{-3}$ (Glassgold, 1996), where $\dot M_{-5}=3$ is the stellar mass loss rate in units of $10^{-5}\,{\rm M_{\odot}\, yr^{-1}}$, and $v_{exp,6}=1.4$ is the expansion of the circumstellar envelope in units of $10^6\,{\rm cm\, s^{-1}}$, we find $7.8 \times 10^{55}$ hydrogen nuclei, assuming a maximum radius of $r_{max}=10^{17}\,$ cm."
 We choose rage=LOM em because we expect nearly all of the OIL to lie inside of this radius. and we do not correct for beam sensitivity since this is within the hall-power beamwidth of AO and any such correction would be at the level of a lew percent at most.," We choose $r_{max}=10^{17}\,$ cm because we expect nearly all of the OH to lie inside of this radius, and we do not correct for beam sensitivity since this is within the half-power beamwidth of AO and any such correction would be at the level of a few percent at most."
 This vields a rough determination of (ΟΠ) which is relatively model independent but somewhat misleading., This yields a rough determination of $x({\rm OH})$ which is relatively model independent but somewhat misleading.
 Since we believe the OII to be in a photodissociated shell or ring around IRC+10216. the OIL fractional abundance in the outer regions of (he circumstellar envelope around IRC+10216 may reach values several “ines larger than our minima.," Since we believe the OH to be in a photodissociated shell or ring around IRC+10216, the OH fractional abundance in the outer regions of the circumstellar envelope around IRC+10216 may reach values several times larger than our minimum."
 We failed to detect anv signal originating in (he envelope of IRC+10216 at the fiveother frequencies we observed., We failed to detect any signal originating in the envelope of IRC+10216 at the fiveother frequencies we observed.
 Severe radio [requency interlerence (RFI) across all observations prevents us from placing meaningful upper limits on the strength of the 1721 MlIz satellite," Severe radio frequency interference (RFI) across all observations prevents us from placing meaningful upper limits on the strength of the $1721\,$ MHz satellite"
to high precision for the ο]σι seveu-feed receiver (R. Ivcller. private conmmumication 2009).,"to high precision for the 21-cm seven-feed receiver (R. Keller, private communication 2009)."
 The thermal noise temperature of the calibration diode. T9. is known. such that one cau obtain C=€(PigocalDyg)/T," The thermal noise temperature of the calibration diode, $T^\mathrm{cal}$, is known, such that one can obtain $G=(P_\mathrm{IF}^\mathrm{cal}-P_\mathrm{IF})/T^\mathrm{cal}$."
 However. a better precision of the absolute flux calibration can be reached by using au astronomical calibration source.," However, a better precision of the absolute flux calibration can be reached by using an astronomical calibration source."
 For this purpose. we utilize TAU standard calibration sources (usually S77. because it is ciremmpolar for Effelsbere. sometimes also S88).," For this purpose, we utilize IAU standard calibration sources (usually 7, because it is circumpolar for Effelsberg, sometimes also 8)."
 The spectral line flux of these calibrators is well known (2). allowing one to determine the gain factor. g=Ge.0). with au accuracy of typically.," The spectral line flux of these calibrators is well known \citep{kalberla82} allowing one to determine the gain factor, $g\equiv G(v_\mathrm{lsr}=0)$, with an accuracy of typically."
 Note. that the calibrators are not continuuni sources. but are well-defined regious in the Milky Way: hence they ouly provide the gain for ey.= 0.," Note, that the calibrators are not continuum sources, but are well-defined regions in the Milky Way; hence they only provide the gain for $v_\mathrm{lsr}=0$ ."
 In refiles7 eaiutactors.. values of g for a time ranec of a few weeks are shown.," In \\ref{figs7gainfactors}, values of $g$ for a time range of a few weeks are shown."
 There is a sheht dependence of time which is expected for a typical receiving system., There is a slight dependence of time which is expected for a typical receiving system.
 To measure the scatter about the long-time behavior a third-order polvuoiial was fitted. showing residual iis of about," To measure the scatter about the long-time behavior a third-order polynomial was fitted, showing residual rms of about."
 Practically. g is micasured by performing a polvnomial fit to the calibration source spectra to separate the spectral line from the basclines and calculating Co are the inteeration Dnits for the chosen TAU position according to ?..," Practically, $g$ is measured by performing a polynomial fit to the calibration source spectra to separate the spectral line from the baselines and calculating $v_{1,2}$ are the integration limits for the chosen IAU position according to \citet{kalberla82}."
 The complete gain curve is easily computed by normalizing GT such that G=GTCNETTES1)--l aud applying the absolute fiux calibration (as obtained usiug the LAU standard calibration sources) by imultiplius with q: Iu rofüeeaincurves.. some of the obtained eain curves G are shown.," The complete gain curve is easily computed by normalizing $GT^\mathrm{cal}$ such that $\hat G\equiv GT^\mathrm{cal}(v_\mathrm{lsr}=0\,\mathrm{km\,s}^{-1})=1$ and applying the absolute flux calibration (as obtained using the IAU standard calibration sources) by multiplying with $g$: In \\ref{figgaincurves}, , some of the obtained gain curves $\hat G$ are shown."
 They were computed by calculating je inedia of G of all spectral dumps., They were computed by calculating the median of $\hat G$ of all spectral dumps.
 Usually us niediau eain curve contains only few outliers lue to REI signals., Usually this median gain curve contains only few outliers due to RFI signals.
 For later application of G to 1ο spectra the eain curves are sinoothed with IGS (using a filter kernel width of &= 6LkITz) to reduce residual noise.," For later application of $\hat G$ to the spectra the gain curves are smoothed with IGS (using a filter kernel width of $\sigma=64\,\mathrm{kHz}$ ) to reduce residual noise."
 Panels (a) and (b) coutain ie. left-hand polarization channel of the ceutral eed for the two differeut frequency shifts., Panels (a) and (b) contain the left-hand polarization channel of the central feed for the two different frequency shifts.
 Several ripples are visible which follow the LO shift aud. rence. cau be attributed to the RF part of the eain curve.," Several ripples are visible which follow the LO shift and, hence, can be attributed to the RF part of the gain curve."
 It is possible that these features are caused by resonances in the waveguide connecting he feed horu auteuua with the receiver., It is possible that these features are caused by resonances in the waveguide connecting the feed horn antenna with the receiver.
 Tn paucl (c) a linear polarization channel of oue of the offset feeds is show.," In panel (c), a linear polarization channel of one of the offset feeds is shown."
 reffigealibratedspectra shows spectra (integrated OVOY oc subscan) for the two differeut LO requencies before (upper panel) and after (ower xuel) calibration., \\ref{figcalibratedspectra} shows spectra (integrated over one subscan) for the two different LO frequencies before (upper panel) and after (lower panel) calibration.
 Features in the raw spectra do rot match exactly., Features in the raw spectra do not match exactly.
 This is due to the yequency dependence ofG., This is due to the frequency dependence of $G$.
 After applying the eain calibration. ))th. LO setups produce nearly identical results (apart frou REI aud noise coutributiou).," After applying the gain calibration, both LO setups produce nearly identical results (apart from RFI and noise contribution)."
 The xaseline level of the calibrated spectra is by definition equal to he syste temperature., The baseline level of the calibrated spectra is by definition equal to the system temperature.
 The spectra shown im the lower paucl of reffiecalibratedspectra— also. reveal imuultiauodal sine-wave contributious., The spectra shown in the lower panel of \\ref{figcalibratedspectra} also reveal multi-modal sine-wave contributions.
 Usually such a pattern is attributed Oo standing waves (SWx) )oetwoeen the primary and secondary focus., Usually such a pattern is attributed to standing waves (SWs) between the primary and secondary focus.
 We tested this hypothesis by performing test measurements with the sinele-fecc receiver (which is constructed in asnmular wav as the nulti-feed)., We tested this hypothesis by performing test measurements with the single-feed receiver (which is constructed in asimilar way as the multi-feed).
 Fortechnical reasons the sub-refiector at the 100-3 telescope is tilted when observing with this instrument., Fortechnical reasons the sub-reflector at the 100-m telescope is tilted when observing with this instrument.
condition along spherical radii not the z-direction.,condition along spherical radii not the $z$ -direction.
 The protoplanetary disk svstem is comprised of a star will one solar mass and a clisk of material in nearly Weplerian rotation with a mass equal to 0.001 M..., The protoplanetary disk system is comprised of a star with one solar mass and a disk of material in nearly Keplerian rotation with a mass equal to 0.091 $M_\odot$.
 The iniGal moclel uses (he Boss(1984). pressure equation of state (EOS) based on an initial temperature profile provided by Boss (2004. private communication). but we derive the specilic internal eneregv densitv by using e=p/(5—1). where 5 is the ratio of specific heats and € is the internal energv density.," The initial model uses the \cite{boss84} pressure equation of state (EOS) based on an initial temperature profile provided by Boss (2004, private communication), but we derive the specific internal energy density by using $ \epsilon = p/ (\gamma - 1)$, where $\gamma$ is the ratio of specific heats and $\epsilon$ is the internal energy density."
 In the subsequent evolution. the EOS is assumed to be that of an ideal gas with 4=/5/3.," In the subsequent evolution, the EOS is assumed to be that of an ideal gas with $\gamma = 5/3$."
 As in previous simulations. the disk begins in a marginally unstable state and is allowed to cool racliatively to instability.," As in previous simulations, the disk begins in a marginally unstable state and is allowed to cool radiatively to instability."
 The initial axisvinmetric moclel is set up using the same analvlic expressions eiven in Boss(2003).. but without infall.," The initial axisymmetric model is set up using the same analytic expressions given in \cite{boss03}, but without infall."
 The latter is nol a serious onission. because. in the DOT simulation. there is little mass in (he inflow. and infall lasts only ~ Iree-Fall time. about 0.2 ORD.," The latter is not a serious omission, because, in the B07 simulation, there is little mass in the inflow, and infall lasts only $\sim$ free-fall time, about 0.2 ORP."
 We included this short accretion phase in preliminary simulations with the Caiοἱal.(2008) version of CHYAMERA and obtained essentially (hie same results reported here., We included this short accretion phase in preliminary simulations with the \cite{cai08} version of CHYMERA and obtained essentially the same results reported here.
 We introduce (he same initial perturbation used in DOT which preferentially seeds power al the percent level into ordered costo) structure with i = 2 to 4 plus a small random component (Boss1998.2000).," We introduce the same initial perturbation used in B07 which preferentially seeds power at the percent level into ordered ${\rm cos}(m\phi)$ structure with $m$ = 2 to 4 plus a small random component \citep{boss98,boss00}."
. We ran (he simulation 250.000 computation steps. equal to 5.0 ORPs.," We ran the simulation 250,000 computation steps, equal to 5.0 ORPs."
 An ORD (outer rotation period) is the orbital period for material initiallv located at 20 AU. or about 90 vrs.," An ORP (outer rotation period) is the orbital period for material initially located at 20 AU, or about 90 yrs."
 The end of the simulation extends a little more than one ORP bevond the time shown in Figures 2 and 3in BOT., The end of the simulation extends a little more than one ORP beyond the time shown in Figures 2 and 3 in B07.
 Though material is allowed to expand off the grid (ancl accrete onto the central star). the disk itself loses less than 0.4 % of its original mass and angular momentum.," Though material is allowed to expand off the grid (and accrete onto the central star), the disk itself loses less than 0.4 $\%$ of its original mass and angular momentum."
 The simulation was conducted on a dedicated IIP. Proliant DEL385 G2 server al Lawrence Universily., The simulation was conducted on a dedicated HP Proliant DL385 G2 server at Lawrence University.
"with n(v)=1/(e”/keT:+#—1), where T,, is the temperature to which the spectrum relaxes for an initial energy addition/loss of AE/E with AT,/T=0.64AE/E+2.5x107? (2),, and AE/E=+4x10? is the energy addition/loss that gives rise to SZ distortion of 107?.","with $n(\nu)=1/(e^{h\nu/\kB T_{\mu}+\mu}-1)$, where $T_{\mu}$ is the temperature to which the spectrum relaxes for an initial energy addition/loss of $\Delta
E/E$ with $\Delta T_{\mu}/T=0.64\Delta E/E=\pm 2.5\times 10^{-9}$ \citep{is1975b}, and $\Delta E/E=\pm 4\times 10^{-9}$ is the energy addition/loss that gives rise to SZ distortion of $10^{-9}$."
 The chemical potential µ is given μς2.2ΔΤ/Τ=+5.6x107°.," The chemical potential $\mu$ is given $\mu=2.2\Delta T/T=\pm 5.6\times
10^{-9}$."
" This is the spectrum that an initial spectrum with Yggc,Ysz=107? will approach at high y at χμ~107?."," This is the spectrum that an initial spectrum with $\YBEC,\YSZ =10^{-9}$ will approach at high $y$ at $x{\gg}\mu\sim10^{-9}$."
 The frequency at which the distortion crosses zero is at x=2.19compared to x=3.83 for the SZ distortion in Fig. [I]., The frequency at which the distortion crosses zero is at $x=2.19$compared to $x=3.83$ for the SZ distortion in Fig. \ref{sz}. .
temperature scale. is not a good one.,"temperature scale, is not a good one."
 Langer(1991) and Takedaetal.(2000) suggest that [O I] is filled in by emission. and this option is discussed and eliminated in the Appendix.," \citet{l91} and \citet{nlte} suggest that [O I] is filled in by emission, and this option is discussed and eliminated in the Appendix."
 There are still several solutions that can solve this discrepancy., There are still several solutions that can solve this discrepancy.
 Giants have large convection zones. so granulation may play an even larger role than in the dwarfs.," Giants have large convection zones, so granulation may play an even larger role than in the dwarfs."
 Giants have thin atmospheres that are penetrable by UV radiation. so NLTE corrections for the permitted lines are important.," Giants have thin atmospheres that are penetrable by UV radiation, so NLTE corrections for the permitted lines are important."
 One-dimensional NLTE calculations may not work if a three-dimensional model is needed to describe the true conditions in the atmosphere., One-dimensional NLTE calculations may not work if a three-dimensional model is needed to describe the true conditions in the atmosphere.
 Until three-dimensional models become widely available. there are still tests that can be done using traditional methods.," Until three-dimensional models become widely available, there are still tests that can be done using traditional methods."
 For example. the gravities of giant stars have larger uncertainties than dwarfs due to the uncertain distance to the stars.," For example, the gravities of giant stars have larger uncertainties than dwarfs due to the uncertain distance to the stars."
 King(2000) discusses whether. like dwarfs. the LTE Fe U/Fe II tonization balance can no longer be used to derive surface gravities 1n metal-poor giants.," \citet{k00} discusses whether, like dwarfs, the LTE Fe I/Fe II ionization balance can no longer be used to derive surface gravities in metal-poor giants."
 As seen in Table 7. Hipparcos parallaxes are of little use to individual giants.," As seen in Table 7, Hipparcos parallaxes are of little use to individual giants."
 Although the changing the surface gravity is not the solution to resolving the controversy. is crucial for calculating the absolute O abundance.," Although the changing the surface gravity is not the solution to resolving the controversy, is crucial for calculating the absolute O abundance."
" Thus. until more reliable data is available from GAIA [O,/O;]or SIM. a study of permitted vs. forbidden Imes in cluster stars with accurately known distances would be helpful."," Thus, until more reliable data is available from GAIA or SIM, a study of permitted vs. forbidden lines in cluster stars with accurately known distances would be helpful."
 The chemical homogeneity of most clusters also makes it possible to use the abundances other heavy elements to help constrain the parameters., The chemical homogeneity of most clusters also makes it possible to use the abundances other heavy elements to help constrain the parameters.
 We have analyzed the forbidden and permitted oxygen lines in 55 stars. including dwarfs and giants and spanning [Fe/H] values from solar to —2.7 in an attempt to understand the discrepancy in these oxygen abundance indicators.," We have analyzed the forbidden and permitted oxygen lines in 55 stars, including dwarfs and giants and spanning [Fe/H] values from solar to $-2.7$ in an attempt to understand the discrepancy in these oxygen abundance indicators."
 We first tried a standard analysis using the temperature scales of Alonso and Houdashelt., We first tried a standard analysis using the temperature scales of Alonso and Houdashelt.
 These models produced «[Op/Of]|- values of +0.35 and +0.09. respectively.," These models produced $<$ $>$ values of $+0.35$ and $+0.09$, respectively."
 The discrepancy was largest for cool giants. but evolved stars of all types favor high values.," The discrepancy was largest for cool giants, but evolved stars of all types favor high values."
 The ratio is most sensitive to temperature of all the atmospheric parameters. and it 15 the only one where the the effect of a change in the parameter 1s opposite for the two indicators.," The ratio is most sensitive to temperature of all the atmospheric parameters, and it is the only one where the the effect of a change in the parameter is opposite for the two indicators."
 Using our understanding of the effects of parameter changes on the abundances. we calculated a new parameter scale that would bring the two sets of oxygen lines into agreement.," Using our understanding of the effects of parameter changes on the abundances, we calculated a new parameter scale that would bring the two sets of oxygen lines into agreement."
 These parameters. however. disagree with other temperature diagnostics. such as colors. the fits to the Balmer lines. and the bolometric luminosities.," These parameters, however, disagree with other temperature diagnostics, such as colors, the fits to the Balmer lines, and the bolometric luminosities."
 We conclude that either improved NLTE corrections for the permitted lines or other phenomena. perhaps associated with convection and granulation. are needed to solve the oxygen problem.," We conclude that either improved NLTE corrections for the permitted lines or other phenomena, perhaps associated with convection and granulation, are needed to solve the oxygen problem."
 JPF and JAJ would like to thank the staffs at the Canada-France-Hawait Telescope. Mauna Kea Observatories. Lick Observatory. and Kitt Peak for their invaluable assistance with the observations for this project.," JPF and JAJ would like to thank the staffs at the Canada-France-Hawaii Telescope, Mauna Kea Observatories, Lick Observatory, and Kitt Peak for their invaluable assistance with the observations for this project."
 We also like to thank Poul Nissen and Garak Israelian for their insightful correspondences on BD +23 3130 and Robert Kraft. Chris Sneden. and James Hesser for their comments on drafts of this paper.," We also like to thank Poul Nissen and Garak Israelian for their insightful correspondences on BD +23 3130 and Robert Kraft, Chris Sneden, and James Hesser for their comments on drafts of this paper."
 Finally. we gladly thank the anonymous referee for his valuable and insightful comments.," Finally, we gladly thank the anonymous referee for his valuable and insightful comments."
 This research has made use of the SIMBAD database. operated at CDS. Strasbourg. France.," This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France."
" This publication makes use of data products from the Two Micron All Sky Survey. which ts a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center. funded by the National Aeronautics and Space Administration and the National Science Foundation,"," This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center, funded by the National Aeronautics and Space Administration and the National Science Foundation."
 Langer(1991) suggested that emission from circumstellar shells could fill in the [O I] lines in giant stars., \citet{l91} suggested that emission from circumstellar shells could fill in the [O I] lines in giant stars.
 These shells are the result of mass loss on the giant branch., These shells are the result of mass loss on the giant branch.
 The resulting lower EW values would then lead to the discrepancy in the oxygen abundance indicators., The resulting lower EW values would then lead to the discrepancy in the oxygen abundance indicators.
 The Langer(1991) model proposes that a mass loss rate of a few 1077 yr! could create an H I region of about 32 AU around the giant., The \citet{l91} model proposes that a mass loss rate of a few $10^{-7}$ $^{-1}$ could create an H I region of about 32 AU around the giant.
 If the temperature of thisregion was about the same as the giant (4500 K in the model) and the density is about 6.8«10° 3. the amount of photons emitted by the 6300 [O I] line from the H I region would reduce the measured EW by 20má.," If the temperature of this region was about the same as the giant (4500 K in the model) and the density is about $6.8 \times 10^6$ $^{-3}$, the amount of photons emitted by the 6300 [O I] line from the H I region would reduce the measured EW by 20."
. Langer(1991) admits that the required mass loss rate 1s a factor of about five too high than expected by theory. but the remaining assumptions are not wildly unreasonable.," \citet{l91} admits that the required mass loss rate is a factor of about five too high than expected by theory, but the remaining assumptions are not wildly unreasonable."
 We therefore examined the 6300.31 region of the 16 stars with My«0 observed with Gecko for signs of emission., We therefore examined the 6300.31 region of the 16 stars with $_{\rm V} < 0$ observed with Gecko for signs of emission.
 The stellar absorption lines of our sample are resolved at the spectral resolution of Gecko., The stellar absorption lines of our sample are resolved at the spectral resolution of Gecko.
 For example. in the 16 giants examined here. the [O I] 6300.31 absorption lines have a mean FWHM of 0.17540.026 (—10 pixels).," For example, in the 16 giants examined here, the [O I] 6300.31 absorption lines have a mean FWHM of $0.175 \pm 0.026$ $\sim 10$ pixels)."
 The tellurie [O I] emission lines in these same spectra have a mean FWHM of 0.0625+0.002 (~3 pixels)., The telluric [O I] emission lines in these same spectra have a mean FWHM of $0.0625 \pm 0.002$ $\sim 3$ pixels).
 The dominant line-broadening mechanism in the H I region is thermal Doppler broadening. which for this case would be 0.045Á.. or less than the instrumental profile of Gecko.," The dominant line-broadening mechanism in the H I region is thermal Doppler broadening, which for this case would be 0.045, or less than the instrumental profile of Gecko."
 Therefore. any emission from an H I region surrounding the giant should be a narrow feature.," Therefore, any emission from an H I region surrounding the giant should be a narrow feature."
 Regions of | (—55 pixels). centered at 6300.31 for these 16 giants are shown in Figures 16 and 17.," Regions of 1 $\sim 55$ pixels), centered at 6300.31 for these 16 giants are shown in Figures 16 and 17."
 No binning or smoothing has been applied to the spectra., No binning or smoothing has been applied to the spectra.
 As can be seen. no significant emission is present.," As can be seen, no significant emission is present."
 Finally. if the 6300.31 [O I| line was producing significant emission. other emission lines may be present.," Finally, if the 6300.31 [O I] line was producing significant emission, other emission lines may be present."
" Langer(1991) estimates that the chromospheric H,, emission (which dominates over the H,, emission from the H I region) from the model system would be several Angstroms in equivalent width.", \citet{l91} estimates that the chromospheric $_{\alpha}$ emission (which dominates over the $_{\alpha}$ emission from the H I region) from the model system would be several ngstroms in equivalent width.
" Therefore. we examined the H,, lines of the 16 giants in the lower resolution spectra used to measure the Fe and permitted O I lines."," Therefore, we examined the $_{\alpha}$ lines of the 16 giants in the lower resolution spectra used to measure the Fe and permitted O I lines."
" Of these giants. only six show any sign of having asymmetric H,, profiles (HIP 17639 is not among these six stars)."," Of these giants, only six show any sign of having asymmetric $_{\alpha}$ profiles (HIP 17639 is not among these six stars)."
" Of these six. only two. BD +30 2611 (= HIP 73960) and HD 165195 (= HIP 88527) show any sign of H,, emission."," Of these six, only two, BD +30 2611 (= HIP 73960) and HD 165195 (= HIP 88527) show any sign of $_{\alpha}$ emission."
 For these two giants. the 6300.31 [O I] profile is deep. symmetric. and free of obvious emission.," For these two giants, the 6300.31 [O I] profile is deep, symmetric, and free of obvious emission."
 We therefore conclude that emission from an H I region as described by Langer(1991) does not affect the equivalent width of the [O I] lines to any significant amount., We therefore conclude that emission from an H I region as described by \citet{l91} does not affect the equivalent width of the [O I] lines to any significant amount.
"multiplets, mode groupings, or small and large spacings, which constrain mode identifications and therefore reduce the number of free parameters.","multiplets, mode groupings, or small and large spacings, which constrain mode identifications and therefore reduce the number of free parameters."
" Following this approach, and encouraged by the results obtained for other sdBV stars, we decided to obtain photometric observations of one of the faintest sdBV stars discovered so far, JJ0455+1305 (hereafter RAT0455)."," Following this approach, and encouraged by the results obtained for other sdBV stars, we decided to obtain photometric observations of one of the faintest sdBV stars discovered so far, J0455+1305 (hereafter RAT0455)."
 Our results clearly show that small and/or moderate telescopes are useful for the asteroseismic study of faint sdBV stars., Our results clearly show that small and/or moderate telescopes are useful for the asteroseismic study of faint sdBV stars.
 RAT0455 was discovered during the RApid Temporal Survey (Ramsay&Hakala2005)., RAT0455 was discovered during the RApid Temporal Survey \citep{ramsey05}.
". The aim of this survey was to search for variability from a few minutes up to several hours, for stars down to mmag to find interacting ultra-compact binary systems with orbital periods less than mmin."," The aim of this survey was to search for variability from a few minutes up to several hours, for stars down to mag to find interacting ultra-compact binary systems with orbital periods less than min."
" The design of the project is also useful for detecting sdBV stars, which can serendipitously occur in the field of view."," The design of the project is also useful for detecting sdBV stars, which can serendipitously occur in the field of view."
" To date, as a by-product of this survey, one sdBV star has been discovered."," To date, as a by-product of this survey, one sdBV star has been discovered."
 It was assigned the designation JJ0455+1305 in accordance with the survey convention., It was assigned the designation J0455+1305 in accordance with the survey convention.
" Discovery observations along with Fourier analysis and a classification spectrum were published by Ramsay,Napi-wotzki,Hakalaetal. (2006).", Discovery observations along with Fourier analysis and a classification spectrum were published by \cite{ramsey06}.
. RAT0455 is mmag in the the V filter and the amplitude spectrum calculated from the discovery data revealed only one frequency in the (p—)mode region with a relatively high amplitude., RAT0455 is mag in the the V filter and the amplitude spectrum calculated from the discovery data revealed only one frequency in the $p-$ )mode region with a relatively high amplitude.
" Placing RAT0455 on the logTeg and logg diagram (Fig.1)), we can see that it is similar to other hybrid stars, and indeed Baran&Fox-Machado(2009) detected peaks at low frequencies which were assigned as (g—)modes."," Placing RAT0455 on the $_{\rm eff}$ and $\log g$ diagram \ref{hr}) ), we can see that it is similar to other hybrid stars, and indeed \cite{baran10} detected peaks at low frequencies which were assigned as $g-$ )modes."
and Sa galaxies. respectively.,"and Sa galaxies, respectively."
 Thus. in our study. all regions in the disk of Category 1 earlv-tvpe spirals have €LOergs! whereas. Category 2 galaxies host at least one regiondisk with luminosity >10°ergs|.," Thus, in our study, all regions in the disk of Category 1 early-type spirals have $< 10^{39}~\lum$ whereas, Category 2 galaxies host at least one region with luminosity $\ge 10^{39}~\lum$."
" We have also identified galaxies with intense nuclear starbursts (NGC 1022. NGC 1482. NGC 3885, NGC 3411) and have included them as Category 1 galaxies because thev have virtually no disk emission."," We have also identified galaxies with intense nuclear starbursts (NGC 1022, NGC 1482, NGC 3885, NGC 3471) and have included them as Category 1 galaxies because they have virtually no disk emission."
 images for Categorv 1 and Category 2 galaxies are presented in Figures 2 and 3. respectively.," images for Category 1 and Category 2 galaxies are presented in Figures 2 and 3, respectively."
 Figures 4 and 5 show the range of global huminosities and equivalent widths for the two categories of earlv-tvpe spirals., Figures 4 and 5 show the range of global luminosities and equivalent widths for the two categories of early-type spirals.
 As expected. Category | galaxies have preferentially lower elobal huninosities and smaller equivalent widths compared to Category. 2 ealaxies.," As expected, Category 1 galaxies have preferentially lower global luminosities and smaller equivalent widths compared to Category 2 galaxies."
 The Iuminosity of the prototypical earlv-tvpe spiral. M 81. is also marked on these ligures.," The luminosity of the prototypical early-type spiral, M 81, is also marked on these figures."
 Despite some overlap. a (wo-tailed Nolmogorov-Sunirnoy (Ix-S) test indicates (hat the (wo categories are not derived [rom (he same population al a confidence level greater than 9954.," Despite some overlap, a two-tailed Kolmogorov-Smirnov (K-S) test indicates that the two categories are not derived from the same population at a confidence level greater than $\%$."
 Within the current sample of 51 nearby galaxies. we find that 59% belong to Category 1.," Within the current sample of 51 nearby galaxies, we find that $\%$ belong to Category 1."
 However. a significant [raction (37%) of earlv-tvpe spirals. host giant regions in their disks.," However, a significant fraction $\%$ ) of early-type spirals, host giant regions in their disks."
 Two galaxies. NGC 660 and NGC 2146. have highly disturbed morphologies aud have not been classified into either of the categories (ILD99).," Two galaxies, NGC 660 and NGC 2146, have highly disturbed morphologies and have not been classified into either of the categories (HD99)."
 Despite having similar optical morphologies. eaulv-(wpe spirals show a wide diversity in llo morphology.," Despite having similar optical morphologies, early-type spirals show a wide diversity in $\alpha$ morphology."
 Most Category 1 galaxies appear undisturbed in the continuum image. but exhibit diversity when it comes to the nuclear Hla emission.," Most Category 1 galaxies appear undisturbed in the continuum image, but exhibit diversity when it comes to the nuclear $\alpha$ emission."
 Almost half (14/30) of all Category 1 galaxies host Extended. Nuclear Einission-line Regions (ENER): a region of diffuse ionizecl gas in the nuclear region., Almost half (14/30) of all Category 1 galaxies host Extended Nuclear Emission-line Regions (ENER); a region of diffuse ionized gas in the nuclear region.
 As has been noted bv Ixeel.(1983).. ENERs are only visible when there is very little or no star formation near the nucleus.," As has been noted by \citet{Keel1983}, ENERs are only visible when there is very little or no star formation near the nucleus."
 Ii seven other Category 1 galaxies. its hard to detect ENERs due to their high inclination.," In seven other Category 1 galaxies, its hard to detect ENERs due to their high inclination."
 Two Category 2 galaxies (NGC 3169 and NGC 7213) also exhibit this diffuse gas., Two Category 2 galaxies (NGC 3169 and NGC 7213) also exhibit this diffuse gas.
 Sevfert nuclei have been identified in flour Category | early-type spirals., Seyfert nuclei have been identified in four Category 1 early-type spirals.
 In I1D99 we had speculated on a possible direct correspondence between the spectroscopic Classification of LINERS and the morphologically identified ENERs., In HD99 we had speculated on a possible direct correspondence between the spectroscopic classification of LINERS and the morphologically identified ENERs.
 However. due to the small number of galaxies with spectroscopic classifications. we could not address (hat assertion statistically in thal paper.," However, due to the small number of galaxies with spectroscopic classifications, we could not address that assertion statistically in that paper."
 Now. wilh a sample of 51 galaxies. we find (hat 12 Category 1 galaxies have been classified as LENEIBs. and 10 of those galaxies also show ENER emission. The nuclei of Category 2 galaxies have been mostly classified as II spectroscopicallv. inclicating the presence of regions (Table 4).," Now, with a sample of 51 galaxies, we find that 12 Category 1 galaxies have been classified as LINERs, and 10 of those galaxies also show ENER emission, The nuclei of Category 2 galaxies have been mostly classified as 'H' spectroscopically, indicating the presence of regions (Table 4)."
 There are. however. flour Category 2 galaxies," There are, however, four Category 2 galaxies"
Goodwin Kroupa (2005) suggested that the observed properties of multiple systems could be reproduced if each core produces 2 or 3 stars.,Goodwin Kroupa (2005) suggested that the observed properties of multiple systems could be reproduced if each core produces 2 or 3 stars.
 Single field stars are then produced by the dynamical decay and destruction of multiple systems in young clusters (Kroupa 1995a.b: Goodwin Kroupa 2005: Goodwin Whitworth 2007; Goodwin et al.," Single field stars are then produced by the dynamical decay and destruction of multiple systems in young clusters (Kroupa 1995a,b; Goodwin Kroupa 2005; Goodwin Whitworth 2007; Goodwin et al."
 2007 and references therein)., 2007 and references therein).
 To model the fully multiple scenario we assume that cores of mass ες«0.75M. form entirely binary systems. and cores with eM;>0.75!» form multiple systems with a ratio of 3:1 binaries-to-triples.," To model the fully multiple scenario we assume that cores of mass $\epsilon M_C < 0.75 M_\odot$ form entirely binary systems, and cores with $\epsilon M_C \ge 0.75 M_\odot$ form multiple systems with a ratio of $3\!:\!1$ binaries-to-triples."
 The SFE is chosen to give a good fit to the canonical IMF with e=0.27., The SFE is chosen to give a good fit to the canonical IMF with $\epsilon = 0.27$.
 In this scenario the multiplicity fraction 1s. unity., In this scenario the multiplicity fraction is unity.
 Single stars and brown dwarfs are produced by the destruction of many (especially low-mass) initially multiple systems (see Section 3)., Single stars and brown dwarfs are produced by the destruction of many (especially low-mass) initially multiple systems (see Section 3).
 The result of the fully multiple model are illustrated in Fig. 2.., The result of the fully multiple model are illustrated in Fig. \ref{fig:gk}.
 This model produces a good fit to the canonical IMF for all masses except the very highest., This model produces a good fit to the canonical IMF for all masses except the very highest.
 The mass functions dip below the canonical slope of —1.3 at high masses due to the steep decline of the log-normal CMF at high The fully multiple model requires. the dynamical destruction (see e.g. Kroupa 1995b: Kroupa et al., The mass functions dip below the canonical slope of $-1.3$ at high masses due to the steep decline of the log-normal CMF at high The fully multiple model requires the dynamical destruction (see e.g. Kroupa 1995b; Kroupa et al.
 2003; Goodwin Kroupa 2005: Goodwin et al., 2003; Goodwin Kroupa 2005; Goodwin et al.
 2007) of significant numbers of low-mass binary systems in young clusters in order to change the initial binary fraction of unity to the field value., 2007) of significant numbers of low-mass binary systems in young clusters in order to change the initial binary fraction of unity to the field value.
 We note that in this model brown dwarfs are not primarily produced as single objects in cores Cstar-like’ formation. e.g. Padoan NordlundA 2004). nor as ejected embryos from high-mass cores (the ejection hypothesis. e.g. Reipurth Clarke 2001).," We note that in this model brown dwarfs are not primarily produced as single objects in cores (`star-like' formation, e.g. Padoan Nordlund 2004), nor as ejected embryos from high-mass cores (the ejection hypothesis, e.g. Reipurth Clarke 2001)."
 Instead they mainly form as the distant companions to M-dwarts which are then disrupted., Instead they mainly form as the distant companions to M-dwarfs which are then disrupted.
 This is the scenario proposed by Goodwin Whitworth (2007) as a major mode of brown dwarf formation., This is the scenario proposed by Goodwin Whitworth (2007) as a major mode of brown dwarf formation.
 We note that this might be consistent with the idea that brown dwarfs form as a separate population of objects. possibly with a discontinuous IMF (Kroupa et al.," We note that this might be consistent with the idea that brown dwarfs form as a separate population of objects, possibly with a discontinuous IMF (Kroupa et al."
 2003: Thies Kroupa 2007: Kumar Schmeja 2007)., 2003; Thies Kroupa 2007; Kumar Schmeja 2007).
 Lada (2006) suggests that M-dwarfs tend to form as single stars. since most M-dwarfs in the field (roughly by total number) are single stars.," Lada (2006) suggests that M-dwarfs tend to form as single stars, since most M-dwarfs in the field (roughly by total number) are single stars."
 In this picture. destructive dynamical processes are unimportant for low-mass stars.," In this picture, destructive dynamical processes are unimportant for low-mass stars."
 However. Solar-type stars (and higher-masses) must still usually form in multiple systems to fit the observed high multiplicity fraction of T Tauri stars (e.g. Mathieu 1994: Patience et al.," However, Solar-type stars (and higher-masses) must still usually form in multiple systems to fit the observed high multiplicity fraction of T Tauri stars (e.g. Mathieu 1994; Patience et al."
 2002: Duchénne et al., 2002; Duchênne et al.
 2007 and Goodwin et al., 2007 and Goodwin et al.
 2007 and references therein)., 2007 and references therein).
similar to that of svnchrotron and SSC! emission maximum observed energies.,similar to that of synchrotron and SSC emission maximum observed energies.
" For electron indices p« 3. ey44,yv cannot exceed significantly the energy at which KN ellects become important and (he scattering cannot be considered elastic."," For electron indices $p < 3 $ , $\epsilon_{peak,KN}$ cannot exceed significantly the energy at which KN effects become important and the scattering cannot be considered elastic."
 For a given seed photon enerev eo ils sels in for electrons with energies 5zz1/e42D., For a given seed photon energy $\epsilon_0$ this sets in for electrons with energies $\gamma\approx 1/\epsilon_0{\cal D}$.
" Selling this limiting value of 5 in equation 6)) we obtain ejoa.Sl/eo. independent of D and 5». provided the system is well into 1ο IN regime. 55De,>1."," Setting this limiting value of $\gamma$ in equation \ref{eq:gmaxkn}) ) we obtain $\epsilon_{peak,KN}\lesssim 1/\epsilon_0$, independent of ${\cal D}$ and $\gamma_2$, provided the system is well into the KN regime, $\gamma_2 {\cal D} \epsilon_0 \gg 1$."
 We demonstrate these points in figure 1.. where we plot the inverse Compton spectral energv distribution for three different observing angles for both the Thomson and INN cases uid for two different. values of 55.," We demonstrate these points in figure \ref{fig1}, where we plot the inverse Compton spectral energy distribution for three different observing angles for both the Thomson and KN cases and for two different values of $\gamma_2$ ."
 We also plot the spectral energy. distribution calculated using the approximation |7=ey for 5;Dey<3/4. 0 otherwise] (e.g. Chiaberge and Ghisellini 1999. Blazejowski et al.," We also plot the spectral energy distribution calculated using the approximation $ \left[ \; \sigma=\sigma_T \right.$ for $ \gamma {\cal D} \epsilon_0< 3/4$, $0$ $\left. \right]$ (e.g. Chiaberge and Ghisellini 1999, Blazejowski et al."
 2000)., 2000).
" In the Thomson case we use (the analvlical expression (10)). while in the INN case we perlorm the integration in equation (3)) numerically,"," In the Thomson case we use the analytical expression \ref{thomsonolo}) ), while in the KN case we perform the integration in equation \ref{eq:sc_int}) ) numerically."
 The Thomson and the Wlein Nishina distributions deviate from each other with the INN spectrum being softer., The Thomson and the Klein Nishina distributions deviate from each other with the KN spectrum being softer.
" Note that the deviation is already significant at €zz101, which corresponds approximately to electrons with Lorentz [actor 5Dz(e/e)!?zz4x10! in the lab."," Note that the deviation is already significant at $\epsilon\approx 10^4$, which corresponds approximately to electrons with Lorentz factor $\gamma {\cal D}\approx(\epsilon/\epsilon_0)^{1/2}\approx 4 \times 10^4$ in the lab."
 frame., frame.
 Therefore. already al 5Deyzz0.2. the Thomson description is inadequate. aud the INN formalism mist be usec.," Therefore, already at $\gamma {\cal D} \epsilon_0 \approx 0.2 $, the Thomson description is inadequate, and the KN formalism must be used."
 Both the maximum and peak energv of the Thomson spectral energy. distribution scale as (53D., Both the maximum and peak energy of the Thomson spectral energy distribution scale as $(\gamma_2{\cal D})^2$.
 Contrary to this behavior. in the KN case the maximum energy scales as 79D. whereas (he peak energy is insensitive {ο variations of both D ancl 55 and it is located αἱ an energy EnrakvnSLey.," Contrary to this behavior, in the KN case the maximum energy scales as $\gamma_2{\cal D}$, whereas the peak energy is insensitive to variations of both ${\cal D}$ and $\gamma_2$ and it is located at an energy $\epsilon_{peak,KN}\lesssim 1/\epsilon_0$."
" The exact value of ej,yv is a function of the electron index p. with steeper electron power laws being characterized bv lower e,,,,,,/(5»& values."," The exact value of $\epsilon_{peak,KN} $ is a function of the electron index $p$, with steeper electron power laws being characterized by lower $\epsilon_{peak,KN} $ values."
 An increase in (he upper cut-off 5» of the electron distribution bv a factor of 10 affects only the steep hieh energv tail of the observed. AN spectral energy. distribution. leaving the peak energy and the peak Iuminosity unchanged.," An increase in the upper cut-off $\gamma_2$ of the electron distribution by a factor of 10 affects only the steep high energy tail of the observed KN spectral energy distribution, leaving the peak energy and the peak luminosity unchanged."
 In. general. as long as the scattering is INN limited ( ?sDey> 1). the peak energy will be insensitive to variations of both 5» and D. in contrast io the Thomson caleulation and the svnchrotron ancl SSC! cases.," In general, as long as the scattering is KN limited ( $\gamma_2{\cal D}\epsilon_0 \gg 1$ ), the peak energy will be insensitive to variations of both $\gamma_2$ and ${\cal D}$, in contrast to the Thomson calculation and the synchrotron and SSC cases."
" The result based on the step function cross section |&=op for 5De,<3/4. 0 otherwise] is practically identical to the Thomson one. up to the cutoff energv L/ej."," The result based on the step function cross section $ \left[ \; \sigma=\sigma_T \right.$ for $ \gamma {\cal D} 
\epsilon_0< 3/4$, $0$ $\left. \right]$ is practically identical to the Thomson one, up to the cutoff energy $1/\epsilon_0$."
 In the case of external Compton scattering of optical-UV photons in blazars. where ει2LOO GeV. the spectrum caleulated under this approximation in theEGRET regime is lor practical purposes the same as that calculated in the Thomson regime.," In the case of external Compton scattering of optical-UV photons in blazars, where $1/\epsilon_0\approx 100$ GeV, the spectrum calculated under this approximation in the regime is for practical purposes the same as that calculated in the Thomson regime."
 As shown in ligure L.. the INN spectral energy distribution resulting [rom a power law electron energy distribution is not a power law. and one cannot assign a unique spectral index to it.," As shown in figure \ref{fig1}, the KN spectral energy distribution resulting from a power law electron energy distribution is not a power law, and one cannot assign a unique spectral index to it."
 The beaming pattern al a given energy is expressed through (he electron index p aud is not a simple function ofthe local spectral index different parts of thespectrum have the same beaming pattern D? independent of the local spectral index., The beaming pattern at a given energy is expressed through the electron index $p$ and is not a simple function ofthe local spectral index — different parts of thespectrum have the same beaming pattern ${\cal D}^{3+p}$ independent of the local spectral index.
 This is in contrast to svnchrotron and SSC emission [rom a power law electron distribution. where the beaming," This is in contrast to synchrotron and SSC emission from a power law electron distribution, where the beaming"
Star formation occurs in dense molecular cloud. cores. and many surveys of such regions have previously been carried out. including the pioneering work of Myers and co-workers (c.g. Benson Myers. 1989. ancl references therein),"Star formation occurs in dense molecular cloud cores, and many surveys of such regions have previously been carried out, including the pioneering work of Myers and co-workers (e.g. Benson Myers 1989 and references therein)."
 ‘They separated. these cloud. cores into those that hacl alreacly formed. stars and. thus contain embedded Young Stellar Objects (YSOs). and those that had. not the so-called sstarless cores (Beichman et al 1986).," They separated these cloud cores into those that had already formed stars and thus contain embedded Young Stellar Objects (YSOs), and those that had not – the so-called `starless cores' (Beichman et al 1986)."
 Ehe starless cores are prime candidates to study observationally the sites of potential future star formation. as thev are believed. to represent the initial conditions for protostellar collapse.," The starless cores are prime candidates to study observationally the sites of potential future star formation, as they are believed to represent the initial conditions for protostellar collapse."
 We have been observing starless cores for a number of years to try to constrain theoretical mocels of protostellar collapse., We have been observing starless cores for a number of years to try to constrain theoretical models of protostellar collapse.
 Ward-Fhompson οἳ al. (, Ward-Thompson et al. (
1994 hereafter Paper 1) showed that many starless cores contain dense central condensations which they named. pre-protostellar cores (or more recentlv ‘pre-stellear cores’ for. brevity).,1994 – hereafter Paper I) showed that many starless cores contain dense central condensations which they named `pre-protostellar cores' (or more recently `pre-stellar cores' for brevity).
 Detailed observational studies of pre-stellar cores offer the opportunity to ascertain the density ancl temperature distribution. within the core. as well as the kinematics and details of the chemistry. including dust-molecule interactions.," Detailed observational studies of pre-stellar cores offer the opportunity to ascertain the density and temperature distribution within the core, as well as the kinematics and details of the chemistry, including dust-molecule interactions."
 ALL of these factors are. thought to. play important roles in governing the way in which a body of eas collapses to form a. protostar., All of these factors are thought to play important roles in governing the way in which a body of gas collapses to form a protostar.
 In Paper Lowe found that the variation of density. (p) with racius (7) in pre-stellar cores is very dillerent from the singular. isothermal. sphere (pxr27 everywhere) originally. suggested by Shu (1977) as the initial conditions for star formation., In Paper I we found that the variation of density $\rho$ ) with radius $r$ ) in pre-stellar cores is very different from the singular isothermal sphere $\rho \propto r^{-2}$ everywhere) originally suggested by Shu (1977) as the initial conditions for star formation.
 Instead the cores appear to have a much Latter density. profile ⋅⋠in the inner. region. (pxr1 ). steepening. towards their edges (px2 r2).," Instead the cores appear to have a much flatter density profile in the inner region $\rho \propto r^{-1}$ ), steepening towards their edges $\rho \propto r^{-2}$ )."
 This was. subsequently confirmedfor the pre-stellar core LIGSOB by André; Ward-Thompson Motte (1996. hereafter Paper 11). and. for other cores by Ward-Thonmpson. Motte André (1999 hereafter Paper LLL).," This was subsequently confirmed for the pre-stellar core L1689B by André,, Ward-Thompson Motte (1996 – hereafter Paper II), and for other cores by Ward-Thompson, Motte André (1999 – hereafter Paper III)."
 Most recently. an ISOCAM study by Jacmann οἱ al. (," Most recently, an ISOCAM study by Bacmann et al. ("
2000) has shown that some cores have very steep edges indeed (pxr 7).,2000) has shown that some cores have very steep edges indeed $\rho \propto r^{-5}$ ).
" In a study of one prestellar core (L1544). ""Tafalla et al. ("," In a study of one prestellar core (L1544), Tafalla et al. ("
1998) discovered. significant large-scale motions of gas. possibly indicating contraction of the core.,"1998) discovered significant large-scale motions of gas, possibly indicating contraction of the core."
 In this paper we present a ο study. of one. pre- core. LIGSOB. which has been previously stuclied at," In this paper we present a $ \rm ^{18}$ O study of one pre-stellar core, L1689B, which has been previously studied at"
Figure 8)).,Figure \ref{ionic1}) ).
 The result we found for the inner rim is closer to the results from the literature., The result we found for the inner rim is closer to the results from the literature.
" Exaniining the ionic distributions of O"" .N . fll and that of in Figure δ and Fieure 9.. we see a region (a diagonal. [rom left to right. that includes the location of the central star) in which ionic fractions coming from the low-ionization species and ) are less abundant when contrasted with the neighbor-nebular portions."," Examining the ionic distributions of $^{0}$ $^{+}$ $^{+}$, $^{+}$ $^{+}$, $^{+}$ $^{+}$, $^{+}$ $^{+}$ and that of $^{++}$ $^{+}$, in Figure \ref{ionic1} and Figure \ref{ionic2}, we see a region (a diagonal, from left to right, that includes the location of the central star) in which ionic fractions coming from the low-ionization species $^{+}$ $^{+}$, $^{+}$ $^{+}$ and $^{+}$ $^{+}$ ) are less abundant when contrasted with the neighbor-nebular portions."
 On the other hand. the map of Η and show values higher than the average at the same region.," On the other hand, the map of $^{++}$ $^{+}$ and $^{+}$ $^{+}$ show values higher than the average at the same region."
" Lt is worth noticing that. even though is à low-ionization specie. a great amount of He"" is also expected to be present in this low ionization nebula."," It is worth noticing that, even though $^{+}$ $^{+}$ is a low-ionization specie, a great amount of $^0$ is also expected to be present in this low ionization nebula."
 In spite of the peculiar behaviour of the low-ionization ions. as well as and the electron. temperature maps (particularly relevant for abundance determinations) have no obvious gradient (see corresponding map in Figure 7)) that would justify this result.," In spite of the peculiar behaviour of the low-ionization ions, as well as $^{++}$ $^{+}$ and $^{+}$ $^{+}$, the electron temperature maps (particularly relevant for abundance determinations) have no obvious gradient (see corresponding map in Figure \ref{temden}) ) that would justify this result."
 Is this higher ionization tunnel of emission in NGC 40 similar to the jet structures of a number of other nebulae?, Is this higher ionization tunnel of emission in NGC 40 similar to the jet structures of a number of other nebulae?
 1n NGC 7009. for instance. two pairs of low-ionization knots are Clearly seen. in addition to a pair of jets. in which the excitation degree is significantlv higher than that of the immediate vicinity. (Goncalvesetal.2003).," In NGC 7009, for instance, two pairs of low-ionization knots are clearly seen, in addition to a pair of jets, in which the excitation degree is significantly higher than that of the immediate vicinity \citep{goncalves03}."
.. Llowever. contrary to what we find [or NGC 40. in the case of NGC 7009 the electron. density of the higher-ionization emission tunnel is a factor of 2 lower than in the other nebular regions.," However, contrary to what we find for NGC 40, in the case of NGC 7009 the electron density of the higher-ionization emission tunnel is a factor of 2 lower than in the other nebular regions."
 But note that in both cases the iis roughly the same throughout the nebula., But note that in both cases the is roughly the same throughout the nebula.
 Concerning the clement abundances of helium in NGC 40. Le1. we found the mean value of 7.08 >.," Concerning the element abundances of helium in NGC 40, He/H, we found the mean value of 7.08 $\times$ $^{-2}$ ."
 This result. has been obtained by summing the αμα ionic abundance maps. and taking its mean value.," This result has been obtained by summing the $^+$ and $^{++}$ ionic abundance maps, and taking its mean value."
 This extremely low total helium abundance can be explained bv the fact that a significant amount of Le? is expected to be present in a low excitation nebula like NGC 40. and lle? was not considered. in the Le/Ll given above.," This extremely low total helium abundance can be explained by the fact that a significant amount of $^0$ is expected to be present in a low excitation nebula like NGC 40, and $^0$ was not considered in the He/H given above."
 ‘Lo circumvent this kine of problem. Zhang&Liu(2003) suggested thatan ICE based on the and — abundances can be used to account for the Ue? abundance. of low excitation PNe.," To circumvent this kind of problem, \citet{zhang03} suggested thatan ICF based on the $^+$ and $^{++}$ abundances can be used to account for the $^0$ abundance of low excitation PNe."
 Using our own data we were not able to calculate as abundance map. nevertheless. if we consider the abundances found. bv. Pottaschetal.(2003) and Liuetal.(200th) (CLable 8)). and the mean value of the map that we calculated: (8.88 10'. in ‘Table 8)). we can determine a more reliable value for the llo total abundance of NGC 40.," Using our own data we were not able to calculate a $^{++}$ abundance map, nevertheless, if we consider the $^{++}$ abundances found by \citet{b17} and \citet{b9} (Table \ref{results}) ), and the mean value of the $^+$ $^{+}$ map that we calculated (8.88 $\times$ $^{-7}$, in Table \ref{results}) ), we can determine a more reliable value for the He total abundance of NGC 40."
 Doing this exercise. we find jp p;29.32 adopting from Pottasch et al. (," Doing this exercise, we find $_{(ICF - P)}$ =9.32 $\times$ $^{-2}$, adopting $^{++}$ $^{+}$ from Pottasch et al. ("
"2003). jc 5,—1.18 + by using from Liu et al. (","2003), and $_{(ICF - L)}$ =1.18 $\times$ $^{-1}$ by using $^{++}$ $^{+}$ from Liu et al. ("
2004b).,2004b).
 These three Hej/ll are shown in Table Ss., These three He/H are shown in Table \ref{results}.
 Notice that the interval of abundances from Pottaschetal.(2003). and. Liuetal.(2004b) contains the mean abundance we found [rom our slit C. if we consider the NS. NI. SIR and SS regions (again. that is not the case for the NN region. because of he contamination from the central star region).," Notice that the interval of $^{++}$ abundances from \citet{b17} and \citet{b9} contains the mean $^{++}$ abundance we found from our slit G, if we consider the NS, NIR, SIR and SS regions (again, that is not the case for the WN region, because of the contamination from the central star region)."
 And. finally. not onlywe believe that 9.32 Sand LIS ! should correspond. to the lower and upper He abundance limits of GC 40. but they are also similar to the previous results ound bv Liuetal. (2004b).. who adopted. the same LCL," And, finally, not onlywe believe that 9.32 $\times$ $^{-2}$ and 1.18 $\times$ $^{-1}$ should correspond to the lower and upper He abundance limits of NGC 40, but they are also similar to the previous results found by \citet{b9}, , who adopted the same ICF"
intermediate redshifts has been in identifving compact red galaxies at these redshifts.,intermediate redshifts has been in identifying compact red galaxies at these redshifts.
 For example. 0.5 kpe at z=0.5 corresponds to 0.087: such galaxies may be unresolved even in LIS surveys.," For example, 0.5 kpc at $z = 0.5$ corresponds to $^{\prime\prime}$; such galaxies may be unresolved even in HST surveys."
 We have implemented a novel approach to find and study intermediate-redshift analogs to the high-: red nugects: we use the SDSS spectroscopic database to find strong gravitational lens candidates that consist of an intermediate-redshift/ carly-twpe galaxy being lensed by a lower-redshift carly-twpe galaxy (we call these carly-tvpe/earlv-tvpe lenses. or 0119).," We have implemented a novel approach to find and study intermediate-redshift analogs to the $z$ red nuggets: we use the SDSS spectroscopic database to find strong gravitational lens candidates that consist of an intermediate-redshift early-type galaxy being lensed by a lower-redshift early-type galaxy (we call these early-type/early-type lenses, or EELs)."
 These natural telescopes provide a unique opportunity to identifv and. study. red nugeets at 2~0.6. as high. magnification is easier to achieve Lor compact sources. (e.g...Marshalletal.2007:Newtonetal.2010) and EVGs are massive.," These natural telescopes provide a unique opportunity to identify and study red nuggets at $z \sim 0.6$, as high magnification is easier to achieve for compact sources \citep[e.g.,][]{marshall,newton} and ETGs are massive."
 Furthermore. the lensing magnification significantly increases the elfective depth of observations (ασ.‘Trea2010).. opening the possibility to explore galaxies of unprecedented conmipactness.," Furthermore, the lensing magnification significantly increases the effective depth of observations \cite[e.g.,][]{treuReview}, opening the possibility to explore galaxies of unprecedented compactness."
 This letter presents the discovery and first analysis of an EEL and demonstrates the unique utility of our approach., This letter presents the discovery and first analysis of an EEL and demonstrates the unique utility of our approach.
 We present the data in Section 2. followed by our lensing and surface brightness fitting in Section 3. and conclude with a cliscussion in Section 4.," We present the data in Section 2, followed by our lensing and surface brightness fitting in Section 3, and conclude with a discussion in Section 4."
" All magnitudes are in the AB svstem. stellar masses are calculated assuming a Salpeter initial mass function (o...Augeretal. 2010a).. and we use a Hat . CDM cosmologv with £34,=0.3 and h=0.7."," All magnitudes are in the AB system, stellar masses are calculated assuming a Salpeter initial mass function \citep[e.g.,][]{augerIMF}, , and we use a flat $\Lambda$ CDM cosmology with $\Omega_{\rm m} = 0.3$ and $h = 0.7$."
 We have used the SDSS spectroscopic database and archive to identily spectra that appear to. be composed of two carly-tvpe galaxy spectra at. cilferent recshifts and are therefore candidate strong gravitational lenses: this selection is similar to that employed by the Sloan Lens ACS (SLACS:δυοetal.2006) survey. although the SLACS survey looked for emission. lines from the background. objects anc therefore. selected late-type sources.," We have used the SDSS spectroscopic database and archive to identify spectra that appear to be composed of two early-type galaxy spectra at different redshifts and are therefore candidate strong gravitational lenses; this selection is similar to that employed by the Sloan Lens ACS \citep[SLACS;][]{slacsi} survey, although the SLACS survey looked for emission lines from the background objects and therefore selected late-type sources."
 “Phe selection method. essentially guarantees that the background. galaxy is intrinsically luminous and therefore massive. as the spectroscopic continuum must be clearly. visible in order to distinguish both the foreground and background redshifts.," The selection method essentially guarantees that the background galaxy is intrinsically luminous and therefore massive, as the spectroscopic continuum must be clearly visible in order to distinguish both the foreground and background redshifts."
 We have observed 7 ELL candidates to date using RC? with the laser guide star adaptive optics (LCOS-AO) system on [xeck. LU and have successfully confirme hat all of the observed. candidates are strong gravitationa enses (Augeretal.2010b).., We have observed 7 EEL candidates to date using NIRC2 with the laser guide star adaptive optics (LGS-AO) system on Keck II and have successfully confirmed that all of the observed candidates are strong gravitational lenses \citep{augerEELs}.
" Here. we focus on the system SDSSJ1347-0101 with lens delleetor recshift =0.39 am ens source redshift 2=0.63. which was observed on 21 Apri 2010 UT in clear skies using a tip-tilt star with magnitude r=16.8 olfset by 56""[rom the lens svstem."," Here we focus on the system SDSSJ1347-0101 with lens deflector redshift $z = 0.39$ and lens source redshift $z = 0.63$, which was observed on 21 April 2010 UT in clear skies using a tip-tilt star with magnitude $r = 16.8$ offset by from the lens system."
 We used the IRC? wide camera (with. pixel ο * ane Y'111 ENLIA resolution curing our observation) with the Wp filter and obtained 30 exposures of length 40s for a tota on-source time of 1200s., We used the NIRC2 wide camera (with pixel scale 04 $^{-1}$ and 11 FWHM resolution during our observation) with the Kp filter and obtained 30 exposures of length 40s for a total on-source time of 1200s.
" Each exposure also includes a star ocated I7""from the lens which we use as the PSE star.", Each exposure also includes a star located from the lens which we use as the PSF star.
 The data were reduced by Datfielding with a sky Lat created. from. the median. of the science. exposures. with all sources masked. and a median. background. was then subtracted from cach image.," The data were reduced by flatfielding with a sky flat created from the median of the science exposures with all sources masked, and a median background was then subtracted from each image."
 These images were resampled toa distortion-corrected [rame and the 30 images were then registered: using eross-correlation and pixel-based techniques which find sub-pixel olfsets between the images., These images were resampled to a distortion-corrected frame and the 30 images were then registered using cross-correlation and pixel-based techniques which find sub-pixel offsets between the images.
 These olfsets and the distortion model were then used to the images onto a common output frame., These offsets and the distortion model were then used to the images onto a common output frame.
 The registration worked very well for the PSE star but we found that the distortion mocel left residual olfsets of up to 0.7 pixels at the lens location. and we therefore re-registered the images with the PSE star masked to obtain an un-smeared [inal image of the lens svstem (Figure 1).," The registration worked very well for the PSF star but we found that the distortion model left residual offsets of up to 0.7 pixels at the lens location, and we therefore re-registered the images with the PSF star masked to obtain an un-smeared final image of the lens system (Figure \ref{F_lens}) )."
 We model the lens surface mass distribution as a singular isothermal ellipsoid. (SUE:e...Ixormannctal.1994). and allow for external shear.," We model the lens surface mass distribution as a singular isothermal ellipsoid \citep[SIE; e.g.,][]{kormann} and allow for external shear."
 The light of the lensing galaxy. is modelled as an elliptical Sersic profile with Sersic index η free to vary between 0.5 and 6. but we do not assume that the mass and the light of the lens are aligned.," The light of the lensing galaxy is modelled as an elliptical Sersic profile with Sersic index $n$ free to vary between 0.5 and 6, but we do not assume that the mass and the light of the lens are aligned."
 The background source was also initially modelled. as a Sersic profile. with Sersic index between 0.5 and 6., The background source was also initially modelled as a Sersic profile with Sersic index between 0.5 and 6.
 We convolve the models with an empirical PSE that was observed: simultaneously with the lensing system and compare the convolved. models with the data., We convolve the models with an empirical PSF that was observed simultaneously with the lensing system and compare the convolved models with the data.
 The best-lit model is obtained. by using a Levenburg-Marquardt optimisation. that minimises the X7. of the difference between the data and the model., The best-fit model is obtained by using a Levenburg-Marquardt optimisation that minimises the $\chi^2$ of the difference between the data and the model.
 The cata are ecncrally well-described by the model. but we find that using a single Sersic component for the source results in a ring of residual lux left in the image (Figure 1)): the amplitude of these residuals is approximately 1.5 to 3 times the noise level.," The data are generally well-described by the model, but we find that using a single Sersic component for the source results in a ring of residual flux left in the image (Figure \ref{F_lens}) ); the amplitude of these residuals is approximately 1.5 to 3 times the noise level."
 We also find that the datado not. provide. precise constraint on n» for the source (they only constrain 7 to be larec. lo. > 3) so we fix the source to have an elliptical de Vaucouleurs profile (n= 4).," We also find that the datado not provide precise constraint on $n$ for the source (they only constrain $n$ to be large, i.e., $n > 3$ ) so we fix the source to have an elliptical de Vaucouleurs profile $n = 4$ )."
 The residual [ux is clearly not associated with the foreground dellector. as adding a second Sersic component does not improve the fit.," The residual flux is clearly not associated with the foreground deflector, as adding a second Sersic component does not improve the fit."
" However. adding a second component to the source surface brightness prolile improves the fit. dramatically, as shown in Figure 1.. and the per-pixel significance of the residuals around the ring is below the noise."," However, adding a second component to the source surface brightness profile improves the fit dramatically, as shown in Figure \ref{F_lens}, and the per-pixel significance of the residuals around the ring is below the noise."
 Lhe best-fit parameters for the lensing mass distribution and the light profiles for the source for both the one- and. two-component models are given in Table 1.., The best-fit parameters for the lensing mass distribution and the light profiles for the source for both the one- and two-component models are given in Table \ref{T_parameters}.
 We find that the foreground. galaxy is well-described bv a single. Sersic component. for the light a SLE for the mass distribution., We find that the foreground galaxy is well-described by a single Sersic component for the light a SIE for the mass distribution.
 The SLE Einstein radius is 07442. which implies a lens velocity dispersion of 210415 km ," The SIE Einstein radius is 42, which implies a lens velocity dispersion of $\pm15$ km $^{-1}$."
This is consistent with the stellar. velocity. dispersion. of 203442 kms 1 that we obtain by fitting velocity-dispersion-broacencd single-burst Bruzual&Charlot(2003). templates to the SDSS spectrum: Figure 2. shows the result of this fit. which we use to decompose the spectrum into lens and sourcecomponents.," This is consistent with the stellar velocity dispersion of $\pm42$ km $^{-1}$ that we obtain by fitting velocity-dispersion-broadened single-burst \citet{bc03} templates to the SDSS spectrum; Figure \ref{F_spectrum} shows the result of this fit, which we use to decompose the spectrum into lens and sourcecomponents."
 Lhe observed lens IXp magnitude Is 17.7 and we use a Druzual&Charlot(2003). instantaneous-burst galaxy template with formation redshift +=3 and solar metallicity to determine rest-f[rame (quantities., The observed lens Kp magnitude is 17.7 and we use a \citet{bc03} instantaneous-burst galaxy template with formation redshift $z = 3$ and solar metallicity to determine rest-frame quantities.
 We find a Ix-band.rest-frame magnitude of 18.4 and a luminosity of Lion.=100773 Ly. with à corresponding stellar mass Aleene=LOM? ALL.," We find a K-bandrest-frame magnitude of 18.4 and a luminosity of $_{\rm K,lens} = 10^{11.4}~L_{\rm K,\odot}$ , with a corresponding stellar mass $_{\rm *,lens} = 10^{11.6}~{\rm M}_\odot$ ."
 We adopt error estimates of 0.1 dex on the luminosity and 0.2 dex on the stellar mass for both the lens and source., We adopt error estimates of 0.1 dex on the luminosity and 0.2 dex on the stellar mass for both the lens and source.
star formation is occurring in unbound molecular cloucds(?)..,star formation is occurring in unbound molecular \citep{Heyeretal2009}.
 Lere we demonstrate that the outcome of a distributed or clustered. population can depend on whether the region is. or is not. globally bound.," Here we demonstrate that the outcome of a distributed or clustered population can depend on whether the region is, or is not, globally bound."
 Cravitationally unbound clouds have been explored. in a series of studies to investigate how this relates to the elliciencv of star formation (??:: ?2)).," Gravitationally unbound clouds have been explored in a series of studies to investigate how this relates to the efficiency of star formation \citealt{ClaBon2004, Clarketal2005}; \citealt*{ClaBonKle2008}) )."
 Low star formation elliciencies are commonly taken to imply that star formation is slow and that molecular clouds are long-lived entities. supported. bv some internal mechanism and lasting for several tens of dynamical times.," Low star formation efficiencies are commonly taken to imply that star formation is slow and that molecular clouds are long-lived entities, supported by some internal mechanism and lasting for several tens of dynamical times."
 In contrast. unbound clouds can also produce low star formation elliciencies on dynamical timescales due to the fact that only a fraction of the cloud becomes gravitationally bound. due to the turbulence and undergoes gravitational collapse and star formation.," In contrast, unbound clouds can also produce low star formation efficiencies on dynamical timescales due to the fact that only a fraction of the cloud becomes gravitationally bound due to the turbulence and undergoes gravitational collapse and star formation."
 In this paper. we explore the importance of the local eravitational binding in one cloud and show that a single cloud. can produce. both a. distributed ancl a clustered population. and a range of star formation elliciencics. depending on the local gravitational binding.," In this paper, we explore the importance of the local gravitational binding in one cloud and show that a single cloud can produce both a distributed and a clustered population, and a range of star formation efficiencies, depending on the local gravitational binding."
 The results. presented here are based. on a. large-scale Smootheed Particle Hvcrodvnanmies (SPLD) simulation of a cvlindrical 10+ mmolecular cloud. LO pe in length and 3 pe in cvlindrical diameter., The results presented here are based on a large-scale Smoothed Particle Hydrodynamics (SPH) simulation of a cylindrical $10^4$ molecular cloud 10 pc in length and 3 pc in cylindrical diameter.
 We have chosen an elongated. cloud rather than the more standard spherical eloud as most molecular clouds are non-sperhical and commonly. elongated. (c.g. Orion A)., We have chosen an elongated cloud rather than the more standard spherical cloud as most molecular clouds are non-sperhical and commonly elongated (e.g. Orion A).
 Such a geometrv can also produce additional structure due to gravitational focussing (2).., Such a geometry can also produce additional structure due to gravitational focussing \citep{HarBur2007}.
 This also allows for the physical properties to be varied. along the cloud. in a straightforward. manner., This also allows for the physical properties to be varied along the cloud in a straightforward manner.
" The cloud has a linear density eradient along its major axis with maximum/minimunm values. at cach end. of the ονμπάσου, 33 percent. high/Iower than the average gas density of 1.35«10 “Vo em."," The cloud has a linear density gradient along its major axis with maximum/minimum values, at each end of the cylinder, $33$ percent high/lower than the average gas density of $ 1.35\times 10^{-20}$ g $^{-3}$."
 Phe gas has internal turbulence following a Larson-tvpe P(&)~&1 power law throughout the cloud. and. is normalised such that the total kinetic energy balances the total gravitational energy in the eloud., The gas has internal turbulence following a Larson-type $P(k) \sim k^{-4}$ power law throughout the cloud and is normalised such that the total kinetic energy balances the total gravitational energy in the cloud.
 This corresponds to a full cloud (10 pe) 3-D velocity dispersion. of order 4.5 km +., This corresponds to a full cloud (10 pc) 3-D velocity dispersion of order 4.5 km $^{-1}$.
 The density eracient applied then results in one end of the cloud being over bound (still super virial) while the other end. of the cloud is unbound., The density gradient applied then results in one end of the cloud being over bound (still super virial) while the other end of the cloud is unbound.
 The cloud is populated with 15.5 million SPL particles on two levels. providing high resolution in regions of interest.," The cloud is populated with 15.5 million SPH particles on two levels, providing high resolution in regions of interest."
 We initially performed a lower resolution run with 5 million SPLIL particles producing an average mass resolution of 0.15M. ?.., We initially performed a lower resolution run with 5 million SPH particles producing an average mass resolution of $0.15 \solm$ \cite{BatBur1997}.
 Upon completion of this low resolution simulation. we used three eriteria to identifv the regions that required higher resolution.," Upon completion of this low resolution simulation, we used three criteria to identify the regions that required higher resolution."
 This included the particles which ormed sinks. and those that were accreted onto sinks.," This included the particles which formed sinks, and those that were accreted onto sinks."
 Lt also included: particles which attained. sulliciently high density such that their local Jeans mass was no longer resolved in he low-resolution run., It also included particles which attained sufficiently high density such that their local Jeans mass was no longer resolved in the low-resolution run.
 ALL of these particles were identified and from the initial conditions of the low resolution run. hey were split into 9. particles cach to create the initial conditions for the high resolution simulations.," All of these particles were identified and from the initial conditions of the low resolution run, they were split into 9 particles each to create the initial conditions for the high resolution simulations."
 Εις particle splitting was performed on the initial conditions to ensure hat the physical quantities of mass. momentum. energy and the energy spectrum were preserved.," This particle splitting was performed on the initial conditions to ensure that the physical quantities of mass, momentum, energy and the energy spectrum were preserved."
 Note that the particle splitting does not introduce finer structure in the turbulent energy spectrum., Note that the particle splitting does not introduce finer structure in the turbulent energy spectrum.
 This produced a mass resolution [or the regions involved in star. formation of 0.0167M.. sullicient to resolve the formation. of higher-mass. brown dwarfs. equivalent to a total number of 4.5Loo SPL particles.," This produced a mass resolution for the regions involved in star formation of $0.0167 \solm$, sufficient to resolve the formation of higher-mass brown dwarfs, equivalent to a total number of $4.5 \times 10^7$ SPH particles."
 The equation of state (below) was specificd in order to ensure that the Jeans mass in the higher resolution run cid not descend below this mass resolution., The equation of state (below) was specified in order to ensure that the Jeans mass in the higher resolution run did not descend below this mass resolution.
 Particle splitting results in a marked. increase in resolution without unmanageable computational costs (??)..," Particle splitting results in a marked increase in resolution without unmanageable computational costs \citep{KitWhi2002,KitWhi2007}."
 Note however some of the unsplit particles. which in the low resolution run neither exceeded their Jeans mass limit nor became involved in the star formation. did σοι aceretecl by the additional stars in the high resolution run.," Note however some of the unsplit particles, which in the low resolution run neither exceeded their Jeans mass limit nor became involved in the star formation, did get accreted by the additional stars in the high resolution run."
 This is to be expected as there are now aclelitional locations of of star formation not present in the low resolution run and these additional sinks will necessarily acerete unsplit particles., This is to be expected as there are now additional locations of of star formation not present in the low resolution run and these additional sinks will necessarily accrete unsplit particles.
" The simulation follows a modified Larson-tvpe equation of state 2? comprised of three barotropic equations of state where and pj=5510Peem""pLegemρω18Boem? "," The simulation follows a modified Larson-type equation of state \cite{Larson2005} comprised of three barotropic equations of state where and $\rho_1= 5.5 \times 10^{-19} {\rm g\ cm}^{-3} , \rho_2=5.5 \times 10^{-15} {\rm g\ cm}^{-3} , \rho_3=2 \times 10^{-13} {\rm g\ cm}^{-3}$ ."
The initial cooling part of the equation of state mimics the clfects of line cooling and ensures that the Jeans mass at the point of fragmentation is appropriate for characteristic stellar mass (??)..," The initial cooling part of the equation of state mimics the effects of line cooling and ensures that the Jeans mass at the point of fragmentation is appropriate for characteristic stellar mass \citep{Jappsenetal2005, BonClaBat2006}."
 The >=1.0 approximates the effect. of dust cooling while the ~=L4 mimics the cllects of an optically thick (to LR radiation) core. although its location at p—5.5.10Meen* at lower densities than is typical. is in order to ensure that the Jeans mass is always Cully resolved and that a single self-gravitating fragment is turned. into a sink particle.," The $\gamma=1.0$ approximates the effect of dust cooling while the $\gamma=1.4$ mimics the effects of an optically thick (to IR radiation) core, although its location at $\rho= 5.5 \times 10^{-15} {\rm g\ cm}^{-3}$, at lower densities than is typical, is in order to ensure that the Jeans mass is always fully resolved and that a single self-gravitating fragment is turned into a sink particle."
 A higher critical density for this optically-thick phase where heating occurs would likely result in an increase in the numbers of low mass objects formed., A higher critical density for this optically-thick phase where heating occurs would likely result in an increase in the numbers of low mass objects formed.
 The physical processes described would be unchanged., The physical processes described would be unchanged.
 The final isothermal phase of the equation of state is simply in order to allow sink-particle formation to occur. which requires a subvirial collapsing fragment.," The final isothermal phase of the equation of state is simply in order to allow sink-particle formation to occur, which requires a subvirial collapsing fragment."
 The initial conditions of the cloud contain SOL thermal Jeans masses CA.7 LLAL.) such that if the cloud. were isothermal. we would expect. of order 900 fragments to form.," The initial conditions of the cloud contain 891 thermal Jeans masses $M_{\rm Jeans} \approx 11 \solm$ ) such that if the cloud were isothermal, we would expect of order 900 fragments to form."
 Star formation in the cloud. is modelled: through the introcluction of sink-particles (2).., Star formation in the cloud is modelled through the introduction of sink-particles \citep*{BatBonPri1995}.
 Sink-particles formation is allowed once the gas density. of a collapsing fragment reaches p=G.8«10 οι. of state ensures that this requires pz2.510Meem , Sink-particles formation is allowed once the gas density of a collapsing fragment reaches $\rho\ge 6.8 \times 10^{-14}$ $^{-3}$ although the equation of state ensures that this requires $\rho\ge 2. \times 10^{-13} {\rm g\ cm}^{-3}$.
The neighbouring SPL particles need. be within a radius of 1.10 pe and that fragment must be subvirial and collapsing., The neighbouring SPH particles need be within a radius of $1. \times 10^{-3}$ pc and that fragment must be subvirial and collapsing.
 Once ereated. the sinks accrete bound gas within 1...10. pe and all gas that comes within 2...10.! pe.," Once created, the sinks accrete bound gas within $1. \times 10^{-3}$ pc and all gas that comes within $2. \times 10^{-4}$ pc."
" The sinks have their mutual gravitational interactions smootheel to 2,«103 pe or 40 au.", The sinks have their mutual gravitational interactions smoothed to $2. \times 10^{-4}$ pc or 40 au.
 No interactions including binary or disc disruptions can occur within this radius., No interactions including binary or disc disruptions can occur within this radius.
 We assume a 100 elliciency of star formation within, We assume a 100 efficiency of star formation within
Since the first direct imaging of a debris disk around by ?.. a dozen other optically thin dust disks have been spatially resolved around nearby main-sequence stars showing an infrared excess (??.andreferencestherem)..,"Since the first direct imaging of a debris disk around by \citet{1984Sci...226.1421S}, a dozen other optically thin dust disks have been spatially resolved around nearby main-sequence stars showing an infrared excess \citep[][and references there
in]{2007ApJ...661L..85K,2006ApJ...650..414S}."
 The images often reveal asymmetric structures and clumps. interpreted as the signature of gravitational perturbations.," The images often reveal asymmetric structures and clumps, interpreted as the signature of gravitational perturbations."
 A planet immersed in à debris disk usually produces structures such as a gap along its orbit. by ejecting particles during close encounters. or density waves (e.g. a one-arm spiral). by modifying the precession rate of the dust particles (?)..," A planet immersed in a debris disk usually produces structures such as a gap along its orbit, by ejecting particles during close encounters, or density waves (e.g. a one-arm spiral), by modifying the precession rate of the dust particles \citep{2005A&A...440..937W}."
 However. such structures cannot explain the observations of clumpy. non-axisymmetric disks (?2).. and resonant mechanisms with unseen planets have been proposedto account for the observed asymmetries (2222)...," However, such structures cannot explain the observations of clumpy, non-axisymmetric disks \citep{2004ASPC..321..305A,2007prpl.conf..573M}, and resonant mechanisms with unseen planets have been proposedto account for the observed asymmetries \citep{2000ApJ...537L.147O,2002ApJ...578L.149Q,2003ApJ...588.1110K,2003ApJ...598.1321W}."
 A particle belongs to a nean motion resonance (MMR) when the particle to planet period ratio is à rational number. 17n with wm and η integers.," A particle belongs to a mean motion resonance (MMR) when the particle to planet period ratio is a rational number, $m:n$ with $m$ and $n$ integers."
 An MMR is located at a semi-major axis & given by άν gnj/ny*. where cy is the planet semi-major axis.," An MMR is located at a semi-major axis $a$ given by $a/a_p=(m/n)^{2/3}$ , where $a_p$ is the planet semi-major axis."
 In the Solar System. forexample. about 15% of the known Kuiper Belt objects. including Pluto. are trapped in the 3:2 resonance with Neptune (?)..," In the Solar System, forexample, about $15\%$ of the known Kuiper Belt objects, including Pluto, are trapped in the $3$ $2$ resonance with Neptune \citep{2007prpl.conf..895C}."
 The interesting property of MMRs for modeling asymmetric disks is that. as explained for example in ?.. resonant objects are not uniformly distributed in azimuth around a star: rather they gather at specific longitudes relative to the perturbing planet and subsequently form clumps.," The interesting property of MMRs for modeling asymmetric disks is that, as explained for example in \citet{2000ssd..book.....M}, resonant objects are not uniformly distributed in azimuth around a star: rather they gather at specific longitudes relative to the perturbing planet and subsequently form clumps."
 This arises from properties specific to MMRs as a given particle trapped in à MMR with a planet undergoes conjunctions with the planet at specific locations along its orbit., This arises from properties specific to MMRs as a given particle trapped in a MMR with a planet undergoes conjunctions with the planet at specific locations along its orbit.
 The particles tend to gather around the most stable orbital configurations that ensure that the conjunctions occur at the maximum relative distance., The particles tend to gather around the most stable orbital configurations that ensure that the conjunctions occur at the maximum relative distance.
 The clumps. which are the result of the collective effects of resonant particles. generally corotate with the planet (?).. while each of these resonant bodies has a different period from that of the planet (except for 1:1 resonant planetesimals): hence the motion of these density waves differs from the orbital motion of the resonant particles.," The clumps, which are the result of the collective effects of resonant particles, generally corotate with the planet \citep{2003ApJ...588.1110K}, while each of these resonant bodies has a different period from that of the planet (except for $1$ $1$ resonant planetesimals): hence the motion of these density waves differs from the orbital motion of the resonant particles."
 However. AMRs are very thin radial structures that usually trap a small number of particles in à given disk.," However, MMRs are very thin radial structures that usually trap a small number of particles in a given disk."
 Therefore. any structure due to MMRs has a high chance of being totally hidden by the emission of the resonant particles. as illustrated in Fig. 1..," Therefore, any structure due to MMRs has a high chance of being totally hidden by the emission of the non-resonant particles, as illustrated in Fig. \ref{withoutMigration}."
 For clumps due to MMRs to be observed. the population of resonant particles must be significantly enhanced by an additional physical process.," For clumps due to MMRs to be observed, the population of resonant particles must be significantly enhanced by an additional physical process."
 Two mechanisms can account for this: Poynting-Robertson (P-R) drag and planet migration., Two mechanisms can account for this: Poynting-Robertson (P-R) drag and planet migration.
 Dust particles that are too large to be ejected from the system by radiation pressure can spiral inward into the star due to P-R drag and to some other minor forces like stellar wind drag ?).., Dust particles that are too large to be ejected from the system by radiation pressure can spiral inward into the star due to P-R drag and to some other minor forces like stellar wind drag \citep[e.g.][]{2006A&A...455..987A}.
 In the course of its inward migration. a dust particle can be trapped into exterior MMRs with a planet. hence increasing the contrast of their asymmetric patterns (??)..," In the course of its inward migration, a dust particle can be trapped into exterior MMRs with a planet, hence increasing the contrast of their asymmetric patterns \citep{2003ApJ...588.1110K,2005ApJ...625..398D}."
 Planet migration. on the other hand. involves particles of all sizes. except those ejected by radiation pressure.," Planet migration, on the other hand, involves particles of all sizes, except those ejected by radiation pressure."
 Many particles can be trapped in MMRs by a planet migrating outward in the disk., Many particles can be trapped in MMRs by a planet migrating outward in the disk.
 Each non-resonant particle crossing an MMR has a chance trapped and subsequently migrating. following the resonance (?)..," Each non-resonant particle crossing an MMR has a chance trapped and subsequently migrating, following the resonance \citep{2003ApJ...598.1321W}."
 Several authors have studied either the effect of P-R drag. or of planet migration. on disk structures. using different methods (analytic. semi-analytic or numerical) and. various planet parameters (mass and orbital eccentricity).," Several authors have studied either the effect of P-R drag, or of planet migration, on disk structures, using different methods (analytic, semi-analytic or numerical) and various planet parameters (mass and orbital eccentricity)."
 A summary of the main previous studies 1s provided in Table 1.., A summary of the main previous studies is provided in Table \ref{previousWorks}. .
 The P-R drag scenario has been extensively studied for a wide range of parameters. while the migrating planet scenario has been investigated only for a planet on a circular orbit by 2...," The P-R drag scenario has been extensively studied for a wide range of parameters, while the migrating planet scenario has been investigated only for a planet on a circular orbit by \citet{2003ApJ...598.1321W}."
 It is thus important to better characterize the latter scenario in order to distinguish which of the two dominates the morphology of debris disks., It is thus important to better characterize the latter scenario in order to distinguish which of the two dominates the morphology of debris disks.
 Moreover. a number of studies (???) have shown that collisions may prevent MMRs from being populated by P-R drag since the collision timescale in massive debris disks might be much shorter than the P-R drag migration timescale.," Moreover, a number of studies \citep{1996Icar..123..168L,2005A&A...433.1007W,2007A&A...462..199K}
 have shown that collisions may prevent MMRs from being populated by P-R drag since the collision timescale in massive debris disks might be much shorter than the P-R drag migration timescale."
 Therefore. we propose in this paper to extensively study the planet migration scenario. using numerical modeling. by generating a synthetic catalog similar to what has been done for the P-R drag scenario using analytical (2) or numerical studies (?)..," Therefore, we propose in this paper to extensively study the planet migration scenario, using numerical modeling, by generating a synthetic catalog similar to what has been done for the P-R drag scenario using analytical \citep{2003ApJ...588.1110K} or numerical studies \citep{2005ApJ...625..398D}."
 We extend the pioneering work done by ? in studying the influence of the planet eccentricity on the visibility of the resonant patterns., We extend the pioneering work done by \citet{2003ApJ...598.1321W} in studying the influence of the planet eccentricity on the visibility of the resonant patterns.
 In Section 3.. we discuss the case of a planet migrating on a cireular or low-eccentricity orbit.," In Section \ref{lowEccOrb}, we discuss the case of a planet migrating on a circular or low-eccentricity orbit."
 In Section 4.. we extend this study to planets on orbits with eccentricities up to 0.7.," In Section \ref{highEccOrb}, , we extend this study to planets on orbits with eccentricities up to $0.7$ ."
 This study is generalized to variousmigration rates and disk initial states in Section 5.. and compared to previous," This study is generalized to variousmigration rates and disk initial states in Section \ref{Generalization}, , and compared to previous"
using the photometric redshift estimates of Caputi et al. (,using the photometric redshift estimates of Caputi et al. (
"2004. 20ἱ5). which will allow us to obtain a more reliable and less model-dependent estimate of their clustering operties than given in RDAOS,.","2004, 2005), which will allow us to obtain a more reliable and less model-dependent estimate of their clustering properties than given in RDA03."
 The angular correlation function. «(8). is a measure of he clustering of galaxies as projected on the plane of the sky.," The angular correlation function, $\omega(\theta)$, is a measure of the clustering of galaxies as projected on the plane of the sky."
 lt is related to themiVreinsic ‘lustering in three dimensions. xwameterised by the correlation radius ro. by means of an integration known as Limber’s formula (see e.g. Efstathiou et al.," It is related to the clustering in three dimensions, parameterised by the correlation radius $r_0$, by means of an integration known as Limber's formula (see e.g. Efstathiou et al."
 1991. RDAOS) If the two-point correlation. function. expressed in proper co-ordinates. £67) is represented by the simple mocel where 52LS (observationally) and ο represents the clustering evolution {ο=ϐ is stable and ο=1.23 is comoving clustering). then Limber's formula gives wl) DS where where ο) is the proper distance and€—3.679 for ~=15.," 1991, RDA03) If the two-point correlation function, expressed in proper co-ordinates, $\xi(r)$ is represented by the simple model where $\gamma\simeq 1.8$ (observationally) and $\epsilon$ represents the clustering evolution $\epsilon=0$ is stable and $\epsilon=-1.2$ is comoving clustering), then Limber's formula gives $\omega(\theta)=A_{\omega}\theta^{-(\gamma-1)}$ , where where $x(z)$ is the proper distance and$C_{\gamma}=3.679$ for $\gamma=1.8$."
 Lenee in order to estimate ry [rom the observable st. model or observed: Ας) is required. and for deep samples. the ry will also depend on e. Llo," Hence in order to estimate $r_0$ from the observable $A_{\omega}$ ,a model or observed $N(z)$ is required, and for deep samples, the $r_0$ will also depend on $\epsilon$."
"wever. we can also express the clustering measured at any redshift in terms of a comoving correlation radius rio. without any assumptions about ο, as in comoving space In this system comoving clustering would be à constan roo ane stable clustering would be rax(1|z) "," However, we can also express the clustering measured at any redshift in terms of a comoving correlation radius $r_{c0}$, without any assumptions about $\epsilon$ , as in comoving space In this system comoving clustering would be a constant $r_{c0}$ and stable clustering would be $r_{c0}\propto(1+z)^{-{2\over 3}}$."
Previously(RDAOS) we calculated the angular correlation function. (0) of the CDES ERGs.," Previously(RDA03) we calculated the angular correlation function, $\omega(\theta)$ of the CDFS ERGs."
We obtainec a 30 detection of clustering at the completeness limit of Wo<21.5. which appeared consistent with the ERG (0) measurements of Dace et al. (,"We obtained a $\sim 3\sigma$ detection of clustering at the completeness limit of $K_{s}\leq 21.5$, which appeared consistent with the ERG $\omega(\theta)$ measurements of Daddi et al. ("
2000). Firth οἱ al. (,"2000), Firth et al. ("
2002) anc Roche et al. (,2002) and Roche et al. (
2002).,2002).
 By combining all these we estimate ro=02.523AAI Alpe for ERGs., By combining all these we estimated $r_{c0}=12.5\pm 1.4 h^{-1}$ Mpc for ERGs.
" However. this estimate is dependent on a model IN(z). taken from a ""merging anc negative density evolution! model. fitted to the EI: number counts without any redshift data."," However, this estimate is dependent on a model $N(z)$, taken from a `merging and negative density evolution' model, fitted to the ERG number counts without any redshift data."
 Furthermore the clustering evolution remains uncetermined., Furthermore the clustering evolution remains undetermined.
 We can now obtain a less model-dependent. estimate of roo. and investigate c. by including redshift cata.," We can now obtain a less model-dependent estimate of $r_{c0}$, and investigate $\epsilon$, by including redshift data."
 We assign o cach ERG a redshift estimate. which for the 16 galaxies in our redshift sample is the €:MOS spectroscopic redshift and for the remainder. the photometric redshift. estimate rom Caputi et al. (," We assign to each ERG a redshift estimate, which for the 16 galaxies in our redshift sample is the GMOS spectroscopic redshift and for the remainder, the photometric redshift estimate from Caputi et al. ("
2004. 2005).,"2004, 2005)."
" Objects with spn,2d are assigned redshifts following Section 4.6 of Caputi ct al. (", Objects with $z_{phot}>4$ are assigned redshifts following Section 4.6 of Caputi et al. (
"2004). in which only two ERGs with A,«22 (one with AN.< 21.5) are accepted as probable z>4 galaxies. anc our of our original sample are reclassified as stars.","2004), in which only two ERGs with $K_{s}<22$ (one with $K_{s}<21.5$ ) are accepted as probable $z>4$ galaxies, and four of our original sample are reclassified as stars."
 Figure 7 shows the clistribution of true/estimatec redshifts for the 175 ERGs brighter than the approximate completeness limit fy.=21.5., Figure 7 shows the distribution of true/estimated redshifts for the 175 ERGs brighter than the approximate completeness limit $K_{s}=21.5$.
 The photometric IN(z) is quite close to the RIXXO3 model. especially at the peak. although more. dispersed. to. lower and higher redshifts. presumably as real galaxies are more varied in their evolution.," The photometric $N(z)$ is quite close to the RDA03 model, especially at the peak, although more dispersed to lower and higher redshifts, presumably as real galaxies are more varied in their evolution."
 The angular correlation functions w(4) were calculated for the CDES ERGs using the same methods as in RDAOS., The angular correlation functions $\omega(\theta)$ were calculated for the CDFS ERGs using the same methods as in RDA03.
 Each (0) was fitted with the function τω7— 12.:24Y (see RDAOS). to obtain a power-law amplitude. ;i..," Each $\omega(\theta)$ was fitted with the function $A_\omega(\theta^{-0.8}-12.24)$ ' (see RDA03), to obtain a power-law amplitude, $A_{\omega}$."
 The errors on the sf. were estimated using the same “bootstrap! method. as RDAOS (essentially repeating the analysis for a series of data catalogs with small regions excluded. and finding the scatter in the resulting estimates)., The errors on the $A_{\omega}$ were estimated using the same `bootstrap' method as RDA03 (essentially repeating the analysis for a series of data catalogs with small regions excluded and finding the scatter in the resulting estimates).
" We first. consider the full A,<21.5 sample of 175 ERGs.", We first consider the full $K_s<21.5$ sample of 175 ERGs.
 From its w(@) amplitude. measurement (Table 6) ancl photometric/spectroscopic /N(z) (Figure 7). Limber's formula οἶνος the comoving correlation radius ray=13.43Sib! Alpe.," From its $\omega(\theta)$ amplitude measurement (Table 6) and photometric/spectroscopic $N(z)$ (Figure 7), Limber's formula gives the comoving correlation radius $r_{c0}=13.13^{+2.12}_{-2.44}\rm h^{-1}$ Mpc."
 This is consistent. with the DAQ3 estimate based. on a model N(2)., This is consistent with the RDA03 estimate based on a model $N(z)$.
 Alternatively io we se 0 this result can be fit with a stable clustering moce with ro=23.91Th Alpe (at z= 0)., Alternatively if we set $\epsilon=0$ this result can be fit with a stable clustering model with $r_0=23.91^{+3.86}_{-4.44}\rm h^{-1}$ Mpc (at $z=0$ ).
 We then recaleulate w(@) for the ERGs divided. into two subsamples in phot/spec redshift., We then recalculate $\omega(\theta)$ for the ERGs divided into two subsamples in phot/spec redshift.
 For both the low anc high redshift subsamples. the w(@) anc IN(z) are usec to derive a comoving ro ClEable 6).," For both the low and high redshift subsamples, the $\omega(\theta)$ and $N(z)$ are used to derive a comoving $r_{c0}$ (Table 6)."
 Dividing the sample reduces the significance of clustering detection. but in most cases i remainedον 2o.," Dividing the sample reduces the significance of clustering detection, but in most cases it remained$>2\sigma$ ."
 We repeat this analysis for redshift dividesab 2= Ld. 16 and LS.," We repeat this analysis for redshift dividesat $z=1.4$ , 1.6 and 1.8."
 The subset w(@) amplitudes are given in Fable 6 anc plotted on Figure S., The subset $\omega(\theta)$ amplitudes are given in Table 6 and plotted on Figure 8.
 Lt can immediately. be seen that the mean of the ra we derive for the low anc high-redshif, It can immediately be seen that the mean of the $r_{c0}$ we derive for the low and high-redshift
"CMDs, respectively.","CMDs, respectively."
" In both figures, solid diamonds correspond to probable counterparts whose distance from the X-ray source falls within the lo X-ray position error."," In both figures, solid diamonds correspond to probable counterparts whose distance from the X-ray source falls within the $1\sigma$ X-ray position error."
 Open diamonds correspond to possible counterparts that have a separation between lo and 1.50 from the X-ray position., Open diamonds correspond to possible counterparts that have a separation between $1\sigma$ and $1.5\sigma$ from the X-ray position.
 Previous studies show that studying X-ray sources on a diagram comparing luminosity to X-ray hardness ratio is an effective diagnostic for source classification (Pooley&Hut2006)., Previous studies show that studying X-ray sources on a diagram comparing luminosity to X-ray hardness ratio is an effective diagnostic for source classification \citep{Pooley06}.
". Hardness ratio here is defined as the number of soft counts (0.2-2.0 keV) divided by the number of hard counts (2.0-6.0 keV) and is essentially an X-ray color, so this diagram can be thought of as an X-ray color-magnitude diagram."," Hardness ratio here is defined as the number of soft counts (0.2–2.0 keV) divided by the number of hard counts (2.0–6.0 keV) and is essentially an X-ray color, so this diagram can be thought of as an X-ray color-magnitude diagram."
" This type of diagnostic separates objects whose X-ray emission mechanisms have characteristically harder spectra, such as cataclysmic variables (CVs), or softer spectra, such as quiescent low- X-ray binaries (qLMXBs)."," This type of diagnostic separates objects whose X-ray emission mechanisms have characteristically harder spectra, such as cataclysmic variables (CVs), or softer spectra, such as quiescent low-mass X-ray binaries (qLMXBs)."
" In Figure 6 we show an X-ray CMD for the 12 sources within the half-light radius of NGC 6819, shown as red squares."," In Figure \ref{xcmd} we show an X-ray CMD for the 12 sources within the half-light radius of NGC 6819, shown as red squares."
" We also show securely identified objects from globular cluster studies of various types as comparison (seePooley&Hut2006,andreferences therein)..", We also show securely identified objects from globular cluster studies of various types as comparison \citep[see][and references therein]{Pooley06}.
" Based on the extensive knowledge and confident identifications of X-ray sources in globular clusters, this diagram can be separated into population I, IL, and III objects."," Based on the extensive knowledge and confident identifications of X-ray sources in globular clusters, this diagram can be separated into population I, II, and III objects."
 The division between population I and II objects is defined for ssources in Pooley&Hut(2006) and has been converted toan ccolor here., The division between population I and II objects is defined for sources in \citet{Pooley06} and has been converted to an color here.
" Although there is some overlap between regions, population I objects are dominated by qLMXBs,"," Although there is some overlap between regions, population I objects are dominated by qLMXBs,"
which has zero central density at op—0. ancl from here on he ring solutions continue.,"which has zero central density at $\rho=0$, and from here on the ring solutions continue."
 In this sequence. in addition o the outer radius pa. the inner radius p; of the ring is also held. fixed.," In this sequence, in addition to the outer radius $\rho\subscr{d}$, the inner radius $\rho\subscr{i}$ of the ring is also held fixed."
 As before. A and © are obtained [rom the ivdrostaties.," As before, $K$ and $\Omega$ are obtained from the hydrostatics."
 The global accuracy of the method. can be ested by comparing the asymptotic behaviour of 7 and w with the total mass and angular momentum of the disc., The global accuracy of the method can be tested by comparing the asymptotic behaviour of $\nu$ and $\omega$ with the total mass and angular momentum of the disc.
 As he spherical radial coordinate r=(p|22)eex Numerically. the evaluation. of AZ ancd at large distances agrees with the values obtained by integration over the dise (18)) and (19)). to within one percent.," As the spherical radial coordinate $r = (\rho^2 + z^2)^{1/2} \rightarrow \infty$ Numerically, the evaluation of $M$ and $J$ at large distances agrees with the values obtained by integration over the disc \ref{J}) ) and \ref{M}) ), to within one percent."
 Only for stronger relativistic disces the agreement. becomes weaker. due to the strong mass concentration in the centre of the disc.," Only for stronger relativistic discs the agreement becomes weaker, due to the strong mass concentration in the centre of the disc."
 Additional test cases for the numerical method. are presented. below in the results section., Additional test cases for the numerical method are presented below in the results section.
 Ideally. any newly developed numerical method needs to be ested against known analvtical solutions.," Ideally, any newly developed numerical method needs to be tested against known analytical solutions."
 Fortunately. there exists a solution in the special case of a Lully relativistic oressure-[ree. dise. (Neugebauer Aleinel L998. 1995).," Fortunately, there exists a solution in the special case of a fully relativistic pressure-free disc (Neugebauer Meinel 1993, 1995)."
 A sequence of dust. disc models were run with a varving central redshift., A sequence of dust disc models were run with a varying central redshift.
 In. Fig., In Fig.
 1 the angular velocity © (solicl-ine. diamonds) and the global quantity AZ. (dotted-line. riangles) are compared. with the analytical solution for different central recshift. z.," 1 the angular velocity $\Omega$ (solid-line, diamonds) and the global quantity $M \Omega$ (dotted-line, triangles) are compared with the analytical solution for different central redshift $z$."
 Phe numerical and: analytical solutions agree very well., The numerical and analytical solutions agree very well.
 Note that the angular velocity € is not a given fixed input parameter. but is determined self-consistently as a Function of z (with fixed outer cise radius pa) during the iterative solution.," Note that the angular velocity $\Omega$ is not a given fixed input parameter, but is determined self-consistently as a function of $z$ (with fixed outer disc radius $\rho\subscr{d}$ ) during the iterative solution."
" The normalized. central redshift 2,=z/(1|z) serves as parameter which measures the strength of relativistic elfects.", The normalized central redshift $z\subscr{n}=z/(1+z)$ serves as parameter which measures the strength of relativistic effects.
" In the Newtonian limit 24=O and in the extreme relativistic limit 2,=I.", In the Newtonian limit $z\subscr{n}=0$ and in the extreme relativistic limit $z\subscr{n}=1$.
 Locally. for the metric potentials. the agreement is very good as well.," Locally, for the metric potentials, the agreement is very good as well."
 The metric potentials clisplavecl in Fig., The metric potentials displayed in Fig.
 2 are those of the line element written in Wevl-Lewis-Papapetrou form which has been used by Neugebauer Meinel (1993)., 2 are those of the line element written in Weyl-Lewis-Papapetrou form which has been used by Neugebauer Meinel (1993).
 They are related to gg. (by The potential D is equal to 1 everywhere. for the dust disc.," They are related to $\nu, \omega, \mu$ by The potential $B$ is equal to 1 everywhere for the dust disc."
 “Phe results are compared for an intermediate redshift 2.97., The results are compared for an intermediate redshift $z=2.97$.
 For the general case. with internal pressure. there exists no analytical solution for a relativistic disc.," For the general case, with internal pressure, there exists no analytical solution for a relativistic disc."
 In the Newtonian limit however. the numerically obtained solutions also agree very well with the known analytic Maclaurin disc solution (24.. 25)) and with the bifureation diagrams found in the Newtonian case (ον 1096).," In the Newtonian limit however, the numerically obtained solutions also agree very well with the known analytic Maclaurin disc solution \ref{newtok}, \ref{newtsig}) ) and with the bifurcation diagrams found in the Newtonian case (Kley 1996)."
 Although a complete test of the numerical approach was not possible. the test cases provide very positive indication as to the reliability of the results.," Although a complete test of the numerical approach was not possible, the test cases provide very positive indication as to the reliability of the results."
 The non-rotating cises with Q=0 are supported purely by internal pressure ancl have. for sequences of a given central," The non-rotating discs with $\Omega=0$ are supported purely by internal pressure and have, for sequences of a given central"
angular velocity ave parallel to the rotational axis.,angular velocity are parallel to the rotational axis.
 To evaluate these results qualitatively. we define a parameter which denotes the morphology of differential rotation.," To evaluate these results quantitatively, we define a parameter which denotes the morphology of differential rotation."
 We call it the Non-Tavlor-Proucdiman parameter (herealter (he NTP parameter). which is expressed as where Oy is the angular velocity of the radiative zone.," We call it the Non-Taylor-Proudman parameter (hereafter the NTP parameter), which is expressed as where $\Omega_0$ is the angular velocity of the radiative zone."
 When the NTP parameter is zero. differential rotation is in the Tavlor-Proudman state.," When the NTP parameter is zero, differential rotation is in the Taylor-Proudman state."
 Conversely. differential rotation is far [rom the Tavlor-Proudiman state with a large absolute value of the NTP parameter.," Conversely, differential rotation is far from the Taylor-Proudman state with a large absolute value of the NTP parameter."
 The value of the NTP parameter with various stellar angular velocities is shown in Fig. 4.., The value of the NTP parameter with various stellar angular velocities is shown in Fig. \ref{npp}.
 The NTP monotonically decreases with increases in stellar angular velocity., The NTP monotonically decreases with increases in stellar angular velocity.
 These results inclicate that with large stellar angular velocity values. dillerential rotation approaches the Tavlor-Prondman state.," These results indicate that with large stellar angular velocity values, differential rotation approaches the Taylor-Proudman state."
 These results are counter-intuitive. however. since we do not expect differential rotation to approach the Tavlor-Proudman state with increasing stellar angular velocity values. since the A effect. which is a driver of the deviation from the Tavlor-Proucdinan state. is proportional to stellar angular velocity. O5.," These results are counter-intuitive, however, since we do not expect differential rotation to approach the Taylor-Proudman state with increasing stellar angular velocity values, since the $\Lambda$ effect, which is a driver of the deviation from the Taylor-Proudman state, is proportional to stellar angular velocity $\Omega_0$."
 These are (he most significant findings of this paper. so hereafter in this section we discuss (hese unexpected results.," These are the most significant findings of this paper, so hereafter in this section we discuss these unexpected results."
 We next discuss the temperature difference between the equator ancl the pole at the base of the convection zone (r=0.11R. )., We next discuss the temperature difference between the equator and the pole at the base of the convection zone $r=0.71R_\odot$ ).
 Since temperature is given as a function of entropy by and il is easier to measure than entropy. we use it here for discussing the thermal structure of the simulation results in the convection zone.," Since temperature is given as a function of entropy by and it is easier to measure than entropy, we use it here for discussing the thermal structure of the simulation results in the convection zone."
 Further. although it is mentioned in 8?? (that entropy gradient is crucial for breaking the Tavlor-Proudiman constraint. the temperature difference can be used as iis proxy.," Further, although it is mentioned in \ref{differential} that entropy gradient is crucial for breaking the Taylor-Proudman constraint, the temperature difference can be used as its proxy."
 Fig., Fig.
 5. shows the relationship, \ref{entropy} shows the relationship
The recent. discovery. of planets orbiting other stars (7exoplanets) has opened a new field of astronomy. with the potential,The recent discovery of planets orbiting other stars (“exoplanets”) has opened a new field of astronomy with the potential
sphere. (hen M4ox£24 and therefore. (he relaxation. time. scalesas /44xrDyflxI4 because the tidal radius scales as £4. l,"sphere, then $M_{\rm cl}\propto
R_{\rm cl}$ and therefore the relaxation time scalesas $t_{\rm rel}\propto r^2/M\propto R_{\rm cl}$ because the tidal radius scales as $R_{\rm cl}$."
lowever. the cluster itself will also evolve dvnaimically.," However, the cluster itself will also evolve dynamically."
 From the Pryor \levlan (1993) cabalog of Galactic globular clusters. the tvpical hall-mass relaxation (ime lor a globular is ~LOS? vy.," From the Pryor Meylan (1993) catalog of Galactic globular clusters, the typical half-mass relaxation time for a globular is $\sim 10^{8-9}$ yr."
" For a cluster with V stars and a crossing lime of fa,=Ra/gea (where oe is (he three-dimensional velocity dispersion of the cluster). the cluster relaxation (ime is FeareLel&(0.L.N∕/InNMau ∣↓⊔↜≼↼↴(e.g.. Binney ↴⊺"," For a cluster with $N$ stars and a crossing time of $t_{\rm cross}
=R_{\rm cl}/\sigma_{\rm cl}$ (where $\sigma_{\rm cl}$ is the three-dimensional velocity dispersion of the cluster), the cluster relaxation time is $t_{\rm rel,cl}\approx (0.1N/\ln N)t_{\rm cross}$ (e.g., Binney Tremaine 1987)."
↕⋅≼↲∐↓≀↧↴↕∐≼↲↓≤∍⋖↽∖⋚⊺↕⋝⋅⊡≻↕⋅≀↧↴∐↕⋟∖⊽∪⊔∐↲↕⋅∐⋯↥⋟∖⊽↕↽≻↥∐↲↕⋅≼↲⋅↼∖⊽∖∫↘⋝∙⊲↓≀↕↴↕∐⇂∕⋅⊲↓−⊓⋝∖∖∖∫↘," For an isothermal sphere, $N\propto R_{\rm cl}$ and $t_{\rm cross}\propto R_{\rm cl}$."
⋝∙⊲↓⋅↴∏⋯⋟∖⊽⋅∕↓⋅≺⋅↥⋡∙⊲↓∖∫↘⋝⋮↓⋅ ," Thus, $t_{\rm rel,cl}\propto R_{\rm cl}^2$."
Once tidal stripping of the cluster begins. therefore. the cluster relaxation (nme will decrease Taster (han (the dynamical friction time.," Once tidal stripping of the cluster begins, therefore, the cluster relaxation time will decrease faster than the dynamical friction time."
 When fee<fap. Cae cluster will disperse and the IMIBIT will be on its own.," When $t_{\rm rel,cl}<t_{\rm df}$, the cluster will disperse and the IMBH will be on its own."
 For (vpical masses aud radii of clusters. (he above simplified treatment would suggest that this will happen when r10 pe.," For typical masses and radii of clusters, the above simplified treatment would suggest that this will happen when $r\sim 10$ pc."
 Given that clusters that form IMDIIs tend to have short relaxation times. there could be à concern that these clusters would disrupt earlier.," Given that clusters that form IMBHs tend to have short relaxation times, there could be a concern that these clusters would disrupt earlier."
 However. simulations by Wim. Figer. Morris (2004) and by A. Gitrrkan F. Rasio Gn preparation) support the suggestion of llansen Milosavljevie (2003) that the presence of an IMDII in the center of a cluster increases (he velocity dispersion οἱ the stars and hence their relaxation time.," However, simulations by Kim, Figer, Morris (2004) and by A. Gürrkan F. Rasio (in preparation) support the suggestion of Hansen Milosavljevic (2003) that the presence of an IMBH in the center of a cluster increases the velocity dispersion of the stars and hence their relaxation time."
 Therefore. it is found numerically that in fact the INIBIT is released αἱ ~lew pc.," Therefore, it is found numerically that in fact the IMBH is released at $\sim$ few pc."
 Thus equation (1) suggests that the IMDILI will take S108vr(o/100kms.D(10*AL./p) to sink to the center.," Thus equation (1) suggests that the IMBH will take $\lta 10^8~{\rm yr} (\sigma/100~{\rm
km~s}^{-1})(10^3\,M_\odot/\mu)$ to sink to the center."
 Clusters (hat start within ~100 pe ol the center will be able to deliver their central intermecliate-mass black holes to the center within a few hundred million vears., Clusters that start within $\sim 100$ pc of the center will be able to deliver their central intermediate-mass black holes to the center within a few hundred million years.
 For completeness. we now discuss another wav in which a cluster could theoretically be dispersed.," For completeness, we now discuss another way in which a cluster could theoretically be dispersed."
 Given that the velocity dispersion of stars in a galactic bulge is much greater than the velocity dispersion of stars in a cluster. passage of bulge stus through the cluster will soften the cluster somewhat. and will eventually cause it (ο evaporate.," Given that the velocity dispersion of stars in a galactic bulge is much greater than the velocity dispersion of stars in a cluster, passage of bulge stars through the cluster will soften the cluster somewhat, and will eventually cause it to evaporate."
 One can show. however. that this effect is unimportant.," One can show, however, that this effect is unimportant."
 From Binnev Tremaine (1987. equation 4-6a). the (vpical change in squared transverse velocity of a particle ofmass m. going al speed v through a cluster of No particles of mass m within a radius J? is where InX~10—20 is a Coulomb logarithan.," From Binney Tremaine (1987, equation 4-6a), the typical change in squared transverse velocity of a particle ofmass $m$ going at speed $v$ through a cluster of $N$ particles of mass $m$ within a radius $R$ is where $\ln\Lambda\sim 10-20$ is a Coulomb logarithm."
" Η we use v=2,44 and assume a cluster velocity dispersionof o2,22 G.Vm/R. then this becomes Because these are softening interactions. we will assume that (he energv of the cluster is alwavs mereased by inae."," If we use $v=\sigma_{\rm gal}$ and assume a cluster velocity dispersionof $\sigma_{\rm cl}^2\approx GNm/R$ , then this becomes Because these are softening interactions, we will assume that the energy of the cluster is always by ${1\over 2}m
\Delta v_\perp^2$ ."
that in six submillimeter galaxies with z > L the dust content of three can be explained by ACB stars. while the remaining three can only be explained by CCSNe.,"that in six submillimeter galaxies with z $>$ 4, the dust content of three can be explained by AGB stars, while the remaining three can only be explained by CCSNe."
 Dust formation in the ejecta of CCSNo can be detected bv certain observational signatures., Dust formation in the ejecta of CCSNe can be detected by certain observational signatures.
 These include a decrease in the optical buuinositv due to dust erains absorbing the visible light. while at the sane time creating an excess in the IR as the eraius re-cuut the liebt at longer wavelengths.," These include a decrease in the optical luminosity due to dust grains absorbing the visible light, while at the same time creating an excess in the IR as the grains re-emit the light at longer wavelengths."
 Lastly. the spectral lines may appear to be asvunuetiic aud blic-shitted as the dust eraius obscure the receding (red) side of the ejecta more so than the approaching (blue) side.," Lastly, the spectral lines may appear to be asymmetric and blue-shifted as the dust grains obscure the receding (red) side of the ejecta more so than the approaching (blue) side."
 All three of these signatures were seen for the first time iu SN 1987À (Lucyetal.1989:Woodenot 1993).. then in SN 2003ed (Suecrinanetal.2006:Moeikle2007)... aud also SN 20010t (Sahuetal.2006:Isotal2009)..," All three of these signatures were seen for the first time in SN 1987A \citep{1989LNP...350..164L,1993ApJS...88..477W}, then in SN 2003gd \citep{2006Sci...313..196S,2007ApJ...665..608M}, and also SN 2004et \citep{2006MNRAS.372.1315S,2009ApJ...704..306K}."
 There have also been several CCSNe in the past few vears that have shown one or two of these indicators of dust formation (IXozasaetal.2009.andreferencestherein).., There have also been several CCSNe in the past few years that have shown one or two of these indicators of dust formation \citep[and references therein]{2009ASPC..414...43K}.
 Although these signatures usually appear between 1 aud 2 vears after the explosion. there has recently been coufirmation of dust forming mach earlier (less than 200 davs) in a few CCSNe with circtuustellar interaction.," Although these signatures usually appear between 1 and 2 years after the explosion, there has recently been confirmation of dust forming much earlier (less than 200 days) in a few CCSNe with circumstellar interaction."
 Normal Type IL RSC progenitors only lose about 0 to 7? M. yr! (Chevalieretal.2006).. which is too tenuous to show any circumstellar medi (CSAD) interaction.," Normal Type II RSG progenitors only lose about $^{-6}$ to $^{-5}$ $_{\sun}$ $^{-1}$ \citep{2006ApJ...641.1029C}, which is too tenuous to show any circumstellar medium (CSM) interaction."
" The progenitors of Type Ilu SNe ou the other haud lose orders of magnitude more material. 7 to + AL, ob (RKRieweetal.2010).. which result in narrow ( 100 lan s 1) cuiissiou lines iu their spectra due to iouization of the pre-existing CSAL which las been excited by the initial flash of the supernova."," The progenitors of Type IIn SNe on the other hand lose orders of magnitude more material, $^{-2}$ to $^{-1}$ $_{\sun}$ $^{-1}$ \citep{2010arXiv1010.2689K}, which result in narrow $\sim$ 100 km $^{-1}$ ) emission lines in their spectra due to ionization of the pre-existing CSM which has been excited by the initial flash of the supernova."
 For example SN 19988 showed dust formation signatures between davs 110 - 268 (Leonardetal.2000).. and SN 2005ip appears to have formed dust both iu the CDS between day. 75-150 and then again in the ejecta after day 750 (Suuithetal.2009:Foxetal. 2009)..," For example SN 1998S showed dust formation signatures between days 140 - 268 \citep{2000ApJ...536..239L}, and SN 2005ip appears to have formed dust both in the CDS between day 75-150 and then again in the ejecta after day 750 \citep{2009ApJ...695.1334S,2009ApJ...691..650F}."
 Although not classified as Type Ilu. the Type Ib/c SN 2006jc also formed dust in the cool deuse shell (CDS) created by the interaction of the ejecta aud the CSM between 50 - 75 days post-explosion (Mattilaetal.2008:Siuith2008). aud the Type TP SN 20070d formed dust sometime between dav 120 - 230 through the same mechanism (Andrewsetal.2010)..," Although not classified as Type IIn, the Type Ib/c SN 2006jc also formed dust in the cool dense shell (CDS) created by the interaction of the ejecta and the CSM between 50 - 75 days post-explosion \citep{2008MNRAS.389..141M,2008ApJ...680..568S} and the Type IIP SN 2007od formed dust sometime between day 120 - 230 through the same mechanism \citep{2010ApJ...715..541A}."
 Iu this paper. we follow the evolution of the Type IIP SN 2007it iu the optical aud IR from day 10 to dav 911.," In this paper, we follow the evolution of the Type IIP SN 2007it in the optical and IR from day 10 to day 944."
 This makes SN 2007it one of only a few Type IP SNe with lone-term and extensive spectral aud photometric observations. along with SN 1990E. SN 19099. SN 1999ei. SN 2002hh. SN 2003ed. SN 2001et. and SN 2005es (Maguirectal.2010.ancrefereucestherein)..," This makes SN 2007it one of only a few Type IIP SNe with long-term and extensive spectral and photometric observations, along with SN 1990E, SN 1999em, SN 1999gi, SN 2002hh, SN 2003gd, SN 2004et, and SN 2005cs \citep[and references therein]{2010MNRAS.tmp..284M}."
 Iu Section 3 we discuss the visible liehteurve evolution. including a possible scattered optical light echo secu at late times.," In Section 3 we discuss the visible lightcurve evolution, including a possible scattered optical light echo seen at late times."
 In Section Lowe preseut the optical spectral evolution aud describe the uuusual spectral evolution of SN 2007t., In Section 4 we present the optical spectral evolution and describe the unusual spectral evolution of SN 2007it.
 The IR lishteurve evolution is discussed iu Section 5. followed by the radiative transfer modeling and SED fitting iu Section 6.," The IR lightcurve evolution is discussed in Section 5, followed by the radiative transfer modeling and SED fitting in Section 6."
 In all four sections we will discuss the evidence that dust has formed in the ejecta of SN 2007it., In all four sections we will discuss the evidence that dust has formed in the ejecta of SN 2007it.
 was discovered In by. BR. Evaus visually on 2007 September 13 with V -— 13.5 imag. (Evansetal.2007:Itagaki2007)..," was discovered in by R. Evans visually on 2007 September 13 with V $\sim$ 13.5 mag. \citep{2007CBET.1065....1E,2007IAUC.8874....3I}."
 Pre-discovery inaeses taken with the All Sky Automated Survey (ASAS-3) coustrain the explosion date between 2007 September L6 (Pojmanski2007).. and for the purposes of this paper we are assume an explosion date of WwXr September 5 (JD 2151318).," Pre-discovery images taken with the All Sky Automated Survey (ASAS-3) constrain the explosion date between 2007 September 4-6 \citep{2007IAUC.8875....1P}, and for the purposes of this paper we are assuming an explosion date of 2007 September 5 (JD 2454348)."
 Tt was. coutirined spectroscopically to be a Type II SN by the Carnegie Supernova Project on 2007 September 15 (Contrerasetal.2007).., It was confirmed spectroscopically to be a Type II SN by the Carnegie Supernova Project on 2007 September 15 \citep{2007CBET.1068....1C}.
 Usine Tillyetal.(2008). which uses distances set bv the 2001 IIST Cepheid dev Project observations. we are adopting a distance of 11.7 Alpe throughout this paper.," Using \citet{2008ApJ...676..184T}, which uses distances set by the 2001 HST Cepheid Key Project observations, we are adopting a distance of 11.7 Mpc throughout this paper."
 However it should be noted that a previous study done by Tully(1988) had sueeested a distance of 16.9 Mpc., However it should be noted that a previous study done by \citet{1988ngc..book.....T} had suggested a distance of 16.9 Mpc.
. We iust. also note here that uo pre-explosion nuages exist of the host galaxwv of SN 20073t., We must also note here that no pre-explosion images exist of the host galaxy of SN 2007it.
 We have obtained visible spectroscopy aud photometry as well as mud-IR photometry of SN 2007t spanning days 107-9L1., We have obtained visible spectroscopy and photometry as well as mid-IR photometry of SN 2007it spanning days 107-944.
 Lists of these observations are presented iu Tables 1 aud 2., Lists of these observations are presented in Tables 1 and 2.
 Optical imaging was obtained in Joliusou-Cousins BVI with the SMARTS consortimm 1.31 telescope at Cerro Tololo Tuter-Aimierican Observatory (οτο). Chile.," Optical imaging was obtained in Johnson-Cousins BVI with the SMARTS consortium 1.3m telescope at Cerro Tololo Inter-American Observatory (CTIO), Chile."
 All nuages were pipeline reduced. shifted. aud stacked.," All images were pipeline reduced, shifted, and stacked."
 Tnaging and spectra were also obtained with CAIOS/Cemini South (CS-2008A-O0-2|. GS-2008B-O-15. GS-2009A-O-I9. CS-2010A-DD-3).," Imaging and spectra were also obtained with GMOS/Gemini South (GS-2008A-Q-24, GS-2008B-Q-45, GS-2009A-Q-49, GS-2010A-DD-3)."
 The er images were reduced aud stacked using the IRAE package., The $^{\prime}$ $^{\prime}$ $^{\prime}$ images were reduced and stacked using the IRAF package.
 The instrumental ας magnitudes were transformed to standard Johuson-Cousius WRI (Welchetal.2007:Fukugita 1996)..," The instrumental $^{\prime}$ $^{\prime}$ $^{\prime}$ magnitudes were transformed to standard Johnson-Cousins VRI \citep{2007ApJ...669..525W,1996AJ....111.1748F}."
 For each might the transformation involved a least-squares fit with a floating zero point., For each night the transformation involved a least-squares fit with a floating zero point.
 Oue epoch of photometry was obtained with the WEPC2/PC1 camera on UST in the F150W. E606W. and FalWW filters.," One epoch of photometry was obtained with the WFPC2/PC1 camera on HST in the F450W, F606W, and F814W filters."
" These images were delivered pipeline reduced. but undrizzled. aud stacking auc cosmic rav removal was accomplished using the Pyrat taskmultidricede,."," These images were delivered pipeline reduced, but undrizzled, and stacking and cosmic ray removal was accomplished using the Pyraf task."
 Transformation iuto the standard Joliusou- BV was doue using methods outlined by IIoltzuinetal.(1995).., Transformation into the standard Johnson-Cousins $BVI$ was done using methods outlined by \citet{1995PASP..107.1065H}.
 Late time images were obtained with the Wide Field Ciimoera AVFC) ou IIST/ÀACS using he F135W. F60GW. and FSIIW filters.," Late time images were obtained with the Wide Field Camera (WFC) on HST/ACS using the F435W, F606W, and F814W filters."
 These images were pipeline reduced. mceludiug drizzling aud cosmic rav renioval. aud transformations to the Jolinsou-C'ousius DV system were accomplished using methods outlined w SimianIetal.(2005).," These images were pipeline reduced, including drizzling and cosmic ray removal, and transformations to the Johnson-Cousins $BVI$ system were accomplished using methods outlined by \citet{2005PASP..117.1049S}."
 A BVRI photometric sequence of tertiary. standard stars (shown in Figure 1) was derived for the SN 2007it field. using the same method as Audrewsctal.(2010)..," A $BVRI$ photometric sequence of tertiary standard stars (shown in Figure 1) was derived for the SN 2007it field, using the same method as \cite{2010ApJ...715..541A}."
 The BVRI maguitudes for these standards are located im Table 3., The $BVRI$ magnitudes for these standards are located in Table 3.
 The BVRI leltcurves of SN 2007it are shown in Figure 2 and the absolute V magnitude is shown in conrparison with other simile Type ID SNe in Figure 3., The $BVRI$ lightcurves of SN 2007it are shown in Figure 2 and the absolute V magnitude is shown in comparison with other similar Type II SNe in Figure 3.
 Early time photometry of SN 2007it from davs 9-20 (shown in Figures 2 and 3) was obtained from the Caruceic Supernova Project., Early time photometry of SN 2007it from days 9-20 (shown in Figures 2 and 3) was obtained from the Carnegie Supernova Project.
 The discrepancies between he SMARTS and Cemini I iiguitudes are likely due to he bandpass of the Cousins I filter covering part of the Ca IL TR-triplet around that is not covered bv the Gemini i' filter., The discrepancies between the SMARTS and Gemini I magnitudes are likely due to the bandpass of the Cousins I filter covering part of the Ca II IR-triplet around that is not covered by the Gemini $^{\prime}$ filter.
 This would cause the SNARTS photometry to appear brighter due o the added Ca II flux., This would cause the SMARTS photometry to appear brighter due to the added Ca II flux.
 Cucertaiutics for the Comin photometry were calculated by adding im quadrature he transformation unucertaintv quoted in Welchetal. (2007).. photon statistics. and the zero point deviation of," Uncertainties for the Gemini photometry were calculated by adding in quadrature the transformation uncertainty quoted in \citet{2007ApJ...669..525W}, , photon statistics, and the zero point deviation of"
in the same reference [rame.,in the same reference frame.
 So. the orientations of the mantle and the cavity are the same. à misalignment of their principal axes would require to consider the mantle as elastic. this is beyond the scope of the paper.," So, the orientations of the mantle and the cavity are the same, a misalignment of their principal axes would require to consider the mantle as elastic, this is beyond the scope of the paper."
" As for the whole Mercury. we have ο<choxD,€."," As for the whole Mercury, we have $0<A_c\leq B_c \leq C_c$."
" In this way. the principal moments of inertia of the mantle are respectively 2b,=24ul. D,-—b D.andC€,—€C Phe principal elliptical radii of the cavity are written respectively1 e. b. 6. vielding5 where p is the density of mass of the Iuid core. the integration being performed over the volume of the core."," In this way, the principal moments of inertia of the mantle are respectively $A_m=A-A_c$ , $B_m=B-B_c$ and $C_m=C-C_c$ The principal elliptical radii of the cavity are written respectively $a$ , $b$, $c$, yielding where $\rho$ is the density of mass of the fluid core, the integration being performed over the volume of the core."
 A Hamiltonian formulation of such a problem is usually composed of a kinetic energy ancl a disturbing potential. here the solar perturbation.," A Hamiltonian formulation of such a problem is usually composed of a kinetic energy and a disturbing potential, here the solar perturbation."
 Therefore. we consider every internal process. as the core-mantle interactions in our case. as part of the kinetic energv of Mercury.," Therefore, we consider every internal process, as the core-mantle interactions in our case, as part of the kinetic energy of Mercury."
 This section is wiclely inspired from Lienrarcl(2008)., This section is widely inspired from \citet{h08}.
. The components (ej.σον03) of the velocity field at the location wr; inside the liquid core. in the frame of the principal axes of inertia of the mantle. are assumed to be: (uw.69.o65) are the components of the angular velocity of the mantle with respect to an inertial frame. ancl the vector of coordinates (74.45. 05)specifies the velocity field of the core with respect to the moving mantle.," The components $(v_1,v_2,v_3)$ of the velocity field at the location $x_i$ inside the liquid core, in the frame of the principal axes of inertia of the mantle, are assumed to be: where $(\omega_1,\omega_2,\omega_3)$ are the components of the angular velocity of the mantle with respect to an inertial frame, and the vector of coordinates $(\nu_1,\nu_2,\nu_3)$ specifies the velocity field of the core with respect to the moving mantle."
 The angular momentum of the core Nfz‘ is obtained by: and the result. is: We now set the following quantities: and wecan wrlte: while theangular momentum of the mantle is, The angular momentum of the core $\vec{N'_c}$ is obtained by: and the result is: We now set the following quantities: and wecan write: while theangular momentum of the mantle is
an almost perpendicular orientation to the object.,an almost perpendicular orientation to the object.
 The large disk shows to be Keplerian and with a contracting velocity of about a few km s! as revealed by ?.., The large disk shows to be Keplerian and with a contracting velocity of about a few km $^{-1}$ as revealed by \citet[][]{zapataetal2009}.
" The models presented in Figure 4 were obtained using a slightly different PA. = 30°, inclination angle of 7=25°, a smaller size (3000 AU), and without an inner cavity than in ?.."," The models presented in Figure 4 were obtained using a slightly different P.A. = $^\circ$, inclination angle of $^\circ$, a smaller size (3000 AU), and without an inner cavity than in \citet[][]{zapataetal2009}."
" In ? and here, we have modeled a contracting flattened disk in Keplerian rotation with a central hole, using the disk parametrization [rom Guilloteau, Dutrey Simon (1999),"," In \citet[][]{zapataetal2009} and here, we have modeled a contracting flattened disk in Keplerian rotation with a central hole, using the disk parametrization from Guilloteau, Dutrey Simon (1999)."
 The contraction is assumed to have the functional form of free-fall (i.e. Vir « TA with a reference velocity at the reference radius.," The contraction is assumed to have the functional form of free-fall (i.e. $_{inf}$ $\propto$ $\frac{1}{\sqrt r}$ ), with a reference velocity at the reference radius."
" However, our resolution 1s insufficient to determine the exact luncüonal form."," However, our resolution is insufficient to determine the exact functional form."
 The model is for the same molecules and transitions., The model is for the same molecules and transitions.
 A better fit than all other trials in our recurrence was found until we obtained similar structures in our model to those imaged (Figure 4)., A better fit than all other trials in our recurrence was found until we obtained similar structures in our model to those imaged (Figure 4).
 Most of the physical parameters in the model were constrained in the process., Most of the physical parameters in the model were constrained in the process.
 The model fits the observations reasonably well., The model fits the observations reasonably well.
" In particular, the molecules HCOCH?OH(062 [349-62 12.50) and HC3N(38-37) (v, ZO) revealed the possible presence of a warm companion located to the northeast of the disk (Figure 2)."," In particular, the molecules $_2$ $_{13,49}$ $_{12,50}$ ) and $_3$ N(38-37) $\nu_t$ =0) revealed the possible presence of a warm companion located to the northeast of the disk (Figure 2)."
" We suggest that the companion could be a consequence of disk fragmentation due gravitational instabiliues because the disk 15 extremely large, see lor a reference of this phenomenon ??.,"," We suggest that the companion could be a consequence of disk fragmentation due gravitational instabilities because the disk is extremely large, see for a reference of this phenomenon \citet{kra2006,kru2009}."
 The mululayer disk imaged in this paper reveals a possible link between the Hyper/Ultra-compact HII regions and the hot cores., The multilayer disk imaged in this paper reveals a possible link between the Hyper/Ultra-compact HII regions and the hot cores.
 These observations suggest a possible sequence on the l'ormation of massive stars., These observations suggest a possible sequence on the formation of massive stars.
 We present this simple sequence in Figure 7. and discuss it as follows:," We present this simple sequence in Figure 7, and discuss it as follows:"
simulation to that used in Steidel et al. (,simulation to that used in Steidel et al. (
1997) to facilitate comparison.,1997) to facilitate comparison.
 We can summarise the conclusions as follows: We have shown that the observations of strong clustering of galaxies at high redshifts are not in conlliet with the popular models of structure formation., We can summarise the conclusions as follows: We have shown that the observations of strong clustering of galaxies at high redshifts are not in conflict with the popular models of structure formation.
 We have demonstrated. this in two clilferent wavs: first by showing that the bias can indeed be very [large at carly times., We have demonstrated this in two different ways: first by showing that the bias can indeed be very large at early times.
 We have also generated svnthetic observations in a [ew models and have. shown that the frequeney of occurrence of large concentrations of galaxies is compatible with observations., We have also generated synthetic observations in a few models and have shown that the frequency of occurrence of large concentrations of galaxies is compatible with observations.
 Fie.2 suggests that still larger structures maybe found in future searches., Fig.2 suggests that still larger structures maybe found in future searches.
 The clistribution of sizes of largest structures in surveys at high recdshif both angular size and the extent in redshift may be used to discriminate between cdillerent mocels., The distribution of sizes of largest structures in surveys at high redshift – both angular size and the extent in redshift – may be used to discriminate between different models.
 Strong clustering of galaxies at. high redshifts implies that the galaxy clustering evolves in a very dilferent manner as compared to clustering in the underlying mass distribution., Strong clustering of galaxies at high redshifts implies that the galaxy clustering evolves in a very different manner as compared to clustering in the underlying mass distribution.
 A detailed study of the evolution of halo clustering and its implications for galaxy clustering has been presented elsewhere (Bagla1997).., A detailed study of the evolution of halo clustering and its implications for galaxy clustering has been presented elsewhere \cite{evolclus}.
 ] thank Max. Pettini for drawing my attention to this observation., I thank Max Pettini for drawing my attention to this observation.
 Lacknowledge the support of PPARC fellowship at the Institute of Astrononiv., I acknowledge the support of PPARC fellowship at the Institute of Astronomy.
equilibrium stratifications. is more likely to be responsible.,"equilibrium stratifications, is more likely to be responsible."
 Indeed. equilibrium solutions can be very different from the stratifications encountered in real stars. which result from non-linear. time-dependent processes. with a competition between several physical processes (atomic diffusion. inhomogeneous mass-loss. complex magnetic geometries. NLTE effects. turbulence. etc.).," Indeed, equilibrium solutions can be very different from the stratifications encountered in real stars, which result from non-linear, time-dependent processes, with a competition between several physical processes (atomic diffusion, inhomogeneous mass-loss, complex magnetic geometries, NLTE effects, turbulence, etc.)."
 The present study constitutes one more step toward the detailed modelling of magnetic atmospheres. but for the first time in this quest. the results we obtain can be compared with observations.," The present study constitutes one more step toward the detailed modelling of magnetic atmospheres, but for the first time in this quest, the results we obtain can be compared with observations."
 Time-dependent atomic diffusion is the next step. which we shall address in the near future.," Time-dependent atomic diffusion is the next step, which we shall address in the near future."
the bottom left one the ACDME?2 model anc the bottom right one the ACDMC2 moclel.,the bottom left one the $\Lambda$ CDMF2 model and the bottom right one the $\Lambda$ CDMC2 model.
 In each cosmology there is a strong and systematic almost linear relation between logAl and logry: the ]xormendy. relation appears to be a good. description. for all situations., In each cosmology there is a strong and systematic almost linear relation between $\log{M}$ and $\log{r_{h}}$: the Kormendy relation appears to be a good description for all situations.
" A visual comparison between SCDAL relation (top left. panel). the ACDAIO2 relation (top right. panel) and the ACDAIP? relation (bottom left panel) shows that clusters of comparable mass have a larger size in the low £8,, cosmology than in the ones with a higher density value."," A visual comparison between SCDM relation (top left panel), the $\Lambda$ CDMO2 relation (top right panel) and the $\Lambda$ CDMF2 relation (bottom left panel) shows that clusters of comparable mass have a larger size in the low $\Omega_{m}$ cosmology than in the ones with a higher density value."
 In other words. clusters are more compact in the SCDAL cosmology.," In other words, clusters are more compact in the SCDM cosmology."
" Not unexpectedly we find objects of a higher density in higher ©,,, mocels.", Not unexpectedly we find objects of a higher density in higher $\Omega_{m}$ models.
 When fitting the plotted point. distributions.we infer the parameter values listed in Table 3..," When fitting the plotted point distributions,we infer the parameter values listed in Table \ref{table:scaling_harm}."
 In each of the panels in Fig., In each of the panels in Fig.
 8 we plotted the linear fits for all of the four depicted cosmologies., \ref{fig:sr_korm} we plotted the linear fits for all of the four depicted cosmologies.
 We find similar slopes for all cosmologies. in the order of e0.36—0.38.," We find similar slopes for all cosmologies, in the order of $a\sim0.36-0.38$."
 Phis seems to imply that the mean density ροκM 1. more massive halos have a slightLy lower average density (see also Lanzonictal. (2004)))., This seems to imply that the mean density $\langle\rho(r_{h})\rangle \propto M^{-0.1}$ : more massive halos have a slightly lower average density (see also \cite{lanzoni04}) ).
 To investigate the dependence of the Wormendsy paranicter ( on the cosmology in Fig., To investigate the dependence of the Kormendy parameter $a$ on the cosmology in Fig.
" 4 we have plotted the slope e as a function of the average mass density. parameter. ©, (top panel). as a function of the cosmological constant Oy (central panel) and as a function of the cosmic curvature. in terms of QO,,,;=O,,|Ox (lower panel)."," \ref{fig:oms_mr} we have plotted the slope $a$ as a function of the average mass density parameter $\Omega_{m}$ (top panel), as a function of the cosmological constant $\Omega_{\Lambda}$ (central panel) and as a function of the cosmic curvature, in terms of $\Omega_{total}=\Omega_{m}+\Omega_{\Lambda}$ (lower panel)."
 There is no evidence for any systematic trends. of the Ixormendy parameter as a function of cosmology., There is no evidence for any systematic trends of the Kormendy parameter as a function of cosmology.
 No evidence for an influence of either cosmic density ο and 4 on the internal structure of the halos could be detected., No evidence for an influence of either cosmic density $\Omega_m$ and $\Omega_{\Lambda}$ on the internal structure of the halos could be detected.
 Fig., Fig.
 ο shows the Faber-Jackson relation: the relation between the mass AZ ancl the velocity clispersion a. of the cluster halos., \ref{fig:sr_fj} shows the Faber-Jackson relation: the relation between the mass $M$ and the velocity dispersion $\sigma_v$ of the cluster halos.
 Like in Fig. 3..," Like in Fig. \ref{fig:sr_korm},"
 cach of the four panels, each of the four panels
 , 
In standard stellar models. it is assumed that there are no rotation and magnetic fields.,"In standard stellar models, it is assumed that there are no rotation and magnetic fields."
 Although this framework is strongly supported by helioseismology. recent advances in the study of solar structure shows that differences exist between the Sun and this model.," Although this framework is strongly supported by helioseismology, recent advances in the study of solar structure shows that differences exist between the Sun and this model."
 Those differences are small and display a very interesting systematic behavior. which ts far from satisfactory. (Christensen-Dalsgaard. 2002)).," Those differences are small and display a very interesting systematic behavior, which is far from satisfactory (Christensen-Dalsgaard \cite{Christensen02}) )."
 The most striking difference is the bump in the sound speed just beneath the convection zone., The most striking difference is the bump in the sound speed just beneath the convection zone.
 Noting both ο«Τμ and the µ-gradient caused by microscopic diffusion and element settling in the radiative region. Gough et al. (1996))," Noting both $c^2\propto T/\mu$ and the $\mu$ -gradient caused by microscopic diffusion and element settling in the radiative region, Gough et al. \cite{Gough96}) )"
 and Christensen-Dalsgaard et al. (1996:; 2002)), and Christensen-Dalsgaard et al. \cite{Christensen96}; \cite{Christensen02}) )
 argued that material mixing may be important but has been neglected., argued that material mixing may be important but has been neglected.
 Heliosemmology also shows that rotation is almost uniform in the solar radiative region: the Sun has a slow rotation core. the angular velocity Q has a small radial gradient and large latitudinal gradient in the convective zone. and the radial angular velocity gradient is positive at low latitudes and negative at high latitudes in the tachocline (Schou et al. 1998:;," Helioseimology also shows that rotation is almost uniform in the solar radiative region: the Sun has a slow rotation core, the angular velocity $\Omega$ has a small radial gradient and large latitudinal gradient in the convective zone, and the radial angular velocity gradient is positive at low latitudes and negative at high latitudes in the tachocline (Schou et al. \cite{Schou};"
 Chaplin et al. 1999))., Chaplin et al. \cite{Chaplin}) ).
 But the calculations of rotational models show that the sun has a fast rotation core and a large gradient of the rotation rate in the radiative region (Pinsonneault et al. 1989:; , But the calculations of rotational models show that the sun has a fast rotation core and a large gradient of the rotation rate in the radiative region (Pinsonneault et al. \cite{Pinsonneault}; ;
Charboyer et al. 1995).," Charboyer et al. \cite{Chaboyer95}) ),"
 which disagrees with the helioseismie results., which disagrees with the helioseismic results.
 Thompson et al. (2003)), Thompson et al. \cite{Thompson}) )
 argues that some mechanisms of angular momentum transport may be missed in these models., argues that some mechanisms of angular momentum transport may be missed in these models.
 Magnetic. and gravity waves mechanisms have been proposed: however. what mechanisms are causing the nearly uniform rotation in the radiative region are poorly understood.," Magnetic and gravity waves mechanisms have been proposed; however, what mechanisms are causing the nearly uniform rotation in the radiative region are poorly understood."
 Rotation is a property that virtually all. stars possess., Rotation is a property that virtually all stars possess.
 Rotation affects stellar structure mainly in two ways., Rotation affects stellar structure mainly in two ways.
 The first is an immediately dynamical effect caused by centrifugal acceleration of the hydrostatic balance., The first is an immediately dynamical effect caused by centrifugal acceleration of the hydrostatic balance.
 In most cases. however. this effect is modest and can be included through modifying the equations of stellar structure.," In most cases, however, this effect is modest and can be included through modifying the equations of stellar structure."
 Although the equations of stellar structure of a rotating star are three-dimensional. the method of Kippenhahn Thomas (1970)). which uses the mass contained within an equipotential surface. My. as an independent variable. allows a one-dimensional evolution code to be modified to incorporate the hydrostatic effects of rotation.," Although the equations of stellar structure of a rotating star are three-dimensional, the method of Kippenhahn Thomas \cite{Kippenhahn70}) ), which uses the mass contained within an equipotential surface, $M_{\Psi}$, as an independent variable, allows a one-dimensional evolution code to be modified to incorporate the hydrostatic effects of rotation."
 This method was modified by Endal Sofia (1976)) and Meynet Maeder (1997)) to apply to shellular rotation (Zahn 1992)). a rotation rate that depends only on the radial coordinate r to a first approximation.," This method was modified by Endal Sofia \cite{Endal76}) ) and Meynet Maeder \cite{ Meynet}) ) to apply to shellular rotation (Zahn \cite{Zahn92}) ), a rotation rate that depends only on the radial coordinate $r$ to a first approximation."
 The other way ts an effect arising from the redistribution of chemical elements due to the instabilities caused by rotation., The other way is an effect arising from the redistribution of chemical elements due to the instabilities caused by rotation.
 This effect is much more important and it has been studied by many investigators (Endal Sofia 1978:: Pinsonneault et al. 1989::, This effect is much more important and it has been studied by many investigators (Endal Sofia \cite{Endal78}; ; Pinsonneault et al. \cite{Pinsonneault};
 Chaboyer Zahn 1992:; Zahn 1992:: Meynet Maeder 1997:; Maeder 1997:: Maeder Zahn 1998:: Maeder Meynet 2000: Huang 2004a.. 2004b)).," Chaboyer Zahn \cite{Chaboyer92}; Zahn \cite{Zahn92}; ; Meynet Maeder \cite{Meynet}; Maeder \cite{Maeder97}; Maeder Zahn \cite{Maeder98}; Maeder Meynet \cite{Maeder00}; Huang \cite{Huang04a}, \cite{Huang04b}) )."
 The method of Kippenhahn Thomas (1970)) as modified by Meynet Maeder (1997)) is used in our model., The method of Kippenhahn Thomas \cite{Kippenhahn70}) ) as modified by Meynet Maeder \cite{Meynet}) ) is used in our model.
 Magnetic fields are another property of stars., Magnetic fields are another property of stars.
 Their effects on a star create a complicated problem., Their effects on a star create a complicated problem.
 The magnetic field ts involved in most problems in astrophysics., The magnetic field is involved in most problems in astrophysics.
 But the generatior of magnetic fields is still a controversial problem., But the generation of magnetic fields is still a controversial problem.
 They may be fossil fields (Cowling 1945:; Moss 1987:: Braithwaite 2004)). which are remnants of the star’s formation. or may be generated by a convective stellar dynamo (Parker 1979:; Charbonneau AacGregor 2001)) in the convective zone or generated by a Tayler-Spruit dynamo (Pitts Tayler 1986: Spuit 2002)) 11 a differential rotation star.," They may be fossil fields (Cowling \cite{Cowling}; Moss \cite{Moss}; ; Braithwaite \cite{Braithwaite}) ), which are remnants of the star's formation, or may be generated by a convective stellar dynamo (Parker \cite{Parker}; Charbonneau MacGregor \cite{Charbonneau01}) ) in the convective zone or generated by a Tayler-Spruit dynamo (Pitts Tayler \cite{Pitts}; Spuit \cite{Spruit02}) ) in a differential rotation star."
 In this paper we assumed that the nagnetic fieldsexist., In this paper we assumed that the magnetic fieldsexist.
 We only consider the process of magnetic angular momentum transport and material mixing., We only consider the process of magnetic angular momentum transport and material mixing.
Although themagnetic angular momentum transport has beentreated by nany investigators (Charbonneau,Although themagnetic angular momentum transport has beentreated by many investigators (Charbonneau
al DDO. Leide de Bond. Toomas Ixarmo anc Archie. de ticleler. for their help.,"at DDO, Heide de Bond, Toomas Karmo and Archie de Ridder, for their help."
 The research made. use of the SIMDAD database. operated. at. the CDS. Strasbourg. France. ancl accessible hrough the Canadian Astronomy Data Centre. which is operated by the Herzberg Institute of Astrophysics. National tescarch Council of Canada.," The research made use of the SIMBAD database, operated at the CDS, Strasbourg, France and accessible through the Canadian Astronomy Data Centre, which is operated by the Herzberg Institute of Astrophysics, National Research Council of Canada."
 This research made also use of he Washington Double Star (WDS) Catalog maintained at he U.S. Naval Observatory., This research made also use of the Washington Double Star (WDS) Catalog maintained at the U.S. Naval Observatory.
analysis.,analysis.
 Tuspection of Figure 3(a) shows considerable overlap in the metallicities of the central H HH regious between tlie eas-celicient and. gas-normial galaxies in the Pegasus cluster., Inspection of Figure \ref{logo} shows considerable overlap in the metallicities of the central H II regions between the gas-deficient and gas-normal galaxies in the Pegasus cluster.
 However. Figure l(a) shows a significant trend of increasing meau log(O/H) with DEF.," However, Figure \ref{avgvdef_comp} shows a significant trend of increasing mean log(O/H) with DEF."
 Allowance for the higher mass of NGC 7591 (see below) streugtheus this conclusion., Allowance for the higher mass of NGC 7591 (see below) strengthens this conclusion.
 We see [rom the mean galactic log(O/H) values that our sample is divided into the expected H I deficient/metal rich and HI normal/immetal poor groups for E of the 5 objects for which we cau determine abundances., We see from the mean galactic log(O/H) values that our sample is divided into the expected H I deficient/metal rich and H I normal/metal poor groups for 4 of the 5 objects for which we can determine abundances.
 However. NGCο. 7591 bears discussion as it only marginally conforms.," However, NGC 7591 bears discussion as it only marginally conforms."
 This object is more than a magnitude brighter than the other galaxies cousicered. aud its circular velocity is the highest of our sample (see Table 1)).," This object is more than a magnitude brighter than the other galaxies considered, and its circular velocity is the highest of our sample (see Table \ref{targettab}) )."
 establish metallicity dependences ou Ve: aud. Mpg-bothli of which are tracers of —tuass—for spiral galaxies., establish metallicity dependences on $V_C$ and $M_{B}$ –both of which are tracers of mass–for spiral galaxies.
" Several inore recent studies have confirmed the observational aud theoretical veracity of tle so-called. ""inass-inetallicity relationship"" (MZB).", Several more recent studies have confirmed the observational and theoretical veracity of the so-called “mass-metallicity relationship” (MZR).
 Frou. Figure 10 of[).. we see that average galactic Ο/Η varies significantly with these properties.," From Figure 10 of, we see that average galactic O/H varies significantly with these properties."
 Given the higher mass indicated by Aly aud Vee. the MZR appears to be a likely reason for the otherwise anomalously high. O/H content of NGC 7591 for its value of DEF.," Given the higher mass indicated by $M_B$ and $V_C$, the MZR appears to be a likely reason for the otherwise anomalously high O/H content of NGC 7591 for its value of DEF."
 πάθος]. similar scatter can be seen for the Vireo cluster. with NGC 1501 (DEF = 0.55) having a higher abundance (log(O/H) = 9.32) than the fainter. more gas-poor NGC L689 (DEF = 0.90. log(O/H = 9.28)2005).," Indeed, similar scatter can be seen for the Virgo cluster, with NGC 4501 (DEF = 0.55) having a higher abundance (log(O/H) = 9.32) than the fainter, more gas-poor NGC 4689 (DEF = 0.90, log(O/H) = 9.28)."
. We therefore couclude that the relatively higl log(O/H) observed for NGC 7591 does not contradict the correlation between H I content anc uebular abundance observed for the other galaxies., We therefore conclude that the relatively high log(O/H) observed for NGC 7591 does not contradict the correlation between H I content and nebular abundance observed for the other galaxies.
 ]t is also interesting to consider the abtuudauces of the Pegasus galaxies in Comparison to fiek galaxies., It is also interesting to consider the abundances of the Pegasus galaxies in comparison to field galaxies.
 Figure 5 plots the mean 12 + log(O/H) for our sample along with a group of unbarrec ield spirals from[)., Figure \ref{avg_field} plots the mean 12 + log(O/H) for our sample along with a group of unbarred field spirals from.
. We see that. as a whole. the cluster galaxies all [all towards he higlierzinetallicity eud of the plot. aud the H I deficient members are among the most meta ‘ich.," We see that, as a whole, the cluster galaxies all fall towards the higher-metallicity end of the plot, and the H I deficient members are among the most metal rich."
 For comparison. Figure 6a of shows the same field galaxies alongside Virgo spirals.," For comparison, Figure 6a of shows the same field galaxies alongside Virgo spirals."
 In the case of Virgo. the most H I deficient galaxies are clearly wore metal rich thar he field. but only slightly more so than our sample.," In the case of Virgo, the most H I deficient galaxies are clearly more metal rich than the field, but only slightly more so than our sample."
 Taking our H I deficient sample as a whole. we linc au average of 9.21 + 0.02 [or the galactic nean 12 + log(O/H). ompared to 9.11 + 0.05 for the H I normal controls (excluding IC 1171).," Taking our H I deficient sample as a whole, we find an average of 9.24 $\pm$ 0.02 for the galactic mean 12 + log(O/H), compared to 9.11 $\pm$ 0.05 for the H I normal controls (excluding IC 1474)."
 The resultant metallicity offset between H I deficient. aud. H E normal spirals is then 0.1340.07 dex., The resultant metallicity offset between H I deficient and H I normal spirals is then $0.13 \pm 0.07$ dex.
 While this offset is adiittedly mareinal at 26. aud cousicerably lower thau the 0.3 dex ollset Claimed for Virgo. a more careful Comparison ofthe two samples shows the metallicity enliaucement oL the clusters to be more similar than these averages suggest.," While this offset is admittedly marginal at $2 \sigma$, and considerably lower than the 0.3 dex offset claimed for Virgo, a more careful comparison of the two samples shows the metallicity enhancement of the clusters to be more similar than these averages suggest."
 While the environments. (IGM density. spiral fraction. velocity dispersion) of the Pegasus cluster differ significautly from Virgo. the individual spirals examined herein represeut a very similar population to the Virgo galaxies analyzed in(1996).," While the environments (IGM density, spiral fraction, velocity dispersion) of the Pegasus cluster differ significantly from Virgo, the individual spirals examined herein represent a very similar population to the Virgo galaxies analyzed in."
.. As shown in Tables 1. ancl 6.. the two samples cover a similar range in Ve: and Ady. indicatiug comparable galactic masses and recent star formation histories.," As shown in Tables \ref{targettab} and \ref{virgofieldtab}, the two samples cover a similar range in $V_C$ and $M_B$, indicating comparable galactic masses and recent star formation histories."
 Furthermore. our targets were selected from the Pegasus surveys of," Furthermore, our targets were selected from the Pegasus surveys of"
draining algorithm (draining | The draining. algorithm is a simple. method. which optimizes the fiber assignment process by ensuring that the maximum number of targets. is assigned. in the first tiles.,draining algorithm (draining + The draining algorithm is a simple method which optimizes the fiber assignment process by ensuring that the maximum number of targets is assigned in the first tiles.
 Such a method provides an optimized solution for our observation plan that normally includes several tiles depending on 7 and the completeness requested.," Such a method provides an optimized solution for our observation plan that normally includes several tiles, depending on $\eta$ and the completeness requested."
 The easiest. wav. to insert. the ROT optimization. into this scheme is to simply allow for rotation at the beginning of the process and find the configuration that maximizes the number of positioners with at least one target in the patrol disc., The easiest way to insert the ROT optimization into this scheme is to simply allow for rotation at the beginning of the process and find the configuration that maximizes the number of positioners with at least one target in the patrol disc.
 However. it is obviously much more cllicient to permit rotation not only at the beginning of the process but also between tiles (iterations of the process).," However, it is obviously much more efficient to permit rotation not only at the beginning of the process but also between tiles (iterations of the process)."
 This ensures that the maximum. number of positioners is in use in each tile ane requires a trivial modification of the above scheme., This ensures that the maximum number of positioners is in use in each tile and requires a trivial modification of the above scheme.
 Now. the draining algorithm is applied “from scratch” in each iteration of the process on the targets left. unobservecl from. the previous. iteration and after the optimal P is found.," Now, the draining algorithm is applied “from scratch” in each iteration of the process on the targets left unobserved from the previous iteration and after the optimal PA is found."
 Obviously. only the first tile from the solution provided by our optimized algorithm. will eventually be performed. for cach step.," Obviously, only the first tile from the solution provided by our optimized algorithm will eventually be performed for each step."
 This does. not jeopardize the proper optimization of the process by. any means. as the algorithm is specifically designed so that the maximum number of assignments is achieved in the first We have assessed the relevance of the ROT optimization in the same 100 catalogs of randomly distributed. targets that we used in Section. 4..," This does not jeopardize the proper optimization of the process by any means, as the algorithm is specifically designed so that the maximum number of assignments is achieved in the first We have assessed the relevance of the ROT optimization in the same 100 catalogs of randomly distributed targets that we used in Section \ref{sec:draining}."
" In order to isolate the cllect of rotation on the ellicteney of the process. we need to conveniently address what we call the ""border scan cllect”."," In order to isolate the effect of rotation on the efficiency of the process, we need to conveniently address what we call the “border scan effect”."
 Usually the target field is a circle on the sky encompassing he most external patrol disces of the array of positioners., Usually the target field is a circle on the sky encompassing the most external patrol discs of the array of positioners.
 As we rotate the focal plane. some of the targets bing oween the outermost perimeter of the patrolled area. which is not a circle. and the border of the target field. can come accessible to some positioners.," As we rotate the focal plane, some of the targets lying between the outermost perimeter of the patrolled area, which is not a circle, and the border of the target field can become accessible to some positioners."
 Lt is important. not ο overestimate the improvement by including targets which would be out of reach of the patrollecl area if no rotation were applied., It is important not to overestimate the improvement by including targets which would be out of reach of the patrolled area if no rotation were applied.
" In order to avoid this ""contamination we mve restricted ourselves to an area of the focal plane where. he total number of targets remains constant under any In Table 2 we presented the average cumulative fractions of targets assigned with the draining algorithm and with a random approach in the first 10 tiles for cillerent values of η,"," In order to avoid this “contamination”, we have restricted ourselves to an area of the focal plane where the total number of targets remains constant under any In Table \ref{tab:random} we presented the average cumulative fractions of targets assigned with the draining algorithm and with a random approach in the first 10 tiles for different values of $\eta$."
 We also show for comparison the same fractions obtained using the combined draining | OT. algorithm described in this section., We also show for comparison the same fractions obtained using the combined draining + ROT algorithm described in this section.
 Interestingly. allowing for rotation reduces drastically the total number of tiles needed. namely only 4 instead. of 7 [ου η=1. as an example.," Interestingly, allowing for rotation reduces drastically the total number of tiles needed, namely only 4 instead of 7 for $\eta=1$, as an example."
 This is no critical as far as a real observation is concerned. unless a 100% completeness were required.," This is not critical as far as a real observation is concerned, unless a $100\%$ completeness were required."
 More. importantly. the increase in the elliciency of the assignment in the relevan tiles provided. by the PA optimization is very significan as compared to the case were rotation is not. permitted: 3B4% even if we were to use the draining algorithm anc 5.6% νο adopted a greedy aproach.," More importantly, the increase in the efficiency of the assignment in the relevant tiles provided by the PA optimization is very significant as compared to the case were rotation is not permitted: $3-4 \%$ even if we were to use the draining algorithm and $5-6\%$ if we adopted a greedy aproach."
 This improvemen, This improvement
into quiescence and through the following outburst in Q2.,into quiescence and through the following outburst in Q2.
" Other systems that have been observed to show (late) superhumps into quiescence more typically have short orbital periods, including V1159 Ori (Pattersonetal. 1995),, ER UMa (Gaoetal.1999;Zhao 2006),, WZ Sge (Pattersonetal.2002b),, and the WZ Sge-like star V466 And (Chocholetal.2010),, among others."," Other systems that have been observed to show (late) superhumps into quiescence more typically have short orbital periods, including V1159 Ori \citep{patterson95}, ER UMa \citep{gao99,zhao06}, WZ Sge \citep{patterson02wzsge}, and the WZ Sge-like star V466 And \citep{chochol10}, among others."
" The identification of late superhumps is a matter of contention in some cases (Katoetal.2009),, and the post-superoutburst coverage of targets is more sparse than the coverage during superoutbursts."," The identification of late superhumps is a matter of contention in some cases \citep{kato09}, and the post-superoutburst coverage of targets is more sparse than the coverage during superoutbursts."
 Thus it is difficult to know if post-superoutburst superhumps are common or rare at this time., Thus it is difficult to know if post-superoutburst superhumps are common or rare at this time.
" As noted above in 82.2, the 2.06-hr (11.4 c/d) signal that dominates the light curve for the first ~35 days of Q2 is now understood to be the result of a negative superhump."," As noted above in 2.2, the 2.06-hr (11.4 c/d) signal that dominates the light curve for the first $\sim$ 35 days of Q2 is now understood to be the result of a negative superhump."
 This yields a value for the period deficit (Equation 3)) of e.=2.5%., This yields a value for the period deficit (Equation \ref{eq: eps-}) ) of $\epsilon_- = 2.5$.
. The maximum amplitude at quiescence is A~0.8 mag., The maximum amplitude at quiescence is $A\sim0.8$ mag.
 Figure 22 shows 10 cycles of the negative superhump signal during this time., Figure \ref{fig: aveneglc} shows 10 cycles of the negative superhump signal during this time.
 The inset shows the mean pulse shape averaged over days 5 to 25 (roughly 230 cycles)., The inset shows the mean pulse shape averaged over days 5 to 25 (roughly 230 cycles).
 The signal is approximately sawtoothed with a rise time roughly twice the fall time., The signal is approximately sawtoothed with a rise time roughly twice the fall time.
 It appears consistent with the pulse shapes Wood&Burke obtained using ray-trace techniques on 3D simulations(2007) of tilted disks (their Figure 3)., It appears consistent with the pulse shapes \citet{wb07} obtained using ray-trace techniques on 3D simulations of tilted disks (their Figure 3).
 Negative superhumps dominate the power in days ~2-35 and again in days ~100-160., Negative superhumps dominate the power in days $\sim$ 2–35 and again in days $\sim$ 100–160.
 The signal observed near the beginning of Q2 reveals a remarkably large rate of period change — large enough that it can be seen in the harmonics of the Fourier transform shown in Figure 10 as a negative slope towards lower frequency with time., The signal observed near the beginning of Q2 reveals a remarkably large rate of period change – large enough that it can be seen in the harmonics of the Fourier transform shown in Figure \ref{fig: 2dDFT} as a negative slope towards lower frequency with time.
 A nonlinear least squares fit to the fundamental period measured during days 2.5-7.5 yields P_=2.05006+0.00005 hr., A nonlinear least squares fit to the fundamental period measured during days 2.5-7.5 yields $P_-=2.05006\pm0.00005$ hr.
" A fit to the data from days 22-26, however, yields P_=2.06273-£0.00005 hr."," A fit to the data from days 22–26, however, yields $P_-=2.06273\pm0.00005$ hr."
" The formal errors from non-linear least squares fits underestimate the true errors by as much an order of magnitude (Montgomery&Odonoghue1999),, but even if this is the case, these two results differ by ~25c."," The formal errors from non-linear least squares fits underestimate the true errors by as much an order of magnitude \citep{mo99}, but even if this is the case, these two results differ by $\sim$ $\sigma$."
" at face value, they yield a rate of period change of TakenP.~3x107?s s~!."," Taken at face value, they yield a rate of period change of $\dot P_- \sim 3\times10^{-5}\rm\
s\ s^{-1}$ ."
" Similarly, we fit the negative superhump periods in two 4-day windows centered on days 112.0 and 121.0."," Similarly, we fit the negative superhump periods in two 4-day windows centered on days 112.0 and 121.0."
" The periods obtained from non-linear least squares are P_=2.0530+0.0002 hr and P.=2.066038+0.00008 hr, respectively, which yields Ρ~6x1075ss-! over this time span."," The periods obtained from non-linear least squares are $P_- = 2.0530 \pm 0.0002$ hr and $P_- =
2.066038 \pm 0.00008$ hr, respectively, which yields $\dot P_- \sim 6\times10^{-5}\rm\ s\ s^{-1}$ over this time span."
" In their recent comprehensive analysis of the evolution of CVs as revealed by their donor stars, Kniggeetal.(2011) estimate that for systems with Porp~2 hr the rate of orbital period change should be Pow~—7x10!4557! their Figure 11)."," In their recent comprehensive analysis of the evolution of CVs as revealed by their donor stars, \citet{knigge11} estimate that for systems with $\Porb\sim2$ hr the rate of orbital period change should be $\dot \Porb\sim-7\times10^{14}\rm\ s\ s^{-1}$ (see their Figure 11)."
 Clearly the ~2.06-hrsignal cannot be (seeorbital in origin., Clearly the $\sim$ 2.06-hrsignal cannot be orbital in origin.
" In some negatively superhumping systems with high inclinations, the precessing tilted disk can modulate the mean brightness"," In some negatively superhumping systems with high inclinations, the precessing tilted disk can modulate the mean brightness"
binary AISPs.,binary MSPs.
 Indeed. the majority of the binary MSPs in the APNE sample (Alanchester et al.," Indeed, the majority of the binary MSPs in the ATNF sample (Manchester et al."
 2005) do not have orbital periods that fall in the most probable region (Pfahl et al., 2005) do not have orbital periods that fall in the most probable region (Pfahl et al.
 2003) predicted for either LAINBOICC) or IMND(CC) evolution., 2003) predicted for either LMXB(CC) or IMXB(CC) evolution.
 There is also the problem with the birth rates mentioned. in section , There is also the problem with the birth rates mentioned in section 1.
Attempts at reconciling the LMXND(GCCO/INXD(GUC) rates with the birth rates of λος have not been successful (Pfall et al., Attempts at reconciling the LMXB(CC)/IMXB(CC) rates with the birth rates of MSPs have not been successful (Pfahl et al.
 2003) and the presen results go in the direction of making this discrepancy larecr., 2003) and the present results go in the direction of making this discrepancy larger.
 ]t has been suggested. that the above. discrepancies may disappear when more realistic models are constructed tha allow for limit evcles that may arise from X-ray irradiation of the donor stars. and for the intricacies in common envelope evolution.," It has been suggested that the above discrepancies may disappear when more realistic models are constructed that allow for limit cycles that may arise from X-ray irradiation of the donor stars, and for the intricacies in common envelope evolution."
 This remains a possibility., This remains a possibility.
 llowever. it. should. be noted that the semi-empirica birth rates are based almost. cntirely on. the observes LMXDs. which. given the arguments above. cannot be the dominant. progenitors of the binary AISPs.," However, it should be noted that the semi-empirical birth rates are based almost entirely on the observed LMXBs, which, given the arguments above, cannot be the dominant progenitors of the binary MSPs."
 The same comment also applies to our discussion of the ALC tha undergo a phase of mass transfer after collapse (see section , The same comment also applies to our discussion of the AIC that undergo a phase of mass transfer after collapse (see section 3.2).
In the evolution that leads. up to LAINBs(CC) anc IMXDsS(CCO. one. of the stellar. components (usually. he initially more massive) evolves into a neutron star hrough core collapse with a field clistribution peaking near ogBiG)=12.5 (as observed in the isolated raclio-pulsars).," In the evolution that leads up to LMXBs(CC) and IMXBs(CC), one of the stellar components (usually, the initially more massive) evolves into a neutron star through core collapse with a field distribution peaking near $\log
B(G)=12.5$ (as observed in the isolated radio-pulsars)."
 The observed. field. distribution of the MSPs. on the other iand. peaks at logBir)=s.4.," The observed field distribution of the MSPs, on the other hand, peaks at $\log B(G) = 8.4$."
 This ciscrepaney is often explained by accretion-induced field decay or evolution., This discrepancy is often explained by accretion-induced field decay or evolution.
 The oresence of AISPs in old systems suggests that if the low value of the magnetic field is due to field decay. it must do so mainiv during the accretion phase prior to the neutron star becoming a racio ΑΙ.," The presence of MSPs in old systems suggests that if the low value of the magnetic field is due to field decay, it must do so mainly during the accretion phase prior to the neutron star becoming a radio MSP."
 The manner in which the field. is expected. to. decay in accreting neutron stars depends on the origin of the magnetic fields. and here there is no consensus.," The manner in which the field is expected to decay in accreting neutron stars depends on the origin of the magnetic fields, and here there is no consensus."
 There is no clear evidence for field decay in ordinary pulsars on a time scale of 105—107. vr., There is no clear evidence for field decay in ordinary pulsars on a time scale of $10^7 - 10^8$ yr.
 However. aceretion can enhance field decay. particularly. if the fields are of crustal origin.," However, accretion can enhance field decay, particularly if the fields are of crustal origin."
 Two competing οσοι» have been considered., Two competing effects have been considered.
 Accretion raises the temperature and reduces the conductivity in regions of the crust that carry the current. thereby. enhancing field decay.," Accretion raises the temperature and reduces the conductivity in regions of the crust that carry the current, thereby enhancing field decay."
 Accretion also pushes the current. forming region inward towards regions of higher density anc conductivity where the field can be frozen., Accretion also pushes the current forming region inward towards regions of higher density and conductivity where the field can be frozen.
" Konar Bhattacharya (1997) have shown that these two elfects. when taken together. could. lead. to an asymptotic ""frozen"" field. strength that is à factor of 10+O! below the initial field. strength."," Konar Bhattacharya (1997) have shown that these two effects, when taken together, could lead to an asymptotic “frozen” field strength that is a factor of $10^{-1}-10^{-4}$ below the initial field strength."
 The asymptotic value depends on the accretion rate and the total mass acereted., The asymptotic value depends on the accretion rate and the total mass accreted.
 On the other hand. Wijers (1997) presented strong evidence against aceretion-induced field decay which is proportional to the accreted mass onto the neutron star.," On the other hand, Wijers (1997) presented strong evidence against accretion-induced field decay which is proportional to the accreted mass onto the neutron star."
 Thus. the standard mocdel does not explain the observed characteristics of the AISP birth field distribution as they switch-on as racio-emitters.," Thus, the standard model does not explain the observed characteristics of the MSP birth field distribution as they switch-on as radio-emitters."
" For instance. if we consider the route that contributes to the majority of binary MSPs. namely those having orbital periods 2,4,>101000 d with low mass Hle. WD companions arising from the evolution of intermediate mass donors. we may expect the accretion history. ancl therefore the birth field distribution. to depend on the orbital period."," For instance, if we consider the route that contributes to the majority of binary MSPs, namely those having orbital periods $P_{\rm orb} \ge 10 -1000$ d with low mass He WD companions arising from the evolution of intermediate mass donors, we may expect the accretion history, and therefore the birth field distribution, to depend on the orbital period."
 It is therefore not immediately apparent why this field should have a nearly Gaussian distribution with such a narrow width., It is therefore not immediately apparent why this field should have a nearly Gaussian distribution with such a narrow width.
 The problem becomes even more severe when more than one channel is considered. (see discussion in. Tout οἱ al., The problem becomes even more severe when more than one channel is considered (see discussion in Tout et al.
 2007)., 2007).
 The detection. of coherent X-ray pulsations with millisecond periods in a baneful of LAINBs (Lamb Yu 2005) is often used. in support of the idea of accretion induced. field. decay. (Wijnancs van der. [xliss 1998)., The detection of coherent X-ray pulsations with millisecond periods in a handful of LMXBs (Lamb Yu 2005) is often used in support of the idea of accretion induced field decay (Wijnands van der Kliss 1998).
 However. whether this is evidence simply for. fick submersion and spin up during an accretion dise phase. or for field. ἄοσαν and. spin up. remains to be established.," However, whether this is evidence simply for field submersion and spin up during an accretion disc phase, or for field decay and spin up, remains to be established."
 Cumming et al. (, Cumming et al. (
2001) have argued that the majority of he LAINBs do not show coherent. pulsations because they may have [fields sienificantly less than 107 Co due to Lele submersion which. at face value. is inconsistent with the idles seen in the racio-AISPs. but their calculations also indicate that the field will re-emerge on a time scale of 1000 vr although it is unclear to what value.,"2001) have argued that the majority of the LMXBs do not show coherent pulsations because they may have fields significantly less than $10^8$ G due to field submersion which, at face value, is inconsistent with the fields seen in the radio-MSPs, but their calculations also indicate that the field will re-emerge on a time scale of $\sim 1000$ yr although it is unclear to what value."
 Indeed. for he LNMDB(GCCO/IMXD(CC) standard scenario to be viable. he field would. be required to re-emerge to values that are similar to those observed in the radio MSPs.," Indeed, for the LXMB(CC)/IMXB(CC) standard scenario to be viable, the field would be required to re-emerge to values that are similar to those observed in the radio MSPs."
 Η we adopt the contentious viewpoint that magnetic fields do not decay due to accretion. but are simplv temporarily submerged. and re-emerge to. their original values of a few ©LOY € at the end of the LMXD(CCO/IMXND(CC) phase. then we may expect a ;»pulation of high Ποια MSIS.," If we adopt the contentious viewpoint that magnetic fields do not decay due to accretion, but are simply temporarily submerged, and re-emerge to their original values of a few $\times 10^{12}$ G at the end of the LMXB(CC)/IMXB(CC) phase, then we may expect a population of high field MSPs."
 The objects in such a xpulation would have a birth rate that is LO3 times the Να rate of normal radio-pulsars ancl would: therefore » unlikely to be represented. in. the current sample of radio-pulsars., The objects in such a population would have a birth rate that is $10^{-4}$ times the birth rate of normal radio-pulsars and would therefore be unlikely to be represented in the current sample of radio-pulsars.
. Furthermore. since they would. spin. down very rapidis to much longer. periods (with characteristic ime scales of only a few hundred. vears).. they would iwe an even smaller chance to be detected. as high. Ποιά raclio-AISPs.," Furthermore, since they would spin down very rapidly to much longer periods (with characteristic time scales of only a few hundred years), they would have an even smaller chance to be detected as high field radio-MSPs."
 Finally. we note that on the LAINBICC)/INMND(CC) hypothesis. we expect the birth spin period distribution of the MSPs as they become racdio-emitters. to be similar to the observed. spin period. distribution of the LAINBs(CC).," Finally, we note that on the LMXB(CC)/IMXB(CC) hypothesis, we expect the birth spin period distribution of the MSPs as they become radio-emitters, to be similar to the observed spin period distribution of the LMXBs(CC)."
 Llowever. observations of accretion ancl nuclear. powered LAINBs show that their spin periods peak near 2 ms (Lamb Yu 2005).," However, observations of accretion and nuclear powered LMXBs show that their spin periods peak near 2 ms (Lamb Yu 2005)."
 This could indicate either a cilferent origin for the radio AISPs (see section. 3.2). or that the braking index is significantly larger than adopted by us.," This could indicate either a different origin for the radio MSPs (see section 3.2), or that the braking index is significantly larger than adopted by us."
 We have carried out calculations for dillerent. braking indices and find that a braking index of η25 (appropriate to angular momenttun loss by gravitational radiation or magnetic multipolar radiation) will bring the two cistributions into closer agreement., We have carried out calculations for different braking indices and find that a braking index of $n= 5$ (appropriate to angular momentum loss by gravitational radiation or magnetic multipolar radiation) will bring the two distributions into closer agreement.
WD 2356—209 whose spectrum is shown in Figure 2 of OIIDIIS aud reproduced here in Figure 4.. exhibits a strong absorption feature near 6000.A.. which has been interpreted bv Salimetal.(2004). as possibly originating from an extiremelv broad Na I doublet.,"WD $-$ 209 whose spectrum is shown in Figure 2 of OHDHS and reproduced here in Figure \ref{fg:f4}, exhibits a strong absorption feature near 6000, which has been interpreted by \citet{salim04} as possibly originating from an extremely broad Na I doublet."
 A similar object has also been reported by Ilarrisetal.(2003.theirFig. 10).., A similar object has also been reported by \citet[][see SDSS J1330+6435 in their Fig.~10]{harris03}.
 Indeed. our modeling of (he Na I D doublet in a belitm-rich atmosphere malches the observed broadband energy. distribution and the observed spectrum quite weLr (see Fie. 4)).," Indeed, our modeling of the Na I D doublet in a helium-rich atmosphere matches the observed broadband energy distribution and the observed spectrum quite well (see Fig. \ref{fg:f4}) )."
 However. il was not possible to constrain effectively the sodium abundance in (his object since variations in the sodium abundance could be compensated by changing the effective lenmmperature (4200 Ix [or £1 dex in sodium abundances) with very little changes iΕν the predicted spectrum in the wavelength range used here.," However, it was not possible to constrain effectively the sodium abundance in this object since variations in the sodium abundance could be compensated by changing the effective temperature $\pm 200$ K for $\pm1$ dex in sodium abundances) with very little changes in the predicted spectrum in the wavelength range used here."
 Large differences are predicted shortweud of 5000A.. however. and high signal-to-noise spectroscopy in this region should help constrain better (he abundances of sodium aud other heavy elements in the atmosphere of WD 2356—209. as well as ils effective temperature.," Large differences are predicted shortward of 5000, however, and high signal-to-noise spectroscopy in this region should help constrain better the abundances of sodium and other heavy elements in the atmosphere of WD $-$ 209, as well as its effective temperature."
 Indeed. all the spectral features predicted in this region of the spectrum are sodium lines.," Indeed, all the spectral features predicted in this region of the spectrum are sodium lines."
 For the moment. we adopt a solution with a sodium abundance close to the solar abundance. N(Na)/N(IIe)=10? and duy=4790 E. which produces enough blankeüng in (he optical to deplete (he flux near the J filter.," For the moment, we adopt a solution with a sodium abundance close to the solar abundance, $N({\rm
Na})/N({\rm He})=10^{-5}$ and $\Te=4790$ K, which produces enough blanketing in the optical to deplete the flux near the $B$ filter."
 This abundance may seem extreme but nearly solar abundances of iron aud magnesium have also been measured in the cool and massive DAZ star GD 362 2004)., This abundance may seem extreme but nearly solar abundances of iron and magnesium have also been measured in the cool and massive DAZ star GD 362 \citep{gianninas04}.
. LIIS 1402 whose spectrum is shown in Figure 2 of OIIDIIS. and reproduced here in Figure 5.. exhibits a strong infrared [Iux celicieney similar to those observed in LIIS 3250 and SDSS 13374-00. ancl in the ultracool white dwarf candidates reported by Gateset 2)..," LHS 1402 whose spectrum is shown in Figure 2 of OHDHS and reproduced here in Figure \ref{fg:f5}, exhibits a strong infrared flux deficiency similar to those observed in LHS 3250 and SDSS $+$ 00, and in the ultracool white dwarf candidates reported by \citet[][their
Fig.~2]{gates04}."
 The detailed photometric aud model atmosphere analysis of the first two objects by Bergeron&Leggett(2002) has revealed that the infrared. [flux deficiency. steep optical spectrum. and Iuminositv (known only for LIIS 3250) could be explained better in terms of an extremely helium-rich. atmospheric composition rather than a pure hydrogen composition.," The detailed photometric and model atmosphere analysis of the first two objects by \citet{bl02} has revealed that the infrared flux deficiency, steep optical spectrum, and luminosity (known only for LHS 3250) could be explained better in terms of an extremely helium-rich atmospheric composition rather than a pure hydrogen composition."
 In the latter case. the infrared flux deficiency is (he result of collision-induced absorplions by molecular hydrogen. a mechanism that becomes important only al very low temperatures when the collisions responsible for the absorption are between hydrogen," In the latter case, the infrared flux deficiency is the result of collision-induced absorptions by molecular hydrogen, a mechanism that becomes important only at very low temperatures when the collisions responsible for the absorption are between hydrogen"
uull hypothesis of no substructure.,null hypothesis of no substructure.
 For the two-dimersional tests. tus null hypotliesis is a smooth. azimiuthally-syiauuetric distribilion of galaxies.," For the two-dimensional tests, this null hypothesis is a smooth, azimuthally-symmetric distribution of galaxies."
 No co‘reation between galaxy position aud velocity is the uull hypothesis for the tree-dimensional tests., No correlation between galaxy position and velocity is the null hypothesis for the three-dimensional tests.
" Tie quoted sieuilicauce level represents Low olten the test result for the acual data had more sust""ucture thaithe Moute Carlo shuffles.", The quoted significance level represents how often the test result for the actual data had more substructure than the Monte Carlo shuffles.
 We adopted a level of 0956 as sigicant (as per the corclisous of PRBB96). or fewer than 1 out of every 100 Moute Carlo simulalous sliowiug greater substructure tlan the real data.," We adopted a level of $99\%$ as significant (as per the conclusions of PRBB96), or fewer than 1 out of every 100 Monte Carlo simulations showing greater substructure than the real data."
 For the mos part. evideix‘e for significant substrιοure was not found.," For the most part, evidence for significant substructure was not found."
 For B2 0120+33. the 2D and 3D Lee tests (Lee1979:Fichett1085.PRBBOG were each significantat abou 95%. and the Aneular Separation Test (Wes.Oemler.&Dekel1958) was signilicaut at about 98stC.," For B2 0120+33, the 2D and 3D Lee tests \citep[][PRBB96]{lee1979,fitc1988} were each significantat about $95\%$, and the Angular Separation Test \citep{west1988} was significant at about $98\%$."
 In total. this represents margial evidence fy the presence of subsructure in this cluster.," In total, this represents marginal evidence for the presence of substructure in this cluster."
 Similary. 3€ 31 had a j des (West.Oeiler.&Dekel1988) that was signilicaut at OS% axl B2 1621438 |ad an Angular Separation Test ienufiCant al 00)4.," Similarly, 3C 31 had a $\beta$ test \citep{west1988} that was significant at $98\%$ and B2 1621+38 had an Angular Separation Test signficant at $99\%$."
 No other tests w'e above 909& significance. as was the case for a tests appied to 3C 296.," No other tests were above $90\%$ significance, as was the case for all tests applied to 3C 296."
 The strougest evideuce for substriCcLure was [oun in 16154351., The strongest evidence for substructure was found in 1615+351.
 [ts [njealaxy distributioi appears to be elongated. as tie. Fourier Elougation Test (PRBB96) was sienjicant at we over 994 coufidence.," Its galaxy distribution appears to be elongated, as the Fourier Elongation Test (PRBB96) was significant at well over $99\%$ confidence."
 Furthermore. is Lee 2D aid 3D tests were also siguificanut at aleit the 99% eve.," Furthermore, its Lee 2D and 3D tests were also significant at about the $99\%$ level."
 While the Fourier test merely iclentilies ane ongated distribution of galaxies whic nay OF thay no be caused by substrucure and 1jergiug. the Lee tests are insensitive to such distributions.," While the Fourier test merely identifies an elongated distribution of galaxies which may or may not be caused by substructure and merging, the Lee tests are insensitive to such distributions."
 HeiCe. the combination of these tests argue for tlie presence of real substructure.," Hence, the combination of these tests argue for the presence of real substructure."
 The ormality tests (based ouly on velocities did1ot show evideuce for substructure. although the velocity of the radio galaxy cliIered from tha oftle parent cluster by 1.90 lo from the galaxies within 250 kpc).," The normality tests (based only on velocities) did not show evidence for substructure, although the velocity of the radio galaxy differed from that of the parent cluster by $\sigma$ $\sigma$ from the galaxies within 250 kpc)."
 The majority of the radio galaxies appear to 'eside in »oor cliisters or groups., The majority of the radio galaxies appear to reside in poor clusters or groups.
 Nineteen of 25 examiuecd fields consisted of at least [ive galaxies with velocities placing them in a system includiug he radio galaxy. (twenty if we include B2 132236)., Nineteen of 25 examined fields consisted of at least five galaxies with velocities placing them in a system including the radio galaxy (twenty if we include B2 1322+36).
 Iu act. over half of the fields (11 of 25) rad in excess of 10 members. and five had more than 20 njembers.," In fact, over half of the fields (14 of 25) had in excess of 10 members, and five had more than 20 members."
 Two of the radio galaxies. B2 01204-33 and 3C 31. were shiowi 1o reside in very ‘ich systeus with 65 and 52 coulirmect velocities. 'espectively.," Two of the radio galaxies, B2 0120+33 and 3C 31, were shown to reside in very rich systems with 65 and 52 confirmed velocities, respectively."
 The calculated velocity clispersions and virial mmAHO urther indicate that the radio galaxies eud to exist in groups aud |IOor clusters., The calculated velocity dispersions and virial masses further indicate that the radio galaxies tend to exist in groups and poor clusters.
 Figure 2 depicts histograms of the derived. velocity dispersions for each the 250 k2ο and 1 Mpe counting radii., Figure \ref{fig-2} depicts histograms of the derived velocity dispersions for each the 250 kpc and 1 Mpc counting radii.
 About a third of the fields have dispersions arouud 200 kim l consistent. with the values found for nearby groups bandamedianmasso faboul2.m«lo AL. 2000).," About a third of the fields have dispersions around 200 km $^{-1}$ , consistent with the values found for nearby groups \citep[e.g., nearly 400 loose groups identified from the Las Campanas Redshift Survey have a median velocity dispersion of 164 km s$^{-1}$ and a median mass of about $2.5 \times 10^{13}$ $_\odot$ ."
 Most of the racio-selected groups in the present study have velocity dispersiousand Wiasses in excess of these, Most of the radio-selected groups in the present study have velocity dispersionsand masses in excess of these
 The three-dimensional fold-out of the & space. where 8ioxlog M. ποXlog£3ML ando WaOXfogAM L.," The three-dimensional fold-out of the $\kappa$ –space, where $\kappa_1 \propto log~M$ $\kappa_2 \propto log~I_e^3 \times M/L$ and $\kappa_3 \propto log~M/L$ ."
 More. we represent elliptical (12) and SO ealaxies with filled circles. SOa galaxies with asterisks and Sa Im/BCD galaxies with empty circless," Here, we represent elliptical (E) and S0 galaxies with filled circles, S0a galaxies with asterisks and Sa -- Im/BCD galaxies with empty circles."
 In each panel. we represent characteristic observationa errors (crosses) and the expected. increase of the three ás- coordinates of IE and SO galaxies when the kinetic energv o‘these stellar svstenis is not negligible.," In each panel, we represent characteristic observational errors (crosses) and the expected increase of the three $\kappa$ -coordinates of E and S0 galaxies when the kinetic energy of these stellar systems is not negligible."
 Late-type galaxies ive higher values of Al/£L than carlier ones of the same mass. contrary to what ound by BBEN in the optical.," Late-type galaxies have higher values of $M/L$ than earlier ones of the same mass, contrary to what found by BBFN in the optical."
 The three-dimensional fold-out) of the & space or cdilferent eroups of morphological tvpes is reproduced., The three-dimensional fold-out of the $\kappa$ –space for different groups of morphological types is reproduced.
 In particular. we represent: I. S0 and SOa galaxies with illecl circles. empty. squares ane asterisks. respectively (a): Sal Sah and Sh galaxies with broad crosses ancl empty jexagons. respectively (b): She and Sc galaxies with filled riangles and empty. circles.respectively," In particular, we represent: E, S0 and S0a galaxies with filled circles, empty squares and asterisks, respectively ); $+$ Sab and Sb galaxies with broad crosses and empty hexagons, respectively ); Sbc and Sc galaxies with filled triangles and empty circles,respectively"
explained by our photospheric models.,explained by our photospheric models.
 These are the detection of flux al ~1 keV (12.4 A) bv O'Dwyerοἱal.(2003).. and the observation of An=I emission lines of O VIII between levels n»= 1-10 at UV and optical wavelengths (WerneretSionetal. 1997).," These are the detection of flux at $\sim 1$ keV (12.4 ) by \citet{O'Dwyer.etal:03}, and the observation of $\Delta n=1$ emission lines of O VIII between levels $n=7$ -10 at UV and optical wavelengths \citep{Werner.etal:94,Sion.Downes:92,Sion.etal:97}."
. It seems likely that the two are related., It seems likely that the two are related.
 We have verilied that there is no trace of anv [lux near 12 me ithe LETGS spectrum. although the flux density reported by ODwyeretal.(2003) based 1i ROSAT observations (5 count + in the Boron filter) les below our LETGS detection --[unmnit in (his short observation: only e18 LETG-A-ILRC-S counts are expected. spread over a fairly large cletector area over which the background is an order of magnitude larger.," We have verified that there is no trace of any flux near 12 in the LETGS spectrum, although the flux density reported by \citet{O'Dwyer.etal:03} based on ROSAT observations (5 count $^{-1}$ in the Boron filter) lies below our LETGS detection limit in this short observation: only $\sim 18$ LETG+HRC-S counts are expected, spread over a fairly large detector area over which the background is an order of magnitude larger."
 Alore puzzling is the lack of O VIII lines in the data: the excited higher n states will decay through. cascades (to lower η. and we would expect to see some [fraction of this decay channel in (he Lyxanan series resonance lines.," More puzzling is the lack of O VIII lines in the data: the excited higher $n$ states will decay through cascades to lower $n$, and we would expect to see some fraction of this decay channel in the Lyman series resonance lines."
 Dased on the Goddard Ες Resolution spectrograph UV spectrum of oobtained on 1994 June I and analvsed by Wernerοἱal.(1996).. the O VIII 2976.57 n=8 — Transition [luris0.07 ph ? +.," Based on the Goddard High Resolution Spectrograph UV spectrum of obtained on 1994 June 1 and analysed by \citet{Werner.etal:96}, the O VIII 2976.57 $n=8$ -7 transition flux is 0.07 ph $^{-2}$ $^{-1}$."
 The upper limit to the flux of the O VILL 18.98 n—2 — ldoublelinihe Chandraspectrumismorethanthreeordersof magnitudelessthanthis., The upper limit to the flux of the O VIII 18.98 $n=2$ -1 doublet in the spectrum is more than three orders of magnitude less than this.
 There are (wo possible explanations lor the absence of the O VIII Lya lines: (1) the source is variable and curing the observation the O VIII lines were much weaker: (2) the X-rav lines are suppressed by some mechanism., There are two possible explanations for the absence of the O VIII $\alpha$ lines: (1) the source is variable and during the observation the O VIII lines were much weaker; (2) the X-ray lines are suppressed by some mechanism.
 While the lack of any simultineous observations accompanving theChandra pointing prevents us drawing definitive conclusions regarding (1). we note that optical spectra of ssimilar (to those described by Werneretal.(1994) and obtained at the Calar Alto 3.5m telescope in 1991 July. 1992 September and 1994 Mas. exhibit identical O VIII ο=10-9 and 9-8 lines and conclude that large amplitude variability in O VIII is unlikely.," While the lack of any simultaneous observations accompanying the pointing prevents us drawing definitive conclusions regarding (1), we note that optical spectra of similar to those described by \citet{Werner.etal:94} and obtained at the Calar Alto 3.5m telescope in 1991 July, 1992 September and 1994 May, exhibit identical O VIII $n=10$ -9 and 9-8 lines and conclude that large amplitude variability in O VIII is unlikely."
 Instead. the most likely explanation lor the lack of prominent X-ray O VIII lines is that (μον are suppressed.," Instead, the most likely explanation for the lack of prominent X-ray O VIII lines is that they are suppressed."
 We speculate that the O VIII Ίνα lines are formed in a low densitymedium or wind surrounding the white dwarl as has been suggested by earlier workers (Sion&Downesal.1997:Werneret 1994).," We speculate that the O VIII $\alpha$ lines are formed in a low densitymedium or wind surrounding the white dwarf, as has been suggested by earlier workers \citep{Sion.Downes:92,Sion.etal:97,Werner.etal:94}."
". In this case. the low 7 resonance lines might be sufficiently optically thick to resonance scattering that line photons are destroyed. by photoelectric absorption as they undergo mulüple scattering events within (he emitting region,"," In this case, the low $n$ resonance lines might be sufficiently optically thick to resonance scattering that line photons are destroyed by photoelectric absorption as they undergo multiple scattering events within the emitting region."
 The line centre optical depth. 7. in a IIe-dominated low-densitv medium can be written (e.g.Acton1973:Mariska 1992):," The line centre optical depth, $\tau$ , in a He-dominated low-density medium can be written \citep[e.g.,][]{Acton:78,Mariska:92}: :"
In order to determine the uncertainty due to reddening. the [Fe/H]=—0.05 isochrones were fit lor E(B-V)=0.07 and 0.11.,"In order to determine the uncertainty due to reddening, the $\feh =
-0.05$ isochrones were fit for $\ebv = 0.07$ and $0.11$."
 These fits inclicate ages of 7.5 Cyr aud 5.5 Cyr. respectively.," These fits indicate ages of 7.5 Gyr and 5.5 Gyr, respectively."
 The three sets of isochrone fits for NGC 188 are stunmarized in Table 1.., The three sets of isochrone fits for NGC 188 are summarized in Table \ref{tabn188}.
 The best age estimate was found to be 6.5x1.0 Gyr. allowing for uncertainty in the metallicity aud recdclening of the cluster.," The best age estimate was found to be $6.5\pm1.0$ Gyr, allowing for uncertainty in the metallicity and reddening of the cluster."
 This error estimate does not include the uncertainty in the input physics in the stellar inodels aud isochroues. auc so should be viewed as the error ou the relative age of NCC 183.," This error estimate does not include the uncertainty in the input physics in the stellar models and isochrones, and so should be viewed as the error on the relative age of NGC 188."
 Berkeley 17 (Be 17) las been suggested to be the oldest open cluster (Phelps1997).., Berkeley 17 (Be 17) has been suggested to be the oldest open cluster \citep{phelps}. .
 It has a metallicity of [Fe/H]=—0.29+0.13 from moderate resolution spectroscopy (Frieletal.1992). while Carraroetal.(19909) estimate [Fe/H]~—0.35 based upon the slope of the red giant branch in thei," It has a metallicity of $\feh = -0.29\pm 0.13$ from moderate resolution spectroscopy \citep{friel}, while \citet{carr2}
 estimate $\feh \sim -0.35$ based upon the slope of the red giant branch in the."
nfrared?.. Phelps(1997) obtained BVI photometry of this cluster which was used in our isochroue fits., \citet{phelps} obtained BVI photometry of this cluster which was used in our isochrone fits.
 A simultaneous fit to the aand pphotometry was attempted. assumiug E(V—/)=1.22«E(B—V).," A simultaneous fit to the and photometry was attempted, assuming $\evi = 1.25*\ebv$."
 We attempted to fit isochrones with [Fe/H]=—0.10.20.21. aud. —0.10 with [a/Fe]=+0.0 aud +0.10 (a total of 6 different compositions) without success.," We attempted to fit isochrones with $\feh = -0.10,
-0.24,$ and $-0.40$ with $[\alpha/{\rm Fe}] = +0.0$ and $+0.40$ (a total of 6 different compositions) without success."
 In all cases. the Be 17 main sequence was redder thai our isochrones in aand bluer than our isochrones in—4.," In all cases, the Be 17 main sequence was redder than our isochrones in and bluer than our isochrones in."
. Our best attempt at a fit is shown in Figure 6.., Our best attempt at a fit is shown in Figure \ref{figbe17}.
 As this is clearly not au acceptable fit to the data. we are unable to assigu an age to Be 17.," As this is clearly not an acceptable fit to the data, we are unable to assign an age to Be 17."
 There are a uumber of possible explanations for the inability of the isochrones to simultaneously fit the aand ddata., There are a number of possible explanations for the inability of the isochrones to simultaneously fit the and data.
 These include: (1) a non-staudard extinction law in the direction of Be 17 V)). (2) a helium abundance significantly different than in our models. (3) errors in our Isochroues (1) errors in the photometry (of order 0.05 mag in the color).," These include: (1) a non-standard extinction law in the direction of Be 17 $\evi \neq 1.25*\ebv$ ), (2) a helium abundance significantly different than in our models, (3) errors in our isochrones (4) errors in the photometry (of order 0.05 mag in the color)."
 Open clusters are expected to dissipate/disrupt in the galactic plane., Open clusters are expected to dissipate/disrupt in the galactic plane.
 Thus. only the most massive opeu clusters or those with orbits which keep them far away [rom the plane for most of their lifetimes are expected to survive for sigulicaut periods of time.," Thus, only the most massive open clusters or those with orbits which keep them far away from the plane for most of their lifetimes are expected to survive for signficant periods of time."
 For this reason. the age of the oldest field stars in the thin disk may provide a better estimate for the age of the thin disk than open clusters.," For this reason, the age of the oldest field stars in the thin disk may provide a better estimate for the age of the thin disk than open clusters."
 An analysisof the age of oldest thin disk stars in the solar neighborhood was mace, An analysisof the age of oldest thin disk stars in the solar neighborhood was made
 2.2Introductio,as discussed in .
n ofspin intothe incident baryon andthe cas- , We then applied our model to hyperon polarization in $hA$ 
" logVaxipir/Myausc]). ~10o107AL, ", $\log[M_{\rm SMBH}/M_{\rm bulge}]$ $\sim 10^7-10^9~M_{\odot}$ 
our beam size.,our beam size.
" Since our measurements of size and velocity dispersion are measured out to a contour equal to twice the rms, not extrapolated to 0 K, we opt to use the Williams method to estimate the sizes and velocity dispersions of the clouds."," Since our measurements of size and velocity dispersion are measured out to a contour equal to twice the rms, not extrapolated to 0 K, we opt to use the Williams method to estimate the sizes and velocity dispersions of the clouds."
" Following e.g. ?, we take the uncertainties in our measurements to be of the spatial beam size (17 pc) and half of our velocity channel width (1.3 s~!))."," Following e.g., \citet{Wilson90}, we take the uncertainties in our measurements to be of the spatial beam size (17 pc) and half of our velocity channel width (1.3 )."
" These values are appropriate for the largest clouds in our sample, but the uncertainties in the clouds with sizes and velocity dispersions near our resolution limits may be larger."," These values are appropriate for the largest clouds in our sample, but the uncertainties in the clouds with sizes and velocity dispersions near our resolution limits may be larger."
" Running CLUMPFIND to a lower minimum contour level (1.50) creates more detections of faint clouds, but the resulting change in Xco within the individual GMCs presented in this paper is well within these quoted measurement errors."," Running $\sc{CLUMPFIND}$ to a lower minimum contour level $\sigma$ ) creates more detections of faint clouds, but the resulting change in $X_{\text{CO}}$ within the individual GMCs presented in this paper is well within these quoted measurement errors."
 We use the cloud measurements to calculate cloud virial masses in the following manner., We use the cloud measurements to calculate cloud virial masses in the following manner.
" Using the definition of potential energy from ? and the kinetic energy in terms of the one-dimensional velocity dispersion, ? express the virial mass as where AR is the circular radius of a clump, σν is the one-dimensional velocity dispersion, G is the gravitational constant, and ανν is the “virial parameter"" which describes a non-uniform density profile."," Using the definition of potential energy from \citet{McKee92} and the kinetic energy in terms of the one-dimensional velocity dispersion, \citet{Williams94} express the virial mass as where $\Delta$ R is the circular radius of a clump, $\sigma_{v}$ is the one-dimensional velocity dispersion, G is the gravitational constant, and $\alpha_{vir}$ is the “virial parameter"" which describes a non-uniform density profile."
" If we parameterize the density profile as we find that integrating over dM=p(r)ydydx yields Substituting the expressions in Equations 5 and 6 into the gravitational energy for a spherical body (Equation 2.32, ?)) yields the relation It follows that for 8-0, o,;,—1; for B=1, a,;-=10/9; and for B=2, Air=5/3 (as also mentioned by ?))."," If we parameterize the density profile as we find that integrating over $\it{dM = \rho(r) y dy dx}$ yields Substituting the expressions in Equations 5 and 6 into the gravitational energy for a spherical body (Equation 2.32, \citealt{BinneyTremaine08}) ) yields the relation It follows that for $\beta$ =0, $\alpha_{vir}$ =1; for $\beta$ =1, $\alpha_{vir}$ =10/9; and for $\beta$ =2, $\alpha_{vir}$ =5/3 (as also mentioned by \citealt{Williams94}) )."
" If we assume that 8=1, as many authors do, (e.g., ???)) and G = 1/232 (using units ofs, parsecs, and solar mass), substituting into Equation 4 yields as shown by ? and similarly by ?.."," If we assume that $\beta$ =1, as many authors do, (e.g., \citealt{Solomon87, Rosolowsky06, Bolatto08}) ) and G = 1/232 (using units of, parsecs, and solar mass), substituting into Equation 4 yields as shown by \citet{Solomon87} and similarly by \citet{Wilson90}."
" We assume that the GMCs are virialized, an assumption consistent with previous studies, and derive virial masses using the measurements of R and c, (corrected for their respective resolution elements) via Equation 8."," We assume that the GMCs are virialized, an assumption consistent with previous studies, and derive virial masses using the measurements of R and $\sigma_{v}$ (corrected for their respective resolution elements) via Equation 8."
" ? describe the virial mass as where f, is called a projection factor and the size of the cloud (S) is related to the effective radius (derived from the circular area of the cloud on the sky) such that R;;; = 1.91 S. However, this projection factor, indicated to equal 2.9, is not explicitly derived and as a result does not appear in many recent papers on this topic."," \citet{Solomon87} describe the virial mass as where $_{p}$ is called a projection factor and the size of the cloud (S) is related to the effective radius (derived from the circular area of the cloud on the sky) such that $_{eff}$ = 1.91 S. However, this projection factor, indicated to equal 2.9, is not explicitly derived and as a result does not appear in many recent papers on this topic."
" Using the formulae shown above, it is trivial to derive that f,=2.9 when a,;,=10/9."," Using the formulae shown above, it is trivial to derive that $_{p}$ =2.9 when $\alpha_{vir}$ =10/9."
" To calculate Xco, in effect the mass-to-light ratio for molecular clouds, we compare the virial masses of each cloud to the luminosities derived from each cloud's integrated CO flux."," To calculate $X_{\text{CO}}$, in effect the mass-to-light ratio for molecular clouds, we compare the virial masses of each cloud to the luminosities derived from each cloud's integrated CO flux."
" We calculate cloud luminosities via where 4 is the observed wavelength (in mm), Fco is the flux in beam""! s'larcsec?, and 0, and 6, are the beam densityaxes (arcsec)."," We calculate cloud luminosities via where $\lambda$ is the observed wavelength (in mm), $_{CO}$ is the flux density in Jy $^{-1}$ $^{2}$ , and $\theta_{a}$ and $\theta_{b}$ are the beam axes (arcsec)."
"Jy Finally, with M,;, in units of solar masses and Lco in units of K pc?, and including a factor of 1.36 to account for helium, we compute Xco (the CO-to-H» conversion factor) as follows: From Figure 1, it is clear that most of the bright CO emission which is included in the resolved GMCs is coincident with spiral arms, but significant emission is also found in the inter-arm regions."," Finally, with $_{vir}$ in units of solar masses and $_{CO}$ in units of K $^{2}$, and including a factor of 1.36 to account for helium, we compute $X_{\text{CO}}$ (the $_{2}$ conversion factor) as follows: From Figure \ref{co}, it is clear that most of the bright CO emission which is included in the resolved GMCs is coincident with spiral arms, but significant emission is also found in the inter-arm regions."
" The GMCs identified by the CLUMPFIND algorithm tend to be the largest, brightest clouds: those in the spiral arms."," The GMCs identified by the $\sc{CLUMPFIND}$ algorithm tend to be the largest, brightest clouds: those in the spiral arms."
" The inter-arm emission to be more extended, which is consistent with it being less appearslikely to display an apparently self-gravitating velocity profile."," The inter-arm emission appears to be more extended, which is consistent with it being less likely to display an apparently self-gravitating velocity profile."
 We resolve total of 134 clouds., We resolve a total of 134 clouds.
" After discarding potential blends, as describeda in Section 3.2, 120 clouds remain in our GMC sample."," After discarding potential blends, as described in Section 3.2, 120 clouds remain in our GMC sample."
" Using the equations in Section 3.2 to account for the instrumental resolution elements, 64clouds have a real velocity dispersion."," Using the equations in Section 3.2 to account for the instrumental resolution elements, 64clouds have a real velocity dispersion."
 We require that clouds have a, We require that clouds have a
SER. of merger-induced starbursts.,SFR of merger-induced starbursts.
 Mihos (2004) has shown that an external potential can mocifs the morphology. of eascous tidal tails developed in galaxy mergers. but did not study the star formation in this context.," Mihos (2004) has shown that an external potential can modify the morphology of gaseous tidal tails developed in galaxy mergers, but did not study the star formation in this context."
 Here we show that ealaxy mergers are statistically more ellicient in triggering strong starbursts if they take place in the vicinity of a larger structure., Here we show that galaxy mergers are statistically more efficient in triggering strong starbursts if they take place in the vicinity of a larger structure.
 This should contribute to the triggering of star formation in dense environments at~l., This should contribute to the triggering of star formation in dense environments at$z \sim 1$.
 Inelecel the triggering of star formation by the larec-seale tidal field garould be ellicient in particular in voung groups and. near forming clusters. where the quenching factors did not have time to act. vet.," Indeed the triggering of star formation by the large-scale tidal field should be efficient in particular in young groups and near forming clusters, where the quenching factors did not have time to act yet."
 The numerical simulations are described in Section 2. and the results are presented. in Section 3.," The numerical simulations are described in Section 2, and the results are presented in Section 3."
 Our conclusions are discussed and summarized in Sections 4 and 5., Our conclusions are discussed and summarized in Sections 4 and 5.
 Galaxies are modelled. as stars. gas and dark matter particles.," Galaxies are modelled as stars, gas and dark matter particles."
 The gravitational potential is computed with an LFI'E-based particle-mesh technique. with a spatial resolution and softening of 190 pe. as described in Bournaucl&Combes(2002. 2003).," The gravitational potential is computed with an FFT-based particle-mesh technique, with a spatial resolution and softening of 190 pc, as described in \citet{BC02, BC03}."
. Gas dynamics is modelled with a sticky-particles scheme with parameters 220.7 and :j; 0.5., Gas dynamics is modelled with a sticky-particles scheme with parameters $\beta_r$ =0.7 and $\beta_t$ =0.5.
 Star formation is computed using a local Schmidt law: the star formation rate is proportional to the local gas density to the exponent 1.5 (Ixennicutt.1998)., Star formation is computed using a local Schmidt law: the star formation rate is proportional to the local gas density to the exponent 1.5 \citep{kennicutt98}.
. In order to directly compare the SER. of an interacting ealaxy and of the same galaxy. isolated. at fixed. gas mass. we implement a gas dise of 107. particles in this galaxy. together with 107 stellar particles and 101 dark matter particles.," In order to directly compare the SFR of an interacting galaxy and of the same galaxy isolated, at fixed gas mass, we implement a gas disc of $10^5$ particles in this galaxy, together with $\times10^4$ stellar particles and $\times10^4$ dark matter particles."
" The. particle mass resolution is 10! AL. for gas. 107 AL. for stars. 10"" AL: for dark matter."," The particle mass resolution is $\times10^4$ $_{\sun}$ for gas, $\times10^5$ $_{\sun}$ for stars, $\times10^5$ $_{\sun}$ for dark matter."
 ENPhe merging. companion. is. modelled with. 1071 stellar particles. and 10°n dark matter particles., The merging companion is modelled with $\times10^4$ stellar particles and $\times10^4$ dark matter particles.
. Because we study star formation mainly in à context of z20. we mocde ealaxies. with. à moderate visibleτον mass of⋅ 1.5«107m AL.," Because we study star formation mainly in a context of $z>0$, we model galaxies with a moderate visible mass of $1.5 \times 10^{10}$ $_{\sun}$."
 Α >=0 this corresponds to somewhat small spirals (similar to AL 33)., At $z=0$ this corresponds to somewhat small spirals (similar to M 33).
 Phe bulge:disc mass ratio is 0.24. the gas mass fraction in the cise is15%.," The bulge:disc mass ratio is 0.24, the gas mass fraction in the disc is."
. The bulge has a seale-leneth of 600 pe. the disc has a Toomre profile with a racial leneth of 1.6 kpe for stars and 4.6 kpe for gas. truncated a 5.6 kpe.," The bulge has a scale-length of 600 pc, the disc has a Toomre profile with a radial scale-length of 1.6 kpc for stars and 4.6 kpc for gas, truncated at 5.6 kpc."
 A dark halo of mass 5.4.1017 AL is implementec with a Plummer profile of scale-leneth 6 kpe truncated a 20 kpe. giving a circular velocity Vo&100 km i," A dark halo of mass $5.4 \times 10^{10}$ $_{\sun}$ is implemented with a Plummer profile of scale-length 6 kpc truncated at 20 kpc, giving a circular velocity $V_{\mathrm{circ}} \simeq 100$ km $^{-1}$."
 Galaxies are evolved as isolated. svstems for 500. Myr »efore. simulations are started., Galaxies are evolved as isolated systems for 500 Myr before simulations are started.
 “Vhis way. galaxies already rave acquired a realistic (barred) spiral structure when hey interact and merge. without having time to undergo a major secular evolution of their bulge mass or disc size.," This way, galaxies already have acquired a realistic (barred) spiral structure when they interact and merge, without having time to undergo a major secular evolution of their bulge mass or disc size."
 Star formation is shut down during this initial period. so hat interactions really start with the gas fraction indicatecd above.," Star formation is shut down during this initial period, so that interactions really start with the gas fraction indicated above."
 The evolution of the SER is thus related to the interaction/merger. without anv bias introduced. Ὃν the ransition from the initial axisvmimetric model to a realistic spiral disc.," The evolution of the SFR is thus related to the interaction/merger, without any bias introduced by the transition from the initial axisymmetric model to a realistic spiral disc."
 We performed simulations of binary equal-mass mergers of two spiral galaxies corresponding to the model above., We performed simulations of binary equal-mass mergers of two spiral galaxies corresponding to the model above.
 The orbital parameters of the merging pair are as follows: We model groups and clusters gravitational potential using a Plummer profile., The orbital parameters of the merging pair are as follows: We model groups and clusters gravitational potential using a Plummer profile.
 Fhis choice is discussed in Section 3.3. and should be representative of most groups and clusters tidal field. at least in the peripheral regions studied: here.," This choice is discussed in Section 3.3, and should be representative of most groups and clusters tidal field at least in the peripheral regions studied here."
 nPhe modelled cluster has a mass ofNE 107 AL. and a racial' scale-leneth of 400 kpe (this choice would be reasonably representative for instance of the Virgo cluster (e.g..Foucuéetal.2001). and the group a mass of 5107 NL. anda scale-Iength of 150 kpc. whieh could be representative of the Local Ciroup depending on its dark:visible ratio.," The modelled cluster has a mass of $10^{15}$ $_{\sun}$, and a radial scale-length of 400 kpc (this choice would be reasonably representative for instance of the Virgo cluster \citep[e.g.,][]{fouque01} and the group a mass of $5\times10^{13}$ $_{\sun}$ and a scale-length of 150 kpc, which could be representative of the Local Group depending on its dark:visible ratio."
 The galaxy pair was initially placed at 400 kpe from the centre ofthe cluster (resp., The galaxy pair was initially placed at 400 kpc from the centre of the cluster (resp.
 150 kpe from the group centre)., 150 kpc from the group centre).
 Galaxies are not placed specifically in central regions. but in the periphery.," Galaxies are not placed specifically in central regions, but in the periphery."
 This is à more general choice. and in the case of clusters it ensures that galaxies there can still contain gas reservoirs and formi stars.," This is a more general choice, and in the case of clusters it ensures that galaxies there can still contain gas reservoirs and form stars."
 We chose four possible configurations for the relative »osition of the galaxy. pair and the group or cluster: Each orbital parameter for the merging. ealaxies has en simulated without any external field. anc with the eroup and the cluster in each configuration: the total number of cases is then as [large as 320.," We chose four possible configurations for the relative position of the galaxy pair and the group or cluster: Each orbital parameter for the merging galaxies has been simulated without any external field, and with the group and the cluster in each configuration; the total number of cases is then as large as 320."
 We restrict ourselves to cases leading to a merger. otherwise the parameter space to explore would be too large.," We restrict ourselves to cases leading to a merger, otherwise the parameter space to explore would be too large."
 We make the choice of the galaxy pair having no initial velocity wort., We make the choice of the galaxy pair having no initial velocity w.r.t.
 the group/cluster (but [ree to move within in) as justified in Sect. ??.., the group/cluster (but free to move within in) as justified in Sect. \ref{312}. .
" In the following. ""relative SER? refers to the SER. of a galaxy with a merging companion and/or a group or cluster tidal Ποιά. cüvided by the SER. of the same galaxy isolated."," In the following, `relative SFR' refers to the SFR of a galaxy with a merging companion and/or a group or cluster tidal field, divided by the SFR of the same galaxy isolated."
 The, The
"and where x= r/Ro, B is Boin Gauss, and fi is n in units of cm?.","and where $x = r/R_{\sun}$ , $\tilde{B}$ is $B_0$in Gauss, and $\tilde{n}$ is $n$ in units of $\mbox{cm}^{-3}$."
 The density in equation (8)) is the value from equation (4) of ? plus an additional r? component chosen to give n—4cm at 1 AU., The density in equation \ref{eq:n}) ) is the value from equation (4) of \cite{feldman97} plus an additional $r^{-2}$ component chosen to give $n=4 \mbox{ cm}^{-3}$ at 1 AU.
" (8)) (10)) give rg= 1.IRG, rm""=1.60Ro, and EquationsU(1AU)through=750km s, and lead to the U and v4 profiles shown in figure 1.."," Equations \ref{eq:n}) ) through \ref{eq:defU}) ) give $r_a=11.1 R_{\sun}$ , $r_m= 1.60 R_{\sun}$, and $U(\mbox{1 AU}) = 750\;
\mbox{km}\; \mbox{s}^{-1}$ , and lead to the $U$ and $v_{\rm A}$ profiles shown in figure \ref{fig:swv_corona}."
" The value of ὃνρ from equation (5)) is also plotted in figure 1,,where the value 8v,=155 km/s has been chosen so that óvo remains bounded by the range of non-thermal line widths obtained ? V2to convert from an rms line-of-sight byvelocity to an multipliedrms byvelocity in the plane perpendicular to B."," The value of $\delta
v_0$ from equation \ref{eq:dv0b}) ) is also plotted in figure \ref{fig:swv_corona},where the value $\delta v_{\rm a} =
155$ km/s has been chosen so that $\delta v_0$ remains bounded by the range of non-thermal line widths obtained by \cite{esser99} multiplied by $\sqrt{2}$to convert from an rms line-of-sight velocity to an rms velocity in the plane perpendicular to ${\rm B}$."
" In Alfvénn-wave turbulence, fluctuation energy cascades from A,~L, to smaller A, and then dissipates at AZ5pp due to some combination of ion and electron "," In Alfvénn-wave turbulence, fluctuation energy cascades from $\lambda_\perp \sim L_\perp$ to smaller $\lambda_\perp$ and then dissipates at $\lambda_\perp \lesssim \rho_{\rm p}$ due to some combination of ion and electron damping."
"It is assumed that dissipation is negligibleat A,>2pp, and damping.that at 2ρρ<A,«L,, where ὄνλ, is the rms amplitude of the fluctuating velocity at perpendicular scale A."," It is assumed that dissipation is negligibleat $\lambda_\perp > 2\rho_{\rm p }$, and that at $2\rho_{\rm p } < \lambda_\perp < L_\perp$, where $\delta
v_{\lambda_\perp}$ is the rms amplitude of the fluctuating velocity at perpendicular scale $\lambda_\perp$."
" The constant a is related to the velocity power spectrum P,(k,).", The constant $a$ is related to the velocity power spectrum $P_{\rm v}(k_\perp)$.
 If Pyock|? for Li!Ski€ then a=(o—1)/2.," If $P_{\rm v}\propto
k_\perp^{-\sigma}$ for $ L_\perp^{-1} \lesssim k_\perp \lesssim
(2\rho_{\rm p})^{-1}$, then $a = (\sigma-1)/2$."
" Observations of solar-wind Qpy)-fluctuations, at 1 AU find that o— (?).. Numerical "," Observations of solar-wind velocity fluctuations at 1 AU find that $\sigma =
3/2$ \citep{podesta07}. ."
velocitysimulations of magnetohydrodynamic 3/2(MHD) turbulence generally find that o=5/3 when ὃνρ~va (???) and o=3/2 when dv<0.2v4 (222222)..," Numerical simulations of magnetohydrodynamic (MHD) turbulence generally find that $\sigma = 5/3$ when $\delta v_0
\sim v_{\rm A}$ \citep{cho00,muller00,haugen04} and $\sigma = 3/2$ when $\delta v_0\lesssim 0.2 v_{\rm
 A}$ \citep{maron01,muller05,boldyrev06,mason08,perez08a,perez09a}."
" From figure 1,, ὄνρ/να«0.3 at r«15Ro, indicating that this region is better described by simulations with óvo<0.2v4 than simulations with dvo~va."," From figure \ref{fig:swv_corona}, $\delta v_0/v_{\rm A} < 0.3$ at $r<
15 R_{\sun}$, indicating that this near-Sun region is better described by simulations with $\delta v_0 \lesssim 0.2 v_{\rm A}$ than simulations with $\delta v_0 \sim v_{\rm A}$."
" Based on the above studies, it is assumed that σ=3/2 and at rX15Ro, the region on which this study focuses."," Based on the above studies, it is assumed that $\sigma = 3/2$ and at $r \leq 15 R_{\sun}$, the region on which this study focuses."
" UVCS observations show that O? has a larger thermal speed than protons at r~2Rc, and hence a gyroradius that is several times larger than py."," UVCS observations show that ${\rm O}^{+5}$ has a larger thermal speed than protons at $r \sim 2 R_{\sun}$, and hence a gyroradius that is several times larger than $\rho_{\rm p}$."
" Based in part on this observation, it is assumed that p;>2p, for minor ions and alpha particles at r=>2Ro."," Based in part on this observation, it is assumed that $\rho_{\rm i} > 2 \rho_{\rm p}$ for minor ions and alpha particles at $r \gtrsim 2 R_{\sun}$."
" Equation (11)) then gives with In the case of protons, electron Landau damping and stochastic proton heating drain energy from the cascade at AL~Pp, reducing ὄνι, at Àj,~py relative to the scaling in equation (11))."," Equation \ref{eq:spectrum}) ) then gives with In the case of protons, electron Landau damping and stochastic proton heating drain energy from the cascade at $\lambda_\perp \sim \rho_{\rm
 p}$, reducing $\delta v_{\lambda_\perp}$ at $\lambda_\perp \sim
\rho_{\rm p}$ relative to the scaling in equation \ref{eq:spectrum}) )."
" To account for this, it is assumed that where the particular value in equation (15)) is chosen so that the results in section 4 match observations of T, in coronal holes, as described furtherin the discussion of figure 3.."," To account for this, it is assumed that where the particular value in equation \ref{eq:alpha2}) ) is chosen so that the results in section \ref{sec:corona} match observations of $T_{\perp \rm p}$ in coronal holes, as described furtherin the discussion of figure \ref{fig:Tcomp}."
" Equations (1)) and (13)) imply that Equation (16)) shows that as 7j; decreases, € increases, which in turn increases the stochastic heating rate."," Equations \ref{eq:defeps}) ) and \ref{eq:spectrumi}) ) imply that Equation \ref{eq:eps2}) ) shows that as $T_{\perp \rm i}$ decreases, $\epsilon_{\rm i}$ increases, which in turn increases the stochastic heating rate."
" One way of understanding this is that Alfvénn-wave/KAW fluctuations with 2,~ cause the electrostatic potential to vary in a complicated p;way in the plane perpendicular to Bo, with an rms variation of δΦ~ριδΕι over a distance pi, where GE;~Ov;Bo/c is the rms amplitude of the electric-field fluctuation at A,=pi. ("," One way of understanding this is that Alfvénn-wave/KAW fluctuations with $\lambda_\perp \sim \rho_{\rm i}$ cause the electrostatic potential $\Phi$ to vary in a complicated way in the plane perpendicular to ${\bf B}_0$, with an rms variation of $\delta \Phi_{\rm i}
\sim \rho_{\rm i} \delta E_{\rm i}$ over a distance $\rho_{\rm i}$, where $\delta E_{\rm i} \sim \delta v_{\rm i } B_0/c$ is the rms amplitude of the electric-field fluctuation at $\lambda_\perp =
\rho_{\rm i}$. ("
"The larger but smoother spatial variations in b associated with Alfvénn-wave fluctuations at A,>>p; are ignored here, as they lead to drift motion rather than stochastic orbits.)","The larger but smoother spatial variations in $\Phi$ associated with Alfvénn-wave fluctuations at $\lambda_\perp \gg
\rho_{\rm i}$ are ignored here, as they lead to drift motion rather than stochastic orbits.)"
" Equation (13)) then gives δΦ;οςvit, and 60;/ναι "," Equation \ref{eq:spectrumi}) ) then gives $\delta \Phi_{\rm i} \propto v_{\perp \rm i}^{1+a}$, and $\delta
\Phi_{\rm i}/ v_{\perp \rm i}^2 \propto v_{\perp \rm i}^{ a-1}$ ."
"For a«1, decreasing νι causes gj5®; to become an vti.increasingly large fraction of the ions' perpendicular kinetic energy, and the ions’ motion in theplane perpendicular to Bo becomes increasingly chaotic as a result."," For $a< 1$, decreasing $v_{\perp \rm i}$ causes $q_{\rm i}\delta \Phi_{\rm
 i}$ to become an increasingly large fraction of the ions' perpendicular kinetic energy, and the ions' motion in theplane perpendicular to ${\bf B}_0$ becomes increasingly chaotic as a result."
" A possible objection to setting pj>20p at r=2Ro for Het* and minor ions is that preferential heating of heavy ions is assumed from the outset, leaving open the question of how such ions first reach temperatures exceeding Τρ."," A possible objection to setting $\rho_{\rm i} > 2 \rho_{\rm p}$ at $r\gtrsim 2 R_{\sun}$ for ${\rm He}^{++}$ and minor ions is that preferential heating of heavy ions is assumed from the outset, leaving open the question of how such ions first reach temperatures exceeding $T_{\perp \rm p}$."
" This initial evolution can be understood by considering He**, Ot, and Fe*!! ions with temperatures ~Τιρ at small r."," This initial evolution can be understood by considering ${\rm He}^{++}$, ${\rm O}^{+5}$, and ${\rm Fe}^{+11}$ ions with temperatures $\sim T_{\perp \rm p}$ at small $r$."
" Given their charge-to-mass ratios, these ions have gyroradii that are comparable to py when T';Τιρ. and hence values of àv; that are to the value."," Given their charge-to-mass ratios, these ions have gyroradii that are comparable to ${\rm \rho}_{\rm p}$ when $T_{\perp \rm i} \sim T_{\perp
 \rm p}$, and hence values of $\delta v_{\rm i}$ that are comparable to the proton value."
" As a result, the slower, heavier ions have comparablelarger ει and protonmuch larger stochastic heating rates than protons whenTj;~ Τιρ."," As a result, the slower, heavier ions have larger $\epsilon_{\rm i}$ and much larger stochastic heating rates than protons when$T_{\perp \rm i} \sim T_{\perp \rm p}$ ."
 These larger heating rates then lead to T;>Τιρ at larger r., These larger heating rates then lead to $T_{\perp \rm i} \gg T_{\perp \rm p}$ at larger $r$ .
" In the measurements at 1 AU analyzed by ?,, the electric-field power spectrum is slightly larger at ki=1than one would expect from an extrapolation of the Pppower-law scaling that is present at smaller k,."," In the measurements at 1 AU analyzed by \cite{bale05}, , the electric-field power spectrum is slightly larger at $k_\perp \rho_{\rm
 p} = 1$than one would expect from an extrapolation of the power-law scaling that is present at smaller $k_\perp$ ."
" The electric-field spectrum is a good proxy for the spectrum of (electron) velocity fluctuations associated with AW/KAW turbulence (?),, and thus o>1 for protons in this data set."," The electric-field spectrum is a good proxy for the spectrum of (electron) velocity fluctuations associated with AW/KAW turbulence \citep{schekochihin09}, , and thus $\alpha_{\rm i} > 1$ for protons in this data set."
" Nevertheless, the valueαι=0.71 is reasonable for protons in coronal holes for two reasons."," Nevertheless, the value$\alpha_{\rm i} = 0.71$ is reasonable for protons in coronal holes for two reasons."
" First, AW/KAW turbulence is more ""imbalanced"" in coronal holes than at 1 AU, with a greater excess of outward-propagating waves over"," First, AW/KAW turbulence is more “imbalanced” in coronal holes than at 1 AU, with a greater excess of outward-propagating waves over"
WFC.,WFC.
 The general trends in burst rate were kuowu previously., The general trends in burst rate were known previously.
 The kuowledge hat our work adds is 1) that there does sec to be a rather consistent burst rate behavior frou one burster o another. and 2) that there is a rather discrete trausitio rin this behavior between 1.1 to «107 eres1.," The knowledge that our work adds is 1) that there does seem to be a rather consistent burst rate behavior from one burster to another, and 2) that there is a rather discrete transition in this behavior between 1.4 to $\times10^{37}$ $\ergs$."
 Qur searclies for (quasi-)veriodicity iu burst recurrence were nieaniueful iu three xnrees: 335L-0. 11731-260 and 11526-2L.," Our searches for (quasi-)periodicity in burst recurrence were meaningful in three sources: 354-0, 1731-260 and 1826-24."
 The pr'eseuce of quasi-periodicitics is uost obvious iu 11526-2 (sce also Ubertini ct al., The presence of quasi-periodicities is most obvious in 1826-24 (see also Ubertini et al.
 1999 and Cocchi et al., 1999 and Cocchi et al.
" 20015). xeseut in 11731-260. but oulv suggestive in 2335I4),"," 2001b), present in 1731-260, but only suggestive in 354-0."
" The quasi-periodicity is oulv oeseut duinug times when t1ο persistent flux is below that or the peak burst rate. as is most clearly demonstrated w RS11731-260 which. thauks to its transient nature. races a relatively wide ranee of fluxes,"," The quasi-periodicity is only present during times when the persistent flux is below that for the peak burst rate, as is most clearly demonstrated by 1731-260 which, thanks to its transient nature, traces a relatively wide range of fluxes."
 11526-21 never eaves this domain whicji explains why its bursts recur quasi-periodicalY., 1826-24 never leaves this domain which explains why its bursts recur quasi-periodically.
 The same appears to apply to 3351-0., The same appears to apply to 354-0.
 Quasi-periodicity has been seen previously with EXOSAT iu à uuuber of other sources: (007Ls-G76 (Gottwald et al., Quasi-periodicity has been seen previously with EXOSAT in a number of other sources: 0748-676 (Gottwald et al.
 1986). 11705-LE (Gottwald et al.," 1986), 1705-44 (Gottwald et al."
 1989). Ser N-L (Sztajuo ct al.," 1989), Ser X-1 (Sztajno et al."
 1983) aud 11636-536 (Lewin e al., 1983) and 1636-536 (Lewin et al.
" 1987) ""n1 ouly for a lanited amount of ine.", 1987) but only for a limited amount of time.
 Our observatious for fhe first time show enipiricall hat the qiasi-periodicity is restricted to a very particular ununositv rango alr that there is a narrow positive relationship between »urst frequency and the persistent flux., Our observations for the first time show empirically that the quasi-periodicity is restricted to a very particular luminosity range and that there is a narrow positive relationship between burst frequency and the persistent flux.
 Our deerniünatious of burst decay fiues in 11731-200 ancl 11705-1 Suggest a clear correspoudence )otwoeen ecay time. burst rate behavior and quasi-veriodicity. in the sense that there is acear transition at a Iuniuosiv between L. band «107 ees+t.," Our determinations of burst decay times in 1731-260 and 1705-44 suggest a clear correspondence between decay time, burst rate behavior and quasi-periodicity, in the sense that there is a clear transition at a luminosity between 1.4 and $\times10^{37}$ $\ergs$."
 However. he decay times observed im (ΝΤ απ 11705-11 do iot follow this trend despite tracing ott similar ranges in huuinositv (formally the sale applies to 1U1]5820-30 mt here we know that the decay times cannot ο long )ecause the mass donor is proven to be a helium white clwart: Stella et al.," However, the decay times observed in 3+1 and 1705-44 do not follow this trend despite tracing out similar ranges in luminosity (formally the same applies to 1820-30 but here we know that the decay times cannot be long because the mass donor is proven to be a helium white dwarf; Stella et al."
 1987)., 1987).
 To suunuuilze: the ceutral finding im our study is he likely identification of a single huninosity between Lb to 2.4107* eres tecymusistent with a single mass accretion rate. where the ]nrstimg behavior changes iu τος basic wavs: cole to higher huuinosities. hiysts 1) )ocomie rather quickly a factor of 5 less frequent. 2) stop reciting quasi-periodically. 3) stop being long.," To summarize: the central finding in our study is the likely identification of a single luminosity between 1.4 to $\times10^{37}$ $\ergs$, consistent with a single mass accretion rate, where the bursting behavior changes in three basic ways: going to higher luminosities, bursts 1) become rather quickly a factor of 5 less frequent, 2) stop recurring quasi-periodically, 3) stop being long."
 From theory it is expected that long bursts can ouly be due to helium flashes in a hiydrogeuaich cuviroument. which is predicted to occur at the highest or lowest accretion reeiues (Fujimoto et al.," From theory it is expected that long bursts can only be due to helium flashes in a hydrogen-rich environment, which is predicted to occur at the highest or lowest accretion regimes (Fujimoto et al."
 1Nl: Bildsten 1998: see also introduction)., 1981; Bildsten 1998; see also introduction).
 Civen the fact that in our sample ouly short bursts are observed at hiebher Iuninuosities. we may identity he transition in burst behavior with the transition from he lowest to the middle accYotion regine.," Given the fact that in our sample only short bursts are observed at higher luminosities, we may identify the transition in burst behavior with the transition from the lowest to the middle accretion regime."
 At the lowest IunuinositicS the heliuni flash is triggered » uustable hwdroseu burning (FujimeQ ct al, At the lowest luminosities the helium flash is triggered by unstable hydrogen burning (Fujimoto et al.
 1981)., 1981).
 Between two bursts no lydr'ogen is birued. audit is oulv he accretion of matter theuw iucreases the pressure axd eniperature to high enough values to start this buruine.," Between two bursts no hydrogen is burned, and it is only the accretion of matter that increases the pressure and temperature to high enough values to start this burning."
 If we asstune that the accretion flow is sable then the burst wait fine is only depeudent ou the aceretion rate. and a asi-periodic behavior is not unexpected. as ds a narrow atiouship between its freqποιον and the persisteut flix.," If we assume that the accretion flow is stable then the burst wait time is only dependent on the accretion rate, and a quasi-periodic behavior is not unexpected, as is a narrow relationship between its frequency and the persistent flux."
 Iu the middle accreion regine. hiists take place ina ptre helimm shell which is fed by stabe hydrogen burning i] a laver above hat.," In the middle accretion regime, bursts take place in a pure helium shell which is fed by stable hydrogen burning in a layer above that."
" When a critical temperature axd pressure are reached tie ieiunii ignies,", When a critical temperature and pressure are reached the helium ignites.
 Tere the onset of the bursts is doetermuue by the heating of the sholl due to the hydrogen tnrni1 and the accretion., Here the onset of the bursts is determined by the heating of the shell due to the hydrogen burning and the accretion.
 But more oeuportantly. the onset of heluni burning ds very seusitive ο the temperature {Dildsen 1998). maius it uehly ependent on loca perurba10115 111 the hydrogen burnine.," But more importantly, the onset of helium burning is very sensitive to the temperature (Bildsten 1998), making it highly dependent on local perturbations in the hydrogen burning."
 This means ha local coiitions decrue the ouse (ancl hus the wait time) of a burs. and quasi-periodic beivlor is not readily expoectec alLnviiore.," This means that local conditions determine the onset (and thus the wait time) of a burst, and quasi-periodic behavior is not readily expected anymore."
 Ilvdrogeu starts burniuο m an unstable fashion at ower col1 dept istan heiuu (Joss 1977)., Hydrogen starts burning in an unstable fashion at lower column depths than helium (Joss 1977).
" This loans vat the conditious for trieoeorle an N-rav burst in the owest accretion reednmue9 alEE reached after accreting a sunaller amount of matter fiui in the middle accretion τοσο, and a higher burst rate is expected."," This means that the conditions for triggering an X-ray burst in the lowest accretion regime are reached after accreting a smaller amount of matter than in the middle accretion regime, and a higher burst rate is expected."
" Asstuine iat only the accretio1 rate can set the condition for the PAat of 1ustable ivdrosenu nunmng. it is expected that Us transition happens iu a fairly sinall range of accretion rates,"," Assuming that only the accretion rate can set the condition for the start of unstable hydrogen burning, it is expected that this transition happens in a fairly small range of accretion rates."
 We remark tiat recently an interesting phenomenon was detected of qiASL periolic oscillajons (QPOs) at 7-5 ullz in a few bursting LAINBs wuch appear to coincide with this transition and w“hose oesence ds coupled to he occurrence of ll bursts (Revuvtsey et al., We remark that recently an interesting phenomenon was detected of quasi periodic oscillations (QPOs) at 7-8 mHz in a few bursting LMXBs which appear to coincide with this transition and whose presence is coupled to the occurrence of I bursts (Revnivtsev et al.
 2001)., 2001).
 Revuivtsey et al., Revnivtsev et al.
 speculate that these QPOs are related ο. special modes. of nucle:wo burinuee., speculate that these QPOs are related to special modes of nuclear burning.
 support for this ivpothesis is provided from trends iu kIIz QPOs observed in one of those sources (Yu van der Ίαν 2002)., Support for this hypothesis is provided from trends in kHz QPOs observed in one of those sources (Yu van der Klis 2002).
 We lave for the first time stown that the largest decrease m burst rate towards higjer faxes is coincident with the onset of stable livcdrogei burning., We have for the first time shown that the largest decrease in burst rate towards higher fluxes is coincident with the onset of stable hydrogen burning.
 Thereby. the aboveaneutioned explanation for the appareutly sudden decrease ii burst rate lay xuwtlv resolve a lone-standing problem for explaining decreasing burst rates.," Thereby, the above-mentioned explanation for the apparently sudden decrease in burst rate may partly resolve a long-standing problem for explaining decreasing burst rates."
 Van Paradijs et al. (, Van Paradijs et al. (
1988) explained this by invoking increased stable eli biruius wit1 dnereasiug accretion vate.,1988) explained this by invoking increased stable helium burning with increasing accretion rate.
 However. such burning is not expected to occur at sub-Eddinetou accretion rates (Fujimoto et al.," However, such burning is not expected to occur at sub-Eddington accretion rates (Fujimoto et al."
 1981)., 1981).
 Bildsten (2000) sugeestecOO that norelobal accretion ou the neutron star (Marshall 1982: Iuos;uuov Suuvaev 1999) inav explain the decreasiug burst rate: the accretion area iav be smaller thu he neutron star surface so that, Bildsten (2000) suggested that non-global accretion on the neutron star (Marshall 1982; Inogamov Sunyaev 1999) may explain the decreasing burst rate: the accretion area may be smaller than the neutron star surface so that
to include a correction to the measured intensity of CRs caused by the instrumental errors and power spectrum.,to include a correction to the measured intensity of CRs caused by the instrumental errors and power spectrum.
" It was shown by Zatsepin(1959) that there should be a difference between the observed intensity of CRs and the original intensity in the case of a rapidly falling energy spectrum, due to instrumental errors and fluctuations in the shower parameters measured."," It was shown by \citet{Ztspn} that there should be a difference between the observed intensity of CRs and the original intensity in the case of a rapidly falling energy spectrum, due to instrumental errors and fluctuations in the shower parameters measured."
" Then Murzin(1965) and Kalmykov(1969) calculated the measured intensity in the case of a lognormal distribution of Sgo9 and the so-called shower size, Ne: where Jo is the actual intensity; oy is the RMS deviation of InN.; κ is the integral energy spectrum index; and ay=dlnNe /dln "," Then \citet{Mrzn} and \citet{NNK} calculated the measured intensity in the case of a lognormal distribution of $S_{600}$ and the so-called shower size, $N_e$: where $J_0$ is the actual intensity; $\sigma_N$ is the RMS deviation of $\ln N_e$ ; $\kappa$ is the integral energy spectrum index; and $a_N=d\ln N_e/d\ln E_0$ ."
"In our case, the target valuesEo. are the parameter E = ‘primary particle energy’ estimated after shower detection, and the actual energy of the CR, Es, that initiated the EAS."," In our case, the target values are the parameter $\hat{E}$ = `primary particle energy' estimated after shower detection, and the actual energy of the CR, $E_0$, that initiated the EAS."
" The estimated energy has a distribution around the mean value formed by the instrumental errors and fluctuations with a RMS deviation, c."," The estimated energy has a distribution around the mean value formed by the instrumental errors and fluctuations with a RMS deviation, $\sigma$."
 The energy fluctuation is small in comparison with instrumental errors and can therefore be neglected., The energy fluctuation is small in comparison with instrumental errors and can therefore be neglected.
" If we assume the lognormal distribution of y=InE, with an average value equal to InEo, then the observed intensity of CRs is given by the convolution of the primary spectrum, Joexp(—&z), and the distribution of instrumental errors: 'The resultant observed-to-initial intensity conversion factor is (Murzin1965;Ivanovetal.2009):: The necessary conditions are a constant index and RMS error."," If we assume the lognormal distribution of $y=\ln\hat{E}$, with an average value equal to $\ln E_0$, then the observed intensity of CRs is given by the convolution of the primary spectrum, $J_0\exp(-\kappa z)$, and the distribution of instrumental errors: The resultant observed-to-initial intensity conversion factor is \citep{Mrzn,NJP}: The necessary conditions are a constant index and RMS error."
" As a crude approach, one can use the broken power law approximation of the energy spectrum given by the HiRes collaboration etal.2008),, and the constant RMS error averaged(Abbasi in the range Eg>1015 eV. In the vicinity (with width σ) of the break points the interpolation of the index can be used to prevent gaps in the spectrum."," As a crude approach, one can use the broken power law approximation of the energy spectrum given by the HiRes collaboration \citep{HiRes08}, and the constant RMS error averaged in the range $E_0>10^{18}$ eV. In the vicinity (with width $\sigma$ ) of the break points the interpolation of the index can be used to prevent gaps in the spectrum."
" The procedure is inevitably iterative: The revised spectrum indexes (2.24, 1.8, and 4.5 below the ankle, between the ankle and the cutoff, and above the cutoff energies, respectively) rather than observed indexes should be used in a correction factor."," The procedure is inevitably iterative: The revised spectrum indexes (2.24, 1.8, and 4.5 below the ankle, between the ankle and the cutoff, and above the cutoff energies, respectively) rather than observed indexes should be used in a correction factor."
 In Fig., In Fig.
 1 the energy spectra presented were observed by giant EAS arrays with CR intensity correction factors calculated using the HiRes power law approximation of the energy spectrum and instrumental errors inherent to arrays (Table 1))., \ref{fig:SpectraRJ} the energy spectra presented were observed by giant EAS arrays with CR intensity correction factors calculated using the HiRes power law approximation of the energy spectrum and instrumental errors inherent to arrays (Table \ref{Table:RJ}) ).
" In the PAO and HP cases, however, the corrections are already applied in the original works (Aveetal.2003;Schussler2009) so no intensity corrections are made."," In the PAO and HP cases, however, the corrections are already applied in the original works \citep{HP,PAO09} so no intensity corrections are made."
" Concerning the HiRes experiment, the monocular reconstruction results (Abbasietal.2008) are used here to yield spectra with the best statistical power over a wide energy range."," Concerning the HiRes experiment, the monocular reconstruction results \citep{HiRes08} are used here to yield spectra with the best statistical power over a wide energy range."
" Energy estimation errors of the two HiRes detectors in the monocular mode are derived based on the original data etal.2009a),, with the ratio distribution of energies(Abbasi measured by HR1 and HR2 independently for the same EAS event."," Energy estimation errors of the two HiRes detectors in the monocular mode are derived based on the original data \citep{HiRes09a}, with the ratio distribution of energies measured by HR1 and HR2 independently for the same EAS event."
 The RMS deviation of the ratio is found to be 0.33+0.01., The RMS deviation of the ratio is found to be $0.33\pm 0.01$.
" An immediate consequence is the average energy estimation accuracy of the Fly's Eye detectors in the monocular mode, óE/E 4/0.5(82,+=0.230.01."," An immediate consequence is the average energy estimation accuracy of the Fly's Eye detectors in the monocular mode, $\delta \hat{E}/\hat{E}\simeq \sqrt{0.5(\delta_{HR1}^2+\delta_{HR2}^2)}=0.23\pm 0.01$."
" Since the preliminary5, 02,54)results from the TA experiment (Bergmanetal.2009) are obtained by fluorescence detectors in monocular mode applying the same data-handling procedure as in the HiRes case, the same energy estimation errors are assigned here to both arrays."," Since the preliminary results from the TA experiment \citep{TA09} are obtained by fluorescence detectors in monocular mode applying the same data-handling procedure as in the HiRes case, the same energy estimation errors are assigned here to both arrays."
" For other experiments, instrumental errors in energy estimation are taken from the original papers."," For other experiments, instrumental errors in energy estimation are taken from the original papers."
" The energy of the primary CR particle initiating the EAS is estimated using model relations between Ep and measured shower parameters, such as the ionization integral, Επ, the particle density at 600 πι from the axis, 9699, and the number of electrons at observational level, Νε."," The energy of the primary CR particle initiating the EAS is estimated using model relations between $E_0$ and measured shower parameters, such as the ionization integral, $E_i$, the particle density at 600 m from the axis, $S_{600}$, and the number of electrons at observational level, $N_e$."
 These relations are more or less dependent on thehigh-energyhadron-nucleus and nucleus-nucleus interaction models used., These relations are more or less dependent on thehigh-energyhadron–nucleus and nucleus–nucleus interaction models used.
" Thus, in addition to including instrumental errors, we must introduce a systematic ‘EAS modeling uncertainty’ into the energy estimation"," Thus, in addition to including instrumental errors, we must introduce a systematic `EAS modeling uncertainty' into the energy estimation"
"The equilibrium temperature of a planet (and thus whether or not water can exist in on. the planet surface) is (he.1/2 same if α x. L,/4.wherethe. bolometric huninosity Ly. isliquidphase to be distinguished from L. the luminosity in the band of observation.","The equilibrium temperature of a planet (and thus whether or not water can exist in liquid phase on the planet surface) is the same if $a\propto L_\bol^{1/2}$, where the bolometric luminosity $L_\bol$ is to be distinguished from $L$, the luminosity in the band of observation."
 Hence. the relative sensitivity of a (ransil survey to habitable planets is llere we asstume that all planets have (he same albedo and neglect atmospheric effects.," Hence, the relative sensitivity of a transit survey to habitable planets is Here we assume that all planets have the same albedo and neglect atmospheric effects."
 LI we compare. for example. G stars (11= 5) with middle M stars (M4:=12). the ratios of the various [actors are [N43Nse6x630.70724*780°F©10.," If we compare, for example, G stars $M_V=5$ ) with middle M stars $M_V=12$ ), the ratios of the various factors are $N_{12}/N_{5} \sim 6\times 630^{-3/2}\times 4^{7/2}\times 80^{5/4}\sim 10$."
 Note that if we were comparing detectability at the vather (han ahabitabiliy. (he last factor would not have entered. and the ratio would have been 0.05.," Note that if we were comparing detectability at the rather than the, the last factor would not have entered, and the ratio would have been 0.05."
aitaHence. while the sensitivity to planets in general is completely dominated by G stars. the to habitable planets is completely dominated by. M stars.," Hence, while the sensitivity to planets in general is completely dominated by G stars, the sensitivity to habitable planets is completely dominated by M stars."
 That is. the lower Iuminosities (ancl so smaller semi-major axes) combined with the smaller radii and greater numerical densitv of M stars more than compensate for the reduced photon counts.," That is, the lower luminosities (and so smaller semi-major axes) combined with the smaller radii and greater numerical density of M stars more than compensate for the reduced photon counts."
 In Figure l.. we show the sensitivity to habitable “Earths” and to Earths all at the same semi-major axis (taken to be | AU).," 	In Figure \ref{fig:one}, we show the sensitivity to habitable “Earths” and to Earths all at the same semi-major axis (taken to be 1 AU)."
 That is. (he histograms show the total munber of planets ENthat will be detected as a function of Af; assuming that each star in the field has one Earth-size planet in the habitable zone or. respectively. one such planet at 1 AU. (," That is, the histograms show the total number of planets $N$that will be detected as a function of $M_V$ assuming that each star in the field has one Earth-size planet in the habitable zone or, respectively, one such planet at 1 AU. ("
The two histograms cross al AA:=5 because the habitable zone is then at 1 AU).,The two histograms cross at $M_V=5$ because the habitable zone is then at 1 AU).
 The absolute normalization of this plot is set according to the characteristics ol theKepler mission (7.8.xLOSehr! at V=12. O=105dee. Ay=0.3. mission-total S/N=8 required for detection). but the form of the histogram would be (he same for any photon-lIimited survey.," The absolute normalization of this plot is set according to the characteristics of the mission $7.8\times 10^8\,e^-\,\rm hr^{-1}$ at $V=12$, $\Omega=105\,\rm deg^2$, $A_V=0.3$, mission-total S/N=8 required for detection), but the form of the histogram would be the same for any photon-limited survey."
 The normalization [or any other planet size should be multiplied bv a [actor (r/r..)?. and the normalization [or any other fixed semi-major axis should be multiplied by (6/XU)7 (see [1].," The normalization for any other planet size should be multiplied by a factor $(r/r_\oplus)^6$, and the normalization for any other fixed semi-major axis should be multiplied by $(a/{\rm AU})^{-5/2}$ (see ])."
 The figure is constructed assuming that detection is in V. band., The figure is constructed assuming that detection is in $V$ band.
 The effect of substituting other bands is approximately to change the ui of (he histogram., The effect of substituting other bands is approximately to change the slope of the histogram.
" For example. since the slope of the main sequence is αλ/d(V—[)=3.31 (Reid1991. substitution of I band would lead to an increase of slope dAlogIN/dMy:un""/2)x0.4/3—0.1T8."," For example, since the slope of the main sequence is $d M_V/d(V-I) =3.37$ \citep{reid91}, substitution of $I$ band would lead to an increase of slope $d\Delta \log N/d M_V = (3/2)\times 0.4/3.37 = 0.178$."
" That is. middle M stars would gain relative to G stars by an additional factor ""ο)P818."," That is, middle M stars would gain relative to G stars by an additional factor of $10^{7\times 0.178} = 18$."
 To compute these histograms. we follow the procedure of Pepper. (2002).," 	To compute these histograms, we follow the procedure of \citet{pgd}."
. An important feature of the color-magnitude diagram is that while the main sequence is fairly narrow [or Mq:>6. it broadens for brighter stars (due to Laster stellar evolution). so that a star of a given M can have a large range of colors.," An important feature of the color-magnitude diagram is that while the main sequence is fairly narrow for $M_V>6$, it broadens for brighter stars (due to faster stellar evolution), so that a star of a given $M_V$ can have a large range of colors."
 Thus. for the well-defined ower main AK 6. we consider the luminosity function (Bessell in 1 mag bins. and evaluate the stellar radius at the center of each," Thus, for the well-defined lower main sequence, $M_V>6$ , we consider the luminosity function \citep{bessell93,zheng01}
 in 1 mag bins, and evaluate the stellar radius at the center of each"
The ΕΠ ΗΕ Πλ. CRBs is probably produced by internal shocks in a relativistic wind whereas the afterglow (frou: N-ravs to radio bands) is duc to the external shock. ic. the forward shock propagating in the ISM because of its interaction with the wind (Rees aud Alésszirros. 1991: Wijers et abl. 1997)).,"The gamma-ray emission from GRBs is probably produced by internal shocks in a relativistic wind whereas the afterglow (from X-rays to radio bands) is due to the external shock, i.e. the forward shock propagating in the ISM because of its interaction with the wind (Rees and Mésszárros, \cite{rees} ; Wijers et al., \cite{wijers}) )."
 Stmaultancously. a reverse shock propagates iu the wind itself.," Simultaneously, a reverse shock propagates in the wind itself."
 We illustrate rere the possible contribution of this reverse shock to au A-rav cluission perdunnues immediately after the eiiuuua-ravs., We illustrate here the possible contribution of this reverse shock to an X-ray emission perduring immediately after the gamma-rays.
 Such an ocndssiou has for been observed iu the first CRB detected by Beppo-SAN. GRDB960720.," Such an emission has for been observed in the first GRB detected by Beppo-SAX, GRB960720."
 We use he detailed N-rayv. data made available bv SAN for this mast (Piro et al.. 1998))," We use the detailed X-ray data made available by SAX for this burst (Piro et al., \cite{piro}) )"
 to male a comparison with our heoretical results., to make a comparison with our theoretical results.
 GRDB960720. has been observed both bx BATSE and Beppo-SAX., GRB960720 has been observed both by BATSE and Beppo-SAX.
 It is a single-pulse burst. with a “FRED” profile.," It is a single-pulse burst, with a “FRED” profile."
 Its duration iu the 50-700 keV baud is around 23 s but the N-rav cussion lasts longer: Piro ct al. (1998)), Its duration in the 50-700 keV band is around 2–3 s but the X-ray emission lasts longer: Piro et al. \cite{piro}) )
" show that the power-law between the width of the pulse aud the energy (already: known in the eamunaray rane) is observed down to 2 keV. They find WE}XE.""16, Wo use a simple model to simulate internal shocks aud build svuthetic bursts: all pressure waves are neglected so that we consider only direct collisious between solid lavers.", show that the power-law between the width of the pulse and the energy (already known in the gamma-ray range) is observed down to 2 keV. They find $W(E) \propto E^{-0.46}$ We use a simple model to simulate internal shocks and build synthetic bursts: all pressure waves are neglected so that we consider only direct collisions between solid layers.
" In the shocked material. the magnetic field reaches equipartition values (10 1000 Co) and the Lorentz factor of the electrous is obtained from the dissipated energy per proton e using the foriiula eiveu by Bykov aud Mésszármos (19963) who suppose that only a fraction ¢ of the electrons is accelerated: For ¢~1 the usual equipartition assumption vields values of D, of a few hundreds: the eamuua-rayv ciission is due to inverse Compton scattering on the svuchrotron photons."," In the shocked material, the magnetic field reaches equipartition values (10 – 1000 G) and the Lorentz factor of the electrons is obtained from the dissipated energy per proton $\epsilon$ using the formula given by Bykov and Mésszárros \cite{bykov}) ) who suppose that only a fraction $\zeta$ of the electrons is accelerated: For $\zeta \sim 1$ the usual equipartition assumption yields values of $\Gamma_{e}$ of a few hundreds: the gamma-ray emission is due to inverse Compton scattering on the synchrotron photons."
" Sinaller values for the fraction of accelerated electrous (à<10 7) lead to larecr Lorenz factors (T, of a few thousands) so that the eamunaravs are directly ποιος. by the svuchnrotron process. which is the asstuuption made here."," Smaller values for the fraction of accelerated electrons $\zeta < 10^{-2}$ ) lead to larger Lorenz factors $\Gamma_{e}$ of a few thousands) so that the gamma-rays are directly produced by the synchrotron process, which is the assumption made here."
 Internal shocks have been shown ο successfully reproduce the main temporal aud spectra xoperties of CRBs (Daigue auc \lochkovitch. 1998)). We model GRB9G6G0720 with a wind euütted during s and consisting ina slow and a rapid part of equal mass (sco figure. 1)).," Internal shocks have been shown to successfully reproduce the main temporal and spectral properties of GRBs (Daigne and Mochkovitch, \cite{daigne}) We model GRB960720 with a wind emitted during 4 s and consisting in a slow and a rapid part of equal mass (see figure \ref{FigGamma}) )."
 Two internal shocks are generated aud we stun both coutributious to the cussion to construc the svuthetic burst., Two internal shocks are generated and we sum both contributions to the emission to construct the synthetic burst.
 The profile in the SAN 50-700 keV baud looks very similar to GRB9GOT2Z0 as can be secu iu, The profile in the SAX 50-700 keV band looks very similar to GRB960720 as can be seen in
In Figure 2. we show the different gas infall laws tested in this work and taken from the literature; the vertical line marks the radius correspondent to the solar vicinity at 8 kpe.,In Figure \ref{tau} we show the different gas infall laws tested in this work and taken from the literature; the vertical line marks the radius correspondent to the solar vicinity at 8 kpc.
 Comparing the results of the dwarf metallicity distributions (figure 3)) obtained with the differents τί) we note that the time scale for the infalling gas affects the total number of dwarf stars produced by each model., Comparing the results of the dwarf metallicity distributions (figure \ref{nane_holmb}) ) obtained with the differents $\tau(R)$ we note that the time scale for the infalling gas affects the total number of dwarf stars produced by each model.
 The law presented by Renda et al. (, The law presented by Renda et al. (
2005) is the one which fits better the fraction of stars observed in the GCS of the solar neighbourhood. but the time scale for the solar radius that they adopted (see figure 2)). around 12 Gyrs. is not realistic.,"2005) is the one which fits better the fraction of stars observed in the GCS of the solar neighbourhood, but the time scale for the solar radius that they adopted (see figure \ref{tau}) ), around $12$ Gyrs, is not realistic."
 In this work the time scale for the infalling gas. was derived based on the distribution of dwarf stars in the solar neighbourhood. from which we know that it should be about 7 to 8 Gyrs assuming that the outermost regions of the Galaxy are still forming now.," In this work the time scale for the infalling gas, was derived based on the distribution of dwarf stars in the solar neighbourhood, from which we know that it should be about 7 to 8 Gyrs assuming that the outermost regions of the Galaxy are still forming now."
 Also. this particular form of the r(R) can fit the abundance. gas and SFR gradients. as we will show in the following sections.," Also, this particular form of the $\tau(R)$ can fit the abundance, gas and SFR gradients, as we will show in the following sections."
 On the other hand. the position of the peak and its wings are more important constraints. since owing to observational difficulties we still have problems to define the completeness of the survey (Holmberg et al.," On the other hand, the position of the peak and its wings are more important constraints, since owing to observational difficulties we still have problems to define the completeness of the survey (Holmberg et al."
 2007)., 2007).
 Focusing on these quantities one can note that time scales given by CMR2001 and this work reproduce very well the position of the peak in the observed distribution as well as the high netallicity wing. whereas in the low metallicity side the number of stars is slightly overestimated. but this effect disappears if we consider other distributions (Figure 3.. right panel).," Focusing on these quantities one can note that time scales given by CMR2001 and this work reproduce very well the position of the peak in the observed distribution as well as the high metallicity wing, whereas in the low metallicity side the number of stars is slightly overestimated, but this effect disappears if we consider other distributions (Figure \ref{nane_holmb}, right panel)."
 Recently. Schónnrich Binney (2009) also reproduced the [Fe/H] distribution in the solar neighbourhood by neans of a chemo-dynamical model suggesting that the G-dwarf distribution can be well explained by stellar migration. without considering a inside-out formation.," Recently, Schönnrich Binney (2009) also reproduced the [Fe/H] distribution in the solar neighbourhood by means of a chemo-dynamical model suggesting that the G-dwarf distribution can be well explained by stellar migration, without considering a inside-out formation."
 However. the churning and blurring mechanisms invoked there imply a gas transfer that results in a similar effect.," However, the churning and blurring mechanisms invoked there imply a gas transfer that results in a similar effect."
 After setting the ideal value for the time scale of the infalling gas (7.=0.75R+1.08). a test with a variable star formation efficiency along the galactic disk was performed.," After setting the ideal value for the time scale of the infalling gas $\tau=0.75R+1.08$ ), a test with a variable star formation efficiency along the galactic disk was performed."
 An efficiency which decreases with the galactic radius was adopted until it reached the lower-limit of O0.SGyr~! at 12 kpe., An efficiency which decreases with the galactic radius was adopted until it reached the lower-limit of $0.5 Gyr^{-1}$ at 12 kpc.
 This value is similar to that adopted in succesful models of dwarf irregular and spheroidal galaxies (see Lanfranchi Matteucci. 2003).," This value is similar to that adopted in succesful models of dwarf irregular and spheroidal galaxies (see Lanfranchi Matteucci, 2003)."
" In order to test our assumption of a variable v. we show in Figure 4 a plot of the empirical v=247,VES obtained by adopting the observed SER and X, for the three galaxies."," In order to test our assumption of a variable $\nu$, we show in Figure 4 a plot of the empirical $\nu={SFR \over \Sigma_{gas}^{1.5}}$, obtained by adopting the observed SFR and $ \Sigma_{gas}$ for the three galaxies."
" As one can see. for all the galaxies the ""observed efficiency"" shows a decreasing profile compatible with the trend used in our models."," As one can see, for all the galaxies the “observed efficiency” shows a decreasing profile compatible with the trend used in our models."
 M31 is à nearby spiral galaxy around two times more massive and 2.4 times larger than the Milky Way (Yin et al., M31 is a nearby spiral galaxy around two times more massive and 2.4 times larger than the Milky Way (Yin et al.
 2009)., 2009).
 It belongs to an earlier type than the Milky Way and possesses a larger bulge., It belongs to an earlier type than the Milky Way and possesses a larger bulge.
 To reproduce the chemical evolution of M31. we adopted the same model used for the Milky Way with the following modifications: assumed to be exponential with the scale-length radius Ry=5.4 kpe and central surface density Xo=460M..pc77. as suggested by Geehan et al. (," To reproduce the chemical evolution of M31, we adopted the same model used for the Milky Way with the following modifications: assumed to be exponential with the scale-length radius $R_D=5.4$ kpc and central surface density $\Sigma_0 = 460 M_{\odot}pc^{-2}$, as suggested by Geehan et al. ("
2006). TUR)=0.62R+1.62.,2006). $\tau(R)=0.62R+1.62$.
 This relation was derived under the assumption that at the galactocentric distance equivalent to the solar radius (the R corresponding to the Rs calculated on the basis of the R/Rp ratio). M31 should have a time seale for the infalling gas similar to that of the solar vicinity.," This relation was derived under the assumption that at the galactocentric distance equivalent to the solar radius (the R corresponding to the $R_{\odot}$ calculated on the basis of the $R/R_D$ ratio), M31 should have a time scale for the infalling gas similar to that of the solar vicinity."
 As well the outermost part of the optical disk is still acereting gas., As well the outermost part of the optical disk is still accreting gas.
 the M31 present day gas profile in the disk shows a different trend relative to the Milky Way: it grows with the galactic radius and. after reaching a peak (at around 12 kpe) decreases steeply towards the center. thus suggesting a different scenario. relative to the Milky Way. for the star formation history of this galaxy.," the M31 present day gas profile in the disk shows a different trend relative to the Milky Way; it grows with the galactic radius and, after reaching a peak (at around 12 kpc) decreases steeply towards the center, thus suggesting a different scenario, relative to the Milky Way, for the star formation history of this galaxy."
 This trend is the signature of a very proeminent spiral arm detectable in M31 thanks to its inclination angle which allows us to neasure the column density of the hydrogen distribution., This trend is the signature of a very proeminent spiral arm detectable in M31 thanks to its inclination angle which allows us to measure the column density of the hydrogen distribution.
 In order to reproduce the gas distribution we adopted three different star formation efficiencies., In order to reproduce the gas distribution we adopted three different star formation efficiencies.
 In model M31-Al we assumed v=1Gyr7! (same as the Milky Way). in model it was set equal to 2Gvyr!. whereas in model M3I-B it was supposed to be a function of the galaxy radius v(R)=24/R— 1.5. until it reached a minimum value of 0.5Gv;! and then is assumed to be constant.," In model M31-A1 we assumed $\nu=1 Gyr^{-1}$ (same as the Milky Way), in model M31-A2 it was set equal to $2 Gyr^{-1}$, whereas in model M31-B it was supposed to be a function of the galaxy radius $\nu(R) = 24/R - 1.5$ , until it reached a minimum value of $0.5 Gyr^{-1}$ and then is assumed to be constant."
 we adopted a threshold in eas density of 5M4J/pc. as suggested in Braun et al. (," we adopted a threshold in gas density of $5 M_{\odot}/pc^{2}$, as suggested in Braun et al. ("
2009).,2009).
 for this galaxy we also tested a model with a different exponent k in the Schmidt law. using the lower limit given by Kennicutt et al. (," for this galaxy we also tested a model with a different exponent k in the Schmidt law, using the lower limit given by Kennicutt et al. ("
1998). k=1.25 (this model is indicated by M31-Bk1.25).,"1998), k=1.25 (this model is indicated by M31-Bk1.25)."
"AM respectively, while the upper lit is not constrained duc to the uncertainties ou the erain size distribution.","$M_{\earth}$ respectively, while the upper limit is not constrained due to the uncertainties on the grain size distribution."
" Assiuniug the standard dust/gas ratio of 0.01, these values correspond to mimi disk asses of 0.009 aud 0.003 AL. for the DC Tau and RY Tau respectively."," Assuming the standard dust/gas ratio of 0.01, these values correspond to minimum disk masses of 0.009 and 0.003 $M_{\sun}$ for the DG Tau and RY Tau respectively."
 Figure 8 shows the comparison between models aud observatious du ferus of hne real part of he correlated flux as a function of the baseliie eugth., Figure \ref{fig:uvamp_deproj_real} shows the comparison between models and observations in terms of the real part of the correlated flux as a function of the baseline length.
 To correct for the disk ielination we deprojected the baseliue assmuinee the inclinatio1s and position aneles listed in Table 3.., To correct for the disk inclination we deprojected the baseline assuming the inclinations and position angles listed in Table \ref{tab:res_clubs}.
 Iu this feure. the results for Lf axd Ldst moctels lead to indistinguishable curves.," In this figure, the results for $H$ and $L$ dust models lead to indistinguishable curves."
 Similarity solution ane oower law models are represented with solid aix dashed curves respectively. aud. the observatio are shown bv black dots with error bars.," Similarity solution and power law models are represented with solid and dashed curves respectively, and the observations are shown by black dots with error bars."
 is clear that both the simulavity solution ane power Luv disk models oovide satisfactorv fits to the observations., It is clear that both the similarity solution and power law disk models provide satisfactory fits to the observations.
 The similarity solution motH provides smaller values of 47 (see Table 3. and 13) aud. in the case of DG. Tan. a better fit to the observations between LOO and ὃX kA.," The similarity solution model provides smaller values of $\chi^2$ (see Table \ref{tab:res_clubs} and \ref{tab:res_spades}) ) and, in the case of DG Tau, a better fit to the observations between 400 and 800 $\lambda$."
 Iu this range of spatia frequencies. the power luv solution is characterized by a wigele due to the sharp truncation of the dust emission at 72 AU.," In this range of spatial frequencies, the power law solution is characterized by a wiggle due to the sharp truncation of the dust emission at 72 AU."
 Ou the other hand. the expoucutia taperis of the πιααν solution leads fo a snoohi visibility profile that matches extreme vowell t1C observations.," On the other hand, the exponential tapering of the similarity solution leads to a smooth visibility profile that matches extremely well the observations."
 The saue behavior is present in f1C lower panel which compares the model aud the observations at 2.5 nuu., The same behavior is present in the lower panel which compares the model and the observations at 2.8 mm.
" Towever. in this case the observations at D,,2 LOOkA are too to distiuguisli between the two models."," However, in this case the observations at $B_{uv} > 400 $ $\lambda$ are too to distinguish between the two models."
 Although not couclusive. this result make the snüluitv solution model a more appealing explanation for the dust emission in civctuustellar disks. covirmune the couclusions of Hughesetal.(2008).," Although not conclusive, this result make the similarity solution model a more appealing explanation for the dust emission in circumstellar disks, confirming the conclusions of \citet{hu08}."
. Figue 9 shows the surface density derived from the 1.3 nun observations for both the power law and the siwilavity solution model in the case of hieh dust opacity., Figure \ref{fig:sigma} shows the surface density derived from the 1.3 mm observations for both the power law and the similarity solution model in the case of high dust opacity.
 The two models lead to simular values of SCR) in the region where most of, The two models lead to similar values of $\Sigma(R)$ in the region where most of
To explore the comparison m more detail and o allow for proper comparison with observations. we will use the mass function defined in terms of he observable quantity of mmass within a specific radius.,"To explore the comparison in more detail, and to allow for proper comparison with observations, we will use the mass function defined in terms of the observable quantity of mass within a specific radius."
 Because P-S theory predicts tle mass inside a virial radius. an adjustment needs to be uade to predict the mass within 1.5/5.!Mpce.," Because P-S theory predicts the mass inside a virial radius, an adjustment needs to be made to predict the mass within $h^{-1}$ Mpc."
 We ollow the prescription of Carlbereetal.(1997) relating the top-hat sinoothiug leneth to 345 rather than the virial mass.," We follow the prescription of \cite{CMYE97}
 relating the top-hat smoothing length to $M_{1.5}$ rather than the virial mass."
" A slope of 3/+=0.6 js asstumed in the relation AZ(R)xBR""5) near the virial radius.", A slope of $3-\gamma=0.6$ is assumed in the relation $M(<R)\propto R^{3-\gamma}$ near the virial radius.
 This slope is cousisteut with the ass profile of observed rich clusters (Carlbere.Yee.&Ellingson1997:Rinesetal. 2000).," This slope is consistent with the mass profile of observed rich clusters \citep{CYE97,RGDMW00}."
".. Also. since N-body simulations eive results in variance with P-S. we treat 9, as a free parameter."," Also, since N-body simulations give results in variance with P-S, we treat $\delta_c$ as a free parameter."
" For a given comoving Af43. 6, was adjusted so that the P-S prediction for mtAs) matched the N-body result at that mass."," For a given comoving $M_{1.5}$, $\delta_c$ was adjusted so that the P-S prediction for $n(>M_{1.5})$ matched the N-body result at that mass."
 This was done for all models aud redshifts. beeimning at the mass of the tenth most massive cluster aud working down to 6«10hTAL...," This was done for all models and redshifts, beginning at the mass of the tenth most massive cluster and working down to $6\times10^{13}h^{-1}M_\odot$."
 The resultius à eas a function of ALYτοι is shown in Figure {νι, The resulting $\delta_c$ as a function of $M_{\rm 1.5com}$ is shown in Figure \ref{figdeltac}.
" It is apparent that the standard P-S approximation (ising à, fo spherical overdensity iu near theory) does not fit the siauulations.", It is apparent that the standard P-S approximation (using $\delta_c$ from spherical overdensity in linear theory) does not fit the simulations.
" The cluster abundance depends on à.- roughly as exp(.dc222far). so a higher⋅⋝ à,- micas fewer clusters have formed."," The cluster abundance depends on $\delta_c$ roughly as $\exp(-\delta_c^2/\sigma^2)$, so a higher $\delta_c$ means fewer clusters have formed."
" The à, required by the simulation ATF varies with mass.", The $\delta_c$ required by the simulation MF varies with mass.
" Iu other words. he shape of the standard P-S mass fiction is incorrect: for the low O,, models it predicts too Πα low mass clusters (since the standard 3. is rot large enough). even if à, is fixed to match the üeh mass clusters (22«1015. ΤΗ)."," In other words, the shape of the standard P-S mass function is incorrect; for the low $\Omega_m$ models it predicts too many low mass clusters (since the standard $\delta_c$ is not large enough), even if $\delta_c$ is fixed to match the high mass clusters $\gtrsim 2\times10^{14}h^{-1}M_\odot$ )."
 The tilted SCDAL model shows the opposite trend we are funding more low mass clusters in the simulations han is predicted., The tilted SCDM model shows the opposite trend— we are finding more low mass clusters in the simulations than is predicted.
 This is due to the assumption hat Af(<R)xRY ju adjusting the virial inass o πιω, This is due to the assumption that $M(<R)\propto R^{0.6}$ in adjusting the virial mass to $M_{1.5}$.
" For O,,=1 the extrapolation from 1.5h !Mpe to B, reaches to radii <15 1Mpe for low mass clusters.", For $\Omega_m=1$ the extrapolation from $1.5h^{-1}$ Mpc to $R_{vir}$ reaches to radii $<1h^{-1}$ Mpc for low mass clusters.
 Allowing a steeper slope (Af(<R)x R) for sinaller SCDAL clusters with a virial radius less than 15 tMpe vields results simular to those seen in the other models., Allowing a steeper slope $M(<R)\propto R$ ) for smaller SCDM clusters with a virial radius less than $h^{-1}$ Mpc yields results similar to those seen in the other models.
" A second trend secu in Fieure Lis that à, is lower at higher redshifts. showing that there are more collapsed objects at z>0 than predicted by standard P-S. The redshift depeudence of 4, can be parameterized as 9,=dy|Ó4/(li) with dy and à; chosen separately for cach model."," A second trend seen in Figure \ref{figdeltac} is that $\delta_c$ is lower at higher redshifts, showing that there are more collapsed objects at $z>0$ than predicted by standard P-S. The redshift dependence of $\delta_c$ can be parameterized as $\delta_c=\delta_0+\delta_1/(1+z)$, with $\delta_0$ and $\delta_1$ chosen separately for each model."
 A iuear fit was mace to the best values at A4secu=ο13. and then the parauicters were adjusted slightly to reduce the difference between ιο P-S predietious aud simulations to below across the entire mass range. if possible.," A linear fit was made to the best values at $M_{\rm 1.5com}=2\times10^{14}h^{-1}M_\odot$ , and then the parameters were adjusted slightly to reduce the difference between the P-S predictions and simulations to below across the entire mass range, if possible."
 The fal thoices of by and 6; are shown in Table 3.., The final choices of $\delta_0$ and $\delta_1$ are shown in Table \ref{tbldeltac}.
 It can )e seen that dy is close to the canonical value of 1.68 aud that 6) is X10% of this value. mcauing je 2 dependence is weak.," It can be seen that $\delta_0$ is close to the canonical value of 1.68 and that $\delta_1$ is $\lesssim 10$ of this value, meaning the $z$ dependence is weak."
 Figure 5 shows both ιο N-body ME. aud the results of the modified P-S formula using the à. from Table 3.. alone with the fractional difference between the two.," Figure \ref{fignofmcomp} shows both the N-body MF and the results of the modified P-S formula using the $\delta_c$ from Table \ref{tbldeltac}, along with the fractional difference between the two."
 The siunulation data are fit well by this modified P-S relation. to within foy: Ὁ-2(or: =∕↽laud AFlol'h1M. for SCDMD.," The simulation data are fit well by this modified P-S relation, to within for $z\lesssim 2$ (or $z\lesssim 1$ and $M>10^{14}h^{-1}M_\odot$ for SCDM)."
" An alternative to the simple power-law density oxofile used here is the proposed universal profile or dark matter halos of Navarro.Freuk.&White(1997) (seo also Lokas&Mammon(2000))): he ""tov iodol of Bullock.etal.(2000) oxovides the mass and redshift dependence of the concentration.", An alternative to the simple power-law density profile used here is the proposed universal profile for dark matter halos of \citet{NFW97} (see also \citet{LM00}) ); the “toy model” of \citet{BKSSKKPD00} provides the mass and redshift dependence of the concentration.
 In order to test whether inchiding his dependence would improve the analytic fit. he above analysis was repeated using the NEW xofile to adjust the virial mass to M44.," In order to test whether including this dependence would improve the analytic fit, the above analysis was repeated using the NFW profile to adjust the virial mass to $M_{1.5}$."
" No inuproveinenut in the fit was secu: à, shows both nass aud redshift depeudence in ΠΠ similar ο that observed using the power-law profile. aud 1ο fit Is somewhat worse for redshifts 22."," No improvement in the fit was seen; $\delta_c$ shows both mass and redshift dependence in a manner similar to that observed using the power-law profile, and the fit is somewhat worse for redshifts $z\gtrsim 2$."
" Qur results are in aereciment with Covernatoct (1999).. who likewise found the best fit 6, to be slightly lower as redshift iuereases."," Our results are in agreement with \cite{GBQTBKL99}, who likewise found the best fit $\delta_c$ to be slightly lower as redshift increases."
 However. the + dependence found here is weaker.," However, the $z$ dependence found here is weaker."
" Governatoctal.(1999) simulated an open model with parameters close to our OCDAL run. and found 39,z:1.65 at τΞ1. aerecing well with our value."," \cite{GBQTBKL99}
 simulated an open model with parameters close to our OCDM run, and found $\delta_c\approx 1.65$ at $z$ =1, agreeing well with our value."
 However. at 2=0 the Covernatoetal.(1999) value is well above ours: this mav be due to the fact that their σς value is ligher as well.," However, at $z$ =0 the \cite{GBQTBKL99}
 value is well above ours; this may be due to the fact that their $\sigma_8$ value is higher as well."
 Au additional simulation was carried out using the same parameters as the LOCDAL run. exceptwith 102175 particles. allowing an examination of the effect of increasing the numerical resolution.," An additional simulation was carried out using the same parameters as the LCDM run, exceptwith $1024^3$ particles, allowing an examination of the effect of increasing the numerical resolution."
 The increased προ of particles reduces the ass of particle bv a factor of eight to 7.75« TAL: the softening length was chosen to, The increased number of particles reduces the mass of particle by a factor of eight to $7.75\times 10^{10}h^{-1}M_\odot$ ; the softening length was chosen to
,.
 ⋅↗↳⊽⊑⋅∖≺↕∙⊟≻↥⋅↑⋅↖↴⋉∖≼⊲∶↴∙⊾⋜↧↕⋜⋯↕↸∖↴∖↴∙↑∐↸∖↕∪↕∏∑↕∐∶↴⋁∶↴⋁⋜↧↴∖↴∐⋜↧↴∖↴↴⋝↸∖↸∖∐ expelled outside the dark matter halo. resulting im an SED with απια) nebular contribution aud a Lycontimmiun escape fraction fc1.," For type C galaxies, the ionizing gas has been expelled outside the dark matter halo, resulting in an SED with minimal nebular contribution and a Lyman-continuum escape fraction $f_\mathrm{esc}\approx 1$."
 While this simple picture acuittedly ucelects the anisotropic outflow of gas and the nreeulavitics within the photoionized medium evident from actual simulation (Johusonetal.2009).. it still captures the salient points when it comes to uodelliue the nebular contribution to the ealaxy SED.," While this simple picture admittedly neglects the anisotropic outflow of gas and the irregularities within the photoionized medium evident from actual simulation \citep{Johnson et al. b}, it still captures the salient points when it comes to modelling the nebular contribution to the galaxy SED."
 Iu this paper. we will ouly treat galaxies that belong o categories A (full uebular contribution) aud C (uo jebular contribution).," In this paper, we will only treat galaxies that belong to categories A (full nebular contribution) and C (no nebular contribution)."
 The intermediate type D would be ar more challenging to model in detail the eas density xofile is highly time-dependent at this stage. the long recombination timescales introduce a time lag between he evolution of the stellar aud uchular SEDs. and οπλο] used sky subtraction strategies may intertere with the predicted contribution from the the nebula to he observed SED.," The intermediate type B would be far more challenging to model in detail – the gas density profile is highly time-dependent at this stage, the long recombination timescales introduce a time lag between the evolution of the stellar and nebular SEDs, and commonly used sky subtraction strategies may interfere with the predicted contribution from the the nebula to the observed SED."
 While the relative tux contribution of he nebula aud therefore the overall huninositv does depend on these— effects; the of type A and tvpe— B ealaxies are nonetheless likely to be similar as loug as the syste is voung and uchulay ciission is dominant.," While the relative flux contribution of the nebula – and therefore the overall luminosity – does depend on these effects, the of type A and type B galaxies are nonetheless likely to be similar as long as the system is young and nebular emission is dominant."
 The vouth criterion comes m because the inüsmateli between he momentary stellar SED and the prior ionizing Ποιά ο which the nebula responds becomes more severe once he ligh-nass stars of the stellar population have died aud many intermediate-miass stars have evolved off the nain sequence., The youth criterion comes in because the mismatch between the momentary stellar SED and the prior ionizing field to which the nebula responds becomes more severe once the high-mass stars of the stellar population have died and many intermediate-mass stars have evolved off the main sequence.
 The nebulu contribution from tvpe A ealaxies is nodelled assuming a coustaut-deusity ΠΠ region with wdrogen density »(ID=100 aud flliug factor fag=0.0L., The nebular contribution from type A galaxies is modelled assuming a constant-density HII region with hydrogen density $n(\mathrm{H})=100$ $^{-3}$ and filling factor $f_\mathrm{fill}=0.01$.
" Iu the case of pop Π"" the gaseous uetallicitv is set fo Za=10' galaxies.(Gwhereas Zita.= ). whereas pop IE (Z= 0.0001) and I (Z= 0.020) ealaxies have Za.Zaaes"," In the case of pop IIIgalaxies, the gaseous metallicity is set to $Z_\mathrm{gas}=10^{-7}$ (whereas $Z_\mathrm{stars}=0$ ), whereas pop II $Z=0.0004$ ) and I $Z=0.020$ ) galaxies have $Z_\mathrm{gas}=Z_\mathrm{stars}$."
 Sealed solu abuudauces are used iu alb cases., Scaled solar abundances are used in all cases.
 The default value for the eas covering factor of type A galaxies is ων=1 Ginplving a Lui continu escape fraction fa.= 0)., The default value for the gas covering factor of type A galaxies is $f_\mathrm{cov}=1$ (implying a Lyman continuum escape fraction $f_\mathrm{esc}=0$ ).
 Towever. iu the case of a compact ΠΠ region. anisotropic feedback. supernova chinmevs and inmeguluities iu the eas deusity may result in large holes iu the nebula. through which lonizing radiation can escape iuto the iutergalactic medium.," However, in the case of a compact HII region, anisotropic feedback, supernova chimneys and irregularities in the gas density may result in large holes in the nebula, through which ionizing radiation can escape into the intergalactic medium."
 Simulations predict that the amount of Laman continu escape may be a function of dark halo mass (Cuediuetal.2008:Razounov&Sonuuer-Larseu2010:Yajimaetal. 2011).. but the likely escape fraction and its exact mass dependence remains controversial.," Simulations predict that the amount of Lyman continuum escape may be a function of dark halo mass \citep{Gnedin et al.,Razoumov & Sommer-Larsen,Yajima et al.}, but the likely escape fraction and its exact mass dependence remains controversial."
 Du our model. the possibility of Lyman continu escape through holes is treated by allowing the gas coveriug factor fos to take ou values 0<fay«1.," In our model, the possibility of Lyman continuum escape through holes is treated by allowing the gas covering factor $f_\mathrm{cov}$ to take on values $0<f_\mathrm{cov}<1$."
 While having a very low but non-zero fie. does not capture all the complexities of a type D galaxy. it still eives some indication of what to expect frou such an object.," While having a very low but non-zero $f_\mathrm{cov}$ does not capture all the complexities of a type B galaxy, it still gives some indication of what to expect from such an object."
 Type € objects are treated by setting feo.=0. which imüplies a Lyuiurcoutinuun escape fraction of unity and an SED composed of stars oulv.," Type C objects are treated by setting $f_\mathrm{cov}=0$, which implies a Lyman-continuum escape fraction of unity and an SED composed of stars only."
 Since no nebula is produced. a photoionization code like Cloudy is not required to model this case.," Since no nebula is produced, a photoionization code like Cloudy is not required to model this case."
 In Fig. L.," In Fig. \ref{Mmin},"
 wo use Yeedrasil to predict the »opulation masses of the faintest star-forming galaxics detectable through JWST broadband imaging when aking extremely long exposures of a small patch of he ska ie. a so-called Ultra Deep Field (UDE).," we use Yggdrasil to predict the population masses of the faintest star-forming galaxies detectable through JWST broadband imaging when taking extremely long exposures of a small patch of the sky, i.e. a so-called Ultra Deep Field (UDF)."
 The nass limits presented are based on the requirement hat galaxies are detected at 106 iuleast one JWST xoadband filter (spectral resolution R= 1) after a 100 Lexposure (per filter)., The mass limits presented are based on the requirement that galaxies are detected at $\sigma$ in one JWST broadband filter (spectral resolution $R=4$ ) after a 100 h exposure (per filter).
 While the detailed specifications of IWST UDFs have not vet been fixed. 100 h represents a reasonable estimate of the longest exposure times that are likely to be relevant.," While the detailed specifications of JWST UDFs have not yet been fixed, 100 h represents a reasonable estimate of the longest exposure times that are likely to be relevant."
" The resulting mass limits cau easily be rescaled to other exposure times Fog, usiug: Qur derived amass limits take «ff of the 17 JWST broadband (R= L) filters iuto account. aud are based ou the actual JWST transiission curves of these"," The resulting mass limits can easily be rescaled to other exposure times $t_\mathrm{exp}$ using: Our derived mass limits take of the 17 JWST broadband $R=4$ ) filters into account, and are based on the actual JWST transmission curves of these"
in the ranee of its uncertainty (£10) aud fouud that the resulting orbital epochs are consistent with the best fit value at the lo level.,in the range of its uncertainty $\pm 1 \sigma$ ) and found that the resulting orbital epochs are consistent with the best fit value at the $\sigma $ level.
" The error in the orbital epoch due to an eror m (a,/e)sin/ may also be expressed (Decter. Bovuton aud Pravdo 1981) as where 0,244,4; IS the uncertiinty in the projected orbital radius."," The error in the orbital epoch due to an error in $(a_x/c)\sin i$ may also be expressed (Deeter, Boynton and Pravdo 1981) as where $\sigma _{a_{x}/c sin i}$ is the uncertainty in the projected orbital radius."
 This value is sull relative to our error estimate for the orbital epoch (see Table 1)., This value is small relative to our error estimate for the orbital epoch (see Table 1).
 Iu Figure 2. we preseut the arrival time delay. the best fit elliptical orbit model. aud arrival time residuals.," In Figure 2, we present the arrival time delay, the best fit elliptical orbit model, and arrival time residuals."
 As seen from Table 1. the orbital epochs for circular and clliptical orbital models agree with cach other at the 1 σ level.," As seen from Table 1, the orbital epochs for circular and elliptical orbital models agree with each other at the 1 $\sigma $ level."
 In order to check our tecluique. we extracted observations of [U 1538-52 done in 1997 (ALJD 50119.93-50153.69) and estimated orbital epochs for those observations.," In order to check our technique, we extracted observations of 4U 1538-52 done in 1997 (MJD 50449.93-50453.69) and estimated orbital epochs for those observations."
 The results agreed with the orbital epochs giveu by Clark (2000)., The results agreed with the orbital epochs given by Clark (2000).
 Iu Table 2. we present the orbital epoch measurements from differcut observatories aud orbital evele προ. (1).," In Table 2, we present the orbital epoch measurements from different observatories and orbital cycle number (n)."
 Iu Figure 3. we present observed mums calculated values of orbital epochs (Tao0<Pag>ToooSPopig >) velative to the constant orbital period (<Pyne»-3.7228366 davs).," In Figure 3, we present observed minus calculated values of orbital epochs $T_{\pi/2}-n<P_{orbit}>-<T_{\pi/2}-n<P_{orbit}>>$ ) relative to the constant orbital period $<P_{orbit}>=3.7228366$ days)."
" A quadratic fit to the epochs from all experiments vielded au estimate of the rate of period change P,,4/DP,,4=(0.11.5)«10Ὁ ft.", A quadratic fit to the epochs from all experiments yielded an estimate of the rate of period change $\dot P_{orb}/P_{orb} =(0.4 \pm 1.8) \times 10^{-6}$ $^{-1}$.
 In Figure Lowe display the long-term pulse frequency. history of the source.," In Figure 4, we display the long-term pulse frequency history of the source."
 Before CORO observations. IU 1538-52 had οσο found to have a long-term spin down trend.," Before CGRO observations, 4U 1538-52 had been found to have a long-term spin down trend."
" A linear- fita to pre-CGRO- pulse frequency. lhistorvH gives+ v/v⋅~os*<ELOP4!D and a linear fit to CGRO and our RNTE result vields ήν~1.15«10.ttsἘν,", A linear fit to pre-CGRO pulse frequency history gives $\dot{\nu} /\nu \sim -8 \times 10^{-12} s^{-1}$ and a linear fit to CGRO and our RXTE result yields $\dot {\nu} /\nu \sim 1.45 \times 10^{-11} s^{-1}$.
 Rubin et al (1997) constructed the power spectrum of pulse frequency derivative fluctuations., Rubin et al (1997) constructed the power spectrum of pulse frequency derivative fluctuations.
a red quasar fraction of31%.,a red quasar fraction of.
. Using the observed byWV distribution of our sample. we therefore estimate the A.:18.4 red quasar fraction to be31%.. and robustly constrain it to be greater than22%.," Using the observed $b_J - K$ distribution of our sample, we therefore estimate the $K \leq 18.4$ red quasar fraction to be, and robustly constrain it to be greater than."
". Lf the majority of red quasars are the result. of dust reddening. our estimate of and lower bound on. the red. quasar fraction is Consistent with that required by Calli,Comastri.&Llasinger(2007). to explain the quasar contribution to the X-Ray Background."," If the majority of red quasars are the result of dust reddening, our estimate of, and lower bound on, the red quasar fraction is consistent with that required by \citet{2007A&A...463...79G} to explain the quasar contribution to the X-Ray Background."
 We tested the ability of our KN method. variant to select quasars bv constructing aby; Lvs. RAx. colour-colour plot in Figure 11.., We tested the ability of our KX method variant to select quasars by constructing a $b_J - R$ vs. $R - K$ colour-colour plot in Figure \ref{colourcolourplot}.
 In Figure 11. the majority of the quasars are distinct [rom the stellar locus. only 7 lie within the stellar locus. successfully. demonstrating the ability of the KN method to select. quasars.," In Figure \ref{colourcolourplot} the majority of the quasars are distinct from the stellar locus, only 7 lie within the stellar locus, successfully demonstrating the ability of the KX method to select quasars."
 At the top right of Figure 1l. the typical (mean) 5; Rand RRAN uncertainties due to photometric uncertainties ancl quasar variability. are plotted. as a cross.," At the top right of Figure \ref{colourcolourplot}, the typical (mean) $b_J - R$ and $R - K$ uncertainties due to photometric uncertainties and quasar variability, are plotted as a cross."
 Examining the uncertainties in the quasar Colours allowed: us to determine how distinct. from the stellar locus the quasars actually are., Examining the uncertainties in the quasar colours allowed us to determine how distinct from the stellar locus the quasars actually are.
 The photometric uncertainties in the 5; anc Ro magnitudes are both taken to be QO.1 magnitudes (Drinkwaterctal.2000).., The photometric uncertainties in the $b_J$ and R magnitudes are both taken to be 0.1 magnitudes \citep{2000A&A...355..900D}.
 The Wk magnitude photometric uncertainties were calculated by SIxtractor during processing., The K magnitude photometric uncertainties were calculated by SExtractor during processing.
 To account for variability. we move both the 56; and Ix photometry to the middle epoch of the r photometry.," To account for variability, we move both the $b_J$ and K photometry to the middle epoch of the r photometry."
 To do this for the 5;RR colour we used the structure function of Hooketal.(1994).. outlined in Section 3.1.. with 2Muu;= 15 vears.," To do this for the $b_J - R$ colour we used the structure function of \citet{1994MNRAS.268..305H}, outlined in Section \ref{detection}, with $\Delta t_{obs} =$ 15 years."
 We did not do this for wRIN colour as a structure function was not available for 10 Ix-band. instead the variability was estimated to be 0.1 magnitudes for all the quasars. from observations in Enyaal. (2002)..," We did not do this for the $R - K$ colour as a structure function was not available for the K-band, instead the variability was estimated to be 0.1 magnitudes for all the quasars, from observations in \citet{2002ApJS..141...31E}."
 Data from Envactal.(2002) was usec as rev measured the Ix band: variability of quasars satisfying 29<Alp«18 and 0<zl1. which closely matches 10 quasar sample constructed here.," Data from \citet{2002ApJS..141...31E} was used as they measured the K band variability of quasars satisfying $-29 < M_B < -18$ and $0 < z < 1$, which closely matches the quasar sample constructed here."
 For the quasars in our sample with redshifts greater than 1. 0.1) magnitude will » an over-estimate of the effect of variabilitv: however. as un is of the order of the typical Ix magnitude photometric ncertaintv. anvover-estimate was negligible compared. to 1e total uncertainty in the Ix magnitudes.," For the quasars in our sample with redshifts greater than 1, 0.1 magnitude will be an over-estimate of the effect of variability; however, as it is of the order of the typical K magnitude photometric uncertainty, anyover-estimate was negligible compared to the total uncertainty in the K magnitudes."
 Combining all 10 relevant uncertainties in quadrature the uncertainties in the byRH and £2?ÁN quasar colours was calculated. and typical (mean) values plotted in Figure 11..," Combining all the relevant uncertainties in quadrature the uncertainties in the $b_J - R$ and $R - K$ quasar colours was calculated, and typical (mean) values plotted in Figure \ref{colourcolourplot}."
 Examining Figure 11.. we concluded that the quasars in our sample were indeed. distinct from the stellar locus: because. the 6;oR and δὲν uncertainties were small enough that the regions bounded by them were distinct from the stellar locus.," Examining Figure \ref{colourcolourplot}, we concluded that the quasars in our sample were indeed distinct from the stellar locus; because, the $b_J - R$ and $R - K$ uncertainties were small enough that the regions bounded by them were distinct from the stellar locus."
 The argument for the use of the KX method in detecting quasars is not that it finds rec quasars: but that dt is relatively bias free in its selection of quasars. whether red or blue.," The argument for the use of the KX method in detecting quasars is not that it finds red quasars; but that it is relatively bias free in its selection of quasars, whether red or blue."
 We experimentally tested this argument by comparing Figures 12 and 13. to Figure H.., We experimentally tested this argument by comparing Figures \ref{UVX} and \ref{multiplot} to Figure \ref{UonlyKX}. .
" Figure 12. is a standard Ub, vs. ba colour-magnitude plot used in selecting quasars in the UVX approach.", Figure \ref{UVX} is a standard $U - b_J$ vs. $b_J$ colour-magnitude plot used in selecting quasars in the UVX approach.
 Figure 19 is al’by vs byR , Figure \ref{multiplot} is a $U - b_J$ vs $b_J - R$ 
We then analyzed the data in our sample using /j;0.47kpe in eq. (5)).,"We then analyzed the data in our sample using $h_\mathrm{e} = h/2 =
0.47\kpc$ in eq. \ref{eq-emp}) ),"
 leaving out 4 pulsars in globular clusters at |x|>3kpe., leaving out 4 pulsars in globular clusters at $|z| > 3\kpc$.
 As only a small part of their lines of sight passes through the electron layer. the mean electron densities along the line of sight are unrealistically low.," As only a small part of their lines of sight passes through the electron layer, the mean electron densities along the line of sight are unrealistically low."
" Figure 2. shows the distribution of EM,sin|6|(z) for all pulsars.", Figure \ref{fig:2} shows the distribution of $EM_\mathrm{p}\sin|b|(z)$ for all pulsars.
" The steady increase of EM,sin|b| with |;| agrees well with the expected variation (full line). but the scatter is larger than in Fig. 1.."," The steady increase of $EM_\mathrm{p} \sin|b|$ with $|z|$ agrees well with the expected variation (full line), but the scatter is larger than in Fig. \ref{fig:1}. ."
 In this section we investigate the dependencies of (1). (zy. N. and Fy. on |z]. and the relationship between Εν and N..," In this section we investigate the dependencies of $\avnel$ , $\langle\nel^2\rangle$, $\Nec$ and $\Filfac$ on $|z|$, and the relationship between $\Filfac$ and $\Nec$."
 The statistical treatment is the same as used by BMM and we refer to that paper for details., The statistical treatment is the same as used by BMM and we refer to that paper for details.
 The results are given in Table 2.., The results are given in Table \ref{tab:2}.
 We first show in Fig., We first show in Fig.
" 3. that EM, is well correlated with DM: the bisector fit yields EM,=(0.13+0.049DMP="" with very high significance."," \ref{fig:3} that $\EM_\mathrm{p}$ is well correlated with $\DM$: the bisector fit yields $\EM_\mathrm{p} = (0.13
\pm 0.04) \DM^{1.15\pm 0.07}$ with very high significance."
 This indicates that both quantities probe the same ionized regions along the line of sight. although the beams used for the Πα observations (up to 1°) also sample regions located around the single sightline to the pulsar.," This indicates that both quantities probe the same ionized regions along the line of sight, although the beams used for the $\alpha$ observations (up to ) also sample regions located around the single sightline to the pulsar."
 Variations in electron density across the beam will contribute to the scatter in Fig. 3.., Variations in electron density across the beam will contribute to the scatter in Fig. \ref{fig:3}.
" The components of EM, and DM along [=| correlate less well than those along the Galactic plane (see Table 2)). because of the different scale heights of n2(<) and n)."," The components of $\EM_\mathrm{p}$ and $\DM$ along $|z|$ correlate less well than those along the Galactic plane (see Table \ref{tab:2}) ), because of the different scale heights of $\nel^2(z)$ and $\nel(z)$."
 Figure + presents the various densities and Εν as a function of |<] in the logY--|z| plane., Figure \ref{fig:4} presents the various densities and $\Filfac$ as a function of $|z|$ in the $\log Y - |z|$ plane.
 Although these variables represent averages along the line of sight. we approximated their |z|-distributions by exponentials with scale height H.," Although these variables represent averages along the line of sight, we approximated their $|z|$ -distributions by exponentials with scale height $H$."
 The fits are listed in Table 2.., The fits are listed in Table \ref{tab:2}.
 The distribution of (n;z) in Fig., The distribution of $\avnel(z)$ in Fig.
 Aaa is effectively constant up to |]=IKkpe (dashed line). a well known fact first noted by Weisberg et al. (1980)).," \ref{fig:4}a a is effectively constant up to $|z| \simeq 1\kpc$ (dashed line), a well known fact first noted by Weisberg et al. \cite{weisberg+80}) )."
 Beyond this height (.) decreases., Beyond this height $\avnel$ decreases.
 A fit to all points (full line) gives a mean value at the midplane of (nay=0.019+0.02cm™. in fair agreement with the expected value Gado=nO)0.023+0.004em? derived in Sect.," A fit to all points (full line) gives a mean value at the midplane of $\avnel_0 = 0.019\pm 0.02\cmcube$, in fair agreement with the expected value $\avnel_0 = \nel(0) = 0.023 \pm
0.004\cmcube$ derived in Sect."
 3., 3.
 The scale height is less well determined. though.," The scale height is less well determined, though."
 The spread in the data clearlydecreases away from the plane. aswas also noted by BMM.," The spread in the data clearlydecreases away from the plane, aswas also noted by BMM."
 This ts not due to longer pathlengths. because the spread in the distribution projected along the plane remains constant (not shown).," This is not due to longer pathlengths, because the spread in the distribution projected along the plane remains constant (not shown)."
 It just shows that the variety in electron, It just shows that the variety in electron
five comparison stars using and the DAOPHOT package.,five comparison stars using and the DAOPHOT package.
 The positions of WASP-19 and the five comparison stars used are marked in Fig. 1.., The positions of WASP-19 and the five comparison stars used are marked in Fig. \ref{fig:field_of_view}.
" Several brighter comparison stars were ruled out either because they were over the linearity limit of the chip, or because they fell too near the edge of the field on some images due to the dithering."," Several brighter comparison stars were ruled out either because they were over the linearity limit of the chip, or because they fell too near the edge of the field on some images due to the dithering."
" An aperture of 12 pixel radius was used for each star, and the remaining sky was estimated using an annulus of width 5 pixels beginning at 20 pixels from the stars’ centres."," An aperture of 12 pixel radius was used for each star, and the remaining sky was estimated using an annulus of width 5 pixels beginning at 20 pixels from the stars' centres."
" The flux of WASP-19 was then divided by the sum of the flux from the five comparison stars to obtain the raw light curve, shown in Fig. 3.."," The flux of WASP-19 was then divided by the sum of the flux from the five comparison stars to obtain the raw light curve, shown in Fig. \ref{fig:lcv_raw}."
" Initial estimates of the photometric errors were calculated using the aperture electron flux, sky and read noise."," Initial estimates of the photometric errors were calculated using the aperture electron flux, sky and read noise."
" Clearly, a trend can be seen in the light curve, likely caused by the PSFs elongating during the observations."," Clearly, a trend can be seen in the light curve, likely caused by the PSFs elongating during the observations."
" This was removed by normalising the light curve by fitting a linear or quadratic function of time to the out-of-transit data, to set the out-of-transit flux equal to 1."," This was removed by normalising the light curve by fitting a linear or quadratic function of time to the out-of-transit data, to set the out-of-transit flux equal to 1."
" The best-fit models using the linear and quadratic functions are shown in Fig. 3,,"," The best-fit models using the linear and quadratic functions are shown in Fig. \ref{fig:lcv_raw},"
 although the linear function is preferred and used to determine the light curve parameters (see Sect. 3))., although the linear function is preferred and used to determine the light curve parameters (see Sect. \ref{sect:modelling}) ).
 The normalisation of the light curves for both functions was strongly affected by outlying points at the start and end of the observations., The normalisation of the light curves for both functions was strongly affected by outlying points at the start and end of the observations.
" As the sky background was estimated from 9 frames at either side of each image, the sky subtraction was not estimated accurately."," As the sky background was estimated from 9 frames at either side of each image, the sky subtraction was not estimated accurately."
" We decided to remove the first and last 20 data points (~30 minutes) from the light curve analysis (shown in grey in Fig. 3)),"," We decided to remove the first and last 20 data points $\sim30$ minutes) from the light curve analysis (shown in grey in Fig. \ref{fig:lcv_raw}) ),"
 which still left substantial out-of-transit data to constrain the normalisation function., which still left substantial out-of-transit data to constrain the normalisation function.
" The HAWK-I light curve was fitted using an MCMC (Markov-Chain Monte-Carlo) routine, which is a method used to explore the multi-dimensional parameter space of a model fit efficiently, allowing a determination of the joint posterior probability distribution for the parameters (see 2008)."," The HAWK-I light curve was fitted using an MCMC (Markov-Chain Monte-Carlo) routine, which is a method used to explore the multi-dimensional parameter space of a model fit efficiently, allowing a determination of the joint posterior probability distribution for the parameters \citep[see e.g.,][]{tegmark_2004, holman_winn_2006, cameron_2007, winn_holman_2008}."
". Our implementation of MCMC uses the x? fitting statistic for a model light curve given by where fops,j is the flux observed at time j, o; is the corresponding uncertainty and feaic,j is the flux calculated from the model for time 7."," Our implementation of MCMC uses the $\chi^2$ fitting statistic for a model light curve given by where $f_{{\rm obs},j}$ is the flux observed at time $j$, $\sigma_j$ is the corresponding uncertainty and $f_{{\rm calc},j}$ is the flux calculated from the model for time $j$."
 The model flux f.uc was constructed using Kepler's laws to determine the normalised separation of the planet and star centres as a function of time assuming a circular orbit., The model flux $f_{{\rm calc}}$ was constructed using Kepler's laws to determine the normalised separation of the planet and star centres as a function of time assuming a circular orbit.
 The analytic equations of Mandel&Agol(2002) were then used to calculate the flux from the normalised separation assuming no limb darkening on the planet's surface (as this will only affect the ingress and egress which the HAWK-I data is unable to constrain)., The analytic equations of \citet{mandel_agol_2002} were then used to calculate the flux from the normalised separation assuming no limb darkening on the planet's surface (as this will only affect the ingress and egress which the HAWK-I data is unable to constrain).
 The system parameters were held fixed at the values determined by Hebbetal.(2010) to determine the shape of the transit., The system parameters were held fixed at the values determined by \citet{hebb_2010} to determine the shape of the transit.
 The depth D and width W of the transit could then be varied by simply scaling the transit shape in both flux and time axes., The depth $D$ and width $W$ of the transit could then be varied by simply scaling the transit shape in both flux and time axes.
 A long chain of model parameter sets is created by adding small Gaussian perturbations to the previous accepted set., A long chain of model parameter sets is created by adding small Gaussian perturbations to the previous accepted set.
 At each step we apply the Metropolis-Hastings rule to decide whether to accept the new parameter set., At each step we apply the Metropolis-Hastings rule to decide whether to accept the new parameter set.
 A model that produces a lower x? than the previous model is always accepted., A model that produces a lower $\chi^2$ than the previous model is always accepted.
 A model that produces a higher x? is, A model that produces a higher $\chi^2$ is
high performance far UV detectors.,high performance far UV detectors.
 This paper focuses on the development of an astronomical detector optimized for use with a monolithic UV spectrograph from 120 to 300nm., This paper focuses on the development of an astronomical detector optimized for use with a monolithic UV spectrograph from 120 to 300nm.
" Due to the highly variable indices of Si, no single material or thickness is sufficient to achieve high QE over the whole range."," Due to the highly variable indices of Si, no single material or thickness is sufficient to achieve high QE over the whole range."
" The lack of a suitable broadband AR-coating in the UV does not rule out alternatives, and one can still achieve excellent performance through a creative use of coatings."," The lack of a suitable broadband AR-coating in the UV does not rule out alternatives, and one can still achieve excellent performance through a creative use of coatings."
" Sacrificing a single coating, and thus broadband imaging potential, and instead using a series of sequential narrowband coatings allows for higher QE overall."," Sacrificing a single coating, and thus broadband imaging potential, and instead using a series of sequential narrowband coatings allows for higher QE overall."
" Following this idea, a delta-doped CCD is to be coated in sections using different materials (an alternative would be a mosaic of devices, each with one coating)."," Following this idea, a delta-doped CCD is to be coated in sections using different materials (an alternative would be a mosaic of devices, each with one coating)."
" This tiling lends itself most readily to a fixed spectrograph, where only one wavelength of light hits a particular region on the CCD."," This tiling lends itself most readily to a fixed spectrograph, where only one wavelength of light hits a particular region on the CCD."
 Spectrographs with a fixed grating are becoming more common since they are relatively easy and low cost to mass-produce., Spectrographs with a fixed grating are becoming more common since they are relatively easy and low cost to mass-produce.
 Space based instruments may also employ a fixed grating to reduce complexity and cost., Space based instruments may also employ a fixed grating to reduce complexity and cost.
" We have selected MgF2, MgO, HfO2, Al2O3, and SiO» to test as suitable AR coatings."," We have selected $_2$ , MgO, $_2$, $_2$ $_3$, and $_2$ to test as suitable AR coatings."
" The materials chosen reflect the unique requirements of a UV AR coating, including a favorable index of refraction and low absorption in the desired waveband."," The materials chosen reflect the unique requirements of a UV AR coating, including a favorable index of refraction and low absorption in the desired waveband."
" One must be able to deposit the film in a uniform way, while not causing damage to the CCD itself."," One must be able to deposit the film in a uniform way, while not causing damage to the CCD itself."
 T'his eliminates electron beam evaporation (a common choice for dielectric coatings) as a potential technique because it causes X-ray damage to the CCDs., This eliminates electron beam evaporation (a common choice for dielectric coatings) as a potential technique because it causes X-ray damage to the CCDs.
" We have tested sputtering, atomic layer deposition and thermal evaporation techniques for consistency (ALD),and measured the reflectance of films on a substrate of bare Si."," We have tested sputtering, atomic layer deposition (ALD), and thermal evaporation techniques for consistency and measured the reflectance of films on a substrate of bare Si."
" This is a low cost, faster alternative to testing on live devices."," This is a low cost, faster alternative to testing on live devices."
" The downside is that testing is limited to reflectance off this surface, which necessarily omits any absorption losses."," The downside is that testing is limited to reflectance off this surface, which necessarily omits any absorption losses."
 We then compare our measurements to the theoretical models., We then compare our measurements to the theoretical models.
" A further discussion of deposition techniques and their effect on film quality will be presented in a forthcoming paper (Greer, 2011 (submitted))."," A further discussion of deposition techniques and their effect on film quality will be presented in a forthcoming paper (Greer, 2011 (submitted))."
 We also quickly report on the application of films onto live devices., We also quickly report on the application of films onto live devices.
" A detailed account of these results are under prepartion to be submitted for publication (Nikzad, 2011 (submitted))."," A detailed account of these results are under prepartion to be submitted for publication (Nikzad, 2011 (submitted))."
" Briefly, thinned and delta-doped standard and EMCCDs were both used in a variety of tests to measure absolute QE."," Briefly, thinned and delta-doped standard and EMCCDs were both used in a variety of tests to measure absolute QE."
 EMCCDs are an advancement in CCD techonology which enables photon-counting., EMCCDs are an advancement in CCD techonology which enables photon-counting.
 À longer explanation is provided in Section 4.., A longer explanation is provided in Section \ref{sec:devices}.
 'These live device tests provide a more realistic view of the performance of these films than simple reflectance tests., These live device tests provide a more realistic view of the performance of these films than simple reflectance tests.
 With live devices we are able to directly measure the effect the AR coating has on transmission into the the Si., With live devices we are able to directly measure the effect the AR coating has on transmission into the the Si.
" Papers are in preparation on the stability and testing of these devices, as well as on detailed live results and future FUV detector technology (Hoenk, 2011 Nikzad 2011 Here we (submitted)"," Papers are in preparation on the stability and testing of these devices, as well as on detailed live results and future FUV detector technology (Hoenk, 2011 (submitted); Nikzad 2011 (submitted); \citep{2011Jacquot}) )."
;report on the growth of (submitted);these (?))).films and the optical testing of reflectance which we have performed., Here we report on the growth of these films and the optical testing of reflectance which we have performed.
 In Section 2. we discuss how films were deposited and what materials were chosen., In Section \ref{sec:Techniques} we discuss how films were deposited and what materials were chosen.
" In Section 3 we discuss the conditions for reflectance testing, following with a discussion of our results in Section 3.1.."," In Section \ref{sec:testing} we discuss the conditions for reflectance testing, following with a discussion of our results in Section \ref{sec:results}."
 We also include dé&tin, We also include a discussion of the data from live devices in Section \ref{sec:devices}.
g models in Secti890 5.., Finally we briefly look to future work and more advanced coating models in Section \ref{sec:future}.
" All film depositions were performed at the Jet Propulsion Laboratory (JPL) using thermal evaporation, Atomic Layer Deposition (ALD), and Radio Frequency (RF) dielectric sputtering."," All film depositions were performed at the Jet Propulsion Laboratory (JPL) using thermal evaporation, Atomic Layer Deposition (ALD), and Radio Frequency (RF) dielectric sputtering."
 We have used thermal evaporation to deposit layers of MgF2 and RF sputtering to deposit layers of MgO and SiOg., We have used thermal evaporation to deposit layers of $_2$ and RF sputtering to deposit layers of MgO and $_2$.
" RF sputtering and ALD were both used for making films of HfOs, and Al1505."," RF sputtering and ALD were both used for making films of $_2$, and $_2$ $_3$."
" All films were grown on 1” (100) P/B 1-20 Ohm- single-side polished wafers of Si, as a proxy for the actual device."," All films were grown on 1” $\langle$ $\rangle$ P/B 1-20 Ohm-cm single-side polished wafers of Si, as a proxy for the actual device."
 The thickness of each material has been selected to minimize reflectance in a specific wavelength range., The thickness of each material has been selected to minimize reflectance in a specific wavelength range.
" Calculations of predicted reflectance were done using the TFcalcM software package, with a bare Si substrate and are shown in Figure 1, along with the current average QE of the GALEX UV space telescope."," Calculations of predicted reflectance were done using the $^{TM}$ software package, with a bare Si substrate and are shown in Figure \ref{fig:ideal}, along with the current average QE of the GALEX UV space telescope."
 The thickness of the model film was varied until a minimum of losses (reflectance back to the observer plus absorption) was achieved in the target wavelength range., The thickness of the model film was varied until a minimum of losses (reflectance back to the observer plus absorption) was achieved in the target wavelength range.
 Contour plots showing potential transmission percentage as a function of wavelength and thickness are shown for each film in Figures 2 through 6.., Contour plots showing potential transmission percentage as a function of wavelength and thickness are shown for each film in Figures \ref{fig:peakHfO2} through \ref{fig:peakMgF2}.
" Each plot shows contours of 50-80 percent potential transmission, given a range to thicknesses."," Each plot shows contours of 50-80 percent potential transmission, given a range to thicknesses."
 A dark vertical line on the plot indicates the absorption edge., A dark vertical line on the plot indicates the absorption edge.
 This edge marks the region where absorption begins to increase rapidly as wavelength decreases; generally this fast increase begins when absorption has reached10-2096.., This edge marks the region where absorption begins to increase rapidly as wavelength decreases; generally this fast increase begins when absorption has reached.
 Thus anything to the right of the line indicates wavelengths where absorption is not a primary concern., Thus anything to the right of the line indicates wavelengths where absorption is not a primary concern.
 Thicknesses which provided close to peak transmission while also maintaining a wide range above 50 percent were selected., Thicknesses which provided close to peak transmission while also maintaining a wide range above 50 percent were selected.
 The reflectance that corresponded to this thickness was then used as a target during testing., The reflectance that corresponded to this thickness was then used as a target during testing.
 We sought to make a range of film thickness that were centered around this target., We sought to make a range of film thickness that were centered around this target.
 Typically we tested several films that varried in thickness between 5-10nm aboveand below the target., Typically we tested several films that varried in thickness between 5-10nm aboveand below the target.
" There are several published indices of refraction for the Si substrate, which contributes to some uncertainty in the predicted reflectance."," There are several published indices of refraction for the Si substrate, which contributes to some uncertainty in the predicted reflectance."
 The indices of, The indices of
production is substantial in metal-poor intermecliatc-mass stars (LMS),production is substantial in metal-poor intermediate-mass stars (IMS).
 In the low-metallicity regime. asvmiptotie giant branch (AGB) stars are believed to generate and from alpha capture onto 77Ne trigeered by Le-shell thermal pulsing.," In the low-metallicity regime, asymptotic giant branch (AGB) stars are believed to generate and from alpha capture onto $^{22}$ Ne triggered by He-shell thermal pulsing."
" More massive AGD stars (4 « mM. modi7""i 6)0relesscommonthanlowermassstarsbulmeaybeasigni, and to ", More massive AGB stars (4 $<$ $m$ $<$ 6) are less common than lower mass stars but may be a significant production site for and.
resolve the , Temperatures at the base of the convective envelope in these stars can be high enough to burn via hot bottom burning (HBB) as well as synthesise large amounts of and.
cliscrepaney between observations ancl previous 1 predictions., We explore the possibility that AGB stars produce sufficient quantities of and to resolve the discrepancy between observations and previous model predictions.
 The temporal ancl racial evolution of the isotopic abundances in the Milky Way was calculated under the assumption that the Galaxy formed. via the accretion of gas at a rate decreasing exponentially with time., The temporal and radial evolution of the isotopic abundances in the Milky Way was calculated under the assumption that the Galaxy formed via the accretion of gas at a rate decreasing exponentially with time.
 For the sake of simplicity. we assuumedl only a single episode of primordial gas accretion. with a timescale of GCGvr at the solar radius.," For the sake of simplicity, we assumed only a single episode of primordial gas accretion, with a timescale of Gyr at the solar radius."
 However the results were not significantly dilferent for a two-phase accretion model., However the results were not significantly different for a two-phase accretion model.
 We traced the chemical elements through the ongoing eveles of star formation. nucleosynthesis. and ejection into the interstellar medium (ISM) via supernovac (SNe) explosions and stellar winds.," We traced the chemical elements through the ongoing cycles of star formation, nucleosynthesis, and ejection into the interstellar medium (ISM) via supernovae (SNe) explosions and stellar winds."
 In order to precisely monitor the abuncances of isotopes with cillerent production sites. masse and metallicitv-dependent stellar lifetimes and. vields were emploved.," In order to precisely monitor the abundances of isotopes with different production sites, mass- and metallicity-dependent stellar lifetimes and yields were employed."
 The rate of star formation in this model varies with the square of the gas surface density and inversely with CGalactocentric radius., The rate of star formation in this model varies with the square of the gas surface density and inversely with Galactocentric radius.
 This tvpe of radiallv-dependent law is motivated by the idea that spiral arm patterns trigger star formation (c.g. Prantzos Silk 1998)., This type of radially-dependent law is motivated by the idea that spiral arm patterns trigger star formation (e.g. Prantzos Silk 1998).
 The mass distribution of each new generation of stars was eoverned by the Ixroupa. Tout Cilmore (1993) three-component initial mass function (AIP). with lower and upper mass limits of 0.8 and LOO M... respectively.," The mass distribution of each new generation of stars was governed by the Kroupa, Tout Gilmore (1993) three-component initial mass function (IMF), with lower and upper mass limits of 0.8 and 100 $_{\odot}$, respectively."
 Theee basic models were constructed. differing only in the adopted nucleosynthesis prescriptions.," Three basic models were constructed, differing only in the adopted nucleosynthesis prescriptions."
 Firstly. refers to a combination of low and intermemass Sen vields from Ixaralkas Lattanzio (2003a.b) and a grid of mass ancl metallicity dependent (Z UN= e0. ma% 0.02) massive star vields provided by Limonei (2001. unpublished). td using the FRANEC in Limongi. Straneiro Chictli (2000) and Limongi Chiclli (2002).," Firstly, refers to a combination of low and intermediate-mass stellar yields from Karakas Lattanzio (2003a,b) and a grid of mass and metallicity dependent (Z = 0, $^{-3}$ 0.02) massive star yields provided by Limongi (2001, unpublished), calculated using the FRANEC code described in Limongi, Straneiro Chieffi (2000) and Limongi Chieffi (2002)."
s The model.AGB... is identical to the first model but ignores the AGB contribution to and secondproduction.," The second model, is identical to the first model but ignores the AGB contribution to and production."
 Finally. the model replicates but using metallicity-cependent Woosley Weaver (1995) vields for massive stars.," Finally, the model replicates but using metallicity-dependent Woosley Weaver (1995) yields for massive stars."
 All models adopt vields for Type la SNe from the W model of Bwamoto et al. (, All models adopt yields for Type Ia SNe from the W7 model of Iwamoto et al. (
1999).,1999).
-- “Phe ion la contribution to chemical evolution was calculated following the method from Matteucci 1986)., The SNe Ia contribution to chemical evolution was calculated following the method from Matteucci Greggio (1986).
 nHt was assumed that οἱ binaries in SNe La. since this fraction provides a good fit to the prese SNe La rate (e.g. Alibes et al.," It was assumed that of binaries culminate in SNe Ia, since this fraction provides a good fit to the present-day SNe Ia rate (e.g. Alibes et al."
 2001)., 2001).
 esPor MUNstars whose metallicity lies below (above) the range covered by the nucleosvnthesis mocels we estimate ir vields by extrapolating from the two lowest (highest) metallicity. grids., For stars whose metallicity lies below (above) the range covered by the nucleosynthesis models we estimate their yields by extrapolating from the two lowest (highest) metallicity grids.
 The Ixarakas Lattanzio (2003a.b) stellar models comprise a eric of Mg isotopic vields covering a range of low to intermediate stellar mass (1 3 mM. π 6) and à variety of compositions (Z = 0.004. 0.008 0.02 supplemented by an unpublished 0.0001. grid. calculated with the same code) that is well-suited for chemical evolution models.," The Karakas Lattanzio (2003a,b) stellar models comprise a grid of Mg isotopic yields covering a range of low to intermediate stellar mass (1 $\le$ $m$ $_{\odot}$ $\le$ 6) and a variety of compositions (Z = 0.004, 0.008 0.02, supplemented by an unpublished 0.0001 grid calculated with the same code) that is well-suited for chemical evolution models."
 These models have been evolved from the pre-main sequence to near the end of the AGB phase., These models have been evolved from the pre-main sequence to near the end of the thermal-pulsing AGB phase.
 The nucleosynthesis caleulations are performed separately to determine the production of the isotopes., The nucleosynthesis calculations are performed separately to determine the production of the isotopes.
 Figure L shows the predicted. evolution of magnesium isotopic ratios with ΜοΗ] from the models tine)) and line)) for the solar region., Figure 1 shows the predicted evolution of magnesium isotopic ratios with [Fe/H] from the models ) and ) for the solar region.
 and ave shown in the upper and lower panels. respectively. along with measured abundance ratios in local dwarfs from Cav Lambert (2000) and cool subdwarfs from. Yong (2003).," and are shown in the upper and lower panels, respectively, along with measured abundance ratios in local dwarfs from Gay Lambert (2000) and cool subdwarfs from Yong (2003)."
 Representative observational errors are indicated by the large crosses., Representative observational errors are indicated by the large crosses.
 Although the quoted errors for and are identical in both studies. is expected to be more accurately determined than because the 7 MgllI line is less blended with 7! Mgll. 3oth models shown in Figure 1. predict ratios larger than solar (indicated by squares) but consistent with the data of Gav Lambert.," Although the quoted errors for and are identical in both studies, is expected to be more accurately determined than because the $^{26}$ MgH line is less blended with $^{24}$ MgH. Both models shown in Figure 1 predict ratios larger than solar (indicated by squares) but consistent with the data of Gay Lambert."
 Iis not surprising that the models reach similar present-day values irrespective of whether AGBs are included. because massive stars are responsible for most of the neutron-rich Mg isotopes in the present-day ISML," It is not surprising that the models reach similar present-day values irrespective of whether AGBs are included, because massive stars are responsible for most of the neutron-rich Mg isotopes in the present-day ISM."
 £n this model of present in the ISM at οΗ] = 0 comes from AGB stars compared with ~ at Fe/l — Land nearly at Fe/H] — 2., In this model of present in the ISM at [Fe/H] = 0 comes from AGB stars compared with $\sim$ at [Fe/H] = $-$ 1 and nearly at [Fe/H] = $-$ 2.
 The dotted. lines reveal that below Fe/H]  — 1. massive stars alone seriously. under. produce and with respect to“Ale.," The dotted lines reveal that below [Fe/H] $\sim$ $-$ 1, massive stars alone seriously under produce and with respect to."
 Much better agreement is obtained by including the contribution from iD stars., Much better agreement is obtained by including the contribution from AGB stars.
" In particular. most of the heavy. Mg isotopic abundance at low metallicity is controlled by the4-6 PM. stars that undergo hot bottom burning and whose Le-shells are hot enough to trigger the δΝοία.η) and ""Ὕνναα.- reactions (Ixarakas"," In particular, most of the heavy Mg isotopic abundance at low metallicity is controlled bythe 4-6 $_{\odot}$ stars that undergo hot bottom burning and whose He-shells are hot enough to trigger the $\alpha,n$ and $\alpha,\gamma$ reactions (Karakas"
llere we are interested in stationary solutions of form: 50. Eq.(7) is reduced (to equation for c: Now. we define a parameter £ by. eeuation: and then. the equation (9) takes the form: This equation can be interpreted as Schróddinger Equation for a potencial of the form of!.,"Here we are interested in stationary solutions of form: So, $\ref{ft2.7}$ ) is reduced to equation for $\psi$: Now, we define a parameter $E$ by equation: and then, the equation $(\ref{ft2.9})$ takes the form: This equation can be interpreted as Schröddinger Equation for a potencial of the form $\phi_{0}^{n-1}$."
 The problem now is. given a static solution oy of the equation (5). find a eeneral solution of the equation (11). On the other hand. Ao-Theory (7=3). the general static solutions of the classical equation of motion to the field © are given by sn-tvpe elliptic functions [10] =—-2esn FH where e is aM belonging to interval (0.1] and ," The problem now is, given a static solution $\phi_{0}$ of the equation $(\ref{ft2.4})$, find a general solution of the equation $(\ref{ft2.11})$ On the other hand, $\lambda\phi^4$ -Theory $(n=3)$, the general static solutions of the classical equation of motion to the field $\phi$ are given by ${\rm sn}$ -type elliptic functions \cite{fl:a1}
 = ( ), where $c$ is aparameter belonging to interval $(0,\frac{1}{2}]$ and l =."
From this relation. clearly /€(0.1]. Now. substituting ój(c) given by Eq.," From this relation, clearly $l \in (0,1]$ Now, substituting $\phi_{0}(x)$ given by Eq."
 (12) in Eq., $(\ref{ft3})$ in Eq.
 (11) with η=3 we get: η EL)psitt n])). where we have used also Eq.," $(\ref{ft2.11})$ with $n=3$ we get: = ( ,l) - E ), where we have used also Eq."
 (10) and the change of variable In ihe literature the general form of Eq. (14)), $\ref{ft2.10}$ ) and the change of variable In the literature the general form of Eq. \ref{ft8}) )
 is the Lameé dillerential equation. which is given by [11) (min sn3(o.) COYyLambdat(a))-0.(15) where m is a positive real number. A? is the parameter of the Jacobian Elliptic Function sn. and C is an arbitrary constant.," is the Lamé differential equation, which is given by ${\cite{fl:aa}}$ - ( ,k) + C )=0, where $m$ is a positive real number, $k^2$ is the parameter of the Jacobian Elliptic Function ${\rm sn}$ , and $C$ is an arbitrary constant."
 Therefore. comparing (14)) with (15))," Therefore, comparing \ref{ft8})) with \ref{ft9}) )"
The gravitational lensing contribution to the temperature power spectra has been computed in the past by several authors(o.e. Blanchard SSchneider 1987. Cole I5bfstathiou 1989. Sasaki 1989. Seljak 1996. Gonzállez. Sanz CCavónn 1997. Zaldarriaga SSeljak 199.,"The gravitational lensing contribution to the temperature power spectra has been computed in the past by several authors (e.g. Blanchard Schneider 1987, Cole Efstathiou 1989, Sasaki 1989, Seljak 1996, nez-Gonz\'{a}llez, Sanz Cayónn 1997, Zaldarriaga Seljak 1998)."
" ""mHere we follow the approach of Seljak(199 and 2 SSeljak (1998).", Here we follow the approach of Seljak (1996) and Zaldarriaga Seljak (1998).
 We denote the linear power spectra as C7. CF: and CO Copfor temperature. polarisation⋠⋠ (E-component: only) and their. cross-correlation respectively.," We denote the linear power spectra as $C_\ell^T,$ $C_\ell^E$ and $C_\ell^C$ for temperature, polarisation (E-component only) and their cross-correlation respectively."
 The CAIB spectra including the gravitational lensing contribution are assigned a tilele., The CMB spectra including the gravitational lensing contribution are assigned a tilde.
 The fall radiation power spectra including gravitational lensing can be expressed as convolutions of the corresponding linear spectra (£=T.1E.C). where the window. functions⋅. YV;;;d are given. as. and photon path “. Llere 7 denotes a conformal time. y=and7)7 (subscripts ) and. LS denote voles at the present last scattering -- and £2.(A.7) is the power spectrum of the gravitational potential of the matter. perturbations.," The full radiation power spectra including gravitational lensing can be expressed as convolutions of the corresponding linear spectra $(I=T,E,C)$, where the window functions ${\cal W}^I_{\ell\ell'}$ are given as, and photon path dispersions, Here $\tau$ denotes a conformal time, $\chi\equiv\tau_0-\tau$ (subscripts $0$ and $LS$ denote values at the present and last scattering respectively), and $P_\phi\l(k,\tau\r)$ is the power spectrum of the gravitational potential of the matter perturbations."
 The window function VW(x.yes) is given by the expression: where singX gives the distance traveled by the photon emitted at τοX The above set of equations has been derived recently by Zaldarriaga SSeljak (1998). sce Zaldarriaga SSeljak (1998) equations (7)-(10)]. except that we have set the upper limit of the 6-integration in equations (G--S)) to infinity to ensure the correct asvimptotic limit CsCy for cí(B).aco(B)+0.," The window function $W\l(\chi,\chi_{LS}\r)$ is given by the expression: where $\sin_K \chi$ gives the distance traveled by the photon emitted at $\tau_0-\chi$ The above set of equations has been derived recently by Zaldarriaga Seljak (1998) [see Zaldarriaga Seljak (1998) equations (7)-(10)], except that we have set the upper limit of the $\theta$ -integration in equations \ref{wT}- \ref{wTE}) ) to infinity to ensure the correct asymptotic limit $\wtilde{C}_\ell\rightarrow C_\ell$ for $\sigma\l(\theta\r), \sigma_2\l(\theta\r) \rightarrow 0$."
 The gravitational lensing correction to the CAIB anisotropies depends on the full matter power spectrum. including non-linear contributions [rom small spatial scales.," The gravitational lensing correction to the CMB anisotropies depends on the full matter power spectrum, including non-linear contributions from small spatial scales."
 Previous caleulations (e.g. Cole EEfstathiou 1989. Seljak 1996 Zaldarriaga Sseljak modes199) have suggestedBS that the contribution of non-incar introduces only minor corrections to the gravitational lensing contribution computed using the linear orm of the matter power spectrum.," Previous calculations (e.g. Cole Efstathiou 1989, Seljak 1996, Zaldarriaga Seljak 1998) have suggested that the contribution of non-linear modes introduces only minor corrections to the gravitational lensing contribution computed using the linear form of the matter power spectrum."
 To check whether non-inear evolution alfects our analvsis we have mocelled the the non-linear corrections to the matter power spectrum using he approach of Peacock Does (Peacock DDocleds 199€3)., To check whether non-linear evolution affects our analysis we have modelled the the non-linear corrections to the matter power spectrum using the approach of Peacock Dodds (Peacock Dodds 1996).
 For values of ox(fo) given in equation (2)). he Peacock-Dodels non-linear corrections are indeed. small," For values of $\sigma_8\l(t_0\r)$ given in equation \ref{cluster}) ), the Peacock-Dodds non-linear corrections are indeed small"
"turned out to be a(72000)—12 10 0.925, 8(072000)— 52? 26/28""1LO in the observation aud o(2000) 12 10"" Onsen, à(J2000)— -52 267287661 in theHRC observations.","turned out to be $\alpha(J2000)$ $^h$ $^m$ $^s$, $\delta (J2000)$ = $^\circ$ 40 in the observation and $\alpha(J2000)$ $^h$ $^m$ $^s$, $\delta (J2000)$ = $^\circ$ 61 in the observations."
 The two positious agree within (L as expected according to astrometric accuracy. (06 at confidence⋅ level)) aud are consistent. with. those computed by using the same data.," The two positions agree within $0\farcs4$, as expected according to astrometric accuracy $0\farcs6$ at confidence ) and are consistent with those computed by using the same data."
 To evaluate the accuracy of the absolute astrometry. we cross-correlated the position of X-ray sources detected witlin oof the optical axis with that of stars in the Two Microu All Sky Survey catalog.," To evaluate the accuracy of the absolute astrometry, we cross-correlated the position of X-ray sources detected within of the optical axis with that of stars in the Two Micron All Sky Survey catalog."
 We found twe natches between 2MASS stars and sources detected both wo theACTS audHRC., We found two matches between 2MASS stars and sources detected both by the and.
 Based ou the source deusitw. we expect a chance aliguinent of 2MÁSS source f a source within the nominal 90% error region o have a probability of and of for andHRC. respectively.," Based on the source density, we expect a chance alignment of 2MASS source to a source within the nominal $90\%$ error region to have a probability of and of for and, respectively."
 Thus. it is very likely that the wo 2MASS SOMTCON are the IR counterparts of the uatchedChandra sources.," Thus, it is very likely that the two 2MASS sources are the IR counterparts of the matched sources."
 The difference. between the iux the 2MLASS coordinates of these sources is of ~OFL ane is consistent with the expected astrometric accuracy ofChandra., The difference between the and the 2MASS coordinates of these sources is of $\sim0\farcs4$ and is consistent with the expected astrometric accuracy of.
 Offsets along Right Ascension aud Declination range frou 0/07 o 0733 and have different directions., Offsets along Right Ascension and Declination range from $0\farcs07$ to $0\farcs33$ and have different directions.
 Thus. no siguificaut plate ranstormation could be computed iu order to further Muprove Chandra astrometry.," Thus, no significant plate transformation could be computed in order to further improve Chandra astrometry."
 Use of he USNO-D1 caalog vields one further possible coincidence (vith a lavecr offset ~ 171). which is of no help.," Use of the USNO-B1 catalog yields one further possible coincidence (with a larger offset $\sim1\farcs1$ ), which is of no help."
 On the optical side. we then re-coluputed the astrometric calibration of the large-field of view lumaee against the positious of 35 well-suited reference stars (ic. not too faint. not saturated. not close to the CCD edges or to diffraction spikes) selected from 2\LASS ideutified in the mosaic of the two echips.," On the optical side, we then re-computed the astrometric calibration of the large-field of view image against the positions of 35 well-suited reference stars (i.e., not too faint, not saturated, not close to the CCD edges or to diffraction spikes) selected from 2MASS identified in the mosaic of the two chips."
 We measured the pixel coordinates of the 2\TASS sources through eaussian fitting with the (GATA) and we computed the pixel-to-sky coordinates transformation using the codeASTROM’., We measured the pixel coordinates of the 2MASS sources through gaussian fitting with the ) and we computed the pixel-to-sky coordinates transformation using the code.
". This vielded an ziis of 0,2:Q711 in our astrometric fif. accounting for the rms of the fit in the rieht ascension and dechnation compoucuts."," This yielded an rms of $\sigma_r \approx 0\farcs11$ in our astrometric fit, accounting for the rms of the fit in the right ascension and declination components."
 Thanks to the pixel scale of theWEC.. we ucelected the uncertaintv on the reference star centroids.," Thanks to the pixel scale of the, we neglected the uncertainty on the reference star centroids."
 Following?.. we also estimated the uncertainty in the reeistration of the Ἡπμασο on the 2ALASS reference frame.," Following, we also estimated the uncertainty in the registration of the image on the 2MASS reference frame."
 This is given as 0j.=VBSσενγω. Where V3fr accounts for the free parameters in the astrometric fit. σε<(072 is the Incan positional eror of the 2MASS coordinates. Ny} is the number of 2ALASS stars used for the astrometric calibration.," This is given as $\sigma_{tr}=\sqrt 3 \times \sigma_{ref} / \sqrt N_{ref}$, where $\sqrt 3$ accounts for the free parameters in the astrometric fit, $\sigma_{ref} \la 0\farcs2$ is the mean positional error of the 2MASS coordinates, $N_{ref}$ is the number of 2MASS stars used for the astrometric calibration."
" Ii our case. we obtain og,=000."," In our case, we obtain $\sigma_{tr}=
0\farcs06$."
 We finally considered the (70015 uncertainty on the link of 2\LASS to the International Celestial Reference. Frame ICRF)., We finally considered the 015 uncertainty on the link of 2MASS to the International Celestial Reference Frame (ICRF).
 Thus. by adding iu quadrature the riis of the astrometric fit and all the above uncertainties. we obtained that the overall positional accuracy of our astrometry is ὃν=Q'13 (1o).," Thus, by adding in quadrature the rms of the astrometric fit and all the above uncertainties, we obtained that the overall positional accuracy of our astrometry is $\delta r =0\farcs13$ $1\sigma$ )."
 Dv finally addius in quadrature tliis value to the 076 error ou the coordinates we obtained au overall uucertaiutv of ~0762 ou the registration of the pposition on the Mage., By finally adding in quadrature this value to the $0\farcs6$ error on the coordinates we obtained an overall uncertainty of $\sim 0\farcs62$ on the registration of the position on the image.
 Results are shown in Figure 1.., Results are shown in Figure \ref{acs}. .
 lies about 171 aud 173 off theHEC audACES position of5209.. respectively.," lies about $1\farcs1$ and $1\farcs3$ off the and position of, respectively."
 Such offsets are larecr than the expected accuracy of Chaudra astromoetry. which is estimated to be of 075 close to the centre of the field of view.," Such offsets are larger than the expected accuracy of Chandra astrometry, which is estimated to be of $0\farcs8$ close to the centre of the field of view."
 As already coucluded by Miguani et al. (, As already concluded by Mignani et al. (
20074) aud7.. the association of source Z to bbased on positional coincidence seenis very unlikely.,"2007a) and, the association of source Z to based on positional coincidence seems very unlikely."
 Results from our TST test allow us to exclude auv association of source Z to5209., Results from our HST test allow us to exclude any association of source Z to.
. Thus. we can use the deep images to set upper liuits to any uudetected source at the position of5209.," Thus, we can use the deep images to set upper limits to any undetected source at the position of."
. We iocus on the two deep oobservatious obtained through the E555W. aud FalAWW filters., We focus on the two deep observations obtained through the F555W and F814W filters.
 To estimate count rates. we used a circular aperture of 075 radius aud then we performed aperture correction lowing?.," To estimate count rates, we used a circular aperture of $0\farcs5$ radius and then we performed aperture correction following."
. Count rate to magnitude conversions was xorforiied. using standard photometric calibration provided by the data processing xpeline., Count rate to magnitude conversions was performed using standard photometric calibration provided by the data processing pipeline.
 Taking into account the observed backeround 10186 In à portion of the image surrounding the position of5209.. we set a 320 upper But of iugajp —28.1 and ΠΕ. 28.," Taking into account the observed background noise in a portion of the image surrounding the position of, we set a $3\sigma$ upper limit of $_{F814W}$ =28.1 and $_{F555W}$ =28.1."
 For completcucss. we also computed ιο flux of source Z. which resulted to be πρ=2[.7140.01 and προσ=26.80£0.05.," For completeness, we also computed the flux of source Z, which resulted to be $_{F814W}=24.71\pm0.01$ and $_{F555W}=26.80\pm0.05$."
" Using the mere recent Πμαρσο, we computed mipsiy=2183dx0.08. consistent with the füux iu the same baud."," Using the more recent image, we computed $_{F814W}=24.83\pm0.08$, consistent with the flux in the same band."
 The quoted values are not eredaeuec., The quoted values are not dereddened.
 Moreover. we include iu our photometric study a series of IR observations collected with the aand available iu the public ESO archive (Programe TO.D-OL36A).," Moreover, we include in our photometric study a series of IR observations collected with the and available in the public ESO archive (Programme 70.D-0436A)."
 and reported preliminary results from such data., and reported preliminary results from such data.
 IR observations of wwere performed in service 110de with the (ISAAC) instrument atthe (Paranal Observatory) between January 27th aud. March Lath 2003., IR observations of were performed in service mode with the ) instrument atthe (Paranal Observatory) between January 27th and March 18th 2003.
 The, The
In addition to the thin flux tube approximation and simulations of rising flux tubes on. stratified. atmospheres. other recent attempts have been made in order to simulate the formation of a magnetic layer through the interaction of an imposed shear in convectively stable (?) and unstable (2) atmospheres. with an imposed vertical magnetic. field.,"In addition to the thin flux tube approximation and simulations of rising flux tubes on stratified atmospheres, other recent attempts have been made in order to simulate the formation of a magnetic layer through the interaction of an imposed shear in convectively stable \citep{vasil+etal_08} and unstable \citep{silvers+etal_09a}
 atmospheres, with an imposed vertical magnetic field."
 They have found that. unlike in the cases of imposed toroidal magnetic layers. buoyancy instability is harder to excite when the magnetic field is generated by the shear.," They have found that, unlike in the cases of imposed toroidal magnetic layers, buoyancy instability is harder to excite when the magnetic field is generated by the shear."
 More recently ?.. have found. with a similar setup. that the buoyancy may be favored by the presence of double-diffusive instabilities (these in turn depend on the ratio between the thermal and magnetic diffusivities. y/ij. often known as the inverse Roberts number).," More recently \cite{silvers+etal_09b}, have found, with a similar setup, that the buoyancy may be favored by the presence of double-diffusive instabilities (these in turn depend on the ratio between the thermal and magnetic diffusivities, $\chi/\eta$, often known as the inverse Roberts number)."
 Later independent study of ? has confirmed this result., Later independent study of \cite{chatterjee_11} has confirmed this result.
 However. in most of the current models. the presence of stratified turbulence. self-consistent generation of the magnetic field. or both. are omitted.," However, in most of the current models, the presence of stratified turbulence, self-consistent generation of the magnetic field, or both, are omitted."
 In view of the above mentioned issues. other mechanisms have been proposed in order to explain sunspots.," In view of the above mentioned issues, other mechanisms have been proposed in order to explain sunspots."
 These are related to instabilities due to the presence of a diffuse large-scale magnetic field in a highly stratified turbulent medium (2???)..," These are related to instabilities due to the presence of a diffuse large-scale magnetic field in a highly stratified turbulent medium \citep{Kleo+Roga_94,roga+kleo_07,bran+etal_10b,bran+etal_10a}."
 Mean-field models using this mechanism are able to produce strong flux concentrations but this has not yet been achieved in direct numerical simulations., Mean-field models using this mechanism are able to produce strong flux concentrations but this has not yet been achieved in direct numerical simulations.
 Here we present numerical simulations of compressible turbulent convection with an imposed radial shear flow located in à sub-adiabatic layer beneath the convective region., Here we present numerical simulations of compressible turbulent convection with an imposed radial shear flow located in a sub-adiabatic layer beneath the convective region.
 For numerical reasons. explained below. we do not include rotation in our setup. tthe turbulence is not helical. and an aQ dynamo is not expected.," For numerical reasons, explained below, we do not include rotation in our setup, the turbulence is not helical, and an $\alpha\Omega$ dynamo is not expected."
 Nevertheless. recent studies have shown that mean-field dynamo action ts possible due to non-helical turbulence and shear (????)..," Nevertheless, recent studies have shown that mean-field dynamo action is possible due to non-helical turbulence and shear \citep{bran05,yousef_etal_08b,yousef_etal_08a,BRRK08}."
 The nature of this dynamo is not yet entirely clear and may be attributed to the so called shear-current effect (??) or to the incoherent. stochastic. o-effect (?)..," The nature of this dynamo is not yet entirely clear and may be attributed to the so called shear-current effect \citep{rog+kleo_03,rog+kleo_04}
 or to the incoherent, stochastic, $\alpha$ -effect \citep{vish+bran_97}."
 According to (?) the latter explanation is consistent with the turbulent transport coefficients., According to \citep{BRRK08} the latter explanation is consistent with the turbulent transport coefficients.
 Based on these results. we expect the development of a mean field magnetic field. i.e. dynamo action. with a system that mimics. as far as possible. the conditions of the solar intertor. specifically in the lower part of the convection zone and the tachoeline.," Based on these results, we expect the development of a mean field magnetic field, i.e. dynamo action, with a system that mimics, as far as possible, the conditions of the solar interior, specifically in the lower part of the convection zone and the tachocline."
 As the shear is localized in a very narrow layer. we also expect the formation of a magnetic layer and the subsequent buoyancy of the magnetic fields.," As the shear is localized in a very narrow layer, we also expect the formation of a magnetic layer and the subsequent buoyancy of the magnetic fields."
 A similar setup was studied recently by ?.., A similar setup was studied recently by \cite{Tobias+etal_08}.
 They reported the appearance of elongated stripes of magnetic field in the directiol of the shear., They reported the appearance of elongated stripes of magnetic field in the direction of the shear.
 However. since they considered the Boussinesq approximation in their simulations. no buoyancy was observed.," However, since they considered the Boussinesq approximation in their simulations, no buoyancy was observed."
" They also do not report the presence of a large scale dynamo,", They also do not report the presence of a large scale dynamo.
 Two important features distinguish the simulations presented here from previous studies in the context of flux tube formation and emergence., Two important features distinguish the simulations presented here from previous studies in the context of flux tube formation and emergence.
 Firstly. we consider a highly stratified domain with z& scale heights in pressure and 76 scale heights in density.," Firstly, we consider a highly stratified domain with $\approx8$ scale heights in pressure and $\approx6$ scale heights in density."
 Secondly. we do not impose a background radial magnetic field but allow the self-consistent development of the field from a initial random seed.," Secondly, we do not impose a background radial magnetic field but allow the self-consistent development of the field from a initial random seed."
 Even though this is a complicated setup where it ts difficult to analyze the different processes occurring independently. we believe that these simulations may give us some light on the current paradigm of sunspot formation.," Even though this is a complicated setup where it is difficult to analyze the different processes occurring independently, we believe that these simulations may give us some light on the current paradigm of sunspot formation."
 There are several important issues that we want to address with the following simulations. (, There are several important issues that we want to address with the following simulations. (
1) What are requirements for dynamo action in the present setup?,1) What are requirements for dynamo action in the present setup?
 This includes the dependence of the dynamo excitation on several parameters such as the amplitude of the shear. thickness and location of the shear layer. and the aspect ratio of the box. (," This includes the dependence of the dynamo excitation on several parameters such as the amplitude of the shear, thickness and location of the shear layer, and the aspect ratio of the box. ("
2) What ts the resulting configuration of the magnetic field?,2) What is the resulting configuration of the magnetic field?
 In particular. whether the field is predominantly in small or large scales. and whether it 1s organized in the form of a magnetic layer or isolated magnetic flux tubes. (," In particular, whether the field is predominantly in small or large scales, and whether it is organized in the form of a magnetic layer or isolated magnetic flux tubes. ("
3) Is the buoyancy instability (?) operating on these magnetic structures?,"3) Is the buoyancy instability \citep{P55}
 operating on these magnetic structures?"
 If yes. (4) how it depends on the parameters listed above? (," If yes, (4) how it depends on the parameters listed above? ("
5) Is it possible to have magnetic structures strong enough to emerge from the shear layer to the surface without being affected by the turbulent convective motions? (,5) Is it possible to have magnetic structures strong enough to emerge from the shear layer to the surface without being affected by the turbulent convective motions? (
6) Finally. it is important to study how these strong structures back-react on the fluid motions. including the shear profile as well as the convective pattern.,"6) Finally, it is important to study how these strong structures back-react on the fluid motions, including the shear profile as well as the convective pattern."
 Another important issue that may be addressed in this context is the mechanism that triggers the dynamo instability., Another important issue that may be addressed in this context is the mechanism that triggers the dynamo instability.
 With the recent developments on the test-field method. 1t is possibly to compute the dynamo transport coefficients and have a better understanding on the underlying mechanism.," With the recent developments on the test-field method, it is possibly to compute the dynamo transport coefficients and have a better understanding on the underlying mechanism."
 We have organized this paper as follow: in Sect., We have organized this paper as follow: in Sect.
 2. we provide the details of the numerical model. in Sect.," \ref{sec:model} we provide the details of the numerical model, in Sect."
 3. we describe our results.," \ref{sec:results}
 we describe our results."
 We summarize and conclude in Sect. 4.., We summarize and conclude in Sect. \ref{sec:conclusions}.
 Our model setup is similar to that used by ? and ?.., Our model setup is similar to that used by \cite{bjnrst96} and \cite{kkb08}.
" A rectangular portion of a star is modeled by a box whose dimensions are (L,.L,.EL.)=(1.L1.2)d8. where ¢ is the depth of the convectively unstable layer. which is also used as the unit of length."," A rectangular portion of a star is modeled by a box whose dimensions are $(L_x,
L_y, L_z) = (4,4,2)d$, where $d$ is the depth of the convectively unstable layer, which is also used as the unit of length."
 The box is divided into three layers. an upper cooling layer. a convectively unstable layer. and a stable overshoot layer (see below).," The box is divided into three layers, an upper cooling layer, a convectively unstable layer, and a stable overshoot layer (see below)."
 The following set of equations for compressible magnetohydrodynamies is being solved: where D/Dt=0f0t|U-N is the total time derivative.," The following set of equations for compressible magnetohydrodynamics is being solved: where $D/Dt = \pd/\pd t + \bm{U} \cdot
\bm{\nabla}$ is the total time derivative."
 A is the magnetic vector potential. B=V«A is the magnetic field. and J=V«Bjjn 15 the current density. jy 1s the," $\bm{A}$ is the magnetic vector potential, $\bm{B} =
\bm{\nabla} \times \bm{A}$ is the magnetic field, and $\bm{J}
=\bm{\nabla} \times \bm{B}/\mu_0$ is the current density, $\mu_0$ is the"
temperature profiles and the direction of heat flow for an SIDM dark halo with a black hole accreting from (he inner regions.,temperature profiles and the direction of heat flow for an SIDM dark halo with a black hole accreting from the inner regions.
" For r€&«r. (7>1). the dark matter behaves like a {nicl and hence heat transfer can be described by a diffusion equation r?mpykracc. where 5 is the entropy. y is the darkmatter particle mass. and T is the temperature defined as 4hp,T=nyc."," 	 	 	For $r<<r_c$ $\tau \gg 1$ ), the dark matter behaves like a fluid and hence heat transfer can be described by a diffusion equation m_p where $S$ is the entropy, $m_p$ is the darkmatter particle mass, and $T$ is the temperature defined as $\frac{1}{2}k_BT\equiv\frac{1}{2}m_pv^2$."
" The coefficient of thermal conductivity for (he monatomic gas is. where c, is the specific heat per particle anclA is the mean free path."," The coefficient of thermal conductivity for the monatomic gas is, where $c_v$ is the specific heat per particle and$\lambda$ is the mean free path."
 The entropy ο relates to the equation of state P=μιx (p., The entropy $S$ relates to the equation of state $P=\frac{\rho}{m_p}k_BT\propto \rho^{\gamma}$ .
 1 can be written Combining equs. (3)). (3)).," It can be written Combining eqns. \ref{therm}) ), \ref{kappa}) ),"
" and (3)) and de-dimensionalizing (hem using the characteristic . . s TmEUN, we obtain for. the. unit of. time ⋟∖⊽↕∠≼↲∣⋮↿⋅⋅≼⇂≼↲∐⋟∖⊽∐∡∖↽∕↗⋖⋡∣⋮↿⋱⋝⋅≀↧↴∐≼⇂∩↲∐↕↕↽≻≼↲↕⋅≀↧↴⊓∐⋅≼↲↕↴⋅∶"," and \ref{S}) ) and de-dimensionalizing them using the characteristic size $r_c$, density $\rho\left(r_c\right)$ , and temperature $T_c\equiv\frac{m_p v^2\left(r_c\right)}{k_B}$ , we obtain for the unit of time"
The source LEOOLOL was) screndipitously detected as bright N-rav cutter bv anc was found to be close to a BAL quasar with :—2.027 (Stocke et al.,The source 0104 was serendipitously detected as bright X-ray emitter by and was found to be close to a BAL quasar with $z$ =2.027 (Stocke et al.
 1981)., 1984).
 Since the QSO is also located very near (10)) to a giant elliptical galaxy at :—0.111. which is part of a small eroup. it remained unclear from which of the three the N-ray emission originated: the QSO. the giant elliptical. or the ICM of the sinall eroup (Stocke et al.," Since the QSO is also located very near ) to a giant elliptical galaxy at $z$ =0.111, which is part of a small group, it remained unclear from which of the three the X-ray emission originated: the QSO, the giant elliptical, or the IGM of the small group (Stocke et al."
 198D)., 1984).
 Caoia ct al. (, Gioia et al. (
1986). in a deep observation. could not detect A-rav chussion in the 0.052 keV band. which they traced back to either variability (intrinsic to the source. or caused by a niücroleusius eveut during the observation: which would favour the quasar identification of the X-rav source). or a stronglv absorbed XN-rav spectu.,"1986), in a deep observation, could not detect X-ray emission in the 0.05–2 keV band, which they traced back to either variability (intrinsic to the source, or caused by a microlensing event during the observation; which would favour the quasar identification of the X-ray source), or a strongly absorbed X-ray spectrum."
 The incidental PSPC observation of tle source was briefly discussed by Ciliegi Maccacaro (1996) ina large salple study of spectra of EXISS ACN., The incidental PSPC observation of the source was briefly discussed by Ciliegi Maccacaro (1996) in a large sample study of spectra of EMSS AGN.
 They applied a powerlaw to the spectrum ancl found excess absorption., They applied a powerlaw to the spectrum and found excess absorption.
 Below. we analyze the N-rav spectral properties iu more detail aud also perform a timine analvsis. in order to get clues on the origin of the X-ray cussion (elliptical ealaxy. group or quasar).," Below, we analyze the X-ray spectral properties in more detail and also perform a timing analysis, in order to get clues on the origin of the X-ray emission (elliptical galaxy, group or quasar)."
 The URI data improve the position of 00101. but nof much. since the source is weak aud located near the border of the fov.," The HRI data improve the position of 0104, but not much, since the source is weak and located near the border of the fov."
 In Fig., In Fig.
 l1. we compare the TRI xositiou with the optical positions of the quasar aud the ealaxies (as given in Stocke ct al, \ref{pos} we compare the HRI position with the optical positions of the quasar and the galaxies (as given in Stocke et al.
 1981: all coordinates were converted to 22000) ax the IPC position., 1984; all coordinates were converted to 2000) and the IPC position.
 Both sources. the quasar aud he elliptical. remain within he error circle.," Both sources, the quasar and the elliptical, remain within the error circle."
 We note. however. that the N-rav. source appears to )o extended.," We note, however, that the X-ray source appears to be extended."
 Although the analysis is complicated by a rewly detected closeby. second. source. a comparison with he X-rav cussion from the Ε star at nearly the same off- angle. clearly suggests that the N-rav. emission from 00101 does not originate frou a point source (see Fig.," Although the analysis is complicated by a newly detected closeby second source, a comparison with the X-ray emission from the F star at nearly the same off-axis angle, clearly suggests that the X-ray emission from 0104 does not originate from a point source (see Fig."
 1: the F star is the brightest source at the right border of the image. 00101 is the one at the lower border).," 1; the F star is the brightest source at the right border of the image, 0104 is the one at the lower border)."
 We do not detect short-time variability during the PSPC observation (Fig. 8))., We do not detect short-time variability during the PSPC observation (Fig. \ref{light}) ).
 To examine the lone-term treud. we converted the PSPC couutrate to WRI countrate assuimiug constant spectral shape.," To examine the long-term trend, we converted the PSPC countrate to HRI countrate assuming constant spectral shape."
 Again. the source CIUISSIOMW 1s found to be constant.," Again, the source emission is found to be constant."
 We then compared with the IPC fiux (this obs., We then compared with the IPC flux (this obs.
 was performed 11 vrs prior to the PSPC observation) given in Stocke et al. (, was performed 11 yrs prior to the PSPC observation) given in Stocke et al. (
1981).,1984).
 To this eud. we first re-fit the data with the same spectral model as iu Stocke et al. (," To this end, we first re-fit the data with the same spectral model as in Stocke et al. ("
"they used 1.5 and Ny=0.3107"" 7: sce Gioia ct al.","they used –1.5 and $N_{\rm H} = 0.3\,10^{20}$ $^{-2}$; see Gioia et al."
 1986 for similar parameters)., 1986 for similar parameters).
" We then derive an observed flux (converted to the 0:3. 3.5 keV baud) of fio,=3.9610.1 fom? /s which is in excellent agreement with the flax of FanLOCGEO.7)1019 fem? /s,"," We then derive an observed flux (converted to the 0.3 – 3.5 keV band) of $f_{\rm ros} = 3.96\,10^{-13}$ $^2$ /s which is in excellent agreement with the flux of $f_{\rm ein} = 4.0(\pm{0.7})\,10^{-13}$ $^2$ /s."
 A powerlaw with absorption fixed to the Calactic value does not give a good fit with = 4κ-— and wuP = 1.5., A powerlaw with absorption fixed to the Galactic value does not give a good fit with = –1.7 and $\chi{^{2}}_{\rm red}$ = 1.5.
 The fit improves after allowing for excess cold absorption., The fit improves after allowing for excess cold absorption.
 This vields Ay=2.9107! 7. = 3.2 ae uad l.l.," This yields $N_{\rm H} = 2.9\,10^{21}$ $^{-2}$, = --3.2 and $\chi{^{2}}_{\rm red}$ = 1.1."
 Alternatively. the spectrum can be successfully described im terms of a rs model.," Alternatively, the spectrum can be successfully described in terms of a rs model."
 Iu this case we used 2=0.111 since rs cuiission is more Likely to originate from the elliptical aucd/or IGAL, In this case we used $z$ =0.111 since rs emission is more likely to originate from the elliptical and/or IGM.
" Tf δι is treated as free parameter if is consistent with Noa, but comes with large errors;", If $N_{\rm H}$ is treated as free parameter it is consistent with $N_{\rm gal}$ but comes with large errors.
 We obtain Vy=(0.6650725)1023 2 and KT=Lsolhsh keV (Tua — L0)," We obtain $N_{\rm H} = (0.66^{+0.34}_{-0.16})\,10^{21}$ $^{-2}$ and $kT = 1.89^{+1.11}_{-0.29}$ keV $\chi{^{2}}_{\rm red}$ = 1.0)."
" For ης Vea. &T — 1.0 keV and Ly=310% ασ», Plugeing this temperature iuto the ὃςT relation for eroups/clusters (Markeviteh. 1998) we predict a (0.12.1 keV) N-ray huuinositv of 110% ereofs which is of the order of the observed value aud thus cousisteut with au identification of 0010£ with the IGAL of the stall eroup."," For $N_{\rm H}$ $N_{\rm gal}$, $kT$ = 1.9 keV and $L_{\rm x} = 3\,10^{43}$ erg/s. Plugging this temperature into the $L_{\rm x} - T$ relation for groups/clusters (Markevitch 1998) we predict a (0.1–2.4 keV) X-ray luminosity of $^{43}$ erg/s which is of the order of the observed value and thus consistent with an identification of 0104 with the IGM of the small group."
 The X-ray emission of 00101 turned out to be constant., The X-ray emission of 0104 turned out to be constant.
 Iu particular. there is excellent agreement with the fiux derived for the observation (adopting the same spectral model).," In particular, there is excellent agreement with the flux derived for the observation (adopting the same spectral model)."
 This reuders one of several possibilities discussed iu Stocke et al. (, This renders one of several possibilities discussed in Stocke et al. (
1981) the one that the quasar was temporarily brightened via wicrolensing during the observation uulikely.,1984) – the one that the quasar was temporarily brightened via microlensing during the observation – unlikely.
 We confi the excess cold absorption iun case of the pl description of the N-rawv. spectrum. not unexpected for a BAL quasay. but find an rs model to be similarly successful.," We confirm the excess cold absorption in case of the pl description of the X-ray spectrum, not unexpected for a BAL quasar, but find an rs model to be similarly successful."
 The best-fit parameters of the latter nodel. which due to its shape would argue for an origin from," The best-fit parameters of the latter model, which due to its shape would argue for an origin from"
 Starting from the COBE experiment using the so called Quadilateralized Sky Cube Projection (see Chan aud ONeill! 1976. O'Neill and i? 1976. Creisen and Calibretta? 1993). the probem of the whole sky CAB pixelization. las attraced. exeat. interest.," Starting from the COBE experiment using the so called Quadrilateralized Sky Cube Projection (see Chan and $^1$ 1976, O'Neill and $^2$ 1976, Greisen and $^3$ 1993), the problem of the whole sky CMB pixelization has attracted great interest."
 At least three inethods of the CAID. celestial sphere yixclization have been proposed arc inpleimenuted: after he CODE pixclization scheme: the Icosahedron pixclizing w Teemark! (1996). the Igloo pixclization by Crittenden and Turok? (1998. hereafter CT98) aid the method by Corrski ct al (1999) (with the ast modification in 2003).," At least three methods of the CMB celestial sphere pixelization have been proposed and implemented after the COBE pixelization scheme: the Icosahedron pixelizing by $^4$ (1996), the Igloo pixelization by Crittenden and $^5$ (1998, hereafter CT98) and the method by Górrski et $^6$ (1999) (with the last modification in 2003)."
 Two iuportant questions neutioned already by: Teguiuwk! (1996) ire now under discussion: a) what is the opnual method for the choice of the Ny. positions of pixel ceuter* shapes and sizes Oo provide (as good as possible) the compact uniforiu coverage of the sky by pixes with equal areas. iud b) what is the best way to approximate auv convolutious of he maps by suis using pixels5," Two important questions mentioned already by $^4$ (1996) are now under discussion: a) what is the optimal method for the choice of the $N_{pix}$ positions of pixel centers, shapes and sizes to provide (as good as possible) the compact uniform coverage of the sky by pixels with equal areas, and b) what is the best way to approximate any convolutions of the maps by sums using pixels?"
 All the above imnoeutioucc pixclization schemes were devoted to solve the first problems as :ieeurate as possible. and the auswer to the seco question usually follows for the chosen pixelization scheme.," All the above mentioned pixelization schemes were devoted to solve the first problem as accurate as possible, and the answer to the second question usually follows for the chosen pixelization scheme."
 Iu this oxeper we chanee the focu sO| fhe probleu to processing oi the sphere ane hen deternine he scheme of pixclization., In this paper we change the focus of the problem to processing on the sphere and then determine the scheme of pixelization.
 We would like to roiiud that pixelizatiou of the CMP1)) data on the sphere is only some part of the general problem. which is the determiuaion of the cocfiicicuts o ‘the spherical larnonc ¢lecommposition of the CXMB signa for both anisotropy aud polarization.," We would like to remind that pixelization of the CMB data on the sphere is only some part of the general problem, which is the determination of the coefficients of the spherical harmonic decomposition of the CMB signal for both anisotropy and polarization."
" These cocficients. which we call (;,,: are used m subsequent steps in the aalysis of the mneasured signal and iu particular. in the determination of the power spectra. C. of the anisotropy aud polarization (see review in Ivon at al* 2002). i some special methods. for componcuts separation (Stolvarov ct al.* 2002: Naselsky ot al? 2003a) and phase statistics (CTdiane ef abi"" 2003: Naselskyv. ct 1-72 20030. 2001: Cok et alt? 2001)."," These coefficients, which we call $a_{\ell m}$, are used in subsequent steps in the analysis of the measured signal, and in particular, in the determination of the power spectra, $C_{\ell}$, of the anisotropy and polarization (see review in Hivon at $^{7}$ 2002), in some special methods for components separation (Stolyarov et $^{8}$ 2002; Naselsky et $^{9}$ 2003a) and phase statistics (Chiang et $^{10}$ 2003; Naselsky et $^{11,12}$ 2003b, 2004; Coles et $^{13}$ 2004)."
 Tere we propose a specific method to caleulate the coefficients ay..., Here we propose a specific method to calculate the coefficients $a_{\ell m}$.
 It is based on the so called Ciaussiau quadratures auk ls presentc¢ In Sec., It is based on the so called Gaussian quadratures and is presented in Sec.
εν In this specific pixelizatioun scheme correspoucd the )osition of nel cencrs along the 0 coordinate to socalled the CassLeeendre quadrature zer‘ON avl it will )e shown (Sec., In this specific pixelization scheme correspond the position of pixel centers along the $\theta$ –coordinate to so–called the Gauss--Legendre quadrature zeros and it will be shown (Sec.
 5) tha this method iucreases the acctracy of calcula10115 CSSCLLially., 5) that this method increases the accuracy of calculations essentially.
 TMs. the method of caculation of the coefficients diy cictates the method of the pixeization.," Thus, the method of calculation of the coefficients $a_{\ell m}$ dictates the method of the pixelization."
 We call our metrod GLESP. the GaussLegeudre Sky Pixelization.," We call our method GLESP, the Gauss–Legendre Sky Pixelization."
" We jiwe developed a special code for the GLESP approach and a package of codes which are necessary for the whole investigatjon of the CAIB data including the «eteriunation of anisotropy and polarization IOWCL spectra. C,. the Minkowshki fincfionals and other statistics."," We have developed a special code for the GLESP approach and a package of codes which are necessary for the whole investigation of the CMB data including the determination of anisotropy and polarization power spectra, $C_\ell$, the Minkowski functionals and other statistics."
 This paper is devoteL to description of the main idea of the CLESP method. he estimation o the accuracy of ie different steps aud ο ‘the final results. the description ft the GLESP code iux| its testing.," This paper is devoted to description of the main idea of the GLESP method, the estimation of the accuracy of the different steps and of the final results, the description of the GLESP code and its testing."
 We do not ¢ISCTISS 16 problem of iuteeratk0i Over a fuite κο] size for the iue ordered data iu fus paper., We do not discuss the problem of integration over a finite pixel size for the time ordered data in this paper.
 The simplest scheme of inteeration over pixel area ds to use equivalent weight relatively to the center o the pixel, The simplest scheme of integration over pixel area is to use equivalent weight relatively to the center of the pixel.
 The GLESP code uses his method as TWEALPix aud Igloo do., The GLESP code uses this method as HEALPix and Igloo do.
 Iu forthcoming papers we shall discuss our GLESP code extension ou the xocessue of CAIB polarization, In forthcoming papers we shall discuss our GLESP code extension on the processing of CMB polarization
We would like to emphasise the following points regarding the choice of models: I0 is possible to choose many variants of the above models and repeat the analysis eiven in this paper.,We would like to emphasise the following points regarding the choice of models: It is possible to choose many variants of the above models and repeat the analysis given in this paper.
 One can choose to normalise the power spectra in a dillerent. manner. e.g. by fixing the amplitude of perturbations at Sf Mpe rather than at very large scales using CODIS observations.," One can choose to normalise the power spectra in a different manner, e.g. by fixing the amplitude of perturbations at $8 h^{-1}$ Mpc rather than at very large scales using COBE observations."
 Other parameters like the Llubble’s constant. the cosmological constant. the density parameter and the primordial spectral index can also be varied [rom the values used here.," Other parameters like the Hubble's constant, the cosmological constant, the density parameter and the primordial spectral index can also be varied from the values used here."
 We have consciously restricted ourselves to a small set of example models for the purpose of illustration., We have consciously restricted ourselves to a small set of example models for the purpose of illustration.
 A more detailed exercise will be warranted if the GAIRP sucececds in. detecting neutral hyerogen at these redshifts and a more meaningful comparison with mocdels can be carried out using real data., A more detailed exercise will be warranted if the GMRT succeeds in detecting neutral hydrogen at these redshifts and a more meaningful comparison with models can be carried out using real data.
 Generating artificial radio maps requires. in. principle. a detailed. Knowledge of the distribution of barvons and. the neutral [fraction ete.," Generating artificial radio maps requires, in principle, a detailed knowledge of the distribution of baryons and the neutral fraction etc."
 However. as mentioned earlier in this xiper. the comoving volume enclosed in cach pixel is very wee and therefore we can get reasonable estimates. by assuming the clistribution of barvons and dark matter to be he same.," However, as mentioned earlier in this paper, the comoving volume enclosed in each pixel is very large and therefore we can get reasonable estimates by assuming the distribution of baryons and dark matter to be the same."
 In the following discussion we will demonstrate. using a simple model. that the assumption of a constant neutral fraction at these scales is not very [ar from the ruth.," In the following discussion we will demonstrate, using a simple model, that the assumption of a constant neutral fraction at these scales is not very far from the truth."
 We will also show that our choice of fy=0.5 for >=3.34 is not unrepresentative., We will also show that our choice of $f_N=0.5$ for $z=3.34$ is not unrepresentative.
 We will show that the neutral fraction of gas in galaxies is largely independent of he depth of the potential well., We will show that the neutral fraction of gas in galaxies is largely independent of the depth of the potential well.
 In the following discussion we estimate the neutral fraction by using the model of star ormation in galaxies of Ixaulfmann. White and Cuiderdoni (1993: hereafter INN€).," In the following discussion we estimate the neutral fraction by using the model of star formation in galaxies of Kauffmann, White and Guiderdoni (1993; hereafter KWG)."
 Here we will brielly summarise the relevant features of thei model ancl use these to estimate the evolution of neutral fraction., Here we will briefly summarise the relevant features of their model and use these to estimate the evolution of neutral fraction.
" 1n this model. dark matter halos are assumed. to be truncated singular isothermal spheres and it is assumed that the temperature Z of the gas is given in terms of the circular velocity. V. as. 2/235.9(0L/kms)"" Ix. The virial radius r, is defined to bethe racius within which the mean overdensity is 200(Le. r,=0.144,fdpz)πε)."," In this model, dark matter halos are assumed to be truncated singular isothermal spheres and it is assumed that the temperature $T$ of the gas is given in terms of the circular velocity, $V_c$, as, $T=35.9 \> (V_c/$ $/$ $)^2$ K. The virial radius $r_v$ is defined to bethe radius within which the mean overdensity is $200$, $r_v=0.1 H_0^{-1} (1+z)^{-3/2} V_c$ )."
 The radius where the cooling time of the gas is equal to the age of the universe is defined as the cooling radius. recur.," The radius where the cooling time of the gas is equal to the age of the universe is defined as the cooling radius, $r_{cool}$."
" Suppose that the fraction of the critical density that is in barvons is Q, and fy is the fraction of the barvons in the form of gas.", Suppose that the fraction of the critical density that is in baryons is $\Omega_b$ and $f_g$ is the fraction of the baryons in the form of gas.
 The amount of cold eas inside the halo at time / is given by the amount of eas with cooling time foo<b, The amount of cold gas inside the halo at time $t$ is given by the amount of gas with cooling time $t_{cool} < t$.
 When roure. Cooling is very rapid. and the rate of increase of cold gas in the halo is governed by the accretion rate of the halo. (WhiteancFrenk1991) In the other limit. rio;re. the rate of inflow of cold gas Can be written as. where py(r) is the gas density at radius r.," When $r_{cool} \gg r_v$, cooling is very rapid and the rate of increase of cold gas in the halo is governed by the accretion rate of the halo, \cite{wf91}
 In the other limit, $r_{cool} \ll r_v$, the rate of inflow of cold gas can be written as, where $\rho_g (r)$ is the gas density at radius $r$."
" In the model o£ AWC. the rate at which cold gas settles inside the halo is given by min(Al;,[-ALoot)."," In the model of KWG, the rate at which cold gas settles inside the halo is given by $\min (\dot M_{inf}, \dot M_{cool})$."
 For the cooling of the gas. we use the cooling function. of Fall and. Rees (1985) for a primordial gas. since the metallicity is any way small for gas at high recdshift.," For the cooling of the gas, we use the cooling function of Fall and Rees (1985) for a primordial gas, since the metallicity is any way small for gas at high redshift."
 l]lowever. with the onset of star formation. the supernovae will begin to heat the gas.," However, with the onset of star formation, the supernovae will begin to heat the gas."
 Following WKAVG. we assume that the number of supernovae per solar mass of stars formed. is ων=+10 AL+.," Following KWG, we assume that the number of supernovae per solar mass of stars formed is $\eta _{SN}=4 \times 10^{-3}$ $_{\odot}
^{-1}$."
" If each of the supernovae have a kinetic energv of the ejecta of order 1013 erg. and a fraction e of this energy is used to heat the cold gas. then the rate of loss of cold. gas to the hot. phase of the interstellar mecdunm is. (Ixaulfian.WhiteandCiuideroni1903) lere. AZ, is the star formation rate. which is given in this moclel as. Lore /,4,, is the dynamical time."," If each of the supernovae have a kinetic energy of the ejecta of order $10^{51}$ erg, and a fraction $\epsilon$ of this energy is used to heat the cold gas, then the rate of loss of cold gas to the hot phase of the interstellar medium is, \cite{kwg}
 Here, $\dot M_{\ast}$ is the star formation rate, which is given in this model as, Here $t_{dyn}$ is the dynamical time."
" Phe authors defined the dvnamical time as (where A~0.05 is the initial dimensionless spinparameter of the gas). These equations govern the evolution of the amount of cold gas. or. in other words. the neutral fraction fas. of gas ina halo of circular velocity V; at a given redshift z. for an assumed value of the onset of inllow of eas z;,. ancl given the values of à and ο.Gas is assumed to be fully ionised ab zs."," The authors defined the dynamical time as (where $\lambda \sim 0.05$ is the initial dimensionless spinparameter of the gas), These equations govern the evolution of the amount of cold gas, or, in other words, the neutral fraction $f_{HI}$ , of gas in a halo of circular velocity $V_c$ at a given redshift $z$ , for an assumed value of the onset of inflow of gas $z_{in}$ , and given the values of $\alpha$ and $\epsilon$ .Gas is assumed to be fully ionised at $z_{in}$ ."
 IKWG estimated the valuesof aand ο from evolving, KWG estimated the valuesof $\alpha$and $\epsilon$ from evolving
 hhacdatotal 1.43-CLHz flux density of 7.0+0.4.-y. with a peal surface brightness at our resolution of 0.62£0.03 corresponding to a brightness temperature of 1500+75 Ix (where the uncertainties are dominated by the assumed uncertainty in the Dux-density calibration).,"had a total 1.43-GHz flux density of $7.0 \pm 0.4$ Jy, with a peak surface brightness at our resolution of $0.62 \pm
0.03$, corresponding to a brightness temperature of $1500\pm75$ K (where the uncertainties are dominated by the assumed uncertainty in the flux-density calibration)."
 On our 327 MlIZ image7).. iis also clearly visible. although only mareinally resolved.," On our 327 MHz image, is also clearly visible, although only marginally resolved."
 Comparison of the Dux density of 1.3+0.7 Jy determined [rom the 321-Allz image with that at 1.4 CGllz vields an integrated. s»ectral index between these frequencies. 1.4GHzos3apgs ο 0.0+OL. consistent with other determinations of ss radio spectral index2).," Comparison of the flux density of $7.3 \pm
0.7$ Jy determined from the 327-MHz image with that at 1.4 GHz yields an integrated spectral index between these frequencies, $\alp$, of $0.0 \pm 0.1$, consistent with other determinations of s radio spectral index."
. There is a0 relatively compact radio source. approximately tto the north of the main body of0.9... which corresponds to the X-ray feature called the “northern7).," There is a relatively compact radio source, approximately to the north of the main body of, which corresponds to the X-ray feature called the “northern."
 D. CGaensler. in a private. communication. reported seeing the northern knot in earlier. 14-GLlz racio observations.," B. Gaensler, in a private communication, reported seeing the northern knot in earlier 1.4-GHz radio observations."
" The northern knot has a total 1.433-CLIz Dux clensity of 20.2+LS mw. and is mareinally resolved in our image. with an intrinsic FWHLIAL size. as estimated. by an clliptical Gaussian fit. of 18""κ” at1105.."," The northern knot has a total 1.43-GHz flux density of $20.2 \pm 1.8$ mJy, and is marginally resolved in our image, with an intrinsic FWHM size, as estimated by an elliptical Gaussian fit, of $18\arcsec \times 8\arcsec$ at."
 The peak brightness position in the radio is consistent with that seen in the X-ray when the latter is convolved to the same resolution. as can be seen in the top ancl bottom panels of Vig. 1..," The peak brightness position in the radio is consistent with that seen in the X-ray when the latter is convolved to the same resolution, as can be seen in the top and bottom panels of Fig. \ref{fwide}. ."
 The northern knot is not discernible on our resolution 327 MllIz image. being blended with iitsell.," The northern knot is not discernible on our lower-resolution 327 MHz image, being blended with itself."
 Phe knot is mareinally visible in an image made from the 5-CGllz data ofregion., The knot is marginally visible in an image made from the 5-GHz data of.
.. We estimate a total 5-ClLlz Lux density for the northern knot of 19257 mJy. resulting a nominal value for the knots spectral index.eH... of 0.04. similaros to that body o£esa.," We estimate a total 5-GHz flux density for the northern knot of $19 \pm
7$ mJy, resulting a nominal value for the knots spectral index, of $-0.04$, similar to that body of."
 Jlowever. the uncertainties on the spectral index are ↓⋜⊔⋅⋏∙≟∢⊾⊳⋜⋯∠⇂↿⇂↥⋖⋅∣↗∶−≻⋅∆⊰⊲∕⋰∣↿∖−≽∫⊤⊐↓↓⊔⊔↿⊳∖∪⊔⋂⊥↓⊽⊔⊽≝⋤ −⋅∣∕− ⋪⊀ ⋜⋯↓⋅∢⊾↓⋅∶⊰⋜⋯∠⊔∪⋅⋅∏⋡ ∖∖⊽↓⋯↿↕≻↓↥∢⋟↥⋜↧∣⋡⇂∙∖⇁⋜↧∣⋡," However, the uncertainties on the spectral index are large, and the $p = 2.3\% \; (2\sigma)$ limits on are $-1.3$ and $+0.5$."
≱∖⋖⋅⊔⇂⇂⋅↓⋅∪⊔↓⋯⊔⋅∠⇂⋖⋅⋖⋅↓≻↓⊳≟−≺∶∐∠⊲↓⊔⋯⋏∙≟∢⊾⊀↓⊳∖ ↓⋅⋯∐∪∢⊾⊔↓⊲↓⊳∖⊳∖⊀↓∪⊔≼∼∪↓⋅↓⋅∢⋅⊳∖↓≻∪↓⊔⇂⋠↓⊔⋏∙≟↿∪↿⇂↥∢⋅↓⊀↓⊔↓∣⋡−∣⋡↓⋰↓⋏∙≟↓∐⋖⊾⊔⋯⇂⇀∖−↓⋅⋜↧∙∖⇁ emission. visible in the bottom panel of Fig. ↓↦⇀∖∐, What is notably absent from our deep 1.4-GHz image is radio emission corresponding to the limb-brightened X-ray emission visible in the bottom panel of Fig. \ref{fwide}.
↓↥∪⊔⋏∙≟↓↥ some cdilfuse racio emission appears north of the northern knot. we believe that it is not the counterpart of the Χ- shell of 0.9. but more likely associated with C21.64.0.84. which we ciscuss below.," Although some diffuse radio emission appears north of the northern knot, we believe that it is not the counterpart of the X-ray shell of $-$ 0.9, but more likely associated with $-$ 0.84, which we discuss below."
 We derive a new upper limit to the radio emission from the SNR shell in dl., We derive a new upper limit to the radio emission from the SNR shell in 4.1.
 A so far uncatalogued source.O.S4.. is distinctly visible in the 1.4-Gllz image in Fig. 1..," A so far uncatalogued source, is distinctly visible in the 1.4-GHz image in Fig. \ref{fwide}."
 Ht is a large elongated structure. which extends from near tto the north-northwest.," It is a large elongated structure, which extends from near to the north-northwest."
 Lt is brightest. in the micelle. reaching a peak 1.43-Cillz brightness of 6.8+0.5 ((corresponding to a brightness temperature of 17+1W)..," It is brightest in the middle, reaching a peak 1.43-GHz brightness of $6.8
\pm 0.5$ (corresponding to a brightness temperature of $17 \pm
1$."
 li has a total length of —10/.., It has a total length of $\sim$.
 Lt seems to consist. of two relatively clistinet ancl roughly parallel curved ridges: of emission. with the western or outer one being better defined. and the eastern or inner. one being. more diffusey and 71.5 dedistant.," It seems to consist of two relatively distinct and roughly parallel curved ridges of emission, with the western or outer one being better defined, and the eastern or inner one being more diffuse and $\sim$ distant."
" ""Phe total L43-CGllz αν density in. the iis 660£50 mJv. with cach of the two ridges having approximately half the total."," The total 1.43-GHz flux density in the is $660 \pm
50$ mJy, with each of the two ridges having approximately half the total."
 iis also visible in he 327 MllIz image. and we show a detail in Fig. 3..," is also visible in the 327 MHz image, and we show a detail in Fig. \ref{fstreamerp}."
" At this requency. due to the larger primary beam. much more of the source is visible thanat 1.4 Cillz. and it can bee seen to be τα relatively circular shell-structure.. The centre of the shel is at RA = 1S"" 33/66 and -10' 22514 oral=21.64.h O"," At this frequency, due to the larger primary beam, much more of the source is visible thanat 1.4 GHz, and it can bee seen to be a relatively circular shell-structure.. The centre of the shell is at RA = $^{\rm h}$ 6 and $-10$ 4, or at $l = 21.64, b = -0.84$ ."
"SLOrname forthissource, isbasedonthece nlrepositionof"," Our name for this source, is based on the centre position of the shell as seen at 327 MHz."
i , The outer angular diameter of the shell is $\sim$.
The total [lux clensity at 32127 MlÓllz is 2.8 Jw. with an estimated uncertainty of 20.5 Jv due to the somewhat uncertain zero-Ievel in the images.," The total flux density at 327 MHz is 2.8 Jy, with an estimated uncertainty of $\sim$ 0.5 Jy due to the somewhat uncertain zero-level in the images."
 The 327-MITz tux density of the part visible in the 1.4 Gllz image is L43:0.2 mv. and over this. region. the integrated. value of lis O540.1.," The 327-MHz flux density of the part visible in the 1.4 GHz image is $1.4 \pm 0.2$ mJy, and over this region the integrated value of is $-0.5 \pm 0.1$."
 A somewhat steeper spectrum is suggested for the northern and eastern. sides of the shell. which are not visible at 1.4 Giz. however due to the uncertain zevo-levels ancl low signal-to-noise ratios. à constant. value OL(qd OnGHeGHz0.6 for the whole shell is probably not excluded.," A somewhat steeper spectrum is suggested for the northern and eastern sides of the shell, which are not visible at 1.4 GHz, however due to the uncertain zero-levels and low signal-to-noise ratios, a constant value of $\alp
\sim -0.6$ for the whole shell is probably not excluded."
 “Phe averaged over the whole of the 327-MllIz surfacebrightness is 2.5 Ll. and," The averaged over the whole of the 327-MHz surfacebrightness is 2.5 , and"
Since the total luminosity of this region at all frequencies is not known. determining the lifetime of the emission due to all radiative energy losses is impossible.,"Since the total luminosity of this region at all frequencies is not known, determining the lifetime of the emission due to all radiative energy losses is impossible."
 In. addition to this. svachrotron loss processes may. be dominant.," In addition to this, synchrotron loss processes may be dominant."
 Under the inlluence of a magnetic field. //. an electron. rotates at the gvrofrequeney. (Rvbicki Lightman. 1979) and the frequency of radiation. £9. is a factor of 5 higher than the evrolrequency. so manipulating Equation 6.4 of Itvbicki Lightman (19079) gives Ξ1148.," Under the influence of a magnetic field $H$, an electron rotates at the gyrofrequency (Rybicki Lightman, 1979) and the frequency of radiation, $\nu$, is a factor of $\gamma^3$ higher than the gyrofrequency, so manipulating Equation 6.4 of Rybicki Lightman (1979) gives $\gamma =1148$."
" An electron. with this Lorentz [actor has energyex 5,07E and radiates with power P so that the lifetime of the svnchrotron radiation is and with the values of 5 and ff=£L, from above. 7—4.7104"" seconds. corresponding to just under 1500 vears."," An electron with this Lorentz factor has energy $\gamma m_e c^2$ and radiates with power $P$ so that the lifetime of the synchrotron radiation is and with the values of $\gamma$ and $H = H_\phi$ from above, $\tau =
4.7\times 10^{10}$ seconds, corresponding to just under 1500 years."
 Such a timescale would imply that svnchrotron radiation would be very long-lived in the circumstellar material. assuming that the magnetic field compression is sustained. by continuous matter injection.," Such a timescale would imply that synchrotron radiation would be very long-lived in the circumstellar material, assuming that the magnetic field compression is sustained by continuous matter injection."
 When there is no matter injection the magnetic field can expand adiabatically and the svnchrotron emission will Face within vears., When there is no matter injection the magnetic field can expand adiabatically and the synchrotron emission will fade within years.
 No non-thermal emission is seen in LOSS., No non-thermal emission is seen in 1988.
 LW indeed there is no svnchrotron emission at this epoch. some other loss-mechanism must be occurring.," If indeed there is no synchrotron emission at this epoch, some other loss-mechanism must be occurring."
 The optical light curve of figure 1. shows LOSS to be a particularly quiet period. over two vears alter the last major outburst.," The optical light curve of figure \ref{fig:ulight} shows 1988 to be a particularly quiet period, over two years after the last major outburst."
 It is therefore likely that there is no matter being ejected into the circumstellar wind. so that no new density enhancements and magnetic field. compressions are. being formect.," It is therefore likely that there is no matter being ejected into the circumstellar wind, so that no new density enhancements and magnetic field compressions are being formed."
 Supporting evidence for this scenario comes from optical spectral. observations., Supporting evidence for this scenario comes from optical spectral observations.
 During this epoch. the blue continuum was very faint and the Balmer lines were not present (λος et al.," During this epoch, the blue continuum was very faint and the Balmer lines were not present (Bode et al."
 1991). strongly implying that there were also no fast winds or jets at this time.," 1991), strongly implying that there were also no fast winds or jets at this time."
 Hence one would not expect to detect shock phenomena resulting from penetration. of highvelocity material into. cireumbinary material ancl. by this model. no non.thermal emission from recently ejected material.," Hence one would not expect to detect shock phenomena resulting from penetration of high–velocity material into circumbinary material and, by this model, no non–thermal emission from recently ejected material."
 Previously. unambiguous non.thermal emission in svmbiotic stars had only been seen in LIAL Sec (Richards et al.," Previously, unambiguous non–thermal emission in symbiotic stars had only been seen in HM Sge (Richards et al."
 1999)., 1999).
 Spatially resolved nonthermal emission is very rare in anv stellar source. and is only seen regularly in very highenergv svstemis such as micro-quasars.," Spatially resolved non–thermal emission is very rare in any stellar source, and is only seen regularly in very high–energy systems such as micro-quasars."
" A potential nonthermal feature in Ro Aqr was subject to such large errors (o,~ 1) that its status could not. be. confirmed (Dougherty et al.", A potential non–thermal feature in R Aqr was subject to such large errors $\sigma_\alpha \sim 1$ ) that its status could not be confirmed (Dougherty et al.
 1995)., 1995).
 Other svmbiotic stars are believed to exhibit entirely. thermal radiation., Other symbiotic stars are believed to exhibit entirely thermal radiation.
 CLL Cvg displays the strongest evidence vet of nonthermal emission due to jetwind interaction., CH Cyg displays the strongest evidence yet of non–thermal emission due to jet--wind interaction.
 CLL Cvg and LAL See share the property of having undergone outbursts in relatively recent. history., CH Cyg and HM Sge share the property of having undergone outbursts in relatively recent history.
 The above arguments suggest that nonthermal emission will decrease rapidly with time after the outburst if the field strength and high energy. particles are not continuously replenishecl as discussed initially in Richards et al. (, The above arguments suggest that non–thermal emission will decrease rapidly with time after the outburst if the field strength and high energy particles are not continuously replenished as discussed initially in Richards et al. (
1999).,1999).
 Since the 1984-86 ejections in CLE Cveni two outbursts have been observed which may have injected further high velocity material into the circumstellar environment and hence given rise to the non-thermal emission seen in the 1995 and 1999 observations., Since the 1984-86 ejections in CH Cygni two outbursts have been observed which may have injected further high velocity material into the circumstellar environment and hence given rise to the non-thermal emission seen in the 1995 and 1999 observations.
 There is definite evidence of nonthermal emission in the ejecta from Cll Cyeni., There is definite evidence of non–thermal emission in the ejecta from CH Cygni.
 This. together with a morphology consistent with high velocity jets. Lgsupports the scenario of ‘Tavlor et al. (," This, together with a morphology consistent with high velocity jets, supports the scenario of Taylor et al. ("
1986). rather than one where the extension is a result of an expanding circumstellar torus.,"1986), rather than one where the extension is a result of an expanding circumstellar torus."
 Lhe proposed mechanism for the creation of the non-thermal emission involves material ejected in high velocity bullets interacting with a previously expelled lower velocity stellar wind., The proposed mechanism for the creation of the non-thermal emission involves material ejected in high velocity bullets interacting with a previously expelled lower velocity stellar wind.
 The ejected matter creates shocks in the circumstellar medium. leacing to locally enhanced magnetic field. density. particle acceleration and svnchrotron emission.," The ejected matter creates shocks in the circumstellar medium, leading to locally enhanced magnetic field density, particle acceleration and synchrotron emission."
 We suggest that the presence of nonthermal emission in svmbiotic stars may be an indicator of outbursts associated with significant cjecta., We suggest that the presence of non–thermal emission in symbiotic stars may be an indicator of outbursts associated with significant ejecta.
 AIC is supported by a grant from the Particle Physies and Astronomy Research Council (PPARC)., MC is supported by a grant from the Particle Physics and Astronomy Research Council (PPARC).
 The contribution of AS was supported by a grant. of the Slovak Academy of Science. number 5038/2000.," The contribution of AS was supported by a grant of the Slovak Academy of Science, number 5038/2000."
 The VLA is operated by the National Science Foundation operated under cooperative agreement with Associated Universities. Inc.," The VLA is operated by the National Science Foundation operated under cooperative agreement with Associated Universities, Inc."
on the >100 MeV fluence implied by the LAT non-detection is derived as follows.,on the $>100$ MeV fluence implied by the LAT non-detection is derived as follows.
" A GRB is tagged as detected by the LAT if the number of photons detected, N,, exceeds 10 and exceeds a 5c fluctuation of the background (Band et al."," A GRB is tagged as detected by the LAT if the number of photons detected, $N_s$, exceeds 10 and exceeds a $5\sigma$ fluctuation of the background (Band et al."
" 2009, Atwood et al."," 2009, Atwood et al."
 2009)., 2009).
" For the current analysis, it is sufficient to consider the N,>10 criterion, since the number of background events detected during the characteristic time of the prompt ~1 MeV ray emission, 799100 s, is low (1, i.e. Ns>10 is above a 5o background fluctuation)."," For the current analysis, it is sufficient to consider the $N_s>10$ criterion, since the number of background events detected during the characteristic time of the prompt $\sim1$ MeV gamma-ray emission, $T_{90}\lsim 100$ s, is low $\sim1$, i.e. $N_s>10$ is above a $\sigma$ background fluctuation)."
 Following Band et al. (, Following Band et al. (
"2009), the expected number of counts from a burst with a time integrated differential photon flux (i.e. differential photon fluence) Q(£) is where Agr¢(E,0) is the effective area (taken from Atwood et al.","2009), the expected number of counts from a burst with a time integrated differential photon flux (i.e. differential photon fluence) $Q(E)$ is where $A_{eff}(E,\theta)$ is the effective area (taken from Atwood et al."
" 2009)that depends on the direction from which the burst is observed, 0, E,=100 MeV and E>=10 GeV. The upper limits on the 100 MeV fluences shown in figures 2 and 3 are obtained by requiring Q(E)<Qo(E) where Qo(E) is the fluence for which N,=10."," 2009)that depends on the direction from which the burst is observed, $\theta$, $E_1=100$ MeV and $E_2=10$ GeV. The upper limits on the $100$ MeV fluences shown in figures 2 and 3 are obtained by requiring $Q(E)<Q_0(E)$ where $Q_0(E)$ is the fluence for which $N_s=10$."
" Since the number of events detected for bursts with fluence that produces, on average, N,=10 events is Poisson distributed with an average equal to 10, the upper limits on the fluxes shown in the figure are ~50% confidence level upper limits."," Since the number of events detected for bursts with fluence that produces, on average, $N_s=10$ events is Poisson distributed with an average equal to $10$, the upper limits on the fluxes shown in the figure are $\sim50\%$ confidence level upper limits."
 The upper limits on the fluence for confidence levels of and are 1.2 and 2 times higher respectively., The upper limits on the fluence for confidence levels of and are 1.2 and 2 times higher respectively.
 The effective area of the LAT is roughly proportional to E in the energy range of 100 MeV to 1 GeV (and roughly energy independent between 1 GeV and 10 GeV)., The effective area of the LAT is roughly proportional to $E$ in the energy range of 100 MeV to 1 GeV (and roughly energy independent between 1 GeV and 10 GeV).
" This implies that the LAT flux sensitivity is roughly energy independent between 100 MeV and 1 GeV, and that the upper limit on N, implies an upper limit on the 0.1-1 GeV fluence, which is independent of the spectrum Ο(Ε)."," This implies that the LAT flux sensitivity is roughly energy independent between 100 MeV and 1 GeV, and that the upper limit on $N_s$ implies an upper limit on the 0.1–1 GeV fluence, which is independent of the spectrum $Q(E)$."
" Indeed, the upper limits on R, the 100 MeV to 1 MeV fluence ratio, obtained assuming Q(E)«E are higher by a factor of ~2 than those obtained for a E~*, implying that the upper limits on the 0.1-1 GeV fluence obtained for both spectral shapes are similar."," Indeed, the upper limits on $R$, the 100 MeV to 1 MeV fluence ratio, obtained assuming $Q(E)\propto E^{-3}$ are higher by a factor of $\sim2$ than those obtained for a $Q(E)\propto E^{-2}$ , implying that the upper limits on the 0.1–1 GeV fluence obtained for both spectral shapes are similar."
 Denoting by RO) , Denoting by $R^{(2)}$ 
5.,.
 In contrast to the small solar Dare and «ΤΙ 138. there is no evidence for a pre-Dare increase in lux.," In contrast to the small solar flare and JTP 138, there is no evidence for a pre-flare increase in flux."
 Both solar [ares last around 11.5 hrs. similar το.) 138.," Both solar flares last around 1–1.5 hrs, similar to JTP 138."
 In Figure 6 we show the energy resolved lisht curve of the small solar Iare., In Figure \ref{solar2} we show the energy resolved light curve of the small solar flare.
 Similar to the Hare seen in JEP 138. the solar are reaches a maximum in hard X-ravs earlier than in soft N-ravs.," Similar to the flare seen in JTP 138, the solar flare reaches a maximum in hard X-rays earlier than in soft X-rays."
 Although the shape ancl duration of these solar [ares ave similar to that of JEP 138. they have lower temperatures and much lower luminosities.," Although the shape and duration of these solar flares are similar to that of JTP 138, they have lower temperatures and much lower luminosities."
 Phe luminosity may simply be a reflection of the volume of the emitting plasma., The luminosity may simply be a reflection of the volume of the emitting plasma.
 In the case of RS CVn systems. the [lare size can extend to the size of the binary svstem (or indeed. originate in the intra-binary region as seen in the RS CVn system CE Tuc. Gunn et al 1997).," In the case of RS CVn systems, the flare size can extend to the size of the binary system (or indeed, originate in the intra-binary region as seen in the RS CVn system CF Tuc, Gunn et al 1997)."
 For reasonable system. parameters and an orbital. period. of ος2 days. the separation ..is 5.1077τι cm.," For reasonable system parameters and an orbital period of 2 days, the separation is $\sim5\times10^{11}$ cm."
 Aloreover. the Suns rotation rate has been slowing clown since it joined the main sequence.," Moreover, the Suns rotation rate has been slowing down since it joined the main sequence."
 Lt therefore has lower magnetic activity compared to stars which have recently joined. the main sequence (as in the case of stars in. NGC 2516)., It therefore has lower magnetic activity compared to stars which have recently joined the main sequence (as in the case of stars in NGC 2516).
 Numerous explanations for the trigeering mechanism of solar [lares have heen developed. over the vears., Numerous explanations for the triggering mechanism of solar flares have been developed over the years.
 The most popular current theory for converting magnetic energy. into kinetic and thermal energies is that of magnetie reconnection (ee Priest Forbes 1999)., The most popular current theory for converting magnetic energy into kinetic and thermal energies is that of magnetic reconnection (eg Priest Forbes 1999).
 The site of the reconnection takes place high in the solar corona above magnetic loops. or between at least two loop svstenis that interact.," The site of the reconnection takes place high in the solar corona above magnetic loops, or between at least two loop systems that interact."
 At the reconnection site. the clectrons are accelerated and move along the loops with a high velocity (e090).," At the reconnection site, the electrons are accelerated and move along the loops with a high velocity $v\sim0.5c$ )."
 Some of these electrons. will bombard the chromosphere which is denser and. cause this plasma to be heated., Some of these electrons will bombard the chromosphere which is denser and cause this plasma to be heated.
 This plasma will then evaporate into the loops causing the soft rav emission such as is shown in Figure 5 (cf Larra 2000 for more details)., This plasma will then evaporate into the loops causing the soft X-ray emission such as is shown in Figure 5 (cf Harra 2000 for more details).
 Although the details are still uncertain. observations support this view.," Although the details are still uncertain, observations support this view."
 Feldman. Laming Doschek (1995) found a correlation between solar and stellar Hare temperatures ancl emission measures.," Feldman, Laming Doschek (1995) found a correlation between solar and stellar flare temperatures and emission measures."
 Shibata Yokovama (1999) proposed. ᾱ- model based on a magnetic reconnection model with heat conduction and Jiromospheric evaporation to account for this correlation., Shibata Yokoyama (1999) proposed a model based on a magnetic reconnection model with heat conduction and chromospheric evaporation to account for this correlation.
 Ased on our spectral fits to JTP 138. we find an emission measure of 7.1075 ? for JEP 138.," Based on our spectral fits to JTP 138, we find an emission measure of $\times10^{53}$ $^{-3}$ for JTP 138."
 For a temperature of 10* IX. for the hot component. Figure 1 of Shibata Yokovama (1990) suggests a magnetic field. strength. of ]100 CG for this source.," For a temperature of $\times10^{7}$ K for the hot component, Figure 1 of Shibata Yokoyama (1999) suggests a magnetic field strength of $\sim$ 100 G for this source."
 Measuring stellar. magnetic. field μαreneths is dillieult., Measuring stellar magnetic field strengths is difficult.
 However. observations of various RSs ο.‘Vin systems show evidence for magnetic field strengths of 10 order ~ 1001000 G (ce Donati 1999). indicating that a field strength of 100 G for JEP 138 is reasonable.," However, observations of various RS CVn systems show evidence for magnetic field strengths of the order $\sim$ 100–1000 G (eg Donati 1999), indicating that a field strength of 100 G for JTP 138 is reasonable."
 We have performed a X-ray. time variability survey of the open cluster NGC 2516., We have performed a X-ray time variability survey of the open cluster NGC 2516.
 We have found 4 systems which have shown significant. variability., We have found 4 systems which have shown significant variability.
 Fhree of these systems show light curves which are characteristic of stellar Haring activity., Three of these systems show light curves which are characteristic of stellar flaring activity.
 Based on the Uare duration. anc their spectral properties we suggest that they are RS CVn systems., Based on the flare duration and their spectral properties we suggest that they are RS CVn systems.
 The fourth system has been identified with a AO V type star and propose that it may have an unseen dwarf AL star which shows llaring activity., The fourth system has been identified with a AO V type star and propose that it may have an unseen dwarf M star which shows flaring activity.
 An optical spectroscopic study of these objects is required., An optical spectroscopic study of these objects is required.
 Finally. this study shows that open clusters are excellent objects to search for stellar Daring activity and may be relatively common.," Finally, this study shows that open clusters are excellent objects to search for stellar flaring activity and may be relatively common."
 This paper is Based on observations obtained with NMM-Newton. an EXX science mission with instruments and contributions cirecthy Funded. by ESA Member States and the USA (NASA).," This paper is Based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and the USA (NASA)."
 We thank Mat. Page for the use of some of his software., We thank Mat Page for the use of some of his software.
 We acknowledge the use of the WEBDA database of galactic clusters., We acknowledge the use of the WEBDA database of galactic clusters.
Bridle for producing and distributing CosmoloGUI which was used to produce the contours in this paper.,Bridle for producing and distributing CosmoloGUI which was used to produce the contours in this paper.
" Finally, FBA acknowledges the Leverhulme Foundation for support through an Early Careers Fellowship."," Finally, FBA acknowledges the Leverhulme Foundation for support through an Early Careers Fellowship."
Black bole binaries (BIIB) exhibit considerable N-rav variability on a wide range of time-scales.,Black hole binaries (BHB) exhibit considerable X-ray variability on a wide range of time-scales.
 The study of X-ray fast time variability has become an important astrophysical research tool that helps us gain better insight into the physical process at work near the black hole (seetherecentreviewofvanderIwlis 2004)., The study of X-ray fast time variability has become an important astrophysical research tool that helps us gain better insight into the physical process at work near the black hole \citep[see the recent review of][]{vdK04}.
.. For instance. the cdynaniic time-scale for the motion within a few Schwarzschilcl racii of a 10A. black hole is at the orcer of milliseconcls.," For instance, the dynamic time-scale for the motion within a few Schwarzschild radii of a $10~M_{\odot}$ black hole is at the order of milliseconds."
 Further considering that most of the gravitational encrey of acerction matter is released in the inner area of a [ew Schwarzschild radii. the variability at short time-scales can be used to probe the aceretion-ow dynamics and geometries within the strong-Lield region.," Further considering that most of the gravitational energy of accretion matter is released in the inner area of a few Schwarzschild radii, the variability at short time-scales can be used to probe the accretion-flow dynamics and geometries within the strong-field region."
 lime variability can be studied. in the time domain or in the frequency omain., Time variability can be studied in the time domain or in the frequency domain.
 The latter is based on the Fourier transform (EE) and. usually is. based. upon. two owe techniques. the Power Density Spectrum (PDS) and he time lag spectrum.," The latter is based on the Fourier transform (FT) and usually is based upon two basic techniques, the Power Density Spectrum (PDS) and the time lag spectrum."
 The square of Fourier. transform amplituces as a function of Fourier frequcney constitutes the DS. which provides the estimate of variance at different requencies.," The square of Fourier transform amplitudes as a function of Fourier frequency constitutes the PDS, which provides the estimate of variance at different frequencies."
 The time lag spectrum is obtained. from the hase lag. ie. the phase angle difference. between: the Fourier vectors at. dillerent. energy. channels.," The time lag spectrum is obtained from the phase lag, i.e. the phase angle difference between the Fourier vectors at different energy channels."
 In. practice. he PDS and the lag spectra are usually averaged: over many segments of observation and frequencies in order to increase the statistical significance.," In practice, the PDS and the lag spectra are usually averaged over many segments of observation and frequencies in order to increase the statistical significance."
 The Fourier transform is reversible: the time series can be reconstructed. [rom its Fourier transform by means of Inverse Fourier transform (ET)., The Fourier transform is reversible: the time series can be reconstructed from its Fourier transform by means of Inverse Fourier transform (IFT).
 On the contrary. the PDS is not reversible. since the phase information in the EE is lost.," On the contrary, the PDS is not reversible, since the phase information in the FT is lost."
 In. principle there is an infinite variety of dillerent signals that will vield the same PDS., In principle there is an infinite variety of different signals that will yield the same PDS.
 The fast variability observed from BIIB is of stochastic nature and as such cannot be mocleled directly., The fast variability observed from BHB is of stochastic nature and as such cannot be modeled directly.
 La other words. it is not possible to reproduce the exact observed variations.," In other words, it is not possible to reproduce the exact observed variations."
 Phe aim of time-series analysis is to characterize le average properties that give rise to the fluctuations. under the assumption that the process is stationary.," The aim of time-series analysis is to characterize the average properties that give rise to the fluctuations, under the assumption that the process is stationary."
 A gsuecessful model should: reproduce the PDS and the [ag μαrectrum. as Να as other statistical properties of the gaignal (see.e.g.Uttlevοἱal.2005).," A successful model should reproduce the PDS and the lag spectrum, as well as other statistical properties of the signal \citep[see, e.g.][]{Utt05}."
.. A conventional moclel escribing the temporal Ductuation is the shot-noise mocel Clerrell1972:Negoroetal.1994).," A conventional model describing the temporal fluctuation is the shot-noise model \citep{Tel72,Neg94}."
.. Le has become clear. however. that in this framework complex shot profiles or istributions of shot durations and. amplitudes have to be assumed to model the variability of DIIDs (ος.Miyamoto 1991).," It has become clear, however, that in this framework complex shot profiles or distributions of shot durations and amplitudes have to be assumed to model the variability of BHBs \citep[e.g.][]{Miy88,BH90,Loc91}."
. An alternative way is to apply Linear State Space Alodels (LSSMs) which are based on stochastic processes. or autoregressive CAL) processes to describe the temporal variability (Ixónig&Timmoer1997:Pottschmidtetal.1998).," An alternative way is to apply Linear State Space Models (LSSMs) which are based on stochastic processes, or autoregressive (AR) processes to describe the temporal variability \citep{KT97,Pot98}."
. Uttlev.etal.(2005) use a non-linear model to explain the lognormal Dux. distribution ancl rms-Hux relation., \citet{Utt05} use a non-linear model to explain the lognormal flux distribution and rms-flux relation.
 AL these models. are phenomenological: based on the PDS alone they try to reproduce the observed. properties through a mathematical model. which can provide constraints on physical models.," All these models are phenomenological; based on the PDS alone they try to reproduce the observed properties through a mathematical model, which can provide constraints on physical models."
 On the other hand.," On the other hand,"
Nearly all types of galaxies contain globular clusters (GC). from dwarfs to giants and from the earliest to the latest types.,"Nearly all types of galaxies contain globular clusters (GC), from dwarfs to giants and from the earliest to the latest types."
 Our most in-depth understanding of individual GCs comes from studies of the Milky Way (MW: see. for example. Dotter et al.," Our most in-depth understanding of individual GCs comes from studies of the Milky Way (MW; see, for example, Dotter et al."
 2010 and references therein)., \cite{dotter} and references therein).
 Among the external galaxies. M31 plays a special role in our studying of GCs.," Among the external galaxies, M31 plays a special role in our studying of GCs."
 It is our nearest bright spiral galaxy neighbor. it is the most prominent member in the Local Group (LG). and it hosts the largest population of GCs: 544 confirmed GCs are listed in the latest version of the Revised Bologna (RBC v4.0. Galleti et al. 20040).," It is our nearest bright spiral galaxy neighbor, it is the most prominent member in the Local Group (LG), and it hosts the largest population of GCs: 544 confirmed GCs are listed in the latest version of the Revised Bologna (RBC v4.0, Galleti et al. \cite{rbc}) )."
 At the distance of M31 (~783 kpe. from MeConnachie et al. 2005)).," At the distance of M31 $\sim783$ kpc, from McConnachie et al. \cite{mcc05}) ),"
" GCs have almost stellar appearance (10 pe correspond to ~ 2.6"") hence the diagnostics based on integrated light that are used for more distant galaxies can be homogeneously applied here."," GCs have almost stellar appearance (10 pc correspond to $\sim 2.6 \arcsec$ ), hence the diagnostics based on integrated light that are used for more distant galaxies can be homogeneously applied here."
 On the other hand. M31 is also close enough that individual stars in GCs can be resolved and measured with the Hubble Space Telescope (HST).," On the other hand, M31 is also close enough that individual stars in GCs can be resolved and measured with the Hubble Space Telescope (HST)."
 In this framework. the GCs system of M31 is a fundamental test bed for checking the consistency between the cluster parameters (in particular age and metallicity) derived from the integrated light and those obtained from the analysis of the color-magnitude diagram (CMD) of individual cluster stars.," In this framework, the GCs system of M31 is a fundamental test bed for checking the consistency between the cluster parameters (in particular age and metallicity) derived from the integrated light and those obtained from the analysis of the color-magnitude diagram (CMD) of individual cluster stars."
 The most powerful method to determine cluster ages relies on the accurate location of the main-sequence turn-off (MSTO) point (Renzini Fusi Pecci 1988))., The most powerful method to determine cluster ages relies on the accurate location of the main-sequence turn-off (MSTO) point (Renzini Fusi Pecci \cite{rfp}) ).
 Unfortunately. this method is limited to the nearest GCs where individual stars can be resolved and measured down to at least z1-2 magnitudes fainter than the MSTO.," Unfortunately, this method is limited to the nearest GCs where individual stars can be resolved and measured down to at least $\simeq$ 1-2 magnitudes fainter than the MSTO."
 At the distance of M3I the task Is made very challenging owing to the effects of crowding and the intrinsic faintness of the feature., At the distance of M31 the task is made very challenging owing to the effects of crowding and the intrinsic faintness of the feature.
 At present only one of M3I's GC has a CMD down to the TO. which has been achieved only with ~3.5 days of HST/ACS integration time (B379: Brown et al. 2004).," At present only one of M31's GC has a CMD down to the TO, which has been achieved only with $\sim$ 3.5 days of HST/ACS integration time (B379; Brown et al. \cite{brown04})."
 In general. typical CMDs of M31 GCs obtained by HST data barely reach the base of the red giant branch (RGB). including most horizontal branch (HB) stars. except the bluest/faintest ones. when present (Ajhar et al. 1996:;," In general, typical CMDs of M31 GCs obtained by HST data barely reach the base of the red giant branch (RGB), including most horizontal branch (HB) stars, except the bluest/faintest ones, when present (Ajhar et al. \cite{ajh96};"
 Rich et al. 1996:;, Rich et al. \cite{ric96a};
 Fusi Pecci et al. 1996::, Fusi Pecci et al. \cite{fp96};
 Holland et al. 1997:;, Holland et al. \cite{holl97};
 Jablonka et al. 2000::, Jablonka et al. \cite{jab00};
 Meylan et al. 2001:; , Meylan et al. \cite{mey01}; ;
Rich et al. 2005::, Rich et al. \cite{rich05};
 Perina et al. 2009b::, Perina et al. \cite{P09b};
 Huxor et al. 2004.2005.2008::," Huxor et al. \cite{hux04,hux05,hux08};"
 Galleti et al. 2006::, Galleti et al. \cite{b514};
 Mackey et al. 2006. 2007)).," Mackey et al. \cite{mack06,mack07}) )."
 In this magnitude range the HB morphology can be used às a rough age indicator. because the presence of RR Lyrae variables and/or blue HB stars implies low-mass progenitors. hence old ages.," In this magnitude range the HB morphology can be used as a rough age indicator, because the presence of RR Lyrae variables and/or blue HB stars implies low-mass progenitors, hence old ages."
 In à recent analysis. Dotter et al.( 2010))," In a recent analysis, Dotter et al.( \cite{dotter}) )"
 conclude that all Galactic GCs with a blue horizontal branch have ages 212.0 Gyr. on a scale in which the oldest GC is =13.5 gyr old.," conclude that all Galactic GCs with a blue horizontal branch have ages $\ga 12.0$ Gyr, on a scale in which the oldest GC is $\simeq 13.5$ gyr old."
 To date. there are relatively few M31 GCs with à CMD (44).," To date, there are relatively few M31 GCs with a CMD (44)."
 As a consequence. our overall characterization of the GC system of that galaxy mainly relies on the analysis of integrated colors and spectra (see Galleti et al. 2004::," As a consequence, our overall characterization of the GC system of that galaxy mainly relies on the analysis of integrated colors and spectra (see Galleti et al. \cite{rbc};"
 Puzia et al. 2005:; , Puzia et al. \cite{puzia}; ;
Caldwell et al. 2009.. 2011..," Caldwell et al. \cite{C09}, \cite{C11},"
 and references therein)., and references therein).
 A widely used technique is based on Lick spectral indices. (Burstein et al. 1984:;, A widely used technique is based on Lick spectral indices (Burstein et al. \cite{lick1};
 Faber et al. 1985:;, Faber et al. \cite{lick2};
 Worthey 1994))., Worthey \cite{worthey}) ).
 Typically. indices that are mainly sensitive to age (75. Hy) are used in combination with others that are more sensitive to metallicity (Meb. [MegFe]). attempting to break the well-known age- degeneracy.," Typically, indices that are mainly sensitive to age $H_{\beta}$, $H_{\gamma}$ ) are used in combination with others that are more sensitive to metallicity (Mgb, [MgFe]), attempting to break the well-known age-metallicity degeneracy."
 At fixedmetallicity. stronger Balmer lines indicate a hotter MSTO.hence younger ages (see for," At fixedmetallicity, stronger Balmer lines indicate a hotter MSTO,hence younger ages (see for"
restricted to a small domain by diffusivity at short wavelengths and advection at long wavelengths.,restricted to a small domain by diffusivity at short wavelengths and advection at long wavelengths.
 The r.m.s., The r.m.s.
 of the velocity and density perturbations saturates at about 10%., of the velocity and density perturbations saturates at about $\%$.
 When Όσοι=2U002 small scale eddies are visible., When $v_{\infty 1}=2v_{\infty 2}$ small scale eddies are visible.
 They are stretched in the direction of the flow., They are stretched in the direction of the flow.
 The position of the shocks is barely affected by the instability., The position of the shocks is barely affected by the instability.
" The perturbations affect a larger zone on both sides of the contact discontinuity but their amplitude remains around a few tens of percent r.m.s.,"," The perturbations affect a larger zone on both sides of the contact discontinuity but their amplitude remains around a few tens of percent r.m.s.,"
 somewhat higher for the density than for the velocity perturbations., somewhat higher for the density than for the velocity perturbations.
 When Όσοι=20Vo02 (fourth panel) the instability has become non-linear judging by the 100% r.m.s., When $v_{\infty 1}=20v_{\infty 2}$ (fourth panel) the instability has become non-linear judging by the $\%$ r.m.s.
 of the velocity (and density) fluctuations., of the velocity (and density) fluctuations.
 The location of the contact discontinuity fluctuates significantly yet the region with the strongest r.m.s., The location of the contact discontinuity fluctuates significantly yet the region with the strongest r.m.s.
 is not much wider than for the previous cases., is not much wider than for the previous cases.
" We also investigated in this last case whether keeping the wind temperature constant as Όσοι is varied, instead of keeping My constant, led to differences."," We also investigated in this last case whether keeping the wind temperature constant as $v_{\infty 1}$ is varied, instead of keeping ${\cal M}_1$ constant, led to differences."
 The outcome was similar., The outcome was similar.
 A similar set of simulations was performed with 0.0625 (Fig 6))., A similar set of simulations was performed with $\eta=1/16=0.0625$ (Fig \ref{fig:KH_eta16}) ).
" There is no velocity shear or contact discontinuity when Όσοι=Uoc», even in the case ηZ 1."," There is no velocity shear or contact discontinuity when $v_{\infty 1}=v_{\infty 2}$, even in the case $\eta\neq 1$ ."
 This can be proven as follows., This can be proven as follows.
 The Bernouilli constant (Eq. 7)), The Bernouilli constant (Eq. \ref{eq:Bernouilli}) )
" has the same value in both shocked region when Όσοι=UVoo2, so the densities are identical at the contact discontinuity (where pressures equalise) on the line-of-centres."," has the same value in both shocked region when $v_{\infty 1}=v_{\infty 2}$, so the densities are identical at the contact discontinuity (where pressures equalise) on the line-of-centres."
 The gas is polytropic with P=Kpο and K constant in each region., The gas is polytropic with $P\equiv K \rho^{-\gamma}$ and $K$ constant in each region.
 Writing that p and P are equal on both sides of the contact discontinuity on the line-of-centres requires that X has the same value in both shocked regions., Writing that $\rho$ and $P$ are equal on both sides of the contact discontinuity on the line-of-centres requires that $K$ has the same value in both shocked regions.
" Therefore, pis=pos along the contact discontinuity."," Therefore, $\rho_{1s}=\rho_{2s}$ along the contact discontinuity."
 Using that the Bernouilli constant is the same in both shocked regions then proves that Όις=vos at the contact discontinuity., Using that the Bernouilli constant is the same in both shocked regions then proves that $v_{1s}=v_{2s}$ at the contact discontinuity.
" Actually, there is no discontinuity in this case."," Actually, there is no discontinuity in this case."
 The simulation with Όσοι=«vss» confirms that there is no velocity shear and that the KHI does not develop., The simulation with $v_{\infty 1}=v_{\infty 2}$ confirms that there is no velocity shear and that the KHI does not develop.
" When Όσοι=1.1U552 only weak perturbations are seen, limited to a small region close to the contact discontinuity."," When $v_{\infty 1}=1.1v_{\infty 2}$ only weak perturbations are seen, limited to a small region close to the contact discontinuity."
 A dominant wavelength can be identified as in the case η=1., A dominant wavelength can be identified as in the case $\eta=1$.
 When vo;1=25» the center line of the perturbations approximately matches the shape of the unperturbed contact discontinuity., When $v_{\infty 1}=2v_{\infty 2}$ the center line of the perturbations approximately matches the shape of the unperturbed contact discontinuity.
 The first shock is not affected by the instability., The first shock is not affected by the instability.
 The velocity perturbations affect all the region of the shocked second wind and part of the shocked wind of the first star., The velocity perturbations affect all the region of the shocked second wind and part of the shocked wind of the first star.
 The density perturbations have a higher r.m.s., The density perturbations have a higher r.m.s.
" than the velocity perturbations, reaching close to 10096 close to the contact discontinuity."," than the velocity perturbations, reaching close to $\%$ close to the contact discontinuity."
 The velocity perturbation are strong when Όσοι=20552 and are mostly confined to the shocked second wind., The velocity perturbation are strong when $v_{\infty 1}=20v_{\infty 2}$ and are mostly confined to the shocked second wind.
 High r.m.s., High r.m.s.
" density fluctuations extend to the first wind, distorting slightly the first shock. ("," density fluctuations extend to the first wind, distorting slightly the first shock. ("
The sawtooth appearance of the wings in the Vico=Va0co r.m.s.,The sawtooth appearance of the wings in the $v_{1\infty}=v_{20\infty}$ r.m.s.
 maps are an artefact of the limited time range over which the average was done.), maps are an artefact of the limited time range over which the average was done.)
" The backward reconfinement of the wind of the second star is affected by the instability, occurring much closer to the second star than in the case with equal wind velocities."," The backward reconfinement of the wind of the second star is affected by the instability, occurring much closer to the second star than in the case with equal wind velocities."
 The KHI modifies the interaction region as soon as the wind velocities are slightly different., The KHI modifies the interaction region as soon as the wind velocities are slightly different.
" The simulations suggest that the relative amplitude of the perturbations becomes significant when v122v», although we cannot rule out that limited numerical resolution does not impact the growth of the instability for smaller velocity shears."," The simulations suggest that the relative amplitude of the perturbations becomes significant when $v_1\ga 2 v_2$, although we cannot rule out that limited numerical resolution does not impact the growth of the instability for smaller velocity shears."
 The instability does not erase completely the contact discontinuity., The instability does not erase completely the contact discontinuity.
" However, the turbulent motions tend to smooth out the initial structures in the region of the wind with the smaller velocity."," However, the turbulent motions tend to smooth out the initial structures in the region of the wind with the smaller velocity."
" When thermal support in the shocked zone is too weak, the shell becomes thin and unstable."," When thermal support in the shocked zone is too weak, the shell becomes thin and unstable."
 This occurs for instance when the adiabatic index is decreased (?).., This occurs for instance when the adiabatic index is decreased \citep{1993ApJ...407..207M}.
" More realistic numerical simulations including radiative cooling functions also show the shocks become thinner and unstable as cooling increases (??,, but see ?))."," More realistic numerical simulations including radiative cooling functions also show the shocks become thinner and unstable as cooling increases \citealt{Stevens:1992on,2009MNRAS.396.1743P}, but see \citealt{1998MNRAS.298.1021M}) )."
" The instability is usually referred to as 'thin shell instability’ although several physical mechanisms may be at work, including the KHI."," The instability is usually referred to as `thin shell instability' although several physical mechanisms may be at work, including the KHI."
" The non-linear thin shell instability (NTSI, ?)) is found in hydrodynamical simulations when the thin shell is moved away from its rest positions by perturbations with an amplitude at least greater than the shell width (?).."," The non-linear thin shell instability (NTSI, \citealt{1994ApJ...428..186V}) ) is found in hydrodynamical simulations when the thin shell is moved away from its rest positions by perturbations with an amplitude at least greater than the shell width \citep{1996NewA....1..235B}."
 The instability is due to an imbalance in the momentum flux within the shell as shocked fluid moves towards opposing kinks., The instability is due to an imbalance in the momentum flux within the shell as shocked fluid moves towards opposing kinks.
" The transverse acceleration instability (TAI, ??)) occurs when at least one of the colliding flows is divergent and assumes an infinitely thin shell."," The transverse acceleration instability (TAI, \citealt{1993A&A...267..155D,1996ApJ...461..927D}) ) occurs when at least one of the colliding flows is divergent and assumes an infinitely thin shell."
 Both linearly unstable breathing and bending modes are found., Both linearly unstable breathing and bending modes are found.
 The breathing mode is due to the acceleration of the flow along the shell whereas the bending mode arises from the mismatch in ram pressure of the wind impacting each side of the thin shell when it is displaced from its equilibrium value., The breathing mode is due to the acceleration of the flow along the shell whereas the bending mode arises from the mismatch in ram pressure of the wind impacting each side of the thin shell when it is displaced from its equilibrium value.
 We studied the growth of thin shell instabilities in colliding wind binaries using 2D simulations with an isothermal equation of state., We studied the growth of thin shell instabilities in colliding wind binaries using 2D simulations with an isothermal equation of state.
 Initial investigations showed that the thin shock structure ref2dstudy)) becomes unstable only if there are a sufficient number of cells available (= 4) to resolve the shock structure., Initial investigations showed that the thin shock structure \\ref{2dstudy}) ) becomes unstable only if there are a sufficient number of cells available $\ga 4$ ) to resolve the shock structure.
 The minimum number of cells required is even larger if a highly diffusive solver is used., The minimum number of cells required is even larger if a highly diffusive solver is used.
 Low resolution simulations without mesh refinement (256x256 cells) do not resolve the shock structure and stay stable., Low resolution simulations without mesh refinement $256\times 256$ cells) do not resolve the shock structure and stay stable.
" We decided to use those steady state solutions as the initialinput for simulations at higher resolution, so as to be able to"," We decided to use those steady state solutions as the initialinput for simulations at higher resolution, so as to be able to"
beyond roo.,beyond $r_{200}$.
 But can we learn something about the dynamics of these galaxies?, But can we learn something about the dynamics of these galaxies?
 Are the galaxies in substructure recent arrivals to the cluster potential?, Are the galaxies in substructure recent arrivals to the cluster potential?
 Are they an infalling sub-population of galaxies?., Are they an infalling sub-population of galaxies?.
 These questions can be answered by studying the shape of the relative velocity histogram of the galaxies located at r>r2oo., These questions can be answered by studying the shape of the relative velocity histogram of the galaxies located at $r>r_{200}$.
 Gill et al. (, Gill et al. (
2005) investigated the dynamics of satellite galaxies in the outskirts of galaxy clusters from a series of high resolution N-body simulations.,2005) investigated the dynamics of satellite galaxies in the outskirts of galaxy clusters from a series of high resolution N-body simulations.
 They found that galaxies in clusters located at r>1200 were formed by two families: infalling galaxies and the so-called back-splash galaxy population., They found that galaxies in clusters located at $r>r_{200}$ were formed by two families: infalling galaxies and the so-called back-splash galaxy population.
 The infalling galaxies are entering the cluster potential for the first time., The infalling galaxies are entering the cluster potential for the first time.
" In contrast, the back-splash galaxies are located at large cluster distances (r>7299) but have previously spent time near the cluster centre."," In contrast, the back-splash galaxies are located at large cluster distances $r>r_{200}$ ) but have previously spent time near the cluster centre."
 This back-splash galaxy population could be significant in number - up to 50% of the galaxy population located in the region 1.4ro99«r2.81209 (see Gill et al., This back-splash galaxy population could be significant in number - up to $\%$ of the galaxy population located in the region $1.4r_{200}<r<2.8r_{200}$ (see Gill et al.
 2005)., 2005).
 The infalling and the back-splash populations can be separated by studying the shape of the relative velocities of the galaxies in the outskirts of the clusters., The infalling and the back-splash populations can be separated by studying the shape of the relative velocities of the galaxies in the outskirts of the clusters.
 At large distances from the cluster centre (r> 1.47290) the relative velocity of the infalling galaxies is always higher than that of the back-splash galaxies (see Gill et al., At large distances from the cluster centre $r>1.4r_{200}$ ) the relative velocity of the infalling galaxies is always higher than that of the back-splash galaxies (see Gill et al.
 2005)., 2005).
" Therefore, if the back-splash galaxy population does not exist, then the relative velocity histogram should show a Gaussian-shaped peak at relative velocities greater than zero."," Therefore, if the back-splash galaxy population does not exist, then the relative velocity histogram should show a Gaussian-shaped peak at relative velocities greater than zero."
" In contrast, the presence of the back-splash population should distort the Gaussian shape of the relative velocity histogram, peaking at zero relative velocity (see Gill et al."," In contrast, the presence of the back-splash population should distort the Gaussian shape of the relative velocity histogram, peaking at zero relative velocity (see Gill et al."
 2005)., 2005).
" Figure 10 shows the relative velocity histograms of all the galaxies, and those located inside and outside substructures for our ensemble clusters EC1 and EC2."," Figure \ref{f8} shows the relative velocity histograms of all the galaxies, and those located inside and outside substructures for our ensemble clusters EC1 and EC2."
 We considered only those galaxies located at r>1.4ra99., We considered only those galaxies located at $r>1.4r_{200}$.
 Figure 10 indicates that the relative velocity histograms of all the galaxies and those located outside substructures peak at zero velocity., Figure \ref{f8} indicates that the relative velocity histograms of all the galaxies and those located outside substructures peak at zero velocity.
" Nevertheless, galaxies in substructures selected by 0,99 show a peak in the relative velocity histogram different from zero."," Nevertheless, galaxies in substructures selected by $\delta_{g,99}$ show a peak in the relative velocity histogram different from zero."
" In order to test the dynamical state of the galaxies in substructures, we have compared the relative velocities of these galaxies with a mock velocity distribution of backsplash plus infalling galaxies from fig."," In order to test the dynamical state of the galaxies in substructures, we have compared the relative velocities of these galaxies with a mock velocity distribution of backsplash plus infalling galaxies from fig."
 8 of Gill et al. (, 8 of Gill et al. (
2005) and Rines et al. (,2005) and Rines et al. (
2005).,2005).
 Figure 11 shows the relative velocity distribution for a model of backsplash and infalling galaxies., Figure \ref{f10} shows the relative velocity distribution for a model of backsplash and infalling galaxies.
 We built several models varying the percentage of infalling galaxies., We built several models varying the percentage of infalling galaxies.
 The relative velocity distribution of the models and the observed galaxies in substructures were compared using a KS test., The relative velocity distribution of the models and the observed galaxies in substructures were compared using a KS test.
 This provides us the percentage of infalling galaxies located in substructure., This provides us the percentage of infalling galaxies located in substructure.
 It should be noticed that the simulations presented by Gill et al. (, It should be noticed that the simulations presented by Gill et al. (
2005) show results for 1.4rooo<r2.87299.,2005) show results for $1.4r_{200}<r<2.8r_{200}$.
" Nevertheless, our cluster sample is complete untill 299."," Nevertheless, our cluster sample is complete untill $r_{200}$."
 We have investigating the variation of the relative velocity distribution of galaxies in substructure taking into account those galaxies in the range 2-2.8Υ200 for those cluster with galaxies out to 2.87299., We have investigating the variation of the relative velocity distribution of galaxies in substructure taking into account those galaxies in the range $r_{200}$ for those cluster with galaxies out to $r_{200}$ .
 No significant difference was found between the relative velocity distributions of galaxies in substructures located in the radius ranges 1.4-2.0r5oo and 1.4-2.8r290., No significant difference was found between the relative velocity distributions of galaxies in substructures located in the radius ranges $r_{200}$ and $r_{200}$.
 The KS test gives that at the 95% C. L. a pure backsplash galaxy population can be ruled out in all cases., The KS test gives that at the $\%$ C. L. a pure backsplash galaxy population can be ruled out in all cases.
" Thus, the galaxies in substructure are allways a combination of backplash and infalling galaxies."," Thus, the galaxies in substructure are allways a combination of backplash and infalling galaxies."
" However, galaxies in substructure selected using 6j99 show relative velocity histograms dominated by backsplash galaxies."," However, galaxies in substructure selected using $\delta_{i,99}$ show relative velocity histograms dominated by backsplash galaxies."
 The KS test reports that only 10% for EC1 and 40% for EC2 could be infalling galaxies., The KS test reports that only $\%$ for EC1 and $\%$ for EC2 could be infalling galaxies.
" In contrast, galaxies in substructures selected by 6¢,99 are dominated by an infall population."," In contrast, galaxies in substructures selected by $\delta_{g,99}$ are dominated by an infall population."
" In this case, the KS test gives that 60% of the galaxies in substructures, for EC1 and EC2 samples, could be infalling galaxies."," In this case, the KS test gives that $\%$ of the galaxies in substructures, for EC1 and EC2 samples, could be infalling galaxies."
 The backsplash scenario in the outskirts of the clusters was also studied in the past by Rines et al. (, The backsplash scenario in the outskirts of the clusters was also studied in the past by Rines et al. (
2005) and Pimbblet et al. (,2005) and Pimbblet et al. (
2006).,2006).
" Similar to the result presented here, they found that the outermost galaxy population in clusters is neither a pure backsplash population or purely infalling for the first time."," Similar to the result presented here, they found that the outermost galaxy population in clusters is neither a pure backsplash population or purely infalling for the first time."
 They concluded that local galaxy density is a fundamental parameter for the transformation of galaxies in clusters., They concluded that local galaxy density is a fundamental parameter for the transformation of galaxies in clusters.
" We have analysed the u—r colours of the galaxies in substructure selected with 6,99 and located at 1.4<r/roo9 2.0."," We have analysed the $u-r$ colours of the galaxies in substructure selected with $\delta_{g,99}$ and located at $<r/r_{200}<2.0$ ."
" The blue galaxies (u—r< 2.22) represent 45% and 50% of this population of galaxies for EC1 and EC2, respectively."," The blue galaxies $u-r<2.22$ ) represent $\%$ and $\%$ of this population of galaxies for EC1 and EC2, respectively."
" As shown before, ~40% of these galaxies in substructure could be backsplash objects."," As shown before, $\sim 40\%$ of these galaxies in substructure could be backsplash objects."
" Assuming, that this percentage of objects would be red galaxies, then the percentage of blue galaxies of the infall populations would be similar to the percentage of blue isolated galaxies (see Sec."," Assuming, that this percentage of objects would be red galaxies, then the percentage of blue galaxies of the infall populations would be similar to the percentage of blue isolated galaxies (see Sec."
 4.1)., 4.1).
" This means that we can not rule out the hypothesis that the infalling galaxies would be pure field ones, as suggested by recent numerical simulations of cluster formation (see Berrier etal."," This means that we can not rule out the hypothesis that the infalling galaxies would be pure field ones, as suggested by recent numerical simulations of cluster formation (see Berrier etal."
 2009)., 2009).
 We have analysed the presence of substructure in a sample of 88 nearby (z< 0.1) and isolated galaxy clusters., We have analysed the presence of substructure in a sample of 88 nearby $z<0.1$ ) and isolated galaxy clusters.
 The galaxy, The galaxy
and Jim Moran. for. advice about the maser observations and. Anderson Caproni and Lincoln. Cireenhill for useful comments.,and Jim Moran for advice about the maser observations and Anderson Caproni and Lincoln Greenhill for useful comments.
question.,question.
 While the photographic photometry is ellective in adequately constraining Zi. smaller errors are obtainable with the SAAO CCD photometry. anc it is used. where available.," While the photographic photometry is effective in adequately constraining $T_{\rm eff}$, smaller errors are obtainable with the SAAO CCD photometry, and it is used where available."
 The resulting X7. Zi distribution vields a [fitted value for Z;r and an estimate of the associated error. which can be used to read. olf interpolated values of absolute V magnitude ancl bolometric Luminosity.," The resulting $\chi^{2}$, $T_{\rm eff}$ distribution yields a fitted value for $T_{\rm eff}$ and an estimate of the associated error, which can be used to read off interpolated values of absolute V magnitude and bolometric luminosity."
 This procedure. is performed. for cach object for both an assumed. LL ancl Le atmosphere., This procedure is performed for each object for both an assumed H and He atmosphere.
 Distance moduli obtained. from these fits allow calculation of tangential velocities via the SuperCOSALOS proper motion measures., Distance moduli obtained from these fits allow calculation of tangential velocities via the SuperCOSMOS proper motion measures.
" ""The distribution of. derived tangential velocities is consistent. with expectations for a sample of Disc stars (Evans 1992). and shows no evidence of contamination from high velocity halo objects."," The distribution of derived tangential velocities is consistent with expectations for a sample of Disc stars (Evans 1992), and shows no evidence of contamination from high velocity halo objects."
" A summary of the results of the fitting procedure is shown in Table 4.. including Zi, and Aj, with associated. errors and Yi values."," A summary of the results of the fitting procedure is shown in Table \ref{analtab}, including $T_{\rm eff}$ and $M_{\rm bol}$ with associated errors and $V_{\rm tan}$ values."
 Space density values for cach object are also presented. in Table 4: these are discussed in the following section., Space density values for each object are also presented in Table \ref{analtab}; these are discussed in the following section.
 An independent cheek on the validity of our initial CWD sample parameters (SupcerCOSA\LOS photometry and astrometrv) can be mace by comparing known CWD samples with our data on the RPMD., An independent check on the validity of our initial CWD sample parameters (SuperCOSMOS photometry and astrometry) can be made by comparing known CWD samples with our data on the RPMD.
 Since the RPALD is the original means of population discrimination 1t is also interesting to overplot. known subclwarl samples on our RPMD to further address the question of potential contamination., Since the RPMD is the original means of population discrimination it is also interesting to overplot known subdwarf samples on our RPMD to further address the question of potential contamination.
 BRL published observations of a sample of 110 οΑν. including most of the coolest. known degenerates.," BRL published observations of a sample of 110 CWDs, including most of the coolest known degenerates."
 Extensive lists of extreme ορας are. less easily obtainable., Extensive lists of extreme subdwarfs are less easily obtainable.
 Ryan (1989) usec a RPM. criterion to extract over 1000 subewarl candidates. from the NLT'T catalogue., Ryan (1989) used a RPM criterion to extract over 1000 subdwarf candidates from the NLTT catalogue.
 Accurate. B anc 1t. photometry was published or these objects. providing a useful means of delineating he bluer portion of the WD RPAID locus.," Accurate B and R photometry was published for these objects, providing a useful means of delineating the bluer portion of the WD RPMD locus."
 Monet et al. (, Monet et al. (
1992) identified a subset of 17 extreme subchwarls [rom heir CCD parallax program also involving Luvten catalogue stars.,1992) identified a subset of 17 extreme subdwarfs from their CCD parallax program also involving Luyten catalogue stars.
 Although only V. EI photometry is published for these stars. we use the photometry published. in. Ryan (1989) o define colour transformations allowing the 17 subcdwarfs rom Monet ct al. (," Although only V, I photometry is published for these stars, we use the photometry published in Ryan (1989) to define colour transformations allowing the 17 subdwarfs from Monet et al. ("
1992) to be plotted on the (2P). UPMD planes.,"1992) to be plotted on the $(B-R)$, RPMD planes."
 These objects define a portion of the RPALD mareinally red-wards of the faintest CWDs where the most extreme contaminants may be expected to Lic., These objects define a portion of the RPMD marginally red-wards of the faintest CWDs where the most extreme contaminants may be expected to lie.
 Figure I8. shows the two RPALD with the four samples plotted., Figure \ref{rpmdcomp} shows the two RPMD with the four samples plotted.
 There are several points to be mace concerning this, There are several points to be made concerning this
of equation. 8)) for a large range of Z.,of equation \ref{eq.vcf}) ) for a large range of $\Rm$.
 This is somehow intriguing since it is known from DNS that shear in domains with open boundaries does indeed help in alleviating the catastrophic quenching., This is somehow intriguing since it is known from DNS that shear in domains with open boundaries does indeed help in alleviating the catastrophic quenching.
" It may be understood. as a result of the large value of Co compared. with C5, and also to he top boundary condition for the azimuthal magnetic field (Brandenburg2005:Kapvla.Ixorpiand.2008)."," It may be understood as a result of the large value of $C_{\Omega}$ compared with $C_{\alpha}$ and also to the top boundary condition for the azimuthal magnetic field \citep{B05,kapyla08}."
. The results presented above indicate that considerable work is still necessary in order to understand the role of arger-scale shear in transporting and. shedding small-scale maenetic helicity [rom the domain., The results presented above indicate that considerable work is still necessary in order to understand the role of larger-scale shear in transporting and shedding small-scale magnetic helicity from the domain.
 In snapshots of the meridional plane as well as in xutterlly. diagrams we notice that the dilfusive fluxes do not significantIy: modify the morphology and the distribution of he magnetic field when compared with cases without f[uxes or even with simulations with algebraic a quenching., In snapshots of the meridional plane as well as in butterfly diagrams we notice that the diffusive fluxes do not significantly modify the morphology and the distribution of the magnetic field when compared with cases without fluxes or even with simulations with algebraic $\alpha$ quenching.
 On he other hand. for models with VC Εν the distribution of ayy becomes dillerent and so does the magnetic field.," On the other hand, for models with VC flux the distribution of $\alpha_{\rm M}$ becomes different and so does the magnetic field."
 This is clear from the butterllye clagram shown in bie., This is clear from the butterfly diagram shown in Fig.
 12bb. which exhibits a magnetic field. confined. to equatorial latitudes reminiscent of the observed. butterllv. diagram of the solar cvcle.," \ref{but.vc.flux}b b, which exhibits a magnetic field confined to equatorial latitudes reminiscent of the observed butterfly diagram of the solar cycle."
 Even though this result. corresponds to a simplified model. it illustrates the importance of considering the dynamical a quenching mechanism for modeling the solar dvnamo.," Even though this result corresponds to a simplified model, it illustrates the importance of considering the dynamical $\alpha$ quenching mechanism for modeling the solar dynamo."
 Similar changes in the distribution of as; and B are expected to happen when advection terms are included in the governing equations., Similar changes in the distribution of $\alpha_{\rm M}$ and $\bm{\overline{B}}$ are expected to happen when advection terms are included in the governing equations.
 In the simulations presented. here. Q and à elfects are present in the same lavers.," In the simulations presented here, $\Omega$ and $\alpha$ effects are present in the same layers."
 An interesting question is whether the quenching of the dynamo is catastrophic when both lavers are segregated. as in the Parker's interface dynamo or the Dux-transport dynamo models.," An interesting question is whether the quenching of the dynamo is catastrophic when both layers are segregated, as in the Parker's interface dynamo or the flux-transport dynamo models."
 We address his question in detail in two companion papers (Chatterjee.Brandenburg 2010).," We address this question in detail in two companion papers \citep{cbg10,cgb10}."
. We should notice that the hack reaction of the magnetic ield alfects not only the a effect. but also the other ονnamo coellicients. including the turbulent cülfusivitv.," We should notice that the back reaction of the magnetic field affects not only the $\alpha$ effect, but also the other dynamo coefficients, including the turbulent diffusivity."
 Contrary to quenching of a. the quenching of jj. may be considered hrough an algebraic quenching function (seec.g. 2009).. Cruerrero.Dikpati&," Contrary to quenching of $\alpha$, the quenching of $\etat$ may be considered through an algebraic quenching function \citep[see
 e.g.][]{ybr03,kb09}."
deGouveiaDalPino(2009) have shown that in a Ilux-transport model these effects could. allect properties. of the models such as the final magnetic field strength anc its distribution in radius and Iatitude., \cite{gddp09} have shown that in a flux-transport model these effects could affect properties of the models such as the final magnetic field strength and its distribution in radius and latitude.
 We leave the study of models with simultaneous dynamical a and ay quenchings for a future paper., We leave the study of models with simultaneous dynamical $\alpha$ and $\eta$ quenchings for a future paper.
 Solar-like profiles of dillerential rotation ancl meridional. circulation along with cvnamical a quenching will also be considered in à forthcoming paper., Solar-like profiles of differential rotation and meridional circulation along with dynamical $\alpha$ quenching will also be considered in a forthcoming paper.
 This work started during the NORDIPA program solar and stellar clvnanios and. eveles ancl is supported. by the European Research Council. under the AstroDvn research project 227952., This work started during the NORDITA program solar and stellar dynamos and cycles and is supported by the European Research Council under the AstroDyn research project 227952.
We have shown that the Magnus force makes the vortex line parabolic on global scale and causes it to incline against the major axis of a crvstal lattice.,We have shown that the Magnus force makes the vortex line parabolic on global scale and causes it to incline against the major axis of a crystal lattice.
 As (he Magnus force increases and (he rotation axis inclines against the major axis of a ervstal lattice. we need to include the major axis components for force and displacement. though neglected in the present study.," As the Magnus force increases and the rotation axis inclines against the major axis of a crystal lattice, we need to include the major axis components for force and displacement, though neglected in the present study."
 We expect that the lattice planes different [rom those considered here max become inportant for pinning., We expect that the lattice planes different from those considered here may become important for pinning.
 The pinning sites are discrete although we have assumed the unilorm pinning potential along the major axis of a crystal lattice., The pinning sites are discrete although we have assumed the uniform pinning potential along the major axis of a crystal lattice.
 Link. Epstein aud Bayi (1993) find that there appears the band structure in the οποίον spectrum for excitations on a vortex line when (he discrete nature is included in the pinnine site distribution.," Link, Epstein and Baym (1993) find that there appears the band structure in the energy spectrum for excitations on a vortex line when the discrete nature is included in the pinning site distribution."
 Ht is also necessary lo take account of the discrete nature of the pinning sites when we consider the vortex equilibrium configurations with the scale leneth comparable to the lattice constant., It is also necessary to take account of the discrete nature of the pinning sites when we consider the vortex equilibrium configurations with the scale length comparable to the lattice constant.
 The above arguments suggest (hat the three dimensional caleulations adopting the discrete pinning sites should be conducted in near Iuture in order to understand the equilibrium vortex configurations and vortex oscillations aud judge the relevance of vortex. pinning Lor the pulsar glitches correctly., The above arguments suggest that the three dimensional calculations adopting the discrete pinning sites should be conducted in near future in order to understand the equilibrium vortex configurations and vortex oscillations and judge the relevance of vortex pinning for the pulsar glitches correctly.
 We thank M. Ruderman. BR. Epstein aud D. Link for many. useful discussions.," We thank M. Ruderman, R. Epstein and B. Link for many useful discussions."
 We also thank ο. Nakamura for his help in calculations., We also thank S. Nakamura for his help in calculations.
 This research was supported in part by the Grant-in Aid for Scientific Research (C) (10640234. 12640229. 12640302).," This research was supported in part by the Grant-in Aid for Scientific Research (C) (10640234, 12640229, 12640302)."
Fundamental stellar parameters are best determined by studying high resolution. high signal-to-noise spectra.,"Fundamental stellar parameters are best determined by studying high resolution, high signal-to-noise spectra."
 High resolution spectroscopy is also essential for studying velocity fields in stellar. atmospheres., High resolution spectroscopy is also essential for studying velocity fields in stellar atmospheres.
 There are a number of astrophysical phenomena leading to the emergence of macroscopic velocity fields in stellar atmospheres. which can be observed as spectral line asymmetries and radial velocity variations.," There are a number of astrophysical phenomena leading to the emergence of macroscopic velocity fields in stellar atmospheres, which can be observed as spectral line asymmetries and radial velocity variations."
 Line bisectors. defined as the the loci of the midpoints on the horizontal lines extending from one side to the other of spectral line profiles. are often employed to study the mechanisms that cause such asymmetries and variations.," Line bisectors, defined as the the loci of the midpoints on the horizontal lines extending from one side to the other of spectral line profiles, are often employed to study the mechanisms that cause such asymmetries and variations."
 ? related line asymmetries to a fundamental stellar parameter by showing that the blue-most point of the Fel (6252 line bisector is a very good indicator of luminosity class for the stars from late G to early K spectral types., \citet{gray2005} related line asymmetries to a fundamental stellar parameter by showing that the blue-most point of the FeI $\lambda$ 6252 line bisector is a very good indicator of luminosity class for the stars from late G to early K spectral types.
 Although it is possible to obtain high-resolution spectra with the use of state of the art telescope-spectrograph configurations. m order to achieve sufficient. signal-to-noise ratio (SNR hereafter). one typically has to either use long exposure times and/or combine many individual exposures.," Although it is possible to obtain high-resolution spectra with the use of state of the art telescope-spectrograph configurations, in order to achieve sufficient signal-to-noise ratio (SNR hereafter), one typically has to either use long exposure times and/or combine many individual exposures."
 With this approach. however. short-term line profile variations cannot be measured.," With this approach, however, short-term line profile variations cannot be measured."
 To overcome this limitation. one can either average bisectors of individual lines or employ cross-correlation functions (CCFs) instead.," To overcome this limitation, one can either average bisectors of individual lines or employ cross-correlation functions (CCFs) instead."
" These functions are computed by cross-correlating observational stellar spectra with synthetic line masks with the objective of preserving line profile information: they can be thought of as near-optimal ""average"" spectral lines because the cross-correlation is based on lines of many different elements (?).."," These functions are computed by cross-correlating observational stellar spectra with synthetic line masks with the objective of preserving line profile information; they can be thought of as near-optimal “average"" spectral lines because the cross-correlation is based on lines of many different elements \citep{dall+2006}."
 Because of this. CCFs have high SNR and represent one single instance of time.," Because of this, CCFs have high SNR and represent one single instance of time."
 In addition. their computation is faster compared to averaging bisectors of many individual lines.," In addition, their computation is faster compared to averaging bisectors of many individual lines."
 On the other hand. averaging bisectors make it easy to select the individual lines according to line strength. excitation potential etc.," On the other hand, averaging bisectors make it easy to select the individual lines according to line strength, excitation potential etc."
 However. one can also design cross-correlation masks by selecting lines with similar strength and/or excitation potential. or with a limited number of elements or ions.," However, one can also design cross-correlation masks by selecting lines with similar strength and/or excitation potential, or with a limited number of elements or ions."
 Designing masks other than the standard masks in the HARPS Data Reduction Software (DRS hereafter) is an ongoing study and will be the subject of another paper., Designing masks other than the standard masks in the HARPS Data Reduction Software (DRS hereafter) is an ongoing study and will be the subject of another paper.
 Line bisectors delineate line asymmetries., Line bisectors delineate line asymmetries.
 In order to quantify the shape of bisectors. measures are defined.," In order to quantify the shape of bisectors, measures are defined."
 Bisector measures frequently used in the literature are mainly based on the detined by ? as the velocity difference between two bisector points at certain flux levels of the continuum on a single line bisector. and the defined by ? as the difference of two velocity spans.," Bisector measures frequently used in the literature are mainly based on the defined by \citet{tonergray1988} as the velocity difference between two bisector points at certain flux levels of the continuum on a single line bisector, and the defined by \citet{grayhatzes1997} as the difference of two velocity spans."
 Most of the extrasolar planet survey studies (??) take the definition of ? as reference for the velocity span and adopt it to CCF bisectors using average velocities in two different regions on the bisector. one at the top and one close to the bottom instead of two real bisector points as ? did.," Most of the extrasolar planet survey studies \citep{queloz+2001,martinezf+2005} take the definition of \citet{tonergray1988} as reference for the velocity span and adopt it to CCF bisectors using average velocities in two different regions on the bisector, one at the top and one close to the bottom instead of two real bisector points as \citet{tonergray1988} did."
 They investigate if the variation of the bisector measure correlates well with that of the radial velocity., They investigate if the variation of the bisector measure correlates well with that of the radial velocity.
 If such a correlation exists. then the radial velocity variation is attributed to stellar mechanisms instead of a planetary companion which would not cause variations in line asymmetry.," If such a correlation exists, then the radial velocity variation is attributed to stellar mechanisms instead of a planetary companion which would not cause variations in line asymmetry."
 It is ? that first gave a quantitative relationship between the stellar parameters (surface gravity. and absolute magnitude) and a combination of two bisector measures. namely the (BIS hereafter) and the curvature.," It is \citet{dall+2006} that first gave a quantitative relationship between the stellar parameters (surface gravity, and absolute magnitude) and a combination of two bisector measures, namely the (BIS hereafter) and the curvature."
 Although their relation ts based on a few data points. they stress that it can be possible to obtain the luminosity of a star from the shape of its average CCF bisector.," Although their relation is based on a few data points, they stress that it can be possible to obtain the luminosity of a star from the shape of its average CCF bisector."
 Hence. the CCF bisector measures can be used as indicators of luminosity similar to the blue-most point on classical single line bisectors as ? has shown.," Hence, the CCF bisector measures can be used as indicators of luminosity similar to the blue-most point on classical single line bisectors as \citet{gray2005} has shown."
 In this paper. we investigate the relationship between stellar parameters (specifically surface gravity and effective temperature). and mean CCF bisector shapes of a number of late type stars observed with HARPS.," In this paper, we investigate the relationship between stellar parameters (specifically surface gravity and effective temperature), and mean CCF bisector shapes of a number of late type stars observed with HARPS."
 In order to do this. we make use of the bisector measures frequently used in the," In order to do this, we make use of the bisector measures frequently used in the"
be larger than a critical value.,be larger than a critical value.
 Otherwise (he magnetic field is dissipated before the field is amplified by MBRI (Tan&Melxee2004:TanBlackman2004).," Otherwise the magnetic field is dissipated before the field is amplified by MRI \citep{TM04,TB04}."
. Thus. it is important to assess (he “initial” magnetic field strength in the accretion disk.," Thus, it is important to assess the “initial” magnetic field strength in the accretion disk."
 As was discussed by Nakano [or preset-day case. magnetic field could be clissipated while prestellar core Collapses.," As was discussed by \citet{nakano86} for preset-day case, magnetic field could be dissipated while prestellar core collapses."
 Llowever. the dissipation processes stronglv depend on the components of the eas as well as the the temperature evolution in the course of the collapse.," However, the dissipation processes strongly depend on the components of the gas as well as the the temperature evolution in the course of the collapse."
 On the other hand. the temperature of the collapsing primordial gas is much higher than that of the present-day case (Onmukai2000).. which might bring about different dissipation history of the magnetic [ield.," On the other hand, the temperature of the collapsing primordial gas is much higher than that of the present-day case \citep{omukai00}, which might bring about different dissipation history of the magnetic field."
 In this paper. we investigate (he dissipation of magnetic lield in collapsing primordial eas cloud.," In this paper, we investigate the dissipation of magnetic field in collapsing primordial gas cloud."
" Consequently, we obtaim (the initial magnetic field strength in the accretion disk of Poplll stars."," Consequently, we obtain the initial magnetic field strength in the accretion disk of PopIII stars."
 In the next section. formulations are described.," In the next section, formulations are described."
 In refresulls.. results of our calculations are shown. and (he importance of MBRI in PopllI star formation is discussed in reldiscussion..," In \\ref{results}, results of our calculations are shown, and the importance of MRI in PopIII star formation is discussed in \\ref{discussion}."
 Final section is devoted to summary., Final section is devoted to summary.
 We consider the collapse of spherical clouds without metals and dusts. but with slight magnetic fields.," We consider the collapse of spherical clouds without metals and dusts, but with slight magnetic fields."
 Then. we caleulate the time evolution of the central density. chemical composition ancl dissipation of magnetic flux from the eravilationally collapsing core.," Then, we calculate the time evolution of the central density, chemical composition and dissipation of magnetic flux from the gravitationally collapsing core."
 The inilial strength: of magnetic fields when primordial clouds begin to contract is given as unknown parameter., The initial strength of magnetic fields when primordial clouds begin to contract is given as unknown parameter.
 We assume that the dynamics is described bv the free-fall relation. where p is the density of the collapsing core and τις=(37/326p)!7 is the free-fall time.," We assume that the dynamics is described by the free-fall relation, where $\rho$ is the density of the collapsing core and $\tau_{\rm ff} = (3 \pi/32G\rho)^{1/2}$ is the free-fall time."
 In fact. as described in Omukai(2000).. thermal evolution of the core in ID lyvclroclvnamic simulation is well described by such one zone model.," In fact, as described in \citet{omukai00}, thermal evolution of the core in 1D hydrodynamic simulation is well described by such one zone model."
 On the other hand. we also have to evaluate the dissipation of magnetic field in (he accretion phase. aud it is not the same as the case of collapsing core.," On the other hand, we also have to evaluate the dissipation of magnetic field in the accretion phase, and it is not the same as the case of collapsing core."
 In this case. the temperature of the accretion flow: would rise," In this case, the temperature of the accretion flow would rise"
where A is the sell-interaction coupling constant.,where $\lambda$ is the self-interaction coupling constant.
 According to Noether's theorem. the energv-momentum tensor can be written as In order to solve the Einstein equations. ib is reasonable (ο assume that where (7) is a real function.," According to Noether's theorem, the energy-momentum tensor can be written as In order to solve the Einstein equations, it is reasonable to assume that where $\Phi(r)$ is a real function."
" The structure equations can then be obtained [rom the Einstein equations (IHenriques 1939). where all physical quantities have been redefined in dimensionless form. The boundary conditions are as follows. In addition. the total gravitational mass Mag, 15 given by the asymptotic value of A ad large5 r: A(x)—(1GMau/r)|."," The structure equations can then be obtained from the Einstein equations (Henriques 1989), where all physical quantities have been redefined in dimensionless form, The boundary conditions are as follows, In addition, the total gravitational mass $M_{\rm grav}$ is given by the asymptotic value of $A$ at large $r$: $A(\infty) \to (1-GM_{\rm
grav}/r)^{-1}$."
 As in the case of the fermion-fermion star. (he equations are linear in by.," As in the case of the fermion-fermion star, the equations are linear in $b_0$."
 Hence. (his parameter may be given anv value and normalized alter the," Hence, this parameter may be given any value and normalized after the"
The dotted line compares our reference caleulation to that of Burrowsetal.(1997).,The dotted line compares our reference calculation to that of \citet{bur97}.
.. Thev employ their own opacity and atmosphere caleulations but still have very similar results to our reference calculation., They employ their own opacity and atmosphere calculations but still have very similar results to our reference calculation.
 The short-dash line compares our reference calculation to that of Siessοἱal...(2000)., The short-dash line compares our reference calculation to that of \citet{sie00}.
. For the atmosphere. {μον use an analvtical fit to the T(7) relation calculated bv Plez(1992).," For the atmosphere, they use an analytical fit to the $T(\tau)$ relation calculated by \citet{ple92}."
. Their equation of state is based on the framework as outlined in Polsetal...(1995)., Their equation of state is based on the framework as outlined in \citet{pol95}.
.. An alternative method to calculate the LDB age uncertainty is to use external comparisons with independent lithium depletion calculations from (he literature (see Figure 7 and Section ??))., An alternative method to calculate the LDB age uncertainty is to use external comparisons with independent lithium depletion calculations from the literature (see Figure \ref{comp} and Section \ref{exterr}) ).
 We adopt the absolute value of the deviations shown in Figure as 1-0 errors., We adopt the absolute value of the deviations shown in Figure \ref{comp} as $\sigma$ errors.
 We average the individual deviations to arrive al the total l-o error shown as the dashed line in Figure 8.., We average the individual deviations to arrive at the total $\sigma$ error shown as the dashed line in Figure \ref{errfig}.
 The four caleulations from D'Antona&Mazzitelli(1994) are not included in the average since they have been superseded by the more recent D'Antona calculations., The four calculations from \citet{dan94} are not included in the average since they have been superseded by the more recent \citet{dan97} calculations.
 For comparisons that do not extend over (he entire range of Iuninosity. we extrapolate by aclopling a constant value equal to the comparison endpoints.," For comparisons that do not extend over the entire range of luminosity, we extrapolate by adopting a constant value equal to the comparison endpoints."
 The external 1-6 error is larger than the internal l-o error (Figure 8.., The external $\sigma$ error is larger than the internal $\sigma$ error (Figure \ref{errfig}.
 The larger external error suggests there are additional svstematic deviations in the LDB calculations that result from either numerical dillerences between the LDD calculations or our calculations have nol fully explored the range of relevant physics., The larger external error suggests there are additional systematic deviations in the LDB calculations that result from either numerical differences between the LDB calculations or our calculations have not fully explored the range of relevant physics.
 However. reconciling (he (wo error estimates only requires an additional error added in quadratiuwe to the internal error estimate.," However, reconciling the two error estimates only requires an additional error added in quadrature to the internal error estimate."
 Since we are interested in (he impact of input physics uncertainties on the LDB ages only. for the 1-o theoretical error in the LDB ages. we adopt the internal l-o errors.," Since we are interested in the impact of input physics uncertainties on the LDB ages only, for the $\sigma$ theoretical error in the LDB ages, we adopt the internal $\sigma$ errors."
 Adopting the larger external error may include numerical effects into our error budget., Adopting the larger external error may include numerical effects into our error budget.
 For a simple analvtical model of the 1-7 theoretical error. we adopt a linear trend in log(L) starting at a value of [or log(L/L. )—-1.5 and decreasing to for log(L/L.. )=-3.0.," For a simple analytical model of the $\sigma$ theoretical error, we adopt a linear trend in $\log$ (L) starting at a value of for $\log$ $_{\odot}$ )=-1.5 and decreasing to for $\log$ $_{\odot}$ )=-3.0."
 For Iuminosities bevond the above Iuminositv range. we adopt a constant percentage error equal to the endpoint values.," For luminosities beyond the above luminosity range, we adopt a constant percentage error equal to the endpoint values."
 The column labeled opyy in Table 1. gives the l-o error in the relerence LDD age as a function of luminosity based on our simple analytical error model., The column labeled $\sigma_{THY}$ in Table \ref{reftab} gives the $\sigma$ error in the reference LDB age as a function of luminosity based on our simple analytical error model.
 Taking into account theoretical errors alone. absolute ages of open clusters accurate to for the oldest clusters increasing to for the voungest clusters using the LDB technique are possible.," Taking into account theoretical errors alone, absolute ages of open clusters accurate to for the oldest clusters increasing to for the youngest clusters using the LDB technique are possible."
 Our calculations of (he errors in the LDB age technique show this to be the most accurate method for determining the ages of open clusters., Our calculations of the errors in the LDB age technique show this to be the most accurate method for determining the ages of open clusters.
 These small errors emphasize the simplicity for calculating the evolutionary rate of fully convective objects powered only by eravitational energv., These small errors emphasize the simplicity for calculating the evolutionary rate of fully convective objects powered only by gravitational energy.
 Even LDD calculations that ignore essential physics (analvlical model, Even LDB calculations that ignore essential physics (analytical model
2ο (2???) ?.. (?)fose. ,"$z>6$ \citep{2010AJ....139..906W,2009ApJ...693....8B,2008ApJ...675...49S,2008AJ....135.1057J}, \citet{2010ApJ...710.1498G}. \citep[][]{1999ApJ...514..648M} ,"
Is mipossible at the epoch of reiouizatiou. because intervening absorbers make the IGAL opaque to LyC photons.," is impossible at the epoch of reionization, because intervening absorbers make the IGM opaque to LyC photons."
 Instead. nuuust be measured at lower redshifts (223.5) in objects that are analogous to the galaxies responsible for reiouization.," Instead, must be measured at lower redshifts $z\lsim3.5$ ) in objects that are analogous to the galaxies responsible for reionization."
 Detection of escaping LyC photons has cluded most surveys., Detection of escaping LyC photons has eluded most surveys.
 Observations of Lyman break ealaxies (LBCs) at 2~3 (277) suegest that in —105€ of starbursts the escape fraction is quite large. ucaring unity.," Observations of Lyman break galaxies (LBGs) at $z\sim 3$ \citep{2001ApJ...546..665S,2006ApJ...651..688S,2009ApJ...692.1287I} suggest that in $\sim$ of starbursts the escape fraction is quite large, nearing unity."
" In coutrast. there are currently no LyC detections locally (+21). despite tremendous effort (2777??7,sceSimiaetal.2010fora review). "," In contrast, there are currently no LyC detections locally $z\lsim1$ ), despite tremendous effort \citep[][see Siana et al. 2010 for a review]{1995ApJ...454L..19L,1997MNRAS.289..629G,2001A&A...375..805D,
 2003ApJ...598..878M,2007ApJ...668...62S,2009ApJ...692.1476C}."
One explanation sugeested bv several authors is that the cosmic average escape fraction evolves with redshift (???)..," One explanation suggested by several authors is that the cosmic average escape fraction evolves with redshift \citep{2006MNRAS.371L...1I,2007ApJ...668...62S,2010arXiv1001.3412S}."
 One notable differeuce between high and low redshift studies of the escape fraction is the waveleugth range used to measure the LyC flux., One notable difference between high and low redshift studies of the escape fraction is the wavelength range used to measure the LyC flux.
 All previous surveys searching for intermediate redshitt LyC leaking galaxies have utilized broad-band photometry which probe ~TOOA while τν23 studies measure the LyC just below the Lyman duit., All previous surveys searching for intermediate redshift LyC leaking galaxies have utilized broad-band photometry which probe $\sim 700$ while $z\sim3$ studies measure the LyC just below the Lyman limit.
 Probing these shorter waveleueths lucreascs the seusitivitv to the star formation history. dust extinction and IGAL absorption.," Probing these shorter wavelengths increases the sensitivity to the star formation history, dust extinction and IGM absorption."
 This means a decrease in star formation within the last 10 Myr would significantly lower the flux at colmpared to. weakening the LyC limits measured from broad-banud photometry.," This means a decrease in star formation within the last 10 Myr would significantly lower the flux at compared to, weakening the LyC limits measured from broad-band photometry."
" It is with this difference im ήτα, that we have uudertaken a large spectroscopic program witli the Telescope (IIST)) to study the escape fraction in huniuous starbursts at 2~0.7 (CO 11236: PI:Teplitz).", It is with this difference in mind that we have undertaken a large spectroscopic program with the ) to study the escape fraction in luminous starbursts at $z\sim 0.7$ (GO 11236; PI:Teplitz).
"where £D, is the distance to the source and .r ds the observer-Iens distance.",where $D_s$ is the distance to the source and $x$ is the observer-lens distance.
" The ΙΑΠΟ collaboration has reported an optical depth toward the LMC of 2.1""10 (2.9""10. 7) corresponding to 6 (8) microlensing events in their 2 vear data (Alcockctal.1997).."," The MACHO collaboration has reported an optical depth toward the LMC of $2.1^{+1.1}_{-0.7} \times 10^{-7}$ $2.9^{+1.4}_{-0.9} \times
10^{-7}$ ) corresponding to 6 (8) microlensing events in their 2 year data \cite{MACHOmass}."
. We consider a lower limit to the optical depth predicted by our models of OQ.10ὃν approxiniately one and a half sigma below the ALACLLO G-event data.," We consider a lower limit to the optical depth predicted by our models of $1.0\times 10^{-7}$, approximately one and a half sigma below the MACHO 6-event data."
 This limit is plotted as a solid line in ligure 1., This limit is plotted as a solid line in Figure 1.
 Because most of the lensing in this class of models akes place close to the observer where the microlensing tube is narrow. high surface densities are required.," Because most of the lensing in this class of models takes place close to the observer where the microlensing tube is narrow, high surface densities are required."
 Further. as he scale height is decreased. the lensing moves closer to the observer where the Einstein radius is smaller and thus it is very clillieult to produce enough lensing even with extremely veh surface densities.," Further, as the scale height is decreased, the lensing moves closer to the observer where the Einstein radius is smaller and thus it is very difficult to produce enough lensing even with extremely high surface densities."
 The first 3 constraints are shown in Figure 1., The first 3 constraints are shown in Figure 1.
 A few points are immediately obvious., A few points are immediately obvious.
 First. the limit on the column density within +—1.0kpe is independent. of the disk model since it is purely a local measure.," First, the limit on the column density within $\pm
1.0$ kpc is independent of the disk model since it is purely a local measure."
 Second. the optical depth is only weakly dependent on the precise model for the disk with the dependence becoming stronger as the scale height increases.," Second, the optical depth is only weakly dependent on the precise model for the disk with the dependence becoming stronger as the scale height increases."
 This again rellects the local nature of the microlensing: since the fall olf above the plane of the disk is exponential for small scale heights most of the microlensing occurs close to the observer where the raclia dependence of the density is relatively unimportant., This again reflects the local nature of the microlensing: since the fall off above the plane of the disk is exponential for small scale heights most of the microlensing occurs close to the observer where the radial dependence of the density is relatively unimportant.
 As the scale height increases however. the microlensing inercasingly. samples regions cistant [rom the observer where the racdia coordinate is substantially dillerent.," As the scale height increases however, the microlensing increasingly samples regions distant from the observer where the radial coordinate is substantially different."
 The most. importan dilference between models is the upper limit on the surface densitv from the rotation constraints. which varies [roni GOAL.pe> for the 3.0kpe exponential disk to 115A.pe for the Alestel disk.," The most important difference between models is the upper limit on the surface density from the rotation constraints, which varies from $60 \Msol pc^{-2}$ for the 3.0kpc exponential disk to $115 \Msol pc^{-2}$ for the Mestel disk."
" Short scale length exponential disks have much more mass within the solar circle for a given. value of ""EBET", Short scale length exponential disks have much more mass within the solar circle for a given value of $\Sigma_0$.
 As expected. models with scale heights smaller than 1 kpe are thoroughly ruled. out.," As expected, models with scale heights smaller than 1 kpc are thoroughly ruled out."
 Thin or thick disks cannot oovide sullicient microlensing optical depth toward: the LAIC., Thin or thick disks cannot provide sufficient microlensing optical depth toward the LMC.
 Microlensing is so incllicient for these small scale reights that column density constraints are as much as an order of magnitude lower than needed for mbar., Microlensing is so inefficient for these small scale heights that column density constraints are as much as an order of magnitude lower than needed for $\tau_{\rm LMC}$.
 As he scale height increases. however. microlensing becomes more cllicient and the required. surface density decreases o meet the column density constraints at about ον= 20kpc. Ma=SOA.pe? in all models.," As the scale height increases, however, microlensing becomes more efficient and the required surface density decreases to meet the column density constraints at about $h_z=2.0 {\rm kpc}$ , $\Sigma_0=80 \Msol pc^{-2}$ in all models."
 This. is where he rotation constraints figure most stronglv., This is where the rotation constraints figure most strongly.
 For the more jighlv condensed model (ry= 3.0kpc). the density increases rapidly towards the center resulting in a higher rotation velocity lor a given surface density.," For the more highly condensed model $r_d=3.0 {\rm kpc}$ ), the density increases rapidly towards the center resulting in a higher rotation velocity for a given surface density."
 Thus taken together. he three constraints eliminate the short scale length models entirely and. restrict. the distributed. mocdoels. (lone scale ength. exponential ancl mestel) to a small allowed: region with scale heights ὃνz2 Ὄκρο ancl surface densities. Mum7010034.pe," Thus taken together, the three constraints eliminate the short scale length models entirely and restrict the distributed models (long scale length exponential and mestel) to a small allowed region with scale heights $h_z \approx 2-3$ kpc and surface densities, $\Sigma_0 \approx 70-100 \Msol pc^{-2}$."
 In these fat. clisk mocels microlensing takes place closer to 1ο observer than in the standard. halo models and thus where the microlensing tube is narrower., In these fat disk models microlensing takes place closer to the observer than in the standard halo models and thus where the microlensing tube is narrower.
 To obtain the same optical depth the density locally must therefore be greater., To obtain the same optical depth the density locally must therefore be greater.
 lt is thus of interest to examine if searches for faint white warls in the Llubble Deep Field can place significant limits on such models., It is thus of interest to examine if searches for faint white dwarfs in the Hubble Deep Field can place significant limits on such models.
 Flynn et al. (, Flynn et al. (
1996) examined the LIDE for objects fainter than m;=24.63 and redder than Vf=Ls down to a limiting magnitude of m;=26.3.,1996) examined the HDF for objects fainter than $m_I=24.63$ and redder than $V-I=1.8$ down to a limiting magnitude of $m_I=26.3$ .
 They found no such objects in the £2=3.72.10° steradian field of the LDP., They found no such objects in the $\Omega=3.72\times10^{-7}$ steradian field of the HDF.
 For an object of I-band absolute magnitude A; the volume probed is thus V=0.9algzuu, For an object of I-band absolute magnitude $M_I$ the volume probed is thus V=0.9 pc^3.
t - Even for relatively bright objects the maximum: distance probed. is not. very. large., Even for relatively bright objects the maximum distance probed is not very large.
 Assuming a constant density the number of NLACTIOs expected in this volume is then N=0.9 πμMna where the <3 isto be consistent with the non-detection of such objects., Assuming a constant density the number of MACHOs expected in this volume is then N=0.9 3 where the $\leq 3$ is to be consistent with the non-detection of such objects.
 For py=Xo/2h. this vields [5] ]118.92., For $\rho_0=\Sigma_0/2h_z$ this yields M_I> ] +18.92.
5) with Xo in M.pe. m in AM. and hi in pe.," with $\Sigma_0$ in $\Msol pc^{-3}$, m in $\Msol$ and $h_z$ in pc."
 For à given mass we can then calculate the minimunr magnitude for NLACTIOs to avoid detection in the ΟΙ as a [unction of both My and h.., For a given mass we can then calculate the minimum magnitude for MACHOs to avoid detection in the HDF as a function of both $\Sigma_0$ and $h_z$.
 Llowever. for any single mass. this procedure will not be consistent for all combinations of Mo and P. since this mass may be unlikely or even ruled out for those values.," However, for any single mass, this procedure will not be consistent for all combinations of $\Sigma_0$ and $h_z$ since this mass may be unlikely or even ruled out for those values."
 Instead. for cach combination we use the mass estimated [rom the microlensing event. durations (see next section for these calculations)., Instead for each combination we use the mass estimated from the microlensing event durations (see next section for these calculations).
 A contour plot of the minimum magnitudes thus obtained is shown in Figure 6., A contour plot of the minimum magnitudes thus obtained is shown in Figure 6.
 Magnitudes for the allowed region are Al;z117.," Magnitudes for the allowed region are $M_I
\approx 16-17$."
 Comparison of the local volume density for a typical Fat clisk model. 0.0234.pe.. to the volume density/age relationship presented by (Cuwalletal.1997). shows that the NLACTIIOs must be at least 13 Gye old and more likely in the 15-17 Gyr range.," Comparison of the local volume density for a typical fat disk model, $0.02 \Msol pc^{-3}$, to the volume density/age relationship presented by \cite{Graffetal} shows that the MACHOs must be at least 13 Gyr old and more likely in the 15-17 Gyr range."
 The fat disk must have formed in the very. earliest stages of the formation of the Galaxy., The fat disk must have formed in the very earliest stages of the formation of the Galaxy.
 The assumption of the velocity structure of the fat disks we are considering allows us to calculate not. only the optical depth. but also the microlensing rate to the LMC.," The assumption of the velocity structure of the fat disks we are considering allows us to calculate not only the optical depth, but also the microlensing rate to the LMC."
 Incombination with the opticaldepth we can find the expected average duration for events for a given model.," Incombination with the opticaldepth we can find the expected average duration for events for a given model,"
prescribed. law. s). with the velocity um aumplitucle being chosen to ensure the final kinetic energv of the expelled envelope. of the order of 107 erg.,"prescribed law, $R_{\mathrm {pis}}(t)$, with the velocity $(\dot R)$ amplitude being chosen to ensure the final kinetic energy of the expelled envelope of the order of $10^{51}$ erg."
 “Phere are two major uncertainties at this point., There are two major uncertainties at this point.
 First. for a given velocity amplitude the resulting nuclear vields are still sensitive to the form of the function. Ze).," First, for a given velocity amplitude the resulting nuclear yields are still sensitive to the form of the function $R_{\mathrm {pis}}(t)$."
 Second. th[unο presupernova structure (especially chemical composition) in the vicinity of m=Mou will always remain ambiguous until the detailec mechanism of the 5 isintegration. ont«c the collapsec core and thrown envelope is established.," Second, the presupernova structure (especially chemical composition) in the vicinity of $m={\cal M}_{\mathrm {cut}}$ will always remain ambiguous until the detailed mechanism of the SN disintegration onto the collapsed core and thrown envelope is established."
 The point is tha such 2D elfects as rotation and large-scale mixing can result in the presupernova structure different from. tha predicted. by the spherically svnimetrical models., The point is that such 2D effects as rotation and large-scale mixing can result in the presupernova structure different from that predicted by the spherically symmetrical models.
" Under such circumstances. it is difficult to find a serious argumen to expel a noticeable amount of against""Nifromthepossibilityrecombination of the neutron-proton shell."," Under such circumstances, it is difficult to find a serious argument against the possibility to expel a noticeable amount of } from the recombination of the neutron-proton shell."
 Thus. we propose a neutron-proton laver which is locates somewhat deeper than the value of Mou assumed. in the current SN. models.," Thus, we propose a neutron-proton layer which is located somewhat deeper than the value of ${\cal M}_{\mathrm {cut}}$ assumed in the current SN models."
 This laver NIrecombinesinto providing the energy sullicient to convert à. steady-state accretion shock into the outgoing blast wave., This layer recombines into } providing the energy sufficient to convert a steady-state accretion shock into the outgoing blast wave.
 In this case a good correlation between ££ and Mopiy is to be expected., In this case a good correlation between $E$ and ${\cal M}_{\mathrm{Ni0}}$ is to be expected.
 The proposed correlation can have a complex nature., The proposed correlation can have a complex nature.
 It is quite probable that the function. f£. in (8)). depends also on M since the supernova mechanism is expected to be sensitive to the presupernova mass.," It is quite probable that the function $f$ in $\,$ \ref{EMcor}) ) depends also on $\cal M$ since the supernova mechanism is expected to be sensitive to the presupernova mass."
 For us only the existence of some correlation is important. which in combination with (1)) (3)) allows to determine. the distance independently.," For us only the existence of some correlation is important which in combination with $\,$ \ref{Evtu}) \ref{Rvtu}) ) allows to determine the distance independently."
 ‘To demonstrate how such a method can work we make the simplest assumption that ZZ is proportional to Ni)., To demonstrate how such a method can work we make the simplest assumption that $E$ is proportional to $E({\mathrm{np}}\rightarrow{\mathrm{Ni}})$ .
 Phen one can write: where. as usual. £ is in 107erg. Mio in Ae and D in Alpe.," Then one can write: where, as usual, $E$ is in $10^{51}\,{\mathrm{erg}}$, ${\cal M}_{\mathrm{Ni0}}$ in ${\cal M}_{\textstyle\odot}$ and $D$ in Mpc."
 This equation implies that the function. f. introduced. in I[q.(8)). reads as fGr)=16.66. where £ is an adjustable parameter. which can be either less or arger than 1.," This equation implies that the function $f$, introduced in $\,$ \ref{EMcor}) ), reads as $f(x)=16.6\,\xi\, x$ where $\xi$ is an adjustable parameter which can be either less or larger than 1."
 H£ there is a noticeable contribution to Mxjy rom the explosive carbon-oxvecn burning then €«I: ifa noticeable contribution to the explosion energy comes from other source rather than the neutron-proton recombination hen £71., If there is a noticeable contribution to ${\cal M}_{Ni0}$ from the explosive carbon-oxygen burning then $\xi < 1$; if a noticeable contribution to the explosion energy comes from other source rather than the neutron-proton recombination then $\xi > 1$.
 Inserting £ from (10)) and. Ady from (4)) into (12) and solving for D. we obtain: where D is in Mpe. Af in days. ancl μι in 1000kinst," Inserting $E$ from $\,$ \ref{Ef}) ) and $M_V$ from $\,$ \ref{MVAD}) ) into $\,$ \ref{Evtu}) ) and solving for $D$, we obtain: where $D$ is in Mpc, $\Delta t$ in days, and $u_{\mathrm{ph}}$ in $1000\,{\mathrm{km}}\,{\mathrm{s}}^{-1}$."
 We will refer to distances derived from (11)) as plateau- distances. Dyο. hereafter.," We will refer to distances derived from $\,$ \ref{DMNi}) ) as `plateau-tail distances', $D_{\mathrm{P-T}}$, hereafter."
 The results are given in ‘Table 3 for nine supernovae selected (rom Table 2.," The results are given in $\,$ 3 for nine supernovae selected from $\,$ 2."
 We did not include SNe 1992am and 1999cr in our analysis because their last available observations may not vet rellect the radioactive tail phase., We did not include SNe 1992am and 1999cr in our analysis because their last available observations may not yet reflect the radioactive tail phase.
 Specifically. there are only two observations of SN1992am at the post-plateau phase of the light curve.," Specifically, there are only two observations of $\,$ 1992am at the post-plateau phase of the light curve."
 Since the observations are separated by a short time interval of 3 days. it is dillicult to derive the inclination of. the xlometric light curve with a required accuracy to be shure hat 1992am is already. in the racioactive-tail phase.," Since the observations are separated by a short time interval of 3 days, it is difficult to derive the inclination of the bolometric light curve with a required accuracy to be shure that $\,$ 1992am is already in the radioactive-tail phase."
 Aloreover. one has to remember that in addition to the Co-cecay the tail luminosity can also be contributed. by he ejecta-wind interaction (see Chugai 1991 and references herein).," Moreover, one has to remember that in addition to the Co-decay the tail luminosity can also be contributed by the ejecta-wind interaction (see Chugai 1991 and references therein)."
 1992am is suspicious in this respect. because its presupernova radius seems to be larger than T; CIable2).," $\,$ 1992am is suspicious in this respect because its presupernova radius seems to be larger than $R_{\textstyle\odot}$ $\,$ 2)."
 Hence. the ;fyi;u- values for these SNe in Table2 could be actually upper limits.," Hence, the ${\cal M}_{\mathrm{Ni0}}$ -values for these SNe in $\,$ 2 could be actually upper limits."
" The different columns. of ‘Table 3 give the following quantities: (2) the distance. Dpm. from. (11)) setting £=1: (3) the corresponding absolute V-magnitude of the mid-point of the plateau AA: (4)(7) the quantities ££. M. HI. and κι as in Table2. but now using the distance D,p as in column (1): the columns (8).(10) are explained above."," The different columns of $\,$ 3 give the following quantities: (2) the distance $D_{\mathrm{P-T}}$ from $\,$ \ref{DMNi}) ) setting $\xi=1$; (3) the corresponding absolute $V$ -magnitude of the mid-point of the plateau $M_V$ ; (4)–(7) the quantities $E$, $\cal M$, $R$ , and ${\cal M}_{\mathrm{Ni0}}$ as in $\,$ 2, but now using the distance $D_{\mathrm{P-T}}$ as in column (1); the columns (8)–(10) are explained above."
 The values of ££. M. Ro and. Mio For the £-values dillerent. from 1: can be found. using the following scaling relations which result from (52). (7)). and (11)): Fora fixed Q. the dependence of the distance Dim. defined by (113). on extinction. sly proves to be very. weak: an error in zl of ΕΙ μιας changes Djy by only E124.," The values of $E$, $\cal M$ , $R$, and ${\cal M}_{\mathrm{Ni0}}$ for the $\xi$ -values different from 1 can be found using the following scaling relations which result from $\,$ \ref{EMRdist}) ), \ref{MNi}) ), and \ref{DMNi}) ): For a fixed $Q$, the dependence of the distance $D_{\mathrm{P-T}}$ , defined by $\,$ \ref{DMNi}) ), on extinction $A_V$ proves to be very weak: an error in $A_V$ of $\pm 1\,$ mag changes $D_{\mathrm{P-T}}$ by only $\pm 12\%$ ."
" llowever. if the tail luminositw £4, is derived. from. the V measurements (just the case of Παινs £j-values we use here) then the le£j. and. consequently IgQ. scale as Ον and leDpop. derived. from. (110). actually varies wilh ely in a standard wav. as 0.2.21."," However, if the tail luminosity $F_{41}$ is derived from the $V$ measurements (just the case of Hamuy's $F_{41}$ -values we use here) then the $\lg\, F_{41}$, and consequently $\lg\, Q$, scale as $0.4\, A_V$ and $\lg\, D_{\mathrm{P-T}}$, derived from $\,$ \ref{DMNi}) ), actually varies with $A_V$ in a standard way, as $-0.2\, A_V$."
 Lf the tail luminosity were clerivedl from. infra-reck measurements then the resulting Dpcp distances would be larecly independent of extinction., If the tail luminosity were derived from infra-red measurements then the resulting $D_{\mathrm{P-T}}$ distances would be largely independent of extinction.
" Note also rather weak dependence on £Q: Dyvo(£Q)""37", Note also rather weak dependence on $\xi Q$: $D_{\mathrm{P-T}}\sim (\xi Q)^{-0.374}$.
 or instance. the decrease in £Q by a [actor of 2 results in an of Dyp by only.," For instance, the decrease in $\xi Q$ by a factor of 2 results in an of $D_{\mathrm{P-T}}$ by only."
 The rancom errors tvpicallvy of 410% for the 9/ and tn Values assumed in Table 1 result in the uncertainty actor οἱ zz1.2 for Dpp and =1.5 for Viyis(D7) given in Table 3., The random errors typically of $\pm 10\% $ for the $\delta t$ and $u_{\mathrm {ph}}$ values assumed in Table 1 result in the uncertainty factor of $\approx 1.2$ for $D_{\mathrm{P-T}}$ and $\approx 1.5$ for ${\cal M}_{\mathrm{Ni0}}(\sim D^2)$ given in Table 3.
 However. one has to keep in mind two main sources of systematic errors: (7) probable deviation of the 1eoretical models (which Eqs. 1-," However, one has to keep in mind two main sources of systematic errors: $(i)$ probable deviation of the theoretical models (which Eqs. \ref{Evtu}-"
3 are based on) from rea UuNe. and (77) the presentation of the £6Mio correlation in the form of the straight proportionality (eq. 10)).," \ref{Rvtu} are based on) from real SNe, and $(ii)$ the presentation of the $E - {\cal M}_{\mathrm{Ni0}}$ correlation in the form of the straight proportionality (Eq. \ref{Ef}) )."
 Both Ίο twpes of systematic errors are dillicult to estimate a esent., Both the types of systematic errors are difficult to estimate at present.
 Although the SN moclels caleulated in LNS3 anc LNS5 rest upon a very simplified: presupernova structure. wey consistently take into account the ionization anc recombination of hydrogen and helium. thereby remaining still useful.," Although the SN models calculated in LN83 and LN85 rest upon a very simplified presupernova structure, they consistently take into account the ionization and recombination of hydrogen and helium thereby remaining still useful."
 When a new grid of the SN. models. basec on modern evolutionary presupernova structure. is ereatec the svstematic error. (7) certainly will be. reduced.," When a new grid of the SN models, based on modern evolutionary presupernova structure, is created the systematic error $(i)$ certainly will be reduced."
 The reduction.of thesvstematic error (//) requires a more profoundknowledge of the SN mechanism., The reductionof thesystematic error $(ii)$ requires a more profoundknowledge of the SN mechanism.
 IEimpiricallv. thisproblem. can be solved. byadjusting the factor £ for each individual SN.," Empirically, thisproblem can be solved byadjusting the factor $\xi$ for each individual SN."
 It is necessary. however. to collect a much more rich statistics (at. least by a factor of 3) than that available nowadays (only 9 SNe in Table 3).," It is necessary, however, to collect a much more rich statistics (at least by a factor of 3) than that available nowadays (only 9 SNe in Table 3)."
The fact that ΟΙ) line emission luminosity is positively correlated with 12yim rest-frame luminosity implies that both quantities trace accretion rate.,"The fact that [OII] line emission luminosity is positively correlated with $12\,\rm \mu m$ rest-frame luminosity implies that both quantities trace accretion rate."
 As Loop is directly linked to the radiative photoionizing power. which is itself a fraction of the bolometric luminosity. Liu. Lou is therefore also a tracer of accretion rate.," As $L_{\rm [OII]}$ is directly linked to the radiative photoionizing power, which is itself a fraction of the bolometric luminosity, $L_{\rm bol}$, $L_{\rm [OII]}$ is therefore also a tracer of accretion rate."
" The relation between £p and. Loisixigz has similar implications as the relation between £L42, and Liqazigz-", The relation between $L_{\rm [OII]}$ and $L_{\nu \rm 151MHz}$ has similar implications as the relation between $\nu L_{\nu \rm 12\mu m}$ and $L_{\nu \rm 151MHz}$.
" In fact we expect that with the inclusion of weaker racio sources. the relation between Lyisisi, and Loop would become less tight and. probably convert into an envelope. in a similar wav to what happens with the radio-Ioud objects [or the ΗλLeian relation."," In fact we expect that with the inclusion of weaker radio sources, the relation between $L_{\nu \rm
 151MHz}$ and $L_{\rm [OII]}$ would become less tight and probably convert into an envelope, in a similar way to what happens with the radio-loud objects for the $L_{\nu\rm 151MHz}$ $\nu L_{\nu \rm 12\mu m}$ relation."
 Some studies of weaker radio sources (e.g. Best ct al., Some studies of weaker radio sources (e.g. Best et al.
 2005b: Shabala ct al., 2005b; Shabala et al.
 2008) indeed suggest that there is a trend for racio-quict sources to scatter beyond the tight correlation observed for our sample of racio loud sources., 2008) indeed suggest that there is a trend for radio-quiet sources to scatter beyond the tight correlation observed for our sample of radio loud sources.
 This could also be related to a cilferent accretion mechanism for the lower power radio sources (e.g. Llarcleastle et al., This could also be related to a different accretion mechanism for the lower power radio sources (e.g. Hardcastle et al.
 2006)., 2006).
 Some attention should be drawn to the fact that radio unminosity is not a perfect tracer of the kinetic jet. power as it also depends on environmental ellects irrespective of he jet. power., Some attention should be drawn to the fact that radio luminosity is not a perfect tracer of the kinetic jet power as it also depends on environmental effects irrespective of the jet power.
 For instance. the characteristics of the jet environment may play a significant role in how ellicientlv he jet power gets converted into radio Luminosity.," For instance, the characteristics of the jet environment may play a significant role in how efficiently the jet power gets converted into radio luminosity."
 Especially in the richer environments inhabited by the strongest racio sources. a dense environment might be. responsible for »oosted radio Iuminosities at a given jet power (e.g. Barthel & Arnaud. 1996. Faleer et al 2010).," Especially in the richer environments inhabited by the strongest radio sources, a dense environment might be responsible for boosted radio luminosities at a given jet power (e.g. Barthel $\&$ Arnaud 1996, Falder et al 2010)."
 Moreover. the. low requency radio emission is radiated over scales that are orders of magnitude larger in extent than the torus and rence slower to react to any changes in the central emission han the cireumnuclear dust or the NLIt.," Moreover, the low frequency radio emission is radiated over scales that are orders of magnitude larger in extent than the torus and hence slower to react to any changes in the central emission than the circumnuclear dust or the NLR."
 Another caveat is that superimposed on the spectrum. at jim there is a silicate feature due to the Si-O streching mode of amorphous silicate erains of dust. (e.g. Elitzur 2008))., Another caveat is that superimposed on the spectrum at $\mu$ m there is a silicate feature due to the Si-O streching mode of amorphous silicate grains of dust (e.g. \citealt{2008NewAR..52..274E}) ).
" This broad feature is generally. present in absorption in radio galaxies and in emission in quasars. and the tail of the feature can alfect the continuum at 12 yam. In addition. due to the ellects of dust. extinction. for the same Ln; quasars can have up to twice as high values o eL,45,4, than radio galaxies (e.g. Martínez-Sansigreetal.2009:Nenkovaetal. 2008))."," This broad feature is generally present in absorption in radio galaxies and in emission in quasars, and the tail of the feature can affect the continuum at 12 $\mu$ m. In addition, due to the effects of dust extinction, for the same $L_{\rm
 bol}$ quasars can have up to twice as high values of $\nu L_{\nu 12
 \mu \rm m}$ than radio galaxies (e.g. \citealt{2009ApJ...706..184M,
 2008ApJ...685..160N}) )."
" These two ellects could moderately. bias the inferred. values of £i,4; by introducing a higher ollsct in ML lor quasars in relation to radio galaxies.", These two effects could moderately bias the inferred values of $L_{\rm bol}$ by introducing a higher offset in $\nu L_{\nu \rm 12\mu m}$ for quasars in relation to radio galaxies.
 This implies that if the racio galaxies have high extinctions. their Iuminosity at. 12imi is underestimated. and therefore Li is in [act higher.," This implies that if the radio galaxies have high extinctions, their luminosity at $12\,\mu \rm m$ is underestimated, and therefore $L_{\rm bol}$ is in fact higher."
 This would in turn bring the radio galaxies closer to the quasars. reducing the scatter of the data points on the right panel of Figure 4.. Haasetal.," This would in turn bring the radio galaxies closer to the quasars, reducing the scatter of the data points on the right panel of Figure \ref{fig:l151_l12}."
(2008). quantify how much extinction and the silicate feature can cause the luminosity of quasars and radio galaxies to deviate from each other for wavelengths up to 1μα.," \cite{2008ApJ...688..122H} quantify how much extinction and the silicate feature can cause the luminosity of quasars and radio galaxies to deviate from each other for wavelengths up to $10\,\mu \rm m$."
 Γον show that at these wavelengths radio galaxies can be on average 4 times less luminous than quasars due to extinction., They show that at these wavelengths radio galaxies can be on average 4 times less luminous than quasars due to extinction.
 Therefore. if the racio loud. galaxies in the sample suller high extinction (Ay~ 50). Lisa for the whole bottom envelope would shift upwards. resulting in jet cllicieney values of η=0.3 with f=M.," Therefore, if the radio loud galaxies in the sample suffer high extinction $\rm A_{V}\sim 50$ ), $L_{\rm bol}$ for the whole bottom envelope would shift upwards, resulting in jet efficiency values of $\eta\approx 0.3$ with $f=10$."
 Further work on this issue will be presented. in Fernandes et al. (, Further work on this issue will be presented in Fernandes et al. (
in prep.),in prep.)
 One other matter of caution is the possibility of nonthermal contamination of the mid-Ilt emission. due to synchrotron emission. [from the radio lobes or a coresjet component., One other matter of caution is the possibility of nonthermal contamination of the mid-IR emission due to synchrotron emission from the radio lobes or a core/jet component.
 Even though this is not a major concern for our sample as nearly all sources are Els and the non-thermal contamination is in general a negligible fraction. of the emitted Dux density at mid-LHIt frequencies. when Doppler-boosted or in the case of stecp-spectrum lobes Iving within the Spitzer beam. synchrotron emission from contaminant components can represent a small fraction of the thermal emission (e.g. Shietal.2005... Clearyetal.2007.. Dickenοἱal.2008)).," Even though this is not a major concern for our sample as nearly all sources are FRIIs and the non-thermal contamination is in general a negligible fraction of the emitted flux density at mid-IR frequencies, when Doppler-boosted or in the case of steep-spectrum lobes lying within the Spitzer beam, synchrotron emission from contaminant components can represent a small fraction of the thermal emission (e.g. \citealt{2005ApJ...629...88S}, \citealt{2007ApJ...660..117C}, \citealt{2008ApJ...678..712D}) )."
 However. given the brightness and radio spectral indices of the sources in our sample this is à minimal elfect.," However, given the brightness and radio spectral indices of the sources in our sample this is a minimal effect."
 ]t is an open question whether there is also a radio quiet. envelope. and. a real gap of objects beyond: this region (to the left of region D in the plot)., It is an open question whether there is also a radio quiet envelope and a real gap of objects beyond this region (to the left of region B in the plot).
 This is Που to infer as the contribution [rom stars begins to contaminate the radio emission. at. such low racio Iuminosities., This is difficult to infer as the contribution from stars begins to contaminate the radio emission at such low radio luminosities.
 For instance. a typical powerful starburst with a star formation rate of massive stars (AlSAL.) of 250ML;/vr. equivalent to a total star formation rate of 1000ALY/vr (Condon1992). assuming a Salpeter initial mass function. is capable of producing radio luminosity densities of the order of ~5LOOWietseI (vertical dotted line in Figure 4)).," For instance, a typical powerful starburst with a star formation rate of massive stars $M\geq 5\rm \,M_{\sun}$ ) of $250\,\rm
M_{\sun}/yr$, equivalent to a total star formation rate of $~1000\,\rm
M_{\sun}/yr$ \citep{1992ARA&A..30..575C} assuming a Salpeter initial mass function, is capable of producing radio luminosity densities of the order of $\sim 5\times10^{23}\rm \,W\,Hz^{-1}\,sr^{-1}$ (vertical dotted line in Figure \ref{fig:l151_l12}) )."
 Moreover. the most. powerful starbursts observed. with a star formation rate of massive stars of the order of 1000δες/vr equivalent to a total star formation rate of 4000XE; vr. produce star-related. racio luminosity densities of 21075NWHz.Fur+. of the sume order as luminosities produced. by weaker radio galaxies (vertical dot-dashed line in Figure 4)).," Moreover, the most powerful starbursts observed, with a star formation rate of massive stars of the order of $1000\,\rm M_{\sun}/yr$ equivalent to a total star formation rate of $~4000\,\rm M_{\sun}/yr$ , produce star-related radio luminosity densities of $\sim 2\times10^{24}\rm
\,W\,Hz^{-1}\,sr^{-1}$, of the same order as luminosities produced by weaker radio galaxies (vertical dot-dashed line in Figure \ref{fig:l151_l12}) )."
 Deep high-resolution multi-frequency radio observations are required. to. cleanly distinguish XCGN from purely star-forming galaxies., Deep high-resolution multi-frequency radio observations are required to cleanly distinguish AGN from purely star-forming galaxies.
" We have studied the relations between £,íj4s1s1Bz- Lois and Low [or à sample of 27 racdio-selected galaxies (at z~ 1). independent of evolutionary. elfects due to redshift. and conclude that these are positively correlated. -"," We have studied the relations between $L_{\nu \rm 151MHz}$, $\nu
L_{\nu \rm 12\mu m}$ and $L_{\rm [OII]}$ for a sample of 27 radio-selected galaxies (at $z\sim 1$ ), independent of evolutionary effects due to redshift, and conclude that these are positively correlated. -"
 A positive correlation between Zíisixigs and Lou confirms the previously known relation for larger samples. supporting the idea that a link exists between the origin of the radio jets and the source of the narrow lines. -," A positive correlation between $L_{\nu \rm 151MHz}$ and $L_{\rm
 [OII]}$ confirms the previously known relation for larger samples, supporting the idea that a link exists between the origin of the radio jets and the source of the narrow lines. -"
" A positive correlation. between £&L,ijsja, and Leow suggests that there is a conmon emission source that excites the eas clouds in the NLR. and the cireumnuclear dust."," A positive correlation between $\nu L_{\nu \rm 12\mu m}$ and $L_{\rm
 [OII]}$ suggests that there is a common emission source that excites the gas clouds in the NLR and the circumnuclear dust."
 Fhis is consistent with accretion onto the central black hole being responsible for both forms of excitation. -, This is consistent with accretion onto the central black hole being responsible for both forms of excitation. -
" A positive correlation between £,421s18; and τομ indicates that racio loud AGN have a high mid-LHi emission."," A positive correlation between $L_{\nu \rm 151MHz}$ and $\nu L_{\nu
 \rm 12\mu m}$ indicates that radio loud AGN have a high mid-IR emission."
 Mid-LH. emission in AGNs have a thermal component due to dust that absorbs radiation from the accretion disc and re-racliates ib at these wavelengths., Mid-IR emission in AGNs have a thermal component due to dust that absorbs radiation from the accretion disc and re-radiates it at these wavelengths.
 Assuming that the non-thermal contamination is not relevant in our sample (see discussion in Section 4.4). this correlation translates into a relationship between jet power and accretion rate. which implies a common mechanism linking these two physical properties (e.g. Rawlings&Saunders 1991)).," Assuming that the non-thermal contamination is not relevant in our sample (see discussion in Section 4.4), this correlation translates into a relationship between jet power and accretion rate, which implies a common mechanism linking these two physical properties (e.g. \citealt{1991Natur.349..138R}) )."
" In addition. by adding a sample of bright.optically selected quasars we populated the &L,iasya v8 Letsisthy plot and found that the objects span a diagonal region. parallel to the correlation found. for the RCs."," In addition, by adding a sample of brightoptically selected quasars we populated the $\nu L_{\nu \rm 12\mu m}$ vs $L_{\nu \rm 151MHz}$ plot and found that the objects span a diagonal region parallel to the correlation found for the RGs."
 Thus. although the," Thus, although the"
Tu their analysis. Bethe Brown use »=1.5.,"In their analysis, Bethe Brown use $n=1.5$."
" Walt of all stars are taken to be close binary svstenmis with separations. n he range 0.011ce ""ecu."," Half of all stars are taken to be close binary systems with separations, $a$, in the range $0.04-4\times10^{13}$ cm."
 The distribution∙∙∙ of. binaryaV. separations within. this10 pauge Is taken to he Hat Ina., The distribution of binary separations within this range is taken to be flat in $\ln a$.
" The distribution of Duas ratios, q. 1 binaries withn nasse prunedes TS uncertain. especially at small Mass ratios. aud we here follow Bethe Brown by taking if to be flat ing."," The distribution of mass ratios, $q$, in binaries with massive primaries is uncertain, especially at small mass ratios, and we here follow Bethe Brown by taking it to be flat in $q$."
 All these assmuptions.& as well as the details of the evolution scenarios. iutroduce some amount of uncertainty. but the good agreement between recent analytic and numerical work sugeests that the formation rates we quote below can be trusted to a factor few.," All these assumptions, as well as the details of the evolution scenarios, introduce some amount of uncertainty, but the good agreement between recent analytic and numerical work suggests that the formation rates we quote below can be trusted to a factor few."
 The results of the discussion on birth rates are sunuuarizediu table L., The results of the discussion on birth rates are summarized in table 1.
 Iu population. svutliesis. . Bethe Brown (19958).] the rate ot AUN ofbinaries cones out to he the107 per formationyear in the Galaxy. or 10 GEM (Galactic per ," In the population synthesis of Bethe Brown (1998), the formation rate of NS-NS binaries comes out to be $10^{-5}$ per year in the Galaxy, or 10 GEM (Galactic Events per Megayear)."
This rate is considerably lower than Events ↓∙Megayear]. with merece (1998). but in ogood aerecmeno the estimated ∙↖↰ from5 the observed ucutron star ⋅⋅ (Phinney rate1991. Van den Heuvel Loruner 1996).," This rate is considerably lower than estimates from population synthesis calculations prior to Bethe Brown (1998) and Portegies Zwart Yungelson (1998), but in good agreement with the estimated merger rate from the observed neutron star binaries (Phinney 1991, Van den Heuvel Lorimer 1996)."
" The binaries:discrepancy between the older theoretical estimates aud newer oues Is mu a ; ;actors: SOM"" CATACHi studies7 dkud uot include: kickfo velocities.Tow aud none included the destruction of; tert MND. m""ho.1 B DMiN 'Ocess ds"," The discrepancy between the older theoretical estimates and newer ones is due to a few factors: some earlier studies did not include kick velocities, and none included the destruction of neutron stars by hypercritical accretion."
 roni shaort:M ⋯↸∖∖↕∖⋠⋯⋯∏⋟↨⋠⋯↕↨⊔↸difference abetwee e ∖⊔↕⋟↕↖Bethe Brown analysis previous Werk: they that when a neutron spiralsaud iuto a red 1 arguedacerctes matter ata very starhigh rate of up to giat.M.//yr.," This last process is an important difference between the Bethe Brown analysis and previous work: they argued that when a neutron star spirals into a red giant, it accretes matter at a very high rate of up to /yr."
 Then photous are trapped in the flow and the flow cools by neutrine clnission. heuce the Eddington limit does not apply.," Then photons are trapped in the flow and the flow cools by neutrino emission, hence the Eddington limit does not apply."
 As a result. the neutron star accretes such a large amount of uass that it exceeds the maxima mass and turus into a low-ass M.) black hole.," As a result, the neutron star accretes such a large amount of mass that it exceeds the maximum mass and turns into a low-mass ) black hole."
" Since the spiralin is an essential part of the usual scenario for forming binary the fcrination rate is ckvu greatly,"," Since the spiral-in is an essential part of the usual scenario for forming binary neutron stars, the formation rate is cut down greatly."
" Ouly hose ieutronstars. iu which stars cutinitially differ by iSS lian AM binariesquaes does a binaryle neutro pstar form,", Only those binaries in which the stars initially differ by less than in mass does a binary neutron star form.
 Is⋅ 0150 in those cases the tine scales of Thisthe wo stars are so close that the initial evolutionarysecoucdary becomes a ejut and eugults the primary when the primary has not vot exploded as a supernova., This is because in those cases the evolutionary time scales of the two stars are so close that the initial secondary becomes a giant and engulfs the primary when the primary has not yet exploded as a supernova.
" Driefly. a close binary of two ilii stars exists, and then both explode as supernovac. disrupting about half the svstems."," Briefly, a close binary of two helium stars exists, and then both explode as supernovae, disrupting about half the systems."
 An inunuediate consequence of this scenario is that the orlation rate for binaries cousisting of a neutron star and a low-mass black hole is an order of magnitude more. 100 GEM. because this is the fate of all the svstems which iu he absence of lawpercritical accretion would have become oinary ueutron stars.," An immediate consequence of this scenario is that the formation rate for binaries consisting of a neutron star and a low-mass black hole is an order of magnitude more, 100 GEM, because this is the fate of all the systems which in the absence of hypercritical accretion would have become binary neutron stars."
 The stun of the formation rates of NS-NS and NS-DII binaries iu the Bethe-Brown scenario is herefore about equal to the NS-NS formation rate in older studies. providing all other assumptions are the same.," The sum of the formation rates of NS-NS and NS-BH binaries in the Bethe-Brown scenario is therefore about equal to the NS-NS formation rate in older studies, providing all other assumptions are the same."
 The chief reason why such DIT-NS binaries are not seeu is the sale as why we eenerallv see only one neutron star of the pair ina NS-NS binary: the first-born neutrou star gets reeveled due to the accretion flow from its companion., The chief reason why such BH-NS binaries are not seen is the same as why we generally see only one neutron star of the pair in a NS-NS binary: the first-born neutron star gets recycled due to the accretion flow from its companion.
 If its maguctic field is reduced by a factor 100. as we observe. its visible lifetime is lenethened by that same factor 100. since if scales as the inverse of the field streneth.," If its magnetic field is reduced by a factor 100, as we observe, its visible lifetime is lengthened by that same factor 100, since it scales as the inverse of the field strength."
 The secoud-born pulsar is not recycled. hence ouly visible for a few uuillion vears aud LOO times less likely to be seen.," The second-born pulsar is not recycled, hence only visible for a few million years and 100 times less likely to be seen."
 Ii DIL-NS biuaries. the neutron star is the secoud-horn compact object. hence wurecveled aud short-lived.," In BH-NS binaries, the neutron star is the second-born compact object, hence unrecycled and short-lived."
 With a ten times higher birth rate but LOO times shorter visible life. one expects to see ten times fewer of them. aud this the fact that none have vet been seen is understandable.," With a ten times higher birth rate but 100 times shorter visible life, one expects to see ten times fewer of them, and thus the fact that none have yet been seen is understandable."
 The rate at which the various progenitors involving WR stars discussed above (Sect. 2.3)), The rate at which the various progenitors involving WR stars discussed above (Sect. \ref{src.WR}) )
 are formed can be calculated casily from the Bethe Brown (1995. 1999) model in the same way they calculated the merger rates.," are formed can be calculated easily from the Bethe Brown (1998, 1999) model in the same way they calculated the merger rates."
 Ποια stars (WR stars) with a low-mass black hole (ΟΠ) iu them are formed from alinost the same binarics that male LDIT plus NS systems: the ouly difference is that they come from inaller imitial orbits. in which the spiral-in does not succeed in ejectiug the companion envelope and thus goes ou to the center.," Helium stars (WR stars) with a low-mass black hole (LBH) in them are formed from almost the same binaries that make LBH plus NS systems; the only difference is that they come from smaller initial orbits, in which the spiral-in does not succeed in ejecting the companion envelope and thus goes on to the center."
 From the total available Pinazies ue unl nrade when LUNi (where ius ↕↴∖↴↑↕∐∖↴∖↴↸∖↻⋜∐⋅⋜↧↑↕∪∐∐⊔∐∐↑↴∖↴∪↕↓∩⊽⋟∩⊳⋯⋝∙↕∐↴∖↴↕≼," From the total available range in orbital separations, $0.04<a_{13}<4$, LBH-NS binaries are only made when $0.5<a_{13}<1.9$ (where $a_{13}$ is the separation in units of $10^{13}$ cm)."
∐∖↑↕⋜↧↑↥⋅⋜↕∐∶↴∙⊾↸∖∙ n for 0.0L<ayy 0.5. the EDIT coalesces with the He core.," Inside that range, for $0.04<a_{13}<0.5$ , the LBH coalesces with the He core."
 Teuce. using a separation distribution flat in lue. coalescences are more colon than LBIT-NS binaries by a factor In(0.5/0.0D/In(1.9/0.5)=1.9.," Hence, using a separation distribution flat in $\ln a$, coalescences are more common than LBH-NS binaries by a factor $\ln(0.5/0.04)/\ln(1.9/0.5)=1.9$."
 In Bethe Brown (1998)ot the Πο starste compact: object binarvary was disrupteddi DUX of the time in the last explosion. which we do not ↕⋜↧↖↽↸∖∐↸∖," In Bethe Brown (1998) the He star compact object binary was disrupted $\sim 50\%$ of the time in the last explosion, which we do not have here."
↥⋅↸∖∙↽∕∏⋯↴∖↴∙↑↕∐∖↥⋅⋜↧↑↸∖∪↕∫⇀↕≧∐∙∐↸∖≓↴∖↴↑⋜∐⋅↕⊔↸∖↥⋅∶↴∙↸∖↥⋅↴∖↴↕↴∖↴⋅≩∙≺∖ : : ⋡⋅∙∖ imes the formation rate of LDILNS binaries which merece. or R=3.8<10‘yr1 in the Galaxy. (GEM.," Thus, the rate of LBH, He-star mergers is $3.8$ times the formation rate of LBH-NS binaries which merge, or $R=3.8\times 10^{-4}{\rm
yr}^{-1}$ in the Galaxy, GEM."
 Bethe Brown (1999) found that single stars need to lave a ZAMS ass of at least to directly forme a quassive BIT. based on evolution calculations by Woosley. Langer aud Weaver (1993).," Bethe Brown (1999) found that single stars need to have a ZAMS mass of at least to directly form a massive BH, based on evolution calculations by Woosley, Langer and Weaver (1993)."
 It is row understood that thei Ibe-star mass loss rates were a factor of at least 2 too high., It is now understood that their He-star mass loss rates were a factor of at least 2 too high.
 Calculations with lower uass loss rates carried out by Wellsteiu Lauger (1999) sive somewhat higher Tlo-star CO core masses., Calculations with lower mass loss rates carried out by Wellstein Langer (1999) give somewhat higher He-star CO core masses.
" The ≯↿∐⋅↑∐↸∖↥⋅↸∖↖⇁∪↕∏⊓∪∐∪↕≯↑↕∐∖≼⊲↻↸⊳∪↥⋅↸∖∐⋜↧↴∖↴∐∪↑↴⋝↸∖↸∖∐↸⊳⋜↧↕↸⊳∏↕⋜↧↑↸∖≼↧ vet. but may lower somewhat the Bethe Brown mass iuit for high-mass"" black-hole formation."," The further evolution of the CO core has not been calculated yet, but may lower somewhat the Bethe Brown mass limit for high-mass black-hole formation."
 StavingmE with the rranege for this route. the rate is 2.5&10tyr+ in the Galaxy.," Staying with the range for this route, the rate is $2.5\times10^{-4}{\rm yr}^{-1}$ in the Galaxy."
 Iu addition. we cousider the formation of massive black holes of about tthat are seen i soft X-ray transicuts like 00.," In addition, we consider the formation of massive black holes of about that are seen in soft X-ray transients like $-$ 00."
 Their evolution was disenssed bv. Brown. Lee. Bethe (1999). who found a formation rate of 9.10Ove Fin the Galaxy.," Their evolution was discussed by Brown, Lee, Bethe (1999), who found a formation rate of $9\times10^{-5}{\rm yr}^{-1}$ in the Galaxy."
 The combination of masses thatwill be well determined by LIGO is the chirp mass, The combination of masses thatwill be well determined by LIGO is the chirp mass
unity coherence.,unity coherence.
 We calculated. the coherence function. of (νο X-1 data with correction for counting noise. following the recipe presented in Vaughan&Nowak(1007).," We calculated the coherence function of Cyg X-1 data with correction for counting noise, following the recipe presented in \citet{VN97}."
. The results are shown in Fig. S..," The results are shown in Fig. \ref{fig_coh},"
 which demonstrate a remarkably high coherence (close to unity) over a wide frequency. range and consistent with previous coherence study of (νο X-1 (e.g.g.mVaughan&Nowak1907:Cuietal.0r 1999).," which demonstrate a remarkably high coherence (close to unity) over a wide frequency range and consistent with previous coherence study of Cyg X-1 \citep[e.g.][]{VN97,Cui97,Now99}."
. Therefore. we can sav that below 10 Liz. the [lux in each energy band can be regarded. as originating from one single coherent component. whose intrinsic phase delay is indicated hy the lag spectrum.," Therefore, we can say that below $\sim$ 10 Hz, the flux in each energy band can be regarded as originating from one single coherent component, whose intrinsic phase delay is indicated by the lag spectrum."
 The coherence becomes slightly lower at higher frequencies. which may indicate the presence of incoherent components.," The coherence becomes slightly lower at higher frequencies, which may indicate the presence of incoherent components."
 We do not attempt to acd them into the simulation because 1t is a laborious and mocel-dependent process ancl bevond the scope of this work., We do not attempt to add them into the simulation because it is a laborious and model-dependent process and beyond the scope of this work.
 ln order to reconstruct the time series from the PDS and time lag spectra. a prior phase distribution has to be assumed. since the PDS does not contain phase information.," In order to reconstruct the time series from the PDS and time lag spectra, a prior phase distribution has to be assumed, since the PDS does not contain phase information."
 We first analyzed) the real cata in order to derive a reasonable phase distribution., We first analyzed the real data in order to derive a reasonable phase distribution.
 We split. the 0.015625-s xnned light curve into GOL segments. cach with a length of 1024 points (16 seconds).," We split the 0.015625-s binned light curve into 694 segments, each with a length of 1024 points (16 seconds)."
 For each segment. we produced a Fourier transform. leading to 694 values of the phase angle or each frequency between 0.0625 Lz and 32 Hz.," For each segment, we produced a Fourier transform, leading to 694 values of the phase angle for each frequency between 0.0625 Hz and 32 Hz."
 Obviously. he phases between separate segments are comparable only alter considering the additional phase shift caused by the imce-delay between their start time.," Obviously, the phases between separate segments are comparable only after considering the additional phase shift caused by the time-delay between their start time."
" H£42;; is the phase angle al [frequency fj of the ith segment. fo.) and fo. are the start imes of the ith segment and the Ist segment respectively. he ""absolute phase at this frequency for the zth segment can be calculated as In Fig. 9.."," If $\varphi_{j,i}$ is the phase angle at frequency $f_{j}$ of the th segment, $t_{0,i}$ and $t_{0,1}$ are the start times of the th segment and the 1st segment respectively, the “absolute” phase at this frequency for the th segment can be calculated as In Fig. \ref{fig_phas},"
 we plot the phase at dillerent. frequencies [or the first. segment. (panel a). the phase at a certain frequeney for cdillerent segments (panel 6) and its histogram of occurrence. (panel d).," we plot the phase at different frequencies for the first segment (panel ), the phase at a certain frequency for different segments (panel ) and its histogram of occurrence (panel )."
 Moreover. we studied the auto correlation function of the phase at different frequencies (shown in panel e)," Moreover, we studied the auto correlation function of the phase at different frequencies (shown in panel )."
 Al these results clearly show that the phase follows a uniform: distribution between —x and παπα. the phases at dilferent frequencies are. random and independent., All these results clearly show that the phase follows a uniform distribution between $-\pi$ and $\pi$ £¬and the phases at different frequencies are random and independent.
 Therefore. in our synthesis. algorithm we generate uniformly. distributed random: numbers in the interval (|π.π] às phase angles for the Fourier transform.," Therefore, in our synthesis algorithm we generate uniformly distributed random numbers in the interval $(-\pi,\pi]$ as phase angles for the Fourier transform."
 Laving obtained the energv-resolved PDS (with Poisson noise subtracted) and the time lag spectra for our eight energy bins. and the average energy spectrum. we followed he following procedure to generate a synthetic light curve:," Having obtained the energy-resolved PDS (with Poisson noise subtracted) and the time lag spectra for our eight energy bins, and the average energy spectrum, we followed the following procedure to generate a synthetic light curve:"
To explore the role of the parameters in the Meudon PDR code (Le Petit 2006) we computed several two-sided illuminated PDR models. as follows: Each model was computed assuming a cosmic ray ionisation rate €=3x107 s! (Dalgarno 2006).,"To explore the role of the parameters in the Meudon PDR code (Le Petit 2006) we computed several two-sided illuminated PDR models, as follows: Each model was computed assuming a cosmic ray ionisation rate $\zeta = 3
\times 10^{-17}$ $^{-1}$ (Dalgarno 2006)."
 The results on the column densities and the column density ratios of HCO™. HCN. HNC. CN. and CH are given in Fig.," The results on the column densities and the column density ratios of $^{+}$, HCN, HNC, CN, and $_2$ H are given in Fig."
 6 which also displays. for comparison. the ranges of observed values.," \ref{FigPDR} which also displays, for comparison, the ranges of observed values."
 This figure shows that the constraints provided by the bearing molecules and by ccannot be reconciled in the framework of this nodel., This figure shows that the constraints provided by the CN-bearing molecules and by cannot be reconciled in the framework of this model.
 On the one hand. both the range of column densities and column density ratios of CN. HCN. HNC. and CH can be explained by PDR models for Ny>1.8x107! em and a gas density larger than 300 em™.," On the one hand, both the range of column densities and column density ratios of CN, HCN, HNC, and $_2$ H can be explained by PDR models for $N_{\rm
 H} > 1.8 \times 10^{21}$ $^{-2}$ and a gas density larger than 300 $^{-3}$."
 But on the other hand. for the same range of density. not only the predicted correlation between the columr densities of CN and HNC ts clearly non-linear and mismatch the observed value by a factor larger than 10. but the columi densities of HCO™ are also underestimated by at least one order of magnitude.," But on the other hand, for the same range of density, not only the predicted correlation between the column densities of CN and HNC is clearly non-linear and mismatch the observed value by a factor larger than 10, but the column densities of $^{+}$ are also underestimated by at least one order of magnitude."
 As expected. if the mean interstellar UV radiation field acreases. the column densities of CN. HCN. HNC. and C:H decrease because the photodissociation is the main destructior process of all these molecules.," As expected, if the mean interstellar UV radiation field increases, the column densities of CN, HCN, HNC, and $_2$ H decrease because the photodissociation is the main destruction process of all these molecules."
 Oppositely. when y is multiplied by 3. the temperature at the edge of the PDR is twice larger anc the O + H charge exchange reaction (with an endothermicity AE/k of 227 K)1s enhanced.," Oppositely, when $\chi$ is multiplied by 3, the temperature at the edge of the PDR is twice larger and the O + $^{+}$ charge exchange reaction (with an endothermicity $\Delta E/k$ of 227 K) is enhanced."
 Since this reaction is at the root of the formation of HCO™ in low density UV-dominated gas phase chemistry (Godard 2009) and since the main destruction mechanism of HCO™ ts its dissociative recombination (whose rate is independent of y) the column density of HCO™ increases (see Fig. 6)).," Since this reaction is at the root of the formation of $^{+}$ in low density UV-dominated gas phase chemistry (Godard 2009) and since the main destruction mechanism of $^{+}$ is its dissociative recombination (whose rate is independent of $\chi$ ), the column density of $^{+}$ increases (see Fig. \ref{FigPDR}) )."
 All those behaviours holds for the ranges of density and radiative conditions explored in Fig. 6.., All those behaviours holds for the ranges of density and radiative conditions explored in Fig. \ref{FigPDR}.
 The dependence of the results on the cosmic ray tonisation rate z Is slightly more complex., The dependence of the results on the cosmic ray ionisation rate $\zeta$ is slightly more complex.
 When Z is multiplied by 10. the abundances of H7 and Hi rise by one order ofmagnitude.," When $\zeta$ is multiplied by 10, the abundances of $^{+}$ and $_3$$^{+}$ rise by one order of."
 Thus. both the hydrogenation chains of nitrogen and oxygen are stimulated by the reactions and respectively. while the hydrogenation chain of carbon. initiated by the slow radiative association is independent of Z.," Thus, both the hydrogenation chains of nitrogen and oxygen are stimulated by the reactions and respectively, while the hydrogenation chain of carbon, initiated by the slow radiative association is independent of $\zeta$."
 Therefore when Z is multiplied by 10: Nevertheless. even at low density. the impact of the cosmic ray ionization rate is not sufficient enough to account for the range of column densities observed in Fig 6..," Therefore when $\zeta$ is multiplied by 10: Nevertheless, even at low density, the impact of the cosmic ray ionization rate is not sufficient enough to account for the range of column densities observed in Fig \ref{FigPDR}. ."
 As suggested by Godard (2009) and by the present observations. we explore the TDR models in the range of parameters: 1077.«a<107!? s7! and 30«ny<500 em for an ambient radiation field characterized by y=|.," As suggested by Godard (2009) and by the present observations, we explore the TDR models in the range of parameters: $10^{-12} < a < 10^{-10}$ $^{-1}$ and $30 < n_{\rm H} < 500$ $^{-2}$ for an ambient radiation field characterized by $\chi = 1$."
 Since the influence of this parameter on the results of the PDR model (see Fig. 6)), Since the influence of this parameter on the results of the PDR model (see Fig. \ref{FigPDR}) )
 seems to be small compared to the role of Ny and ng. We did not explore a broader range of values for y.," seems to be small compared to the role of $N_{\rm H}$ and $n_{\rm H}$, we did not explore a broader range of values for $\chi$."
 The shielding from the ISRF ts assumed uniform. Ay=0.5 anc the amount of gas sampled is fixed to Ny=1.8xI07! em.," The shielding from the ISRF is assumed uniform, $A_V = 0.5$ and the amount of gas sampled is fixed to $N_{\rm H} = 1.8 \times 10^{21}$ $^{-2}$ ."
 ote that. in the TDR model. Ay is the actual UV-shielding of the gas and is no longer identical to the total hydrogen columi density sampled by the line of sight (as it is the case in the PDR nodel).," Note that, in the TDR model, $A_V$ is the actual UV-shielding of the gas and is no longer identical to the total hydrogen column density sampled by the line of sight (as it is the case in the PDR model)."
 Fig., Fig.
 7 displays the comparison. between the observec nolecular column densities and the predictions of the TDR nodels., \ref{FigRadio} displays the comparison between the observed molecular column densities and the predictions of the TDR models.
 Since the results of the TDR model are simply proportional to Ny. the computec values for higher (or lower) values of Ny are easily inferred from the display.," Since the results of the TDR model are simply proportional to $N_{\rm H}$, the computed values for higher (or lower) values of $N_{\rm H}$ are easily inferred from the display."
 TDR models. without fine tuning of the parameters. are consistent with the data.," TDR models, without fine tuning of the parameters, are consistent with the data."
 Over a broad range of turbulent rates of strain 10707 sv! xa< 107! s! and for a gas density 30 em? <ny 200 em™. the absolute column densities and column density ratios of HCO. C:H. CN. HCN. and HNC are reproduced.," Over a broad range of turbulent rates of strain $10^{-12}$ $^{-1}$ $\leqslant a \leqslant$ $10^{-10}$ $^{-1}$ and for a gas density 30 $^{-3}$ $\leqslant n_{\rm H}
\leqslant$ 200 $^{-3}$, the absolute column densities and column density ratios of $^{+}$, $_2$ H, CN, HCN, and HNC are reproduced."
" The case n,=500 em™ is ruled out because the computed HCO™ column densities are too small compared to the observed values. even if the total hydrogen column density Ny or the averaged turbulent dissipative rate & are multiplied by a factor of 10."," The case $n_{\rm H} = 500$ $^{-3}$ is ruled out because the computed $^{+}$ column densities are too small compared to the observed values, even if the total hydrogen column density $N_{\rm H}$ or the averaged turbulent dissipative rate $\varepsilon$ are multiplied by a factor of 10."
 For the CN-bearing species. all deriving from during the dissipationstage. the agreement with the observations holds over a broader range of gas density : 30em «ny< 500 em™.," For the CN-bearing species, all deriving from $^+$ during the dissipationstage, the agreement with the observations holds over a broader range of gas density : 30$^{-3}$ $\leqslant n_{\rm H} \leqslant$ 500 $^{-3}$."
 A trend. that was already found in Godard (2009). is that the observedcolumn densities," A trend, that was already found in Godard (2009), is that the observedcolumn densities"
"dust would be evacuated from the bubble on timescales of order 104 yyears, much less than the bubble age.","dust would be evacuated from the bubble on timescales of order $10^4$ years, much less than the bubble age."
" In fact, gas-grain friction would evacuate dust from the bubble on shorter timescales than the sputtering timescale; the sputtering timescale is smaller only for very small grains with sizes of order 0.001jum."," In fact, gas-grain friction would evacuate dust from the bubble on shorter timescales than the sputtering timescale; the sputtering timescale is smaller only for very small grains with sizes of order $0.001\um$."
" So, both indicate a much shorter dwell time for dust than theprocesses approximate age of the bubble, although gas-grain friction is the primary mechanism of grain removal for grains of all sizes."," So, both processes indicate a much shorter dwell time for dust than the approximate age of the bubble, although gas-grain friction is the primary mechanism of dust-grain removal for grains of all sizes."
" One possible explanation for the presence of dust in this environment (that we will investigate in more detail in Section ??)) is that dust grains could be the product of evaporating, colder, more dense condensations, or *cloudlets', within the wind-blown bubble."," One possible explanation for the presence of dust in this environment (that we will investigate in more detail in Section \ref{proposedModel}) ) is that dust grains could be the product of evaporating, colder, more dense condensations, or `cloudlets', within the wind-blown bubble."
" Perhaps dusty cloudlets are advected into the WBB, and are then stripped away by the post-shock gas within the bubble."," Perhaps dusty cloudlets are advected into the WBB, and are then stripped away by the post-shock gas within the bubble."
" This process of cloudlet advection and destruction has, of course, been studied by researchers before albeit not including the effects of dusty cloudlets, to our knowledge."," This process of cloudlet advection and destruction has, of course, been studied by researchers before albeit not including the effects of dusty cloudlets, to our knowledge."
" Another possible source of dust replenishment might be debris disks of low-mass stars formed with the OSV star in N49, which could be ejecting dust alongparticles."," Another possible source of dust replenishment might be debris disks of low-mass stars formed along with the O5V star in N49, which could be ejecting dust particles."
" As dust emission seems to fit the observations, we continue to pursue the role of dust in cooling the bubble in the following sub-sections."," As dust emission seems to fit the observations, we continue to pursue the role of dust in cooling the bubble in the following sub-sections."
" We first show how the charge on dust varies within the bubble, and then what effect the dust cooling has on the bubble; we will then assemble these results into a model of N49."," We first show how the charge on dust varies within the bubble, and then what effect the dust cooling has on the bubble; we will then assemble these results into a model of N49."
 The impact of dust on the thermal balance of the dusty WBB is determined largely by the charge on the grains., The impact of dust on the thermal balance of the dusty WBB is determined largely by the charge on the grains.
" In Figures 7 and 8, the average graphite grain charges are presented: in Figure 7,, the average grain charge is computed over all grain sizes and over all radii (with no weighting to take into account the greater volume at larger radii, or the greater number of smaller-diameter dust particles)."," In Figures \ref{avgGraphiteCharge} and \ref{avgSmallGraphiteCharge}, the average graphite grain charges are presented: in Figure \ref{avgGraphiteCharge}, the average grain charge is computed over all grain sizes and over all radii (with no weighting to take into account the greater volume at larger radii, or the greater number of smaller-diameter dust particles)."
 Figure shows the average charge of grains with radii <0.01wm., Figure \ref{avgSmallGraphiteCharge} shows the average charge of grains with radii $\la 0.01\um$.
 We investigate these trends to better understand the role of dust in WBBs., We investigate these trends to better understand the role of dust in WBBs.
" There are two trends to note in 7 and 8: first, as the luminosity increases, the Figuresincreased UV flux ejects more photo-electrons from the grains, pushing the grains to more positive charges."," There are two trends to note in Figures \ref{avgGraphiteCharge} and \ref{avgSmallGraphiteCharge}: first, as the luminosity increases, the increased UV flux ejects more photo-electrons from the grains, pushing the grains to more positive charges."
" But, as the average ambient density decreases, the ambient electron density decreases, leading to fewer collisions with electrons, and resulting in more positively charged grains."," But, as the average ambient density decreases, the ambient electron density decreases, leading to fewer collisions with electrons, and resulting in more positively charged grains."
" Grain charge impacts both heating and cooling, which are important in our simulations: collisional heating of grains accounts for approximately of the grain heating, while radiative heating of grains represents the remaining of grain heating."," Grain charge impacts both heating and cooling, which are important in our simulations: collisional heating of grains accounts for approximately of the grain heating, while radiative heating of grains represents the remaining of grain heating."
" In Figures 7 and 8,, we consider only grains, but the average charge on silicate grains is very graphitesimilar to the graphite grains; the average silicate-grain charge transitions to negative values at slightly higher luminosity and lower density 0.3 dex), compared to the graphite grain(by charge, but approximatelyotherwise the trends are very averagesimilar."," In Figures \ref{avgGraphiteCharge} and \ref{avgSmallGraphiteCharge}, we consider only graphite grains, but the average charge on silicate grains is very similar to the graphite grains; the average silicate-grain charge transitions to negative values at slightly higher luminosity and lower density (by approximately 0.3 dex), compared to the average graphite grain charge, but otherwise the trends are very similar."
" If dust can survive, dust will be dominant in the hot, post-shocked gas of a wind-blowncooling bubble."," If dust can survive, dust cooling will be dominant in the hot, post-shocked gas of a wind-blown bubble."
" This is illustrated in Figure 9,, where we compare cooling curves from Cloudy where dust has not been included in the model (solid line) and where dust has been included (dashed line)."," This is illustrated in Figure \ref{coolingCurveComparison}, where we compare cooling curves from Cloudy where dust has not been included in the model (solid line) and where dust has been included (dashed line)."
" We can see from Figure 9 that in the hot, post-shocked gas of the WBB?),, dust cooling will be dominant for T>5x10° KK. We can see this for a wider range of parameters in Figure 10.."," We can see from Figure \ref{coolingCurveComparison} that in the hot, post-shocked gas of the WBB, dust cooling will be dominant for $T \ga 5 \times 10^5$ K. We can see this for a wider range of parameters in Figure \ref{dustCoolingFraction}."
 But how does dust impact the WBB dynamics?, But how does dust impact the WBB dynamics?
" First, in considering the size of the WBB, the dust column that we find is not large enough (in the post-shocked region of the nebula) to absorb a significant fraction of the ionizing radiation; overall, dust absorbs less than of the stellar flux in the energy range of RRyd to RRyd (see Fig. 11))."," First, in considering the size of the WBB, the dust column that we find is not large enough (in the post-shocked region of the nebula) to absorb a significant fraction of the ionizing radiation; overall, dust absorbs less than of the stellar flux in the energy range of Ryd to Ryd (see Fig. \ref{dustAbsorptionFraction}) )."
" And yet, this small amount of dust can impact the cooling and evolution of the WBB."," And yet, this small amount of dust can impact the cooling and evolution of the WBB."
 We present a simplified numerical model for N49 by integrating the equations of motion for a WBB and including dust cooling., We present a simplified numerical model for N49 by integrating the equations of motion for a WBB and including dust cooling.
" For this, we use the standard equations of wind-blown bubble expansion from"," For this, we use the standard equations of wind-blown bubble expansion from"
 , 
remnants (e.g.???)..,"remnants \citep[e.g.,][]{Sanwaletal02a,Morietal05a,Kargaltsevetal05a}."
 In Chis paper. we locus on emission from ANPs and SGRs. which comprise (he population of maenetars. NSs that leature quiescent ancl bursting emission powered by the decay of strong interior magnetic fields with surface strengths B~ G (e.e..?.andthereferencestherein)..," In this paper, we focus on emission from AXPs and SGRs, which comprise the population of magnetars, NSs that feature quiescent and bursting emission powered by the decay of strong interior magnetic fields with surface strengths $B\sim 10^{14}-10^{15}$ G \citep[e.g.,][and the
references therein]{WoodsThompson06a}."
 There is a near consensus in the literature that the magnetar hypothesis is correct., There is a near consensus in the literature that the magnetar hypothesis is correct.
" Evidence favoring the magnetar model includes {he energetics. fIux. and timing properties of SGR and AXP flares. long magnetar rotation periods and inferred ages. ancl (he lack of sufficient NS rotational energv to power the observed quiescent emission (e.g..ον,"," Evidence favoring the magnetar model includes the energetics, flux, and timing properties of SGR and AXP flares, long magnetar rotation periods and inferred ages, and the lack of sufficient NS rotational energy to power the observed quiescent emission \citep[e.g.,][]{Kaspi04a}."
 This phenomenology is consistent with internal NS magnetic fields strengths of B>LOY G. However. other than the large magnetic dipole components calculated from timing measurements. there are no direct empirical constraints on external magnetar-strength magnetic fields.," This phenomenology is consistent with internal NS magnetic fields strengths of $B\ga 10^{15}$ G. However, other than the large magnetic dipole components calculated from timing measurements, there are no direct empirical constraints on external magnetar-strength magnetic fields."
 This is in part due to the lack of leatures in inagnelar thermal spectra. à characteristic (hat is dillieult to explain. since broad features have been observed in the spectra of NSs with lower magnetic fields aud temperatures (e.g.. XDINS and pulsars).," This is in part due to the lack of features in magnetar thermal spectra, a characteristic that is difficult to explain, since broad features have been observed in the spectra of NSs with lower magnetic fields and temperatures (e.g., XDINS and pulsars)."
 Moreover. differences between the observed characteristics of magnetars and other classes of high field NSs are sill poorly understood.," Moreover, differences between the observed characteristics of magnetars and other classes of high field NSs are still poorly understood."
 The recently discovered population of radio pulsars is similar in most respects to canonical pulsus (they are powered bv rotational kinetic energv and emit persistently in the radio band)., The recently discovered population of high-field radio pulsars is similar in most respects to canonical pulsars (they are powered by rotational kinetic energy and emit persistently in the radio band).
 However. the high-field radio pulsars have long periods and inferred magnetic field strengths of order B=+xLoh G (e.g..2??7?)..," However, the high-field radio pulsars have long periods and inferred magnetic field strengths of order $B\ga 4\times 10^{13}$ G \citep[e.g.,][]{Camiloetal00a,Gonzalezetal04a,KaspiMcLaughlin05a,Livingstoneetal06a}."
 Several authors have speculated that the distinct behaviors of magnetars and hieh field radio pulsars suggest differences in their magnetic field geometries ancl possible evolutionary connections between (he (wo populations (e.g..?)..," Several authors have speculated that the distinct behaviors of magnetars and high field radio pulsars suggest differences in their magnetic field geometries and possible evolutionary connections between the two populations \citep[e.g.,][]{Gonzalezetal04a}."
 One of the kevs (o understuxding the nature of magnets and (heir relationship to other NS populations is in the production of plausible theoretical models [ον interpreting observations., One of the keys to understanding the nature of magnetars and their relationship to other NS populations is in the production of plausible theoretical models for interpreting observations.
 While signilicant progress has been made in modeling the spectra of thermal raciation from NS atmospheres. (ae use of such models to explain observational data is still in its infancy.," While significant progress has been made in modeling the spectra of thermal radiation from NS atmospheres, the use of such models to explain observational data is still in its infancy."
 In practice. typical soft X-ray magnetar spectra are fit equally well by blackbocdy or atmosphere models plus a power-law.," In practice, typical soft X-ray magnetar spectra are fit equally well by blackbody or atmosphere models plus a power-law."
 The incorporation of vacuum polarization elfects into NS atmosphere calculations has improved model fits to observed spectra. and has offered a possible explanation for the absence of magnetar spectral lines.," The incorporation of vacuum polarization effects into NS atmosphere calculations has improved model fits to observed spectra, and has offered a possible explanation for the absence of magnetar spectral lines."
 In principle. predictions of the beaming pattern of radiation along the surface magnetic field can be coupled to plase- spectroscopy to discriminate between NS atmospheres and other emission models.," In principle, predictions of the beaming pattern of radiation along the surface magnetic field can be coupled to phase-resolved spectroscopy to discriminate between NS atmospheres and other emission models."
 llowever. the relatively low photon count rates from many magnetar sources. as well as the," However, the relatively low photon count rates from many magnetar sources, as well as the"
eradieuts aud IR luminosities (both Zo; aud Ley) for Sevtert 2s. in the sense of blucr eradicuts at larger IB≻ huuinmositfies.,"gradients and IR luminosities (both $L_{25}$ and $L_{FIR}$ ) for Seyfert 2s, in the sense of bluer gradients at larger IR luminosities."
⋅⋅⋅ Iu fact.. these correlations. become fight if ⋅we exclude the two points deviating⋅⋅⋝ ⋅∶↴∙⊾↕⋅⋜↧≺∐↸∖∐↑↴∖↴↕∪↥⋅⋯∐⋅↴∖↴⋜↧∐∏≻↕↸∖∶↴∙⊾⋜↧↕⋜⋯↕↸∖↴∖∷↖↖↽↸∖↸⊳∪∐∏≻⋜∐⋅↸∖∐∪↖↖↽⋯∐⋅ eradieuts. that represent⋅ the galaxies TRAS 13536datato | 1836and11298 | 5313Wiuneutionedearlier to have unusually steep eradieuts compared to the rest of the sample.," In fact, these correlations become very tight if we exclude the two points deviating towards steeper gradients, that represent the galaxies IRAS 13536+1836 and 11298+5313W mentioned earlier to have unusually steep gradients compared to the rest of the sample."
" A Spearman Rauk or a Nendall’s Tau non-parametrc test for the significauce of the correlations give 0.02 for fracA(B Rp aud 0.007 for fracA(B Rj),", A Spearman Rank or a Kendall's Tau non-parametric test for the significance of the correlations give 0.02 for vs $L_{25}$ and 0.007 for vs $L_{FIR}$.
 A similar trend is seen. e M -- ⋟∙∖⋅∖∙⋝≽⋅∖↴(BR) gradients to Comm⋡∖⊽⋅late with Erin or the Cold sample. but the data points are fewer aud he scatter larger (correlation. significance⋅⋅⋅ 0.01).," A similar trend is seen, for the inner $(B-R)$ gradients to correlate with $L_{FIR}$ for the Cold sample, but the data points are fewer and the scatter larger (correlation significance 0.04)."
" are two possible wavs to interpret the tight correlation seen for Sevfert 2s. given that the IR unünositv scales with the amount of (wari) dust within a galaxy: (a) if the dust is concentrated im he central regions. we expect negative (outwards) colour gradieuts that are steeper the larecr is the effect. f ofdust s reddening11n e (center""u1 u(b)| if Ithe Ewar""UR dust eris distributed."" MONthroughoutoi"" the disk. larger Ik Iuimuinosities ∙∙∙∙∙indicate a stronger‘ source of MELilluuination. most ]probablyablCUM strongE disk- unstar fformation‘. that1 “asalso1 causes the optical colours to bien outwards,"," There are two possible ways to interpret the tight correlation seen for Seyfert 2s, given that the IR luminosity scales with the amount of (warm) dust within a galaxy: (a) if the dust is concentrated in the central regions, we expect negative (outwards) colour gradients that are steeper the larger is the effect of dust reddening in the center (b) if the warm dust is distributed throughout the disk, larger IR luminosities indicate a stronger source of illumination, most probably strong disk star formation that also causes the optical colours to bluen outwards."
 Tf alternative (a) is correct. then we would expect that a fair amount of dust heating iu the ceuter would be due to the AGN aud thus the above correlation would be better defined versus £55.," If alternative (a) is correct, then we would expect that a fair amount of dust heating in the center would be due to the AGN and thus the above correlation would be better defined versus $L_{25}$."
 Alternative (b) on the other haud. would be better represeuted by the correlation versus Leip.," Alternative (b) on the other hand, would be better represented by the correlation versus $L_{FIR}$."
 Tu fact.. since- both correlations. are. observed. the most probable explanation is a combination of the two effects. (," In fact, since both correlations are observed, the most probable explanation is a combination of the two effects. ("
v) To seek an explanation for the above correlations. weτν inspected1aocte the ∖⊳σοι1απ nuages1SPOON (Paper2.nU D aud; colour iiaps (Appendix of Paper HT) for our Sevfert 2 saluple.,"v) To seek an explanation for the above correlations, we inspected the continuum images (Paper I) and colour maps (Appendix of Paper III) for our Seyfert 2 sample."
oo We fiud a Theclear correlationdiffetrius between mucreasiusgcolour 1∖⋅⋠⊳⋅ ↴⋅∖⋉ . ⋠⋅⋉∖⋅ > ∐↕↑↸⋯↸⊓∪∐↴∖⊓↸∐∶↴∙↑∐∡⋯≼↧∡∐∶↴∙↸↥∐↴↕∏∐∐⋯↴∖↕⊓↸↴∖∪↥:⋅ steper eo1 gradi∙, We find a clear correlation between increasing interaction strength and larger IR luminosities or steeper colour gradients.
" This‘ result cani be undrstood if stroug interactionsa US larger anion ot en and dust to the center, wane,mene strong stat tsformation events throughout the disk aud iu the ceutral reeious and maybe feed the AGN. thus increasing the level of uuclear activity."," This result can be understood if strong interactions bring larger amounts of gas and dust to the center, induce strong star formation events throughout the disk and in the central regions and maybe feed the AGN, thus increasing the level of nuclear activity."
 Bushouse&WernerL990 have also noticed larger scale and steeper optical aud ucar-TR> colourolo⋅ gradientseyaclicutsEH1 MEMin interacting1eracting. and star-fo]star-formingEVEN1ο. ealaxies. ‘comparednwed tto »normalD madspirals.," \cite{bushouse90} have also noticed larger scale and steeper optical and near-IR colour gradients in interacting and star-forming galaxies, compared to normal spirals."
 vrThis resultres willVI 0 waneexplored] in 1uore detailt in a]Paper V. Having⋅ explored the colour distributions⋅⋅⋅ aud radial⋅ very. . . normal galaxies and otherE Sevfert samples. towards⋝⋅ steeper ," This result will be explored in more detail in Paper V. Having explored the colour distributions and radial gradients for our sample galaxies, we compare now our data to normal galaxies and other Seyfert samples."
Elliptical and early type galaxies are evolved systcus. almost cutirely composed by old red stars.," Elliptical and early type galaxies are evolved systems, almost entirely composed by old red stars."
 Colour eraclicuts in these galaxies are always negative outwards and can mostly be explained by imoetallieitv. effects., Colour gradients in these galaxies are always negative outwards and can mostly be explained by metallicity effects.
 This is probably also the case for the bulges of carly type spirals. although their colours are in general bluer than ellipticals. idicatiug that the bulee stellar populatious are vouuger and/or more metal poor (Baleclls&Peletier1991)).," This is probably also the case for the bulges of early type spirals, although their colours are in general bluer than ellipticals, indicating that the bulge stellar populations are younger and/or more metal poor \cite{balcells94}) )."
 Moreover. them colour .∩⊾↥⋅⋜↧≺∐↸∖∐↑↴∖↴≼⇂∪∐∪↑↴∖↴↸∖↸∖⋯↑∪↸⊳∪↥⋅↥⋅↸∖↕⋜↧↑↸∖↖↖↽↕↑∐∩⊾⋜↧↕⋜⋯↖↽↑↖↴⋉∖ .⋅⋅⋅ There . 27 ≺↖↖↽↕∐↸⊳∐↕↴∖↴⋜↧↕↴∖↴∪↖↖⇁↕⋜↧↑↖↖↽↸∖↕∪∏∐≼⊔∪↥⋅↑∐↸∖∐∐∐∖↥⋅∶↴∙⊾↥⋅⋜∥∐↸∖∐↑↴∖↴ ofour suuple galaxies}.," Moreover, their colour gradients do not seem to correlate with galaxy type (which is also what we found for the inner gradients of our sample galaxies)."
 Negative colour eradients are also typical for iutermeciate and late type spirals., Negative colour gradients are also typical for intermediate and late type spirals.
 Tere. many other effects are preseut besides metallicity oeradicuts: variable internal extinction. dust re-radiation ivd the distribution of different stellar. population types. can all iuftueuce the observed (bulge aud disk) colours aud eradicuts: Bell&DeJous↽1999.Jong:⋅ 1996)).," Here, many other effects are present besides metallicity gradients: variable internal extinction, dust re-radiation and the distribution of different stellar population types, can all influence the observed (bulge and disk) colours and gradients \cite{jong99,jong96c}) )."
 It is⋅ clear that the behaviour⋅ of: our WarmLuo SesQuaeort 2 and Cold galaxies is: closer to that observed for: normal spirals.: the former: having∙↜ steeper colour gradieuts than the latter. indicating that dust effects in their central regions are important.," It is clear that the behaviour of our Warm Seyfert 2 and Cold galaxies is closer to that observed for normal spirals, the former having steeper colour gradients than the latter, indicating that dust effects in their central regions are important."
 Although he inteerated colour eradieuts of Sevtert Ls are iufiueuced x the presence of the AGN in their centers. it is not clear why the inverse (positive outwards) eradieuts )oysist also outside the ceutral 2 kpe region (surface colour eradieuts).," Although the integrated colour gradients of Seyfert 1s are influenced by the presence of the AGN in their centers, it is not clear why the inverse (positive outwards) gradients persist also outside the central 2 kpc region (surface colour gradients)."
" Positive exadieuts. when found iu dwazt ellipticals. are interpreted as stellar age gradieuts: he evolution iu these objects is dominated by internal xocesses, such as galactic winds aud dissipation. that xeveut the formationd. of. metallicity2. eracdicuts. in. these objects (Vaderetal."," Positive gradients, when found in dwarf ellipticals, are interpreted as stellar age gradients: the evolution in these objects is dominated by internal processes, such as galactic winds and dissipation, that prevent the formation of metallicity gradients in these objects \cite{vader98}) )."
 1998)). properties of− the disks∙ ofani] oe ‘ So ∖↖⇁⋮∐⋅⋯⊰⋠∖↖↽↕⊳⋠∖↕↾↕⋮↕↓⋠↧⊀⋗∩↜⋮↕↕⋮↕↸↕⋠∖∖↴⋮∐⋅⋠∖↕∐∖↽⋠∖↕↖↽↾↭↴⋝⊏∖↕∐∏⋅↕∐∖↴↕≼⋡ 2 ealaxics and thus difficult to recoucile with a simple orientation effect., The differing colour properties of the disks of Warm Seyfert 1 and 2 galaxies are likely to be intrinsic and thus difficult to reconcile with a simple orientation effect.
 There is little iuforiiation in the recent literature about Sevfert colour eradieuts., There is little information in the recent literature about Seyfert colour gradients.
 EKotiluüneun&Ward1091. computed optical and near-IR colour eradicuts for a sample of hard. N-ray selected. mainly Seyfert 1 elaxies.," \cite{kotilainen94} computed optical and near-IR colour gradients for a sample of hard X-ray selected, mainly Seyfert 1 galaxies."
 After subtracting the ACN contributions they find negative optical aud IR eracicuts. comparable to those of. normal galaxies. and certainly. smaller than those found: im ∙∙interacting∙ and starburst galaxies.," After subtracting the AGN contributions they find negative optical and IR gradients, comparable to those of normal galaxies and certainly smaller than those found in interacting and starburst galaxies."
∙ Thev give: ACB- W)=-0.07- which is comparable to the immer surface colour eracieuts that we found for, They give $\Delta(B-V)$ =-0.07 which is comparable to the inner surface colour gradients that we found for
possible that quasars drive even more powerful outfows during phases of super-Lclelington accretion (??) or during obscured phases when the ACGN's radiation is trapped. in the galactic nucleus. enhancing the force on the ambient eas (?7)..,"possible that quasars drive even more powerful outflows during phases of super-Eddington accretion \citep{kingpounds03, king11} or during obscured phases when the AGN's radiation is trapped in the galactic nucleus, enhancing the force on the ambient gas \citep{debuhr10, debuhr11}."
 ‘To characterize the impact of AGN winds on their host galaxy. we carry out. numerical simulations of major galaxy mergers with models for DII growth and feedback.," To characterize the impact of AGN winds on their host galaxy, we carry out numerical simulations of major galaxy mergers with models for BH growth and feedback."
 Although itis bv no means certain that all quasars are associated with mergers. this provides a convenient ancl well-posed ποσο) in which to study. gas inflow in galactic nuclei.," Although it is by no means certain that all quasars are associated with mergers, this provides a convenient and well-posed model in which to study gas inflow in galactic nuclei."
 Lt also allows us to readily compare our results to the extensive previous literature on AGN feedback during mergers., It also allows us to readily compare our results to the extensive previous literature on AGN feedback during mergers.
 In the next section (5321) Wwe summarize our methocls. emphasizing our implementation of AGN winds and our treatment of ISM cooling.," In the next section \ref{sec:methods}) ) we summarize our methods, emphasizing our implementation of AGN winds and our treatment of ISM cooling."
 We then describe our key results in €3.., We then describe our key results in \ref{sec:results}. .
 We conclude in δε by discussing the implications of our results for. models of AGN feedback. and for. galactic winds driven by AGN., We conclude in \ref{sec:discussion} by discussing the implications of our results for models of AGN feedback and for galactic winds driven by AGN.
 We also compare our. results. to observations of high-velocity outllows from. post-starburst ealaxies and ultra-bIuminous infrared galaxies and summarize the theoretical processes that can produce the large niass-Ioacing and momentum ILuxes we find are necessary for ACN winds to have a substantial impact on the surrounding ISM., We also compare our results to observations of high-velocity outflows from post-starburst galaxies and ultra-luminous infrared galaxies and summarize the theoretical processes that can produce the large mass-loading and momentum fluxes we find are necessary for AGN winds to have a substantial impact on the surrounding ISM.
 We use a modified version of the TreesPLI code GADGET-2 (?) to perform simulations of equal-mass galaxy mergers., We use a modified version of the TreeSPH code GADGET-2 \citep{springel05} to perform simulations of equal-mass galaxy mergers.
 This version of the code includes the elective star formation model of 2? (hereafter. SIIO3) and the radiation pressure AGN feedback model of 2. (hereafter DOM)., This version of the code includes the effective star formation model of \cite{springel03} (hereafter SH03) and the radiation pressure AGN feedback model of \cite{debuhr11} (hereafter DQM).
 As described below. we modified the code further to implement à model of feedback via AGN winds. and to implement a more physical moclel of how the interstellar gas cools.," As described below, we modified the code further to implement a model of feedback via AGN winds, and to implement a more physical model of how the interstellar gas cools."
 We carry out simulations of major mergers of two equal mass galaxies., We carry out simulations of major mergers of two equal mass galaxies.
 We simulate only a single galaxy mass and ocus our resources on studving the cllects of feedback. via AGN winds produced. at. small radii., We simulate only a single galaxy mass and focus our resources on studying the effects of feedback via AGN winds produced at small radii.
 Each galaxy moclel las à rotationally supported disk of gas and stars and a stellar bulge. all embedded in a halo of dark matter.," Each galaxy model has a rotationally supported disk of gas and stars and a stellar bulge, all embedded in a halo of dark matter."
 Both he stellar ancl gaseous. disks have an exponential radial »ofile with a scale length of 3.51 kpe., Both the stellar and gaseous disks have an exponential radial profile with a scale length of 3.51 kpc.
 The vertical profile of the stellar disk is that of an isothermal sheet with a scale height of 702 pe., The vertical profile of the stellar disk is that of an isothermal sheet with a scale height of 702 pc.
 The vertical structure of the gas disk is set by hyelrostatic equilibrium., The vertical structure of the gas disk is set by hydrostatic equilibrium.
 The halo and stellar ;ulee both have ? profiles with a halo virial ancl half mass radius of 229 and 02 kpe. respectively (à concentration of 9.0) and with a bulge elective. radiusof 1.27 kpe.," The halo and stellar bulge both have \cite{hernquist90} profiles with a halo virial and half mass radius of 229 and 102 kpc, respectively (a concentration of 9.0) and with a bulge effective radiusof 1.27 kpc."
 Each ealaxy has a total dvnamical mass of 1.94.5107M. a total disk mass of 7.96«10173]. and a bulge of mass 2.66QUAL: 10€ of the disk mass is gas.," Each galaxy has a total dynamical mass of $1.94 \times 10^{12} \msun$ , a total disk mass of $7.96 \times 10^{10}
\msun$ and a bulge of mass $2.66 \times 10^{10} \msun$; $10 \%$ of the disk mass is gas."
 We have performed an additional simulation with a disk gas fraction of BO this run gives qualitatively similar. results. and so is not discussed in detail., We have performed an additional simulation with a disk gas fraction of 30; this run gives qualitatively similar results and so is not discussed in detail.
 The black holes are modeled as additional collisionless particles with initial masses of 10141., The black holes are modeled as additional collisionless particles with initial masses of $10^{5} M_\odot$.
 For our fiducial simulations. each galaxy is formed fron 2.4.107 particles: the halo has Ὁ107 dark matter particles. the clisk has 6.LO? stellar particles ancl 6.107 eas particles. and the bulge has 3.107 stellar particles.," For our fiducial simulations, each galaxy is formed from $2.4 \times 10^5$ particles: the halo has $9 \times 10^4$ dark matter particles, the disk has $6 \times 10^4$ stellar particles and $6 \times 10^4$ gas particles, and the bulge has $3 \times 10^4$ stellar particles."
 The gravitational force softening length is €=70 pe for the disk ancl bulge particles and e=176 pe for the halo particles., The gravitational force softening length is $\epsilon = 70$ pc for the disk and bulge particles and $\epsilon = 176$ pc for the halo particles.
 We describe resolution tests in 3.8., We describe resolution tests in 3.3.
 For the merger simulations. the two equal mass galaxies are placed on a prograde orbit with an initial separation of 142.8 kpc and an initial velocity of each. galaxy of 160 km + directed at an angle of 28° from the line connecting the galaxies.," For the merger simulations, the two equal mass galaxies are placed on a prograde orbit with an initial separation of $142.8$ kpc and an initial velocity of each galaxy of $160$ km $^{-1}$ directed at an angle of $28^{\circ}$ from the line connecting the galaxies."
 The corresponding orbital energy is approximately zero., The corresponding orbital energy is approximately zero.
 The spin of the two galaxies are not aligned with the orbital angular momentum of the svstem: the relative angle between the spin directions is 41. with one galaxy’s spin making an angle of LO” degrees relative to the orbital angular momentun.," The spin of the two galaxies are not aligned with the orbital angular momentum of the system; the relative angle between the spin directions is $41^{\circ}$, with one galaxy's spin making an angle of $10^{\circ}$ degrees relative to the orbital angular momentum."
 In this section we brielly review the sub-grid accretion model presented in detail in DOM., In this section we briefly review the sub-grid accretion model presented in detail in DQM.
 The sub-grid accretion rate on scales smaller than our resolution (both gravitational forcesoftening and SPII smoothing) is estimated. with a model motivated by the redistribution of angular momentum in the eas., The sub-grid accretion rate on scales smaller than our resolution (both gravitational forcesoftening and SPH smoothing) is estimated with a model motivated by the redistribution of angular momentum in the gas.
" For eas with a surface density X. a sound. speed c, and a rotational angular frequency Q. the mass accretion rate into the nuclear region is: Lere α is a free parameter of the model characterizing not only the ellicieney of angular momentum transport. but also the amount of gas that turns into stars (on scales below our resolution) insteac of falling into the black hole."," For gas with a surface density $\Sigma$, a sound speed $c_s$ and a rotational angular frequency $\Omega$, the mass accretion rate into the nuclear region is: Here $\alpha$ is a free parameter of the model characterizing not only the efficiency of angular momentum transport, but also the amount of gas that turns into stars (on scales below our resolution) instead of falling into the black hole."
 Our fiducial values of à range from 0.050.15. motivated (at the order of magnitude level) by comparison to thesimulations of gas inflow from 0.1.100 pe of ?..," Our fiducial values of $\alpha$ range from $0.05-0.15$, motivated (at the order of magnitude level) by comparison to thesimulations of gas inflow from $\sim 0.1-100$ pc of \citet{hopkins10c}."
 Over this range of a. there is little dependence of our simulation results on à (see DOM).," Over this range of $\alpha$, there is little dependence of our simulation results on $\alpha$ (see DQM)."
 To perform the sub-grid estimate of the gas properties in equation (1)). we take averages of the properties of the SPILL particles inside a region of radius Roo300 pc centered on the black hole.," To perform the sub-grid estimate of the gas properties in equation \ref{eqn:Mdvisc}) ), we take averages of the properties of the SPH particles inside a region of radius $R_{acc} \sim 300$ pc centered on the black hole."
 For reasons described in DOM we take this radius to be four times the gravitational force softening. c. of the particlesin the simulation.," For reasons described in DQM we take this radius to be four times the gravitational force softening, $\epsilon$ , of the particlesin the simulation."
 The 115 in our simulation are modeleck as specially markecl collisionless particles., The BHs in our simulation are modeled as specially marked collisionless particles.
 Vhe luminosity of the black hole is taken to be a fraction. 7—0.1. of the rest mass energy of the acereted material:," The luminosity of the black hole is taken to be a fraction, $\eta = 0.1$, of the rest mass energy of the accreted material:"
"different from observed (e.g.,the‘Mouse’G359.23—0.82,Gaensleretal.2004) and simulated (e.g.,Bucciantinietal.2005) bow-shock PWNe, in which the emission is tightly confined along the proper motion direction.","different from observed \citep[e.g., the `Mouse' G359.23--0.82,][]{gaensler04} and simulated \citep[e.g.,][]{bucciantini05} bow-shock PWNe, in which the emission is tightly confined along the proper motion direction."
" The halo forms instead a broad diffuse region behind the pulsar, almost perpendicular to the proper motion direction."," The halo forms instead a broad diffuse region behind the pulsar, almost perpendicular to the proper motion direction."
" In this work, we presented a new timing solution for bbased on a phase-coherent analysis ofXMM-Newton,,Swift,, and ddata and valid in the range from MJD 55274.775 to 55499.170."," In this work, we presented a new timing solution for based on a phase-coherent analysis of, and data and valid in the range from MJD 55274.775 to 55499.170."
" Under the standard assumption that the neutron star slows down because of magnetic braking, it implies a characteristic age T.~35 kyr, a dipolar magnetic field Bzz1.6x1014 G and a rotational energy loss rate E~3.2x10° ((see reftiming-fit))."," Under the standard assumption that the neutron star slows down because of magnetic braking, it implies a characteristic age $\tau_c\simeq 35$ kyr, a dipolar magnetic field $B\approx1.6\times10^{14}$ G and a rotational energy loss rate $\dot{E}\simeq3.2\times10^{32}$ (see \\ref{timing-fit}) )."
 The modelling of the phase shifts required a fourth-order polynomial which in general is an indication for timing noise (polynomial whitening')., The modelling of the phase shifts required a fourth-order polynomial which in general is an indication for timing noise (`polynomial whitening').
" However, it is worth noting that the second derivative we measured is unlikely to be related to a random change of the pulse profiles, which is expected to introduce only a random distribution of the phase residuals, rather then a cubic term."," However, it is worth noting that the second derivative we measured is unlikely to be related to a random change of the pulse profiles, which is expected to introduce only a random distribution of the phase residuals, rather then a cubic term."
 Recent studies on a sample of 366 radio pulsars showed that cubic terms in the phase residuals are actually possible but smaller by several orders of magnitudes than those detected in and recorded on time-scales longer (years) than those we are, Recent studies on a sample of 366 radio pulsars showed that cubic terms in the phase residuals are actually possible but smaller by several orders of magnitudes than those detected in and recorded on time-scales longer (years) than those we are
Let us consider now an orbiting source of radiation localized on the disk. such as a hot spot. a spiral shock. or anv other steady perturbation. lasting with an approximate constaul flux for a Gime much longer than the orbital period νιwith py=322x104mtrwv? llz.,"Let us consider now an orbiting source of radiation localized on the disk, such as a hot spot, a spiral shock, or any other steady perturbation, lasting with an approximate constant flux for a time much longer than the orbital period $\nk^{-1}$, with $\nk = 3.22\times 10^4 m^{-1}\, r^{-3/2}$ Hz."
 The formation of this kind of instabilities. where a substantial fraction of the accretion enerev is clissipatec. is discussed e.g. bv TaggeranclPellat(1999).," The formation of this kind of instabilities, where a substantial fraction of the accretion energy is dissipated, is discussed e.g. by \cite{tag99}."
. They are associated with the development of powerful standing waves in moderately magnetized disks and are similar. in some aspects. to the Great Red Spot in Jupiter.," They are associated with the development of powerful standing waves in moderately magnetized disks and are similar, in some aspects, to the Great Red Spot in Jupiter."
 Because the differential (Thomson) cross section. is. proportional. to 1+cos?>O'. with. the total [Iux measured by distant. observer consists of the superposition of a nearly constant background. plus a modulated: component due (o (he reprocessed radiation.," Because the differential (Thomson) cross section is proportional to $1+\cos^2\Theta'$, with the total flux measured by distant observer consists of the superposition of a nearly constant background plus a modulated component due to the reprocessed radiation."
 In equation ( 3)) primed angles are measured in (the electron local rest [rame. and are related to the corresponding unprimed quantities via the standard Lorentz (ranslormations.," In equation ( \ref{Theta}) ) primed angles are measured in the electron local rest frame, and are related to the corresponding unprimed quantities via the standard Lorentz transformations."
 For the sake of simplicity. ancl because we are mainly interested in the non linear effects in the harmonic functions. we will not consider here (he possibly weak variation of huminosity associated with the orbital revolution of (he source and caused. for instance. by the kinematic Doppler shift.," For the sake of simplicity, and because we are mainly interested in the non linear effects in the harmonic functions, we will not consider here the possibly weak variation of luminosity associated with the orbital revolution of the source and caused, for instance, by the kinematic Doppler shift."
 We point out that. in addition to the quadratic dependence given by equation ( 3)). (here is a further element of non linearity in the signal.," We point out that, in addition to the quadratic dependence given by equation ( \ref{Theta}) ), there is a further element of non linearity in the signal."
 This effect is caused by the dependence of the arrival time of the signal on the angular coordinate © of the source.," This effect is caused by the dependence of the arrival time of the signal on the angular coordinate $\,\phi$ of the source."
" Al any given instanl laps. the component of the observed Πιν varies as 1+cos?O'(10,4,,)). where (ens) is a non linear function of the time of observation. oblainecl by inverting equation ( 2)) with Oo=2z1,l."," At any given instant $\, t_{obs}$, the component of the observed flux varies as $\, 1+\cos^2\Theta'(t(t_{obs}))$, where $\, t(t_{obs})\, $ is a non linear function of the time of observation, obtained by inverting equation ( \ref{time}) ) with $\phi=2\pi\nk t$."
 As shown in Figures 5 and G.. this double non linear variation generates a number of harmonies with different signs for the lags.," As shown in Figures \ref{Fig2} and \ref{Fig3}, this double non linear variation generates a number of harmonics with different signs for the lags."
" The curves were obtained simply. applying a standard PDS technique to the function. cos?O'(1,,,)."," The curves were obtained simply applying a standard PDS technique to the function $\,\cos^2\Theta'(t_{obs})$."
 These figures are only representative. because the strength and the relative sign for the lags of the fundamental and sub-harmonics (urn out to depend sensibly on the model parameters. ie. Cae outflow velocity 2. the place of emission r. the range in z where scattering occurs and. finally. the direction 64 between the mean electron bulk velocity and the line of sight.," These figures are only representative, because the strength and the relative sign for the lags of the fundamental and sub-harmonics turn out to depend sensibly on the model parameters, i.e. the outflow velocity $\beta$ , the place of emission $r$, the range in $z$ where scattering occurs and, finally, the direction $\theta_1$ between the mean electron bulk velocity and the line of sight."
 Although the first and second harmonics seem (o exhibit preferentially lags of (he same sense. we cannot exclude that a clifferent parametrization could produce lags with opposite sign.," Although the first and second harmonics seem to exhibit preferentially lags of the same sense, we cannot exclude that a different parametrization could produce lags with opposite sign."
 Unfortunately the sensitivity of the results to so many parameters is rather troublesome and represent a severe obstacle for a reliable test of the model., Unfortunately the sensitivity of the results to so many parameters is rather troublesome and represent a severe obstacle for a reliable test of the model.
 Yet. we cannotexclude that precisely (hese intricate relationships cause(he complex evolutionary behavior of microquasars.," Yet, we cannotexclude that precisely these intricate relationships causethe complex evolutionary behavior of microquasars."
8.8x10/? cm.,$8.8 \times 10^{15}$ cm.
" If gas continues to collapse and needs higher resolution beyond the maximum refinement level, sink particles are created thereby taking density away from the gas such that mass and momentum is conserved and the resolution criterion is not violated."," If gas continues to collapse and needs higher resolution beyond the maximum refinement level, sink particles are created thereby taking density away from the gas such that mass and momentum is conserved and the resolution criterion is not violated."
" We give sink particles an accretion radius of effectively 3 cells, that is, 2.6x1016 cm ~ 1760 AU."," We give sink particles an accretion radius of effectively 3 cells, that is, $2.6 \times 10^{16}$ cm $\simeq$ 1760 AU."
" The temperature in both simulations is initialized at 10 K, but for the simulation with X-rays, the temperature is updated by the XDR code, and changes quickly (<10~+tg = 1 timestep) after initialization."," The temperature in both simulations is initialized at 10 K, but for the simulation with X-rays, the temperature is updated by the XDR code, and changes quickly $\lesssim$ $^{-4} \rm ~t_{ff}$ = 1 timestep) after initialization."
" Both simulations, A and B, are followed for 2x10? years."," Both simulations, A and B, are followed for $\times$ $^{5}$ years."
 This is approximately two free-fall times for a 10?cm? cloud., This is approximately two free-fall times for a $10^{5} \rm ~cm^{-3}$ cloud.
" rays can heat the cloud to as high as 6000 K at low column densities («10?! cm""?), this is the case for the side that is directly exposed to the X-ray source, but also to as low as 10 K at high column densities (>1074 cm?)."," X-rays can heat the cloud to as high as 6000 K at low column densities $< 10^{21} \rm ~cm^{-2}$ ), this is the case for the side that is directly exposed to the X-ray source, but also to as low as 10 K at high column densities $> 10^{24} \rm ~cm^{-2}$ )."
 Fig., Fig.
 1 shows a column density plot to this effect., \ref{fig:column} shows a column density plot to this effect.
 The directional heating increases the pressure and causes the gas to expand and evaporate on the irradiated face of the cloud., The directional heating increases the pressure and causes the gas to expand and evaporate on the irradiated face of the cloud.
" The molecular cloud is compressed, loses mass, and an ionizing pressure flow travels inward."," The molecular cloud is compressed, loses mass, and an ionizing pressure flow travels inward."
" We see that this compression creates a density increase of about half an order of magnitude within a free-fall time as compared to simulation B. The conical compression front is disrupted where the turbulence creates sub-pc scale gaps (0.01-0.05 pc) and radiation is able to penetrate, as is illustrated in Fig. 2.."," We see that this compression creates a density increase of about half an order of magnitude within a free-fall time as compared to simulation B. The conical compression front is disrupted where the turbulence creates sub-pc scale gaps (0.01-0.05 pc) and radiation is able to penetrate, as is illustrated in Fig. \ref{fig:gaps}."
 Those regions are also heated up and pressurized., Those regions are also heated up and pressurized.
 This causes the pressure front of the irradiated side of the cloud to break up., This causes the pressure front of the irradiated side of the cloud to break up.
" We see finger-like shapes forming, with a high density head, and the gas that is lying in its shadow is well shielded and very cold (about 10 K)."," We see finger-like shapes forming, with a high density head, and the gas that is lying in its shadow is well shielded and very cold (about 10 K)."
 The increased density induces star formation., The increased density induces star formation.
 We find that sink particles are created in the compressed cloud edge much earlier than in the shielded and colder parts., We find that sink particles are created in the compressed cloud edge much earlier than in the shielded and colder parts.
 A phase diagram is plotted in Fig., A phase diagram is plotted in Fig.
 3 that shows the decline of temperature as the density increases., \ref{fig:phase} that shows the decline of temperature as the density increases.
 The secondary band with a steep decrease in temperature at low densities is the direct result of shielding., The secondary band with a steep decrease in temperature at low densities is the direct result of shielding.
 We note that the reason that fewer points appear in the plot in the shielded regions is merely due to the difference in resolution determined by the refinement criteria., We note that the reason that fewer points appear in the plot in the shielded regions is merely due to the difference in resolution determined by the refinement criteria.
that speeds of interplanetary CMEs (ICMESs) corresponding to CMESs with speeds ranging from 100—2000kis1. as measured [rom coronagraphs. lie within LOO—200kms+ of the ambient solar wind.,"that speeds of interplanetary CMEs (ICMEs) corresponding to CMEs with speeds ranging from $100-2000\kmps$, as measured from coronagraphs, lie within $100-200\kmps$ of the ambient solar wind."
 However. the time a CME takes to reach (he Earth. the transit time. is known to vary [rom less than a day to over four davs.," However, the time a CME takes to reach the Earth, the transit time, is known to vary from less than a day to over four days."
 This indicates that most of the CME dynamics occurs closer to the Sun., This indicates that most of the CME dynamics occurs closer to the Sun.
 Vrsnaketal.(2010) have reported (hat transit times of broad. low-mass CMESs depend mainly oi the surrounding solar wind speed. while (hose of narrow. massive CMESs depend mainly on the initial speeds of the CMEs.," \citet{Vrsnak.etal2010} have reported that transit times of broad, low-mass CMEs depend mainly on the surrounding solar wind speed, while those of narrow, massive CMEs depend mainly on the initial speeds of the CMEs."
 Recently. Manoharan&MujiberRahman(2011) have also found that most of the ICMESs tend to altain speeds close to that of the ambient solar wind. ancl have estimated travel (mes οἱ the CAIEs to reach a distance of based on the CME initial speed and drag due to solar wind.," Recently, \citet{Manoharan.Rahman2011} have also found that most of the ICMEs tend to attain speeds close to that of the ambient solar wind, and have estimated travel times of the CMEs to reach a distance of based on the CME initial speed and drag due to solar wind."
 CAMIEs have been classified on the basis of their source regions. Goslingetal.(1976).," CMEs have been classified on the basis of their source regions. \citet{Gosling.etal1976},"
. using the coronagraph on Skvlab spacecraft. were the first ones to report Chat CALEs associated with flares are faster than those associated wilh prominences.," using the coronagraph on Skylab spacecraft, were the first ones to report that CMEs associated with flares are faster than those associated with prominences."
 This was supported bv observation of CAIEs by MacQueen&Fisher(1983). who used (he A--coronameter al Mauna Loa Solar Observatory., This was supported by observation of CMEs by \citet{MacQueen.Fisher1983} who used the -coronameter at Mauna Loa Solar Observatory.
 In. addition. they also observed that the former tvpe showed smaller acceleration with increase in height than the latter.," In addition, they also observed that the former type showed smaller acceleration with increase in height than the latter."
 have also reported a similar result. based on their technique to track features observed in SolIO/LASCO coronagraphs., \citet{Sheeley.etal1999} have also reported a similar result based on their technique to track features observed in SoHO/LASCO coronagraphs.
 Moonetal.(2002) in a statistical study. involving over 3200 CMIESs observed from SollO/LASCO have reported that flare-associated CMESs have a hieher median speed (han those associated with EPs., \citet{Moon.etal2002} in a statistical study involving over 3200 CMEs observed from SoHO/LASCO have reported that flare-associated CMEs have a higher median speed than those associated with EPs.
 Their study also found that although the median acceleration of all the events is zero. it decreases a little for CMESs with high speeds (>500kms +).," Their study also found that although the median acceleration of all the events is zero, it decreases a little for CMEs with high speeds $>500\kmps$ )."
 Srivastavaetal. (1999:: 2000)) have found that gradual CMEs allain the speed of the ambient solar wind at about 2015. [rom the Sun., \citeauthor{Srivastava.etal1999a} \citeyear{Srivastava.etal1999a}; \citeyear{Srivastava.etal2000}) ) have found that gradual CMEs attain the speed of the ambient solar wind at about $20\Rsun$ from the Sun.
 Results from Gopalswanmwetal.(2001) also are consistent will (his studs. who reported deceleration as high as —100ms? for fast CMEs (speed >900knms ') [rom a combined. study of," Results from \citet{Gopalswamy.etal2001b} also are consistent with this study, who reported deceleration as high as $-100\mpss$ for fast CMEs (speed $>900\kmps$ ) from a combined study of"
,.
 where we have written the radius of curvature of the field lines in units of the light cylinder radius. p.=prj. and have inserted the expressions (129)) and (136)) for the accelerating fields.," where we have written the radius of curvature of the field lines in units of the light cylinder radius, $\rho=\rhostar\rlight$, and have inserted the expressions \ref{Evac}) ) and \ref{Espace}) ) for the accelerating fields."
 If Yu>Yea Cmax< You). Curvature radiation (linear acceleration emission) is the appropriate description.," If $\gamma_{\rm max}>\gamma_{\rm crit}$ $\gamma_{\rm max}<\gamma_{\rm crit}$ ), curvature radiation (linear acceleration emission) is the appropriate description."
" Alternatively. the curvature photon formation length Zou, can be evaluated: -4x"," Alternatively, the curvature photon formation length $L_{\rm curv}$ can be evaluated: = ."
 According to (140)). curvature radiation is an appropriate description of the radiation from a vacuum gap (space-charge flow limited gap) provided its height exceeds roughly 200cm (3x107 em).," According to \ref{hcrit}) ), curvature radiation is an appropriate description of the radiation from a vacuum gap (space-charge flow limited gap) provided its height exceeds roughly $200\,\textrm{cm}$ $4\times10^4\,\textrm{cm}$ )."
 Note. however. that these conditions are relaxed (in the sense that the critical gap size is reduced) if the radius of curvature of the field lines is small compared to the light-cylinder radius. and also if the accelerating field fails to reach the full value given by (129)) or (136)) — both of which were assumed in the original Ruderman&Sutherland(1975) model.," Note, however, that these conditions are relaxed (in the sense that the critical gap size is reduced) if the radius of curvature of the field lines is small compared to the light-cylinder radius, and also if the accelerating field fails to reach the full value given by \ref{Evac}) ) or \ref{Espace}) ) — both of which were assumed in the original \citet{rudermansutherland75} model."
 In current static models. the assumed gap heights greatly exceed L4. so that liear acceleration emission does not play a role.," In current static models, the assumed gap heights greatly exceed $L_{\rm curv}$, so that linear acceleration emission does not play a role."
 Recently. however. time-dependent gap models have been proposed (Levinsonetal.2005:Timokhin2009).," Recently, however, time-dependent gap models have been proposed \citep{levinsonetal05,timokhin09}."
. These models assume accelerating fields that are of the order of. or larger than the vacuum field given in (129)).," These models assume accelerating fields that are of the order of, or larger than the vacuum field given in \ref{Evac}) )."
 In addition. time-dependent screening leads to structure on a length scale determined essentially by the electron inertial length f£.= Where Is the local plasma frequency.," In addition, time-dependent screening leads to structure on a length scale determined essentially by the electron inertial length $\ell_{\rm e}=c/\omega_{\rm pe}$ , where $\omega_{\rm pe}$ is the local plasma frequency."
" Estimating the c/o.electron/positroncy, charge density as roughly equal to the charge-density required to screen the electric field (the ddensity) implies so that —5x", Estimating the electron/positron charge density as roughly equal to the charge-density required to screen the electric field (the density) implies so that = .
 Therefore. linear acceleration emission Is àn essential ingredient in these models. because the formation length for curvature radiation photons substantially exceeds the anticipated length-scale of the structure in the accelerating electric field.," Therefore, linear acceleration emission is an essential ingredient in these models, because the formation length for curvature radiation photons substantially exceeds the anticipated length-scale of the structure in the accelerating electric field."
 The radiation produced by a particle whose acceleration is parallel to its velocity. linear acceleration emission. has been investigated for a number of special cases.," The radiation produced by a particle whose acceleration is parallel to its velocity, linear acceleration emission, has been investigated for a number of special cases."
 Particle motion of this type is expected to occur in the intense magnetic fields close to the surface of a pulsar., Particle motion of this type is expected to occur in the intense magnetic fields close to the surface of a pulsar.
 The emission produced by these particles is conceptually difficult due to the macroscopic size of the photon formation length., The emission produced by these particles is conceptually difficult due to the macroscopic size of the photon formation length.
 For the particular case of hyperbolic motion. corresponding to acceleration in a uniform electric field. the formation lereth is comparable to the length of the entire accelerating regio1.," For the particular case of hyperbolic motion, corresponding to acceleration in a uniform electric field, the formation length is comparable to the length of the entire accelerating region."
 Linear acceleration emission is similar to both synchrotron and eurvature radiation in the sense that a photon is emitted with a probability o; when a particle traverses a formation |ength., Linear acceleration emission is similar to both synchrotron and curvature radiation in the sense that a photon is emitted with a probability $\alpha_{\rm f}$ when a particle traverses a formation length.
 The essential properties of the radiation produced by a particle on a hyperbolic trajectory can be understood in terms of two key parameters: the length £L of the hyperbolic part of the trajectory. and the length a’ over which the particle increases its energy by me.," The essential properties of the radiation produced by a particle on a hyperbolic trajectory can be understood in terms of two key parameters: the length $L$ of the hyperbolic part of the trajectory, and the length $\accel$ over which the particle increases its energy by $mc^2$."
 Some generic features of the emission mechanism in different electric field configurations can also be deseribed using these quantities., Some generic features of the emission mechanism in different electric field configurations can also be described using these quantities.
 In particular. provided L and αἲ are interpreted appropriately (see section 4. for some examples) the critical frequency can be expressed as Wei=Le/a’n," In particular, provided $L$ and $\accel$ are interpreted appropriately (see section \ref{special} for some examples) the critical frequency can be expressed as $\omega_{\rm crit}\approx Lc/\accel^2$."
 Current models of pair production in. pulsar magnetospheres typically— assume that high energy photons that induce the secondary pair cascade. are produced via either curvature radiation or inverse-Compton scattering.," Current models of pair production in pulsar magnetospheres typically assume that high energy photons that induce the secondary pair cascade, are produced via either curvature radiation or inverse-Compton scattering."
 An alternative to these processes is linear acceleration emission. as investigated by Melrose&Luo(2009).," An alternative to these processes is linear acceleration emission, as investigated by \citet{melroseluo09}."
. We have demonstrated that this process is in fact complementary to curvature radiation. the transition between the two regimes depending only on the ratio of the system size to the formation length of curvature photons.," We have demonstrated that this process is in fact complementary to curvature radiation, the transition between the two regimes depending only on the ratio of the system size to the formation length of curvature photons."
 For existing static polar gap models. linear acceleration is unlikely to play an important role. although this relies on the environmental parameters being close to the canonical values.," For existing static polar gap models, linear acceleration is unlikely to play an important role, although this relies on the environmental parameters being close to the canonical values."
 The limits for both vacuum gap models and space-charge limited models are presented in section 5.., The limits for both vacuum gap models and space-charge limited models are presented in section \ref{pulsars}.
 Recent numerical studies provide evidence that the above stationary models are unstable to perturbations (e.g.Levin-sonetal.2005:Timokhin 2009).," Recent numerical studies provide evidence that the above stationary models are unstable to perturbations \cite[e.g.][]{levinsonetal05, timokhin09}."
. Several analytic models have been developed in which particles are accelerated in large amplitude electrostatic waves that propagate parallel to the magnetic field (seee.g.Luo&Melrose2008.andref-erences therein).., Several analytic models have been developed in which particles are accelerated in large amplitude electrostatic waves that propagate parallel to the magnetic field \cite[see e.g.][and references therein]{luomelrose08}.
 Since the characteristic length scale of the electric fields in these models ts on the order of the electron inertial length. linear acceleration emission ts likely to be a more appropriate description of the resulting radiation.," Since the characteristic length scale of the electric fields in these models is on the order of the electron inertial length, linear acceleration emission is likely to be a more appropriate description of the resulting radiation."
 We thank Don Melrose. Qinghuan Luo and Mohammed Rafat for stimulating discussions.," We thank Don Melrose, Qinghuan Luo and Mohammed Rafat for stimulating discussions."
" Β.. gratefully acknowledges support from— the Alexander von Humboldt foundation,", B.R. gratefully acknowledges support from the Alexander von Humboldt foundation.
Here we provide a short summary of our analytical model.,Here we provide a short summary of our analytical model.
 In this model. light curves are calculated by numerical integration over an infinitesimally thin homogeneous blast wave front.," In this model, light curves are calculated by numerical integration over an infinitesimally thin homogeneous blast wave front."
 The received flux is given by when we ignore the redshift 7., The received flux is given by when we ignore the redshift $z$.
" Here e, is the comoving frame emissivity and j/ the angle between observer direction and local velocity.", Here $\epsilon'_{\nu'}$ is the comoving frame emissivity and $\mu$ the angle between observer direction and local velocity.
" The dependence of the beaming and emissivity on the observer time 7,4, is kept implicit (see also eqn. A8:", The dependence of the beaming and emissivity on the observer time $t_{obs}$ is kept implicit (see also eqn. \ref{te2tobs_equation};
 the volume integral needs to be taken across different emission times)., the volume integral needs to be taken across different emission times).
 Assuming the radiation is produced by an infinitesimally thin shell with width AR we get For every observer time we integrate over jet angles and o (we define @ such that it is the angle between observer and local fluid velocity. but that between local fluid velocity and jet axis). while taking into account that radiation from different emission angles.," Assuming the radiation is produced by an infinitesimally thin shell with width $\Delta R$ we get For every observer time we integrate over jet angles $\theta$ and $\phi$ (we define $\theta$ such that it is the angle between observer and local fluid velocity, but that between local fluid velocity and jet axis), while taking into account that radiation from different emission angles."
 The emissivity can be calculated from the local fluid conditions. which we know in turn in terms of emission time ἐς.," The emissivity can be calculated from the local fluid conditions, which we know in turn in terms of emission time $t_e$."
 For the blast wave radius we have by definition: Where the subscript s/ indicates velocity., For the blast wave radius we have by definition: Where the subscript $sh$ indicates velocity.
 From the shock jump conditions it follows for arbitrary strong shocks that The comoving downstream number density 7 in both the relativistic and nonrelativistic regime is given by with >| in the nonrelativistic limit., From the shock jump conditions it follows for arbitrary strong shocks that The comoving downstream number density $n'$ in both the relativistic and nonrelativistic regime is given by with $\gamma \to 1$ in the nonrelativistic limit.
 We assume this equation to remain valid in the intermediate regime as well., We assume this equation to remain valid in the intermediate regime as well.
 This ts not implied by the expression above. where we have kept implicit the dependence on the fluid adiabatie index (which changes from 3/3 to 5/3 over the course of the blast wave evolution).," This is not implied by the expression above, where we have kept implicit the dependence on the fluid adiabatic index (which changes from $4/3$ to $5/3$ over the course of the blast wave evolution)."
 We set the width of the shell at a single emission time by demanding that the shell contains all swept-up particles. leading to: where we have used 725!=4757. again assumed valid throughout theentire evolution of the fluid.," We set the width of the shell at a single emission time by demanding that the shell contains all swept-up particles, leading to: where we have used $n = \gamma n' = 4 n_0 \gamma^2$, again assumed valid throughout theentire evolution of the fluid."
 The subscript f denotes the front of the shock and the subscript 5 denotes the back of the shock., The subscript $f$ denotes the front of the shock and the subscript $b$ denotes the back of the shock.
 Setting the shock width through the number of particles is to some extent an arbitrary choice. and we could also have used the total energy which would have yielded a different width (since the downstream energy density profile is different from the downstream number density profile).," Setting the shock width through the number of particles is to some extent an arbitrary choice, and we could also have used the total energy which would have yielded a different width (since the downstream energy density profile is different from the downstream number density profile)."
 The width of the shell AR in equation À2 has to take into account the emission time difference between the front and back of the shell and is given by Because the shell is very thin. Αρ)zzRj(t;)— or.," The width of the shell $\Delta R$ in equation \ref{flux_model2_equation} has to take into account the emission time difference between the front and back of the shell and is given by Because the shell is very thin, $R_f (t_b) \approx R_f (t_f) -
\beta_{sh} c \Delta t$ ."
" We integrate over emission arriving at a single observer time. and for given values of µ and £,5, we have which yields AR=Arc/j(! when differentiated."," We integrate over emission arriving at a single observer time, and for given values of $\mu$ and $t_{obs}$ we have which yields $\Delta R = \Delta t c / \mu$ when differentiated."
 Combining the above. we eventually find For the shock velocity we have in the BM and ST regime respectively.," Combining the above, we eventually find For the shock velocity we have in the BM and ST regime respectively."
 We artificially combine the two simply by adding them (after squaring): Note that the BM quantities depend on Ej. while the ST quantities depend on E;.," We artificially combine the two simply by adding them (after squaring): Note that the BM quantities depend on $E_{iso}$, while the ST quantities depend on $E_{j}$."
 The two are related via £j=Exo;2.," The two are related via $E_j = E_{iso}
\theta_j^2 / 2 $."
 Here E; is the total energy in jets. and 0; the opening angle of a jet.," Here $E_j$ is the total energy in jets, and $\theta_j$ the opening angle of a jet."
 The fluid Lorentz factor in the relativistic regime is related to the shock Lorentz factor via ?=M 2. while the fluid velocity inthe non-relativistic regime is related to the shock," The fluid Lorentz factor in the relativistic regime is related to the shock Lorentz factor via $\gamma^2 = \gamma_{sh}^2 / 2$ , while the fluid velocity inthe non-relativistic regime is related to the shock"
we also fied the index of the power-law component for the simultaneous fit and allowed the normalisation of this coniponent to vary from one observation ο another.,we also tied the index of the power-law component for the simultaneous fit and allowed the normalisation of this component to vary from one observation to another.
 Similarly. we allowed the temperature of the NS atmosphere componcut to vary between observations to account for the expected cooling of he NS crust.," Similarly, we allowed the temperature of the NS atmosphere component to vary between observations to account for the expected cooling of the NS crust."
 Table shows the results of the best-fit iioclel or 3 values of distance: 5.9. 7.1 aud 8.3 kpc.," Table \ref{tab:fit-sim} shows the results of the best-fit model for 3 values of the distance: 5.9, 7.1 and 8.3 kpc."
 The fi sare acceptae wi a oof 1.03 for L119 d.o.f., The fits are acceptable with a of 1.03 for 1419 d.o.f.
 Fig., Fig.
 3. shows he results of fits for a distance of 7.1 kpe (note tlat we onlv show EPIC pu spectra for clarity. but the fit included the EPIC MOS1 and MOS2 and the RCGSs spectra too).," \ref{fig:fits} shows the results of the fits for a distance of 7.1 kpc (note that we only show the EPIC pn spectra for clarity, but the fit included the EPIC MOS1 and MOS2 and the RGSs spectra too)."
" Fits of 1ο thermal component to a blackbody model vielded similar(ze πι iuplied an cuutting area much smaller than a neutron stars surface. in agreement with the expectations (since the eiergeut spectra at Ty, «& 1109 KK is very differen from à. blackbody. T)."," Fits of the thermal component to a blackbody model yielded similar, but implied an emitting area much smaller than a neutron star's surface, in agreement with the expectations (since the emergent spectra at $_{eff}$ $\approxlt$ $\times$ $^6$ K is very different from a blackbody, \citet{brown98apjl}) )."
 Trerefore. we do lot cliscuss he blacsbody fits further.," Therefore, we do not discuss the blackbody fits further."
 Suwtitutiug the power-law compoucut by a thermal Comptunüsation coniponeut (anodel iu NSPEC) vielded a similar-H aand the paraucters of the NS atinosphere were not affected. ie. the values otained for the mass. radius aud temperature of the NS are robust againste changes of the model for the cussion conmponeut above ~3 keV. Fie.," Substituting the power-law component by a thermal Comptonisation component (model in XSPEC) yielded a similar and the parameters of the NS atmosphere were not affected, i.e. the values obtained for the mass, radius and temperature of the NS are robust against changes of the model for the emission component above $\sim$ 3 keV. Fig."
 L shows the contour plots obtained for the mass and radius of the NS for he three distances considered oeiu Table 3.., \ref{fig:contours} shows the contour plots obtained for the mass and radius of the NS for the three distances considered in Table \ref{tab:fit-sim}.
 As we inerease he distance of the source im the model. both the best-fit xvalues of the mass aud the racius aud the allowed region for these parameters crease.," As we increase the distance of the source in the model, both the best-fit values of the mass and the radius and the allowed region for these parameters increase."
 Next. we investigated how the errors of the fit vary when some parameters are fixed or untied in the fit.," Next, we investigated how the errors of the fit vary when some parameters are fixed or untied in the fit."
 First. since we have indications from the individual fits performed iu Sect.," First, since we have indications from the individual fits performed in Sect."
 3.2.2 that the value of nunav be ciffercut anong observations. we allowed this paraneter to vary in he fits (Case Lin Table 1D).," \ref{sec:epic-rgs} that the value of may be different among observations, we allowed this parameter to vary in the fits (Case 1 in Table \ref{tab:epic-all-trials}) )."
 Second. since the iudex of the power-law comporent is not well constrained. we fitted the spectra fixing the iudex to the best-fit value (D—2 00.21) and to 1 (Cases 2 and 3 in Table 1).," Second, since the index of the power-law component is not well constrained, we fitted the spectra fixing the index to the best-fit value $\Gamma$ 0.24) and to 1 (Cases 2 and 3 in Table \ref{tab:epic-all-trials}) )."
 Finally. we fixed the mass to the best-fit value of 1.78 AL.. aud to amore canonical value of 1.10 AL... but allowed to vary the 1idex of the power law (Cases. [and 5in Table 1).," Finally, we fixed the mass to the best-fit value of 1.78 $\Msun$ and to a more canonical value of 1.40 $\Msun$, but allowed to vary the index of the power law (Cases 4 and 5 in Table \ref{tab:epic-all-trials}) )."
 The aadopts slieltly different values when allowed to vary among observatious., The adopts slightly different values when allowed to vary among observations.
 However. this snall chauge of ddoes not influence the values of the other parameters sienificatly.," However, this small change of does not influence the values of the other parameters significantly."
 In contrast. Table | shows that the large uncertaiity iu the mass oft1ο NS dives the uucertaiuties of the other parameters of the fit to unrealistically large values.," In contrast, Table \ref{tab:epic-all-trials} shows that the large uncertainty in the mass of the NS drives the uncertainties of the other parameters of the fit to unrealistically large values."
 For example. we detect variations iu the effective teniperaure of the NS atiuosphiere between observations as stnall as Lo eV. but tιο calculated uncertainty is more than an order of magnitude larger.," For example, we detect variations in the effective temperature of the NS atmosphere between observations as small as 1 eV, but the calculated uncertainty is more than an order of magnitude larger."
" The large uncertaintv in the mass arises from the act that there aro three parameters required to specify a NS inodel fully: ifs mass, radius aud effective temperature (?).."," The large uncertainty in the mass arises from the fact that there are three parameters required to specify a NS model fully: its mass, radius and effective temperature \citep{heinke06apj}."
 Therefore. for a given effective. teniperaure. there are several acceptable pais Mys-Rys. (seeAppendixBof?.for details)...," Therefore, for a given effective temperature, there are several acceptable pairs $_{NS}$ $_{NS}$ \citep[see Appendix B of][for details]{heinke06apj}."
 The uncertainty in the index of the power- component does not have a siguificait effect in the nucertaintics of the other parameters., The uncertainty in the index of the power-law component does not have a significant effect in the uncertainties of the other parameters.
" Therefore. iu the studies of the variations of the temperaure of the NS atmosphere amoug observations that follow we took iuto account the errors listed in Table Lt for Case 1,"," Therefore, in the studies of the variations of the temperature of the NS atmosphere among observations that follow we took into account the errors listed in Table \ref{tab:epic-all-trials} for Case 4."
 We also observe that changing the index of the power-law, We also observe that changing the index of the power-law
The realisation that obscuration plays a eritical role in the classification of AGN fundamentally inspired. the current research.,The realisation that obscuration plays a critical role in the classification of AGN fundamentally inspired the current research.
 Attempts to overcome the limitations of dust extinction and to identify the entire AGN population — including type 2 and dust-enshrouded AGN — encompass surveys in the near-IR. radio. and X-ray regimes.," Attempts to overcome the limitations of dust extinction and to identify the entire AGN population -- including type 2 and dust-enshrouded AGN – encompass surveys in the near-IR, radio, and X-ray regimes."
 However. searching for very red AGN the colour selection via ο;A.2 (Cutri et al.," However, searching for very red AGN the colour selection via $J - K_{\rm s} > 2$ (Cutri et al."
 2001) excludes most of the known AGN (Barkhouse and Hall 2001). only about of AGN are radio-loud (Urry Padovani 1995). and there seems to exist many X-ray faint AGN (Wilkes et al.," 2001) excludes most of the known AGN (Barkhouse and Hall 2001), only about of AGN are radio-loud (Urry Padovani 1995), and there seems to exist many X-ray faint AGN (Wilkes et al."
 2002)., 2002).
 Thus. a considerable fraction of the AGN population must have escaped detection due to observational bias.," Thus, a considerable fraction of the AGN population must have escaped detection due to observational bias."
 Webster et al. (, Webster et al. (
1995) found that their radio-selected quasar sample is significantly redder than an optical comparison sample and concluded that up to of the quasars have been missed in conventional optical surveys. provided that the redder colours of the radio-loud quasars are due to dust reddening and that the radio-quiet quasars contain as much dust as the radio-loud ones.,"1995) found that their radio-selected quasar sample is significantly redder than an optical comparison sample and concluded that up to of the quasars have been missed in conventional optical surveys, provided that the redder colours of the radio-loud quasars are due to dust reddening and that the radio-quiet quasars contain as much dust as the radio-loud ones."
 By new strategies in the optical. assuming. that the narrow-line regions are sufficiently extended and that only the continuum emission is hidden. type-2 quasar candidates have been selected as objects with narrow permitted emission lines and high I11]|A5007 equivalent widths (Djorgovski et al.," By new strategies in the optical, assuming that the narrow-line regions are sufficiently extended and that only the continuum emission is hidden, type-2 quasar candidates have been selected as objects with narrow permitted emission lines and high $\lambda$ 5007 equivalent widths (Djorgovski et al."
 2001. Zakamska et al.," 2001, Zakamska et al."
 2003)., 2003).
 Applying a moderate colour cut JAL>1.2. from about 1500 sources in 2MASS Francis et al. (," Applying a moderate colour cut $J-K_{\rm s} > 1.2$, from about 1500 sources in 2MASS Francis et al. ("
2004) find only tentative evidence that 22 nuclei are more common in the NIR selected survey than in blue selectec galaxy surveys. and they can place only very weak constraints on any population of dusty AGN.,"2004) find only tentative evidence that 2 nuclei are more common in the NIR selected survey than in blue selected galaxy surveys, and they can place only very weak constraints on any population of dusty AGN."
 The disadvantage of heavy extinction. in. optical anc NIR surveys can turn into a valuable detection tool. whe observing dust-surrounded AGN at MIR wavelengths.," The disadvantage of heavy extinction in optical and NIR surveys can turn into a valuable detection tool, when observing dust-surrounded AGN at MIR wavelengths."
 There. the reemission of the hiding dust heated by the strong radiatio field of the AGN should be seen easily as MIR excess.," There, the reemission of the hiding dust heated by the strong radiation field of the AGN should be seen easily as MIR excess."
 | fact. for known (powerful) AGN of both type 1 and type 2 à steep near- to mid-IR slope has been revealed by sensitive MIR observations (e.g. Haas et al.," In fact, for known (powerful) AGN of both type 1 and type 2 a steep near- to mid-IR slope has been revealed by sensitive MIR observations (e.g. Haas et al."
 2003. Haas et al.," 2003, Haas et al."
 2004. Siebenmorgen et al.," 2004, Siebenmorgen et al."
 2004)., 2004).
 We therefore started à new approach. searching for AGN by means of their MIR. emission of the nuclear dust torus.," We therefore started a new approach, searching for AGN by means of their MIR emission of the nuclear dust torus."
 However. one complication with this method has to be solved: Since luminous IR starburst galaxies may also show a pronouncec MIR emission due to the PAH emission bands around 7.7 jm. it is of special importance to distinguish them from AGN.," However, one complication with this method has to be solved: Since luminous IR starburst galaxies may also show a pronounced MIR emission due to the PAH emission bands around $7.7\,\mu$ m, it is of special importance to distinguish them from AGN."
 In this Letter we describe the new technique for the mid-IR selection of AGN candidates using IR colour diagrams and report about first results from optical spectroscopy., In this Letter we describe the new technique for the mid-IR selection of AGN candidates using IR colour diagrams and report about first results from optical spectroscopy.
 ISO has performed a serendipitous survey at 6.7 j/m (LIT2 band). the Survey. with 6” spatial resolution and a positional accuracy of better than 3” (Siebenmorgen et al.," ISO has performed a serendipitous survey at $6.7\,\mu$ m $LW2$ band), the , with $\arcsec$ spatial resolution and a positional accuracy of better than $\arcsec$ (Siebenmorgen et al."
 1996. Ott et al.," 1996, Ott et al."
 2003)., 2003).
 Over 27 square degrees of the sky are processed and currently being catalogued., Over 27 square degrees of the sky are processed and currently being catalogued.
 For point sources the 36 detection limit is about mmJy.," For point sources the $3\,\sigma$ detection limit is about mJy."
 Within the scientific. verification of the 17000 detected sources (Ott et al., Within the scientific verification of the 17000 detected sources (Ott et al.
 2004 in prep.), 2004 in prep.)
 we have selected unresolved sources at galactic latitude |b]>20°., we have selected unresolved sources at galactic latitude $|b| > 20^\circ$.
 We then performed cross correlations with the 2MASS all sky point source catalogue (Cutri et al., We then performed cross correlations with the 2MASS all sky point source catalogue (Cutri et al.
 2003). with the USNO-B. DSS and UCAC optical catalogues. aswell as the NVSS and FIRST radio surveys.," 2003), with the USNO-B, DSS and UCAC optical catalogues, aswell as the NVSS and FIRST radio surveys,"
prompt and flare emission within the same GRB could in principle shed light on the mechanism powering the flaring activity.,prompt and flare emission within the same GRB could in principle shed light on the mechanism powering the flaring activity.
" However we found no correlation between the prompt luminosity and the total energy and luminosity of the flaring component; the same is true if one were to consider the 15-150 keV prompt energy; no correlation has been found between the prompt luminosity (or energy) and the peak time of the last flare; the peak time of the last flare is also not correlated with the prompt T9o; the number of prompt pulses is not the key factor determining the number of flares to appear at &=50 s (Chincarinietal. 2007)); finally, a hint for a prompt-fluence vs. flare- correlation was recently reported by C10: however, the weak correlation is mostly due to the presence of two short GRBs."," However we found no correlation between the prompt luminosity and the total energy and luminosity of the flaring component; the same is true if one were to consider the 15-150 keV prompt energy; no correlation has been found between the prompt luminosity (or energy) and the peak time of the last flare; the peak time of the last flare is also not correlated with the prompt $T_{90}$; the number of prompt pulses is not the key factor determining the number of flares to appear at $t\gtrsim 50$ s \citealt{Chincarini07}) ); finally, a hint for a prompt-fluence vs. flare-fluence correlation was recently reported by C10: however, the weak correlation is mostly due to the presence of two short GRBs."
" The conclusion is that, while flares do share with prompt pulses several key observational properties (a notable example is the lag-luminosity relation of M10), at the moment it is not possible to infer the flaring activity of a burst starting from its prompt emission."," The conclusion is that, while flares do share with prompt pulses several key observational properties (a notable example is the lag-luminosity relation of M10), at the moment it is not possible to infer the flaring activity of a burst starting from its prompt emission."
 Flares are under-represented in simple power law X- afterglows (M10)., Flares are under-represented in simple power law X-ray afterglows (M10).
 The X-ray afterglow morphology - flaring activity connection is here further explored starting from the findings of Sec. 6.1::, The X-ray afterglow morphology - flaring activity connection is here further explored starting from the findings of Sec. \ref{SubSec:tslope}:
 multiple flare GRBs have on average flatter flare luminosity functions (ie. ct with a< 2.7)., multiple flare GRBs have on average flatter flare luminosity functions (i.e. $\propto t^{-\alpha}$ with $\alpha< 2.7$ ).
" This, together with the observation that the flare detection threshold of Fig. 2,,"," This, together with the observation that the flare detection threshold of Fig. \ref{Fig:avelum},"
" upper panel, closely tracks the temporal decay of the average flaring activity for tS300 s, brought us to consider the possibility of a correlation between the X-ray flare luminosity decay and the underlying continuum emission decay."," upper panel, closely tracks the temporal decay of the average flaring activity for $t\lesssim 300$ s, brought us to consider the possibility of a correlation between the X-ray flare luminosity decay and the underlying continuum emission decay."
 The average continuum is shown in Fig. 6::, The average continuum is shown in Fig. \ref{Fig:continuum}:
" the best fitting power-law index Qsteep=2.8+0.1 is consistent with the flare function decay οςt?**?,", the best fitting power-law index $\alpha_{\rm{steep}}=2.8\pm0.1$ is consistent with the flare function decay $\propto t^{-2.7\pm0.1}$.
" Suggestively, this happens for t<1000 s: at later times the continuum is likely to be dominated by the shallow decay component instead of the steep decay emission (Figure 6,, lower panel, shows a decreasing flare-to-continuum ratio around t~400 s due to the progressively increasing contribution of the shallow decay component to the continuum)."," Suggestively, this happens for $t\lesssim1000$ s: at later times the continuum is likely to be dominated by the shallow decay component instead of the steep decay emission (Figure \ref{Fig:continuum}, lower panel, shows a decreasing flare-to-continuum ratio around $t\sim 400$ s due to the progressively increasing contribution of the shallow decay component to the continuum)."
 During the first ~1000 s the is Laare/Lsteep=4.7 (median value) albeit with a large scatter., During the first $\sim1000$ s the is $L_{\rm{flare}}/L_{\rm{steep}}=4.7$ (median value) albeit with a large scatter.
" Using the data from C10 we obtain a similar median value Faare/Fsteep=4.3 (Fig. 6,,"," Using the data from C10 we obtain a similar median value $F_{\rm{flare}}/F_{\rm{steep}}=4.3$ (Fig. \ref{Fig:continuum},"
" upper panel, inset)."," upper panel, inset)."
 The physical mechanism powering each flare emission is therefore required to release an average amount of energy Egare: where At is the flare duration., The physical mechanism powering each flare emission is therefore required to release an average amount of energy $E_{\rm{flare}}$: where $\Delta t$ is the flare duration.
 The median value from C10 has been used., The median value $\Delta t/t=0.23$ from C10 has been used.
 The continuum vs. flare function temporal behaviour of Fig., The continuum vs. flare function temporal behaviour of Fig.
 6 results from the presence of a correlation linking the steep decay flux evolution to the flaring activity within GRBs., \ref{Fig:continuum} results from the presence of a correlation linking the steep decay flux evolution to the flaring activity within GRBs.
" Modelling the steep decay and the flaring activity of each burst with decaying power-laws of index Qsteep and fare, respectively, we obtain the result drawn in Fig. 5A1.::"," Modelling the steep decay and the flaring activity of each burst with decaying power-laws of index $\alpha_{\rm{steep}}$ and $\alpha_{\rm{flare}}$, respectively, we obtain the result drawn in Fig. \ref{Fig:slopetoslope}:"
 flares seems to be linked to the contemporaneous steep decay flux evolution in a way that causes flatter flare luminosity functions to be associated to more gradual steep decays., flares seems to be linked to the contemporaneous steep decay flux evolution in a way that causes flatter flare luminosity functions to be associated to more gradual steep decays.
" Generically speaking, these observations are consistent with a model where a first physical mechanism is responsible for the steep decay continuum (without flares), while mechanism 2 powers X-ray flares."," Generically speaking, these observations are consistent with a model where a first physical mechanism is responsible for the steep decay continuum (without flares), while mechanism 2 powers X-ray flares."
 The presence of the Astcep VS. Qflare relation suggests that the two mechanisms are in some way related and that the sporadic appearance of mechanism 2 is triggered by some properties of mechanism 1., The presence of the $\alpha_{\rm{steep}}$ vs. $\alpha_{\rm{flare}}$ relation suggests that the two mechanisms are in some way related and that the sporadic appearance of mechanism 2 is triggered by some properties of mechanism 1.
 Instabilities affecting mechanism 1 can in principle provide the source of episodic releases of energy manifesting as flares., Instabilities affecting mechanism 1 can in principle provide the source of episodic releases of energy manifesting as flares.
" If this is the case, instabilities are likely to be triggered by some physical quantity related to the decay of continuum flux at time t£: this would explain why late-time flares are so rare (only ~5% GRBs show clear flaring activity for t>1000 s), but also the paucity of flares in GRBs with simple power-law decay X-ray afterglows."," If this is the case, instabilities are likely to be triggered by some physical quantity related to the decay of continuum flux at time $t$: this would explain why late-time flares are so rare (only $\sim5$ GRBs show clear flaring activity for $t > 1000$ s), but also the paucity of flares in GRBs with simple power-law decay X-ray afterglows."
" In those GRBs, the steep decay is likely to be hidden by a contemporaneous but physically different emission component (see Marguttietal.2010a for a detailed analysis of the two emission components in GRB0081028)."," In those GRBs, the steep decay is likely to be hidden by a contemporaneous but physically different emission component (see \citealt{Margutti10a} for a detailed analysis of the two emission components in 081028)."
" We speculate that, given the remarkable similarity between X-ray flares and prompt pulses, it is possible that both mechanisms also operate during the y-ray prompt emission producing slowly varying (mechanism 1) and fast varying (mechanism 2) emission components."," We speculate that, given the remarkable similarity between X-ray flares and prompt pulses, it is possible that both mechanisms also operate during the $\gamma$ -ray prompt emission producing slowly varying (mechanism 1) and fast varying (mechanism 2) emission components."
 The presence of both long (several seconds) and short (z ms) variability time-scales in the same burst, The presence of both long (several seconds) and short $\approx$ ms) variability time-scales in the same burst
separation and initial mass of the secondary must also be varied.,separation and initial mass of the secondary must also be varied.
 This increases the computer time required to cover the full range of possibly evolutionary paths., This increases the computer time required to cover the full range of possibly evolutionary paths.
" llere we use the set of detailed binary evolution moclels created by Eldridge.Izzare&""Tout.(2008). to determine a new age for 57. Velorum.", Here we use the set of detailed binary evolution models created by \citet{EIT} to determine a new age for $\gamma^2$ Velorum.
 First. considering the possible ages of the OAL. WIR star.," First, considering the possible ages of the $9M_{\odot}$ WR star."
 Second. searching through our binary models for svstenis that agree with the masses ancl orbital separations of the system today.," Second, searching through our binary models for systems that agree with the masses and orbital separations of the system today."
 Third. the age of the secondary star is considered.," Third, the age of the secondary star is considered."
 Afterwards. our results and the implications of the new age we derive are discussed.," Afterwards, our results and the implications of the new age we derive are discussed."
" The stellar models we used were calculated. with the Cambridge SPARS code anc were described in Eldridec.lzzard&""Tout.", The stellar models we used were calculated with the Cambridge STARS code and were described in \citet{EIT}.
 (2008).. Llere. we restrict ourselves to use models with a metallicity mass fraction of Z=0.020. which we take to be Solar.," Here, we restrict ourselves to use models with a metallicity mass fraction of $Z=0.020$, which we take to be Solar."
 These models are all based on circular orbits., These models are all based on circular orbits.
 However as discussed by Hurley.Tout&Pols(2002) circular and eccentric orbits with the same semi-Latus rectum should produce equivalent. evolution., However as discussed by \citet{HPT02} circular and eccentric orbits with the same semi-latus rectum should produce equivalent evolution.
 lt is dilicult to accurately determine the age of a WR star., It is difficult to accurately determine the age of a WR star.
 The star has lost at least half of its initial mass which could have been 20 to 1004.., The star has lost at least half of its initial mass which could have been 20 to $100M_{\odot}$.
 Llowever Ht is possible ο estimate an age range for a WR. star from its current mass ancl WR subtype., However it is possible to estimate an age range for a WR star from its current mass and WR subtype.
 Phe star is designated as WIUL in he catalogue of vanderLlucht(2001). and. is. identified as a WC star., The star is designated as WR11 in the catalogue of \citet{wrcat7} and is identified as a WC star.
 This means it is a highlv stripped star hat has lost all its hydrogen and most of its helium with he atmosphere dominated by carbon., This means it is a highly stripped star that has lost all its hydrogen and most of its helium with the atmosphere dominated by carbon.
 We therefore search hrough our stellar models and record the age of WC stars with masses between 8.4 and 9.6A7.. the inferred. mass of he WR star in 57. Velorum.," We therefore search through our stellar models and record the age of WC stars with masses between 8.4 and $M_{\odot}$, the inferred mass of the WR star in $\gamma^2$ Velorum."
 Here we consider the WIL star alone and not the companion or binary orbit., Here we consider the WR star alone and not the companion or binary orbit.
 We assume a model is a WC star when there is no hydrogen: present and (CX6/3|Xo/4)/Y.z0.03. where Yo. No and Y. are the mass fraction abundance of carbon. oxvgen and helium respectively (Maeder&Meynet.1994).," We assume a model is a WC star when there is no hydrogen present and $(X_{\rm
 C}/3+X_{\rm O}/4)/Y \ge 0.03$, where $X_{\rm C}$, $X_{\rm O}$ and $Y$ are the mass fraction abundance of carbon, oxygen and helium respectively \citep{mm1994}."
. We find that our mocels indicate a range of possible ages [rom 3.3 to 6.4 Alves for WC stars with masses similar to that of the WR star in 57. Velorum., We find that our models indicate a range of possible ages from 3.3 to 6.4 Myrs for WC stars with masses similar to that of the WR star in $\gamma^2$ Velorum.
 Our lower estiniate of 3.4 Alves agrees with the age derived by Northetal.(2007) for the O star. although this was with older single star isochrones.," Our lower estimate of 3.4 Myrs agrees with the age derived by \cite{north07} for the O star, although this was with older single star isochrones."
 Phe voungest WC stars are [rom stars with initial masses above GOAL. and the older WC stars are [rom stars with an initial mass of 30A.., The youngest WC stars are from stars with initial masses above $60M_{\odot}$ and the older WC stars are from stars with an initial mass of $30M_{\odot}$.